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/* multimin/directional_minimize.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 2 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.
*/
static void
take_step (const gsl_vector * x, const gsl_vector * p,
double step, double lambda, gsl_vector * x1, gsl_vector * dx)
{
gsl_vector_set_zero (dx);
gsl_blas_daxpy (-step * lambda, p, dx);
gsl_vector_memcpy (x1, x);
gsl_blas_daxpy (1.0, dx, x1);
}
static void
intermediate_point (gsl_multimin_function_fdf * fdf,
const gsl_vector * x, const gsl_vector * p,
double lambda,
double pg,
double stepa, double stepc,
double fa, double fc,
gsl_vector * x1, gsl_vector * dx, gsl_vector * gradient,
double * step, double * f)
{
double stepb, fb;
trial:
{
double u = fabs (pg * lambda * stepc);
stepb = 0.5 * stepc * u / ((fc - fa) + u);
}
take_step (x, p, stepb, lambda, x1, dx);
fb = GSL_MULTIMIN_FN_EVAL_F (fdf, x1);
#ifdef DEBUG
printf ("trying stepb = %g fb = %.18e\n", stepb, fb);
#endif
if (fb >= fa && stepb > 0.0)
{
/* downhill step failed, reduce step-size and try again */
fc = fb;
stepc = stepb;
goto trial;
}
#ifdef DEBUG
printf ("ok!\n");
#endif
*step = stepb;
*f = fb;
GSL_MULTIMIN_FN_EVAL_DF(fdf, x1, gradient);
}
static void
minimize (gsl_multimin_function_fdf * fdf,
const gsl_vector * x, const gsl_vector * p,
double lambda,
double stepa, double stepb, double stepc,
double fa, double fb, double fc, double tol,
gsl_vector * x1, gsl_vector * dx1,
gsl_vector * x2, gsl_vector * dx2, gsl_vector * gradient,
double * step, double * f, double * gnorm)
{
/* Starting at (x0, f0) move along the direction p to find a minimum
f(x0 - lambda * p), returning the new point x1 = x0-lambda*p,
f1=f(x1) and g1 = grad(f) at x1. */
double u = stepb;
double v = stepa;
double w = stepc;
double fu = fb;
double fv = fa;
double fw = fc;
double old2 = fabs(w - v);
double old1 = fabs(v - u);
double stepm, fm, pg, gnorm1;
int iter = 0;
gsl_vector_memcpy (x2, x1);
gsl_vector_memcpy (dx2, dx1);
*f = fb;
*step = stepb;
*gnorm = gsl_blas_dnrm2 (gradient);
mid_trial:
iter++;
if (iter > 10)
{
return; /* MAX ITERATIONS */
}
{
double dw = w - u;
double dv = v - u;
double du = 0.0;
double e1 = ((fv - fu) * dw * dw + (fu - fw) * dv * dv);
double e2 = 2.0 * ((fv - fu) * dw + (fu - fw) * dv);
if (e2 != 0.0)
{
du = e1 / e2;
}
if (du > 0.0 && du < (stepc - stepb) && fabs(du) < 0.5 * old2)
{
stepm = u + du;
}
else if (du < 0.0 && du > (stepa - stepb) && fabs(du) < 0.5 * old2)
{
stepm = u + du;
}
else if ((stepc - stepb) > (stepb - stepa))
{
stepm = 0.38 * (stepc - stepb) + stepb;
}
else
{
stepm = stepb - 0.38 * (stepb - stepa);
}
}
take_step (x, p, stepm, lambda, x1, dx1);
fm = GSL_MULTIMIN_FN_EVAL_F (fdf, x1);
#ifdef DEBUG
printf ("trying stepm = %g fm = %.18e\n", stepm, fm);
#endif
if (fm > fb)
{
if (fm < fv)
{
w = v;
v = stepm;
fw = fv;
fv = fm;
}
else if (fm < fw)
{
w = stepm;
fw = fm;
}
if (stepm < stepb)
{
stepa = stepm;
fa = fm;
}
else
{
stepc = stepm;
fc = fm;
}
goto mid_trial;
}
else if (fm <= fb)
{
old2 = old1;
old1 = fabs(u - stepm);
w = v;
v = u;
u = stepm;
fw = fv;
fv = fu;
fu = fm;
gsl_vector_memcpy (x2, x1);
gsl_vector_memcpy (dx2, dx1);
GSL_MULTIMIN_FN_EVAL_DF (fdf, x1, gradient);
gsl_blas_ddot (p, gradient, &pg);
gnorm1 = gsl_blas_dnrm2 (gradient);
#ifdef DEBUG
printf ("p: "); gsl_vector_fprintf(stdout, p, "%g");
printf ("g: "); gsl_vector_fprintf(stdout, gradient, "%g");
printf ("gnorm: %.18e\n", gnorm1);
printf ("pg: %.18e\n", pg);
printf ("orth: %g\n", fabs (pg * lambda/ gnorm1));
#endif
*f = fm;
*step = stepm;
*gnorm = gnorm1;
if (fabs (pg * lambda / gnorm1) < tol)
{
#ifdef DEBUG
printf("ok!\n");
#endif
return; /* SUCCESS */
}
if (stepm < stepb)
{
stepc = stepb;
fc = fb;
stepb = stepm;
fb = fm;
}
else
{
stepa = stepb;
fa = fb;
stepb = stepm;
fb = fm;
}
goto mid_trial;
}
}
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