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- /* multimin/vector_bfgs.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000 Fabrice Rossi
- *
- * 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.
- */
- /* vector_bfgs.c -- Limited memory Broyden-Fletcher-Goldfarb-Shanno method */
- /* Modified by Brian Gough to use single iteration structure */
- #include "gsl__config.h"
- #include "gsl_multimin.h"
- #include "gsl_blas.h"
- #include "gsl_multimin__directional_minimize.c"
- typedef struct
- {
- int iter;
- double step;
- double max_step;
- double tol;
- gsl_vector *x1;
- gsl_vector *dx1;
- gsl_vector *x2;
- double g0norm;
- double pnorm;
- gsl_vector *p;
- gsl_vector *x0;
- gsl_vector *g0;
- gsl_vector *dx0;
- gsl_vector *dg0;
- }
- vector_bfgs_state_t;
- static int
- vector_bfgs_alloc (void *vstate, size_t n)
- {
- vector_bfgs_state_t *state = (vector_bfgs_state_t *) vstate;
- state->x1 = gsl_vector_calloc (n);
- if (state->x1 == 0)
- {
- GSL_ERROR ("failed to allocate space for x1", GSL_ENOMEM);
- }
- state->dx1 = gsl_vector_calloc (n);
- if (state->dx1 == 0)
- {
- gsl_vector_free (state->x1);
- GSL_ERROR ("failed to allocate space for dx1", GSL_ENOMEM);
- }
- state->x2 = gsl_vector_calloc (n);
- if (state->x2 == 0)
- {
- gsl_vector_free (state->dx1);
- gsl_vector_free (state->x1);
- GSL_ERROR ("failed to allocate space for x2", GSL_ENOMEM);
- }
- state->p = gsl_vector_calloc (n);
- if (state->p == 0)
- {
- gsl_vector_free (state->x2);
- gsl_vector_free (state->dx1);
- gsl_vector_free (state->x1);
- GSL_ERROR ("failed to allocate space for p", GSL_ENOMEM);
- }
- state->x0 = gsl_vector_calloc (n);
- if (state->x0 == 0)
- {
- gsl_vector_free (state->p);
- gsl_vector_free (state->x2);
- gsl_vector_free (state->dx1);
- gsl_vector_free (state->x1);
- GSL_ERROR ("failed to allocate space for g0", GSL_ENOMEM);
- }
- state->g0 = gsl_vector_calloc (n);
- if (state->g0 == 0)
- {
- gsl_vector_free (state->x0);
- gsl_vector_free (state->p);
- gsl_vector_free (state->x2);
- gsl_vector_free (state->dx1);
- gsl_vector_free (state->x1);
- GSL_ERROR ("failed to allocate space for g0", GSL_ENOMEM);
- }
- state->dx0 = gsl_vector_calloc (n);
- if (state->dx0 == 0)
- {
- gsl_vector_free (state->g0);
- gsl_vector_free (state->x0);
- gsl_vector_free (state->p);
- gsl_vector_free (state->x2);
- gsl_vector_free (state->dx1);
- gsl_vector_free (state->x1);
- GSL_ERROR ("failed to allocate space for g0", GSL_ENOMEM);
- }
- state->dg0 = gsl_vector_calloc (n);
- if (state->dg0 == 0)
- {
- gsl_vector_free (state->dx0);
- gsl_vector_free (state->g0);
- gsl_vector_free (state->x0);
- gsl_vector_free (state->p);
- gsl_vector_free (state->x2);
- gsl_vector_free (state->dx1);
- gsl_vector_free (state->x1);
- GSL_ERROR ("failed to allocate space for g0", GSL_ENOMEM);
- }
- return GSL_SUCCESS;
- }
- static int
- vector_bfgs_set (void *vstate, gsl_multimin_function_fdf * fdf,
- const gsl_vector * x, double *f, gsl_vector * gradient,
- double step_size, double tol)
- {
- vector_bfgs_state_t *state = (vector_bfgs_state_t *) vstate;
- state->iter = 0;
- state->step = step_size;
- state->max_step = step_size;
- state->tol = tol;
- GSL_MULTIMIN_FN_EVAL_F_DF (fdf, x, f, gradient);
- /* Use the gradient as the initial direction */
- gsl_vector_memcpy (state->x0, x);
- gsl_vector_memcpy (state->p, gradient);
- gsl_vector_memcpy (state->g0, gradient);
- {
- double gnorm = gsl_blas_dnrm2 (gradient);
- state->pnorm = gnorm;
- state->g0norm = gnorm;
- }
- return GSL_SUCCESS;
- }
- static void
- vector_bfgs_free (void *vstate)
- {
- vector_bfgs_state_t *state = (vector_bfgs_state_t *) vstate;
- gsl_vector_free (state->dg0);
- gsl_vector_free (state->dx0);
- gsl_vector_free (state->g0);
- gsl_vector_free (state->x0);
- gsl_vector_free (state->p);
- gsl_vector_free (state->x2);
- gsl_vector_free (state->dx1);
- gsl_vector_free (state->x1);
- }
- static int
- vector_bfgs_restart (void *vstate)
- {
- vector_bfgs_state_t *state = (vector_bfgs_state_t *) vstate;
- state->iter = 0;
- return GSL_SUCCESS;
- }
- static int
- vector_bfgs_iterate (void *vstate, gsl_multimin_function_fdf * fdf,
- gsl_vector * x, double *f,
- gsl_vector * gradient, gsl_vector * dx)
- {
- vector_bfgs_state_t *state = (vector_bfgs_state_t *) vstate;
- gsl_vector *x1 = state->x1;
- gsl_vector *dx1 = state->dx1;
- gsl_vector *x2 = state->x2;
- gsl_vector *p = state->p;
- gsl_vector *g0 = state->g0;
- gsl_vector *x0 = state->x0;
- double pnorm = state->pnorm;
- double g0norm = state->g0norm;
- double fa = *f, fb, fc;
- double dir;
- double stepa = 0.0, stepb, stepc = state->step, tol = state->tol;
- double g1norm;
- double pg;
- if (pnorm == 0.0 || g0norm == 0.0)
- {
- gsl_vector_set_zero (dx);
- return GSL_ENOPROG;
- }
- /* Determine which direction is downhill, +p or -p */
- gsl_blas_ddot (p, gradient, &pg);
- dir = (pg >= 0.0) ? +1.0 : -1.0;
- /* Compute new trial point at x_c= x - step * p, where p is the
- current direction */
- take_step (x, p, stepc, dir / pnorm, x1, dx);
- /* Evaluate function and gradient at new point xc */
- fc = GSL_MULTIMIN_FN_EVAL_F (fdf, x1);
- if (fc < fa)
- {
- /* Success, reduced the function value */
- state->step = stepc * 2.0;
- *f = fc;
- gsl_vector_memcpy (x, x1);
- GSL_MULTIMIN_FN_EVAL_DF (fdf, x1, gradient);
- return GSL_SUCCESS;
- }
- #ifdef DEBUG
- printf ("got stepc = %g fc = %g\n", stepc, fc);
- #endif
- /* Do a line minimisation in the region (xa,fa) (xc,fc) to find an
- intermediate (xb,fb) satisifying fa > fb < fc. Choose an initial
- xb based on parabolic interpolation */
- intermediate_point (fdf, x, p, dir / pnorm, pg,
- stepa, stepc, fa, fc, x1, dx1, gradient, &stepb, &fb);
- if (stepb == 0.0)
- {
- return GSL_ENOPROG;
- }
- minimize (fdf, x, p, dir / pnorm,
- stepa, stepb, stepc, fa, fb, fc, tol,
- x1, dx1, x2, dx, gradient, &(state->step), f, &g1norm);
- gsl_vector_memcpy (x, x2);
- /* Choose a new direction for the next step */
- state->iter = (state->iter + 1) % x->size;
- if (state->iter == 0)
- {
- gsl_vector_memcpy (p, gradient);
- state->pnorm = g1norm;
- }
- else
- {
- /* This is the BFGS update: */
- /* p' = g1 - A dx - B dg */
- /* A = - (1+ dg.dg/dx.dg) B + dg.g/dx.dg */
- /* B = dx.g/dx.dg */
- gsl_vector *dx0 = state->dx0;
- gsl_vector *dg0 = state->dg0;
- double dxg, dgg, dxdg, dgnorm, A, B;
- /* dx0 = x - x0 */
- gsl_vector_memcpy (dx0, x);
- gsl_blas_daxpy (-1.0, x0, dx0);
- /* dg0 = g - g0 */
- gsl_vector_memcpy (dg0, gradient);
- gsl_blas_daxpy (-1.0, g0, dg0);
- gsl_blas_ddot (dx0, gradient, &dxg);
- gsl_blas_ddot (dg0, gradient, &dgg);
- gsl_blas_ddot (dx0, dg0, &dxdg);
- dgnorm = gsl_blas_dnrm2 (dg0);
- if (dxdg != 0)
- {
- B = dxg / dxdg;
- A = -(1.0 + dgnorm * dgnorm / dxdg) * B + dgg / dxdg;
- }
- else
- {
- B = 0;
- A = 0;
- }
- gsl_vector_memcpy (p, gradient);
- gsl_blas_daxpy (-A, dx0, p);
- gsl_blas_daxpy (-B, dg0, p);
- state->pnorm = gsl_blas_dnrm2 (p);
- }
- gsl_vector_memcpy (g0, gradient);
- gsl_vector_memcpy (x0, x);
- state->g0norm = gsl_blas_dnrm2 (g0);
- #ifdef DEBUG
- printf ("updated directions\n");
- printf ("p: ");
- gsl_vector_fprintf (stdout, p, "%g");
- printf ("g: ");
- gsl_vector_fprintf (stdout, gradient, "%g");
- #endif
- return GSL_SUCCESS;
- }
- static const gsl_multimin_fdfminimizer_type vector_bfgs_type = {
- "vector_bfgs", /* name */
- sizeof (vector_bfgs_state_t),
- &vector_bfgs_alloc,
- &vector_bfgs_set,
- &vector_bfgs_iterate,
- &vector_bfgs_restart,
- &vector_bfgs_free
- };
- const gsl_multimin_fdfminimizer_type
- * gsl_multimin_fdfminimizer_vector_bfgs = &vector_bfgs_type;
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