/* multifit/lmpar.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 <gsl/gsl_permute_vector_double.h>
#include "qrsolv.c"
static size_t
count_nsing (const gsl_matrix * r)
{
/* Count the number of nonsingular entries. Returns the index of the
first entry which is singular. */
size_t n = r->size2;
size_t i;
for (i = 0; i < n; i++)
{
double rii = gsl_matrix_get (r, i, i);
if (rii == 0)
{
break;
}
}
return i;
}
static void
compute_newton_direction (const gsl_matrix * r, const gsl_permutation * perm,
const gsl_vector * qtf, gsl_vector * x)
{
/* Compute and store in x the Gauss-Newton direction. If the
Jacobian is rank-deficient then obtain a least squares
solution. */
const size_t n = r->size2;
size_t i, j, nsing;
for (i = 0 ; i < n ; i++)
{
double qtfi = gsl_vector_get (qtf, i);
gsl_vector_set (x, i, qtfi);
}
nsing = count_nsing (r);
#ifdef DEBUG
printf("nsing = %d\n", nsing);
printf("r = "); gsl_matrix_fprintf(stdout, r, "%g"); printf("\n");
printf("qtf = "); gsl_vector_fprintf(stdout, x, "%g"); printf("\n");
#endif
for (i = nsing; i < n; i++)
{
gsl_vector_set (x, i, 0.0);
}
if (nsing > 0)
{
for (j = nsing; j > 0 && j--;)
{
double rjj = gsl_matrix_get (r, j, j);
double temp = gsl_vector_get (x, j) / rjj;
gsl_vector_set (x, j, temp);
for (i = 0; i < j; i++)
{
double rij = gsl_matrix_get (r, i, j);
double xi = gsl_vector_get (x, i);
gsl_vector_set (x, i, xi - rij * temp);
}
}
}
gsl_permute_vector_inverse (perm, x);
}
static void
compute_newton_correction (const gsl_matrix * r, const gsl_vector * sdiag,
const gsl_permutation * p, gsl_vector * x,
double dxnorm,
const gsl_vector * diag, gsl_vector * w)
{
size_t n = r->size2;
size_t i, j;
for (i = 0; i < n; i++)
{
size_t pi = gsl_permutation_get (p, i);
double dpi = gsl_vector_get (diag, pi);
double xpi = gsl_vector_get (x, pi);
gsl_vector_set (w, i, dpi * (dpi * xpi) / dxnorm);
}
for (j = 0; j < n; j++)
{
double sj = gsl_vector_get (sdiag, j);
double wj = gsl_vector_get (w, j);
double tj = wj / sj;
gsl_vector_set (w, j, tj);
for (i = j + 1; i < n; i++)
{
double rij = gsl_matrix_get (r, i, j);
double wi = gsl_vector_get (w, i);
gsl_vector_set (w, i, wi - rij * tj);
}
}
}
static void
compute_newton_bound (const gsl_matrix * r, const gsl_vector * x,
double dxnorm, const gsl_permutation * perm,
const gsl_vector * diag, gsl_vector * w)
{
/* If the jacobian is not rank-deficient then the Newton step
provides a lower bound for the zero of the function. Otherwise
set this bound to zero. */
size_t n = r->size2;
size_t i, j;
size_t nsing = count_nsing (r);
if (nsing < n)
{
gsl_vector_set_zero (w);
return;
}
for (i = 0; i < n; i++)
{
size_t pi = gsl_permutation_get (perm, i);
double dpi = gsl_vector_get (diag, pi);
double xpi = gsl_vector_get (x, pi);
gsl_vector_set (w, i, dpi * (dpi * xpi / dxnorm));
}
for (j = 0; j < n; j++)
{
double sum = 0;
for (i = 0; i < j; i++)
{
sum += gsl_matrix_get (r, i, j) * gsl_vector_get (w, i);
}
{
double rjj = gsl_matrix_get (r, j, j);
double wj = gsl_vector_get (w, j);
gsl_vector_set (w, j, (wj - sum) / rjj);
}
}
}
/* compute scaled gradient g = D^{-1} J^T f (see More' eq 7.2) */
static void
compute_gradient_direction (const gsl_matrix * r, const gsl_permutation * p,
const gsl_vector * qtf, const gsl_vector * diag,
gsl_vector * g)
{
const size_t n = r->size2;
size_t i, j;
for (j = 0; j < n; j++)
{
double sum = 0;
for (i = 0; i <= j; i++)
{
sum += gsl_matrix_get (r, i, j) * gsl_vector_get (qtf, i);
}
{
size_t pj = gsl_permutation_get (p, j);
double dpj = gsl_vector_get (diag, pj);
gsl_vector_set (g, j, sum / dpj);
}
}
}
/* compute gradient g = J^T f */
static void
compute_gradient (const gsl_matrix * r, const gsl_vector * qtf,
gsl_vector * g)
{
const size_t n = r->size2;
size_t i, j;
for (j = 0; j < n; j++)
{
double sum = 0;
for (i = 0; i <= j; i++)
{
sum += gsl_matrix_get (r, i, j) * gsl_vector_get (qtf, i);
}
gsl_vector_set (g, j, sum);
}
}
static int
lmpar (gsl_matrix * r, const gsl_permutation * perm, const gsl_vector * qtf,
const gsl_vector * diag, double delta, double * par_inout,
gsl_vector * newton, gsl_vector * gradient, gsl_vector * sdiag,
gsl_vector * x, gsl_vector * w)
{
double dxnorm, gnorm, fp, fp_old, par_lower, par_upper, par_c;
double par = *par_inout;
size_t iter = 0;
#ifdef DEBUG
printf("ENTERING lmpar\n");
#endif
compute_newton_direction (r, perm, qtf, newton);
#ifdef DEBUG
printf ("newton = ");
gsl_vector_fprintf (stdout, newton, "%g");
printf ("\n");
printf ("diag = ");
gsl_vector_fprintf (stdout, diag, "%g");
printf ("\n");
#endif
/* Evaluate the function at the origin and test for acceptance of
the Gauss-Newton direction. */
dxnorm = scaled_enorm (diag, newton);
fp = dxnorm - delta;
#ifdef DEBUG
printf ("dxnorm = %g, delta = %g, fp = %g\n", dxnorm, delta, fp);
#endif
if (fp <= 0.1 * delta)
{
gsl_vector_memcpy (x, newton);
#ifdef DEBUG
printf ("took newton (fp = %g, delta = %g)\n", fp, delta);
#endif
*par_inout = 0;
return GSL_SUCCESS;
}
#ifdef DEBUG
printf ("r = ");
gsl_matrix_fprintf (stdout, r, "%g");
printf ("\n");
printf ("newton = ");
gsl_vector_fprintf (stdout, newton, "%g");
printf ("\n");
printf ("dxnorm = %g\n", dxnorm);
#endif
compute_newton_bound (r, newton, dxnorm, perm, diag, w);
#ifdef DEBUG
printf("perm = "); gsl_permutation_fprintf(stdout, perm, "%d");
printf ("diag = ");
gsl_vector_fprintf (stdout, diag, "%g");
printf ("\n");
printf ("w = ");
gsl_vector_fprintf (stdout, w, "%g");
printf ("\n");
#endif
{
double wnorm = enorm (w);
double phider = wnorm * wnorm;
/* w == zero if r rank-deficient,
then set lower bound to zero form MINPACK, lmder.f
Hans E. Plesser 2002-02-25 (hans.plesser@itf.nlh.no) */
if ( wnorm > 0 )
par_lower = fp / (delta * phider);
else
par_lower = 0.0;
}
#ifdef DEBUG
printf("par = %g\n", par );
printf("par_lower = %g\n", par_lower);
#endif
compute_gradient_direction (r, perm, qtf, diag, gradient);
gnorm = enorm (gradient);
#ifdef DEBUG
printf("gradient = "); gsl_vector_fprintf(stdout, gradient, "%g"); printf("\n");
printf("gnorm = %g\n", gnorm);
#endif
par_upper = gnorm / delta;
if (par_upper == 0)
{
par_upper = GSL_DBL_MIN / GSL_MIN_DBL(delta, 0.1);
}
#ifdef DEBUG
printf("par_upper = %g\n", par_upper);
#endif
if (par > par_upper)
{
#ifdef DEBUG
printf("set par to par_upper\n");
#endif
par = par_upper;
}
else if (par < par_lower)
{
#ifdef DEBUG
printf("set par to par_lower\n");
#endif
par = par_lower;
}
if (par == 0)
{
par = gnorm / dxnorm;
#ifdef DEBUG
printf("set par to gnorm/dxnorm = %g\n", par);
#endif
}
/* Beginning of iteration */
iteration:
iter++;
#ifdef DEBUG
printf("lmpar iteration = %d\n", iter);
#endif
#ifdef BRIANSFIX
/* Seems like this is described in the paper but not in the MINPACK code */
if (par < par_lower || par > par_upper)
{
par = GSL_MAX_DBL (0.001 * par_upper, sqrt(par_lower * par_upper));
}
#endif
/* Evaluate the function at the current value of par */
if (par == 0)
{
par = GSL_MAX_DBL (0.001 * par_upper, GSL_DBL_MIN);
#ifdef DEBUG
printf("par = 0, set par to = %g\n", par);
#endif
}
/* Compute the least squares solution of [ R P x - Q^T f, sqrt(par) D x]
for A = Q R P^T */
#ifdef DEBUG
printf ("calling qrsolv with par = %g\n", par);
#endif
{
double sqrt_par = sqrt(par);
qrsolv (r, perm, sqrt_par, diag, qtf, x, sdiag, w);
}
dxnorm = scaled_enorm (diag, x);
fp_old = fp;
fp = dxnorm - delta;
#ifdef DEBUG
printf ("After qrsolv dxnorm = %g, delta = %g, fp = %g\n", dxnorm, delta, fp);
printf ("sdiag = ") ; gsl_vector_fprintf(stdout, sdiag, "%g"); printf("\n");
printf ("x = ") ; gsl_vector_fprintf(stdout, x, "%g"); printf("\n");
printf ("r = ") ; gsl_matrix_fprintf(stdout, r, "%g"); printf("\nXXX\n");
#endif
/* If the function is small enough, accept the current value of par */
if (fabs (fp) <= 0.1 * delta)
goto line220;
if (par_lower == 0 && fp <= fp_old && fp_old < 0)
goto line220;
/* Check for maximum number of iterations */
if (iter == 10)
goto line220;
/* Compute the Newton correction */
compute_newton_correction (r, sdiag, perm, x, dxnorm, diag, w);
#ifdef DEBUG
printf ("newton_correction = ");
gsl_vector_fprintf(stdout, w, "%g"); printf("\n");
#endif
{
double wnorm = enorm (w);
par_c = fp / (delta * wnorm * wnorm);
}
#ifdef DEBUG
printf("fp = %g\n", fp);
printf("par_lower = %g\n", par_lower);
printf("par_upper = %g\n", par_upper);
printf("par_c = %g\n", par_c);
#endif
/* Depending on the sign of the function, update par_lower or par_upper */
if (fp > 0)
{
if (par > par_lower)
{
par_lower = par;
#ifdef DEBUG
printf("fp > 0: set par_lower = par = %g\n", par);
#endif
}
}
else if (fp < 0)
{
if (par < par_upper)
{
#ifdef DEBUG
printf("fp < 0: set par_upper = par = %g\n", par);
#endif
par_upper = par;
}
}
/* Compute an improved estimate for par */
#ifdef DEBUG
printf("improved estimate par = MAX(%g, %g) \n", par_lower, par+par_c);
#endif
par = GSL_MAX_DBL (par_lower, par + par_c);
#ifdef DEBUG
printf("improved estimate par = %g \n", par);
#endif
goto iteration;
line220:
#ifdef DEBUG
printf("LEAVING lmpar, par = %g\n", par);
#endif
*par_inout = par;
return GSL_SUCCESS;
}