/* 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_tsvd (const gsl_matrix * X,

                          const gsl_vector * y,

                          const double tol,

                          gsl_vector * c,

                          gsl_matrix * cov,

                          double * chisq,

                          size_t * rank,

                          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);

size_t

gsl_multifit_linear_rank(const double tol, const 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_tsvd (const gsl_matrix * X,

                           const gsl_vector * w,

                           const gsl_vector * y,

                           const double tol,

                           gsl_vector * c,

                           gsl_matrix * cov,

                           double * chisq,

                           size_t * rank,

                           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);

/* gcv.c */

int

gsl_multifit_linear_gcv_init(const gsl_vector * y,

                             gsl_vector * reg_param,

                             gsl_vector * UTy,

                             double * delta0,

                             gsl_multifit_linear_workspace * work);

int

gsl_multifit_linear_gcv_curve(const gsl_vector * reg_param,

                              const gsl_vector * UTy,

                              const double delta0,

                              gsl_vector * G,

                              gsl_multifit_linear_workspace * work);

int

gsl_multifit_linear_gcv_min(const gsl_vector * reg_param,

                            const gsl_vector * UTy,

                            const gsl_vector * G,

                            const double delta0,

                            double * lambda,

                            gsl_multifit_linear_workspace * work);

double

gsl_multifit_linear_gcv_calc(const double lambda,

                             const gsl_vector * UTy,

                             const double delta0,

                             gsl_multifit_linear_workspace * work);

int

gsl_multifit_linear_gcv(const gsl_vector * y,

                        gsl_vector * reg_param,

                        gsl_vector * G,

                        double * lambda,

                        double * G_lambda,

                        gsl_multifit_linear_workspace * work);

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__ */