/*
NOTE: This is generated code. Look in Misc/lapack_lite for information on
remaking this file.
*/
#include "f2c.h"
#ifdef HAVE_CONFIG
#include "config.h"
#else
extern doublereal dlamch_(char *);
#define EPSILON dlamch_("Epsilon")
#define SAFEMINIMUM dlamch_("Safe minimum")
#define PRECISION dlamch_("Precision")
#define BASE dlamch_("Base")
#endif
extern doublereal dlapy2_(doublereal *x, doublereal *y);
/*
f2c knows the exact rules for precedence, and so omits parentheses where not
strictly necessary. Since this is generated code, we don't really care if
it's readable, and we know what is written is correct. So don't warn about
them.
*/
#if defined(__GNUC__)
#pragma GCC diagnostic ignored "-Wparentheses"
#endif
/* Table of constant values */
static complex c_b21 = {1.f,0.f};
static doublecomplex c_b1078 = {1.,0.};
/* Subroutine */ int caxpy_(integer *n, complex *ca, complex *cx, integer *
incx, complex *cy, integer *incy)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
complex q__1, q__2;
/* Local variables */
static integer i__, ix, iy;
extern doublereal scabs1_(complex *);
/*
Purpose
=======
CAXPY constant times a vector plus a vector.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--cy;
--cx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (scabs1_(ca) == 0.f) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
i__3 = iy;
i__4 = ix;
q__2.r = ca->r * cx[i__4].r - ca->i * cx[i__4].i, q__2.i = ca->r * cx[
i__4].i + ca->i * cx[i__4].r;
q__1.r = cy[i__3].r + q__2.r, q__1.i = cy[i__3].i + q__2.i;
cy[i__2].r = q__1.r, cy[i__2].i = q__1.i;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
q__2.r = ca->r * cx[i__4].r - ca->i * cx[i__4].i, q__2.i = ca->r * cx[
i__4].i + ca->i * cx[i__4].r;
q__1.r = cy[i__3].r + q__2.r, q__1.i = cy[i__3].i + q__2.i;
cy[i__2].r = q__1.r, cy[i__2].i = q__1.i;
/* L30: */
}
return 0;
} /* caxpy_ */
/* Subroutine */ int ccopy_(integer *n, complex *cx, integer *incx, complex *
cy, integer *incy)
{
/* System generated locals */
integer i__1, i__2, i__3;
/* Local variables */
static integer i__, ix, iy;
/*
Purpose
=======
CCOPY copies a vector x to a vector y.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--cy;
--cx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
i__3 = ix;
cy[i__2].r = cx[i__3].r, cy[i__2].i = cx[i__3].i;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
cy[i__2].r = cx[i__3].r, cy[i__2].i = cx[i__3].i;
/* L30: */
}
return 0;
} /* ccopy_ */
/* Complex */ VOID cdotc_(complex * ret_val, integer *n, complex *cx, integer
*incx, complex *cy, integer *incy)
{
/* System generated locals */
integer i__1, i__2;
complex q__1, q__2, q__3;
/* Local variables */
static integer i__, ix, iy;
static complex ctemp;
/*
Purpose
=======
forms the dot product of two vectors, conjugating the first
vector.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--cy;
--cx;
/* Function Body */
ctemp.r = 0.f, ctemp.i = 0.f;
ret_val->r = 0.f, ret_val->i = 0.f;
if (*n <= 0) {
return ;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
r_cnjg(&q__3, &cx[ix]);
i__2 = iy;
q__2.r = q__3.r * cy[i__2].r - q__3.i * cy[i__2].i, q__2.i = q__3.r *
cy[i__2].i + q__3.i * cy[i__2].r;
q__1.r = ctemp.r + q__2.r, q__1.i = ctemp.i + q__2.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
ix += *incx;
iy += *incy;
/* L10: */
}
ret_val->r = ctemp.r, ret_val->i = ctemp.i;
return ;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
r_cnjg(&q__3, &cx[i__]);
i__2 = i__;
q__2.r = q__3.r * cy[i__2].r - q__3.i * cy[i__2].i, q__2.i = q__3.r *
cy[i__2].i + q__3.i * cy[i__2].r;
q__1.r = ctemp.r + q__2.r, q__1.i = ctemp.i + q__2.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
/* L30: */
}
ret_val->r = ctemp.r, ret_val->i = ctemp.i;
return ;
} /* cdotc_ */
/* Complex */ VOID cdotu_(complex * ret_val, integer *n, complex *cx, integer
*incx, complex *cy, integer *incy)
{
/* System generated locals */
integer i__1, i__2, i__3;
complex q__1, q__2;
/* Local variables */
static integer i__, ix, iy;
static complex ctemp;
/*
Purpose
=======
CDOTU forms the dot product of two vectors.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--cy;
--cx;
/* Function Body */
ctemp.r = 0.f, ctemp.i = 0.f;
ret_val->r = 0.f, ret_val->i = 0.f;
if (*n <= 0) {
return ;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ix;
i__3 = iy;
q__2.r = cx[i__2].r * cy[i__3].r - cx[i__2].i * cy[i__3].i, q__2.i =
cx[i__2].r * cy[i__3].i + cx[i__2].i * cy[i__3].r;
q__1.r = ctemp.r + q__2.r, q__1.i = ctemp.i + q__2.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
ix += *incx;
iy += *incy;
/* L10: */
}
ret_val->r = ctemp.r, ret_val->i = ctemp.i;
return ;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
q__2.r = cx[i__2].r * cy[i__3].r - cx[i__2].i * cy[i__3].i, q__2.i =
cx[i__2].r * cy[i__3].i + cx[i__2].i * cy[i__3].r;
q__1.r = ctemp.r + q__2.r, q__1.i = ctemp.i + q__2.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
/* L30: */
}
ret_val->r = ctemp.r, ret_val->i = ctemp.i;
return ;
} /* cdotu_ */
/* Subroutine */ int cgemm_(char *transa, char *transb, integer *m, integer *
n, integer *k, complex *alpha, complex *a, integer *lda, complex *b,
integer *ldb, complex *beta, complex *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3, i__4, i__5, i__6;
complex q__1, q__2, q__3, q__4;
/* Local variables */
static integer i__, j, l, info;
static logical nota, notb;
static complex temp;
static logical conja, conjb;
static integer ncola;
extern logical lsame_(char *, char *);
static integer nrowa, nrowb;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
CGEMM performs one of the matrix-matrix operations
C := alpha*op( A )*op( B ) + beta*C,
where op( X ) is one of
op( X ) = X or op( X ) = X' or op( X ) = conjg( X' ),
alpha and beta are scalars, and A, B and C are matrices, with op( A )
an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
Arguments
==========
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n', op( A ) = A.
TRANSA = 'T' or 't', op( A ) = A'.
TRANSA = 'C' or 'c', op( A ) = conjg( A' ).
Unchanged on exit.
TRANSB - CHARACTER*1.
On entry, TRANSB specifies the form of op( B ) to be used in
the matrix multiplication as follows:
TRANSB = 'N' or 'n', op( B ) = B.
TRANSB = 'T' or 't', op( B ) = B'.
TRANSB = 'C' or 'c', op( B ) = conjg( B' ).
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix
op( A ) and of the matrix C. M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix
op( B ) and the number of columns of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry, K specifies the number of columns of the matrix
op( A ) and the number of rows of the matrix op( B ). K must
be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is
k when TRANSA = 'N' or 'n', and is m otherwise.
Before entry with TRANSA = 'N' or 'n', the leading m by k
part of the array A must contain the matrix A, otherwise
the leading k by m part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANSA = 'N' or 'n' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, k ).
Unchanged on exit.
B - COMPLEX array of DIMENSION ( LDB, kb ), where kb is
n when TRANSB = 'N' or 'n', and is k otherwise.
Before entry with TRANSB = 'N' or 'n', the leading k by n
part of the array B must contain the matrix B, otherwise
the leading n by k part of the array B must contain the
matrix B.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANSB = 'N' or 'n' then
LDB must be at least max( 1, k ), otherwise LDB must be at
least max( 1, n ).
Unchanged on exit.
BETA - COMPLEX .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
Unchanged on exit.
C - COMPLEX array of DIMENSION ( LDC, n ).
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n matrix
( alpha*op( A )*op( B ) + beta*C ).
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Set NOTA and NOTB as true if A and B respectively are not
conjugated or transposed, set CONJA and CONJB as true if A and
B respectively are to be transposed but not conjugated and set
NROWA, NCOLA and NROWB as the number of rows and columns of A
and the number of rows of B respectively.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
nota = lsame_(transa, "N");
notb = lsame_(transb, "N");
conja = lsame_(transa, "C");
conjb = lsame_(transb, "C");
if (nota) {
nrowa = *m;
ncola = *k;
} else {
nrowa = *k;
ncola = *m;
}
if (notb) {
nrowb = *k;
} else {
nrowb = *n;
}
/* Test the input parameters. */
info = 0;
if (! nota && ! conja && ! lsame_(transa, "T")) {
info = 1;
} else if (! notb && ! conjb && ! lsame_(transb, "T")) {
info = 2;
} else if (*m < 0) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*k < 0) {
info = 5;
} else if (*lda < max(1,nrowa)) {
info = 8;
} else if (*ldb < max(1,nrowb)) {
info = 10;
} else if (*ldc < max(1,*m)) {
info = 13;
}
if (info != 0) {
xerbla_("CGEMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || (alpha->r == 0.f && alpha->i == 0.f || *k == 0)
&& (beta->r == 1.f && beta->i == 0.f)) {
return 0;
}
/* And when alpha.eq.zero. */
if (alpha->r == 0.f && alpha->i == 0.f) {
if (beta->r == 0.f && beta->i == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i,
q__1.i = beta->r * c__[i__4].i + beta->i * c__[
i__4].r;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L30: */
}
/* L40: */
}
}
return 0;
}
/* Start the operations. */
if (notb) {
if (nota) {
/* Form C := alpha*A*B + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (beta->r == 0.f && beta->i == 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L50: */
}
} else if (beta->r != 1.f || beta->i != 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, q__1.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L60: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = l + j * b_dim1;
if (b[i__3].r != 0.f || b[i__3].i != 0.f) {
i__3 = l + j * b_dim1;
q__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i,
q__1.i = alpha->r * b[i__3].i + alpha->i * b[
i__3].r;
temp.r = q__1.r, temp.i = q__1.i;
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
q__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
q__2.i = temp.r * a[i__6].i + temp.i * a[
i__6].r;
q__1.r = c__[i__5].r + q__2.r, q__1.i = c__[i__5]
.i + q__2.i;
c__[i__4].r = q__1.r, c__[i__4].i = q__1.i;
/* L70: */
}
}
/* L80: */
}
/* L90: */
}
} else if (conja) {
/* Form C := alpha*conjg( A' )*B + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0.f, temp.i = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
r_cnjg(&q__3, &a[l + i__ * a_dim1]);
i__4 = l + j * b_dim1;
q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4].i,
q__2.i = q__3.r * b[i__4].i + q__3.i * b[i__4]
.r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L100: */
}
if (beta->r == 0.f && beta->i == 0.f) {
i__3 = i__ + j * c_dim1;
q__1.r = alpha->r * temp.r - alpha->i * temp.i,
q__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
} else {
i__3 = i__ + j * c_dim1;
q__2.r = alpha->r * temp.r - alpha->i * temp.i,
q__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, q__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
}
/* L110: */
}
/* L120: */
}
} else {
/* Form C := alpha*A'*B + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0.f, temp.i = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
i__4 = l + i__ * a_dim1;
i__5 = l + j * b_dim1;
q__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5]
.i, q__2.i = a[i__4].r * b[i__5].i + a[i__4]
.i * b[i__5].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L130: */
}
if (beta->r == 0.f && beta->i == 0.f) {
i__3 = i__ + j * c_dim1;
q__1.r = alpha->r * temp.r - alpha->i * temp.i,
q__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
} else {
i__3 = i__ + j * c_dim1;
q__2.r = alpha->r * temp.r - alpha->i * temp.i,
q__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, q__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
}
/* L140: */
}
/* L150: */
}
}
} else if (nota) {
if (conjb) {
/* Form C := alpha*A*conjg( B' ) + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (beta->r == 0.f && beta->i == 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L160: */
}
} else if (beta->r != 1.f || beta->i != 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, q__1.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L170: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * b_dim1;
if (b[i__3].r != 0.f || b[i__3].i != 0.f) {
r_cnjg(&q__2, &b[j + l * b_dim1]);
q__1.r = alpha->r * q__2.r - alpha->i * q__2.i,
q__1.i = alpha->r * q__2.i + alpha->i *
q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
q__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
q__2.i = temp.r * a[i__6].i + temp.i * a[
i__6].r;
q__1.r = c__[i__5].r + q__2.r, q__1.i = c__[i__5]
.i + q__2.i;
c__[i__4].r = q__1.r, c__[i__4].i = q__1.i;
/* L180: */
}
}
/* L190: */
}
/* L200: */
}
} else {
/* Form C := alpha*A*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (beta->r == 0.f && beta->i == 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L210: */
}
} else if (beta->r != 1.f || beta->i != 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, q__1.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L220: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * b_dim1;
if (b[i__3].r != 0.f || b[i__3].i != 0.f) {
i__3 = j + l * b_dim1;
q__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i,
q__1.i = alpha->r * b[i__3].i + alpha->i * b[
i__3].r;
temp.r = q__1.r, temp.i = q__1.i;
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
q__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
q__2.i = temp.r * a[i__6].i + temp.i * a[
i__6].r;
q__1.r = c__[i__5].r + q__2.r, q__1.i = c__[i__5]
.i + q__2.i;
c__[i__4].r = q__1.r, c__[i__4].i = q__1.i;
/* L230: */
}
}
/* L240: */
}
/* L250: */
}
}
} else if (conja) {
if (conjb) {
/* Form C := alpha*conjg( A' )*conjg( B' ) + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0.f, temp.i = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
r_cnjg(&q__3, &a[l + i__ * a_dim1]);
r_cnjg(&q__4, &b[j + l * b_dim1]);
q__2.r = q__3.r * q__4.r - q__3.i * q__4.i, q__2.i =
q__3.r * q__4.i + q__3.i * q__4.r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L260: */
}
if (beta->r == 0.f && beta->i == 0.f) {
i__3 = i__ + j * c_dim1;
q__1.r = alpha->r * temp.r - alpha->i * temp.i,
q__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
} else {
i__3 = i__ + j * c_dim1;
q__2.r = alpha->r * temp.r - alpha->i * temp.i,
q__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, q__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
}
/* L270: */
}
/* L280: */
}
} else {
/* Form C := alpha*conjg( A' )*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0.f, temp.i = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
r_cnjg(&q__3, &a[l + i__ * a_dim1]);
i__4 = j + l * b_dim1;
q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4].i,
q__2.i = q__3.r * b[i__4].i + q__3.i * b[i__4]
.r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L290: */
}
if (beta->r == 0.f && beta->i == 0.f) {
i__3 = i__ + j * c_dim1;
q__1.r = alpha->r * temp.r - alpha->i * temp.i,
q__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
} else {
i__3 = i__ + j * c_dim1;
q__2.r = alpha->r * temp.r - alpha->i * temp.i,
q__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, q__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
}
/* L300: */
}
/* L310: */
}
}
} else {
if (conjb) {
/* Form C := alpha*A'*conjg( B' ) + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0.f, temp.i = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
i__4 = l + i__ * a_dim1;
r_cnjg(&q__3, &b[j + l * b_dim1]);
q__2.r = a[i__4].r * q__3.r - a[i__4].i * q__3.i,
q__2.i = a[i__4].r * q__3.i + a[i__4].i *
q__3.r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L320: */
}
if (beta->r == 0.f && beta->i == 0.f) {
i__3 = i__ + j * c_dim1;
q__1.r = alpha->r * temp.r - alpha->i * temp.i,
q__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
} else {
i__3 = i__ + j * c_dim1;
q__2.r = alpha->r * temp.r - alpha->i * temp.i,
q__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, q__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
}
/* L330: */
}
/* L340: */
}
} else {
/* Form C := alpha*A'*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0.f, temp.i = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
i__4 = l + i__ * a_dim1;
i__5 = j + l * b_dim1;
q__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5]
.i, q__2.i = a[i__4].r * b[i__5].i + a[i__4]
.i * b[i__5].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L350: */
}
if (beta->r == 0.f && beta->i == 0.f) {
i__3 = i__ + j * c_dim1;
q__1.r = alpha->r * temp.r - alpha->i * temp.i,
q__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
} else {
i__3 = i__ + j * c_dim1;
q__2.r = alpha->r * temp.r - alpha->i * temp.i,
q__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
q__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, q__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
}
/* L360: */
}
/* L370: */
}
}
}
return 0;
/* End of CGEMM . */
} /* cgemm_ */
/* Subroutine */ int cgemv_(char *trans, integer *m, integer *n, complex *
alpha, complex *a, integer *lda, complex *x, integer *incx, complex *
beta, complex *y, integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
complex q__1, q__2, q__3;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static complex temp;
static integer lenx, leny;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical noconj;
/*
Purpose
=======
CGEMV performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or
y := alpha*conjg( A' )*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an
m by n matrix.
Arguments
==========
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
X - COMPLEX array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
Before entry, the incremented array X must contain the
vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - COMPLEX .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - COMPLEX array of DIMENSION at least
( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
Before entry with BETA non-zero, the incremented array Y
must contain the vector y. On exit, Y is overwritten by the
updated vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")
) {
info = 1;
} else if (*m < 0) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*lda < max(1,*m)) {
info = 6;
} else if (*incx == 0) {
info = 8;
} else if (*incy == 0) {
info = 11;
}
if (info != 0) {
xerbla_("CGEMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || alpha->r == 0.f && alpha->i == 0.f && (beta->r
== 1.f && beta->i == 0.f)) {
return 0;
}
noconj = lsame_(trans, "T");
/*
Set LENX and LENY, the lengths of the vectors x and y, and set
up the start points in X and Y.
*/
if (lsame_(trans, "N")) {
lenx = *n;
leny = *m;
} else {
lenx = *m;
leny = *n;
}
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (lenx - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (leny - 1) * *incy;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
First form y := beta*y.
*/
if (beta->r != 1.f || beta->i != 0.f) {
if (*incy == 1) {
if (beta->r == 0.f && beta->i == 0.f) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
y[i__2].r = 0.f, y[i__2].i = 0.f;
/* L10: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
/* L20: */
}
}
} else {
iy = ky;
if (beta->r == 0.f && beta->i == 0.f) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
y[i__2].r = 0.f, y[i__2].i = 0.f;
iy += *incy;
/* L30: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
i__3 = iy;
q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
iy += *incy;
/* L40: */
}
}
}
}
if (alpha->r == 0.f && alpha->i == 0.f) {
return 0;
}
if (lsame_(trans, "N")) {
/* Form y := alpha*A*x + y. */
jx = kx;
if (*incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
if (x[i__2].r != 0.f || x[i__2].i != 0.f) {
i__2 = jx;
q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
q__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
temp.r = q__1.r, temp.i = q__1.i;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__ + j * a_dim1;
q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
q__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i +
q__2.i;
y[i__3].r = q__1.r, y[i__3].i = q__1.i;
/* L50: */
}
}
jx += *incx;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
if (x[i__2].r != 0.f || x[i__2].i != 0.f) {
i__2 = jx;
q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
q__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
temp.r = q__1.r, temp.i = q__1.i;
iy = ky;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = iy;
i__4 = iy;
i__5 = i__ + j * a_dim1;
q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
q__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i +
q__2.i;
y[i__3].r = q__1.r, y[i__3].i = q__1.i;
iy += *incy;
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
} else {
/* Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. */
jy = ky;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp.r = 0.f, temp.i = 0.f;
if (noconj) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__;
q__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4]
.i, q__2.i = a[i__3].r * x[i__4].i + a[i__3]
.i * x[i__4].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L90: */
}
} else {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__3 = i__;
q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i,
q__2.i = q__3.r * x[i__3].i + q__3.i * x[i__3]
.r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L100: */
}
}
i__2 = jy;
i__3 = jy;
q__2.r = alpha->r * temp.r - alpha->i * temp.i, q__2.i =
alpha->r * temp.i + alpha->i * temp.r;
q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
jy += *incy;
/* L110: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp.r = 0.f, temp.i = 0.f;
ix = kx;
if (noconj) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = ix;
q__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4]
.i, q__2.i = a[i__3].r * x[i__4].i + a[i__3]
.i * x[i__4].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
ix += *incx;
/* L120: */
}
} else {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__3 = ix;
q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i,
q__2.i = q__3.r * x[i__3].i + q__3.i * x[i__3]
.r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
ix += *incx;
/* L130: */
}
}
i__2 = jy;
i__3 = jy;
q__2.r = alpha->r * temp.r - alpha->i * temp.i, q__2.i =
alpha->r * temp.i + alpha->i * temp.r;
q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
jy += *incy;
/* L140: */
}
}
}
return 0;
/* End of CGEMV . */
} /* cgemv_ */
/* Subroutine */ int cgerc_(integer *m, integer *n, complex *alpha, complex *
x, integer *incx, complex *y, integer *incy, complex *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
complex q__1, q__2;
/* Local variables */
static integer i__, j, ix, jy, kx, info;
static complex temp;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
CGERC performs the rank 1 operation
A := alpha*x*conjg( y' ) + A,
where alpha is a scalar, x is an m element vector, y is an n element
vector and A is an m by n matrix.
Arguments
==========
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - COMPLEX array of dimension at least
( 1 + ( m - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the m
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - COMPLEX array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients. On exit, A is
overwritten by the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
info = 0;
if (*m < 0) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*m)) {
info = 9;
}
if (info != 0) {
xerbla_("CGERC ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || alpha->r == 0.f && alpha->i == 0.f) {
return 0;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (*incy > 0) {
jy = 1;
} else {
jy = 1 - (*n - 1) * *incy;
}
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jy;
if (y[i__2].r != 0.f || y[i__2].i != 0.f) {
r_cnjg(&q__2, &y[jy]);
q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i =
alpha->r * q__2.i + alpha->i * q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = i__;
q__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, q__2.i =
x[i__5].r * temp.i + x[i__5].i * temp.r;
q__1.r = a[i__4].r + q__2.r, q__1.i = a[i__4].i + q__2.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L10: */
}
}
jy += *incy;
/* L20: */
}
} else {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*m - 1) * *incx;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jy;
if (y[i__2].r != 0.f || y[i__2].i != 0.f) {
r_cnjg(&q__2, &y[jy]);
q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i =
alpha->r * q__2.i + alpha->i * q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
ix = kx;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = ix;
q__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, q__2.i =
x[i__5].r * temp.i + x[i__5].i * temp.r;
q__1.r = a[i__4].r + q__2.r, q__1.i = a[i__4].i + q__2.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
ix += *incx;
/* L30: */
}
}
jy += *incy;
/* L40: */
}
}
return 0;
/* End of CGERC . */
} /* cgerc_ */
/* Subroutine */ int cgeru_(integer *m, integer *n, complex *alpha, complex *
x, integer *incx, complex *y, integer *incy, complex *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
complex q__1, q__2;
/* Local variables */
static integer i__, j, ix, jy, kx, info;
static complex temp;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
CGERU performs the rank 1 operation
A := alpha*x*y' + A,
where alpha is a scalar, x is an m element vector, y is an n element
vector and A is an m by n matrix.
Arguments
==========
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - COMPLEX array of dimension at least
( 1 + ( m - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the m
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - COMPLEX array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients. On exit, A is
overwritten by the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
info = 0;
if (*m < 0) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*m)) {
info = 9;
}
if (info != 0) {
xerbla_("CGERU ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || alpha->r == 0.f && alpha->i == 0.f) {
return 0;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (*incy > 0) {
jy = 1;
} else {
jy = 1 - (*n - 1) * *incy;
}
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jy;
if (y[i__2].r != 0.f || y[i__2].i != 0.f) {
i__2 = jy;
q__1.r = alpha->r * y[i__2].r - alpha->i * y[i__2].i, q__1.i =
alpha->r * y[i__2].i + alpha->i * y[i__2].r;
temp.r = q__1.r, temp.i = q__1.i;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = i__;
q__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, q__2.i =
x[i__5].r * temp.i + x[i__5].i * temp.r;
q__1.r = a[i__4].r + q__2.r, q__1.i = a[i__4].i + q__2.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L10: */
}
}
jy += *incy;
/* L20: */
}
} else {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*m - 1) * *incx;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jy;
if (y[i__2].r != 0.f || y[i__2].i != 0.f) {
i__2 = jy;
q__1.r = alpha->r * y[i__2].r - alpha->i * y[i__2].i, q__1.i =
alpha->r * y[i__2].i + alpha->i * y[i__2].r;
temp.r = q__1.r, temp.i = q__1.i;
ix = kx;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = ix;
q__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, q__2.i =
x[i__5].r * temp.i + x[i__5].i * temp.r;
q__1.r = a[i__4].r + q__2.r, q__1.i = a[i__4].i + q__2.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
ix += *incx;
/* L30: */
}
}
jy += *incy;
/* L40: */
}
}
return 0;
/* End of CGERU . */
} /* cgeru_ */
/* Subroutine */ int chemv_(char *uplo, integer *n, complex *alpha, complex *
a, integer *lda, complex *x, integer *incx, complex *beta, complex *y,
integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
real r__1;
complex q__1, q__2, q__3, q__4;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static complex temp1, temp2;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
CHEMV performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n hermitian matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the hermitian matrix and the strictly
lower triangular part of A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the hermitian matrix and the strictly
upper triangular part of A is not referenced.
Note that the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - COMPLEX array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - COMPLEX .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - COMPLEX array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y. On exit, Y is overwritten by the updated
vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*lda < max(1,*n)) {
info = 5;
} else if (*incx == 0) {
info = 7;
} else if (*incy == 0) {
info = 10;
}
if (info != 0) {
xerbla_("CHEMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || alpha->r == 0.f && alpha->i == 0.f && (beta->r == 1.f &&
beta->i == 0.f)) {
return 0;
}
/* Set up the start points in X and Y. */
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through the triangular part
of A.
First form y := beta*y.
*/
if (beta->r != 1.f || beta->i != 0.f) {
if (*incy == 1) {
if (beta->r == 0.f && beta->i == 0.f) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
y[i__2].r = 0.f, y[i__2].i = 0.f;
/* L10: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
/* L20: */
}
}
} else {
iy = ky;
if (beta->r == 0.f && beta->i == 0.f) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
y[i__2].r = 0.f, y[i__2].i = 0.f;
iy += *incy;
/* L30: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
i__3 = iy;
q__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
q__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
iy += *incy;
/* L40: */
}
}
}
}
if (alpha->r == 0.f && alpha->i == 0.f) {
return 0;
}
if (lsame_(uplo, "U")) {
/* Form y when A is stored in upper triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
temp1.r = q__1.r, temp1.i = q__1.i;
temp2.r = 0.f, temp2.i = 0.f;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__ + j * a_dim1;
q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
.r;
q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
y[i__3].r = q__1.r, y[i__3].i = q__1.i;
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__3 = i__;
q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =
q__3.r * x[i__3].i + q__3.i * x[i__3].r;
q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
temp2.r = q__1.r, temp2.i = q__1.i;
/* L50: */
}
i__2 = j;
i__3 = j;
i__4 = j + j * a_dim1;
r__1 = a[i__4].r;
q__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;
q__2.r = y[i__3].r + q__3.r, q__2.i = y[i__3].i + q__3.i;
q__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i =
alpha->r * temp2.i + alpha->i * temp2.r;
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
/* L60: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
temp1.r = q__1.r, temp1.i = q__1.i;
temp2.r = 0.f, temp2.i = 0.f;
ix = kx;
iy = ky;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = iy;
i__4 = iy;
i__5 = i__ + j * a_dim1;
q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
.r;
q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
y[i__3].r = q__1.r, y[i__3].i = q__1.i;
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__3 = ix;
q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =
q__3.r * x[i__3].i + q__3.i * x[i__3].r;
q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
temp2.r = q__1.r, temp2.i = q__1.i;
ix += *incx;
iy += *incy;
/* L70: */
}
i__2 = jy;
i__3 = jy;
i__4 = j + j * a_dim1;
r__1 = a[i__4].r;
q__3.r = r__1 * temp1.r, q__3.i = r__1 * temp1.i;
q__2.r = y[i__3].r + q__3.r, q__2.i = y[i__3].i + q__3.i;
q__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i =
alpha->r * temp2.i + alpha->i * temp2.r;
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
jx += *incx;
jy += *incy;
/* L80: */
}
}
} else {
/* Form y when A is stored in lower triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
temp1.r = q__1.r, temp1.i = q__1.i;
temp2.r = 0.f, temp2.i = 0.f;
i__2 = j;
i__3 = j;
i__4 = j + j * a_dim1;
r__1 = a[i__4].r;
q__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;
q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__ + j * a_dim1;
q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
.r;
q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
y[i__3].r = q__1.r, y[i__3].i = q__1.i;
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__3 = i__;
q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =
q__3.r * x[i__3].i + q__3.i * x[i__3].r;
q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
temp2.r = q__1.r, temp2.i = q__1.i;
/* L90: */
}
i__2 = j;
i__3 = j;
q__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i =
alpha->r * temp2.i + alpha->i * temp2.r;
q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
/* L100: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
q__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, q__1.i =
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
temp1.r = q__1.r, temp1.i = q__1.i;
temp2.r = 0.f, temp2.i = 0.f;
i__2 = jy;
i__3 = jy;
i__4 = j + j * a_dim1;
r__1 = a[i__4].r;
q__2.r = r__1 * temp1.r, q__2.i = r__1 * temp1.i;
q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
ix = jx;
iy = jy;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
iy += *incy;
i__3 = iy;
i__4 = iy;
i__5 = i__ + j * a_dim1;
q__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
q__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
.r;
q__1.r = y[i__4].r + q__2.r, q__1.i = y[i__4].i + q__2.i;
y[i__3].r = q__1.r, y[i__3].i = q__1.i;
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__3 = ix;
q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i, q__2.i =
q__3.r * x[i__3].i + q__3.i * x[i__3].r;
q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
temp2.r = q__1.r, temp2.i = q__1.i;
/* L110: */
}
i__2 = jy;
i__3 = jy;
q__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i =
alpha->r * temp2.i + alpha->i * temp2.r;
q__1.r = y[i__3].r + q__2.r, q__1.i = y[i__3].i + q__2.i;
y[i__2].r = q__1.r, y[i__2].i = q__1.i;
jx += *incx;
jy += *incy;
/* L120: */
}
}
}
return 0;
/* End of CHEMV . */
} /* chemv_ */
/* Subroutine */ int cher2_(char *uplo, integer *n, complex *alpha, complex *
x, integer *incx, complex *y, integer *incy, complex *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
real r__1;
complex q__1, q__2, q__3, q__4;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static complex temp1, temp2;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
CHER2 performs the hermitian rank 2 operation
A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
where alpha is a scalar, x and y are n element vectors and A is an n
by n hermitian matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - COMPLEX array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - COMPLEX array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the hermitian matrix and the strictly
lower triangular part of A is not referenced. On exit, the
upper triangular part of the array A is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the hermitian matrix and the strictly
upper triangular part of A is not referenced. On exit, the
lower triangular part of the array A is overwritten by the
lower triangular part of the updated matrix.
Note that the imaginary parts of the diagonal elements need
not be set, they are assumed to be zero, and on exit they
are set to zero.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*n)) {
info = 9;
}
if (info != 0) {
xerbla_("CHER2 ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || alpha->r == 0.f && alpha->i == 0.f) {
return 0;
}
/*
Set up the start points in X and Y if the increments are not both
unity.
*/
if (*incx != 1 || *incy != 1) {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
jx = kx;
jy = ky;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through the triangular part
of A.
*/
if (lsame_(uplo, "U")) {
/* Form A when A is stored in the upper triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
i__3 = j;
if (x[i__2].r != 0.f || x[i__2].i != 0.f || (y[i__3].r != 0.f
|| y[i__3].i != 0.f)) {
r_cnjg(&q__2, &y[j]);
q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i =
alpha->r * q__2.i + alpha->i * q__2.r;
temp1.r = q__1.r, temp1.i = q__1.i;
i__2 = j;
q__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
q__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
r_cnjg(&q__1, &q__2);
temp2.r = q__1.r, temp2.i = q__1.i;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = i__;
q__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i,
q__3.i = x[i__5].r * temp1.i + x[i__5].i *
temp1.r;
q__2.r = a[i__4].r + q__3.r, q__2.i = a[i__4].i +
q__3.i;
i__6 = i__;
q__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i,
q__4.i = y[i__6].r * temp2.i + y[i__6].i *
temp2.r;
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L10: */
}
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
i__4 = j;
q__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i,
q__2.i = x[i__4].r * temp1.i + x[i__4].i *
temp1.r;
i__5 = j;
q__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i,
q__3.i = y[i__5].r * temp2.i + y[i__5].i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
r__1 = a[i__3].r + q__1.r;
a[i__2].r = r__1, a[i__2].i = 0.f;
} else {
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
r__1 = a[i__3].r;
a[i__2].r = r__1, a[i__2].i = 0.f;
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
i__3 = jy;
if (x[i__2].r != 0.f || x[i__2].i != 0.f || (y[i__3].r != 0.f
|| y[i__3].i != 0.f)) {
r_cnjg(&q__2, &y[jy]);
q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i =
alpha->r * q__2.i + alpha->i * q__2.r;
temp1.r = q__1.r, temp1.i = q__1.i;
i__2 = jx;
q__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
q__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
r_cnjg(&q__1, &q__2);
temp2.r = q__1.r, temp2.i = q__1.i;
ix = kx;
iy = ky;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = ix;
q__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i,
q__3.i = x[i__5].r * temp1.i + x[i__5].i *
temp1.r;
q__2.r = a[i__4].r + q__3.r, q__2.i = a[i__4].i +
q__3.i;
i__6 = iy;
q__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i,
q__4.i = y[i__6].r * temp2.i + y[i__6].i *
temp2.r;
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
ix += *incx;
iy += *incy;
/* L30: */
}
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
i__4 = jx;
q__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i,
q__2.i = x[i__4].r * temp1.i + x[i__4].i *
temp1.r;
i__5 = jy;
q__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i,
q__3.i = y[i__5].r * temp2.i + y[i__5].i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
r__1 = a[i__3].r + q__1.r;
a[i__2].r = r__1, a[i__2].i = 0.f;
} else {
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
r__1 = a[i__3].r;
a[i__2].r = r__1, a[i__2].i = 0.f;
}
jx += *incx;
jy += *incy;
/* L40: */
}
}
} else {
/* Form A when A is stored in the lower triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
i__3 = j;
if (x[i__2].r != 0.f || x[i__2].i != 0.f || (y[i__3].r != 0.f
|| y[i__3].i != 0.f)) {
r_cnjg(&q__2, &y[j]);
q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i =
alpha->r * q__2.i + alpha->i * q__2.r;
temp1.r = q__1.r, temp1.i = q__1.i;
i__2 = j;
q__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
q__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
r_cnjg(&q__1, &q__2);
temp2.r = q__1.r, temp2.i = q__1.i;
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
i__4 = j;
q__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i,
q__2.i = x[i__4].r * temp1.i + x[i__4].i *
temp1.r;
i__5 = j;
q__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i,
q__3.i = y[i__5].r * temp2.i + y[i__5].i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
r__1 = a[i__3].r + q__1.r;
a[i__2].r = r__1, a[i__2].i = 0.f;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = i__;
q__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i,
q__3.i = x[i__5].r * temp1.i + x[i__5].i *
temp1.r;
q__2.r = a[i__4].r + q__3.r, q__2.i = a[i__4].i +
q__3.i;
i__6 = i__;
q__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i,
q__4.i = y[i__6].r * temp2.i + y[i__6].i *
temp2.r;
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L50: */
}
} else {
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
r__1 = a[i__3].r;
a[i__2].r = r__1, a[i__2].i = 0.f;
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
i__3 = jy;
if (x[i__2].r != 0.f || x[i__2].i != 0.f || (y[i__3].r != 0.f
|| y[i__3].i != 0.f)) {
r_cnjg(&q__2, &y[jy]);
q__1.r = alpha->r * q__2.r - alpha->i * q__2.i, q__1.i =
alpha->r * q__2.i + alpha->i * q__2.r;
temp1.r = q__1.r, temp1.i = q__1.i;
i__2 = jx;
q__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
q__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
r_cnjg(&q__1, &q__2);
temp2.r = q__1.r, temp2.i = q__1.i;
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
i__4 = jx;
q__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i,
q__2.i = x[i__4].r * temp1.i + x[i__4].i *
temp1.r;
i__5 = jy;
q__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i,
q__3.i = y[i__5].r * temp2.i + y[i__5].i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
r__1 = a[i__3].r + q__1.r;
a[i__2].r = r__1, a[i__2].i = 0.f;
ix = jx;
iy = jy;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
iy += *incy;
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = ix;
q__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i,
q__3.i = x[i__5].r * temp1.i + x[i__5].i *
temp1.r;
q__2.r = a[i__4].r + q__3.r, q__2.i = a[i__4].i +
q__3.i;
i__6 = iy;
q__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i,
q__4.i = y[i__6].r * temp2.i + y[i__6].i *
temp2.r;
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L70: */
}
} else {
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
r__1 = a[i__3].r;
a[i__2].r = r__1, a[i__2].i = 0.f;
}
jx += *incx;
jy += *incy;
/* L80: */
}
}
}
return 0;
/* End of CHER2 . */
} /* cher2_ */
/* Subroutine */ int cher2k_(char *uplo, char *trans, integer *n, integer *k,
complex *alpha, complex *a, integer *lda, complex *b, integer *ldb,
real *beta, complex *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3, i__4, i__5, i__6, i__7;
real r__1;
complex q__1, q__2, q__3, q__4, q__5, q__6;
/* Local variables */
static integer i__, j, l, info;
static complex temp1, temp2;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
CHER2K performs one of the hermitian rank 2k operations
C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,
or
C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C,
where alpha and beta are scalars with beta real, C is an n by n
hermitian matrix and A and B are n by k matrices in the first case
and k by n matrices in the second case.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*conjg( B' ) +
conjg( alpha )*B*conjg( A' ) +
beta*C.
TRANS = 'C' or 'c' C := alpha*conjg( A' )*B +
conjg( alpha )*conjg( B' )*A +
beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrices A and B, and on entry with
TRANS = 'C' or 'c', K specifies the number of rows of the
matrices A and B. K must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
B - COMPLEX array of DIMENSION ( LDB, kb ), where kb is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array B must contain the matrix B, otherwise
the leading k by n part of the array B must contain the
matrix B.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDB must be at least max( 1, n ), otherwise LDB must
be at least max( 1, k ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - COMPLEX array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the hermitian matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the hermitian matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
Note that the imaginary parts of the diagonal elements need
not be set, they are assumed to be zero, and on exit they
are set to zero.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
-- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
Ed Anderson, Cray Research Inc.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
if (lsame_(trans, "N")) {
nrowa = *n;
} else {
nrowa = *k;
}
upper = lsame_(uplo, "U");
info = 0;
if (! upper && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"C")) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*k < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldb < max(1,nrowa)) {
info = 9;
} else if (*ldc < max(1,*n)) {
info = 12;
}
if (info != 0) {
xerbla_("CHER2K", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || (alpha->r == 0.f && alpha->i == 0.f || *k == 0) && *beta ==
1.f) {
return 0;
}
/* And when alpha.eq.zero. */
if (alpha->r == 0.f && alpha->i == 0.f) {
if (upper) {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[
i__4].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L30: */
}
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = *beta * c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
/* L40: */
}
}
} else {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = *beta * c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[
i__4].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L70: */
}
/* L80: */
}
}
}
return 0;
}
/* Start the operations. */
if (lsame_(trans, "N")) {
/*
Form C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) +
C.
*/
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L90: */
}
} else if (*beta != 1.f) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[
i__4].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L100: */
}
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = *beta * c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * a_dim1;
i__4 = j + l * b_dim1;
if (a[i__3].r != 0.f || a[i__3].i != 0.f || (b[i__4].r !=
0.f || b[i__4].i != 0.f)) {
r_cnjg(&q__2, &b[j + l * b_dim1]);
q__1.r = alpha->r * q__2.r - alpha->i * q__2.i,
q__1.i = alpha->r * q__2.i + alpha->i *
q__2.r;
temp1.r = q__1.r, temp1.i = q__1.i;
i__3 = j + l * a_dim1;
q__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i,
q__2.i = alpha->r * a[i__3].i + alpha->i * a[
i__3].r;
r_cnjg(&q__1, &q__2);
temp2.r = q__1.r, temp2.i = q__1.i;
i__3 = j - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
q__3.r = a[i__6].r * temp1.r - a[i__6].i *
temp1.i, q__3.i = a[i__6].r * temp1.i + a[
i__6].i * temp1.r;
q__2.r = c__[i__5].r + q__3.r, q__2.i = c__[i__5]
.i + q__3.i;
i__7 = i__ + l * b_dim1;
q__4.r = b[i__7].r * temp2.r - b[i__7].i *
temp2.i, q__4.i = b[i__7].r * temp2.i + b[
i__7].i * temp2.r;
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i +
q__4.i;
c__[i__4].r = q__1.r, c__[i__4].i = q__1.i;
/* L110: */
}
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
i__5 = j + l * a_dim1;
q__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i,
q__2.i = a[i__5].r * temp1.i + a[i__5].i *
temp1.r;
i__6 = j + l * b_dim1;
q__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i,
q__3.i = b[i__6].r * temp2.i + b[i__6].i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
r__1 = c__[i__4].r + q__1.r;
c__[i__3].r = r__1, c__[i__3].i = 0.f;
}
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L140: */
}
} else if (*beta != 1.f) {
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[
i__4].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L150: */
}
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = *beta * c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * a_dim1;
i__4 = j + l * b_dim1;
if (a[i__3].r != 0.f || a[i__3].i != 0.f || (b[i__4].r !=
0.f || b[i__4].i != 0.f)) {
r_cnjg(&q__2, &b[j + l * b_dim1]);
q__1.r = alpha->r * q__2.r - alpha->i * q__2.i,
q__1.i = alpha->r * q__2.i + alpha->i *
q__2.r;
temp1.r = q__1.r, temp1.i = q__1.i;
i__3 = j + l * a_dim1;
q__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i,
q__2.i = alpha->r * a[i__3].i + alpha->i * a[
i__3].r;
r_cnjg(&q__1, &q__2);
temp2.r = q__1.r, temp2.i = q__1.i;
i__3 = *n;
for (i__ = j + 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
q__3.r = a[i__6].r * temp1.r - a[i__6].i *
temp1.i, q__3.i = a[i__6].r * temp1.i + a[
i__6].i * temp1.r;
q__2.r = c__[i__5].r + q__3.r, q__2.i = c__[i__5]
.i + q__3.i;
i__7 = i__ + l * b_dim1;
q__4.r = b[i__7].r * temp2.r - b[i__7].i *
temp2.i, q__4.i = b[i__7].r * temp2.i + b[
i__7].i * temp2.r;
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i +
q__4.i;
c__[i__4].r = q__1.r, c__[i__4].i = q__1.i;
/* L160: */
}
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
i__5 = j + l * a_dim1;
q__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i,
q__2.i = a[i__5].r * temp1.i + a[i__5].i *
temp1.r;
i__6 = j + l * b_dim1;
q__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i,
q__3.i = b[i__6].r * temp2.i + b[i__6].i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
r__1 = c__[i__4].r + q__1.r;
c__[i__3].r = r__1, c__[i__3].i = 0.f;
}
/* L170: */
}
/* L180: */
}
}
} else {
/*
Form C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A +
C.
*/
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
temp1.r = 0.f, temp1.i = 0.f;
temp2.r = 0.f, temp2.i = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
r_cnjg(&q__3, &a[l + i__ * a_dim1]);
i__4 = l + j * b_dim1;
q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4].i,
q__2.i = q__3.r * b[i__4].i + q__3.i * b[i__4]
.r;
q__1.r = temp1.r + q__2.r, q__1.i = temp1.i + q__2.i;
temp1.r = q__1.r, temp1.i = q__1.i;
r_cnjg(&q__3, &b[l + i__ * b_dim1]);
i__4 = l + j * a_dim1;
q__2.r = q__3.r * a[i__4].r - q__3.i * a[i__4].i,
q__2.i = q__3.r * a[i__4].i + q__3.i * a[i__4]
.r;
q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
temp2.r = q__1.r, temp2.i = q__1.i;
/* L190: */
}
if (i__ == j) {
if (*beta == 0.f) {
i__3 = j + j * c_dim1;
q__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
q__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
r_cnjg(&q__4, alpha);
q__3.r = q__4.r * temp2.r - q__4.i * temp2.i,
q__3.i = q__4.r * temp2.i + q__4.i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i +
q__3.i;
r__1 = q__1.r;
c__[i__3].r = r__1, c__[i__3].i = 0.f;
} else {
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
q__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
q__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
r_cnjg(&q__4, alpha);
q__3.r = q__4.r * temp2.r - q__4.i * temp2.i,
q__3.i = q__4.r * temp2.i + q__4.i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i +
q__3.i;
r__1 = *beta * c__[i__4].r + q__1.r;
c__[i__3].r = r__1, c__[i__3].i = 0.f;
}
} else {
if (*beta == 0.f) {
i__3 = i__ + j * c_dim1;
q__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
q__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
r_cnjg(&q__4, alpha);
q__3.r = q__4.r * temp2.r - q__4.i * temp2.i,
q__3.i = q__4.r * temp2.i + q__4.i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i +
q__3.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
} else {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__3.r = *beta * c__[i__4].r, q__3.i = *beta *
c__[i__4].i;
q__4.r = alpha->r * temp1.r - alpha->i * temp1.i,
q__4.i = alpha->r * temp1.i + alpha->i *
temp1.r;
q__2.r = q__3.r + q__4.r, q__2.i = q__3.i +
q__4.i;
r_cnjg(&q__6, alpha);
q__5.r = q__6.r * temp2.r - q__6.i * temp2.i,
q__5.i = q__6.r * temp2.i + q__6.i *
temp2.r;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i +
q__5.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
}
}
/* L200: */
}
/* L210: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
temp1.r = 0.f, temp1.i = 0.f;
temp2.r = 0.f, temp2.i = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
r_cnjg(&q__3, &a[l + i__ * a_dim1]);
i__4 = l + j * b_dim1;
q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4].i,
q__2.i = q__3.r * b[i__4].i + q__3.i * b[i__4]
.r;
q__1.r = temp1.r + q__2.r, q__1.i = temp1.i + q__2.i;
temp1.r = q__1.r, temp1.i = q__1.i;
r_cnjg(&q__3, &b[l + i__ * b_dim1]);
i__4 = l + j * a_dim1;
q__2.r = q__3.r * a[i__4].r - q__3.i * a[i__4].i,
q__2.i = q__3.r * a[i__4].i + q__3.i * a[i__4]
.r;
q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
temp2.r = q__1.r, temp2.i = q__1.i;
/* L220: */
}
if (i__ == j) {
if (*beta == 0.f) {
i__3 = j + j * c_dim1;
q__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
q__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
r_cnjg(&q__4, alpha);
q__3.r = q__4.r * temp2.r - q__4.i * temp2.i,
q__3.i = q__4.r * temp2.i + q__4.i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i +
q__3.i;
r__1 = q__1.r;
c__[i__3].r = r__1, c__[i__3].i = 0.f;
} else {
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
q__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
q__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
r_cnjg(&q__4, alpha);
q__3.r = q__4.r * temp2.r - q__4.i * temp2.i,
q__3.i = q__4.r * temp2.i + q__4.i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i +
q__3.i;
r__1 = *beta * c__[i__4].r + q__1.r;
c__[i__3].r = r__1, c__[i__3].i = 0.f;
}
} else {
if (*beta == 0.f) {
i__3 = i__ + j * c_dim1;
q__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
q__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
r_cnjg(&q__4, alpha);
q__3.r = q__4.r * temp2.r - q__4.i * temp2.i,
q__3.i = q__4.r * temp2.i + q__4.i *
temp2.r;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i +
q__3.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
} else {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__3.r = *beta * c__[i__4].r, q__3.i = *beta *
c__[i__4].i;
q__4.r = alpha->r * temp1.r - alpha->i * temp1.i,
q__4.i = alpha->r * temp1.i + alpha->i *
temp1.r;
q__2.r = q__3.r + q__4.r, q__2.i = q__3.i +
q__4.i;
r_cnjg(&q__6, alpha);
q__5.r = q__6.r * temp2.r - q__6.i * temp2.i,
q__5.i = q__6.r * temp2.i + q__6.i *
temp2.r;
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i +
q__5.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
}
}
/* L230: */
}
/* L240: */
}
}
}
return 0;
/* End of CHER2K. */
} /* cher2k_ */
/* Subroutine */ int cherk_(char *uplo, char *trans, integer *n, integer *k,
real *alpha, complex *a, integer *lda, real *beta, complex *c__,
integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4, i__5,
i__6;
real r__1;
complex q__1, q__2, q__3;
/* Local variables */
static integer i__, j, l, info;
static complex temp;
extern logical lsame_(char *, char *);
static integer nrowa;
static real rtemp;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
CHERK performs one of the hermitian rank k operations
C := alpha*A*conjg( A' ) + beta*C,
or
C := alpha*conjg( A' )*A + beta*C,
where alpha and beta are real scalars, C is an n by n hermitian
matrix and A is an n by k matrix in the first case and a k by n
matrix in the second case.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*conjg( A' ) + beta*C.
TRANS = 'C' or 'c' C := alpha*conjg( A' )*A + beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrix A, and on entry with
TRANS = 'C' or 'c', K specifies the number of rows of the
matrix A. K must be at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - COMPLEX array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the hermitian matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the hermitian matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
Note that the imaginary parts of the diagonal elements need
not be set, they are assumed to be zero, and on exit they
are set to zero.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
-- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
Ed Anderson, Cray Research Inc.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
if (lsame_(trans, "N")) {
nrowa = *n;
} else {
nrowa = *k;
}
upper = lsame_(uplo, "U");
info = 0;
if (! upper && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"C")) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*k < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldc < max(1,*n)) {
info = 10;
}
if (info != 0) {
xerbla_("CHERK ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || (*alpha == 0.f || *k == 0) && *beta == 1.f) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.f) {
if (upper) {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[
i__4].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L30: */
}
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = *beta * c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
/* L40: */
}
}
} else {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = *beta * c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[
i__4].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L70: */
}
/* L80: */
}
}
}
return 0;
}
/* Start the operations. */
if (lsame_(trans, "N")) {
/* Form C := alpha*A*conjg( A' ) + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L90: */
}
} else if (*beta != 1.f) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[
i__4].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L100: */
}
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = *beta * c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * a_dim1;
if (a[i__3].r != 0.f || a[i__3].i != 0.f) {
r_cnjg(&q__2, &a[j + l * a_dim1]);
q__1.r = *alpha * q__2.r, q__1.i = *alpha * q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
i__3 = j - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
q__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
q__2.i = temp.r * a[i__6].i + temp.i * a[
i__6].r;
q__1.r = c__[i__5].r + q__2.r, q__1.i = c__[i__5]
.i + q__2.i;
c__[i__4].r = q__1.r, c__[i__4].i = q__1.i;
/* L110: */
}
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
i__5 = i__ + l * a_dim1;
q__1.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
q__1.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
r__1 = c__[i__4].r + q__1.r;
c__[i__3].r = r__1, c__[i__3].i = 0.f;
}
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0.f, c__[i__3].i = 0.f;
/* L140: */
}
} else if (*beta != 1.f) {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = *beta * c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
q__1.r = *beta * c__[i__4].r, q__1.i = *beta * c__[
i__4].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L150: */
}
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * a_dim1;
if (a[i__3].r != 0.f || a[i__3].i != 0.f) {
r_cnjg(&q__2, &a[j + l * a_dim1]);
q__1.r = *alpha * q__2.r, q__1.i = *alpha * q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
i__5 = j + l * a_dim1;
q__1.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
q__1.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
r__1 = c__[i__4].r + q__1.r;
c__[i__3].r = r__1, c__[i__3].i = 0.f;
i__3 = *n;
for (i__ = j + 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
q__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
q__2.i = temp.r * a[i__6].i + temp.i * a[
i__6].r;
q__1.r = c__[i__5].r + q__2.r, q__1.i = c__[i__5]
.i + q__2.i;
c__[i__4].r = q__1.r, c__[i__4].i = q__1.i;
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
}
} else {
/* Form C := alpha*conjg( A' )*A + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0.f, temp.i = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
r_cnjg(&q__3, &a[l + i__ * a_dim1]);
i__4 = l + j * a_dim1;
q__2.r = q__3.r * a[i__4].r - q__3.i * a[i__4].i,
q__2.i = q__3.r * a[i__4].i + q__3.i * a[i__4]
.r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L190: */
}
if (*beta == 0.f) {
i__3 = i__ + j * c_dim1;
q__1.r = *alpha * temp.r, q__1.i = *alpha * temp.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
} else {
i__3 = i__ + j * c_dim1;
q__2.r = *alpha * temp.r, q__2.i = *alpha * temp.i;
i__4 = i__ + j * c_dim1;
q__3.r = *beta * c__[i__4].r, q__3.i = *beta * c__[
i__4].i;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
}
/* L200: */
}
rtemp = 0.f;
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
r_cnjg(&q__3, &a[l + j * a_dim1]);
i__3 = l + j * a_dim1;
q__2.r = q__3.r * a[i__3].r - q__3.i * a[i__3].i, q__2.i =
q__3.r * a[i__3].i + q__3.i * a[i__3].r;
q__1.r = rtemp + q__2.r, q__1.i = q__2.i;
rtemp = q__1.r;
/* L210: */
}
if (*beta == 0.f) {
i__2 = j + j * c_dim1;
r__1 = *alpha * rtemp;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = *alpha * rtemp + *beta * c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
}
/* L220: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
rtemp = 0.f;
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
r_cnjg(&q__3, &a[l + j * a_dim1]);
i__3 = l + j * a_dim1;
q__2.r = q__3.r * a[i__3].r - q__3.i * a[i__3].i, q__2.i =
q__3.r * a[i__3].i + q__3.i * a[i__3].r;
q__1.r = rtemp + q__2.r, q__1.i = q__2.i;
rtemp = q__1.r;
/* L230: */
}
if (*beta == 0.f) {
i__2 = j + j * c_dim1;
r__1 = *alpha * rtemp;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
r__1 = *alpha * rtemp + *beta * c__[i__3].r;
c__[i__2].r = r__1, c__[i__2].i = 0.f;
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
temp.r = 0.f, temp.i = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
r_cnjg(&q__3, &a[l + i__ * a_dim1]);
i__4 = l + j * a_dim1;
q__2.r = q__3.r * a[i__4].r - q__3.i * a[i__4].i,
q__2.i = q__3.r * a[i__4].i + q__3.i * a[i__4]
.r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i + q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L240: */
}
if (*beta == 0.f) {
i__3 = i__ + j * c_dim1;
q__1.r = *alpha * temp.r, q__1.i = *alpha * temp.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
} else {
i__3 = i__ + j * c_dim1;
q__2.r = *alpha * temp.r, q__2.i = *alpha * temp.i;
i__4 = i__ + j * c_dim1;
q__3.r = *beta * c__[i__4].r, q__3.i = *beta * c__[
i__4].i;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
}
/* L250: */
}
/* L260: */
}
}
}
return 0;
/* End of CHERK . */
} /* cherk_ */
/* Subroutine */ int cscal_(integer *n, complex *ca, complex *cx, integer *
incx)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
complex q__1;
/* Local variables */
static integer i__, nincx;
/*
Purpose
=======
CSCAL scales a vector by a constant.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--cx;
/* Function Body */
if (*n <= 0 || *incx <= 0) {
return 0;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
nincx = *n * *incx;
i__1 = nincx;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
i__3 = i__;
i__4 = i__;
q__1.r = ca->r * cx[i__4].r - ca->i * cx[i__4].i, q__1.i = ca->r * cx[
i__4].i + ca->i * cx[i__4].r;
cx[i__3].r = q__1.r, cx[i__3].i = q__1.i;
/* L10: */
}
return 0;
/* code for increment equal to 1 */
L20:
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__1 = i__;
i__3 = i__;
q__1.r = ca->r * cx[i__3].r - ca->i * cx[i__3].i, q__1.i = ca->r * cx[
i__3].i + ca->i * cx[i__3].r;
cx[i__1].r = q__1.r, cx[i__1].i = q__1.i;
/* L30: */
}
return 0;
} /* cscal_ */
/* Subroutine */ int csrot_(integer *n, complex *cx, integer *incx, complex *
cy, integer *incy, real *c__, real *s)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
complex q__1, q__2, q__3;
/* Local variables */
static integer i__, ix, iy;
static complex ctemp;
/*
Purpose
=======
CSROT applies a plane rotation, where the cos and sin (c and s) are real
and the vectors cx and cy are complex.
jack dongarra, linpack, 3/11/78.
Arguments
==========
N (input) INTEGER
On entry, N specifies the order of the vectors cx and cy.
N must be at least zero.
Unchanged on exit.
CX (input) COMPLEX array, dimension at least
( 1 + ( N - 1 )*abs( INCX ) ).
Before entry, the incremented array CX must contain the n
element vector cx. On exit, CX is overwritten by the updated
vector cx.
INCX (input) INTEGER
On entry, INCX specifies the increment for the elements of
CX. INCX must not be zero.
Unchanged on exit.
CY (input) COMPLEX array, dimension at least
( 1 + ( N - 1 )*abs( INCY ) ).
Before entry, the incremented array CY must contain the n
element vector cy. On exit, CY is overwritten by the updated
vector cy.
INCY (input) INTEGER
On entry, INCY specifies the increment for the elements of
CY. INCY must not be zero.
Unchanged on exit.
C (input) REAL
On entry, C specifies the cosine, cos.
Unchanged on exit.
S (input) REAL
On entry, S specifies the sine, sin.
Unchanged on exit.
=====================================================================
*/
/* Parameter adjustments */
--cy;
--cx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments not equal
to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ix;
q__2.r = *c__ * cx[i__2].r, q__2.i = *c__ * cx[i__2].i;
i__3 = iy;
q__3.r = *s * cy[i__3].r, q__3.i = *s * cy[i__3].i;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
i__2 = iy;
i__3 = iy;
q__2.r = *c__ * cy[i__3].r, q__2.i = *c__ * cy[i__3].i;
i__4 = ix;
q__3.r = *s * cx[i__4].r, q__3.i = *s * cx[i__4].i;
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
cy[i__2].r = q__1.r, cy[i__2].i = q__1.i;
i__2 = ix;
cx[i__2].r = ctemp.r, cx[i__2].i = ctemp.i;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
q__2.r = *c__ * cx[i__2].r, q__2.i = *c__ * cx[i__2].i;
i__3 = i__;
q__3.r = *s * cy[i__3].r, q__3.i = *s * cy[i__3].i;
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
ctemp.r = q__1.r, ctemp.i = q__1.i;
i__2 = i__;
i__3 = i__;
q__2.r = *c__ * cy[i__3].r, q__2.i = *c__ * cy[i__3].i;
i__4 = i__;
q__3.r = *s * cx[i__4].r, q__3.i = *s * cx[i__4].i;
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
cy[i__2].r = q__1.r, cy[i__2].i = q__1.i;
i__2 = i__;
cx[i__2].r = ctemp.r, cx[i__2].i = ctemp.i;
/* L30: */
}
return 0;
} /* csrot_ */
/* Subroutine */ int csscal_(integer *n, real *sa, complex *cx, integer *incx)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
real r__1, r__2;
complex q__1;
/* Local variables */
static integer i__, nincx;
/*
Purpose
=======
CSSCAL scales a complex vector by a real constant.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--cx;
/* Function Body */
if (*n <= 0 || *incx <= 0) {
return 0;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
nincx = *n * *incx;
i__1 = nincx;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
i__3 = i__;
i__4 = i__;
r__1 = *sa * cx[i__4].r;
r__2 = *sa * r_imag(&cx[i__]);
q__1.r = r__1, q__1.i = r__2;
cx[i__3].r = q__1.r, cx[i__3].i = q__1.i;
/* L10: */
}
return 0;
/* code for increment equal to 1 */
L20:
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__1 = i__;
i__3 = i__;
r__1 = *sa * cx[i__3].r;
r__2 = *sa * r_imag(&cx[i__]);
q__1.r = r__1, q__1.i = r__2;
cx[i__1].r = q__1.r, cx[i__1].i = q__1.i;
/* L30: */
}
return 0;
} /* csscal_ */
/* Subroutine */ int cswap_(integer *n, complex *cx, integer *incx, complex *
cy, integer *incy)
{
/* System generated locals */
integer i__1, i__2, i__3;
/* Local variables */
static integer i__, ix, iy;
static complex ctemp;
/*
Purpose
=======
CSWAP interchanges two vectors.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--cy;
--cx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments not equal
to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ix;
ctemp.r = cx[i__2].r, ctemp.i = cx[i__2].i;
i__2 = ix;
i__3 = iy;
cx[i__2].r = cy[i__3].r, cx[i__2].i = cy[i__3].i;
i__2 = iy;
cy[i__2].r = ctemp.r, cy[i__2].i = ctemp.i;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
ctemp.r = cx[i__2].r, ctemp.i = cx[i__2].i;
i__2 = i__;
i__3 = i__;
cx[i__2].r = cy[i__3].r, cx[i__2].i = cy[i__3].i;
i__2 = i__;
cy[i__2].r = ctemp.r, cy[i__2].i = ctemp.i;
/* L30: */
}
return 0;
} /* cswap_ */
/* Subroutine */ int ctrmm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, complex *alpha, complex *a, integer *lda,
complex *b, integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5,
i__6;
complex q__1, q__2, q__3;
/* Local variables */
static integer i__, j, k, info;
static complex temp;
extern logical lsame_(char *, char *);
static logical lside;
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical noconj, nounit;
/*
Purpose
=======
CTRMM performs one of the matrix-matrix operations
B := alpha*op( A )*B, or B := alpha*B*op( A )
where alpha is a scalar, B is an m by n matrix, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ).
Arguments
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) multiplies B from
the left or right as follows:
SIDE = 'L' or 'l' B := alpha*op( A )*B.
SIDE = 'R' or 'r' B := alpha*B*op( A ).
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A'.
TRANSA = 'C' or 'c' op( A ) = conjg( A' ).
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
B - COMPLEX array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the matrix B, and on exit is overwritten by the
transformed matrix.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
lside = lsame_(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
noconj = lsame_(transa, "T");
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
info = 0;
if (! lside && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (! lsame_(transa, "N") && ! lsame_(transa,
"T") && ! lsame_(transa, "C")) {
info = 3;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < max(1,nrowa)) {
info = 9;
} else if (*ldb < max(1,*m)) {
info = 11;
}
if (info != 0) {
xerbla_("CTRMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (alpha->r == 0.f && alpha->i == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (lsame_(transa, "N")) {
/* Form B := alpha*A*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * b_dim1;
if (b[i__3].r != 0.f || b[i__3].i != 0.f) {
i__3 = k + j * b_dim1;
q__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3]
.i, q__1.i = alpha->r * b[i__3].i +
alpha->i * b[i__3].r;
temp.r = q__1.r, temp.i = q__1.i;
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = i__ + k * a_dim1;
q__2.r = temp.r * a[i__6].r - temp.i * a[i__6]
.i, q__2.i = temp.r * a[i__6].i +
temp.i * a[i__6].r;
q__1.r = b[i__5].r + q__2.r, q__1.i = b[i__5]
.i + q__2.i;
b[i__4].r = q__1.r, b[i__4].i = q__1.i;
/* L30: */
}
if (nounit) {
i__3 = k + k * a_dim1;
q__1.r = temp.r * a[i__3].r - temp.i * a[i__3]
.i, q__1.i = temp.r * a[i__3].i +
temp.i * a[i__3].r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__3 = k + j * b_dim1;
b[i__3].r = temp.r, b[i__3].i = temp.i;
}
/* L40: */
}
/* L50: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (k = *m; k >= 1; --k) {
i__2 = k + j * b_dim1;
if (b[i__2].r != 0.f || b[i__2].i != 0.f) {
i__2 = k + j * b_dim1;
q__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2]
.i, q__1.i = alpha->r * b[i__2].i +
alpha->i * b[i__2].r;
temp.r = q__1.r, temp.i = q__1.i;
i__2 = k + j * b_dim1;
b[i__2].r = temp.r, b[i__2].i = temp.i;
if (nounit) {
i__2 = k + j * b_dim1;
i__3 = k + j * b_dim1;
i__4 = k + k * a_dim1;
q__1.r = b[i__3].r * a[i__4].r - b[i__3].i *
a[i__4].i, q__1.i = b[i__3].r * a[
i__4].i + b[i__3].i * a[i__4].r;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
}
i__2 = *m;
for (i__ = k + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = i__ + k * a_dim1;
q__2.r = temp.r * a[i__5].r - temp.i * a[i__5]
.i, q__2.i = temp.r * a[i__5].i +
temp.i * a[i__5].r;
q__1.r = b[i__4].r + q__2.r, q__1.i = b[i__4]
.i + q__2.i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L60: */
}
}
/* L70: */
}
/* L80: */
}
}
} else {
/* Form B := alpha*A'*B or B := alpha*conjg( A' )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
i__2 = i__ + j * b_dim1;
temp.r = b[i__2].r, temp.i = b[i__2].i;
if (noconj) {
if (nounit) {
i__2 = i__ + i__ * a_dim1;
q__1.r = temp.r * a[i__2].r - temp.i * a[i__2]
.i, q__1.i = temp.r * a[i__2].i +
temp.i * a[i__2].r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__2 = i__ - 1;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * a_dim1;
i__4 = k + j * b_dim1;
q__2.r = a[i__3].r * b[i__4].r - a[i__3].i *
b[i__4].i, q__2.i = a[i__3].r * b[
i__4].i + a[i__3].i * b[i__4].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L90: */
}
} else {
if (nounit) {
r_cnjg(&q__2, &a[i__ + i__ * a_dim1]);
q__1.r = temp.r * q__2.r - temp.i * q__2.i,
q__1.i = temp.r * q__2.i + temp.i *
q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__2 = i__ - 1;
for (k = 1; k <= i__2; ++k) {
r_cnjg(&q__3, &a[k + i__ * a_dim1]);
i__3 = k + j * b_dim1;
q__2.r = q__3.r * b[i__3].r - q__3.i * b[i__3]
.i, q__2.i = q__3.r * b[i__3].i +
q__3.i * b[i__3].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L100: */
}
}
i__2 = i__ + j * b_dim1;
q__1.r = alpha->r * temp.r - alpha->i * temp.i,
q__1.i = alpha->r * temp.i + alpha->i *
temp.r;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L110: */
}
/* L120: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
temp.r = b[i__3].r, temp.i = b[i__3].i;
if (noconj) {
if (nounit) {
i__3 = i__ + i__ * a_dim1;
q__1.r = temp.r * a[i__3].r - temp.i * a[i__3]
.i, q__1.i = temp.r * a[i__3].i +
temp.i * a[i__3].r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__3 = *m;
for (k = i__ + 1; k <= i__3; ++k) {
i__4 = k + i__ * a_dim1;
i__5 = k + j * b_dim1;
q__2.r = a[i__4].r * b[i__5].r - a[i__4].i *
b[i__5].i, q__2.i = a[i__4].r * b[
i__5].i + a[i__4].i * b[i__5].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L130: */
}
} else {
if (nounit) {
r_cnjg(&q__2, &a[i__ + i__ * a_dim1]);
q__1.r = temp.r * q__2.r - temp.i * q__2.i,
q__1.i = temp.r * q__2.i + temp.i *
q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__3 = *m;
for (k = i__ + 1; k <= i__3; ++k) {
r_cnjg(&q__3, &a[k + i__ * a_dim1]);
i__4 = k + j * b_dim1;
q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4]
.i, q__2.i = q__3.r * b[i__4].i +
q__3.i * b[i__4].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L140: */
}
}
i__3 = i__ + j * b_dim1;
q__1.r = alpha->r * temp.r - alpha->i * temp.i,
q__1.i = alpha->r * temp.i + alpha->i *
temp.r;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L150: */
}
/* L160: */
}
}
}
} else {
if (lsame_(transa, "N")) {
/* Form B := alpha*B*A. */
if (upper) {
for (j = *n; j >= 1; --j) {
temp.r = alpha->r, temp.i = alpha->i;
if (nounit) {
i__1 = j + j * a_dim1;
q__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i,
q__1.i = temp.r * a[i__1].i + temp.i * a[i__1]
.r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
q__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i,
q__1.i = temp.r * b[i__3].i + temp.i * b[i__3]
.r;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L170: */
}
i__1 = j - 1;
for (k = 1; k <= i__1; ++k) {
i__2 = k + j * a_dim1;
if (a[i__2].r != 0.f || a[i__2].i != 0.f) {
i__2 = k + j * a_dim1;
q__1.r = alpha->r * a[i__2].r - alpha->i * a[i__2]
.i, q__1.i = alpha->r * a[i__2].i +
alpha->i * a[i__2].r;
temp.r = q__1.r, temp.i = q__1.i;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = i__ + k * b_dim1;
q__2.r = temp.r * b[i__5].r - temp.i * b[i__5]
.i, q__2.i = temp.r * b[i__5].i +
temp.i * b[i__5].r;
q__1.r = b[i__4].r + q__2.r, q__1.i = b[i__4]
.i + q__2.i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L180: */
}
}
/* L190: */
}
/* L200: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp.r = alpha->r, temp.i = alpha->i;
if (nounit) {
i__2 = j + j * a_dim1;
q__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
q__1.i = temp.r * a[i__2].i + temp.i * a[i__2]
.r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
q__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i,
q__1.i = temp.r * b[i__4].i + temp.i * b[i__4]
.r;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L210: */
}
i__2 = *n;
for (k = j + 1; k <= i__2; ++k) {
i__3 = k + j * a_dim1;
if (a[i__3].r != 0.f || a[i__3].i != 0.f) {
i__3 = k + j * a_dim1;
q__1.r = alpha->r * a[i__3].r - alpha->i * a[i__3]
.i, q__1.i = alpha->r * a[i__3].i +
alpha->i * a[i__3].r;
temp.r = q__1.r, temp.i = q__1.i;
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = i__ + k * b_dim1;
q__2.r = temp.r * b[i__6].r - temp.i * b[i__6]
.i, q__2.i = temp.r * b[i__6].i +
temp.i * b[i__6].r;
q__1.r = b[i__5].r + q__2.r, q__1.i = b[i__5]
.i + q__2.i;
b[i__4].r = q__1.r, b[i__4].i = q__1.i;
/* L220: */
}
}
/* L230: */
}
/* L240: */
}
}
} else {
/* Form B := alpha*B*A' or B := alpha*B*conjg( A' ). */
if (upper) {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
i__2 = k - 1;
for (j = 1; j <= i__2; ++j) {
i__3 = j + k * a_dim1;
if (a[i__3].r != 0.f || a[i__3].i != 0.f) {
if (noconj) {
i__3 = j + k * a_dim1;
q__1.r = alpha->r * a[i__3].r - alpha->i * a[
i__3].i, q__1.i = alpha->r * a[i__3]
.i + alpha->i * a[i__3].r;
temp.r = q__1.r, temp.i = q__1.i;
} else {
r_cnjg(&q__2, &a[j + k * a_dim1]);
q__1.r = alpha->r * q__2.r - alpha->i *
q__2.i, q__1.i = alpha->r * q__2.i +
alpha->i * q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = i__ + k * b_dim1;
q__2.r = temp.r * b[i__6].r - temp.i * b[i__6]
.i, q__2.i = temp.r * b[i__6].i +
temp.i * b[i__6].r;
q__1.r = b[i__5].r + q__2.r, q__1.i = b[i__5]
.i + q__2.i;
b[i__4].r = q__1.r, b[i__4].i = q__1.i;
/* L250: */
}
}
/* L260: */
}
temp.r = alpha->r, temp.i = alpha->i;
if (nounit) {
if (noconj) {
i__2 = k + k * a_dim1;
q__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
q__1.i = temp.r * a[i__2].i + temp.i * a[
i__2].r;
temp.r = q__1.r, temp.i = q__1.i;
} else {
r_cnjg(&q__2, &a[k + k * a_dim1]);
q__1.r = temp.r * q__2.r - temp.i * q__2.i,
q__1.i = temp.r * q__2.i + temp.i *
q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
}
}
if (temp.r != 1.f || temp.i != 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + k * b_dim1;
i__4 = i__ + k * b_dim1;
q__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i,
q__1.i = temp.r * b[i__4].i + temp.i * b[
i__4].r;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L270: */
}
}
/* L280: */
}
} else {
for (k = *n; k >= 1; --k) {
i__1 = *n;
for (j = k + 1; j <= i__1; ++j) {
i__2 = j + k * a_dim1;
if (a[i__2].r != 0.f || a[i__2].i != 0.f) {
if (noconj) {
i__2 = j + k * a_dim1;
q__1.r = alpha->r * a[i__2].r - alpha->i * a[
i__2].i, q__1.i = alpha->r * a[i__2]
.i + alpha->i * a[i__2].r;
temp.r = q__1.r, temp.i = q__1.i;
} else {
r_cnjg(&q__2, &a[j + k * a_dim1]);
q__1.r = alpha->r * q__2.r - alpha->i *
q__2.i, q__1.i = alpha->r * q__2.i +
alpha->i * q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = i__ + k * b_dim1;
q__2.r = temp.r * b[i__5].r - temp.i * b[i__5]
.i, q__2.i = temp.r * b[i__5].i +
temp.i * b[i__5].r;
q__1.r = b[i__4].r + q__2.r, q__1.i = b[i__4]
.i + q__2.i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L290: */
}
}
/* L300: */
}
temp.r = alpha->r, temp.i = alpha->i;
if (nounit) {
if (noconj) {
i__1 = k + k * a_dim1;
q__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i,
q__1.i = temp.r * a[i__1].i + temp.i * a[
i__1].r;
temp.r = q__1.r, temp.i = q__1.i;
} else {
r_cnjg(&q__2, &a[k + k * a_dim1]);
q__1.r = temp.r * q__2.r - temp.i * q__2.i,
q__1.i = temp.r * q__2.i + temp.i *
q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
}
}
if (temp.r != 1.f || temp.i != 0.f) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + k * b_dim1;
i__3 = i__ + k * b_dim1;
q__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i,
q__1.i = temp.r * b[i__3].i + temp.i * b[
i__3].r;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L310: */
}
}
/* L320: */
}
}
}
}
return 0;
/* End of CTRMM . */
} /* ctrmm_ */
/* Subroutine */ int ctrmv_(char *uplo, char *trans, char *diag, integer *n,
complex *a, integer *lda, complex *x, integer *incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
complex q__1, q__2, q__3;
/* Local variables */
static integer i__, j, ix, jx, kx, info;
static complex temp;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical noconj, nounit;
/*
Purpose
=======
CTRMV performs one of the matrix-vector operations
x := A*x, or x := A'*x, or x := conjg( A' )*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A'*x.
TRANS = 'C' or 'c' x := conjg( A' )*x.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - COMPLEX array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x. On exit, X is overwritten with the
tranformed vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*lda < max(1,*n)) {
info = 6;
} else if (*incx == 0) {
info = 8;
}
if (info != 0) {
xerbla_("CTRMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
noconj = lsame_(trans, "T");
nounit = lsame_(diag, "N");
/*
Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops.
*/
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (lsame_(trans, "N")) {
/* Form x := A*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
if (x[i__2].r != 0.f || x[i__2].i != 0.f) {
i__2 = j;
temp.r = x[i__2].r, temp.i = x[i__2].i;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__ + j * a_dim1;
q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
q__2.i = temp.r * a[i__5].i + temp.i * a[
i__5].r;
q__1.r = x[i__4].r + q__2.r, q__1.i = x[i__4].i +
q__2.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
/* L10: */
}
if (nounit) {
i__2 = j;
i__3 = j;
i__4 = j + j * a_dim1;
q__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[
i__4].i, q__1.i = x[i__3].r * a[i__4].i +
x[i__3].i * a[i__4].r;
x[i__2].r = q__1.r, x[i__2].i = q__1.i;
}
}
/* L20: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
if (x[i__2].r != 0.f || x[i__2].i != 0.f) {
i__2 = jx;
temp.r = x[i__2].r, temp.i = x[i__2].i;
ix = kx;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = ix;
i__4 = ix;
i__5 = i__ + j * a_dim1;
q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
q__2.i = temp.r * a[i__5].i + temp.i * a[
i__5].r;
q__1.r = x[i__4].r + q__2.r, q__1.i = x[i__4].i +
q__2.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
ix += *incx;
/* L30: */
}
if (nounit) {
i__2 = jx;
i__3 = jx;
i__4 = j + j * a_dim1;
q__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[
i__4].i, q__1.i = x[i__3].r * a[i__4].i +
x[i__3].i * a[i__4].r;
x[i__2].r = q__1.r, x[i__2].i = q__1.i;
}
}
jx += *incx;
/* L40: */
}
}
} else {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
i__1 = j;
if (x[i__1].r != 0.f || x[i__1].i != 0.f) {
i__1 = j;
temp.r = x[i__1].r, temp.i = x[i__1].i;
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__ + j * a_dim1;
q__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
q__2.i = temp.r * a[i__4].i + temp.i * a[
i__4].r;
q__1.r = x[i__3].r + q__2.r, q__1.i = x[i__3].i +
q__2.i;
x[i__2].r = q__1.r, x[i__2].i = q__1.i;
/* L50: */
}
if (nounit) {
i__1 = j;
i__2 = j;
i__3 = j + j * a_dim1;
q__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[
i__3].i, q__1.i = x[i__2].r * a[i__3].i +
x[i__2].i * a[i__3].r;
x[i__1].r = q__1.r, x[i__1].i = q__1.i;
}
}
/* L60: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
i__1 = jx;
if (x[i__1].r != 0.f || x[i__1].i != 0.f) {
i__1 = jx;
temp.r = x[i__1].r, temp.i = x[i__1].i;
ix = kx;
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
i__2 = ix;
i__3 = ix;
i__4 = i__ + j * a_dim1;
q__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
q__2.i = temp.r * a[i__4].i + temp.i * a[
i__4].r;
q__1.r = x[i__3].r + q__2.r, q__1.i = x[i__3].i +
q__2.i;
x[i__2].r = q__1.r, x[i__2].i = q__1.i;
ix -= *incx;
/* L70: */
}
if (nounit) {
i__1 = jx;
i__2 = jx;
i__3 = j + j * a_dim1;
q__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[
i__3].i, q__1.i = x[i__2].r * a[i__3].i +
x[i__2].i * a[i__3].r;
x[i__1].r = q__1.r, x[i__1].i = q__1.i;
}
}
jx -= *incx;
/* L80: */
}
}
}
} else {
/* Form x := A'*x or x := conjg( A' )*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
i__1 = j;
temp.r = x[i__1].r, temp.i = x[i__1].i;
if (noconj) {
if (nounit) {
i__1 = j + j * a_dim1;
q__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i,
q__1.i = temp.r * a[i__1].i + temp.i * a[
i__1].r;
temp.r = q__1.r, temp.i = q__1.i;
}
for (i__ = j - 1; i__ >= 1; --i__) {
i__1 = i__ + j * a_dim1;
i__2 = i__;
q__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[
i__2].i, q__2.i = a[i__1].r * x[i__2].i +
a[i__1].i * x[i__2].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L90: */
}
} else {
if (nounit) {
r_cnjg(&q__2, &a[j + j * a_dim1]);
q__1.r = temp.r * q__2.r - temp.i * q__2.i,
q__1.i = temp.r * q__2.i + temp.i *
q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
}
for (i__ = j - 1; i__ >= 1; --i__) {
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__1 = i__;
q__2.r = q__3.r * x[i__1].r - q__3.i * x[i__1].i,
q__2.i = q__3.r * x[i__1].i + q__3.i * x[
i__1].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L100: */
}
}
i__1 = j;
x[i__1].r = temp.r, x[i__1].i = temp.i;
/* L110: */
}
} else {
jx = kx + (*n - 1) * *incx;
for (j = *n; j >= 1; --j) {
i__1 = jx;
temp.r = x[i__1].r, temp.i = x[i__1].i;
ix = jx;
if (noconj) {
if (nounit) {
i__1 = j + j * a_dim1;
q__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i,
q__1.i = temp.r * a[i__1].i + temp.i * a[
i__1].r;
temp.r = q__1.r, temp.i = q__1.i;
}
for (i__ = j - 1; i__ >= 1; --i__) {
ix -= *incx;
i__1 = i__ + j * a_dim1;
i__2 = ix;
q__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[
i__2].i, q__2.i = a[i__1].r * x[i__2].i +
a[i__1].i * x[i__2].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L120: */
}
} else {
if (nounit) {
r_cnjg(&q__2, &a[j + j * a_dim1]);
q__1.r = temp.r * q__2.r - temp.i * q__2.i,
q__1.i = temp.r * q__2.i + temp.i *
q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
}
for (i__ = j - 1; i__ >= 1; --i__) {
ix -= *incx;
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__1 = ix;
q__2.r = q__3.r * x[i__1].r - q__3.i * x[i__1].i,
q__2.i = q__3.r * x[i__1].i + q__3.i * x[
i__1].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L130: */
}
}
i__1 = jx;
x[i__1].r = temp.r, x[i__1].i = temp.i;
jx -= *incx;
/* L140: */
}
}
} else {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
temp.r = x[i__2].r, temp.i = x[i__2].i;
if (noconj) {
if (nounit) {
i__2 = j + j * a_dim1;
q__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
q__1.i = temp.r * a[i__2].i + temp.i * a[
i__2].r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__;
q__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[
i__4].i, q__2.i = a[i__3].r * x[i__4].i +
a[i__3].i * x[i__4].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L150: */
}
} else {
if (nounit) {
r_cnjg(&q__2, &a[j + j * a_dim1]);
q__1.r = temp.r * q__2.r - temp.i * q__2.i,
q__1.i = temp.r * q__2.i + temp.i *
q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__3 = i__;
q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i,
q__2.i = q__3.r * x[i__3].i + q__3.i * x[
i__3].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L160: */
}
}
i__2 = j;
x[i__2].r = temp.r, x[i__2].i = temp.i;
/* L170: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
temp.r = x[i__2].r, temp.i = x[i__2].i;
ix = jx;
if (noconj) {
if (nounit) {
i__2 = j + j * a_dim1;
q__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
q__1.i = temp.r * a[i__2].i + temp.i * a[
i__2].r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
i__3 = i__ + j * a_dim1;
i__4 = ix;
q__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[
i__4].i, q__2.i = a[i__3].r * x[i__4].i +
a[i__3].i * x[i__4].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L180: */
}
} else {
if (nounit) {
r_cnjg(&q__2, &a[j + j * a_dim1]);
q__1.r = temp.r * q__2.r - temp.i * q__2.i,
q__1.i = temp.r * q__2.i + temp.i *
q__2.r;
temp.r = q__1.r, temp.i = q__1.i;
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__3 = ix;
q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i,
q__2.i = q__3.r * x[i__3].i + q__3.i * x[
i__3].r;
q__1.r = temp.r + q__2.r, q__1.i = temp.i +
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L190: */
}
}
i__2 = jx;
x[i__2].r = temp.r, x[i__2].i = temp.i;
jx += *incx;
/* L200: */
}
}
}
}
return 0;
/* End of CTRMV . */
} /* ctrmv_ */
/* Subroutine */ int ctrsm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, complex *alpha, complex *a, integer *lda,
complex *b, integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5,
i__6, i__7;
complex q__1, q__2, q__3;
/* Local variables */
static integer i__, j, k, info;
static complex temp;
extern logical lsame_(char *, char *);
static logical lside;
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical noconj, nounit;
/*
Purpose
=======
CTRSM solves one of the matrix equations
op( A )*X = alpha*B, or X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ).
The matrix X is overwritten on B.
Arguments
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:
SIDE = 'L' or 'l' op( A )*X = alpha*B.
SIDE = 'R' or 'r' X*op( A ) = alpha*B.
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A'.
TRANSA = 'C' or 'c' op( A ) = conjg( A' ).
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - COMPLEX .
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
B - COMPLEX array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the right-hand side matrix B, and on exit is
overwritten by the solution matrix X.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
lside = lsame_(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
noconj = lsame_(transa, "T");
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
info = 0;
if (! lside && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (! lsame_(transa, "N") && ! lsame_(transa,
"T") && ! lsame_(transa, "C")) {
info = 3;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < max(1,nrowa)) {
info = 9;
} else if (*ldb < max(1,*m)) {
info = 11;
}
if (info != 0) {
xerbla_("CTRSM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (alpha->r == 0.f && alpha->i == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (lsame_(transa, "N")) {
/* Form B := alpha*inv( A )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (alpha->r != 1.f || alpha->i != 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
q__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, q__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L30: */
}
}
for (k = *m; k >= 1; --k) {
i__2 = k + j * b_dim1;
if (b[i__2].r != 0.f || b[i__2].i != 0.f) {
if (nounit) {
i__2 = k + j * b_dim1;
c_div(&q__1, &b[k + j * b_dim1], &a[k + k *
a_dim1]);
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
}
i__2 = k - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = k + j * b_dim1;
i__6 = i__ + k * a_dim1;
q__2.r = b[i__5].r * a[i__6].r - b[i__5].i *
a[i__6].i, q__2.i = b[i__5].r * a[
i__6].i + b[i__5].i * a[i__6].r;
q__1.r = b[i__4].r - q__2.r, q__1.i = b[i__4]
.i - q__2.i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L40: */
}
}
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (alpha->r != 1.f || alpha->i != 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
q__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, q__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L70: */
}
}
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * b_dim1;
if (b[i__3].r != 0.f || b[i__3].i != 0.f) {
if (nounit) {
i__3 = k + j * b_dim1;
c_div(&q__1, &b[k + j * b_dim1], &a[k + k *
a_dim1]);
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
}
i__3 = *m;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = k + j * b_dim1;
i__7 = i__ + k * a_dim1;
q__2.r = b[i__6].r * a[i__7].r - b[i__6].i *
a[i__7].i, q__2.i = b[i__6].r * a[
i__7].i + b[i__6].i * a[i__7].r;
q__1.r = b[i__5].r - q__2.r, q__1.i = b[i__5]
.i - q__2.i;
b[i__4].r = q__1.r, b[i__4].i = q__1.i;
/* L80: */
}
}
/* L90: */
}
/* L100: */
}
}
} else {
/*
Form B := alpha*inv( A' )*B
or B := alpha*inv( conjg( A' ) )*B.
*/
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
q__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i,
q__1.i = alpha->r * b[i__3].i + alpha->i * b[
i__3].r;
temp.r = q__1.r, temp.i = q__1.i;
if (noconj) {
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
i__4 = k + i__ * a_dim1;
i__5 = k + j * b_dim1;
q__2.r = a[i__4].r * b[i__5].r - a[i__4].i *
b[i__5].i, q__2.i = a[i__4].r * b[
i__5].i + a[i__4].i * b[i__5].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L110: */
}
if (nounit) {
c_div(&q__1, &temp, &a[i__ + i__ * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
}
} else {
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
r_cnjg(&q__3, &a[k + i__ * a_dim1]);
i__4 = k + j * b_dim1;
q__2.r = q__3.r * b[i__4].r - q__3.i * b[i__4]
.i, q__2.i = q__3.r * b[i__4].i +
q__3.i * b[i__4].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L120: */
}
if (nounit) {
r_cnjg(&q__2, &a[i__ + i__ * a_dim1]);
c_div(&q__1, &temp, &q__2);
temp.r = q__1.r, temp.i = q__1.i;
}
}
i__3 = i__ + j * b_dim1;
b[i__3].r = temp.r, b[i__3].i = temp.i;
/* L130: */
}
/* L140: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
i__2 = i__ + j * b_dim1;
q__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2].i,
q__1.i = alpha->r * b[i__2].i + alpha->i * b[
i__2].r;
temp.r = q__1.r, temp.i = q__1.i;
if (noconj) {
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
i__3 = k + i__ * a_dim1;
i__4 = k + j * b_dim1;
q__2.r = a[i__3].r * b[i__4].r - a[i__3].i *
b[i__4].i, q__2.i = a[i__3].r * b[
i__4].i + a[i__3].i * b[i__4].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L150: */
}
if (nounit) {
c_div(&q__1, &temp, &a[i__ + i__ * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
}
} else {
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
r_cnjg(&q__3, &a[k + i__ * a_dim1]);
i__3 = k + j * b_dim1;
q__2.r = q__3.r * b[i__3].r - q__3.i * b[i__3]
.i, q__2.i = q__3.r * b[i__3].i +
q__3.i * b[i__3].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L160: */
}
if (nounit) {
r_cnjg(&q__2, &a[i__ + i__ * a_dim1]);
c_div(&q__1, &temp, &q__2);
temp.r = q__1.r, temp.i = q__1.i;
}
}
i__2 = i__ + j * b_dim1;
b[i__2].r = temp.r, b[i__2].i = temp.i;
/* L170: */
}
/* L180: */
}
}
}
} else {
if (lsame_(transa, "N")) {
/* Form B := alpha*B*inv( A ). */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (alpha->r != 1.f || alpha->i != 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
q__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, q__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L190: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * a_dim1;
if (a[i__3].r != 0.f || a[i__3].i != 0.f) {
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = k + j * a_dim1;
i__7 = i__ + k * b_dim1;
q__2.r = a[i__6].r * b[i__7].r - a[i__6].i *
b[i__7].i, q__2.i = a[i__6].r * b[
i__7].i + a[i__6].i * b[i__7].r;
q__1.r = b[i__5].r - q__2.r, q__1.i = b[i__5]
.i - q__2.i;
b[i__4].r = q__1.r, b[i__4].i = q__1.i;
/* L200: */
}
}
/* L210: */
}
if (nounit) {
c_div(&q__1, &c_b21, &a[j + j * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
q__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i,
q__1.i = temp.r * b[i__4].i + temp.i * b[
i__4].r;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L220: */
}
}
/* L230: */
}
} else {
for (j = *n; j >= 1; --j) {
if (alpha->r != 1.f || alpha->i != 0.f) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
q__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3]
.i, q__1.i = alpha->r * b[i__3].i +
alpha->i * b[i__3].r;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L240: */
}
}
i__1 = *n;
for (k = j + 1; k <= i__1; ++k) {
i__2 = k + j * a_dim1;
if (a[i__2].r != 0.f || a[i__2].i != 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = k + j * a_dim1;
i__6 = i__ + k * b_dim1;
q__2.r = a[i__5].r * b[i__6].r - a[i__5].i *
b[i__6].i, q__2.i = a[i__5].r * b[
i__6].i + a[i__5].i * b[i__6].r;
q__1.r = b[i__4].r - q__2.r, q__1.i = b[i__4]
.i - q__2.i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L250: */
}
}
/* L260: */
}
if (nounit) {
c_div(&q__1, &c_b21, &a[j + j * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
q__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i,
q__1.i = temp.r * b[i__3].i + temp.i * b[
i__3].r;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L270: */
}
}
/* L280: */
}
}
} else {
/*
Form B := alpha*B*inv( A' )
or B := alpha*B*inv( conjg( A' ) ).
*/
if (upper) {
for (k = *n; k >= 1; --k) {
if (nounit) {
if (noconj) {
c_div(&q__1, &c_b21, &a[k + k * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
} else {
r_cnjg(&q__2, &a[k + k * a_dim1]);
c_div(&q__1, &c_b21, &q__2);
temp.r = q__1.r, temp.i = q__1.i;
}
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + k * b_dim1;
i__3 = i__ + k * b_dim1;
q__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i,
q__1.i = temp.r * b[i__3].i + temp.i * b[
i__3].r;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L290: */
}
}
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j + k * a_dim1;
if (a[i__2].r != 0.f || a[i__2].i != 0.f) {
if (noconj) {
i__2 = j + k * a_dim1;
temp.r = a[i__2].r, temp.i = a[i__2].i;
} else {
r_cnjg(&q__1, &a[j + k * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = i__ + k * b_dim1;
q__2.r = temp.r * b[i__5].r - temp.i * b[i__5]
.i, q__2.i = temp.r * b[i__5].i +
temp.i * b[i__5].r;
q__1.r = b[i__4].r - q__2.r, q__1.i = b[i__4]
.i - q__2.i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L300: */
}
}
/* L310: */
}
if (alpha->r != 1.f || alpha->i != 0.f) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + k * b_dim1;
i__3 = i__ + k * b_dim1;
q__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3]
.i, q__1.i = alpha->r * b[i__3].i +
alpha->i * b[i__3].r;
b[i__2].r = q__1.r, b[i__2].i = q__1.i;
/* L320: */
}
}
/* L330: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (nounit) {
if (noconj) {
c_div(&q__1, &c_b21, &a[k + k * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
} else {
r_cnjg(&q__2, &a[k + k * a_dim1]);
c_div(&q__1, &c_b21, &q__2);
temp.r = q__1.r, temp.i = q__1.i;
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + k * b_dim1;
i__4 = i__ + k * b_dim1;
q__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i,
q__1.i = temp.r * b[i__4].i + temp.i * b[
i__4].r;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L340: */
}
}
i__2 = *n;
for (j = k + 1; j <= i__2; ++j) {
i__3 = j + k * a_dim1;
if (a[i__3].r != 0.f || a[i__3].i != 0.f) {
if (noconj) {
i__3 = j + k * a_dim1;
temp.r = a[i__3].r, temp.i = a[i__3].i;
} else {
r_cnjg(&q__1, &a[j + k * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
}
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = i__ + k * b_dim1;
q__2.r = temp.r * b[i__6].r - temp.i * b[i__6]
.i, q__2.i = temp.r * b[i__6].i +
temp.i * b[i__6].r;
q__1.r = b[i__5].r - q__2.r, q__1.i = b[i__5]
.i - q__2.i;
b[i__4].r = q__1.r, b[i__4].i = q__1.i;
/* L350: */
}
}
/* L360: */
}
if (alpha->r != 1.f || alpha->i != 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + k * b_dim1;
i__4 = i__ + k * b_dim1;
q__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, q__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L370: */
}
}
/* L380: */
}
}
}
}
return 0;
/* End of CTRSM . */
} /* ctrsm_ */
/* Subroutine */ int ctrsv_(char *uplo, char *trans, char *diag, integer *n,
complex *a, integer *lda, complex *x, integer *incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
complex q__1, q__2, q__3;
/* Local variables */
static integer i__, j, ix, jx, kx, info;
static complex temp;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical noconj, nounit;
/*
Purpose
=======
CTRSV solves one of the systems of equations
A*x = b, or A'*x = b, or conjg( A' )*x = b,
where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular matrix.
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the equations to be solved as
follows:
TRANS = 'N' or 'n' A*x = b.
TRANS = 'T' or 't' A'*x = b.
TRANS = 'C' or 'c' conjg( A' )*x = b.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
A - COMPLEX array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - COMPLEX array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element right-hand side vector b. On exit, X is overwritten
with the solution vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*lda < max(1,*n)) {
info = 6;
} else if (*incx == 0) {
info = 8;
}
if (info != 0) {
xerbla_("CTRSV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
noconj = lsame_(trans, "T");
nounit = lsame_(diag, "N");
/*
Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops.
*/
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (lsame_(trans, "N")) {
/* Form x := inv( A )*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
i__1 = j;
if (x[i__1].r != 0.f || x[i__1].i != 0.f) {
if (nounit) {
i__1 = j;
c_div(&q__1, &x[j], &a[j + j * a_dim1]);
x[i__1].r = q__1.r, x[i__1].i = q__1.i;
}
i__1 = j;
temp.r = x[i__1].r, temp.i = x[i__1].i;
for (i__ = j - 1; i__ >= 1; --i__) {
i__1 = i__;
i__2 = i__;
i__3 = i__ + j * a_dim1;
q__2.r = temp.r * a[i__3].r - temp.i * a[i__3].i,
q__2.i = temp.r * a[i__3].i + temp.i * a[
i__3].r;
q__1.r = x[i__2].r - q__2.r, q__1.i = x[i__2].i -
q__2.i;
x[i__1].r = q__1.r, x[i__1].i = q__1.i;
/* L10: */
}
}
/* L20: */
}
} else {
jx = kx + (*n - 1) * *incx;
for (j = *n; j >= 1; --j) {
i__1 = jx;
if (x[i__1].r != 0.f || x[i__1].i != 0.f) {
if (nounit) {
i__1 = jx;
c_div(&q__1, &x[jx], &a[j + j * a_dim1]);
x[i__1].r = q__1.r, x[i__1].i = q__1.i;
}
i__1 = jx;
temp.r = x[i__1].r, temp.i = x[i__1].i;
ix = jx;
for (i__ = j - 1; i__ >= 1; --i__) {
ix -= *incx;
i__1 = ix;
i__2 = ix;
i__3 = i__ + j * a_dim1;
q__2.r = temp.r * a[i__3].r - temp.i * a[i__3].i,
q__2.i = temp.r * a[i__3].i + temp.i * a[
i__3].r;
q__1.r = x[i__2].r - q__2.r, q__1.i = x[i__2].i -
q__2.i;
x[i__1].r = q__1.r, x[i__1].i = q__1.i;
/* L30: */
}
}
jx -= *incx;
/* L40: */
}
}
} else {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
if (x[i__2].r != 0.f || x[i__2].i != 0.f) {
if (nounit) {
i__2 = j;
c_div(&q__1, &x[j], &a[j + j * a_dim1]);
x[i__2].r = q__1.r, x[i__2].i = q__1.i;
}
i__2 = j;
temp.r = x[i__2].r, temp.i = x[i__2].i;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__ + j * a_dim1;
q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
q__2.i = temp.r * a[i__5].i + temp.i * a[
i__5].r;
q__1.r = x[i__4].r - q__2.r, q__1.i = x[i__4].i -
q__2.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
/* L50: */
}
}
/* L60: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
if (x[i__2].r != 0.f || x[i__2].i != 0.f) {
if (nounit) {
i__2 = jx;
c_div(&q__1, &x[jx], &a[j + j * a_dim1]);
x[i__2].r = q__1.r, x[i__2].i = q__1.i;
}
i__2 = jx;
temp.r = x[i__2].r, temp.i = x[i__2].i;
ix = jx;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
i__3 = ix;
i__4 = ix;
i__5 = i__ + j * a_dim1;
q__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
q__2.i = temp.r * a[i__5].i + temp.i * a[
i__5].r;
q__1.r = x[i__4].r - q__2.r, q__1.i = x[i__4].i -
q__2.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
}
} else {
/* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
temp.r = x[i__2].r, temp.i = x[i__2].i;
if (noconj) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__;
q__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[
i__4].i, q__2.i = a[i__3].r * x[i__4].i +
a[i__3].i * x[i__4].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L90: */
}
if (nounit) {
c_div(&q__1, &temp, &a[j + j * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
}
} else {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__3 = i__;
q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i,
q__2.i = q__3.r * x[i__3].i + q__3.i * x[
i__3].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L100: */
}
if (nounit) {
r_cnjg(&q__2, &a[j + j * a_dim1]);
c_div(&q__1, &temp, &q__2);
temp.r = q__1.r, temp.i = q__1.i;
}
}
i__2 = j;
x[i__2].r = temp.r, x[i__2].i = temp.i;
/* L110: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
ix = kx;
i__2 = jx;
temp.r = x[i__2].r, temp.i = x[i__2].i;
if (noconj) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = ix;
q__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[
i__4].i, q__2.i = a[i__3].r * x[i__4].i +
a[i__3].i * x[i__4].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
ix += *incx;
/* L120: */
}
if (nounit) {
c_div(&q__1, &temp, &a[j + j * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
}
} else {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__3 = ix;
q__2.r = q__3.r * x[i__3].r - q__3.i * x[i__3].i,
q__2.i = q__3.r * x[i__3].i + q__3.i * x[
i__3].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
ix += *incx;
/* L130: */
}
if (nounit) {
r_cnjg(&q__2, &a[j + j * a_dim1]);
c_div(&q__1, &temp, &q__2);
temp.r = q__1.r, temp.i = q__1.i;
}
}
i__2 = jx;
x[i__2].r = temp.r, x[i__2].i = temp.i;
jx += *incx;
/* L140: */
}
}
} else {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
i__1 = j;
temp.r = x[i__1].r, temp.i = x[i__1].i;
if (noconj) {
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
i__2 = i__ + j * a_dim1;
i__3 = i__;
q__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[
i__3].i, q__2.i = a[i__2].r * x[i__3].i +
a[i__2].i * x[i__3].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L150: */
}
if (nounit) {
c_div(&q__1, &temp, &a[j + j * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
}
} else {
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__2 = i__;
q__2.r = q__3.r * x[i__2].r - q__3.i * x[i__2].i,
q__2.i = q__3.r * x[i__2].i + q__3.i * x[
i__2].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
/* L160: */
}
if (nounit) {
r_cnjg(&q__2, &a[j + j * a_dim1]);
c_div(&q__1, &temp, &q__2);
temp.r = q__1.r, temp.i = q__1.i;
}
}
i__1 = j;
x[i__1].r = temp.r, x[i__1].i = temp.i;
/* L170: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
ix = kx;
i__1 = jx;
temp.r = x[i__1].r, temp.i = x[i__1].i;
if (noconj) {
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
i__2 = i__ + j * a_dim1;
i__3 = ix;
q__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[
i__3].i, q__2.i = a[i__2].r * x[i__3].i +
a[i__2].i * x[i__3].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
ix -= *incx;
/* L180: */
}
if (nounit) {
c_div(&q__1, &temp, &a[j + j * a_dim1]);
temp.r = q__1.r, temp.i = q__1.i;
}
} else {
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
r_cnjg(&q__3, &a[i__ + j * a_dim1]);
i__2 = ix;
q__2.r = q__3.r * x[i__2].r - q__3.i * x[i__2].i,
q__2.i = q__3.r * x[i__2].i + q__3.i * x[
i__2].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i -
q__2.i;
temp.r = q__1.r, temp.i = q__1.i;
ix -= *incx;
/* L190: */
}
if (nounit) {
r_cnjg(&q__2, &a[j + j * a_dim1]);
c_div(&q__1, &temp, &q__2);
temp.r = q__1.r, temp.i = q__1.i;
}
}
i__1 = jx;
x[i__1].r = temp.r, x[i__1].i = temp.i;
jx -= *incx;
/* L200: */
}
}
}
}
return 0;
/* End of CTRSV . */
} /* ctrsv_ */
/* Subroutine */ int daxpy_(integer *n, doublereal *da, doublereal *dx,
integer *incx, doublereal *dy, integer *incy)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__, m, ix, iy, mp1;
/*
Purpose
=======
DAXPY constant times a vector plus a vector.
uses unrolled loops for increments equal to one.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--dy;
--dx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*da == 0.) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dy[iy] += *da * dx[ix];
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/*
code for both increments equal to 1
clean-up loop
*/
L20:
m = *n % 4;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
dy[i__] += *da * dx[i__];
/* L30: */
}
if (*n < 4) {
return 0;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 4) {
dy[i__] += *da * dx[i__];
dy[i__ + 1] += *da * dx[i__ + 1];
dy[i__ + 2] += *da * dx[i__ + 2];
dy[i__ + 3] += *da * dx[i__ + 3];
/* L50: */
}
return 0;
} /* daxpy_ */
doublereal dcabs1_(doublecomplex *z__)
{
/* System generated locals */
doublereal ret_val, d__1, d__2;
/*
Purpose
=======
DCABS1 computes absolute value of a double complex number
=====================================================================
*/
ret_val = (d__1 = z__->r, abs(d__1)) + (d__2 = d_imag(z__), abs(d__2));
return ret_val;
} /* dcabs1_ */
/* Subroutine */ int dcopy_(integer *n, doublereal *dx, integer *incx,
doublereal *dy, integer *incy)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__, m, ix, iy, mp1;
/*
Purpose
=======
DCOPY copies a vector, x, to a vector, y.
uses unrolled loops for increments equal to one.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--dy;
--dx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dy[iy] = dx[ix];
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/*
code for both increments equal to 1
clean-up loop
*/
L20:
m = *n % 7;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
dy[i__] = dx[i__];
/* L30: */
}
if (*n < 7) {
return 0;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 7) {
dy[i__] = dx[i__];
dy[i__ + 1] = dx[i__ + 1];
dy[i__ + 2] = dx[i__ + 2];
dy[i__ + 3] = dx[i__ + 3];
dy[i__ + 4] = dx[i__ + 4];
dy[i__ + 5] = dx[i__ + 5];
dy[i__ + 6] = dx[i__ + 6];
/* L50: */
}
return 0;
} /* dcopy_ */
doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy,
integer *incy)
{
/* System generated locals */
integer i__1;
doublereal ret_val;
/* Local variables */
static integer i__, m, ix, iy, mp1;
static doublereal dtemp;
/*
Purpose
=======
DDOT forms the dot product of two vectors.
uses unrolled loops for increments equal to one.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--dy;
--dx;
/* Function Body */
ret_val = 0.;
dtemp = 0.;
if (*n <= 0) {
return ret_val;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp += dx[ix] * dy[iy];
ix += *incx;
iy += *incy;
/* L10: */
}
ret_val = dtemp;
return ret_val;
/*
code for both increments equal to 1
clean-up loop
*/
L20:
m = *n % 5;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp += dx[i__] * dy[i__];
/* L30: */
}
if (*n < 5) {
goto L60;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 5) {
dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + dx[
i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + dx[i__ +
4] * dy[i__ + 4];
/* L50: */
}
L60:
ret_val = dtemp;
return ret_val;
} /* ddot_ */
/* Subroutine */ int dgemm_(char *transa, char *transb, integer *m, integer *
n, integer *k, doublereal *alpha, doublereal *a, integer *lda,
doublereal *b, integer *ldb, doublereal *beta, doublereal *c__,
integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3;
/* Local variables */
static integer i__, j, l, info;
static logical nota, notb;
static doublereal temp;
static integer ncola;
extern logical lsame_(char *, char *);
static integer nrowa, nrowb;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
DGEMM performs one of the matrix-matrix operations
C := alpha*op( A )*op( B ) + beta*C,
where op( X ) is one of
op( X ) = X or op( X ) = X',
alpha and beta are scalars, and A, B and C are matrices, with op( A )
an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
Arguments
==========
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n', op( A ) = A.
TRANSA = 'T' or 't', op( A ) = A'.
TRANSA = 'C' or 'c', op( A ) = A'.
Unchanged on exit.
TRANSB - CHARACTER*1.
On entry, TRANSB specifies the form of op( B ) to be used in
the matrix multiplication as follows:
TRANSB = 'N' or 'n', op( B ) = B.
TRANSB = 'T' or 't', op( B ) = B'.
TRANSB = 'C' or 'c', op( B ) = B'.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix
op( A ) and of the matrix C. M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix
op( B ) and the number of columns of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry, K specifies the number of columns of the matrix
op( A ) and the number of rows of the matrix op( B ). K must
be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
k when TRANSA = 'N' or 'n', and is m otherwise.
Before entry with TRANSA = 'N' or 'n', the leading m by k
part of the array A must contain the matrix A, otherwise
the leading k by m part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANSA = 'N' or 'n' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, k ).
Unchanged on exit.
B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
n when TRANSB = 'N' or 'n', and is k otherwise.
Before entry with TRANSB = 'N' or 'n', the leading k by n
part of the array B must contain the matrix B, otherwise
the leading n by k part of the array B must contain the
matrix B.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANSB = 'N' or 'n' then
LDB must be at least max( 1, k ), otherwise LDB must be at
least max( 1, n ).
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
Unchanged on exit.
C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n matrix
( alpha*op( A )*op( B ) + beta*C ).
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Set NOTA and NOTB as true if A and B respectively are not
transposed and set NROWA, NCOLA and NROWB as the number of rows
and columns of A and the number of rows of B respectively.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
nota = lsame_(transa, "N");
notb = lsame_(transb, "N");
if (nota) {
nrowa = *m;
ncola = *k;
} else {
nrowa = *k;
ncola = *m;
}
if (notb) {
nrowb = *k;
} else {
nrowb = *n;
}
/* Test the input parameters. */
info = 0;
if (! nota && ! lsame_(transa, "C") && ! lsame_(
transa, "T")) {
info = 1;
} else if (! notb && ! lsame_(transb, "C") && !
lsame_(transb, "T")) {
info = 2;
} else if (*m < 0) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*k < 0) {
info = 5;
} else if (*lda < max(1,nrowa)) {
info = 8;
} else if (*ldb < max(1,nrowb)) {
info = 10;
} else if (*ldc < max(1,*m)) {
info = 13;
}
if (info != 0) {
xerbla_("DGEMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
return 0;
}
/* And if alpha.eq.zero. */
if (*alpha == 0.) {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L30: */
}
/* L40: */
}
}
return 0;
}
/* Start the operations. */
if (notb) {
if (nota) {
/* Form C := alpha*A*B + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L50: */
}
} else if (*beta != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L60: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (b[l + j * b_dim1] != 0.) {
temp = *alpha * b[l + j * b_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L70: */
}
}
/* L80: */
}
/* L90: */
}
} else {
/* Form C := alpha*A'*B + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * b[l + j * b_dim1];
/* L100: */
}
if (*beta == 0.) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L110: */
}
/* L120: */
}
}
} else {
if (nota) {
/* Form C := alpha*A*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L130: */
}
} else if (*beta != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L140: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (b[j + l * b_dim1] != 0.) {
temp = *alpha * b[j + l * b_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L150: */
}
}
/* L160: */
}
/* L170: */
}
} else {
/* Form C := alpha*A'*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * b[j + l * b_dim1];
/* L180: */
}
if (*beta == 0.) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L190: */
}
/* L200: */
}
}
}
return 0;
/* End of DGEMM . */
} /* dgemm_ */
/* Subroutine */ int dgemv_(char *trans, integer *m, integer *n, doublereal *
alpha, doublereal *a, integer *lda, doublereal *x, integer *incx,
doublereal *beta, doublereal *y, integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static doublereal temp;
static integer lenx, leny;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
DGEMV performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an
m by n matrix.
Arguments
==========
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
TRANS = 'C' or 'c' y := alpha*A'*x + beta*y.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
X - DOUBLE PRECISION array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
Before entry, the incremented array X must contain the
vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - DOUBLE PRECISION array of DIMENSION at least
( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
Before entry with BETA non-zero, the incremented array Y
must contain the vector y. On exit, Y is overwritten by the
updated vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")
) {
info = 1;
} else if (*m < 0) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*lda < max(1,*m)) {
info = 6;
} else if (*incx == 0) {
info = 8;
} else if (*incy == 0) {
info = 11;
}
if (info != 0) {
xerbla_("DGEMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) {
return 0;
}
/*
Set LENX and LENY, the lengths of the vectors x and y, and set
up the start points in X and Y.
*/
if (lsame_(trans, "N")) {
lenx = *n;
leny = *m;
} else {
lenx = *m;
leny = *n;
}
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (lenx - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (leny - 1) * *incy;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
First form y := beta*y.
*/
if (*beta != 1.) {
if (*incy == 1) {
if (*beta == 0.) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = 0.;
/* L10: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = *beta * y[i__];
/* L20: */
}
}
} else {
iy = ky;
if (*beta == 0.) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = 0.;
iy += *incy;
/* L30: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = *beta * y[iy];
iy += *incy;
/* L40: */
}
}
}
}
if (*alpha == 0.) {
return 0;
}
if (lsame_(trans, "N")) {
/* Form y := alpha*A*x + y. */
jx = kx;
if (*incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = *alpha * x[jx];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__] += temp * a[i__ + j * a_dim1];
/* L50: */
}
}
jx += *incx;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = *alpha * x[jx];
iy = ky;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
y[iy] += temp * a[i__ + j * a_dim1];
iy += *incy;
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
} else {
/* Form y := alpha*A'*x + y. */
jy = ky;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = 0.;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp += a[i__ + j * a_dim1] * x[i__];
/* L90: */
}
y[jy] += *alpha * temp;
jy += *incy;
/* L100: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = 0.;
ix = kx;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp += a[i__ + j * a_dim1] * x[ix];
ix += *incx;
/* L110: */
}
y[jy] += *alpha * temp;
jy += *incy;
/* L120: */
}
}
}
return 0;
/* End of DGEMV . */
} /* dgemv_ */
/* Subroutine */ int dger_(integer *m, integer *n, doublereal *alpha,
doublereal *x, integer *incx, doublereal *y, integer *incy,
doublereal *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j, ix, jy, kx, info;
static doublereal temp;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
DGER performs the rank 1 operation
A := alpha*x*y' + A,
where alpha is a scalar, x is an m element vector, y is an n element
vector and A is an m by n matrix.
Arguments
==========
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( m - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the m
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients. On exit, A is
overwritten by the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
info = 0;
if (*m < 0) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*m)) {
info = 9;
}
if (info != 0) {
xerbla_("DGER ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0.) {
return 0;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (*incy > 0) {
jy = 1;
} else {
jy = 1 - (*n - 1) * *incy;
}
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (y[jy] != 0.) {
temp = *alpha * y[jy];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] += x[i__] * temp;
/* L10: */
}
}
jy += *incy;
/* L20: */
}
} else {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*m - 1) * *incx;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (y[jy] != 0.) {
temp = *alpha * y[jy];
ix = kx;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] += x[ix] * temp;
ix += *incx;
/* L30: */
}
}
jy += *incy;
/* L40: */
}
}
return 0;
/* End of DGER . */
} /* dger_ */
doublereal dnrm2_(integer *n, doublereal *x, integer *incx)
{
/* System generated locals */
integer i__1, i__2;
doublereal ret_val, d__1;
/* Local variables */
static integer ix;
static doublereal ssq, norm, scale, absxi;
/*
Purpose
=======
DNRM2 returns the euclidean norm of a vector via the function
name, so that
DNRM2 := sqrt( x'*x )
Further Details
===============
-- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to DLASSQ.
Sven Hammarling, Nag Ltd.
=====================================================================
*/
/* Parameter adjustments */
--x;
/* Function Body */
if (*n < 1 || *incx < 1) {
norm = 0.;
} else if (*n == 1) {
norm = abs(x[1]);
} else {
scale = 0.;
ssq = 1.;
/*
The following loop is equivalent to this call to the LAPACK
auxiliary routine:
CALL DLASSQ( N, X, INCX, SCALE, SSQ )
*/
i__1 = (*n - 1) * *incx + 1;
i__2 = *incx;
for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
if (x[ix] != 0.) {
absxi = (d__1 = x[ix], abs(d__1));
if (scale < absxi) {
/* Computing 2nd power */
d__1 = scale / absxi;
ssq = ssq * (d__1 * d__1) + 1.;
scale = absxi;
} else {
/* Computing 2nd power */
d__1 = absxi / scale;
ssq += d__1 * d__1;
}
}
/* L10: */
}
norm = scale * sqrt(ssq);
}
ret_val = norm;
return ret_val;
/* End of DNRM2. */
} /* dnrm2_ */
/* Subroutine */ int drot_(integer *n, doublereal *dx, integer *incx,
doublereal *dy, integer *incy, doublereal *c__, doublereal *s)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__, ix, iy;
static doublereal dtemp;
/*
Purpose
=======
DROT applies a plane rotation.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--dy;
--dx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments not equal
to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp = *c__ * dx[ix] + *s * dy[iy];
dy[iy] = *c__ * dy[iy] - *s * dx[ix];
dx[ix] = dtemp;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp = *c__ * dx[i__] + *s * dy[i__];
dy[i__] = *c__ * dy[i__] - *s * dx[i__];
dx[i__] = dtemp;
/* L30: */
}
return 0;
} /* drot_ */
/* Subroutine */ int dscal_(integer *n, doublereal *da, doublereal *dx,
integer *incx)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
static integer i__, m, mp1, nincx;
/*
Purpose
=======
DSCAL scales a vector by a constant.
uses unrolled loops for increment equal to one.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--dx;
/* Function Body */
if (*n <= 0 || *incx <= 0) {
return 0;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
nincx = *n * *incx;
i__1 = nincx;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
dx[i__] = *da * dx[i__];
/* L10: */
}
return 0;
/*
code for increment equal to 1
clean-up loop
*/
L20:
m = *n % 5;
if (m == 0) {
goto L40;
}
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
dx[i__] = *da * dx[i__];
/* L30: */
}
if (*n < 5) {
return 0;
}
L40:
mp1 = m + 1;
i__2 = *n;
for (i__ = mp1; i__ <= i__2; i__ += 5) {
dx[i__] = *da * dx[i__];
dx[i__ + 1] = *da * dx[i__ + 1];
dx[i__ + 2] = *da * dx[i__ + 2];
dx[i__ + 3] = *da * dx[i__ + 3];
dx[i__ + 4] = *da * dx[i__ + 4];
/* L50: */
}
return 0;
} /* dscal_ */
/* Subroutine */ int dswap_(integer *n, doublereal *dx, integer *incx,
doublereal *dy, integer *incy)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__, m, ix, iy, mp1;
static doublereal dtemp;
/*
Purpose
=======
interchanges two vectors.
uses unrolled loops for increments equal one.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--dy;
--dx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments not equal
to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp = dx[ix];
dx[ix] = dy[iy];
dy[iy] = dtemp;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/*
code for both increments equal to 1
clean-up loop
*/
L20:
m = *n % 3;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
dtemp = dx[i__];
dx[i__] = dy[i__];
dy[i__] = dtemp;
/* L30: */
}
if (*n < 3) {
return 0;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 3) {
dtemp = dx[i__];
dx[i__] = dy[i__];
dy[i__] = dtemp;
dtemp = dx[i__ + 1];
dx[i__ + 1] = dy[i__ + 1];
dy[i__ + 1] = dtemp;
dtemp = dx[i__ + 2];
dx[i__ + 2] = dy[i__ + 2];
dy[i__ + 2] = dtemp;
/* L50: */
}
return 0;
} /* dswap_ */
/* Subroutine */ int dsymv_(char *uplo, integer *n, doublereal *alpha,
doublereal *a, integer *lda, doublereal *x, integer *incx, doublereal
*beta, doublereal *y, integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static doublereal temp1, temp2;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
DSYMV performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n symmetric matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y. On exit, Y is overwritten by the updated
vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*lda < max(1,*n)) {
info = 5;
} else if (*incx == 0) {
info = 7;
} else if (*incy == 0) {
info = 10;
}
if (info != 0) {
xerbla_("DSYMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0. && *beta == 1.) {
return 0;
}
/* Set up the start points in X and Y. */
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through the triangular part
of A.
First form y := beta*y.
*/
if (*beta != 1.) {
if (*incy == 1) {
if (*beta == 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = 0.;
/* L10: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = *beta * y[i__];
/* L20: */
}
}
} else {
iy = ky;
if (*beta == 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = 0.;
iy += *incy;
/* L30: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = *beta * y[iy];
iy += *incy;
/* L40: */
}
}
}
}
if (*alpha == 0.) {
return 0;
}
if (lsame_(uplo, "U")) {
/* Form y when A is stored in upper triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[j];
temp2 = 0.;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__] += temp1 * a[i__ + j * a_dim1];
temp2 += a[i__ + j * a_dim1] * x[i__];
/* L50: */
}
y[j] = y[j] + temp1 * a[j + j * a_dim1] + *alpha * temp2;
/* L60: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[jx];
temp2 = 0.;
ix = kx;
iy = ky;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
y[iy] += temp1 * a[i__ + j * a_dim1];
temp2 += a[i__ + j * a_dim1] * x[ix];
ix += *incx;
iy += *incy;
/* L70: */
}
y[jy] = y[jy] + temp1 * a[j + j * a_dim1] + *alpha * temp2;
jx += *incx;
jy += *incy;
/* L80: */
}
}
} else {
/* Form y when A is stored in lower triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[j];
temp2 = 0.;
y[j] += temp1 * a[j + j * a_dim1];
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
y[i__] += temp1 * a[i__ + j * a_dim1];
temp2 += a[i__ + j * a_dim1] * x[i__];
/* L90: */
}
y[j] += *alpha * temp2;
/* L100: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[jx];
temp2 = 0.;
y[jy] += temp1 * a[j + j * a_dim1];
ix = jx;
iy = jy;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
iy += *incy;
y[iy] += temp1 * a[i__ + j * a_dim1];
temp2 += a[i__ + j * a_dim1] * x[ix];
/* L110: */
}
y[jy] += *alpha * temp2;
jx += *incx;
jy += *incy;
/* L120: */
}
}
}
return 0;
/* End of DSYMV . */
} /* dsymv_ */
/* Subroutine */ int dsyr2_(char *uplo, integer *n, doublereal *alpha,
doublereal *x, integer *incx, doublereal *y, integer *incy,
doublereal *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static doublereal temp1, temp2;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
DSYR2 performs the symmetric rank 2 operation
A := alpha*x*y' + alpha*y*x' + A,
where alpha is a scalar, x and y are n element vectors and A is an n
by n symmetric matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced. On exit, the
upper triangular part of the array A is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced. On exit, the
lower triangular part of the array A is overwritten by the
lower triangular part of the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*n)) {
info = 9;
}
if (info != 0) {
xerbla_("DSYR2 ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0.) {
return 0;
}
/*
Set up the start points in X and Y if the increments are not both
unity.
*/
if (*incx != 1 || *incy != 1) {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
jx = kx;
jy = ky;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through the triangular part
of A.
*/
if (lsame_(uplo, "U")) {
/* Form A when A is stored in the upper triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0. || y[j] != 0.) {
temp1 = *alpha * y[j];
temp2 = *alpha * x[j];
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] *
temp1 + y[i__] * temp2;
/* L10: */
}
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0. || y[jy] != 0.) {
temp1 = *alpha * y[jy];
temp2 = *alpha * x[jx];
ix = kx;
iy = ky;
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] *
temp1 + y[iy] * temp2;
ix += *incx;
iy += *incy;
/* L30: */
}
}
jx += *incx;
jy += *incy;
/* L40: */
}
}
} else {
/* Form A when A is stored in the lower triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0. || y[j] != 0.) {
temp1 = *alpha * y[j];
temp2 = *alpha * x[j];
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] *
temp1 + y[i__] * temp2;
/* L50: */
}
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0. || y[jy] != 0.) {
temp1 = *alpha * y[jy];
temp2 = *alpha * x[jx];
ix = jx;
iy = jy;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] *
temp1 + y[iy] * temp2;
ix += *incx;
iy += *incy;
/* L70: */
}
}
jx += *incx;
jy += *incy;
/* L80: */
}
}
}
return 0;
/* End of DSYR2 . */
} /* dsyr2_ */
/* Subroutine */ int dsyr2k_(char *uplo, char *trans, integer *n, integer *k,
doublereal *alpha, doublereal *a, integer *lda, doublereal *b,
integer *ldb, doublereal *beta, doublereal *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3;
/* Local variables */
static integer i__, j, l, info;
static doublereal temp1, temp2;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
DSYR2K performs one of the symmetric rank 2k operations
C := alpha*A*B' + alpha*B*A' + beta*C,
or
C := alpha*A'*B + alpha*B'*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A and B are n by k matrices in the first case and k by n
matrices in the second case.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' +
beta*C.
TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A +
beta*C.
TRANS = 'C' or 'c' C := alpha*A'*B + alpha*B'*A +
beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrices A and B, and on entry with
TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
of rows of the matrices A and B. K must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array B must contain the matrix B, otherwise
the leading k by n part of the array B must contain the
matrix B.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDB must be at least max( 1, n ), otherwise LDB must
be at least max( 1, k ).
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
if (lsame_(trans, "N")) {
nrowa = *n;
} else {
nrowa = *k;
}
upper = lsame_(uplo, "U");
info = 0;
if (! upper && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*k < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldb < max(1,nrowa)) {
info = 9;
} else if (*ldc < max(1,*n)) {
info = 12;
}
if (info != 0) {
xerbla_("DSYR2K", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
if (upper) {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L30: */
}
/* L40: */
}
}
} else {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L70: */
}
/* L80: */
}
}
}
return 0;
}
/* Start the operations. */
if (lsame_(trans, "N")) {
/* Form C := alpha*A*B' + alpha*B*A' + C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L90: */
}
} else if (*beta != 1.) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L100: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a[j + l * a_dim1] != 0. || b[j + l * b_dim1] != 0.) {
temp1 = *alpha * b[j + l * b_dim1];
temp2 = *alpha * a[j + l * a_dim1];
i__3 = j;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[
i__ + l * a_dim1] * temp1 + b[i__ + l *
b_dim1] * temp2;
/* L110: */
}
}
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L140: */
}
} else if (*beta != 1.) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L150: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a[j + l * a_dim1] != 0. || b[j + l * b_dim1] != 0.) {
temp1 = *alpha * b[j + l * b_dim1];
temp2 = *alpha * a[j + l * a_dim1];
i__3 = *n;
for (i__ = j; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[
i__ + l * a_dim1] * temp1 + b[i__ + l *
b_dim1] * temp2;
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
}
} else {
/* Form C := alpha*A'*B + alpha*B'*A + C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
temp1 = 0.;
temp2 = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1];
temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1];
/* L190: */
}
if (*beta == 0.) {
c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha *
temp2;
} else {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
+ *alpha * temp1 + *alpha * temp2;
}
/* L200: */
}
/* L210: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
temp1 = 0.;
temp2 = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1];
temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1];
/* L220: */
}
if (*beta == 0.) {
c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha *
temp2;
} else {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
+ *alpha * temp1 + *alpha * temp2;
}
/* L230: */
}
/* L240: */
}
}
}
return 0;
/* End of DSYR2K. */
} /* dsyr2k_ */
/* Subroutine */ int dsyrk_(char *uplo, char *trans, integer *n, integer *k,
doublereal *alpha, doublereal *a, integer *lda, doublereal *beta,
doublereal *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j, l, info;
static doublereal temp;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
DSYRK performs one of the symmetric rank k operations
C := alpha*A*A' + beta*C,
or
C := alpha*A'*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A is an n by k matrix in the first case and a k by n matrix
in the second case.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*A' + beta*C.
TRANS = 'T' or 't' C := alpha*A'*A + beta*C.
TRANS = 'C' or 'c' C := alpha*A'*A + beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrix A, and on entry with
TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
of rows of the matrix A. K must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
if (lsame_(trans, "N")) {
nrowa = *n;
} else {
nrowa = *k;
}
upper = lsame_(uplo, "U");
info = 0;
if (! upper && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*k < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldc < max(1,*n)) {
info = 10;
}
if (info != 0) {
xerbla_("DSYRK ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
if (upper) {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L30: */
}
/* L40: */
}
}
} else {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L70: */
}
/* L80: */
}
}
}
return 0;
}
/* Start the operations. */
if (lsame_(trans, "N")) {
/* Form C := alpha*A*A' + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L90: */
}
} else if (*beta != 1.) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L100: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a[j + l * a_dim1] != 0.) {
temp = *alpha * a[j + l * a_dim1];
i__3 = j;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L110: */
}
}
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L140: */
}
} else if (*beta != 1.) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L150: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a[j + l * a_dim1] != 0.) {
temp = *alpha * a[j + l * a_dim1];
i__3 = *n;
for (i__ = j; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
}
} else {
/* Form C := alpha*A'*A + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * a[l + j * a_dim1];
/* L190: */
}
if (*beta == 0.) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L200: */
}
/* L210: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
temp = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * a[l + j * a_dim1];
/* L220: */
}
if (*beta == 0.) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L230: */
}
/* L240: */
}
}
}
return 0;
/* End of DSYRK . */
} /* dsyrk_ */
/* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, doublereal *alpha, doublereal *a, integer *
lda, doublereal *b, integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j, k, info;
static doublereal temp;
static logical lside;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
/*
Purpose
=======
DTRMM performs one of the matrix-matrix operations
B := alpha*op( A )*B, or B := alpha*B*op( A ),
where alpha is a scalar, B is an m by n matrix, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A'.
Arguments
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) multiplies B from
the left or right as follows:
SIDE = 'L' or 'l' B := alpha*op( A )*B.
SIDE = 'R' or 'r' B := alpha*B*op( A ).
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A'.
TRANSA = 'C' or 'c' op( A ) = A'.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the matrix B, and on exit is overwritten by the
transformed matrix.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
lside = lsame_(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
info = 0;
if (! lside && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (! lsame_(transa, "N") && ! lsame_(transa,
"T") && ! lsame_(transa, "C")) {
info = 3;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < max(1,nrowa)) {
info = 9;
} else if (*ldb < max(1,*m)) {
info = 11;
}
if (info != 0) {
xerbla_("DTRMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = 0.;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (lsame_(transa, "N")) {
/* Form B := alpha*A*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
if (b[k + j * b_dim1] != 0.) {
temp = *alpha * b[k + j * b_dim1];
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] += temp * a[i__ + k *
a_dim1];
/* L30: */
}
if (nounit) {
temp *= a[k + k * a_dim1];
}
b[k + j * b_dim1] = temp;
}
/* L40: */
}
/* L50: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (k = *m; k >= 1; --k) {
if (b[k + j * b_dim1] != 0.) {
temp = *alpha * b[k + j * b_dim1];
b[k + j * b_dim1] = temp;
if (nounit) {
b[k + j * b_dim1] *= a[k + k * a_dim1];
}
i__2 = *m;
for (i__ = k + 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] += temp * a[i__ + k *
a_dim1];
/* L60: */
}
}
/* L70: */
}
/* L80: */
}
}
} else {
/* Form B := alpha*A'*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
temp = b[i__ + j * b_dim1];
if (nounit) {
temp *= a[i__ + i__ * a_dim1];
}
i__2 = i__ - 1;
for (k = 1; k <= i__2; ++k) {
temp += a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L90: */
}
b[i__ + j * b_dim1] = *alpha * temp;
/* L100: */
}
/* L110: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = b[i__ + j * b_dim1];
if (nounit) {
temp *= a[i__ + i__ * a_dim1];
}
i__3 = *m;
for (k = i__ + 1; k <= i__3; ++k) {
temp += a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L120: */
}
b[i__ + j * b_dim1] = *alpha * temp;
/* L130: */
}
/* L140: */
}
}
}
} else {
if (lsame_(transa, "N")) {
/* Form B := alpha*B*A. */
if (upper) {
for (j = *n; j >= 1; --j) {
temp = *alpha;
if (nounit) {
temp *= a[j + j * a_dim1];
}
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L150: */
}
i__1 = j - 1;
for (k = 1; k <= i__1; ++k) {
if (a[k + j * a_dim1] != 0.) {
temp = *alpha * a[k + j * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] += temp * b[i__ + k *
b_dim1];
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = *alpha;
if (nounit) {
temp *= a[j + j * a_dim1];
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L190: */
}
i__2 = *n;
for (k = j + 1; k <= i__2; ++k) {
if (a[k + j * a_dim1] != 0.) {
temp = *alpha * a[k + j * a_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] += temp * b[i__ + k *
b_dim1];
/* L200: */
}
}
/* L210: */
}
/* L220: */
}
}
} else {
/* Form B := alpha*B*A'. */
if (upper) {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
i__2 = k - 1;
for (j = 1; j <= i__2; ++j) {
if (a[j + k * a_dim1] != 0.) {
temp = *alpha * a[j + k * a_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] += temp * b[i__ + k *
b_dim1];
/* L230: */
}
}
/* L240: */
}
temp = *alpha;
if (nounit) {
temp *= a[k + k * a_dim1];
}
if (temp != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L250: */
}
}
/* L260: */
}
} else {
for (k = *n; k >= 1; --k) {
i__1 = *n;
for (j = k + 1; j <= i__1; ++j) {
if (a[j + k * a_dim1] != 0.) {
temp = *alpha * a[j + k * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] += temp * b[i__ + k *
b_dim1];
/* L270: */
}
}
/* L280: */
}
temp = *alpha;
if (nounit) {
temp *= a[k + k * a_dim1];
}
if (temp != 1.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L290: */
}
}
/* L300: */
}
}
}
}
return 0;
/* End of DTRMM . */
} /* dtrmm_ */
/* Subroutine */ int dtrmv_(char *uplo, char *trans, char *diag, integer *n,
doublereal *a, integer *lda, doublereal *x, integer *incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j, ix, jx, kx, info;
static doublereal temp;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
/*
Purpose
=======
DTRMV performs one of the matrix-vector operations
x := A*x, or x := A'*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A'*x.
TRANS = 'C' or 'c' x := A'*x.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x. On exit, X is overwritten with the
tranformed vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*lda < max(1,*n)) {
info = 6;
} else if (*incx == 0) {
info = 8;
}
if (info != 0) {
xerbla_("DTRMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
nounit = lsame_(diag, "N");
/*
Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops.
*/
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (lsame_(trans, "N")) {
/* Form x := A*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.) {
temp = x[j];
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__] += temp * a[i__ + j * a_dim1];
/* L10: */
}
if (nounit) {
x[j] *= a[j + j * a_dim1];
}
}
/* L20: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.) {
temp = x[jx];
ix = kx;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
x[ix] += temp * a[i__ + j * a_dim1];
ix += *incx;
/* L30: */
}
if (nounit) {
x[jx] *= a[j + j * a_dim1];
}
}
jx += *incx;
/* L40: */
}
}
} else {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
if (x[j] != 0.) {
temp = x[j];
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
x[i__] += temp * a[i__ + j * a_dim1];
/* L50: */
}
if (nounit) {
x[j] *= a[j + j * a_dim1];
}
}
/* L60: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
if (x[jx] != 0.) {
temp = x[jx];
ix = kx;
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
x[ix] += temp * a[i__ + j * a_dim1];
ix -= *incx;
/* L70: */
}
if (nounit) {
x[jx] *= a[j + j * a_dim1];
}
}
jx -= *incx;
/* L80: */
}
}
}
} else {
/* Form x := A'*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
temp = x[j];
if (nounit) {
temp *= a[j + j * a_dim1];
}
for (i__ = j - 1; i__ >= 1; --i__) {
temp += a[i__ + j * a_dim1] * x[i__];
/* L90: */
}
x[j] = temp;
/* L100: */
}
} else {
jx = kx + (*n - 1) * *incx;
for (j = *n; j >= 1; --j) {
temp = x[jx];
ix = jx;
if (nounit) {
temp *= a[j + j * a_dim1];
}
for (i__ = j - 1; i__ >= 1; --i__) {
ix -= *incx;
temp += a[i__ + j * a_dim1] * x[ix];
/* L110: */
}
x[jx] = temp;
jx -= *incx;
/* L120: */
}
}
} else {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[j];
if (nounit) {
temp *= a[j + j * a_dim1];
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
temp += a[i__ + j * a_dim1] * x[i__];
/* L130: */
}
x[j] = temp;
/* L140: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[jx];
ix = jx;
if (nounit) {
temp *= a[j + j * a_dim1];
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
temp += a[i__ + j * a_dim1] * x[ix];
/* L150: */
}
x[jx] = temp;
jx += *incx;
/* L160: */
}
}
}
}
return 0;
/* End of DTRMV . */
} /* dtrmv_ */
/* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, doublereal *alpha, doublereal *a, integer *
lda, doublereal *b, integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j, k, info;
static doublereal temp;
static logical lside;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
/*
Purpose
=======
DTRSM solves one of the matrix equations
op( A )*X = alpha*B, or X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A'.
The matrix X is overwritten on B.
Arguments
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:
SIDE = 'L' or 'l' op( A )*X = alpha*B.
SIDE = 'R' or 'r' X*op( A ) = alpha*B.
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A'.
TRANSA = 'C' or 'c' op( A ) = A'.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the right-hand side matrix B, and on exit is
overwritten by the solution matrix X.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
lside = lsame_(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
info = 0;
if (! lside && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (! lsame_(transa, "N") && ! lsame_(transa,
"T") && ! lsame_(transa, "C")) {
info = 3;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < max(1,nrowa)) {
info = 9;
} else if (*ldb < max(1,*m)) {
info = 11;
}
if (info != 0) {
xerbla_("DTRSM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = 0.;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (lsame_(transa, "N")) {
/* Form B := alpha*inv( A )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L30: */
}
}
for (k = *m; k >= 1; --k) {
if (b[k + j * b_dim1] != 0.) {
if (nounit) {
b[k + j * b_dim1] /= a[k + k * a_dim1];
}
i__2 = k - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
i__ + k * a_dim1];
/* L40: */
}
}
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L70: */
}
}
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
if (b[k + j * b_dim1] != 0.) {
if (nounit) {
b[k + j * b_dim1] /= a[k + k * a_dim1];
}
i__3 = *m;
for (i__ = k + 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
i__ + k * a_dim1];
/* L80: */
}
}
/* L90: */
}
/* L100: */
}
}
} else {
/* Form B := alpha*inv( A' )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = *alpha * b[i__ + j * b_dim1];
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L110: */
}
if (nounit) {
temp /= a[i__ + i__ * a_dim1];
}
b[i__ + j * b_dim1] = temp;
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
temp = *alpha * b[i__ + j * b_dim1];
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L140: */
}
if (nounit) {
temp /= a[i__ + i__ * a_dim1];
}
b[i__ + j * b_dim1] = temp;
/* L150: */
}
/* L160: */
}
}
}
} else {
if (lsame_(transa, "N")) {
/* Form B := alpha*B*inv( A ). */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L170: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
if (a[k + j * a_dim1] != 0.) {
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
i__ + k * b_dim1];
/* L180: */
}
}
/* L190: */
}
if (nounit) {
temp = 1. / a[j + j * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L200: */
}
}
/* L210: */
}
} else {
for (j = *n; j >= 1; --j) {
if (*alpha != 1.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L220: */
}
}
i__1 = *n;
for (k = j + 1; k <= i__1; ++k) {
if (a[k + j * a_dim1] != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
i__ + k * b_dim1];
/* L230: */
}
}
/* L240: */
}
if (nounit) {
temp = 1. / a[j + j * a_dim1];
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L250: */
}
}
/* L260: */
}
}
} else {
/* Form B := alpha*B*inv( A' ). */
if (upper) {
for (k = *n; k >= 1; --k) {
if (nounit) {
temp = 1. / a[k + k * a_dim1];
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L270: */
}
}
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
if (a[j + k * a_dim1] != 0.) {
temp = a[j + k * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= temp * b[i__ + k *
b_dim1];
/* L280: */
}
}
/* L290: */
}
if (*alpha != 1.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
;
/* L300: */
}
}
/* L310: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (nounit) {
temp = 1. / a[k + k * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L320: */
}
}
i__2 = *n;
for (j = k + 1; j <= i__2; ++j) {
if (a[j + k * a_dim1] != 0.) {
temp = a[j + k * a_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= temp * b[i__ + k *
b_dim1];
/* L330: */
}
}
/* L340: */
}
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
;
/* L350: */
}
}
/* L360: */
}
}
}
}
return 0;
/* End of DTRSM . */
} /* dtrsm_ */
doublereal dzasum_(integer *n, doublecomplex *zx, integer *incx)
{
/* System generated locals */
integer i__1;
doublereal ret_val;
/* Local variables */
static integer i__, ix;
static doublereal stemp;
extern doublereal dcabs1_(doublecomplex *);
/*
Purpose
=======
DZASUM takes the sum of the absolute values.
Further Details
===============
jack dongarra, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--zx;
/* Function Body */
ret_val = 0.;
stemp = 0.;
if (*n <= 0 || *incx <= 0) {
return ret_val;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
ix = 1;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp += dcabs1_(&zx[ix]);
ix += *incx;
/* L10: */
}
ret_val = stemp;
return ret_val;
/* code for increment equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp += dcabs1_(&zx[i__]);
/* L30: */
}
ret_val = stemp;
return ret_val;
} /* dzasum_ */
doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublereal ret_val, d__1;
/* Local variables */
static integer ix;
static doublereal ssq, temp, norm, scale;
/*
Purpose
=======
DZNRM2 returns the euclidean norm of a vector via the function
name, so that
DZNRM2 := sqrt( conjg( x' )*x )
Further Details
===============
-- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to ZLASSQ.
Sven Hammarling, Nag Ltd.
=====================================================================
*/
/* Parameter adjustments */
--x;
/* Function Body */
if (*n < 1 || *incx < 1) {
norm = 0.;
} else {
scale = 0.;
ssq = 1.;
/*
The following loop is equivalent to this call to the LAPACK
auxiliary routine:
CALL ZLASSQ( N, X, INCX, SCALE, SSQ )
*/
i__1 = (*n - 1) * *incx + 1;
i__2 = *incx;
for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
i__3 = ix;
if (x[i__3].r != 0.) {
i__3 = ix;
temp = (d__1 = x[i__3].r, abs(d__1));
if (scale < temp) {
/* Computing 2nd power */
d__1 = scale / temp;
ssq = ssq * (d__1 * d__1) + 1.;
scale = temp;
} else {
/* Computing 2nd power */
d__1 = temp / scale;
ssq += d__1 * d__1;
}
}
if (d_imag(&x[ix]) != 0.) {
temp = (d__1 = d_imag(&x[ix]), abs(d__1));
if (scale < temp) {
/* Computing 2nd power */
d__1 = scale / temp;
ssq = ssq * (d__1 * d__1) + 1.;
scale = temp;
} else {
/* Computing 2nd power */
d__1 = temp / scale;
ssq += d__1 * d__1;
}
}
/* L10: */
}
norm = scale * sqrt(ssq);
}
ret_val = norm;
return ret_val;
/* End of DZNRM2. */
} /* dznrm2_ */
integer icamax_(integer *n, complex *cx, integer *incx)
{
/* System generated locals */
integer ret_val, i__1;
/* Local variables */
static integer i__, ix;
static real smax;
extern doublereal scabs1_(complex *);
/*
Purpose
=======
ICAMAX finds the index of element having max. absolute value.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--cx;
/* Function Body */
ret_val = 0;
if (*n < 1 || *incx <= 0) {
return ret_val;
}
ret_val = 1;
if (*n == 1) {
return ret_val;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
ix = 1;
smax = scabs1_(&cx[1]);
ix += *incx;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if (scabs1_(&cx[ix]) <= smax) {
goto L5;
}
ret_val = i__;
smax = scabs1_(&cx[ix]);
L5:
ix += *incx;
/* L10: */
}
return ret_val;
/* code for increment equal to 1 */
L20:
smax = scabs1_(&cx[1]);
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if (scabs1_(&cx[i__]) <= smax) {
goto L30;
}
ret_val = i__;
smax = scabs1_(&cx[i__]);
L30:
;
}
return ret_val;
} /* icamax_ */
integer idamax_(integer *n, doublereal *dx, integer *incx)
{
/* System generated locals */
integer ret_val, i__1;
doublereal d__1;
/* Local variables */
static integer i__, ix;
static doublereal dmax__;
/*
Purpose
=======
IDAMAX finds the index of element having max. absolute value.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--dx;
/* Function Body */
ret_val = 0;
if (*n < 1 || *incx <= 0) {
return ret_val;
}
ret_val = 1;
if (*n == 1) {
return ret_val;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
ix = 1;
dmax__ = abs(dx[1]);
ix += *incx;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if ((d__1 = dx[ix], abs(d__1)) <= dmax__) {
goto L5;
}
ret_val = i__;
dmax__ = (d__1 = dx[ix], abs(d__1));
L5:
ix += *incx;
/* L10: */
}
return ret_val;
/* code for increment equal to 1 */
L20:
dmax__ = abs(dx[1]);
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if ((d__1 = dx[i__], abs(d__1)) <= dmax__) {
goto L30;
}
ret_val = i__;
dmax__ = (d__1 = dx[i__], abs(d__1));
L30:
;
}
return ret_val;
} /* idamax_ */
integer isamax_(integer *n, real *sx, integer *incx)
{
/* System generated locals */
integer ret_val, i__1;
real r__1;
/* Local variables */
static integer i__, ix;
static real smax;
/*
Purpose
=======
ISAMAX finds the index of element having max. absolute value.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--sx;
/* Function Body */
ret_val = 0;
if (*n < 1 || *incx <= 0) {
return ret_val;
}
ret_val = 1;
if (*n == 1) {
return ret_val;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
ix = 1;
smax = dabs(sx[1]);
ix += *incx;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if ((r__1 = sx[ix], dabs(r__1)) <= smax) {
goto L5;
}
ret_val = i__;
smax = (r__1 = sx[ix], dabs(r__1));
L5:
ix += *incx;
/* L10: */
}
return ret_val;
/* code for increment equal to 1 */
L20:
smax = dabs(sx[1]);
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if ((r__1 = sx[i__], dabs(r__1)) <= smax) {
goto L30;
}
ret_val = i__;
smax = (r__1 = sx[i__], dabs(r__1));
L30:
;
}
return ret_val;
} /* isamax_ */
integer izamax_(integer *n, doublecomplex *zx, integer *incx)
{
/* System generated locals */
integer ret_val, i__1;
/* Local variables */
static integer i__, ix;
static doublereal smax;
extern doublereal dcabs1_(doublecomplex *);
/*
Purpose
=======
IZAMAX finds the index of element having max. absolute value.
Further Details
===============
jack dongarra, 1/15/85.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--zx;
/* Function Body */
ret_val = 0;
if (*n < 1 || *incx <= 0) {
return ret_val;
}
ret_val = 1;
if (*n == 1) {
return ret_val;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
ix = 1;
smax = dcabs1_(&zx[1]);
ix += *incx;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if (dcabs1_(&zx[ix]) <= smax) {
goto L5;
}
ret_val = i__;
smax = dcabs1_(&zx[ix]);
L5:
ix += *incx;
/* L10: */
}
return ret_val;
/* code for increment equal to 1 */
L20:
smax = dcabs1_(&zx[1]);
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
if (dcabs1_(&zx[i__]) <= smax) {
goto L30;
}
ret_val = i__;
smax = dcabs1_(&zx[i__]);
L30:
;
}
return ret_val;
} /* izamax_ */
/* Subroutine */ int saxpy_(integer *n, real *sa, real *sx, integer *incx,
real *sy, integer *incy)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__, m, ix, iy, mp1;
/*
Purpose
=======
SAXPY constant times a vector plus a vector.
uses unrolled loop for increments equal to one.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--sy;
--sx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*sa == 0.f) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
sy[iy] += *sa * sx[ix];
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/*
code for both increments equal to 1
clean-up loop
*/
L20:
m = *n % 4;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
sy[i__] += *sa * sx[i__];
/* L30: */
}
if (*n < 4) {
return 0;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 4) {
sy[i__] += *sa * sx[i__];
sy[i__ + 1] += *sa * sx[i__ + 1];
sy[i__ + 2] += *sa * sx[i__ + 2];
sy[i__ + 3] += *sa * sx[i__ + 3];
/* L50: */
}
return 0;
} /* saxpy_ */
doublereal scabs1_(complex *z__)
{
/* System generated locals */
real ret_val, r__1, r__2;
/*
Purpose
=======
SCABS1 computes absolute value of a complex number
=====================================================================
*/
ret_val = (r__1 = z__->r, dabs(r__1)) + (r__2 = r_imag(z__), dabs(r__2));
return ret_val;
} /* scabs1_ */
doublereal scasum_(integer *n, complex *cx, integer *incx)
{
/* System generated locals */
integer i__1, i__2, i__3;
real ret_val, r__1, r__2;
/* Local variables */
static integer i__, nincx;
static real stemp;
/*
Purpose
=======
SCASUM takes the sum of the absolute values of a complex vector and
returns a single precision result.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--cx;
/* Function Body */
ret_val = 0.f;
stemp = 0.f;
if (*n <= 0 || *incx <= 0) {
return ret_val;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
nincx = *n * *incx;
i__1 = nincx;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
i__3 = i__;
stemp = stemp + (r__1 = cx[i__3].r, dabs(r__1)) + (r__2 = r_imag(&cx[
i__]), dabs(r__2));
/* L10: */
}
ret_val = stemp;
return ret_val;
/* code for increment equal to 1 */
L20:
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__1 = i__;
stemp = stemp + (r__1 = cx[i__1].r, dabs(r__1)) + (r__2 = r_imag(&cx[
i__]), dabs(r__2));
/* L30: */
}
ret_val = stemp;
return ret_val;
} /* scasum_ */
doublereal scnrm2_(integer *n, complex *x, integer *incx)
{
/* System generated locals */
integer i__1, i__2, i__3;
real ret_val, r__1;
/* Local variables */
static integer ix;
static real ssq, temp, norm, scale;
/*
Purpose
=======
SCNRM2 returns the euclidean norm of a vector via the function
name, so that
SCNRM2 := sqrt( conjg( x' )*x )
Further Details
===============
-- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to CLASSQ.
Sven Hammarling, Nag Ltd.
=====================================================================
*/
/* Parameter adjustments */
--x;
/* Function Body */
if (*n < 1 || *incx < 1) {
norm = 0.f;
} else {
scale = 0.f;
ssq = 1.f;
/*
The following loop is equivalent to this call to the LAPACK
auxiliary routine:
CALL CLASSQ( N, X, INCX, SCALE, SSQ )
*/
i__1 = (*n - 1) * *incx + 1;
i__2 = *incx;
for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
i__3 = ix;
if (x[i__3].r != 0.f) {
i__3 = ix;
temp = (r__1 = x[i__3].r, dabs(r__1));
if (scale < temp) {
/* Computing 2nd power */
r__1 = scale / temp;
ssq = ssq * (r__1 * r__1) + 1.f;
scale = temp;
} else {
/* Computing 2nd power */
r__1 = temp / scale;
ssq += r__1 * r__1;
}
}
if (r_imag(&x[ix]) != 0.f) {
temp = (r__1 = r_imag(&x[ix]), dabs(r__1));
if (scale < temp) {
/* Computing 2nd power */
r__1 = scale / temp;
ssq = ssq * (r__1 * r__1) + 1.f;
scale = temp;
} else {
/* Computing 2nd power */
r__1 = temp / scale;
ssq += r__1 * r__1;
}
}
/* L10: */
}
norm = scale * sqrt(ssq);
}
ret_val = norm;
return ret_val;
/* End of SCNRM2. */
} /* scnrm2_ */
/* Subroutine */ int scopy_(integer *n, real *sx, integer *incx, real *sy,
integer *incy)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__, m, ix, iy, mp1;
/*
Purpose
=======
SCOPY copies a vector, x, to a vector, y.
uses unrolled loops for increments equal to 1.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--sy;
--sx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
sy[iy] = sx[ix];
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/*
code for both increments equal to 1
clean-up loop
*/
L20:
m = *n % 7;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
sy[i__] = sx[i__];
/* L30: */
}
if (*n < 7) {
return 0;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 7) {
sy[i__] = sx[i__];
sy[i__ + 1] = sx[i__ + 1];
sy[i__ + 2] = sx[i__ + 2];
sy[i__ + 3] = sx[i__ + 3];
sy[i__ + 4] = sx[i__ + 4];
sy[i__ + 5] = sx[i__ + 5];
sy[i__ + 6] = sx[i__ + 6];
/* L50: */
}
return 0;
} /* scopy_ */
doublereal sdot_(integer *n, real *sx, integer *incx, real *sy, integer *incy)
{
/* System generated locals */
integer i__1;
real ret_val;
/* Local variables */
static integer i__, m, ix, iy, mp1;
static real stemp;
/*
Purpose
=======
SDOT forms the dot product of two vectors.
uses unrolled loops for increments equal to one.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--sy;
--sx;
/* Function Body */
stemp = 0.f;
ret_val = 0.f;
if (*n <= 0) {
return ret_val;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp += sx[ix] * sy[iy];
ix += *incx;
iy += *incy;
/* L10: */
}
ret_val = stemp;
return ret_val;
/*
code for both increments equal to 1
clean-up loop
*/
L20:
m = *n % 5;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp += sx[i__] * sy[i__];
/* L30: */
}
if (*n < 5) {
goto L60;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 5) {
stemp = stemp + sx[i__] * sy[i__] + sx[i__ + 1] * sy[i__ + 1] + sx[
i__ + 2] * sy[i__ + 2] + sx[i__ + 3] * sy[i__ + 3] + sx[i__ +
4] * sy[i__ + 4];
/* L50: */
}
L60:
ret_val = stemp;
return ret_val;
} /* sdot_ */
/* Subroutine */ int sgemm_(char *transa, char *transb, integer *m, integer *
n, integer *k, real *alpha, real *a, integer *lda, real *b, integer *
ldb, real *beta, real *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3;
/* Local variables */
static integer i__, j, l, info;
static logical nota, notb;
static real temp;
static integer ncola;
extern logical lsame_(char *, char *);
static integer nrowa, nrowb;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
SGEMM performs one of the matrix-matrix operations
C := alpha*op( A )*op( B ) + beta*C,
where op( X ) is one of
op( X ) = X or op( X ) = X',
alpha and beta are scalars, and A, B and C are matrices, with op( A )
an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
Arguments
==========
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n', op( A ) = A.
TRANSA = 'T' or 't', op( A ) = A'.
TRANSA = 'C' or 'c', op( A ) = A'.
Unchanged on exit.
TRANSB - CHARACTER*1.
On entry, TRANSB specifies the form of op( B ) to be used in
the matrix multiplication as follows:
TRANSB = 'N' or 'n', op( B ) = B.
TRANSB = 'T' or 't', op( B ) = B'.
TRANSB = 'C' or 'c', op( B ) = B'.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix
op( A ) and of the matrix C. M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix
op( B ) and the number of columns of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry, K specifies the number of columns of the matrix
op( A ) and the number of rows of the matrix op( B ). K must
be at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, ka ), where ka is
k when TRANSA = 'N' or 'n', and is m otherwise.
Before entry with TRANSA = 'N' or 'n', the leading m by k
part of the array A must contain the matrix A, otherwise
the leading k by m part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANSA = 'N' or 'n' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, k ).
Unchanged on exit.
B - REAL array of DIMENSION ( LDB, kb ), where kb is
n when TRANSB = 'N' or 'n', and is k otherwise.
Before entry with TRANSB = 'N' or 'n', the leading k by n
part of the array B must contain the matrix B, otherwise
the leading n by k part of the array B must contain the
matrix B.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANSB = 'N' or 'n' then
LDB must be at least max( 1, k ), otherwise LDB must be at
least max( 1, n ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
Unchanged on exit.
C - REAL array of DIMENSION ( LDC, n ).
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n matrix
( alpha*op( A )*op( B ) + beta*C ).
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Set NOTA and NOTB as true if A and B respectively are not
transposed and set NROWA, NCOLA and NROWB as the number of rows
and columns of A and the number of rows of B respectively.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
nota = lsame_(transa, "N");
notb = lsame_(transb, "N");
if (nota) {
nrowa = *m;
ncola = *k;
} else {
nrowa = *k;
ncola = *m;
}
if (notb) {
nrowb = *k;
} else {
nrowb = *n;
}
/* Test the input parameters. */
info = 0;
if (! nota && ! lsame_(transa, "C") && ! lsame_(
transa, "T")) {
info = 1;
} else if (! notb && ! lsame_(transb, "C") && !
lsame_(transb, "T")) {
info = 2;
} else if (*m < 0) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*k < 0) {
info = 5;
} else if (*lda < max(1,nrowa)) {
info = 8;
} else if (*ldb < max(1,nrowb)) {
info = 10;
} else if (*ldc < max(1,*m)) {
info = 13;
}
if (info != 0) {
xerbla_("SGEMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || (*alpha == 0.f || *k == 0) && *beta == 1.f) {
return 0;
}
/* And if alpha.eq.zero. */
if (*alpha == 0.f) {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L30: */
}
/* L40: */
}
}
return 0;
}
/* Start the operations. */
if (notb) {
if (nota) {
/* Form C := alpha*A*B + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L50: */
}
} else if (*beta != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L60: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (b[l + j * b_dim1] != 0.f) {
temp = *alpha * b[l + j * b_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L70: */
}
}
/* L80: */
}
/* L90: */
}
} else {
/* Form C := alpha*A'*B + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * b[l + j * b_dim1];
/* L100: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L110: */
}
/* L120: */
}
}
} else {
if (nota) {
/* Form C := alpha*A*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L130: */
}
} else if (*beta != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L140: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (b[j + l * b_dim1] != 0.f) {
temp = *alpha * b[j + l * b_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L150: */
}
}
/* L160: */
}
/* L170: */
}
} else {
/* Form C := alpha*A'*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * b[j + l * b_dim1];
/* L180: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L190: */
}
/* L200: */
}
}
}
return 0;
/* End of SGEMM . */
} /* sgemm_ */
/* Subroutine */ int sgemv_(char *trans, integer *m, integer *n, real *alpha,
real *a, integer *lda, real *x, integer *incx, real *beta, real *y,
integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static real temp;
static integer lenx, leny;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
SGEMV performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an
m by n matrix.
Arguments
==========
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
TRANS = 'C' or 'c' y := alpha*A'*x + beta*y.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
X - REAL array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
Before entry, the incremented array X must contain the
vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - REAL array of DIMENSION at least
( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
Before entry with BETA non-zero, the incremented array Y
must contain the vector y. On exit, Y is overwritten by the
updated vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")
) {
info = 1;
} else if (*m < 0) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*lda < max(1,*m)) {
info = 6;
} else if (*incx == 0) {
info = 8;
} else if (*incy == 0) {
info = 11;
}
if (info != 0) {
xerbla_("SGEMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0.f && *beta == 1.f) {
return 0;
}
/*
Set LENX and LENY, the lengths of the vectors x and y, and set
up the start points in X and Y.
*/
if (lsame_(trans, "N")) {
lenx = *n;
leny = *m;
} else {
lenx = *m;
leny = *n;
}
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (lenx - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (leny - 1) * *incy;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
First form y := beta*y.
*/
if (*beta != 1.f) {
if (*incy == 1) {
if (*beta == 0.f) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = 0.f;
/* L10: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = *beta * y[i__];
/* L20: */
}
}
} else {
iy = ky;
if (*beta == 0.f) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = 0.f;
iy += *incy;
/* L30: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = *beta * y[iy];
iy += *incy;
/* L40: */
}
}
}
}
if (*alpha == 0.f) {
return 0;
}
if (lsame_(trans, "N")) {
/* Form y := alpha*A*x + y. */
jx = kx;
if (*incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.f) {
temp = *alpha * x[jx];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__] += temp * a[i__ + j * a_dim1];
/* L50: */
}
}
jx += *incx;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.f) {
temp = *alpha * x[jx];
iy = ky;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
y[iy] += temp * a[i__ + j * a_dim1];
iy += *incy;
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
} else {
/* Form y := alpha*A'*x + y. */
jy = ky;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = 0.f;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp += a[i__ + j * a_dim1] * x[i__];
/* L90: */
}
y[jy] += *alpha * temp;
jy += *incy;
/* L100: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = 0.f;
ix = kx;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp += a[i__ + j * a_dim1] * x[ix];
ix += *incx;
/* L110: */
}
y[jy] += *alpha * temp;
jy += *incy;
/* L120: */
}
}
}
return 0;
/* End of SGEMV . */
} /* sgemv_ */
/* Subroutine */ int sger_(integer *m, integer *n, real *alpha, real *x,
integer *incx, real *y, integer *incy, real *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j, ix, jy, kx, info;
static real temp;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
SGER performs the rank 1 operation
A := alpha*x*y' + A,
where alpha is a scalar, x is an m element vector, y is an n element
vector and A is an m by n matrix.
Arguments
==========
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - REAL array of dimension at least
( 1 + ( m - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the m
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - REAL array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients. On exit, A is
overwritten by the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
info = 0;
if (*m < 0) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*m)) {
info = 9;
}
if (info != 0) {
xerbla_("SGER ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0.f) {
return 0;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (*incy > 0) {
jy = 1;
} else {
jy = 1 - (*n - 1) * *incy;
}
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (y[jy] != 0.f) {
temp = *alpha * y[jy];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] += x[i__] * temp;
/* L10: */
}
}
jy += *incy;
/* L20: */
}
} else {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*m - 1) * *incx;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (y[jy] != 0.f) {
temp = *alpha * y[jy];
ix = kx;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] += x[ix] * temp;
ix += *incx;
/* L30: */
}
}
jy += *incy;
/* L40: */
}
}
return 0;
/* End of SGER . */
} /* sger_ */
doublereal snrm2_(integer *n, real *x, integer *incx)
{
/* System generated locals */
integer i__1, i__2;
real ret_val, r__1;
/* Local variables */
static integer ix;
static real ssq, norm, scale, absxi;
/*
Purpose
=======
SNRM2 returns the euclidean norm of a vector via the function
name, so that
SNRM2 := sqrt( x'*x ).
Further Details
===============
-- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to SLASSQ.
Sven Hammarling, Nag Ltd.
=====================================================================
*/
/* Parameter adjustments */
--x;
/* Function Body */
if (*n < 1 || *incx < 1) {
norm = 0.f;
} else if (*n == 1) {
norm = dabs(x[1]);
} else {
scale = 0.f;
ssq = 1.f;
/*
The following loop is equivalent to this call to the LAPACK
auxiliary routine:
CALL SLASSQ( N, X, INCX, SCALE, SSQ )
*/
i__1 = (*n - 1) * *incx + 1;
i__2 = *incx;
for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) {
if (x[ix] != 0.f) {
absxi = (r__1 = x[ix], dabs(r__1));
if (scale < absxi) {
/* Computing 2nd power */
r__1 = scale / absxi;
ssq = ssq * (r__1 * r__1) + 1.f;
scale = absxi;
} else {
/* Computing 2nd power */
r__1 = absxi / scale;
ssq += r__1 * r__1;
}
}
/* L10: */
}
norm = scale * sqrt(ssq);
}
ret_val = norm;
return ret_val;
/* End of SNRM2. */
} /* snrm2_ */
/* Subroutine */ int srot_(integer *n, real *sx, integer *incx, real *sy,
integer *incy, real *c__, real *s)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__, ix, iy;
static real stemp;
/*
Purpose
=======
applies a plane rotation.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--sy;
--sx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments not equal
to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp = *c__ * sx[ix] + *s * sy[iy];
sy[iy] = *c__ * sy[iy] - *s * sx[ix];
sx[ix] = stemp;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp = *c__ * sx[i__] + *s * sy[i__];
sy[i__] = *c__ * sy[i__] - *s * sx[i__];
sx[i__] = stemp;
/* L30: */
}
return 0;
} /* srot_ */
/* Subroutine */ int sscal_(integer *n, real *sa, real *sx, integer *incx)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
static integer i__, m, mp1, nincx;
/*
Purpose
=======
scales a vector by a constant.
uses unrolled loops for increment equal to 1.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--sx;
/* Function Body */
if (*n <= 0 || *incx <= 0) {
return 0;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
nincx = *n * *incx;
i__1 = nincx;
i__2 = *incx;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
sx[i__] = *sa * sx[i__];
/* L10: */
}
return 0;
/*
code for increment equal to 1
clean-up loop
*/
L20:
m = *n % 5;
if (m == 0) {
goto L40;
}
i__2 = m;
for (i__ = 1; i__ <= i__2; ++i__) {
sx[i__] = *sa * sx[i__];
/* L30: */
}
if (*n < 5) {
return 0;
}
L40:
mp1 = m + 1;
i__2 = *n;
for (i__ = mp1; i__ <= i__2; i__ += 5) {
sx[i__] = *sa * sx[i__];
sx[i__ + 1] = *sa * sx[i__ + 1];
sx[i__ + 2] = *sa * sx[i__ + 2];
sx[i__ + 3] = *sa * sx[i__ + 3];
sx[i__ + 4] = *sa * sx[i__ + 4];
/* L50: */
}
return 0;
} /* sscal_ */
/* Subroutine */ int sswap_(integer *n, real *sx, integer *incx, real *sy,
integer *incy)
{
/* System generated locals */
integer i__1;
/* Local variables */
static integer i__, m, ix, iy, mp1;
static real stemp;
/*
Purpose
=======
interchanges two vectors.
uses unrolled loops for increments equal to 1.
Further Details
===============
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--sy;
--sx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments not equal
to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp = sx[ix];
sx[ix] = sy[iy];
sy[iy] = stemp;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/*
code for both increments equal to 1
clean-up loop
*/
L20:
m = *n % 3;
if (m == 0) {
goto L40;
}
i__1 = m;
for (i__ = 1; i__ <= i__1; ++i__) {
stemp = sx[i__];
sx[i__] = sy[i__];
sy[i__] = stemp;
/* L30: */
}
if (*n < 3) {
return 0;
}
L40:
mp1 = m + 1;
i__1 = *n;
for (i__ = mp1; i__ <= i__1; i__ += 3) {
stemp = sx[i__];
sx[i__] = sy[i__];
sy[i__] = stemp;
stemp = sx[i__ + 1];
sx[i__ + 1] = sy[i__ + 1];
sy[i__ + 1] = stemp;
stemp = sx[i__ + 2];
sx[i__ + 2] = sy[i__ + 2];
sy[i__ + 2] = stemp;
/* L50: */
}
return 0;
} /* sswap_ */
/* Subroutine */ int ssymv_(char *uplo, integer *n, real *alpha, real *a,
integer *lda, real *x, integer *incx, real *beta, real *y, integer *
incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static real temp1, temp2;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
SSYMV performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n symmetric matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - REAL array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - REAL array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y. On exit, Y is overwritten by the updated
vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*lda < max(1,*n)) {
info = 5;
} else if (*incx == 0) {
info = 7;
} else if (*incy == 0) {
info = 10;
}
if (info != 0) {
xerbla_("SSYMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0.f && *beta == 1.f) {
return 0;
}
/* Set up the start points in X and Y. */
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through the triangular part
of A.
First form y := beta*y.
*/
if (*beta != 1.f) {
if (*incy == 1) {
if (*beta == 0.f) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = 0.f;
/* L10: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[i__] = *beta * y[i__];
/* L20: */
}
}
} else {
iy = ky;
if (*beta == 0.f) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = 0.f;
iy += *incy;
/* L30: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
y[iy] = *beta * y[iy];
iy += *incy;
/* L40: */
}
}
}
}
if (*alpha == 0.f) {
return 0;
}
if (lsame_(uplo, "U")) {
/* Form y when A is stored in upper triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[j];
temp2 = 0.f;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__] += temp1 * a[i__ + j * a_dim1];
temp2 += a[i__ + j * a_dim1] * x[i__];
/* L50: */
}
y[j] = y[j] + temp1 * a[j + j * a_dim1] + *alpha * temp2;
/* L60: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[jx];
temp2 = 0.f;
ix = kx;
iy = ky;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
y[iy] += temp1 * a[i__ + j * a_dim1];
temp2 += a[i__ + j * a_dim1] * x[ix];
ix += *incx;
iy += *incy;
/* L70: */
}
y[jy] = y[jy] + temp1 * a[j + j * a_dim1] + *alpha * temp2;
jx += *incx;
jy += *incy;
/* L80: */
}
}
} else {
/* Form y when A is stored in lower triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[j];
temp2 = 0.f;
y[j] += temp1 * a[j + j * a_dim1];
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
y[i__] += temp1 * a[i__ + j * a_dim1];
temp2 += a[i__ + j * a_dim1] * x[i__];
/* L90: */
}
y[j] += *alpha * temp2;
/* L100: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * x[jx];
temp2 = 0.f;
y[jy] += temp1 * a[j + j * a_dim1];
ix = jx;
iy = jy;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
iy += *incy;
y[iy] += temp1 * a[i__ + j * a_dim1];
temp2 += a[i__ + j * a_dim1] * x[ix];
/* L110: */
}
y[jy] += *alpha * temp2;
jx += *incx;
jy += *incy;
/* L120: */
}
}
}
return 0;
/* End of SSYMV . */
} /* ssymv_ */
/* Subroutine */ int ssyr2_(char *uplo, integer *n, real *alpha, real *x,
integer *incx, real *y, integer *incy, real *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static real temp1, temp2;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
SSYR2 performs the symmetric rank 2 operation
A := alpha*x*y' + alpha*y*x' + A,
where alpha is a scalar, x and y are n element vectors and A is an n
by n symmetric matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - REAL array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - REAL array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced. On exit, the
upper triangular part of the array A is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced. On exit, the
lower triangular part of the array A is overwritten by the
lower triangular part of the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*n)) {
info = 9;
}
if (info != 0) {
xerbla_("SSYR2 ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *alpha == 0.f) {
return 0;
}
/*
Set up the start points in X and Y if the increments are not both
unity.
*/
if (*incx != 1 || *incy != 1) {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
jx = kx;
jy = ky;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through the triangular part
of A.
*/
if (lsame_(uplo, "U")) {
/* Form A when A is stored in the upper triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.f || y[j] != 0.f) {
temp1 = *alpha * y[j];
temp2 = *alpha * x[j];
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] *
temp1 + y[i__] * temp2;
/* L10: */
}
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.f || y[jy] != 0.f) {
temp1 = *alpha * y[jy];
temp2 = *alpha * x[jx];
ix = kx;
iy = ky;
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] *
temp1 + y[iy] * temp2;
ix += *incx;
iy += *incy;
/* L30: */
}
}
jx += *incx;
jy += *incy;
/* L40: */
}
}
} else {
/* Form A when A is stored in the lower triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.f || y[j] != 0.f) {
temp1 = *alpha * y[j];
temp2 = *alpha * x[j];
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] *
temp1 + y[i__] * temp2;
/* L50: */
}
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.f || y[jy] != 0.f) {
temp1 = *alpha * y[jy];
temp2 = *alpha * x[jx];
ix = jx;
iy = jy;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] *
temp1 + y[iy] * temp2;
ix += *incx;
iy += *incy;
/* L70: */
}
}
jx += *incx;
jy += *incy;
/* L80: */
}
}
}
return 0;
/* End of SSYR2 . */
} /* ssyr2_ */
/* Subroutine */ int ssyr2k_(char *uplo, char *trans, integer *n, integer *k,
real *alpha, real *a, integer *lda, real *b, integer *ldb, real *beta,
real *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3;
/* Local variables */
static integer i__, j, l, info;
static real temp1, temp2;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
SSYR2K performs one of the symmetric rank 2k operations
C := alpha*A*B' + alpha*B*A' + beta*C,
or
C := alpha*A'*B + alpha*B'*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A and B are n by k matrices in the first case and k by n
matrices in the second case.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' +
beta*C.
TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A +
beta*C.
TRANS = 'C' or 'c' C := alpha*A'*B + alpha*B'*A +
beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrices A and B, and on entry with
TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
of rows of the matrices A and B. K must be at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
B - REAL array of DIMENSION ( LDB, kb ), where kb is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array B must contain the matrix B, otherwise
the leading k by n part of the array B must contain the
matrix B.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDB must be at least max( 1, n ), otherwise LDB must
be at least max( 1, k ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - REAL array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
if (lsame_(trans, "N")) {
nrowa = *n;
} else {
nrowa = *k;
}
upper = lsame_(uplo, "U");
info = 0;
if (! upper && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*k < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldb < max(1,nrowa)) {
info = 9;
} else if (*ldc < max(1,*n)) {
info = 12;
}
if (info != 0) {
xerbla_("SSYR2K", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || (*alpha == 0.f || *k == 0) && *beta == 1.f) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.f) {
if (upper) {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L30: */
}
/* L40: */
}
}
} else {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L70: */
}
/* L80: */
}
}
}
return 0;
}
/* Start the operations. */
if (lsame_(trans, "N")) {
/* Form C := alpha*A*B' + alpha*B*A' + C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L90: */
}
} else if (*beta != 1.f) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L100: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a[j + l * a_dim1] != 0.f || b[j + l * b_dim1] != 0.f)
{
temp1 = *alpha * b[j + l * b_dim1];
temp2 = *alpha * a[j + l * a_dim1];
i__3 = j;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[
i__ + l * a_dim1] * temp1 + b[i__ + l *
b_dim1] * temp2;
/* L110: */
}
}
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L140: */
}
} else if (*beta != 1.f) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L150: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a[j + l * a_dim1] != 0.f || b[j + l * b_dim1] != 0.f)
{
temp1 = *alpha * b[j + l * b_dim1];
temp2 = *alpha * a[j + l * a_dim1];
i__3 = *n;
for (i__ = j; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[
i__ + l * a_dim1] * temp1 + b[i__ + l *
b_dim1] * temp2;
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
}
} else {
/* Form C := alpha*A'*B + alpha*B'*A + C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
temp1 = 0.f;
temp2 = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1];
temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1];
/* L190: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha *
temp2;
} else {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
+ *alpha * temp1 + *alpha * temp2;
}
/* L200: */
}
/* L210: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
temp1 = 0.f;
temp2 = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1];
temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1];
/* L220: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha *
temp2;
} else {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
+ *alpha * temp1 + *alpha * temp2;
}
/* L230: */
}
/* L240: */
}
}
}
return 0;
/* End of SSYR2K. */
} /* ssyr2k_ */
/* Subroutine */ int ssyrk_(char *uplo, char *trans, integer *n, integer *k,
real *alpha, real *a, integer *lda, real *beta, real *c__, integer *
ldc)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j, l, info;
static real temp;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
SSYRK performs one of the symmetric rank k operations
C := alpha*A*A' + beta*C,
or
C := alpha*A'*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A is an n by k matrix in the first case and a k by n matrix
in the second case.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*A' + beta*C.
TRANS = 'T' or 't' C := alpha*A'*A + beta*C.
TRANS = 'C' or 'c' C := alpha*A'*A + beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrix A, and on entry with
TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
of rows of the matrix A. K must be at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
BETA - REAL .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - REAL array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
if (lsame_(trans, "N")) {
nrowa = *n;
} else {
nrowa = *k;
}
upper = lsame_(uplo, "U");
info = 0;
if (! upper && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*k < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldc < max(1,*n)) {
info = 10;
}
if (info != 0) {
xerbla_("SSYRK ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || (*alpha == 0.f || *k == 0) && *beta == 1.f) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.f) {
if (upper) {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L30: */
}
/* L40: */
}
}
} else {
if (*beta == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L70: */
}
/* L80: */
}
}
}
return 0;
}
/* Start the operations. */
if (lsame_(trans, "N")) {
/* Form C := alpha*A*A' + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L90: */
}
} else if (*beta != 1.f) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L100: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a[j + l * a_dim1] != 0.f) {
temp = *alpha * a[j + l * a_dim1];
i__3 = j;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L110: */
}
}
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.f) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.f;
/* L140: */
}
} else if (*beta != 1.f) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L150: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
if (a[j + l * a_dim1] != 0.f) {
temp = *alpha * a[j + l * a_dim1];
i__3 = *n;
for (i__ = j; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp * a[i__ + l *
a_dim1];
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
}
} else {
/* Form C := alpha*A'*A + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * a[l + j * a_dim1];
/* L190: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L200: */
}
/* L210: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
temp = 0.f;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
temp += a[l + i__ * a_dim1] * a[l + j * a_dim1];
/* L220: */
}
if (*beta == 0.f) {
c__[i__ + j * c_dim1] = *alpha * temp;
} else {
c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[
i__ + j * c_dim1];
}
/* L230: */
}
/* L240: */
}
}
}
return 0;
/* End of SSYRK . */
} /* ssyrk_ */
/* Subroutine */ int strmm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, real *alpha, real *a, integer *lda, real *b,
integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j, k, info;
static real temp;
static logical lside;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
/*
Purpose
=======
STRMM performs one of the matrix-matrix operations
B := alpha*op( A )*B, or B := alpha*B*op( A ),
where alpha is a scalar, B is an m by n matrix, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A'.
Arguments
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) multiplies B from
the left or right as follows:
SIDE = 'L' or 'l' B := alpha*op( A )*B.
SIDE = 'R' or 'r' B := alpha*B*op( A ).
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A'.
TRANSA = 'C' or 'c' op( A ) = A'.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
B - REAL array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the matrix B, and on exit is overwritten by the
transformed matrix.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
lside = lsame_(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
info = 0;
if (! lside && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (! lsame_(transa, "N") && ! lsame_(transa,
"T") && ! lsame_(transa, "C")) {
info = 3;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < max(1,nrowa)) {
info = 9;
} else if (*ldb < max(1,*m)) {
info = 11;
}
if (info != 0) {
xerbla_("STRMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (lsame_(transa, "N")) {
/* Form B := alpha*A*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
if (b[k + j * b_dim1] != 0.f) {
temp = *alpha * b[k + j * b_dim1];
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] += temp * a[i__ + k *
a_dim1];
/* L30: */
}
if (nounit) {
temp *= a[k + k * a_dim1];
}
b[k + j * b_dim1] = temp;
}
/* L40: */
}
/* L50: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (k = *m; k >= 1; --k) {
if (b[k + j * b_dim1] != 0.f) {
temp = *alpha * b[k + j * b_dim1];
b[k + j * b_dim1] = temp;
if (nounit) {
b[k + j * b_dim1] *= a[k + k * a_dim1];
}
i__2 = *m;
for (i__ = k + 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] += temp * a[i__ + k *
a_dim1];
/* L60: */
}
}
/* L70: */
}
/* L80: */
}
}
} else {
/* Form B := alpha*A'*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
temp = b[i__ + j * b_dim1];
if (nounit) {
temp *= a[i__ + i__ * a_dim1];
}
i__2 = i__ - 1;
for (k = 1; k <= i__2; ++k) {
temp += a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L90: */
}
b[i__ + j * b_dim1] = *alpha * temp;
/* L100: */
}
/* L110: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = b[i__ + j * b_dim1];
if (nounit) {
temp *= a[i__ + i__ * a_dim1];
}
i__3 = *m;
for (k = i__ + 1; k <= i__3; ++k) {
temp += a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L120: */
}
b[i__ + j * b_dim1] = *alpha * temp;
/* L130: */
}
/* L140: */
}
}
}
} else {
if (lsame_(transa, "N")) {
/* Form B := alpha*B*A. */
if (upper) {
for (j = *n; j >= 1; --j) {
temp = *alpha;
if (nounit) {
temp *= a[j + j * a_dim1];
}
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L150: */
}
i__1 = j - 1;
for (k = 1; k <= i__1; ++k) {
if (a[k + j * a_dim1] != 0.f) {
temp = *alpha * a[k + j * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] += temp * b[i__ + k *
b_dim1];
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = *alpha;
if (nounit) {
temp *= a[j + j * a_dim1];
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L190: */
}
i__2 = *n;
for (k = j + 1; k <= i__2; ++k) {
if (a[k + j * a_dim1] != 0.f) {
temp = *alpha * a[k + j * a_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] += temp * b[i__ + k *
b_dim1];
/* L200: */
}
}
/* L210: */
}
/* L220: */
}
}
} else {
/* Form B := alpha*B*A'. */
if (upper) {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
i__2 = k - 1;
for (j = 1; j <= i__2; ++j) {
if (a[j + k * a_dim1] != 0.f) {
temp = *alpha * a[j + k * a_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] += temp * b[i__ + k *
b_dim1];
/* L230: */
}
}
/* L240: */
}
temp = *alpha;
if (nounit) {
temp *= a[k + k * a_dim1];
}
if (temp != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L250: */
}
}
/* L260: */
}
} else {
for (k = *n; k >= 1; --k) {
i__1 = *n;
for (j = k + 1; j <= i__1; ++j) {
if (a[j + k * a_dim1] != 0.f) {
temp = *alpha * a[j + k * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] += temp * b[i__ + k *
b_dim1];
/* L270: */
}
}
/* L280: */
}
temp = *alpha;
if (nounit) {
temp *= a[k + k * a_dim1];
}
if (temp != 1.f) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L290: */
}
}
/* L300: */
}
}
}
}
return 0;
/* End of STRMM . */
} /* strmm_ */
/* Subroutine */ int strmv_(char *uplo, char *trans, char *diag, integer *n,
real *a, integer *lda, real *x, integer *incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__, j, ix, jx, kx, info;
static real temp;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
/*
Purpose
=======
STRMV performs one of the matrix-vector operations
x := A*x, or x := A'*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A'*x.
TRANS = 'C' or 'c' x := A'*x.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - REAL array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x. On exit, X is overwritten with the
tranformed vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*lda < max(1,*n)) {
info = 6;
} else if (*incx == 0) {
info = 8;
}
if (info != 0) {
xerbla_("STRMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
nounit = lsame_(diag, "N");
/*
Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops.
*/
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (lsame_(trans, "N")) {
/* Form x := A*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[j] != 0.f) {
temp = x[j];
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__] += temp * a[i__ + j * a_dim1];
/* L10: */
}
if (nounit) {
x[j] *= a[j + j * a_dim1];
}
}
/* L20: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (x[jx] != 0.f) {
temp = x[jx];
ix = kx;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
x[ix] += temp * a[i__ + j * a_dim1];
ix += *incx;
/* L30: */
}
if (nounit) {
x[jx] *= a[j + j * a_dim1];
}
}
jx += *incx;
/* L40: */
}
}
} else {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
if (x[j] != 0.f) {
temp = x[j];
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
x[i__] += temp * a[i__ + j * a_dim1];
/* L50: */
}
if (nounit) {
x[j] *= a[j + j * a_dim1];
}
}
/* L60: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
if (x[jx] != 0.f) {
temp = x[jx];
ix = kx;
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
x[ix] += temp * a[i__ + j * a_dim1];
ix -= *incx;
/* L70: */
}
if (nounit) {
x[jx] *= a[j + j * a_dim1];
}
}
jx -= *incx;
/* L80: */
}
}
}
} else {
/* Form x := A'*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
temp = x[j];
if (nounit) {
temp *= a[j + j * a_dim1];
}
for (i__ = j - 1; i__ >= 1; --i__) {
temp += a[i__ + j * a_dim1] * x[i__];
/* L90: */
}
x[j] = temp;
/* L100: */
}
} else {
jx = kx + (*n - 1) * *incx;
for (j = *n; j >= 1; --j) {
temp = x[jx];
ix = jx;
if (nounit) {
temp *= a[j + j * a_dim1];
}
for (i__ = j - 1; i__ >= 1; --i__) {
ix -= *incx;
temp += a[i__ + j * a_dim1] * x[ix];
/* L110: */
}
x[jx] = temp;
jx -= *incx;
/* L120: */
}
}
} else {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[j];
if (nounit) {
temp *= a[j + j * a_dim1];
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
temp += a[i__ + j * a_dim1] * x[i__];
/* L130: */
}
x[j] = temp;
/* L140: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = x[jx];
ix = jx;
if (nounit) {
temp *= a[j + j * a_dim1];
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
temp += a[i__ + j * a_dim1] * x[ix];
/* L150: */
}
x[jx] = temp;
jx += *incx;
/* L160: */
}
}
}
}
return 0;
/* End of STRMV . */
} /* strmv_ */
/* Subroutine */ int strsm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, real *alpha, real *a, integer *lda, real *b,
integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j, k, info;
static real temp;
static logical lside;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical nounit;
/*
Purpose
=======
STRSM solves one of the matrix equations
op( A )*X = alpha*B, or X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A'.
The matrix X is overwritten on B.
Arguments
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:
SIDE = 'L' or 'l' op( A )*X = alpha*B.
SIDE = 'R' or 'r' X*op( A ) = alpha*B.
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A'.
TRANSA = 'C' or 'c' op( A ) = A'.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - REAL .
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - REAL array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
B - REAL array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the right-hand side matrix B, and on exit is
overwritten by the solution matrix X.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
lside = lsame_(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
info = 0;
if (! lside && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (! lsame_(transa, "N") && ! lsame_(transa,
"T") && ! lsame_(transa, "C")) {
info = 3;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < max(1,nrowa)) {
info = 9;
} else if (*ldb < max(1,*m)) {
info = 11;
}
if (info != 0) {
xerbla_("STRSM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.f) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = 0.f;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (lsame_(transa, "N")) {
/* Form B := alpha*inv( A )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L30: */
}
}
for (k = *m; k >= 1; --k) {
if (b[k + j * b_dim1] != 0.f) {
if (nounit) {
b[k + j * b_dim1] /= a[k + k * a_dim1];
}
i__2 = k - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
i__ + k * a_dim1];
/* L40: */
}
}
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L70: */
}
}
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
if (b[k + j * b_dim1] != 0.f) {
if (nounit) {
b[k + j * b_dim1] /= a[k + k * a_dim1];
}
i__3 = *m;
for (i__ = k + 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[
i__ + k * a_dim1];
/* L80: */
}
}
/* L90: */
}
/* L100: */
}
}
} else {
/* Form B := alpha*inv( A' )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = *alpha * b[i__ + j * b_dim1];
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L110: */
}
if (nounit) {
temp /= a[i__ + i__ * a_dim1];
}
b[i__ + j * b_dim1] = temp;
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
temp = *alpha * b[i__ + j * b_dim1];
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1];
/* L140: */
}
if (nounit) {
temp /= a[i__ + i__ * a_dim1];
}
b[i__ + j * b_dim1] = temp;
/* L150: */
}
/* L160: */
}
}
}
} else {
if (lsame_(transa, "N")) {
/* Form B := alpha*B*inv( A ). */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L170: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
if (a[k + j * a_dim1] != 0.f) {
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
i__ + k * b_dim1];
/* L180: */
}
}
/* L190: */
}
if (nounit) {
temp = 1.f / a[j + j * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L200: */
}
}
/* L210: */
}
} else {
for (j = *n; j >= 1; --j) {
if (*alpha != 1.f) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]
;
/* L220: */
}
}
i__1 = *n;
for (k = j + 1; k <= i__1; ++k) {
if (a[k + j * a_dim1] != 0.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[
i__ + k * b_dim1];
/* L230: */
}
}
/* L240: */
}
if (nounit) {
temp = 1.f / a[j + j * a_dim1];
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
/* L250: */
}
}
/* L260: */
}
}
} else {
/* Form B := alpha*B*inv( A' ). */
if (upper) {
for (k = *n; k >= 1; --k) {
if (nounit) {
temp = 1.f / a[k + k * a_dim1];
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L270: */
}
}
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
if (a[j + k * a_dim1] != 0.f) {
temp = a[j + k * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] -= temp * b[i__ + k *
b_dim1];
/* L280: */
}
}
/* L290: */
}
if (*alpha != 1.f) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
;
/* L300: */
}
}
/* L310: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (nounit) {
temp = 1.f / a[k + k * a_dim1];
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
/* L320: */
}
}
i__2 = *n;
for (j = k + 1; j <= i__2; ++j) {
if (a[j + k * a_dim1] != 0.f) {
temp = a[j + k * a_dim1];
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b[i__ + j * b_dim1] -= temp * b[i__ + k *
b_dim1];
/* L330: */
}
}
/* L340: */
}
if (*alpha != 1.f) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]
;
/* L350: */
}
}
/* L360: */
}
}
}
}
return 0;
/* End of STRSM . */
} /* strsm_ */
/* Subroutine */ int zaxpy_(integer *n, doublecomplex *za, doublecomplex *zx,
integer *incx, doublecomplex *zy, integer *incy)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
doublecomplex z__1, z__2;
/* Local variables */
static integer i__, ix, iy;
extern doublereal dcabs1_(doublecomplex *);
/*
Purpose
=======
ZAXPY constant times a vector plus a vector.
Further Details
===============
jack dongarra, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--zy;
--zx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (dcabs1_(za) == 0.) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
i__3 = iy;
i__4 = ix;
z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * zx[
i__4].i + za->i * zx[i__4].r;
z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i;
zy[i__2].r = z__1.r, zy[i__2].i = z__1.i;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * zx[
i__4].i + za->i * zx[i__4].r;
z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i;
zy[i__2].r = z__1.r, zy[i__2].i = z__1.i;
/* L30: */
}
return 0;
} /* zaxpy_ */
/* Subroutine */ int zcopy_(integer *n, doublecomplex *zx, integer *incx,
doublecomplex *zy, integer *incy)
{
/* System generated locals */
integer i__1, i__2, i__3;
/* Local variables */
static integer i__, ix, iy;
/*
Purpose
=======
ZCOPY copies a vector, x, to a vector, y.
Further Details
===============
jack dongarra, linpack, 4/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--zy;
--zx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
i__3 = ix;
zy[i__2].r = zx[i__3].r, zy[i__2].i = zx[i__3].i;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
zy[i__2].r = zx[i__3].r, zy[i__2].i = zx[i__3].i;
/* L30: */
}
return 0;
} /* zcopy_ */
/* Double Complex */ VOID zdotc_(doublecomplex * ret_val, integer *n,
doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy)
{
/* System generated locals */
integer i__1, i__2;
doublecomplex z__1, z__2, z__3;
/* Local variables */
static integer i__, ix, iy;
static doublecomplex ztemp;
/*
Purpose
=======
ZDOTC forms the dot product of a vector.
Further Details
===============
jack dongarra, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--zy;
--zx;
/* Function Body */
ztemp.r = 0., ztemp.i = 0.;
ret_val->r = 0., ret_val->i = 0.;
if (*n <= 0) {
return ;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d_cnjg(&z__3, &zx[ix]);
i__2 = iy;
z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = z__3.r *
zy[i__2].i + z__3.i * zy[i__2].r;
z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i;
ztemp.r = z__1.r, ztemp.i = z__1.i;
ix += *incx;
iy += *incy;
/* L10: */
}
ret_val->r = ztemp.r, ret_val->i = ztemp.i;
return ;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d_cnjg(&z__3, &zx[i__]);
i__2 = i__;
z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = z__3.r *
zy[i__2].i + z__3.i * zy[i__2].r;
z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i;
ztemp.r = z__1.r, ztemp.i = z__1.i;
/* L30: */
}
ret_val->r = ztemp.r, ret_val->i = ztemp.i;
return ;
} /* zdotc_ */
/* Double Complex */ VOID zdotu_(doublecomplex * ret_val, integer *n,
doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublecomplex z__1, z__2;
/* Local variables */
static integer i__, ix, iy;
static doublecomplex ztemp;
/*
Purpose
=======
ZDOTU forms the dot product of two vectors.
Further Details
===============
jack dongarra, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--zy;
--zx;
/* Function Body */
ztemp.r = 0., ztemp.i = 0.;
ret_val->r = 0., ret_val->i = 0.;
if (*n <= 0) {
return ;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments
not equal to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ix;
i__3 = iy;
z__2.r = zx[i__2].r * zy[i__3].r - zx[i__2].i * zy[i__3].i, z__2.i =
zx[i__2].r * zy[i__3].i + zx[i__2].i * zy[i__3].r;
z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i;
ztemp.r = z__1.r, ztemp.i = z__1.i;
ix += *incx;
iy += *incy;
/* L10: */
}
ret_val->r = ztemp.r, ret_val->i = ztemp.i;
return ;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
z__2.r = zx[i__2].r * zy[i__3].r - zx[i__2].i * zy[i__3].i, z__2.i =
zx[i__2].r * zy[i__3].i + zx[i__2].i * zy[i__3].r;
z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i;
ztemp.r = z__1.r, ztemp.i = z__1.i;
/* L30: */
}
ret_val->r = ztemp.r, ret_val->i = ztemp.i;
return ;
} /* zdotu_ */
/* Subroutine */ int zdrot_(integer *n, doublecomplex *cx, integer *incx,
doublecomplex *cy, integer *incy, doublereal *c__, doublereal *s)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
doublecomplex z__1, z__2, z__3;
/* Local variables */
static integer i__, ix, iy;
static doublecomplex ctemp;
/*
Purpose
=======
Applies a plane rotation, where the cos and sin (c and s) are real
and the vectors cx and cy are complex.
jack dongarra, linpack, 3/11/78.
Arguments
==========
N (input) INTEGER
On entry, N specifies the order of the vectors cx and cy.
N must be at least zero.
Unchanged on exit.
CX (input) COMPLEX*16 array, dimension at least
( 1 + ( N - 1 )*abs( INCX ) ).
Before entry, the incremented array CX must contain the n
element vector cx. On exit, CX is overwritten by the updated
vector cx.
INCX (input) INTEGER
On entry, INCX specifies the increment for the elements of
CX. INCX must not be zero.
Unchanged on exit.
CY (input) COMPLEX*16 array, dimension at least
( 1 + ( N - 1 )*abs( INCY ) ).
Before entry, the incremented array CY must contain the n
element vector cy. On exit, CY is overwritten by the updated
vector cy.
INCY (input) INTEGER
On entry, INCY specifies the increment for the elements of
CY. INCY must not be zero.
Unchanged on exit.
C (input) DOUBLE PRECISION
On entry, C specifies the cosine, cos.
Unchanged on exit.
S (input) DOUBLE PRECISION
On entry, S specifies the sine, sin.
Unchanged on exit.
=====================================================================
*/
/* Parameter adjustments */
--cy;
--cx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments not equal
to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ix;
z__2.r = *c__ * cx[i__2].r, z__2.i = *c__ * cx[i__2].i;
i__3 = iy;
z__3.r = *s * cy[i__3].r, z__3.i = *s * cy[i__3].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = iy;
i__3 = iy;
z__2.r = *c__ * cy[i__3].r, z__2.i = *c__ * cy[i__3].i;
i__4 = ix;
z__3.r = *s * cx[i__4].r, z__3.i = *s * cx[i__4].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
cy[i__2].r = z__1.r, cy[i__2].i = z__1.i;
i__2 = ix;
cx[i__2].r = ctemp.r, cx[i__2].i = ctemp.i;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
z__2.r = *c__ * cx[i__2].r, z__2.i = *c__ * cx[i__2].i;
i__3 = i__;
z__3.r = *s * cy[i__3].r, z__3.i = *s * cy[i__3].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = i__;
i__3 = i__;
z__2.r = *c__ * cy[i__3].r, z__2.i = *c__ * cy[i__3].i;
i__4 = i__;
z__3.r = *s * cx[i__4].r, z__3.i = *s * cx[i__4].i;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
cy[i__2].r = z__1.r, cy[i__2].i = z__1.i;
i__2 = i__;
cx[i__2].r = ctemp.r, cx[i__2].i = ctemp.i;
/* L30: */
}
return 0;
} /* zdrot_ */
/* Subroutine */ int zdscal_(integer *n, doublereal *da, doublecomplex *zx,
integer *incx)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublecomplex z__1, z__2;
/* Local variables */
static integer i__, ix;
/*
Purpose
=======
ZDSCAL scales a vector by a constant.
Further Details
===============
jack dongarra, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--zx;
/* Function Body */
if (*n <= 0 || *incx <= 0) {
return 0;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
ix = 1;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ix;
z__2.r = *da, z__2.i = 0.;
i__3 = ix;
z__1.r = z__2.r * zx[i__3].r - z__2.i * zx[i__3].i, z__1.i = z__2.r *
zx[i__3].i + z__2.i * zx[i__3].r;
zx[i__2].r = z__1.r, zx[i__2].i = z__1.i;
ix += *incx;
/* L10: */
}
return 0;
/* code for increment equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
z__2.r = *da, z__2.i = 0.;
i__3 = i__;
z__1.r = z__2.r * zx[i__3].r - z__2.i * zx[i__3].i, z__1.i = z__2.r *
zx[i__3].i + z__2.i * zx[i__3].r;
zx[i__2].r = z__1.r, zx[i__2].i = z__1.i;
/* L30: */
}
return 0;
} /* zdscal_ */
/* Subroutine */ int zgemm_(char *transa, char *transb, integer *m, integer *
n, integer *k, doublecomplex *alpha, doublecomplex *a, integer *lda,
doublecomplex *b, integer *ldb, doublecomplex *beta, doublecomplex *
c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3, i__4, i__5, i__6;
doublecomplex z__1, z__2, z__3, z__4;
/* Local variables */
static integer i__, j, l, info;
static logical nota, notb;
static doublecomplex temp;
static logical conja, conjb;
static integer ncola;
extern logical lsame_(char *, char *);
static integer nrowa, nrowb;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
ZGEMM performs one of the matrix-matrix operations
C := alpha*op( A )*op( B ) + beta*C,
where op( X ) is one of
op( X ) = X or op( X ) = X' or op( X ) = conjg( X' ),
alpha and beta are scalars, and A, B and C are matrices, with op( A )
an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
Arguments
==========
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n', op( A ) = A.
TRANSA = 'T' or 't', op( A ) = A'.
TRANSA = 'C' or 'c', op( A ) = conjg( A' ).
Unchanged on exit.
TRANSB - CHARACTER*1.
On entry, TRANSB specifies the form of op( B ) to be used in
the matrix multiplication as follows:
TRANSB = 'N' or 'n', op( B ) = B.
TRANSB = 'T' or 't', op( B ) = B'.
TRANSB = 'C' or 'c', op( B ) = conjg( B' ).
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix
op( A ) and of the matrix C. M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix
op( B ) and the number of columns of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry, K specifies the number of columns of the matrix
op( A ) and the number of rows of the matrix op( B ). K must
be at least zero.
Unchanged on exit.
ALPHA - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
k when TRANSA = 'N' or 'n', and is m otherwise.
Before entry with TRANSA = 'N' or 'n', the leading m by k
part of the array A must contain the matrix A, otherwise
the leading k by m part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANSA = 'N' or 'n' then
LDA must be at least max( 1, m ), otherwise LDA must be at
least max( 1, k ).
Unchanged on exit.
B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
n when TRANSB = 'N' or 'n', and is k otherwise.
Before entry with TRANSB = 'N' or 'n', the leading k by n
part of the array B must contain the matrix B, otherwise
the leading n by k part of the array B must contain the
matrix B.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANSB = 'N' or 'n' then
LDB must be at least max( 1, k ), otherwise LDB must be at
least max( 1, n ).
Unchanged on exit.
BETA - COMPLEX*16 .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then C need not be set on input.
Unchanged on exit.
C - COMPLEX*16 array of DIMENSION ( LDC, n ).
Before entry, the leading m by n part of the array C must
contain the matrix C, except when beta is zero, in which
case C need not be set on entry.
On exit, the array C is overwritten by the m by n matrix
( alpha*op( A )*op( B ) + beta*C ).
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Set NOTA and NOTB as true if A and B respectively are not
conjugated or transposed, set CONJA and CONJB as true if A and
B respectively are to be transposed but not conjugated and set
NROWA, NCOLA and NROWB as the number of rows and columns of A
and the number of rows of B respectively.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
nota = lsame_(transa, "N");
notb = lsame_(transb, "N");
conja = lsame_(transa, "C");
conjb = lsame_(transb, "C");
if (nota) {
nrowa = *m;
ncola = *k;
} else {
nrowa = *k;
ncola = *m;
}
if (notb) {
nrowb = *k;
} else {
nrowb = *n;
}
/* Test the input parameters. */
info = 0;
if (! nota && ! conja && ! lsame_(transa, "T")) {
info = 1;
} else if (! notb && ! conjb && ! lsame_(transb, "T")) {
info = 2;
} else if (*m < 0) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*k < 0) {
info = 5;
} else if (*lda < max(1,nrowa)) {
info = 8;
} else if (*ldb < max(1,nrowb)) {
info = 10;
} else if (*ldc < max(1,*m)) {
info = 13;
}
if (info != 0) {
xerbla_("ZGEMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) &&
(beta->r == 1. && beta->i == 0.)) {
return 0;
}
/* And when alpha.eq.zero. */
if (alpha->r == 0. && alpha->i == 0.) {
if (beta->r == 0. && beta->i == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i,
z__1.i = beta->r * c__[i__4].i + beta->i * c__[
i__4].r;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L30: */
}
/* L40: */
}
}
return 0;
}
/* Start the operations. */
if (notb) {
if (nota) {
/* Form C := alpha*A*B + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (beta->r == 0. && beta->i == 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L50: */
}
} else if (beta->r != 1. || beta->i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, z__1.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L60: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = l + j * b_dim1;
if (b[i__3].r != 0. || b[i__3].i != 0.) {
i__3 = l + j * b_dim1;
z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i,
z__1.i = alpha->r * b[i__3].i + alpha->i * b[
i__3].r;
temp.r = z__1.r, temp.i = z__1.i;
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
z__2.i = temp.r * a[i__6].i + temp.i * a[
i__6].r;
z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5]
.i + z__2.i;
c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
/* L70: */
}
}
/* L80: */
}
/* L90: */
}
} else if (conja) {
/* Form C := alpha*conjg( A' )*B + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0., temp.i = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
d_cnjg(&z__3, &a[l + i__ * a_dim1]);
i__4 = l + j * b_dim1;
z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i,
z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4]
.r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L100: */
}
if (beta->r == 0. && beta->i == 0.) {
i__3 = i__ + j * c_dim1;
z__1.r = alpha->r * temp.r - alpha->i * temp.i,
z__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
} else {
i__3 = i__ + j * c_dim1;
z__2.r = alpha->r * temp.r - alpha->i * temp.i,
z__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, z__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
}
/* L110: */
}
/* L120: */
}
} else {
/* Form C := alpha*A'*B + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0., temp.i = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
i__4 = l + i__ * a_dim1;
i__5 = l + j * b_dim1;
z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5]
.i, z__2.i = a[i__4].r * b[i__5].i + a[i__4]
.i * b[i__5].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L130: */
}
if (beta->r == 0. && beta->i == 0.) {
i__3 = i__ + j * c_dim1;
z__1.r = alpha->r * temp.r - alpha->i * temp.i,
z__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
} else {
i__3 = i__ + j * c_dim1;
z__2.r = alpha->r * temp.r - alpha->i * temp.i,
z__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, z__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
}
/* L140: */
}
/* L150: */
}
}
} else if (nota) {
if (conjb) {
/* Form C := alpha*A*conjg( B' ) + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (beta->r == 0. && beta->i == 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L160: */
}
} else if (beta->r != 1. || beta->i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, z__1.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L170: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * b_dim1;
if (b[i__3].r != 0. || b[i__3].i != 0.) {
d_cnjg(&z__2, &b[j + l * b_dim1]);
z__1.r = alpha->r * z__2.r - alpha->i * z__2.i,
z__1.i = alpha->r * z__2.i + alpha->i *
z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
z__2.i = temp.r * a[i__6].i + temp.i * a[
i__6].r;
z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5]
.i + z__2.i;
c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
/* L180: */
}
}
/* L190: */
}
/* L200: */
}
} else {
/* Form C := alpha*A*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (beta->r == 0. && beta->i == 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L210: */
}
} else if (beta->r != 1. || beta->i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, z__1.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L220: */
}
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * b_dim1;
if (b[i__3].r != 0. || b[i__3].i != 0.) {
i__3 = j + l * b_dim1;
z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i,
z__1.i = alpha->r * b[i__3].i + alpha->i * b[
i__3].r;
temp.r = z__1.r, temp.i = z__1.i;
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
z__2.i = temp.r * a[i__6].i + temp.i * a[
i__6].r;
z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5]
.i + z__2.i;
c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
/* L230: */
}
}
/* L240: */
}
/* L250: */
}
}
} else if (conja) {
if (conjb) {
/* Form C := alpha*conjg( A' )*conjg( B' ) + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0., temp.i = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
d_cnjg(&z__3, &a[l + i__ * a_dim1]);
d_cnjg(&z__4, &b[j + l * b_dim1]);
z__2.r = z__3.r * z__4.r - z__3.i * z__4.i, z__2.i =
z__3.r * z__4.i + z__3.i * z__4.r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L260: */
}
if (beta->r == 0. && beta->i == 0.) {
i__3 = i__ + j * c_dim1;
z__1.r = alpha->r * temp.r - alpha->i * temp.i,
z__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
} else {
i__3 = i__ + j * c_dim1;
z__2.r = alpha->r * temp.r - alpha->i * temp.i,
z__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, z__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
}
/* L270: */
}
/* L280: */
}
} else {
/* Form C := alpha*conjg( A' )*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0., temp.i = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
d_cnjg(&z__3, &a[l + i__ * a_dim1]);
i__4 = j + l * b_dim1;
z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i,
z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4]
.r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L290: */
}
if (beta->r == 0. && beta->i == 0.) {
i__3 = i__ + j * c_dim1;
z__1.r = alpha->r * temp.r - alpha->i * temp.i,
z__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
} else {
i__3 = i__ + j * c_dim1;
z__2.r = alpha->r * temp.r - alpha->i * temp.i,
z__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, z__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
}
/* L300: */
}
/* L310: */
}
}
} else {
if (conjb) {
/* Form C := alpha*A'*conjg( B' ) + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0., temp.i = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
i__4 = l + i__ * a_dim1;
d_cnjg(&z__3, &b[j + l * b_dim1]);
z__2.r = a[i__4].r * z__3.r - a[i__4].i * z__3.i,
z__2.i = a[i__4].r * z__3.i + a[i__4].i *
z__3.r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L320: */
}
if (beta->r == 0. && beta->i == 0.) {
i__3 = i__ + j * c_dim1;
z__1.r = alpha->r * temp.r - alpha->i * temp.i,
z__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
} else {
i__3 = i__ + j * c_dim1;
z__2.r = alpha->r * temp.r - alpha->i * temp.i,
z__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, z__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
}
/* L330: */
}
/* L340: */
}
} else {
/* Form C := alpha*A'*B' + beta*C */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0., temp.i = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
i__4 = l + i__ * a_dim1;
i__5 = j + l * b_dim1;
z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5]
.i, z__2.i = a[i__4].r * b[i__5].i + a[i__4]
.i * b[i__5].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L350: */
}
if (beta->r == 0. && beta->i == 0.) {
i__3 = i__ + j * c_dim1;
z__1.r = alpha->r * temp.r - alpha->i * temp.i,
z__1.i = alpha->r * temp.i + alpha->i *
temp.r;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
} else {
i__3 = i__ + j * c_dim1;
z__2.r = alpha->r * temp.r - alpha->i * temp.i,
z__2.i = alpha->r * temp.i + alpha->i *
temp.r;
i__4 = i__ + j * c_dim1;
z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4]
.i, z__3.i = beta->r * c__[i__4].i + beta->i *
c__[i__4].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
}
/* L360: */
}
/* L370: */
}
}
}
return 0;
/* End of ZGEMM . */
} /* zgemm_ */
/* Subroutine */ int zgemv_(char *trans, integer *m, integer *n,
doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex *
x, integer *incx, doublecomplex *beta, doublecomplex *y, integer *
incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1, z__2, z__3;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static doublecomplex temp;
static integer lenx, leny;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical noconj;
/*
Purpose
=======
ZGEMV performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or
y := alpha*conjg( A' )*x + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an
m by n matrix.
Arguments
==========
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
X - COMPLEX*16 array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
Before entry, the incremented array X must contain the
vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - COMPLEX*16 .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - COMPLEX*16 array of DIMENSION at least
( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
and at least
( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
Before entry with BETA non-zero, the incremented array Y
must contain the vector y. On exit, Y is overwritten by the
updated vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")
) {
info = 1;
} else if (*m < 0) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*lda < max(1,*m)) {
info = 6;
} else if (*incx == 0) {
info = 8;
} else if (*incy == 0) {
info = 11;
}
if (info != 0) {
xerbla_("ZGEMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r ==
1. && beta->i == 0.)) {
return 0;
}
noconj = lsame_(trans, "T");
/*
Set LENX and LENY, the lengths of the vectors x and y, and set
up the start points in X and Y.
*/
if (lsame_(trans, "N")) {
lenx = *n;
leny = *m;
} else {
lenx = *m;
leny = *n;
}
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (lenx - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (leny - 1) * *incy;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
First form y := beta*y.
*/
if (beta->r != 1. || beta->i != 0.) {
if (*incy == 1) {
if (beta->r == 0. && beta->i == 0.) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
y[i__2].r = 0., y[i__2].i = 0.;
/* L10: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
/* L20: */
}
}
} else {
iy = ky;
if (beta->r == 0. && beta->i == 0.) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
y[i__2].r = 0., y[i__2].i = 0.;
iy += *incy;
/* L30: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
i__3 = iy;
z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
iy += *incy;
/* L40: */
}
}
}
}
if (alpha->r == 0. && alpha->i == 0.) {
return 0;
}
if (lsame_(trans, "N")) {
/* Form y := alpha*A*x + y. */
jx = kx;
if (*incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
if (x[i__2].r != 0. || x[i__2].i != 0.) {
i__2 = jx;
z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
temp.r = z__1.r, temp.i = z__1.i;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__ + j * a_dim1;
z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i +
z__2.i;
y[i__3].r = z__1.r, y[i__3].i = z__1.i;
/* L50: */
}
}
jx += *incx;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
if (x[i__2].r != 0. || x[i__2].i != 0.) {
i__2 = jx;
z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
temp.r = z__1.r, temp.i = z__1.i;
iy = ky;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = iy;
i__4 = iy;
i__5 = i__ + j * a_dim1;
z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i +
z__2.i;
y[i__3].r = z__1.r, y[i__3].i = z__1.i;
iy += *incy;
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
} else {
/* Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. */
jy = ky;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp.r = 0., temp.i = 0.;
if (noconj) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__;
z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4]
.i, z__2.i = a[i__3].r * x[i__4].i + a[i__3]
.i * x[i__4].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L90: */
}
} else {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__3 = i__;
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i,
z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3]
.r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L100: */
}
}
i__2 = jy;
i__3 = jy;
z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i =
alpha->r * temp.i + alpha->i * temp.r;
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
jy += *incy;
/* L110: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp.r = 0., temp.i = 0.;
ix = kx;
if (noconj) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = ix;
z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4]
.i, z__2.i = a[i__3].r * x[i__4].i + a[i__3]
.i * x[i__4].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix += *incx;
/* L120: */
}
} else {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__3 = ix;
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i,
z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3]
.r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix += *incx;
/* L130: */
}
}
i__2 = jy;
i__3 = jy;
z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i =
alpha->r * temp.i + alpha->i * temp.r;
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
jy += *incy;
/* L140: */
}
}
}
return 0;
/* End of ZGEMV . */
} /* zgemv_ */
/* Subroutine */ int zgerc_(integer *m, integer *n, doublecomplex *alpha,
doublecomplex *x, integer *incx, doublecomplex *y, integer *incy,
doublecomplex *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1, z__2;
/* Local variables */
static integer i__, j, ix, jy, kx, info;
static doublecomplex temp;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
ZGERC performs the rank 1 operation
A := alpha*x*conjg( y' ) + A,
where alpha is a scalar, x is an m element vector, y is an n element
vector and A is an m by n matrix.
Arguments
==========
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - COMPLEX*16 array of dimension at least
( 1 + ( m - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the m
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients. On exit, A is
overwritten by the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
info = 0;
if (*m < 0) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*m)) {
info = 9;
}
if (info != 0) {
xerbla_("ZGERC ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0.) {
return 0;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (*incy > 0) {
jy = 1;
} else {
jy = 1 - (*n - 1) * *incy;
}
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jy;
if (y[i__2].r != 0. || y[i__2].i != 0.) {
d_cnjg(&z__2, &y[jy]);
z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i =
alpha->r * z__2.i + alpha->i * z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = i__;
z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i =
x[i__5].r * temp.i + x[i__5].i * temp.r;
z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L10: */
}
}
jy += *incy;
/* L20: */
}
} else {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*m - 1) * *incx;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jy;
if (y[i__2].r != 0. || y[i__2].i != 0.) {
d_cnjg(&z__2, &y[jy]);
z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i =
alpha->r * z__2.i + alpha->i * z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
ix = kx;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = ix;
z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i =
x[i__5].r * temp.i + x[i__5].i * temp.r;
z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
ix += *incx;
/* L30: */
}
}
jy += *incy;
/* L40: */
}
}
return 0;
/* End of ZGERC . */
} /* zgerc_ */
/* Subroutine */ int zgeru_(integer *m, integer *n, doublecomplex *alpha,
doublecomplex *x, integer *incx, doublecomplex *y, integer *incy,
doublecomplex *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1, z__2;
/* Local variables */
static integer i__, j, ix, jy, kx, info;
static doublecomplex temp;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
ZGERU performs the rank 1 operation
A := alpha*x*y' + A,
where alpha is a scalar, x is an m element vector, y is an n element
vector and A is an m by n matrix.
Arguments
==========
M - INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - COMPLEX*16 array of dimension at least
( 1 + ( m - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the m
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, n ).
Before entry, the leading m by n part of the array A must
contain the matrix of coefficients. On exit, A is
overwritten by the updated matrix.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
info = 0;
if (*m < 0) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*m)) {
info = 9;
}
if (info != 0) {
xerbla_("ZGERU ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0.) {
return 0;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (*incy > 0) {
jy = 1;
} else {
jy = 1 - (*n - 1) * *incy;
}
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jy;
if (y[i__2].r != 0. || y[i__2].i != 0.) {
i__2 = jy;
z__1.r = alpha->r * y[i__2].r - alpha->i * y[i__2].i, z__1.i =
alpha->r * y[i__2].i + alpha->i * y[i__2].r;
temp.r = z__1.r, temp.i = z__1.i;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = i__;
z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i =
x[i__5].r * temp.i + x[i__5].i * temp.r;
z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L10: */
}
}
jy += *incy;
/* L20: */
}
} else {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*m - 1) * *incx;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jy;
if (y[i__2].r != 0. || y[i__2].i != 0.) {
i__2 = jy;
z__1.r = alpha->r * y[i__2].r - alpha->i * y[i__2].i, z__1.i =
alpha->r * y[i__2].i + alpha->i * y[i__2].r;
temp.r = z__1.r, temp.i = z__1.i;
ix = kx;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = ix;
z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i =
x[i__5].r * temp.i + x[i__5].i * temp.r;
z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
ix += *incx;
/* L30: */
}
}
jy += *incy;
/* L40: */
}
}
return 0;
/* End of ZGERU . */
} /* zgeru_ */
/* Subroutine */ int zhemv_(char *uplo, integer *n, doublecomplex *alpha,
doublecomplex *a, integer *lda, doublecomplex *x, integer *incx,
doublecomplex *beta, doublecomplex *y, integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1;
doublecomplex z__1, z__2, z__3, z__4;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static doublecomplex temp1, temp2;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
ZHEMV performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n hermitian matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the hermitian matrix and the strictly
lower triangular part of A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the hermitian matrix and the strictly
upper triangular part of A is not referenced.
Note that the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
BETA - COMPLEX*16 .
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
Y - COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y. On exit, Y is overwritten by the updated
vector y.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*lda < max(1,*n)) {
info = 5;
} else if (*incx == 0) {
info = 7;
} else if (*incy == 0) {
info = 10;
}
if (info != 0) {
xerbla_("ZHEMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. &&
beta->i == 0.)) {
return 0;
}
/* Set up the start points in X and Y. */
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through the triangular part
of A.
First form y := beta*y.
*/
if (beta->r != 1. || beta->i != 0.) {
if (*incy == 1) {
if (beta->r == 0. && beta->i == 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
y[i__2].r = 0., y[i__2].i = 0.;
/* L10: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
/* L20: */
}
}
} else {
iy = ky;
if (beta->r == 0. && beta->i == 0.) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
y[i__2].r = 0., y[i__2].i = 0.;
iy += *incy;
/* L30: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
i__3 = iy;
z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
iy += *incy;
/* L40: */
}
}
}
}
if (alpha->r == 0. && alpha->i == 0.) {
return 0;
}
if (lsame_(uplo, "U")) {
/* Form y when A is stored in upper triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
temp1.r = z__1.r, temp1.i = z__1.i;
temp2.r = 0., temp2.i = 0.;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__ + j * a_dim1;
z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
.r;
z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
y[i__3].r = z__1.r, y[i__3].i = z__1.i;
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__3 = i__;
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
z__3.r * x[i__3].i + z__3.i * x[i__3].r;
z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
temp2.r = z__1.r, temp2.i = z__1.i;
/* L50: */
}
i__2 = j;
i__3 = j;
i__4 = j + j * a_dim1;
d__1 = a[i__4].r;
z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i;
z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
alpha->r * temp2.i + alpha->i * temp2.r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
/* L60: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
temp1.r = z__1.r, temp1.i = z__1.i;
temp2.r = 0., temp2.i = 0.;
ix = kx;
iy = ky;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = iy;
i__4 = iy;
i__5 = i__ + j * a_dim1;
z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
.r;
z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
y[i__3].r = z__1.r, y[i__3].i = z__1.i;
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__3 = ix;
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
z__3.r * x[i__3].i + z__3.i * x[i__3].r;
z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
temp2.r = z__1.r, temp2.i = z__1.i;
ix += *incx;
iy += *incy;
/* L70: */
}
i__2 = jy;
i__3 = jy;
i__4 = j + j * a_dim1;
d__1 = a[i__4].r;
z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i;
z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
alpha->r * temp2.i + alpha->i * temp2.r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
jx += *incx;
jy += *incy;
/* L80: */
}
}
} else {
/* Form y when A is stored in lower triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
temp1.r = z__1.r, temp1.i = z__1.i;
temp2.r = 0., temp2.i = 0.;
i__2 = j;
i__3 = j;
i__4 = j + j * a_dim1;
d__1 = a[i__4].r;
z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__ + j * a_dim1;
z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
.r;
z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
y[i__3].r = z__1.r, y[i__3].i = z__1.i;
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__3 = i__;
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
z__3.r * x[i__3].i + z__3.i * x[i__3].r;
z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
temp2.r = z__1.r, temp2.i = z__1.i;
/* L90: */
}
i__2 = j;
i__3 = j;
z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
alpha->r * temp2.i + alpha->i * temp2.r;
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
/* L100: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
temp1.r = z__1.r, temp1.i = z__1.i;
temp2.r = 0., temp2.i = 0.;
i__2 = jy;
i__3 = jy;
i__4 = j + j * a_dim1;
d__1 = a[i__4].r;
z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
ix = jx;
iy = jy;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
iy += *incy;
i__3 = iy;
i__4 = iy;
i__5 = i__ + j * a_dim1;
z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
.r;
z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
y[i__3].r = z__1.r, y[i__3].i = z__1.i;
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__3 = ix;
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i =
z__3.r * x[i__3].i + z__3.i * x[i__3].r;
z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
temp2.r = z__1.r, temp2.i = z__1.i;
/* L110: */
}
i__2 = jy;
i__3 = jy;
z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
alpha->r * temp2.i + alpha->i * temp2.r;
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
jx += *incx;
jy += *incy;
/* L120: */
}
}
}
return 0;
/* End of ZHEMV . */
} /* zhemv_ */
/* Subroutine */ int zher2_(char *uplo, integer *n, doublecomplex *alpha,
doublecomplex *x, integer *incx, doublecomplex *y, integer *incy,
doublecomplex *a, integer *lda)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
doublereal d__1;
doublecomplex z__1, z__2, z__3, z__4;
/* Local variables */
static integer i__, j, ix, iy, jx, jy, kx, ky, info;
static doublecomplex temp1, temp2;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
ZHER2 performs the hermitian rank 2 operation
A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
where alpha is a scalar, x and y are n element vectors and A is an n
by n hermitian matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of A
is to be referenced.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
X - COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Y - COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.
Unchanged on exit.
INCY - INTEGER.
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the hermitian matrix and the strictly
lower triangular part of A is not referenced. On exit, the
upper triangular part of the array A is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the hermitian matrix and the strictly
upper triangular part of A is not referenced. On exit, the
lower triangular part of the array A is overwritten by the
lower triangular part of the updated matrix.
Note that the imaginary parts of the diagonal elements need
not be set, they are assumed to be zero, and on exit they
are set to zero.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
--x;
--y;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*incx == 0) {
info = 5;
} else if (*incy == 0) {
info = 7;
} else if (*lda < max(1,*n)) {
info = 9;
}
if (info != 0) {
xerbla_("ZHER2 ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || alpha->r == 0. && alpha->i == 0.) {
return 0;
}
/*
Set up the start points in X and Y if the increments are not both
unity.
*/
if (*incx != 1 || *incy != 1) {
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (*n - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (*n - 1) * *incy;
}
jx = kx;
jy = ky;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through the triangular part
of A.
*/
if (lsame_(uplo, "U")) {
/* Form A when A is stored in the upper triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
i__3 = j;
if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. ||
y[i__3].i != 0.)) {
d_cnjg(&z__2, &y[j]);
z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i =
alpha->r * z__2.i + alpha->i * z__2.r;
temp1.r = z__1.r, temp1.i = z__1.i;
i__2 = j;
z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
d_cnjg(&z__1, &z__2);
temp2.r = z__1.r, temp2.i = z__1.i;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = i__;
z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i,
z__3.i = x[i__5].r * temp1.i + x[i__5].i *
temp1.r;
z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i +
z__3.i;
i__6 = i__;
z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i,
z__4.i = y[i__6].r * temp2.i + y[i__6].i *
temp2.r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L10: */
}
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
i__4 = j;
z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i,
z__2.i = x[i__4].r * temp1.i + x[i__4].i *
temp1.r;
i__5 = j;
z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i,
z__3.i = y[i__5].r * temp2.i + y[i__5].i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
d__1 = a[i__3].r + z__1.r;
a[i__2].r = d__1, a[i__2].i = 0.;
} else {
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
i__3 = jy;
if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. ||
y[i__3].i != 0.)) {
d_cnjg(&z__2, &y[jy]);
z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i =
alpha->r * z__2.i + alpha->i * z__2.r;
temp1.r = z__1.r, temp1.i = z__1.i;
i__2 = jx;
z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
d_cnjg(&z__1, &z__2);
temp2.r = z__1.r, temp2.i = z__1.i;
ix = kx;
iy = ky;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = ix;
z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i,
z__3.i = x[i__5].r * temp1.i + x[i__5].i *
temp1.r;
z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i +
z__3.i;
i__6 = iy;
z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i,
z__4.i = y[i__6].r * temp2.i + y[i__6].i *
temp2.r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
ix += *incx;
iy += *incy;
/* L30: */
}
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
i__4 = jx;
z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i,
z__2.i = x[i__4].r * temp1.i + x[i__4].i *
temp1.r;
i__5 = jy;
z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i,
z__3.i = y[i__5].r * temp2.i + y[i__5].i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
d__1 = a[i__3].r + z__1.r;
a[i__2].r = d__1, a[i__2].i = 0.;
} else {
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
}
jx += *incx;
jy += *incy;
/* L40: */
}
}
} else {
/* Form A when A is stored in the lower triangle. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
i__3 = j;
if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. ||
y[i__3].i != 0.)) {
d_cnjg(&z__2, &y[j]);
z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i =
alpha->r * z__2.i + alpha->i * z__2.r;
temp1.r = z__1.r, temp1.i = z__1.i;
i__2 = j;
z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
d_cnjg(&z__1, &z__2);
temp2.r = z__1.r, temp2.i = z__1.i;
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
i__4 = j;
z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i,
z__2.i = x[i__4].r * temp1.i + x[i__4].i *
temp1.r;
i__5 = j;
z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i,
z__3.i = y[i__5].r * temp2.i + y[i__5].i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
d__1 = a[i__3].r + z__1.r;
a[i__2].r = d__1, a[i__2].i = 0.;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = i__;
z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i,
z__3.i = x[i__5].r * temp1.i + x[i__5].i *
temp1.r;
z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i +
z__3.i;
i__6 = i__;
z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i,
z__4.i = y[i__6].r * temp2.i + y[i__6].i *
temp2.r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L50: */
}
} else {
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
i__3 = jy;
if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. ||
y[i__3].i != 0.)) {
d_cnjg(&z__2, &y[jy]);
z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i =
alpha->r * z__2.i + alpha->i * z__2.r;
temp1.r = z__1.r, temp1.i = z__1.i;
i__2 = jx;
z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
d_cnjg(&z__1, &z__2);
temp2.r = z__1.r, temp2.i = z__1.i;
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
i__4 = jx;
z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i,
z__2.i = x[i__4].r * temp1.i + x[i__4].i *
temp1.r;
i__5 = jy;
z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i,
z__3.i = y[i__5].r * temp2.i + y[i__5].i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
d__1 = a[i__3].r + z__1.r;
a[i__2].r = d__1, a[i__2].i = 0.;
ix = jx;
iy = jy;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
iy += *incy;
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = ix;
z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i,
z__3.i = x[i__5].r * temp1.i + x[i__5].i *
temp1.r;
z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i +
z__3.i;
i__6 = iy;
z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i,
z__4.i = y[i__6].r * temp2.i + y[i__6].i *
temp2.r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L70: */
}
} else {
i__2 = j + j * a_dim1;
i__3 = j + j * a_dim1;
d__1 = a[i__3].r;
a[i__2].r = d__1, a[i__2].i = 0.;
}
jx += *incx;
jy += *incy;
/* L80: */
}
}
}
return 0;
/* End of ZHER2 . */
} /* zher2_ */
/* Subroutine */ int zher2k_(char *uplo, char *trans, integer *n, integer *k,
doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex *
b, integer *ldb, doublereal *beta, doublecomplex *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3, i__4, i__5, i__6, i__7;
doublereal d__1;
doublecomplex z__1, z__2, z__3, z__4, z__5, z__6;
/* Local variables */
static integer i__, j, l, info;
static doublecomplex temp1, temp2;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
ZHER2K performs one of the hermitian rank 2k operations
C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,
or
C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C,
where alpha and beta are scalars with beta real, C is an n by n
hermitian matrix and A and B are n by k matrices in the first case
and k by n matrices in the second case.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*conjg( B' ) +
conjg( alpha )*B*conjg( A' ) +
beta*C.
TRANS = 'C' or 'c' C := alpha*conjg( A' )*B +
conjg( alpha )*conjg( B' )*A +
beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrices A and B, and on entry with
TRANS = 'C' or 'c', K specifies the number of rows of the
matrices A and B. K must be at least zero.
Unchanged on exit.
ALPHA - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array B must contain the matrix B, otherwise
the leading k by n part of the array B must contain the
matrix B.
Unchanged on exit.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDB must be at least max( 1, n ), otherwise LDB must
be at least max( 1, k ).
Unchanged on exit.
BETA - DOUBLE PRECISION .
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - COMPLEX*16 array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the hermitian matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the hermitian matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
Note that the imaginary parts of the diagonal elements need
not be set, they are assumed to be zero, and on exit they
are set to zero.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
-- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
Ed Anderson, Cray Research Inc.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
if (lsame_(trans, "N")) {
nrowa = *n;
} else {
nrowa = *k;
}
upper = lsame_(uplo, "U");
info = 0;
if (! upper && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"C")) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*k < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldb < max(1,nrowa)) {
info = 9;
} else if (*ldc < max(1,*n)) {
info = 12;
}
if (info != 0) {
xerbla_("ZHER2K", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) && *beta ==
1.) {
return 0;
}
/* And when alpha.eq.zero. */
if (alpha->r == 0. && alpha->i == 0.) {
if (upper) {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
i__4].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L30: */
}
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = *beta * c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
/* L40: */
}
}
} else {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = *beta * c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
i__4].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L70: */
}
/* L80: */
}
}
}
return 0;
}
/* Start the operations. */
if (lsame_(trans, "N")) {
/*
Form C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) +
C.
*/
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L90: */
}
} else if (*beta != 1.) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
i__4].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L100: */
}
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = *beta * c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * a_dim1;
i__4 = j + l * b_dim1;
if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r !=
0. || b[i__4].i != 0.)) {
d_cnjg(&z__2, &b[j + l * b_dim1]);
z__1.r = alpha->r * z__2.r - alpha->i * z__2.i,
z__1.i = alpha->r * z__2.i + alpha->i *
z__2.r;
temp1.r = z__1.r, temp1.i = z__1.i;
i__3 = j + l * a_dim1;
z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i,
z__2.i = alpha->r * a[i__3].i + alpha->i * a[
i__3].r;
d_cnjg(&z__1, &z__2);
temp2.r = z__1.r, temp2.i = z__1.i;
i__3 = j - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
z__3.r = a[i__6].r * temp1.r - a[i__6].i *
temp1.i, z__3.i = a[i__6].r * temp1.i + a[
i__6].i * temp1.r;
z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5]
.i + z__3.i;
i__7 = i__ + l * b_dim1;
z__4.r = b[i__7].r * temp2.r - b[i__7].i *
temp2.i, z__4.i = b[i__7].r * temp2.i + b[
i__7].i * temp2.r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i +
z__4.i;
c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
/* L110: */
}
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
i__5 = j + l * a_dim1;
z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i,
z__2.i = a[i__5].r * temp1.i + a[i__5].i *
temp1.r;
i__6 = j + l * b_dim1;
z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i,
z__3.i = b[i__6].r * temp2.i + b[i__6].i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
d__1 = c__[i__4].r + z__1.r;
c__[i__3].r = d__1, c__[i__3].i = 0.;
}
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L140: */
}
} else if (*beta != 1.) {
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
i__4].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L150: */
}
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = *beta * c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * a_dim1;
i__4 = j + l * b_dim1;
if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r !=
0. || b[i__4].i != 0.)) {
d_cnjg(&z__2, &b[j + l * b_dim1]);
z__1.r = alpha->r * z__2.r - alpha->i * z__2.i,
z__1.i = alpha->r * z__2.i + alpha->i *
z__2.r;
temp1.r = z__1.r, temp1.i = z__1.i;
i__3 = j + l * a_dim1;
z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i,
z__2.i = alpha->r * a[i__3].i + alpha->i * a[
i__3].r;
d_cnjg(&z__1, &z__2);
temp2.r = z__1.r, temp2.i = z__1.i;
i__3 = *n;
for (i__ = j + 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
z__3.r = a[i__6].r * temp1.r - a[i__6].i *
temp1.i, z__3.i = a[i__6].r * temp1.i + a[
i__6].i * temp1.r;
z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5]
.i + z__3.i;
i__7 = i__ + l * b_dim1;
z__4.r = b[i__7].r * temp2.r - b[i__7].i *
temp2.i, z__4.i = b[i__7].r * temp2.i + b[
i__7].i * temp2.r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i +
z__4.i;
c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
/* L160: */
}
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
i__5 = j + l * a_dim1;
z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i,
z__2.i = a[i__5].r * temp1.i + a[i__5].i *
temp1.r;
i__6 = j + l * b_dim1;
z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i,
z__3.i = b[i__6].r * temp2.i + b[i__6].i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
d__1 = c__[i__4].r + z__1.r;
c__[i__3].r = d__1, c__[i__3].i = 0.;
}
/* L170: */
}
/* L180: */
}
}
} else {
/*
Form C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A +
C.
*/
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
temp1.r = 0., temp1.i = 0.;
temp2.r = 0., temp2.i = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
d_cnjg(&z__3, &a[l + i__ * a_dim1]);
i__4 = l + j * b_dim1;
z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i,
z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4]
.r;
z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i;
temp1.r = z__1.r, temp1.i = z__1.i;
d_cnjg(&z__3, &b[l + i__ * b_dim1]);
i__4 = l + j * a_dim1;
z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i,
z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4]
.r;
z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
temp2.r = z__1.r, temp2.i = z__1.i;
/* L190: */
}
if (i__ == j) {
if (*beta == 0.) {
i__3 = j + j * c_dim1;
z__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
z__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
d_cnjg(&z__4, alpha);
z__3.r = z__4.r * temp2.r - z__4.i * temp2.i,
z__3.i = z__4.r * temp2.i + z__4.i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
d__1 = z__1.r;
c__[i__3].r = d__1, c__[i__3].i = 0.;
} else {
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
z__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
z__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
d_cnjg(&z__4, alpha);
z__3.r = z__4.r * temp2.r - z__4.i * temp2.i,
z__3.i = z__4.r * temp2.i + z__4.i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
d__1 = *beta * c__[i__4].r + z__1.r;
c__[i__3].r = d__1, c__[i__3].i = 0.;
}
} else {
if (*beta == 0.) {
i__3 = i__ + j * c_dim1;
z__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
z__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
d_cnjg(&z__4, alpha);
z__3.r = z__4.r * temp2.r - z__4.i * temp2.i,
z__3.i = z__4.r * temp2.i + z__4.i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
} else {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__3.r = *beta * c__[i__4].r, z__3.i = *beta *
c__[i__4].i;
z__4.r = alpha->r * temp1.r - alpha->i * temp1.i,
z__4.i = alpha->r * temp1.i + alpha->i *
temp1.r;
z__2.r = z__3.r + z__4.r, z__2.i = z__3.i +
z__4.i;
d_cnjg(&z__6, alpha);
z__5.r = z__6.r * temp2.r - z__6.i * temp2.i,
z__5.i = z__6.r * temp2.i + z__6.i *
temp2.r;
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i +
z__5.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
}
}
/* L200: */
}
/* L210: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
temp1.r = 0., temp1.i = 0.;
temp2.r = 0., temp2.i = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
d_cnjg(&z__3, &a[l + i__ * a_dim1]);
i__4 = l + j * b_dim1;
z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i,
z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4]
.r;
z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i;
temp1.r = z__1.r, temp1.i = z__1.i;
d_cnjg(&z__3, &b[l + i__ * b_dim1]);
i__4 = l + j * a_dim1;
z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i,
z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4]
.r;
z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
temp2.r = z__1.r, temp2.i = z__1.i;
/* L220: */
}
if (i__ == j) {
if (*beta == 0.) {
i__3 = j + j * c_dim1;
z__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
z__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
d_cnjg(&z__4, alpha);
z__3.r = z__4.r * temp2.r - z__4.i * temp2.i,
z__3.i = z__4.r * temp2.i + z__4.i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
d__1 = z__1.r;
c__[i__3].r = d__1, c__[i__3].i = 0.;
} else {
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
z__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
z__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
d_cnjg(&z__4, alpha);
z__3.r = z__4.r * temp2.r - z__4.i * temp2.i,
z__3.i = z__4.r * temp2.i + z__4.i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
d__1 = *beta * c__[i__4].r + z__1.r;
c__[i__3].r = d__1, c__[i__3].i = 0.;
}
} else {
if (*beta == 0.) {
i__3 = i__ + j * c_dim1;
z__2.r = alpha->r * temp1.r - alpha->i * temp1.i,
z__2.i = alpha->r * temp1.i + alpha->i *
temp1.r;
d_cnjg(&z__4, alpha);
z__3.r = z__4.r * temp2.r - z__4.i * temp2.i,
z__3.i = z__4.r * temp2.i + z__4.i *
temp2.r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
z__3.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
} else {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__3.r = *beta * c__[i__4].r, z__3.i = *beta *
c__[i__4].i;
z__4.r = alpha->r * temp1.r - alpha->i * temp1.i,
z__4.i = alpha->r * temp1.i + alpha->i *
temp1.r;
z__2.r = z__3.r + z__4.r, z__2.i = z__3.i +
z__4.i;
d_cnjg(&z__6, alpha);
z__5.r = z__6.r * temp2.r - z__6.i * temp2.i,
z__5.i = z__6.r * temp2.i + z__6.i *
temp2.r;
z__1.r = z__2.r + z__5.r, z__1.i = z__2.i +
z__5.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
}
}
/* L230: */
}
/* L240: */
}
}
}
return 0;
/* End of ZHER2K. */
} /* zher2k_ */
/* Subroutine */ int zherk_(char *uplo, char *trans, integer *n, integer *k,
doublereal *alpha, doublecomplex *a, integer *lda, doublereal *beta,
doublecomplex *c__, integer *ldc)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4, i__5,
i__6;
doublereal d__1;
doublecomplex z__1, z__2, z__3;
/* Local variables */
static integer i__, j, l, info;
static doublecomplex temp;
extern logical lsame_(char *, char *);
static integer nrowa;
static doublereal rtemp;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
/*
Purpose
=======
ZHERK performs one of the hermitian rank k operations
C := alpha*A*conjg( A' ) + beta*C,
or
C := alpha*conjg( A' )*A + beta*C,
where alpha and beta are real scalars, C is an n by n hermitian
matrix and A is an n by k matrix in the first case and a k by n
matrix in the second case.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*conjg( A' ) + beta*C.
TRANS = 'C' or 'c' C := alpha*conjg( A' )*A + beta*C.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
K - INTEGER.
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrix A, and on entry with
TRANS = 'C' or 'c', K specifies the number of rows of the
matrix A. K must be at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
k when TRANS = 'N' or 'n', and is n otherwise.
Before entry with TRANS = 'N' or 'n', the leading n by k
part of the array A must contain the matrix A, otherwise
the leading k by n part of the array A must contain the
matrix A.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
BETA - DOUBLE PRECISION.
On entry, BETA specifies the scalar beta.
Unchanged on exit.
C - COMPLEX*16 array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the hermitian matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the hermitian matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
Note that the imaginary parts of the diagonal elements need
not be set, they are assumed to be zero, and on exit they
are set to zero.
LDC - INTEGER.
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, n ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
-- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
Ed Anderson, Cray Research Inc.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
if (lsame_(trans, "N")) {
nrowa = *n;
} else {
nrowa = *k;
}
upper = lsame_(uplo, "U");
info = 0;
if (! upper && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"C")) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*k < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldc < max(1,*n)) {
info = 10;
}
if (info != 0) {
xerbla_("ZHERK ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
if (upper) {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
i__4].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L30: */
}
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = *beta * c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
/* L40: */
}
}
} else {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = *beta * c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
i__4].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L70: */
}
/* L80: */
}
}
}
return 0;
}
/* Start the operations. */
if (lsame_(trans, "N")) {
/* Form C := alpha*A*conjg( A' ) + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L90: */
}
} else if (*beta != 1.) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
i__4].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L100: */
}
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = *beta * c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * a_dim1;
if (a[i__3].r != 0. || a[i__3].i != 0.) {
d_cnjg(&z__2, &a[j + l * a_dim1]);
z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
i__3 = j - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
z__2.i = temp.r * a[i__6].i + temp.i * a[
i__6].r;
z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5]
.i + z__2.i;
c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
/* L110: */
}
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
i__5 = i__ + l * a_dim1;
z__1.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__1.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
d__1 = c__[i__4].r + z__1.r;
c__[i__3].r = d__1, c__[i__3].i = 0.;
}
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*beta == 0.) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
c__[i__3].r = 0., c__[i__3].i = 0.;
/* L140: */
}
} else if (*beta != 1.) {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = *beta * c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[
i__4].i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
/* L150: */
}
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
}
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
i__3 = j + l * a_dim1;
if (a[i__3].r != 0. || a[i__3].i != 0.) {
d_cnjg(&z__2, &a[j + l * a_dim1]);
z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
i__3 = j + j * c_dim1;
i__4 = j + j * c_dim1;
i__5 = j + l * a_dim1;
z__1.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__1.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
d__1 = c__[i__4].r + z__1.r;
c__[i__3].r = d__1, c__[i__3].i = 0.;
i__3 = *n;
for (i__ = j + 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * c_dim1;
i__6 = i__ + l * a_dim1;
z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i,
z__2.i = temp.r * a[i__6].i + temp.i * a[
i__6].r;
z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5]
.i + z__2.i;
c__[i__4].r = z__1.r, c__[i__4].i = z__1.i;
/* L160: */
}
}
/* L170: */
}
/* L180: */
}
}
} else {
/* Form C := alpha*conjg( A' )*A + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
temp.r = 0., temp.i = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
d_cnjg(&z__3, &a[l + i__ * a_dim1]);
i__4 = l + j * a_dim1;
z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i,
z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4]
.r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L190: */
}
if (*beta == 0.) {
i__3 = i__ + j * c_dim1;
z__1.r = *alpha * temp.r, z__1.i = *alpha * temp.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
} else {
i__3 = i__ + j * c_dim1;
z__2.r = *alpha * temp.r, z__2.i = *alpha * temp.i;
i__4 = i__ + j * c_dim1;
z__3.r = *beta * c__[i__4].r, z__3.i = *beta * c__[
i__4].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
}
/* L200: */
}
rtemp = 0.;
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
d_cnjg(&z__3, &a[l + j * a_dim1]);
i__3 = l + j * a_dim1;
z__2.r = z__3.r * a[i__3].r - z__3.i * a[i__3].i, z__2.i =
z__3.r * a[i__3].i + z__3.i * a[i__3].r;
z__1.r = rtemp + z__2.r, z__1.i = z__2.i;
rtemp = z__1.r;
/* L210: */
}
if (*beta == 0.) {
i__2 = j + j * c_dim1;
d__1 = *alpha * rtemp;
c__[i__2].r = d__1, c__[i__2].i = 0.;
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = *alpha * rtemp + *beta * c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
}
/* L220: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
rtemp = 0.;
i__2 = *k;
for (l = 1; l <= i__2; ++l) {
d_cnjg(&z__3, &a[l + j * a_dim1]);
i__3 = l + j * a_dim1;
z__2.r = z__3.r * a[i__3].r - z__3.i * a[i__3].i, z__2.i =
z__3.r * a[i__3].i + z__3.i * a[i__3].r;
z__1.r = rtemp + z__2.r, z__1.i = z__2.i;
rtemp = z__1.r;
/* L230: */
}
if (*beta == 0.) {
i__2 = j + j * c_dim1;
d__1 = *alpha * rtemp;
c__[i__2].r = d__1, c__[i__2].i = 0.;
} else {
i__2 = j + j * c_dim1;
i__3 = j + j * c_dim1;
d__1 = *alpha * rtemp + *beta * c__[i__3].r;
c__[i__2].r = d__1, c__[i__2].i = 0.;
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
temp.r = 0., temp.i = 0.;
i__3 = *k;
for (l = 1; l <= i__3; ++l) {
d_cnjg(&z__3, &a[l + i__ * a_dim1]);
i__4 = l + j * a_dim1;
z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i,
z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4]
.r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L240: */
}
if (*beta == 0.) {
i__3 = i__ + j * c_dim1;
z__1.r = *alpha * temp.r, z__1.i = *alpha * temp.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
} else {
i__3 = i__ + j * c_dim1;
z__2.r = *alpha * temp.r, z__2.i = *alpha * temp.i;
i__4 = i__ + j * c_dim1;
z__3.r = *beta * c__[i__4].r, z__3.i = *beta * c__[
i__4].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
}
/* L250: */
}
/* L260: */
}
}
}
return 0;
/* End of ZHERK . */
} /* zherk_ */
/* Subroutine */ int zscal_(integer *n, doublecomplex *za, doublecomplex *zx,
integer *incx)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublecomplex z__1;
/* Local variables */
static integer i__, ix;
/*
Purpose
=======
ZSCAL scales a vector by a constant.
Further Details
===============
jack dongarra, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--zx;
/* Function Body */
if (*n <= 0 || *incx <= 0) {
return 0;
}
if (*incx == 1) {
goto L20;
}
/* code for increment not equal to 1 */
ix = 1;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ix;
i__3 = ix;
z__1.r = za->r * zx[i__3].r - za->i * zx[i__3].i, z__1.i = za->r * zx[
i__3].i + za->i * zx[i__3].r;
zx[i__2].r = z__1.r, zx[i__2].i = z__1.i;
ix += *incx;
/* L10: */
}
return 0;
/* code for increment equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
z__1.r = za->r * zx[i__3].r - za->i * zx[i__3].i, z__1.i = za->r * zx[
i__3].i + za->i * zx[i__3].r;
zx[i__2].r = z__1.r, zx[i__2].i = z__1.i;
/* L30: */
}
return 0;
} /* zscal_ */
/* Subroutine */ int zswap_(integer *n, doublecomplex *zx, integer *incx,
doublecomplex *zy, integer *incy)
{
/* System generated locals */
integer i__1, i__2, i__3;
/* Local variables */
static integer i__, ix, iy;
static doublecomplex ztemp;
/*
Purpose
=======
ZSWAP interchanges two vectors.
Further Details
===============
jack dongarra, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
=====================================================================
*/
/* Parameter adjustments */
--zy;
--zx;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (*incx == 1 && *incy == 1) {
goto L20;
}
/*
code for unequal increments or equal increments not equal
to 1
*/
ix = 1;
iy = 1;
if (*incx < 0) {
ix = (-(*n) + 1) * *incx + 1;
}
if (*incy < 0) {
iy = (-(*n) + 1) * *incy + 1;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ix;
ztemp.r = zx[i__2].r, ztemp.i = zx[i__2].i;
i__2 = ix;
i__3 = iy;
zx[i__2].r = zy[i__3].r, zx[i__2].i = zy[i__3].i;
i__2 = iy;
zy[i__2].r = ztemp.r, zy[i__2].i = ztemp.i;
ix += *incx;
iy += *incy;
/* L10: */
}
return 0;
/* code for both increments equal to 1 */
L20:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
ztemp.r = zx[i__2].r, ztemp.i = zx[i__2].i;
i__2 = i__;
i__3 = i__;
zx[i__2].r = zy[i__3].r, zx[i__2].i = zy[i__3].i;
i__2 = i__;
zy[i__2].r = ztemp.r, zy[i__2].i = ztemp.i;
/* L30: */
}
return 0;
} /* zswap_ */
/* Subroutine */ int ztrmm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, doublecomplex *alpha, doublecomplex *a,
integer *lda, doublecomplex *b, integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5,
i__6;
doublecomplex z__1, z__2, z__3;
/* Local variables */
static integer i__, j, k, info;
static doublecomplex temp;
static logical lside;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical noconj, nounit;
/*
Purpose
=======
ZTRMM performs one of the matrix-matrix operations
B := alpha*op( A )*B, or B := alpha*B*op( A )
where alpha is a scalar, B is an m by n matrix, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ).
Arguments
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) multiplies B from
the left or right as follows:
SIDE = 'L' or 'l' B := alpha*op( A )*B.
SIDE = 'R' or 'r' B := alpha*B*op( A ).
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A'.
TRANSA = 'C' or 'c' op( A ) = conjg( A' ).
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
B - COMPLEX*16 array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the matrix B, and on exit is overwritten by the
transformed matrix.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
lside = lsame_(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
noconj = lsame_(transa, "T");
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
info = 0;
if (! lside && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (! lsame_(transa, "N") && ! lsame_(transa,
"T") && ! lsame_(transa, "C")) {
info = 3;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < max(1,nrowa)) {
info = 9;
} else if (*ldb < max(1,*m)) {
info = 11;
}
if (info != 0) {
xerbla_("ZTRMM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (alpha->r == 0. && alpha->i == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0., b[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (lsame_(transa, "N")) {
/* Form B := alpha*A*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * b_dim1;
if (b[i__3].r != 0. || b[i__3].i != 0.) {
i__3 = k + j * b_dim1;
z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3]
.i, z__1.i = alpha->r * b[i__3].i +
alpha->i * b[i__3].r;
temp.r = z__1.r, temp.i = z__1.i;
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = i__ + k * a_dim1;
z__2.r = temp.r * a[i__6].r - temp.i * a[i__6]
.i, z__2.i = temp.r * a[i__6].i +
temp.i * a[i__6].r;
z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5]
.i + z__2.i;
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L30: */
}
if (nounit) {
i__3 = k + k * a_dim1;
z__1.r = temp.r * a[i__3].r - temp.i * a[i__3]
.i, z__1.i = temp.r * a[i__3].i +
temp.i * a[i__3].r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__3 = k + j * b_dim1;
b[i__3].r = temp.r, b[i__3].i = temp.i;
}
/* L40: */
}
/* L50: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (k = *m; k >= 1; --k) {
i__2 = k + j * b_dim1;
if (b[i__2].r != 0. || b[i__2].i != 0.) {
i__2 = k + j * b_dim1;
z__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2]
.i, z__1.i = alpha->r * b[i__2].i +
alpha->i * b[i__2].r;
temp.r = z__1.r, temp.i = z__1.i;
i__2 = k + j * b_dim1;
b[i__2].r = temp.r, b[i__2].i = temp.i;
if (nounit) {
i__2 = k + j * b_dim1;
i__3 = k + j * b_dim1;
i__4 = k + k * a_dim1;
z__1.r = b[i__3].r * a[i__4].r - b[i__3].i *
a[i__4].i, z__1.i = b[i__3].r * a[
i__4].i + b[i__3].i * a[i__4].r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
}
i__2 = *m;
for (i__ = k + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = i__ + k * a_dim1;
z__2.r = temp.r * a[i__5].r - temp.i * a[i__5]
.i, z__2.i = temp.r * a[i__5].i +
temp.i * a[i__5].r;
z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4]
.i + z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L60: */
}
}
/* L70: */
}
/* L80: */
}
}
} else {
/* Form B := alpha*A'*B or B := alpha*conjg( A' )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
i__2 = i__ + j * b_dim1;
temp.r = b[i__2].r, temp.i = b[i__2].i;
if (noconj) {
if (nounit) {
i__2 = i__ + i__ * a_dim1;
z__1.r = temp.r * a[i__2].r - temp.i * a[i__2]
.i, z__1.i = temp.r * a[i__2].i +
temp.i * a[i__2].r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = i__ - 1;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * a_dim1;
i__4 = k + j * b_dim1;
z__2.r = a[i__3].r * b[i__4].r - a[i__3].i *
b[i__4].i, z__2.i = a[i__3].r * b[
i__4].i + a[i__3].i * b[i__4].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L90: */
}
} else {
if (nounit) {
d_cnjg(&z__2, &a[i__ + i__ * a_dim1]);
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
z__1.i = temp.r * z__2.i + temp.i *
z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = i__ - 1;
for (k = 1; k <= i__2; ++k) {
d_cnjg(&z__3, &a[k + i__ * a_dim1]);
i__3 = k + j * b_dim1;
z__2.r = z__3.r * b[i__3].r - z__3.i * b[i__3]
.i, z__2.i = z__3.r * b[i__3].i +
z__3.i * b[i__3].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L100: */
}
}
i__2 = i__ + j * b_dim1;
z__1.r = alpha->r * temp.r - alpha->i * temp.i,
z__1.i = alpha->r * temp.i + alpha->i *
temp.r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L110: */
}
/* L120: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
temp.r = b[i__3].r, temp.i = b[i__3].i;
if (noconj) {
if (nounit) {
i__3 = i__ + i__ * a_dim1;
z__1.r = temp.r * a[i__3].r - temp.i * a[i__3]
.i, z__1.i = temp.r * a[i__3].i +
temp.i * a[i__3].r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__3 = *m;
for (k = i__ + 1; k <= i__3; ++k) {
i__4 = k + i__ * a_dim1;
i__5 = k + j * b_dim1;
z__2.r = a[i__4].r * b[i__5].r - a[i__4].i *
b[i__5].i, z__2.i = a[i__4].r * b[
i__5].i + a[i__4].i * b[i__5].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L130: */
}
} else {
if (nounit) {
d_cnjg(&z__2, &a[i__ + i__ * a_dim1]);
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
z__1.i = temp.r * z__2.i + temp.i *
z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__3 = *m;
for (k = i__ + 1; k <= i__3; ++k) {
d_cnjg(&z__3, &a[k + i__ * a_dim1]);
i__4 = k + j * b_dim1;
z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4]
.i, z__2.i = z__3.r * b[i__4].i +
z__3.i * b[i__4].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L140: */
}
}
i__3 = i__ + j * b_dim1;
z__1.r = alpha->r * temp.r - alpha->i * temp.i,
z__1.i = alpha->r * temp.i + alpha->i *
temp.r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L150: */
}
/* L160: */
}
}
}
} else {
if (lsame_(transa, "N")) {
/* Form B := alpha*B*A. */
if (upper) {
for (j = *n; j >= 1; --j) {
temp.r = alpha->r, temp.i = alpha->i;
if (nounit) {
i__1 = j + j * a_dim1;
z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i,
z__1.i = temp.r * a[i__1].i + temp.i * a[i__1]
.r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i,
z__1.i = temp.r * b[i__3].i + temp.i * b[i__3]
.r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L170: */
}
i__1 = j - 1;
for (k = 1; k <= i__1; ++k) {
i__2 = k + j * a_dim1;
if (a[i__2].r != 0. || a[i__2].i != 0.) {
i__2 = k + j * a_dim1;
z__1.r = alpha->r * a[i__2].r - alpha->i * a[i__2]
.i, z__1.i = alpha->r * a[i__2].i +
alpha->i * a[i__2].r;
temp.r = z__1.r, temp.i = z__1.i;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = i__ + k * b_dim1;
z__2.r = temp.r * b[i__5].r - temp.i * b[i__5]
.i, z__2.i = temp.r * b[i__5].i +
temp.i * b[i__5].r;
z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4]
.i + z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L180: */
}
}
/* L190: */
}
/* L200: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp.r = alpha->r, temp.i = alpha->i;
if (nounit) {
i__2 = j + j * a_dim1;
z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
z__1.i = temp.r * a[i__2].i + temp.i * a[i__2]
.r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i,
z__1.i = temp.r * b[i__4].i + temp.i * b[i__4]
.r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L210: */
}
i__2 = *n;
for (k = j + 1; k <= i__2; ++k) {
i__3 = k + j * a_dim1;
if (a[i__3].r != 0. || a[i__3].i != 0.) {
i__3 = k + j * a_dim1;
z__1.r = alpha->r * a[i__3].r - alpha->i * a[i__3]
.i, z__1.i = alpha->r * a[i__3].i +
alpha->i * a[i__3].r;
temp.r = z__1.r, temp.i = z__1.i;
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = i__ + k * b_dim1;
z__2.r = temp.r * b[i__6].r - temp.i * b[i__6]
.i, z__2.i = temp.r * b[i__6].i +
temp.i * b[i__6].r;
z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5]
.i + z__2.i;
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L220: */
}
}
/* L230: */
}
/* L240: */
}
}
} else {
/* Form B := alpha*B*A' or B := alpha*B*conjg( A' ). */
if (upper) {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
i__2 = k - 1;
for (j = 1; j <= i__2; ++j) {
i__3 = j + k * a_dim1;
if (a[i__3].r != 0. || a[i__3].i != 0.) {
if (noconj) {
i__3 = j + k * a_dim1;
z__1.r = alpha->r * a[i__3].r - alpha->i * a[
i__3].i, z__1.i = alpha->r * a[i__3]
.i + alpha->i * a[i__3].r;
temp.r = z__1.r, temp.i = z__1.i;
} else {
d_cnjg(&z__2, &a[j + k * a_dim1]);
z__1.r = alpha->r * z__2.r - alpha->i *
z__2.i, z__1.i = alpha->r * z__2.i +
alpha->i * z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = i__ + k * b_dim1;
z__2.r = temp.r * b[i__6].r - temp.i * b[i__6]
.i, z__2.i = temp.r * b[i__6].i +
temp.i * b[i__6].r;
z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5]
.i + z__2.i;
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L250: */
}
}
/* L260: */
}
temp.r = alpha->r, temp.i = alpha->i;
if (nounit) {
if (noconj) {
i__2 = k + k * a_dim1;
z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
z__1.i = temp.r * a[i__2].i + temp.i * a[
i__2].r;
temp.r = z__1.r, temp.i = z__1.i;
} else {
d_cnjg(&z__2, &a[k + k * a_dim1]);
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
z__1.i = temp.r * z__2.i + temp.i *
z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
}
}
if (temp.r != 1. || temp.i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + k * b_dim1;
i__4 = i__ + k * b_dim1;
z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i,
z__1.i = temp.r * b[i__4].i + temp.i * b[
i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L270: */
}
}
/* L280: */
}
} else {
for (k = *n; k >= 1; --k) {
i__1 = *n;
for (j = k + 1; j <= i__1; ++j) {
i__2 = j + k * a_dim1;
if (a[i__2].r != 0. || a[i__2].i != 0.) {
if (noconj) {
i__2 = j + k * a_dim1;
z__1.r = alpha->r * a[i__2].r - alpha->i * a[
i__2].i, z__1.i = alpha->r * a[i__2]
.i + alpha->i * a[i__2].r;
temp.r = z__1.r, temp.i = z__1.i;
} else {
d_cnjg(&z__2, &a[j + k * a_dim1]);
z__1.r = alpha->r * z__2.r - alpha->i *
z__2.i, z__1.i = alpha->r * z__2.i +
alpha->i * z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = i__ + k * b_dim1;
z__2.r = temp.r * b[i__5].r - temp.i * b[i__5]
.i, z__2.i = temp.r * b[i__5].i +
temp.i * b[i__5].r;
z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4]
.i + z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L290: */
}
}
/* L300: */
}
temp.r = alpha->r, temp.i = alpha->i;
if (nounit) {
if (noconj) {
i__1 = k + k * a_dim1;
z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i,
z__1.i = temp.r * a[i__1].i + temp.i * a[
i__1].r;
temp.r = z__1.r, temp.i = z__1.i;
} else {
d_cnjg(&z__2, &a[k + k * a_dim1]);
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
z__1.i = temp.r * z__2.i + temp.i *
z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
}
}
if (temp.r != 1. || temp.i != 0.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + k * b_dim1;
i__3 = i__ + k * b_dim1;
z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i,
z__1.i = temp.r * b[i__3].i + temp.i * b[
i__3].r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L310: */
}
}
/* L320: */
}
}
}
}
return 0;
/* End of ZTRMM . */
} /* ztrmm_ */
/* Subroutine */ int ztrmv_(char *uplo, char *trans, char *diag, integer *n,
doublecomplex *a, integer *lda, doublecomplex *x, integer *incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1, z__2, z__3;
/* Local variables */
static integer i__, j, ix, jx, kx, info;
static doublecomplex temp;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical noconj, nounit;
/*
Purpose
=======
ZTRMV performs one of the matrix-vector operations
x := A*x, or x := A'*x, or x := conjg( A' )*x,
where x is an n element vector and A is an n by n unit, or non-unit,
upper or lower triangular matrix.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' x := A*x.
TRANS = 'T' or 't' x := A'*x.
TRANS = 'C' or 'c' x := conjg( A' )*x.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x. On exit, X is overwritten with the
tranformed vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*lda < max(1,*n)) {
info = 6;
} else if (*incx == 0) {
info = 8;
}
if (info != 0) {
xerbla_("ZTRMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
noconj = lsame_(trans, "T");
nounit = lsame_(diag, "N");
/*
Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops.
*/
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (lsame_(trans, "N")) {
/* Form x := A*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
if (x[i__2].r != 0. || x[i__2].i != 0.) {
i__2 = j;
temp.r = x[i__2].r, temp.i = x[i__2].i;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__ + j * a_dim1;
z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__2.i = temp.r * a[i__5].i + temp.i * a[
i__5].r;
z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i +
z__2.i;
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
/* L10: */
}
if (nounit) {
i__2 = j;
i__3 = j;
i__4 = j + j * a_dim1;
z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[
i__4].i, z__1.i = x[i__3].r * a[i__4].i +
x[i__3].i * a[i__4].r;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
}
}
/* L20: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
if (x[i__2].r != 0. || x[i__2].i != 0.) {
i__2 = jx;
temp.r = x[i__2].r, temp.i = x[i__2].i;
ix = kx;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = ix;
i__4 = ix;
i__5 = i__ + j * a_dim1;
z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__2.i = temp.r * a[i__5].i + temp.i * a[
i__5].r;
z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i +
z__2.i;
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
ix += *incx;
/* L30: */
}
if (nounit) {
i__2 = jx;
i__3 = jx;
i__4 = j + j * a_dim1;
z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[
i__4].i, z__1.i = x[i__3].r * a[i__4].i +
x[i__3].i * a[i__4].r;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
}
}
jx += *incx;
/* L40: */
}
}
} else {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
i__1 = j;
if (x[i__1].r != 0. || x[i__1].i != 0.) {
i__1 = j;
temp.r = x[i__1].r, temp.i = x[i__1].i;
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__ + j * a_dim1;
z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
z__2.i = temp.r * a[i__4].i + temp.i * a[
i__4].r;
z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i +
z__2.i;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
/* L50: */
}
if (nounit) {
i__1 = j;
i__2 = j;
i__3 = j + j * a_dim1;
z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[
i__3].i, z__1.i = x[i__2].r * a[i__3].i +
x[i__2].i * a[i__3].r;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
}
}
/* L60: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
i__1 = jx;
if (x[i__1].r != 0. || x[i__1].i != 0.) {
i__1 = jx;
temp.r = x[i__1].r, temp.i = x[i__1].i;
ix = kx;
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
i__2 = ix;
i__3 = ix;
i__4 = i__ + j * a_dim1;
z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
z__2.i = temp.r * a[i__4].i + temp.i * a[
i__4].r;
z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i +
z__2.i;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
ix -= *incx;
/* L70: */
}
if (nounit) {
i__1 = jx;
i__2 = jx;
i__3 = j + j * a_dim1;
z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[
i__3].i, z__1.i = x[i__2].r * a[i__3].i +
x[i__2].i * a[i__3].r;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
}
}
jx -= *incx;
/* L80: */
}
}
}
} else {
/* Form x := A'*x or x := conjg( A' )*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
i__1 = j;
temp.r = x[i__1].r, temp.i = x[i__1].i;
if (noconj) {
if (nounit) {
i__1 = j + j * a_dim1;
z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i,
z__1.i = temp.r * a[i__1].i + temp.i * a[
i__1].r;
temp.r = z__1.r, temp.i = z__1.i;
}
for (i__ = j - 1; i__ >= 1; --i__) {
i__1 = i__ + j * a_dim1;
i__2 = i__;
z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[
i__2].i, z__2.i = a[i__1].r * x[i__2].i +
a[i__1].i * x[i__2].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L90: */
}
} else {
if (nounit) {
d_cnjg(&z__2, &a[j + j * a_dim1]);
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
z__1.i = temp.r * z__2.i + temp.i *
z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
}
for (i__ = j - 1; i__ >= 1; --i__) {
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__1 = i__;
z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i,
z__2.i = z__3.r * x[i__1].i + z__3.i * x[
i__1].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L100: */
}
}
i__1 = j;
x[i__1].r = temp.r, x[i__1].i = temp.i;
/* L110: */
}
} else {
jx = kx + (*n - 1) * *incx;
for (j = *n; j >= 1; --j) {
i__1 = jx;
temp.r = x[i__1].r, temp.i = x[i__1].i;
ix = jx;
if (noconj) {
if (nounit) {
i__1 = j + j * a_dim1;
z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i,
z__1.i = temp.r * a[i__1].i + temp.i * a[
i__1].r;
temp.r = z__1.r, temp.i = z__1.i;
}
for (i__ = j - 1; i__ >= 1; --i__) {
ix -= *incx;
i__1 = i__ + j * a_dim1;
i__2 = ix;
z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[
i__2].i, z__2.i = a[i__1].r * x[i__2].i +
a[i__1].i * x[i__2].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L120: */
}
} else {
if (nounit) {
d_cnjg(&z__2, &a[j + j * a_dim1]);
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
z__1.i = temp.r * z__2.i + temp.i *
z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
}
for (i__ = j - 1; i__ >= 1; --i__) {
ix -= *incx;
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__1 = ix;
z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i,
z__2.i = z__3.r * x[i__1].i + z__3.i * x[
i__1].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L130: */
}
}
i__1 = jx;
x[i__1].r = temp.r, x[i__1].i = temp.i;
jx -= *incx;
/* L140: */
}
}
} else {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
temp.r = x[i__2].r, temp.i = x[i__2].i;
if (noconj) {
if (nounit) {
i__2 = j + j * a_dim1;
z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
z__1.i = temp.r * a[i__2].i + temp.i * a[
i__2].r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__;
z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[
i__4].i, z__2.i = a[i__3].r * x[i__4].i +
a[i__3].i * x[i__4].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L150: */
}
} else {
if (nounit) {
d_cnjg(&z__2, &a[j + j * a_dim1]);
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
z__1.i = temp.r * z__2.i + temp.i *
z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__3 = i__;
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i,
z__2.i = z__3.r * x[i__3].i + z__3.i * x[
i__3].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L160: */
}
}
i__2 = j;
x[i__2].r = temp.r, x[i__2].i = temp.i;
/* L170: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
temp.r = x[i__2].r, temp.i = x[i__2].i;
ix = jx;
if (noconj) {
if (nounit) {
i__2 = j + j * a_dim1;
z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
z__1.i = temp.r * a[i__2].i + temp.i * a[
i__2].r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
i__3 = i__ + j * a_dim1;
i__4 = ix;
z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[
i__4].i, z__2.i = a[i__3].r * x[i__4].i +
a[i__3].i * x[i__4].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L180: */
}
} else {
if (nounit) {
d_cnjg(&z__2, &a[j + j * a_dim1]);
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
z__1.i = temp.r * z__2.i + temp.i *
z__2.r;
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__3 = ix;
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i,
z__2.i = z__3.r * x[i__3].i + z__3.i * x[
i__3].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L190: */
}
}
i__2 = jx;
x[i__2].r = temp.r, x[i__2].i = temp.i;
jx += *incx;
/* L200: */
}
}
}
}
return 0;
/* End of ZTRMV . */
} /* ztrmv_ */
/* Subroutine */ int ztrsm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, doublecomplex *alpha, doublecomplex *a,
integer *lda, doublecomplex *b, integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5,
i__6, i__7;
doublecomplex z__1, z__2, z__3;
/* Local variables */
static integer i__, j, k, info;
static doublecomplex temp;
static logical lside;
extern logical lsame_(char *, char *);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical noconj, nounit;
/*
Purpose
=======
ZTRSM solves one of the matrix equations
op( A )*X = alpha*B, or X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ).
The matrix X is overwritten on B.
Arguments
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:
SIDE = 'L' or 'l' op( A )*X = alpha*B.
SIDE = 'R' or 'r' X*op( A ) = alpha*B.
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A'.
TRANSA = 'C' or 'c' op( A ) = conjg( A' ).
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
B - COMPLEX*16 array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the right-hand side matrix B, and on exit is
overwritten by the solution matrix X.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
Further Details
===============
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
lside = lsame_(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
noconj = lsame_(transa, "T");
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
info = 0;
if (! lside && ! lsame_(side, "R")) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L")) {
info = 2;
} else if (! lsame_(transa, "N") && ! lsame_(transa,
"T") && ! lsame_(transa, "C")) {
info = 3;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < max(1,nrowa)) {
info = 9;
} else if (*ldb < max(1,*m)) {
info = 11;
}
if (info != 0) {
xerbla_("ZTRSM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (alpha->r == 0. && alpha->i == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0., b[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (lsame_(transa, "N")) {
/* Form B := alpha*inv( A )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (alpha->r != 1. || alpha->i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, z__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L30: */
}
}
for (k = *m; k >= 1; --k) {
i__2 = k + j * b_dim1;
if (b[i__2].r != 0. || b[i__2].i != 0.) {
if (nounit) {
i__2 = k + j * b_dim1;
z_div(&z__1, &b[k + j * b_dim1], &a[k + k *
a_dim1]);
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
}
i__2 = k - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = k + j * b_dim1;
i__6 = i__ + k * a_dim1;
z__2.r = b[i__5].r * a[i__6].r - b[i__5].i *
a[i__6].i, z__2.i = b[i__5].r * a[
i__6].i + b[i__5].i * a[i__6].r;
z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4]
.i - z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L40: */
}
}
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (alpha->r != 1. || alpha->i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, z__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L70: */
}
}
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * b_dim1;
if (b[i__3].r != 0. || b[i__3].i != 0.) {
if (nounit) {
i__3 = k + j * b_dim1;
z_div(&z__1, &b[k + j * b_dim1], &a[k + k *
a_dim1]);
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
}
i__3 = *m;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = k + j * b_dim1;
i__7 = i__ + k * a_dim1;
z__2.r = b[i__6].r * a[i__7].r - b[i__6].i *
a[i__7].i, z__2.i = b[i__6].r * a[
i__7].i + b[i__6].i * a[i__7].r;
z__1.r = b[i__5].r - z__2.r, z__1.i = b[i__5]
.i - z__2.i;
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L80: */
}
}
/* L90: */
}
/* L100: */
}
}
} else {
/*
Form B := alpha*inv( A' )*B
or B := alpha*inv( conjg( A' ) )*B.
*/
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i,
z__1.i = alpha->r * b[i__3].i + alpha->i * b[
i__3].r;
temp.r = z__1.r, temp.i = z__1.i;
if (noconj) {
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
i__4 = k + i__ * a_dim1;
i__5 = k + j * b_dim1;
z__2.r = a[i__4].r * b[i__5].r - a[i__4].i *
b[i__5].i, z__2.i = a[i__4].r * b[
i__5].i + a[i__4].i * b[i__5].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L110: */
}
if (nounit) {
z_div(&z__1, &temp, &a[i__ + i__ * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
d_cnjg(&z__3, &a[k + i__ * a_dim1]);
i__4 = k + j * b_dim1;
z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4]
.i, z__2.i = z__3.r * b[i__4].i +
z__3.i * b[i__4].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L120: */
}
if (nounit) {
d_cnjg(&z__2, &a[i__ + i__ * a_dim1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__3 = i__ + j * b_dim1;
b[i__3].r = temp.r, b[i__3].i = temp.i;
/* L130: */
}
/* L140: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
i__2 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2].i,
z__1.i = alpha->r * b[i__2].i + alpha->i * b[
i__2].r;
temp.r = z__1.r, temp.i = z__1.i;
if (noconj) {
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
i__3 = k + i__ * a_dim1;
i__4 = k + j * b_dim1;
z__2.r = a[i__3].r * b[i__4].r - a[i__3].i *
b[i__4].i, z__2.i = a[i__3].r * b[
i__4].i + a[i__3].i * b[i__4].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L150: */
}
if (nounit) {
z_div(&z__1, &temp, &a[i__ + i__ * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
d_cnjg(&z__3, &a[k + i__ * a_dim1]);
i__3 = k + j * b_dim1;
z__2.r = z__3.r * b[i__3].r - z__3.i * b[i__3]
.i, z__2.i = z__3.r * b[i__3].i +
z__3.i * b[i__3].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L160: */
}
if (nounit) {
d_cnjg(&z__2, &a[i__ + i__ * a_dim1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__2 = i__ + j * b_dim1;
b[i__2].r = temp.r, b[i__2].i = temp.i;
/* L170: */
}
/* L180: */
}
}
}
} else {
if (lsame_(transa, "N")) {
/* Form B := alpha*B*inv( A ). */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (alpha->r != 1. || alpha->i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, z__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L190: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * a_dim1;
if (a[i__3].r != 0. || a[i__3].i != 0.) {
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = k + j * a_dim1;
i__7 = i__ + k * b_dim1;
z__2.r = a[i__6].r * b[i__7].r - a[i__6].i *
b[i__7].i, z__2.i = a[i__6].r * b[
i__7].i + a[i__6].i * b[i__7].r;
z__1.r = b[i__5].r - z__2.r, z__1.i = b[i__5]
.i - z__2.i;
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L200: */
}
}
/* L210: */
}
if (nounit) {
z_div(&z__1, &c_b1078, &a[j + j * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i,
z__1.i = temp.r * b[i__4].i + temp.i * b[
i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L220: */
}
}
/* L230: */
}
} else {
for (j = *n; j >= 1; --j) {
if (alpha->r != 1. || alpha->i != 0.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3]
.i, z__1.i = alpha->r * b[i__3].i +
alpha->i * b[i__3].r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L240: */
}
}
i__1 = *n;
for (k = j + 1; k <= i__1; ++k) {
i__2 = k + j * a_dim1;
if (a[i__2].r != 0. || a[i__2].i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = k + j * a_dim1;
i__6 = i__ + k * b_dim1;
z__2.r = a[i__5].r * b[i__6].r - a[i__5].i *
b[i__6].i, z__2.i = a[i__5].r * b[
i__6].i + a[i__5].i * b[i__6].r;
z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4]
.i - z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L250: */
}
}
/* L260: */
}
if (nounit) {
z_div(&z__1, &c_b1078, &a[j + j * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i,
z__1.i = temp.r * b[i__3].i + temp.i * b[
i__3].r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L270: */
}
}
/* L280: */
}
}
} else {
/*
Form B := alpha*B*inv( A' )
or B := alpha*B*inv( conjg( A' ) ).
*/
if (upper) {
for (k = *n; k >= 1; --k) {
if (nounit) {
if (noconj) {
z_div(&z__1, &c_b1078, &a[k + k * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
} else {
d_cnjg(&z__2, &a[k + k * a_dim1]);
z_div(&z__1, &c_b1078, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + k * b_dim1;
i__3 = i__ + k * b_dim1;
z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i,
z__1.i = temp.r * b[i__3].i + temp.i * b[
i__3].r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L290: */
}
}
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j + k * a_dim1;
if (a[i__2].r != 0. || a[i__2].i != 0.) {
if (noconj) {
i__2 = j + k * a_dim1;
temp.r = a[i__2].r, temp.i = a[i__2].i;
} else {
d_cnjg(&z__1, &a[j + k * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = i__ + k * b_dim1;
z__2.r = temp.r * b[i__5].r - temp.i * b[i__5]
.i, z__2.i = temp.r * b[i__5].i +
temp.i * b[i__5].r;
z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4]
.i - z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L300: */
}
}
/* L310: */
}
if (alpha->r != 1. || alpha->i != 0.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + k * b_dim1;
i__3 = i__ + k * b_dim1;
z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3]
.i, z__1.i = alpha->r * b[i__3].i +
alpha->i * b[i__3].r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L320: */
}
}
/* L330: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (nounit) {
if (noconj) {
z_div(&z__1, &c_b1078, &a[k + k * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
} else {
d_cnjg(&z__2, &a[k + k * a_dim1]);
z_div(&z__1, &c_b1078, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + k * b_dim1;
i__4 = i__ + k * b_dim1;
z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i,
z__1.i = temp.r * b[i__4].i + temp.i * b[
i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L340: */
}
}
i__2 = *n;
for (j = k + 1; j <= i__2; ++j) {
i__3 = j + k * a_dim1;
if (a[i__3].r != 0. || a[i__3].i != 0.) {
if (noconj) {
i__3 = j + k * a_dim1;
temp.r = a[i__3].r, temp.i = a[i__3].i;
} else {
d_cnjg(&z__1, &a[j + k * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = i__ + k * b_dim1;
z__2.r = temp.r * b[i__6].r - temp.i * b[i__6]
.i, z__2.i = temp.r * b[i__6].i +
temp.i * b[i__6].r;
z__1.r = b[i__5].r - z__2.r, z__1.i = b[i__5]
.i - z__2.i;
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L350: */
}
}
/* L360: */
}
if (alpha->r != 1. || alpha->i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + k * b_dim1;
i__4 = i__ + k * b_dim1;
z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, z__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L370: */
}
}
/* L380: */
}
}
}
}
return 0;
/* End of ZTRSM . */
} /* ztrsm_ */
/* Subroutine */ int ztrsv_(char *uplo, char *trans, char *diag, integer *n,
doublecomplex *a, integer *lda, doublecomplex *x, integer *incx)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1, z__2, z__3;
/* Local variables */
static integer i__, j, ix, jx, kx, info;
static doublecomplex temp;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static logical noconj, nounit;
/*
Purpose
=======
ZTRSV solves one of the systems of equations
A*x = b, or A'*x = b, or conjg( A' )*x = b,
where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular matrix.
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
Arguments
==========
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANS - CHARACTER*1.
On entry, TRANS specifies the equations to be solved as
follows:
TRANS = 'N' or 'n' A*x = b.
TRANS = 'T' or 't' A'*x = b.
TRANS = 'C' or 'c' conjg( A' )*x = b.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
Unchanged on exit.
X - COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element right-hand side vector b. On exit, X is overwritten
with the solution vector x.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
Further Details
===============
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
/* Function Body */
info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
info = 1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
info = 2;
} else if (! lsame_(diag, "U") && ! lsame_(diag,
"N")) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*lda < max(1,*n)) {
info = 6;
} else if (*incx == 0) {
info = 8;
}
if (info != 0) {
xerbla_("ZTRSV ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
noconj = lsame_(trans, "T");
nounit = lsame_(diag, "N");
/*
Set up the start point in X if the increment is not unity. This
will be ( N - 1 )*INCX too small for descending loops.
*/
if (*incx <= 0) {
kx = 1 - (*n - 1) * *incx;
} else if (*incx != 1) {
kx = 1;
}
/*
Start the operations. In this version the elements of A are
accessed sequentially with one pass through A.
*/
if (lsame_(trans, "N")) {
/* Form x := inv( A )*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
i__1 = j;
if (x[i__1].r != 0. || x[i__1].i != 0.) {
if (nounit) {
i__1 = j;
z_div(&z__1, &x[j], &a[j + j * a_dim1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
}
i__1 = j;
temp.r = x[i__1].r, temp.i = x[i__1].i;
for (i__ = j - 1; i__ >= 1; --i__) {
i__1 = i__;
i__2 = i__;
i__3 = i__ + j * a_dim1;
z__2.r = temp.r * a[i__3].r - temp.i * a[i__3].i,
z__2.i = temp.r * a[i__3].i + temp.i * a[
i__3].r;
z__1.r = x[i__2].r - z__2.r, z__1.i = x[i__2].i -
z__2.i;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
/* L10: */
}
}
/* L20: */
}
} else {
jx = kx + (*n - 1) * *incx;
for (j = *n; j >= 1; --j) {
i__1 = jx;
if (x[i__1].r != 0. || x[i__1].i != 0.) {
if (nounit) {
i__1 = jx;
z_div(&z__1, &x[jx], &a[j + j * a_dim1]);
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
}
i__1 = jx;
temp.r = x[i__1].r, temp.i = x[i__1].i;
ix = jx;
for (i__ = j - 1; i__ >= 1; --i__) {
ix -= *incx;
i__1 = ix;
i__2 = ix;
i__3 = i__ + j * a_dim1;
z__2.r = temp.r * a[i__3].r - temp.i * a[i__3].i,
z__2.i = temp.r * a[i__3].i + temp.i * a[
i__3].r;
z__1.r = x[i__2].r - z__2.r, z__1.i = x[i__2].i -
z__2.i;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
/* L30: */
}
}
jx -= *incx;
/* L40: */
}
}
} else {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
if (x[i__2].r != 0. || x[i__2].i != 0.) {
if (nounit) {
i__2 = j;
z_div(&z__1, &x[j], &a[j + j * a_dim1]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
}
i__2 = j;
temp.r = x[i__2].r, temp.i = x[i__2].i;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__ + j * a_dim1;
z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__2.i = temp.r * a[i__5].i + temp.i * a[
i__5].r;
z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i -
z__2.i;
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
/* L50: */
}
}
/* L60: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
if (x[i__2].r != 0. || x[i__2].i != 0.) {
if (nounit) {
i__2 = jx;
z_div(&z__1, &x[jx], &a[j + j * a_dim1]);
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
}
i__2 = jx;
temp.r = x[i__2].r, temp.i = x[i__2].i;
ix = jx;
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
ix += *incx;
i__3 = ix;
i__4 = ix;
i__5 = i__ + j * a_dim1;
z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__2.i = temp.r * a[i__5].i + temp.i * a[
i__5].r;
z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i -
z__2.i;
x[i__3].r = z__1.r, x[i__3].i = z__1.i;
/* L70: */
}
}
jx += *incx;
/* L80: */
}
}
}
} else {
/* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. */
if (lsame_(uplo, "U")) {
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
temp.r = x[i__2].r, temp.i = x[i__2].i;
if (noconj) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__;
z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[
i__4].i, z__2.i = a[i__3].r * x[i__4].i +
a[i__3].i * x[i__4].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L90: */
}
if (nounit) {
z_div(&z__1, &temp, &a[j + j * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__3 = i__;
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i,
z__2.i = z__3.r * x[i__3].i + z__3.i * x[
i__3].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L100: */
}
if (nounit) {
d_cnjg(&z__2, &a[j + j * a_dim1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__2 = j;
x[i__2].r = temp.r, x[i__2].i = temp.i;
/* L110: */
}
} else {
jx = kx;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
ix = kx;
i__2 = jx;
temp.r = x[i__2].r, temp.i = x[i__2].i;
if (noconj) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = ix;
z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[
i__4].i, z__2.i = a[i__3].r * x[i__4].i +
a[i__3].i * x[i__4].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix += *incx;
/* L120: */
}
if (nounit) {
z_div(&z__1, &temp, &a[j + j * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__3 = ix;
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i,
z__2.i = z__3.r * x[i__3].i + z__3.i * x[
i__3].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix += *incx;
/* L130: */
}
if (nounit) {
d_cnjg(&z__2, &a[j + j * a_dim1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__2 = jx;
x[i__2].r = temp.r, x[i__2].i = temp.i;
jx += *incx;
/* L140: */
}
}
} else {
if (*incx == 1) {
for (j = *n; j >= 1; --j) {
i__1 = j;
temp.r = x[i__1].r, temp.i = x[i__1].i;
if (noconj) {
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
i__2 = i__ + j * a_dim1;
i__3 = i__;
z__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[
i__3].i, z__2.i = a[i__2].r * x[i__3].i +
a[i__2].i * x[i__3].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L150: */
}
if (nounit) {
z_div(&z__1, &temp, &a[j + j * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__2 = i__;
z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i,
z__2.i = z__3.r * x[i__2].i + z__3.i * x[
i__2].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L160: */
}
if (nounit) {
d_cnjg(&z__2, &a[j + j * a_dim1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__1 = j;
x[i__1].r = temp.r, x[i__1].i = temp.i;
/* L170: */
}
} else {
kx += (*n - 1) * *incx;
jx = kx;
for (j = *n; j >= 1; --j) {
ix = kx;
i__1 = jx;
temp.r = x[i__1].r, temp.i = x[i__1].i;
if (noconj) {
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
i__2 = i__ + j * a_dim1;
i__3 = ix;
z__2.r = a[i__2].r * x[i__3].r - a[i__2].i * x[
i__3].i, z__2.i = a[i__2].r * x[i__3].i +
a[i__2].i * x[i__3].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix -= *incx;
/* L180: */
}
if (nounit) {
z_div(&z__1, &temp, &a[j + j * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
i__1 = j + 1;
for (i__ = *n; i__ >= i__1; --i__) {
d_cnjg(&z__3, &a[i__ + j * a_dim1]);
i__2 = ix;
z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i,
z__2.i = z__3.r * x[i__2].i + z__3.i * x[
i__2].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix -= *incx;
/* L190: */
}
if (nounit) {
d_cnjg(&z__2, &a[j + j * a_dim1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__1 = jx;
x[i__1].r = temp.r, x[i__1].i = temp.i;
jx -= *incx;
/* L200: */
}
}
}
}
return 0;
/* End of ZTRSV . */
} /* ztrsv_ */