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);
if (gsl_vector_equal (x, x1))
{
/* Take fast exit if trial point does not move from initial point */
#ifdef DEBUG
printf ("fast exit x == x1 for stepb = %g\n", stepb);
#endif
*step = 0;
*f = fa;
GSL_MULTIMIN_FN_EVAL_DF(fdf, x1, gradient);
return ;
}
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 double wrap_df(double alpha, void *params)
{
wrapper_t *w = (wrapper_t *) params;
if (alpha == w->df_cache_key) { /* using previously cached df(alpha) */
return w->df_alpha;
}
moveto(alpha, w);
if (alpha != w->g_cache_key) {
GSL_MULTIMIN_FN_EVAL_DF(w->fdf, w->x_alpha, w->g_alpha);
w->g_cache_key = alpha;
}
w->df_alpha = slope(w);
w->df_cache_key = alpha;
return w->df_alpha;
}
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;
}
}
static int
conjugate_fr_iterate (void *vstate, gsl_multimin_function_fdf * fdf,
gsl_vector * x, double *f,
gsl_vector * gradient, gsl_vector * dx)
{
conjugate_fr_state_t *state = (conjugate_fr_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;
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 conjugate 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
{
/* p' = g1 - beta * p */
double beta = -pow (g1norm / g0norm, 2.0);
gsl_blas_dscal (-beta, p);
gsl_blas_daxpy (1.0, gradient, p);
state->pnorm = gsl_blas_dnrm2 (p);
}
state->g0norm = g1norm;
gsl_vector_memcpy (g0, gradient);
#ifdef DEBUG
printf ("updated conjugate directions\n");
printf ("p: ");
gsl_vector_fprintf (stdout, p, "%g");
printf ("g: ");
gsl_vector_fprintf (stdout, gradient, "%g");
#endif
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;
}