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static int
iterate (void *vstate, gsl_multifit_function_fdf * fdf, gsl_vector * x, gsl_vector * f, gsl_matrix * J, gsl_vector * dx, int scale)
{
lmder_state_t *state = (lmder_state_t *) vstate;
gsl_matrix *r = state->r;
gsl_vector *tau = state->tau;
gsl_vector *diag = state->diag;
gsl_vector *qtf = state->qtf;
gsl_vector *x_trial = state->x_trial;
gsl_vector *f_trial = state->f_trial;
gsl_vector *rptdx = state->rptdx;
gsl_vector *newton = state->newton;
gsl_vector *gradient = state->gradient;
gsl_vector *sdiag = state->sdiag;
gsl_vector *w = state->w;
gsl_vector *work1 = state->work1;
gsl_permutation *perm = state->perm;
double prered, actred;
double pnorm, fnorm1, fnorm1p, gnorm;
double ratio;
double dirder;
int iter = 0;
double p1 = 0.1, p25 = 0.25, p5 = 0.5, p75 = 0.75, p0001 = 0.0001;
if (state->fnorm == 0.0)
{
return GSL_SUCCESS;
}
/* Compute qtf = Q^T f */
gsl_vector_memcpy (qtf, f);
gsl_linalg_QR_QTvec (r, tau, qtf);
/* Compute norm of scaled gradient */
compute_gradient_direction (r, perm, qtf, diag, gradient);
{
size_t iamax = gsl_blas_idamax (gradient);
gnorm = fabs(gsl_vector_get (gradient, iamax) / state->fnorm);
}
/* Determine the Levenberg-Marquardt parameter */
lm_iteration:
iter++ ;
{
int status = lmpar (r, perm, qtf, diag, state->delta, &(state->par), newton, gradient, sdiag, dx, w);
if (status)
return status;
}
/* Take a trial step */
gsl_vector_scale (dx, -1.0); /* reverse the step to go downhill */
compute_trial_step (x, dx, state->x_trial);
pnorm = scaled_enorm (diag, dx);
if (state->iter == 1)
{
if (pnorm < state->delta)
{
#ifdef DEBUG
printf("set delta = pnorm = %g\n" , pnorm);
#endif
state->delta = pnorm;
}
}
/* Evaluate function at x + p */
/* return immediately if evaluation raised error */
{
int status = GSL_MULTIFIT_FN_EVAL_F (fdf, x_trial, f_trial);
if (status)
return status;
}
fnorm1 = enorm (f_trial);
/* Compute the scaled actual reduction */
actred = compute_actual_reduction (state->fnorm, fnorm1);
#ifdef DEBUG
printf("lmiterate: fnorm = %g fnorm1 = %g actred = %g\n", state->fnorm, fnorm1, actred);
#endif
/* Compute rptdx = R P^T dx, noting that |J dx| = |R P^T dx| */
compute_rptdx (r, perm, dx, rptdx);
fnorm1p = enorm (rptdx);
/* Compute the scaled predicted reduction = |J dx|^2 + 2 par |D dx|^2 */
{
double t1 = fnorm1p / state->fnorm;
double t2 = (sqrt(state->par) * pnorm) / state->fnorm;
prered = t1 * t1 + t2 * t2 / p5;
dirder = -(t1 * t1 + t2 * t2);
}
/* compute the ratio of the actual to predicted reduction */
if (prered > 0)
{
ratio = actred / prered;
}
else
{
ratio = 0;
}
#ifdef DEBUG
printf("lmiterate: prered = %g dirder = %g ratio = %g\n", prered, dirder,ratio);
#endif
/* update the step bound */
if (ratio > p25)
{
#ifdef DEBUG
printf("ratio > p25\n");
#endif
if (state->par == 0 || ratio >= p75)
{
state->delta = pnorm / p5;
state->par *= p5;
#ifdef DEBUG
printf("updated step bounds: delta = %g, par = %g\n", state->delta, state->par);
#endif
}
}
else
{
double temp = (actred >= 0) ? p5 : p5*dirder / (dirder + p5 * actred);
#ifdef DEBUG
printf("ratio < p25\n");
#endif
if (p1 * fnorm1 >= state->fnorm || temp < p1 )
{
temp = p1;
}
state->delta = temp * GSL_MIN_DBL (state->delta, pnorm/p1);
state->par /= temp;
#ifdef DEBUG
printf("updated step bounds: delta = %g, par = %g\n", state->delta, state->par);
#endif
}
/* test for successful iteration, termination and stringent tolerances */
if (ratio >= p0001)
{
gsl_vector_memcpy (x, x_trial);
gsl_vector_memcpy (f, f_trial);
/* return immediately if evaluation raised error */
{
int status = GSL_MULTIFIT_FN_EVAL_DF (fdf, x_trial, J);
if (status)
return status;
}
/* wa2_j = diag_j * x_j */
state->xnorm = scaled_enorm(diag, x);
state->fnorm = fnorm1;
state->iter++;
/* Rescale if necessary */
if (scale)
{
update_diag (J, diag);
}
{
int signum;
gsl_matrix_memcpy (r, J);
gsl_linalg_QRPT_decomp (r, tau, perm, &signum, work1);
}
return GSL_SUCCESS;
}
else if (fabs(actred) <= GSL_DBL_EPSILON && prered <= GSL_DBL_EPSILON
&& p5 * ratio <= 1.0)
{
return GSL_ETOLF ;
}
else if (state->delta <= GSL_DBL_EPSILON * state->xnorm)
{
return GSL_ETOLX;
}
else if (gnorm <= GSL_DBL_EPSILON)
{
return GSL_ETOLG;
}
else if (iter < 10)
{
/* Repeat inner loop if unsuccessful */
goto lm_iteration;
}
return GSL_CONTINUE;
}
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