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- /* multiroots/dogleg.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_multiroots__enorm.c"
- static void compute_diag (const gsl_matrix * J, gsl_vector * diag);
- static void update_diag (const gsl_matrix * J, gsl_vector * diag);
- static double compute_delta (gsl_vector * diag, gsl_vector * x);
- static void compute_df (const gsl_vector * f_trial, const gsl_vector * f, gsl_vector * df);
- static void compute_wv (const gsl_vector * qtdf, const gsl_vector *rdx, const gsl_vector *dx, const gsl_vector *diag, double pnorm, gsl_vector * w, gsl_vector * v);
- static double scaled_enorm (const gsl_vector * d, const gsl_vector * f);
- static double scaled_enorm (const gsl_vector * d, const gsl_vector * f) {
- double e2 = 0 ;
- size_t i, n = f->size ;
- for (i = 0; i < n ; i++) {
- double fi= gsl_vector_get(f, i);
- double di= gsl_vector_get(d, i);
- double u = di * fi;
- e2 += u * u ;
- }
- return sqrt(e2);
- }
- static double enorm_sum (const gsl_vector * a, const gsl_vector * b);
- static double enorm_sum (const gsl_vector * a, const gsl_vector * b) {
- double e2 = 0 ;
- size_t i, n = a->size ;
- for (i = 0; i < n ; i++) {
- double ai= gsl_vector_get(a, i);
- double bi= gsl_vector_get(b, i);
- double u = ai + bi;
- e2 += u * u ;
- }
- return sqrt(e2);
- }
- static void
- compute_wv (const gsl_vector * qtdf, const gsl_vector *rdx, const gsl_vector *dx, const gsl_vector *diag, double pnorm, gsl_vector * w, gsl_vector * v)
- {
- size_t i, n = qtdf->size;
- for (i = 0; i < n; i++)
- {
- double qtdfi = gsl_vector_get (qtdf, i);
- double rdxi = gsl_vector_get (rdx, i);
- double dxi = gsl_vector_get (dx, i);
- double diagi = gsl_vector_get (diag, i);
- gsl_vector_set (w, i, (qtdfi - rdxi) / pnorm);
- gsl_vector_set (v, i, diagi * diagi * dxi / pnorm);
- }
- }
- static void
- compute_df (const gsl_vector * f_trial, const gsl_vector * f, gsl_vector * df)
- {
- size_t i, n = f->size;
- for (i = 0; i < n; i++)
- {
- double dfi = gsl_vector_get (f_trial, i) - gsl_vector_get (f, i);
- gsl_vector_set (df, i, dfi);
- }
- }
- static void
- compute_diag (const gsl_matrix * J, gsl_vector * diag)
- {
- size_t i, j, n = diag->size;
- for (j = 0; j < n; j++)
- {
- double sum = 0;
- for (i = 0; i < n; i++)
- {
- double Jij = gsl_matrix_get (J, i, j);
- sum += Jij * Jij;
- }
- if (sum == 0)
- sum = 1.0;
- gsl_vector_set (diag, j, sqrt (sum));
- }
- }
- static void
- update_diag (const gsl_matrix * J, gsl_vector * diag)
- {
- size_t i, j, n = diag->size;
- for (j = 0; j < n; j++)
- {
- double cnorm, diagj, sum = 0;
- for (i = 0; i < n; i++)
- {
- double Jij = gsl_matrix_get (J, i, j);
- sum += Jij * Jij;
- }
- if (sum == 0)
- sum = 1.0;
- cnorm = sqrt (sum);
- diagj = gsl_vector_get (diag, j);
- if (cnorm > diagj)
- gsl_vector_set (diag, j, cnorm);
- }
- }
- static double
- compute_delta (gsl_vector * diag, gsl_vector * x)
- {
- double Dx = scaled_enorm (diag, x);
- double factor = 100;
- return (Dx > 0) ? factor * Dx : factor;
- }
- static double
- compute_actual_reduction (double fnorm, double fnorm1)
- {
- double actred;
- if (fnorm1 < fnorm)
- {
- double u = fnorm1 / fnorm;
- actred = 1 - u * u;
- }
- else
- {
- actred = -1;
- }
- return actred;
- }
- static double
- compute_predicted_reduction (double fnorm, double fnorm1)
- {
- double prered;
- if (fnorm1 < fnorm)
- {
- double u = fnorm1 / fnorm;
- prered = 1 - u * u;
- }
- else
- {
- prered = 0;
- }
- return prered;
- }
- static void
- compute_qtf (const gsl_matrix * q, const gsl_vector * f, gsl_vector * qtf)
- {
- size_t i, j, N = f->size ;
- for (j = 0; j < N; j++)
- {
- double sum = 0;
- for (i = 0; i < N; i++)
- sum += gsl_matrix_get (q, i, j) * gsl_vector_get (f, i);
- gsl_vector_set (qtf, j, sum);
- }
- }
- static void
- compute_rdx (const gsl_matrix * r, const gsl_vector * dx, gsl_vector * rdx)
- {
- size_t i, j, N = dx->size ;
- for (i = 0; i < N; i++)
- {
- double sum = 0;
- for (j = i; j < N; j++)
- {
- sum += gsl_matrix_get (r, i, j) * gsl_vector_get (dx, j);
- }
- gsl_vector_set (rdx, i, sum);
- }
- }
- static void
- compute_trial_step (gsl_vector *x, gsl_vector * dx, gsl_vector * x_trial)
- {
- size_t i, N = x->size;
- for (i = 0; i < N; i++)
- {
- double pi = gsl_vector_get (dx, i);
- double xi = gsl_vector_get (x, i);
- gsl_vector_set (x_trial, i, xi + pi);
- }
- }
- static int
- newton_direction (const gsl_matrix * r, const gsl_vector * qtf, gsl_vector * p)
- {
- const size_t N = r->size2;
- size_t i;
- int status;
- status = gsl_linalg_R_solve (r, qtf, p);
- #ifdef DEBUG
- printf("rsolve status = %d\n", status);
- #endif
- for (i = 0; i < N; i++)
- {
- double pi = gsl_vector_get (p, i);
- gsl_vector_set (p, i, -pi);
- }
- return status;
- }
- static void
- gradient_direction (const gsl_matrix * r, const gsl_vector * qtf,
- const gsl_vector * diag, gsl_vector * g)
- {
- const size_t M = r->size1;
- const size_t N = r->size2;
- size_t i, j;
- for (j = 0; j < M; j++)
- {
- double sum = 0;
- double dj;
- for (i = 0; i < N; i++)
- {
- sum += gsl_matrix_get (r, i, j) * gsl_vector_get (qtf, i);
- }
- dj = gsl_vector_get (diag, j);
- gsl_vector_set (g, j, -sum / dj);
- }
- }
- static void
- minimum_step (double gnorm, const gsl_vector * diag, gsl_vector * g)
- {
- const size_t N = g->size;
- size_t i;
- for (i = 0; i < N; i++)
- {
- double gi = gsl_vector_get (g, i);
- double di = gsl_vector_get (diag, i);
- gsl_vector_set (g, i, (gi / gnorm) / di);
- }
- }
- static void
- compute_Rg (const gsl_matrix * r, const gsl_vector * gradient, gsl_vector * Rg)
- {
- const size_t N = r->size2;
- size_t i, j;
- for (i = 0; i < N; i++)
- {
- double sum = 0;
- for (j = i; j < N; j++)
- {
- double gj = gsl_vector_get (gradient, j);
- double rij = gsl_matrix_get (r, i, j);
- sum += rij * gj;
- }
- gsl_vector_set (Rg, i, sum);
- }
- }
- static void
- scaled_addition (double alpha, gsl_vector * newton, double beta, gsl_vector * gradient, gsl_vector * p)
- {
- const size_t N = p->size;
- size_t i;
- for (i = 0; i < N; i++)
- {
- double ni = gsl_vector_get (newton, i);
- double gi = gsl_vector_get (gradient, i);
- gsl_vector_set (p, i, alpha * ni + beta * gi);
- }
- }
- static int
- dogleg (const gsl_matrix * r, const gsl_vector * qtf,
- const gsl_vector * diag, double delta,
- gsl_vector * newton, gsl_vector * gradient, gsl_vector * p)
- {
- double qnorm, gnorm, sgnorm, bnorm, temp;
- newton_direction (r, qtf, newton);
- #ifdef DEBUG
- printf("newton = "); gsl_vector_fprintf(stdout, newton, "%g"); printf("\n");
- #endif
- qnorm = scaled_enorm (diag, newton);
- if (qnorm <= delta)
- {
- gsl_vector_memcpy (p, newton);
- #ifdef DEBUG
- printf("took newton (qnorm = %g <= delta = %g)\n", qnorm, delta);
- #endif
- return GSL_SUCCESS;
- }
- gradient_direction (r, qtf, diag, gradient);
- #ifdef DEBUG
- printf("grad = "); gsl_vector_fprintf(stdout, gradient, "%g"); printf("\n");
- #endif
- gnorm = enorm (gradient);
- if (gnorm == 0)
- {
- double alpha = delta / qnorm;
- double beta = 0;
- scaled_addition (alpha, newton, beta, gradient, p);
- #ifdef DEBUG
- printf("took scaled newton because gnorm = 0\n");
- #endif
- return GSL_SUCCESS;
- }
- minimum_step (gnorm, diag, gradient);
- compute_Rg (r, gradient, p); /* Use p as temporary space to compute Rg */
- #ifdef DEBUG
- printf("mingrad = "); gsl_vector_fprintf(stdout, gradient, "%g"); printf("\n");
- printf("Rg = "); gsl_vector_fprintf(stdout, p, "%g"); printf("\n");
- #endif
- temp = enorm (p);
- sgnorm = (gnorm / temp) / temp;
- if (sgnorm > delta)
- {
- double alpha = 0;
- double beta = delta;
- scaled_addition (alpha, newton, beta, gradient, p);
- #ifdef DEBUG
- printf("took gradient\n");
- #endif
- return GSL_SUCCESS;
- }
- bnorm = enorm (qtf);
- {
- double bg = bnorm / gnorm;
- double bq = bnorm / qnorm;
- double dq = delta / qnorm;
- double dq2 = dq * dq;
- double sd = sgnorm / delta;
- double sd2 = sd * sd;
- double t1 = bg * bq * sd;
- double u = t1 - dq;
- double t2 = t1 - dq * sd2 + sqrt (u * u + (1-dq2) * (1 - sd2));
- double alpha = dq * (1 - sd2) / t2;
- double beta = (1 - alpha) * sgnorm;
- #ifdef DEBUG
- printf("bnorm = %g\n", bnorm);
- printf("gnorm = %g\n", gnorm);
- printf("qnorm = %g\n", qnorm);
- printf("delta = %g\n", delta);
- printf("alpha = %g beta = %g\n", alpha, beta);
- printf("took scaled combination of newton and gradient\n");
- #endif
- scaled_addition (alpha, newton, beta, gradient, p);
- }
- return GSL_SUCCESS;
- }
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