/* integration/qmomof.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include <config.h>
#include <stdlib.h>
#include <gsl/gsl_integration.h>
#include <gsl/gsl_errno.h>
static void
compute_moments (double par, double * cheb);
static int
dgtsl (size_t n, double *c, double *d, double *e, double *b);
gsl_integration_qawo_table *
gsl_integration_qawo_table_alloc (double omega, double L,
enum gsl_integration_qawo_enum sine,
size_t n)
{
gsl_integration_qawo_table *t;
double * chebmo;
if (n == 0)
{
GSL_ERROR_VAL ("table length n must be positive integer",
GSL_EDOM, 0);
}
t = (gsl_integration_qawo_table *)
malloc (sizeof (gsl_integration_qawo_table));
if (t == 0)
{
GSL_ERROR_VAL ("failed to allocate space for qawo_table struct",
GSL_ENOMEM, 0);
}
chebmo = (double *) malloc (25 * n * sizeof (double));
if (chebmo == 0)
{
free (t);
GSL_ERROR_VAL ("failed to allocate space for chebmo block",
GSL_ENOMEM, 0);
}
t->n = n;
t->sine = sine;
t->omega = omega;
t->L = L;
t->par = 0.5 * omega * L;
t->chebmo = chebmo;
/* precompute the moments */
{
size_t i;
double scale = 1.0;
for (i = 0 ; i < t->n; i++)
{
compute_moments (t->par * scale, t->chebmo + 25*i);
scale *= 0.5;
}
}
return t;
}
int
gsl_integration_qawo_table_set (gsl_integration_qawo_table * t,
double omega, double L,
enum gsl_integration_qawo_enum sine)
{
t->omega = omega;
t->sine = sine;
t->L = L;
t->par = 0.5 * omega * L;
/* recompute the moments */
{
size_t i;
double scale = 1.0;
for (i = 0 ; i < t->n; i++)
{
compute_moments (t->par * scale, t->chebmo + 25*i);
scale *= 0.5;
}
}
return GSL_SUCCESS;
}
int
gsl_integration_qawo_table_set_length (gsl_integration_qawo_table * t,
double L)
{
/* return immediately if the length is the same as the old length */
if (L == t->L)
return GSL_SUCCESS;
/* otherwise reset the table and compute the new parameters */
t->L = L;
t->par = 0.5 * t->omega * L;
/* recompute the moments */
{
size_t i;
double scale = 1.0;
for (i = 0 ; i < t->n; i++)
{
compute_moments (t->par * scale, t->chebmo + 25*i);
scale *= 0.5;
}
}
return GSL_SUCCESS;
}
void
gsl_integration_qawo_table_free (gsl_integration_qawo_table * t)
{
RETURN_IF_NULL (t);
free (t->chebmo);
free (t);
}
static void
compute_moments (double par, double *chebmo)
{
double v[28], d[25], d1[25], d2[25];
const size_t noeq = 25;
const double par2 = par * par;
const double par4 = par2 * par2;
const double par22 = par2 + 2.0;
const double sinpar = sin (par);
const double cospar = cos (par);
size_t i;
/* compute the chebyschev moments with respect to cosine */
double ac = 8 * cospar;
double as = 24 * par * sinpar;
v[0] = 2 * sinpar / par;
v[1] = (8 * cospar + (2 * par2 - 8) * sinpar / par) / par2;
v[2] = (32 * (par2 - 12) * cospar
+ (2 * ((par2 - 80) * par2 + 192) * sinpar) / par) / par4;
if (fabs (par) <= 24)
{
/* compute the moments as the solution of a boundary value
problem using the asyptotic expansion as an endpoint */
double an2, ass, asap;
double an = 6;
size_t k;
for (k = 0; k < noeq - 1; k++)
{
an2 = an * an;
d[k] = -2 * (an2 - 4) * (par22 - 2 * an2);
d2[k] = (an - 1) * (an - 2) * par2;
d1[k + 1] = (an + 3) * (an + 4) * par2;
v[k + 3] = as - (an2 - 4) * ac;
an = an + 2.0;
}
an2 = an * an;
d[noeq - 1] = -2 * (an2 - 4) * (par22 - 2 * an2);
v[noeq + 2] = as - (an2 - 4) * ac;
v[3] = v[3] - 56 * par2 * v[2];
ass = par * sinpar;
asap = (((((210 * par2 - 1) * cospar - (105 * par2 - 63) * ass) / an2
- (1 - 15 * par2) * cospar + 15 * ass) / an2
- cospar + 3 * ass) / an2
- cospar) / an2;
v[noeq + 2] = v[noeq + 2] - 2 * asap * par2 * (an - 1) * (an - 2);
dgtsl (noeq, d1, d, d2, v + 3);
}
else
{
/* compute the moments by forward recursion */
size_t k;
double an = 4;
for (k = 3; k < 13; k++)
{
double an2 = an * an;
v[k] = ((an2 - 4) * (2 * (par22 - 2 * an2) * v[k - 1] - ac)
+ as - par2 * (an + 1) * (an + 2) * v[k - 2])
/ (par2 * (an - 1) * (an - 2));
an = an + 2.0;
}
}
for (i = 0; i < 13; i++)
{
chebmo[2 * i] = v[i];
}
/* compute the chebyschev moments with respect to sine */
v[0] = 2 * (sinpar - par * cospar) / par2;
v[1] = (18 - 48 / par2) * sinpar / par2 + (-2 + 48 / par2) * cospar / par;
ac = -24 * par * cospar;
as = -8 * sinpar;
if (fabs (par) <= 24)
{
/* compute the moments as the solution of a boundary value
problem using the asyptotic expansion as an endpoint */
size_t k;
double an2, ass, asap;
double an = 5;
for (k = 0; k < noeq - 1; k++)
{
an2 = an * an;
d[k] = -2 * (an2 - 4) * (par22 - 2 * an2);
d2[k] = (an - 1) * (an - 2) * par2;
d1[k + 1] = (an + 3) * (an + 4) * par2;
v[k + 2] = ac + (an2 - 4) * as;
an = an + 2.0;
}
an2 = an * an;
d[noeq - 1] = -2 * (an2 - 4) * (par22 - 2 * an2);
v[noeq + 1] = ac + (an2 - 4) * as;
v[2] = v[2] - 42 * par2 * v[1];
ass = par * cospar;
asap = (((((105 * par2 - 63) * ass - (210 * par2 - 1) * sinpar) / an2
+ (15 * par2 - 1) * sinpar
- 15 * ass) / an2 - sinpar - 3 * ass) / an2 - sinpar) / an2;
v[noeq + 1] = v[noeq + 1] - 2 * asap * par2 * (an - 1) * (an - 2);
dgtsl (noeq, d1, d, d2, v + 2);
}
else
{
/* compute the moments by forward recursion */
size_t k;
double an = 3;
for (k = 2; k < 12; k++)
{
double an2 = an * an;
v[k] = ((an2 - 4) * (2 * (par22 - 2 * an2) * v[k - 1] + as)
+ ac - par2 * (an + 1) * (an + 2) * v[k - 2])
/ (par2 * (an - 1) * (an - 2));
an = an + 2.0;
}
}
for (i = 0; i < 12; i++)
{
chebmo[2 * i + 1] = v[i];
}
}
static int
dgtsl (size_t n, double *c, double *d, double *e, double *b)
{
/* solves a tridiagonal matrix A x = b
c[1 .. n - 1] subdiagonal of the matrix A
d[0 .. n - 1] diagonal of the matrix A
e[0 .. n - 2] superdiagonal of the matrix A
b[0 .. n - 1] right hand side, replaced by the solution vector x */
size_t k;
c[0] = d[0];
if (n == 0)
{
return GSL_SUCCESS;
}
if (n == 1)
{
b[0] = b[0] / d[0] ;
return GSL_SUCCESS;
}
d[0] = e[0];
e[0] = 0;
e[n - 1] = 0;
for (k = 0; k < n - 1; k++)
{
size_t k1 = k + 1;
if (fabs (c[k1]) >= fabs (c[k]))
{
{
double t = c[k1];
c[k1] = c[k];
c[k] = t;
};
{
double t = d[k1];
d[k1] = d[k];
d[k] = t;
};
{
double t = e[k1];
e[k1] = e[k];
e[k] = t;
};
{
double t = b[k1];
b[k1] = b[k];
b[k] = t;
};
}
if (c[k] == 0)
{
return GSL_FAILURE ;
}
{
double t = -c[k1] / c[k];
c[k1] = d[k1] + t * d[k];
d[k1] = e[k1] + t * e[k];
e[k1] = 0;
b[k1] = b[k1] + t * b[k];
}
}
if (c[n - 1] == 0)
{
return GSL_FAILURE;
}
b[n - 1] = b[n - 1] / c[n - 1];
b[n - 2] = (b[n - 2] - d[n - 2] * b[n - 1]) / c[n - 2];
for (k = n ; k > 2; k--)
{
size_t kb = k - 3;
b[kb] = (b[kb] - d[kb] * b[kb + 1] - e[kb] * b[kb + 2]) / c[kb];
}
return GSL_SUCCESS;
}