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/* multifit/gsl_multifit.h
*
* Copyright (C) 2000, 2007, 2010 Brian Gough
* Copyright (C) 2013, 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_MULTIFIT_H__
#define __GSL_MULTIFIT_H__
#include <stdlib.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_types.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 struct
{
size_t nmax; /* maximum number of observations */
size_t pmax; /* maximum number of parameters */
size_t n; /* number of observations in current SVD decomposition */
size_t p; /* number of parameters in current SVD decomposition */
gsl_matrix * A; /* least squares matrix for SVD, n-by-p */
gsl_matrix * Q;
gsl_matrix * QSI;
gsl_vector * S;
gsl_vector * t;
gsl_vector * xt;
gsl_vector * D;
double rcond; /* reciprocal condition number */
}
gsl_multifit_linear_workspace;
gsl_multifit_linear_workspace *
gsl_multifit_linear_alloc (const size_t n, const size_t p);
void
gsl_multifit_linear_free (gsl_multifit_linear_workspace * w);
int
gsl_multifit_linear (const gsl_matrix * X,
const gsl_vector * y,
gsl_vector * c,
gsl_matrix * cov,
double * chisq,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_svd (const gsl_matrix * X,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_bsvd (const gsl_matrix * X,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_solve (const double lambda,
const gsl_matrix * X,
const gsl_vector * y,
gsl_vector * c,
double *rnorm,
double *snorm,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_applyW(const gsl_matrix * X,
const gsl_vector * w,
const gsl_vector * y,
gsl_matrix * WX,
gsl_vector * Wy);
int
gsl_multifit_linear_stdform1 (const gsl_vector * L,
const gsl_matrix * X,
const gsl_vector * y,
gsl_matrix * Xs,
gsl_vector * ys,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_wstdform1 (const gsl_vector * L,
const gsl_matrix * X,
const gsl_vector * w,
const gsl_vector * y,
gsl_matrix * Xs,
gsl_vector * ys,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_L_decomp (gsl_matrix * L, gsl_vector * tau);
int
gsl_multifit_linear_stdform2 (const gsl_matrix * LQR,
const gsl_vector * Ltau,
const gsl_matrix * X,
const gsl_vector * y,
gsl_matrix * Xs,
gsl_vector * ys,
gsl_matrix * M,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_wstdform2 (const gsl_matrix * LQR,
const gsl_vector * Ltau,
const gsl_matrix * X,
const gsl_vector * w,
const gsl_vector * y,
gsl_matrix * Xs,
gsl_vector * ys,
gsl_matrix * M,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_genform1 (const gsl_vector * L,
const gsl_vector * cs,
gsl_vector * c,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_genform2 (const gsl_matrix * LQR,
const gsl_vector * Ltau,
const gsl_matrix * X,
const gsl_vector * y,
const gsl_vector * cs,
const gsl_matrix * M,
gsl_vector * c,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_wgenform2 (const gsl_matrix * LQR,
const gsl_vector * Ltau,
const gsl_matrix * X,
const gsl_vector * w,
const gsl_vector * y,
const gsl_vector * cs,
const gsl_matrix * M,
gsl_vector * c,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_lreg (const double smin, const double smax,
gsl_vector * reg_param);
int
gsl_multifit_linear_lcurve (const gsl_vector * y,
gsl_vector * reg_param,
gsl_vector * rho, gsl_vector * eta,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_lcorner(const gsl_vector *rho,
const gsl_vector *eta,
size_t *idx);
int
gsl_multifit_linear_lcorner2(const gsl_vector *reg_param,
const gsl_vector *eta,
size_t *idx);
int
gsl_multifit_linear_Lk(const size_t p, const size_t k, gsl_matrix *L);
int
gsl_multifit_linear_Lsobolev(const size_t p, const size_t kmax,
const gsl_vector *alpha, gsl_matrix *L,
gsl_multifit_linear_workspace *work);
int
gsl_multifit_wlinear (const gsl_matrix * X,
const gsl_vector * w,
const gsl_vector * y,
gsl_vector * c,
gsl_matrix * cov,
double * chisq,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_wlinear_svd (const gsl_matrix * X,
const gsl_vector * w,
const gsl_vector * y,
double tol,
size_t * rank,
gsl_vector * c,
gsl_matrix * cov,
double *chisq,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_wlinear_usvd (const gsl_matrix * X,
const gsl_vector * w,
const gsl_vector * y,
double tol,
size_t * rank,
gsl_vector * c,
gsl_matrix * cov,
double *chisq,
gsl_multifit_linear_workspace * work);
int
gsl_multifit_linear_est (const gsl_vector * x,
const gsl_vector * c,
const gsl_matrix * cov, double *y, double *y_err);
double
gsl_multifit_linear_rcond (const gsl_multifit_linear_workspace * w);
int
gsl_multifit_linear_residuals (const gsl_matrix *X, const gsl_vector *y,
const gsl_vector *c, gsl_vector *r);
typedef struct
{
const char * name; /* method name */
int (*wfun)(const gsl_vector *r, gsl_vector *w);
int (*psi_deriv)(const gsl_vector *r, gsl_vector *dpsi);
double tuning_default; /* default tuning constant */
} gsl_multifit_robust_type;
typedef struct
{
double sigma_ols; /* OLS estimate of sigma */
double sigma_mad; /* MAD estimate of sigma */
double sigma_rob; /* robust estimate of sigma */
double sigma; /* final estimate of sigma */
double Rsq; /* R^2 coefficient of determination */
double adj_Rsq; /* degree of freedom adjusted R^2 */
double rmse; /* root mean squared error */
double sse; /* residual sum of squares */
size_t dof; /* degrees of freedom */
size_t numit; /* number of iterations */
gsl_vector *weights; /* final weights */
gsl_vector *r; /* final residuals y - X c */
} gsl_multifit_robust_stats;
typedef struct
{
size_t n; /* number of observations */
size_t p; /* number of parameters */
size_t numit; /* number of iterations */
size_t maxiter; /* maximum iterations */
const gsl_multifit_robust_type *type;
double tune; /* tuning parameter */
gsl_vector *r; /* residuals at current iteration */
gsl_vector *weights; /* weights at current iteration */
gsl_vector *c_prev; /* coefficients from previous iteration */
gsl_vector *resfac; /* multiplicative factors for residuals */
gsl_vector *psi; /* psi(r) */
gsl_vector *dpsi; /* psi'(r) */
gsl_matrix *QSI; /* Q S^{-1} of original matrix X */
gsl_vector *D; /* balancing parameters of original matrix X */
gsl_vector *workn; /* workspace of length n */
gsl_multifit_robust_stats stats; /* various statistics */
gsl_multifit_linear_workspace *multifit_p;
} gsl_multifit_robust_workspace;
/* available types */
GSL_VAR const gsl_multifit_robust_type * gsl_multifit_robust_default;
GSL_VAR const gsl_multifit_robust_type * gsl_multifit_robust_bisquare;
GSL_VAR const gsl_multifit_robust_type * gsl_multifit_robust_cauchy;
GSL_VAR const gsl_multifit_robust_type * gsl_multifit_robust_fair;
GSL_VAR const gsl_multifit_robust_type * gsl_multifit_robust_huber;
GSL_VAR const gsl_multifit_robust_type * gsl_multifit_robust_ols;
GSL_VAR const gsl_multifit_robust_type * gsl_multifit_robust_welsch;
gsl_multifit_robust_workspace *gsl_multifit_robust_alloc(const gsl_multifit_robust_type *T,
const size_t n, const size_t p);
void gsl_multifit_robust_free(gsl_multifit_robust_workspace *w);
int gsl_multifit_robust_tune(const double tune,
gsl_multifit_robust_workspace *w);
int gsl_multifit_robust_maxiter(const size_t maxiter,
gsl_multifit_robust_workspace *w);
const char *gsl_multifit_robust_name(const gsl_multifit_robust_workspace *w);
gsl_multifit_robust_stats gsl_multifit_robust_statistics(const gsl_multifit_robust_workspace *w);
int gsl_multifit_robust_weights(const gsl_vector *r, gsl_vector *wts,
gsl_multifit_robust_workspace *w);
int gsl_multifit_robust(const gsl_matrix * X, const gsl_vector * y,
gsl_vector * c, gsl_matrix *cov,
gsl_multifit_robust_workspace *w);
int gsl_multifit_robust_est(const gsl_vector * x, const gsl_vector * c,
const gsl_matrix * cov, double *y, double *y_err);
int gsl_multifit_robust_residuals(const gsl_matrix * X,
const gsl_vector * y,
const gsl_vector * c, gsl_vector * r,
gsl_multifit_robust_workspace * w);
__END_DECLS
#endif /* __GSL_MULTIFIT_H__ */
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