/* multifit_nlinear/fdjac.c

 * 

 * Copyright (C) 2013, 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.

 *

 *

 * This module contains routines for approximating the Jacobian with

 * finite differences for nonlinear least-squares fitting.

 */

#include <config.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_multifit_nlinear.h>

#include <gsl/gsl_vector.h>

#include <gsl/gsl_matrix.h>

static int forward_jac(const double h, const gsl_vector *x,

                       const gsl_vector *wts,

                       gsl_multifit_nlinear_fdf *fdf,

                       const gsl_vector *f, gsl_matrix *J);

static int center_jac(const double h, const gsl_vector *x, const gsl_vector *wts,

                      gsl_multifit_nlinear_fdf *fdf, gsl_matrix *J, gsl_vector *work);

/*

forward_jac()

  Compute approximate Jacobian using forward differences

Inputs: h   - finite difference step size

        x   - parameter vector

        wts - data weights

        fdf - fdf struct

        f   - (input) vector of function values f_i(x)

        J   - (output) Jacobian matrix

Return: success or error

*/

static int

forward_jac(const double h, const gsl_vector *x, const gsl_vector *wts,

            gsl_multifit_nlinear_fdf *fdf, const gsl_vector *f, gsl_matrix *J)

{

  int status = 0;

  size_t i, j;

  double delta;

  for (j = 0; j < fdf->p; ++j)

    {

      double xj = gsl_vector_get(x, j);

      /* use column j of J as temporary storage for f(x + dx) */

      gsl_vector_view v = gsl_matrix_column(J, j);

      delta = h * fabs(xj);

      if (delta == 0.0)

        delta = h;

      /* perturb x_j to compute forward difference */

      gsl_vector_set((gsl_vector *) x, j, xj + delta);

      status += gsl_multifit_nlinear_eval_f (fdf, x, wts, &v.vector);

      if (status)

        return status;

      /* restore x_j */

      gsl_vector_set((gsl_vector *) x, j, xj);

      delta = 1.0 / delta;

      for (i = 0; i < fdf->n; ++i)

        {

          double fnext = gsl_vector_get(&v.vector, i);

          double fi = gsl_vector_get(f, i);

          gsl_matrix_set(J, i, j, (fnext - fi) * delta);

        }

    }

  return status;

}

/*

center_jac()

  Compute approximate Jacobian using centered differences

Inputs: h    - finite difference step size

        x    - parameter vector

        wts  - data weights

        fdf  - fdf struct

        J    - (output) Jacobian matrix

        work - additional workspace, size n

Return: success or error

*/

static int

center_jac(const double h, const gsl_vector *x, const gsl_vector *wts,

           gsl_multifit_nlinear_fdf *fdf, gsl_matrix *J, gsl_vector *work)

{

  int status = 0;

  size_t i, j;

  double delta;

  for (j = 0; j < fdf->p; ++j)

    {

      double xj = gsl_vector_get(x, j);

      /* use column j of J as temporary storage for f(x + dx) */

      gsl_vector_view v = gsl_matrix_column(J, j);

      delta = h * fabs(xj);

      if (delta == 0.0)

        delta = h;

      /* perturb x_j to compute forward difference, f(x + 1/2 delta e_j) */

      gsl_vector_set((gsl_vector *) x, j, xj + 0.5 * delta);

      status += gsl_multifit_nlinear_eval_f (fdf, x, wts, &v.vector);

      if (status)

        return status;

      /* perturb x_j to compute backward difference, f(x - 1/2 delta e_j) */

      gsl_vector_set((gsl_vector *) x, j, xj - 0.5 * delta);

      status += gsl_multifit_nlinear_eval_f (fdf, x, wts, work);

      if (status)

        return status;

      /* restore x_j */

      gsl_vector_set((gsl_vector *) x, j, xj);

      delta = 1.0 / delta;

      for (i = 0; i < fdf->n; ++i)

        {

          double fnext = gsl_vector_get(&v.vector, i);

          double fprev = gsl_vector_get(work, i);

          gsl_matrix_set(J, i, j, (fnext - fprev) * delta);

        }

    }

  return status;

}

/*

gsl_multifit_nlinear_df()

  Compute approximate Jacobian using finite differences

Inputs: h      - finite difference step size

        fdtype - finite difference method

        x      - parameter vector

        wts    - data weights (set to NULL if not needed)

        fdf    - fdf

        f      - (input) function values f_i(x)

        J      - (output) approximate (weighted) Jacobian matrix, sqrt(W) * J

        work   - additional workspace for centered differences, size n

Return: success or error

*/

int

gsl_multifit_nlinear_df(const double h, const gsl_multifit_nlinear_fdtype fdtype,

                        const gsl_vector *x, const gsl_vector *wts,

                        gsl_multifit_nlinear_fdf *fdf,

                        const gsl_vector *f, gsl_matrix *J, gsl_vector *work)

{

  int status;

  if (fdtype == GSL_MULTIFIT_NLINEAR_FWDIFF)

    {

      status = forward_jac(h, x, wts, fdf, f, J);

    }

  else if (fdtype == GSL_MULTIFIT_NLINEAR_CTRDIFF)

    {

      status = center_jac(h, x, wts, fdf, J, work);

    }

  else

    {

      GSL_ERROR("invalid specified fdtype", GSL_EINVAL);

    }

  return status;

}