/* multifit_nlinear/fdfvv.c

 * 

 * Copyright (C) 2015 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.

 */

#include <config.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_multifit_nlinear.h>

#include <gsl/gsl_vector.h>

#include <gsl/gsl_matrix.h>

#include <gsl/gsl_blas.h>

/*

fdfvv()

  Compute approximate second directional derivative using

finite differences.

See Eq. 19 of:

M. K. Transtrum, J. P. Sethna, Improvements to the Levenberg

Marquardt algorithm for nonlinear least-squares minimization,

arXiv:1201.5885, 2012.

Inputs: h     - step size for finite difference

        x     - parameter vector, size p

        v     - geodesic velocity, size p

        f     - vector of function values f_i(x), size n

        J     - Jacobian matrix J(x), n-by-p

        swts  - data weights

        fdf   - fdf struct

        fvv   - (output) approximate second directional derivative

                vector D_v^2 f(x)

        work  - workspace, size p

Return: success or error

*/

static int

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_multifit_nlinear_fdf *fdf, gsl_vector *fvv, gsl_vector *work)

{

  int status;

  const size_t n = fdf->n;

  const size_t p = fdf->p;

  const double hinv = 1.0 / h;

  size_t i;

  /* compute work = x + h*v */

  for (i = 0; i < p; ++i)

    {

      double xi = gsl_vector_get(x, i);

      double vi = gsl_vector_get(v, i);

      gsl_vector_set(work, i, xi + h * vi);

    }

  /* compute f(x + h*v) */

  status = gsl_multifit_nlinear_eval_f (fdf, work, swts, fvv);

  if (status)

    return status;

  for (i = 0; i < n; ++i)

    {

      double fi = gsl_vector_get(f, i);    /* f_i(x) */

      double fip = gsl_vector_get(fvv, i); /* f_i(x + h*v) */

      gsl_vector_const_view row = gsl_matrix_const_row(J, i);

      double u, fvvi;

      /* compute u = sum_{ij} J_{ij} D v_j */

      gsl_blas_ddot(&row.vector, v, &u);

      fvvi = (2.0 * hinv) * ((fip - fi) * hinv - u);

      gsl_vector_set(fvv, i, fvvi);

    }

  return status;

}

/*

gsl_multifit_nlinear_fdfvv()

  Compute approximate second directional derivative

using finite differences

Inputs: h    - step size for finite difference

        x    - parameter vector, size p

        v    - geodesic velocity, size p

        f    - function values f_i(x), size n

        J    - Jacobian matrix J(x), n-by-p

        swts - sqrt data weights (set to NULL if not needed)

        fdf  - fdf

        fvv  - (output) approximate (weighted) second directional derivative

               vector, size n, sqrt(W) fvv

        work - workspace, size p

Return: success or error

*/

int

gsl_multifit_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_multifit_nlinear_fdf *fdf,

                           gsl_vector *fvv, gsl_vector *work)

{

  return fdfvv(h, x, v, f, J, swts, fdf, fvv, work);

}