/* multilarge_nlinear/gsl_multilarge_nlinear.h
*
* Copyright (C) 2015, 2016 Patrick Alken
*
* 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.
*/
#ifndef __GSL_MULTILARGE_NLINEAR_H__
#define __GSL_MULTILARGE_NLINEAR_H__
#include <stdlib.h>
#include <gsl/gsl_types.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_permutation.h>
#include <gsl/gsl_blas.h>
#undef __BEGIN_DECLS
#undef __END_DECLS
#ifdef __cplusplus
# define __BEGIN_DECLS extern "C" {
# define __END_DECLS }
#else
# define __BEGIN_DECLS /* empty */
# define __END_DECLS /* empty */
#endif
__BEGIN_DECLS
typedef enum
{
GSL_MULTILARGE_NLINEAR_FWDIFF,
GSL_MULTILARGE_NLINEAR_CTRDIFF
} gsl_multilarge_nlinear_fdtype;
/* Definition of vector-valued functions and gradient with parameters
based on gsl_vector */
typedef struct
{
int (* f) (const gsl_vector * x, void * params, gsl_vector * f);
int (* df) (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
const gsl_vector * u, void * params, gsl_vector * v,
gsl_matrix * JTJ);
int (* fvv) (const gsl_vector * x, const gsl_vector * v, void * params,
gsl_vector * fvv);
size_t n; /* number of functions */
size_t p; /* number of independent variables */
void * params; /* user parameters */
size_t nevalf; /* number of function evaluations */
size_t nevaldfu; /* number of Jacobian matrix-vector evaluations */
size_t nevaldf2; /* number of Jacobian J^T J evaluations */
size_t nevalfvv; /* number of fvv evaluations */
} gsl_multilarge_nlinear_fdf;
/* trust region subproblem method */
typedef struct
{
const char *name;
void * (*alloc) (const void * params, const size_t n, const size_t p);
int (*init) (const void * vtrust_state, void * vstate);
int (*preloop) (const void * vtrust_state, void * vstate);
int (*step) (const void * vtrust_state, const double delta,
gsl_vector * dx, void * vstate);
int (*preduction) (const void * vtrust_state, const gsl_vector * dx,
double * pred, void * vstate);
void (*free) (void * vstate);
} gsl_multilarge_nlinear_trs;
/* scaling matrix specification */
typedef struct
{
const char *name;
int (*init) (const gsl_matrix * JTJ, gsl_vector * diag);
int (*update) (const gsl_matrix * JTJ, gsl_vector * diag);
} gsl_multilarge_nlinear_scale;
/*
* linear least squares solvers - there are three steps to
* solving a least squares problem using a direct method:
*
* 1. init: called once per iteration when a new Jacobian matrix
* is required; form normal equations matrix J^T J
* 2. presolve: called each time a new LM parameter value mu is available;
* used for cholesky method in order to factor
* the (J^T J + mu D^T D) matrix
* 3. solve: solve the least square system for a given rhs
*/
typedef struct
{
const char *name;
void * (*alloc) (const size_t n, const size_t p);
int (*init) (const void * vtrust_state, void * vstate);
int (*presolve) (const double mu, const void * vtrust_state, void * vstate);
int (*solve) (const gsl_vector * g, gsl_vector * x,
const void * vtrust_state, void * vstate);
int (*rcond) (double * rcond, const gsl_matrix * JTJ, void * vstate);
int (*covar) (const gsl_matrix * JTJ, gsl_matrix * covar, void * vstate);
void (*free) (void * vstate);
} gsl_multilarge_nlinear_solver;
/* tunable parameters */
typedef struct
{
const gsl_multilarge_nlinear_trs *trs; /* trust region subproblem method */
const gsl_multilarge_nlinear_scale *scale; /* scaling method */
const gsl_multilarge_nlinear_solver *solver; /* solver method */
gsl_multilarge_nlinear_fdtype fdtype; /* finite difference method */
double factor_up; /* factor for increasing trust radius */
double factor_down; /* factor for decreasing trust radius */
double avmax; /* max allowed |a|/|v| */
double h_df; /* step size for finite difference Jacobian */
double h_fvv; /* step size for finite difference fvv */
size_t max_iter; /* maximum iterations for trs method */
double tol; /* tolerance for solving trs */
} gsl_multilarge_nlinear_parameters;
typedef struct
{
const char *name;
void * (*alloc) (const gsl_multilarge_nlinear_parameters * params,
const size_t n, const size_t p);
int (*init) (void * state, const gsl_vector * wts,
gsl_multilarge_nlinear_fdf * fdf, const gsl_vector * x,
gsl_vector * f, gsl_vector * g, gsl_matrix * JTJ);
int (*iterate) (void * state, const gsl_vector * wts,
gsl_multilarge_nlinear_fdf * fdf, gsl_vector * x,
gsl_vector * f, gsl_vector * g, gsl_matrix * JTJ,
gsl_vector * dx);
int (*rcond) (double * rcond, const gsl_matrix * JTJ, void * state);
int (*covar) (const gsl_matrix * JTJ, gsl_matrix * covar, void * state);
double (*avratio) (void * state);
void (*free) (void * state);
} gsl_multilarge_nlinear_type;
/* current state passed to low-level trust region algorithms */
typedef struct
{
const gsl_vector * x; /* parameter values x */
const gsl_vector * f; /* residual vector f(x) */
const gsl_vector * g; /* gradient J^T f */
const gsl_matrix * JTJ; /* matrix J^T J */
const gsl_vector * diag; /* scaling matrix D */
const gsl_vector * sqrt_wts; /* sqrt(diag(W)) or NULL for unweighted */
const double *mu; /* LM parameter */
const gsl_multilarge_nlinear_parameters * params;
void *solver_state; /* workspace for direct least squares solver */
gsl_multilarge_nlinear_fdf * fdf;
double *avratio; /* |a| / |v| */
} gsl_multilarge_nlinear_trust_state;
typedef struct
{
const gsl_multilarge_nlinear_type * type;
gsl_multilarge_nlinear_fdf * fdf ;
gsl_vector * x; /* parameter values x */
gsl_vector * f; /* residual vector f(x) */
gsl_vector * dx; /* step dx */
gsl_vector * g; /* gradient J^T f */
gsl_matrix * JTJ; /* matrix J^T J */
gsl_vector * sqrt_wts_work; /* sqrt(W) */
gsl_vector * sqrt_wts; /* ptr to sqrt_wts_work, or NULL if not using weights */
size_t n; /* number of residuals */
size_t p; /* number of parameters */
size_t niter; /* number of iterations performed */
gsl_multilarge_nlinear_parameters params;
void *state;
} gsl_multilarge_nlinear_workspace;
gsl_multilarge_nlinear_workspace *
gsl_multilarge_nlinear_alloc (const gsl_multilarge_nlinear_type * T,
const gsl_multilarge_nlinear_parameters * params,
size_t n, size_t p);
void gsl_multilarge_nlinear_free (gsl_multilarge_nlinear_workspace * w);
gsl_multilarge_nlinear_parameters gsl_multilarge_nlinear_default_parameters(void);
int
gsl_multilarge_nlinear_init (const gsl_vector * x,
gsl_multilarge_nlinear_fdf * fdf,
gsl_multilarge_nlinear_workspace * w);
int gsl_multilarge_nlinear_winit (const gsl_vector * x,
const gsl_vector * wts,
gsl_multilarge_nlinear_fdf * fdf,
gsl_multilarge_nlinear_workspace * w);
int
gsl_multilarge_nlinear_iterate (gsl_multilarge_nlinear_workspace * w);
double
gsl_multilarge_nlinear_avratio (const gsl_multilarge_nlinear_workspace * w);
int
gsl_multilarge_nlinear_rcond (double * rcond, const gsl_multilarge_nlinear_workspace * w);
int
gsl_multilarge_nlinear_covar (gsl_matrix * covar, gsl_multilarge_nlinear_workspace * w);
int
gsl_multilarge_nlinear_driver (const size_t maxiter,
const double xtol,
const double gtol,
const double ftol,
void (*callback)(const size_t iter, void *params,
const gsl_multilarge_nlinear_workspace *w),
void *callback_params,
int *info,
gsl_multilarge_nlinear_workspace * w);
const char *
gsl_multilarge_nlinear_name (const gsl_multilarge_nlinear_workspace * w);
gsl_vector *
gsl_multilarge_nlinear_position (const gsl_multilarge_nlinear_workspace * w);
gsl_vector *
gsl_multilarge_nlinear_residual (const gsl_multilarge_nlinear_workspace * w);
gsl_vector *
gsl_multilarge_nlinear_step (const gsl_multilarge_nlinear_workspace * w);
size_t
gsl_multilarge_nlinear_niter (const gsl_multilarge_nlinear_workspace * w);
const char *
gsl_multilarge_nlinear_trs_name (const gsl_multilarge_nlinear_workspace * w);
int gsl_multilarge_nlinear_eval_f(gsl_multilarge_nlinear_fdf *fdf,
const gsl_vector *x,
const gsl_vector *swts,
gsl_vector *y);
int
gsl_multilarge_nlinear_eval_df(const CBLAS_TRANSPOSE_t TransJ,
const gsl_vector *x,
const gsl_vector *f,
const gsl_vector *u,
const gsl_vector *swts,
const double h,
const gsl_multilarge_nlinear_fdtype fdtype,
gsl_multilarge_nlinear_fdf *fdf,
gsl_vector *v,
gsl_matrix *JTJ,
gsl_vector *work);
int
gsl_multilarge_nlinear_eval_fvv(const double h,
const gsl_vector *x,
const gsl_vector *v,
const gsl_vector *f,
const gsl_vector *swts,
gsl_multilarge_nlinear_fdf *fdf,
gsl_vector *yvv,
gsl_vector *work);
/* convergence.c */
int
gsl_multilarge_nlinear_test (const double xtol, const double gtol,
const double ftol, int *info,
const gsl_multilarge_nlinear_workspace * w);
/* fdjac.c */
int
gsl_multilarge_nlinear_df(const double h, const gsl_multilarge_nlinear_fdtype fdtype,
const gsl_vector *x, const gsl_vector *wts,
gsl_multilarge_nlinear_fdf *fdf,
const gsl_vector *f, gsl_matrix *J, gsl_vector *work);
/* fdfvv.c */
int
gsl_multilarge_nlinear_fdfvv(const double h, const gsl_vector *x, const gsl_vector *v,
const gsl_vector *f, const gsl_matrix *J,
const gsl_vector *swts, gsl_multilarge_nlinear_fdf *fdf,
gsl_vector *fvv, gsl_vector *work);
/* top-level algorithms */
GSL_VAR const gsl_multilarge_nlinear_type * gsl_multilarge_nlinear_trust;
/* trust region subproblem methods */
GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_lm;
GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_lmaccel;
GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_dogleg;
GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_ddogleg;
GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_subspace2D;
GSL_VAR const gsl_multilarge_nlinear_trs * gsl_multilarge_nlinear_trs_cgst;
/* scaling matrix strategies */
GSL_VAR const gsl_multilarge_nlinear_scale * gsl_multilarge_nlinear_scale_levenberg;
GSL_VAR const gsl_multilarge_nlinear_scale * gsl_multilarge_nlinear_scale_marquardt;
GSL_VAR const gsl_multilarge_nlinear_scale * gsl_multilarge_nlinear_scale_more;
/* linear solvers */
GSL_VAR const gsl_multilarge_nlinear_solver * gsl_multilarge_nlinear_solver_cholesky;
GSL_VAR const gsl_multilarge_nlinear_solver * gsl_multilarge_nlinear_solver_none;
__END_DECLS
#endif /* __GSL_MULTILARGE_NLINEAR_H__ */