/* multifit/test_nonlinear.c

 * 

 * Copyright (C) 2007, 2013, 2014 Brian Gough, 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.

 */

typedef struct

{

  const char *name;

  double *x0;       /* initial parameters (size p) */

  double *sigma;

  double *epsrel;   /* relative tolerance for solution checking */

  size_t ntries;

  void (*checksol) (const double x[], const double sumsq,

                    const double epsrel, const char *sname,

                    const char *pname);

  gsl_multifit_function_fdf *fdf;

} test_fdf_problem;

#include "test_bard.c"

#include "test_beale.c"

#include "test_biggs.c"

#include "test_box.c"

#include "test_boxbod.c"

#include "test_brown1.c"

#include "test_brown2.c"

#include "test_brown3.c"

#include "test_eckerle.c"

#include "test_enso.c"

#include "test_exp1.c"

#include "test_gaussian.c"

#include "test_hahn1.c"

#include "test_helical.c"

#include "test_jennrich.c"

#include "test_kirby2.c"

#include "test_kowalik.c"

#include "test_lin1.c"

#include "test_lin2.c"

#include "test_lin3.c"

#include "test_meyer.c"

#include "test_meyerscal.c"

#include "test_osborne.c"

#include "test_penalty1.c"

#include "test_penalty2.c"

#include "test_powell1.c"

#include "test_powell2.c"

#include "test_powell3.c"

#include "test_rat42.c"

#include "test_rat43.c"

#include "test_rosenbrock.c"

#include "test_rosenbrocke.c"

#include "test_roth.c"

#include "test_thurber.c"

#include "test_vardim.c"

#include "test_watson.c"

#include "test_wood.c"

#include "test_wnlin.c"

static void test_fdf(const gsl_multifit_fdfsolver_type * T,

                     const double xtol, const double gtol,

                     const double ftol, const double epsrel,

                     const double x0_scale, test_fdf_problem *problem,

                     const double *wts);

static void test_fdfridge(const gsl_multifit_fdfsolver_type * T,

                          const double xtol, const double gtol,

                          const double ftol, const double epsrel,

                          const double x0_scale, test_fdf_problem *problem,

                          const double *wts);

static void test_fdf_checksol(const char *sname, const char *pname,

                              const double epsrel,

                              gsl_multifit_fdfsolver *s,

                              test_fdf_problem *problem);

static void test_scale_x0(gsl_vector *x0, const double scale);

/*

 * These test problems are taken from

 *

 * H. B. Nielsen, UCTP test problems for unconstrained optimization,

 * IMM Department of Mathematical Modeling, Tech. Report IMM-REP-2000-17,

 * 2000.

 */

static test_fdf_problem *test_fdf_nielsen[] = {

  &lin1_problem,       /* 1 */

  &lin2_problem,       /* 2 */

  &lin3_problem,       /* 3 */

  &rosenbrock_problem, /* 4 */

  &helical_problem,    /* 5 */

  &powell1_problem,    /* 6 */

  &roth_problem,       /* 7 */

  &bard_problem,       /* 8 */

  &kowalik_problem,    /* 9 */

  &meyer_problem,      /* 10 */

  &watson_problem,     /* 11 */

  &box_problem,        /* 12 */

  &jennrich_problem,   /* 13 */

  &brown1_problem,     /* 14 */

  &brown2_problem,     /* 16 */

  &osborne_problem,    /* 17 */

  &exp1_problem,       /* 18 */

  &meyerscal_problem,  /* 20 */

  &powell2_problem,

  NULL

};

/*

 * These tests are from

 *

 * J. J. More, B. S. Garbow and K. E. Hillstrom, Testing

 * Unconstrained Optimization Software, ACM Trans. Math. Soft.

 * Vol 7, No 1, 1981.

 *

 * Many of these overlap with the Nielsen tests

 */

static test_fdf_problem *test_fdf_more[] = {

  &rosenbrock_problem,   /* 1 */

  &roth_problem,         /* 2 */

  &powell3_problem,      /* 3 */

  &brown3_problem,       /* 4 */

  &beale_problem,        /* 5 */

  &jennrich_problem,     /* 6 */

  &helical_problem,      /* 7 */

  &bard_problem,         /* 8 */

  &gaussian_problem,     /* 9 */

  &meyer_problem,        /* 10 */

  &box_problem,          /* 12 */

  &powell1_problem,      /* 13 */

  &wood_problem,         /* 14 */

  &kowalik_problem,      /* 15 */

  &brown1_problem,       /* 16 */

  &osborne_problem,      /* 17 */

  &biggs_problem,        /* 18 */

  &watson_problem,       /* 20 */

  &rosenbrocke_problem,  /* 21 */

  &penalty1_problem,     /* 23 */

  &penalty2_problem,     /* 24 */

  &vardim_problem,       /* 25 */

  &brown2_problem,       /* 27 */

  &lin1_problem,         /* 32 */

  &lin2_problem,         /* 33 */

  &lin3_problem,         /* 34 */

  NULL

};

/* NIST test cases */

static test_fdf_problem *test_fdf_nist[] = {

  &kirby2_problem,

  &hahn1_problem,

  &enso_problem,

  &thurber_problem,

  &boxbod_problem,

  &rat42_problem,

  &eckerle_problem,

  &rat43_problem,

  NULL

};

static void

test_nonlinear(void)

{

  const double xtol = pow(GSL_DBL_EPSILON, 0.9) * 10.0;

  const double gtol = pow(GSL_DBL_EPSILON, 0.9) * 10.0;

  const double ftol = 0.0;

  size_t i, j;

  /* Nielsen tests */

  for (i = 0; test_fdf_nielsen[i] != NULL; ++i)

    {

      test_fdf_problem *problem = test_fdf_nielsen[i];

      double epsrel = *(problem->epsrel);

      double scale = 1.0;

      for (j = 0; j < problem->ntries; ++j)

        {

          double eps_scale = epsrel * scale;

          test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                   eps_scale, scale, problem, NULL);

          test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                        eps_scale, scale, problem, NULL);

          /* test finite difference Jacobian */

          {

            gsl_multifit_function_fdf fdf;

            fdf.df = problem->fdf->df;

            problem->fdf->df = NULL;

            test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                     1.0e5 * eps_scale, 1.0, problem, NULL);

            test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                          1.0e5 * eps_scale, 1.0, problem, NULL);

            problem->fdf->df = fdf.df;

          }

          scale *= 10.0;

        }

      test_fdf(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,

               10.0 * epsrel, 1.0, problem, NULL);

    }

  /* More tests */

  for (i = 0; test_fdf_more[i] != NULL; ++i)

    {

      test_fdf_problem *problem = test_fdf_more[i];

      double epsrel = *(problem->epsrel);

      double scale = 1.0;

      for (j = 0; j < problem->ntries; ++j)

        {

          double eps_scale = epsrel * scale;

          test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                   eps_scale, scale, problem, NULL);

          test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                        eps_scale, scale, problem, NULL);

          /* test finite difference Jacobian */

          {

            gsl_multifit_function_fdf fdf;

            fdf.df = problem->fdf->df;

            problem->fdf->df = NULL;

            test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                     1.0e5 * eps_scale, 1.0, problem, NULL);

            test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                          1.0e5 * eps_scale, 1.0, problem, NULL);

            problem->fdf->df = fdf.df;

          }

          scale *= 10.0;

        }

      test_fdf(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,

               10.0 * epsrel, 1.0, problem, NULL);

    }

  /* NIST tests */

  for (i = 0; test_fdf_nist[i] != NULL; ++i)

    {

      test_fdf_problem *problem = test_fdf_nist[i];

      double epsrel = *(problem->epsrel);

      double scale = 1.0;

      for (j = 0; j < problem->ntries; ++j)

        {

          double eps_scale = epsrel * scale;

          test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                   eps_scale, scale, problem, NULL);

          test_fdf(gsl_multifit_fdfsolver_lmder, xtol, gtol, ftol,

                   eps_scale, scale, problem, NULL);

          /* test finite difference Jacobian */

          {

            gsl_multifit_function_fdf fdf;

            fdf.df = problem->fdf->df;

            problem->fdf->df = NULL;

            test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                     eps_scale, 1.0, problem, NULL);

            test_fdf(gsl_multifit_fdfsolver_lmder, xtol, gtol, ftol,

                     eps_scale, scale, problem, NULL);

            problem->fdf->df = fdf.df;

          }

          scale *= 10.0;

        }

      test_fdf(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,

               epsrel, 1.0, problem, NULL);

    }

  /* test weighted nonlinear least squares */

  /* internal weighting in _f and _df functions */

  test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

           wnlin_epsrel, 1.0, &wnlin_problem1, NULL);

  test_fdf(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,

           wnlin_epsrel, 1.0, &wnlin_problem1, NULL);

  test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                wnlin_epsrel, 1.0, &wnlin_problem1, NULL);

  test_fdfridge(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,

                wnlin_epsrel, 1.0, &wnlin_problem1, NULL);

  /* weighting through fdfsolver_wset */

  test_fdf(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

           wnlin_epsrel, 1.0, &wnlin_problem2, wnlin_W);

  test_fdf(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,

           wnlin_epsrel, 1.0, &wnlin_problem2, wnlin_W);

  test_fdfridge(gsl_multifit_fdfsolver_lmsder, xtol, gtol, ftol,

                wnlin_epsrel, 1.0, &wnlin_problem2, wnlin_W);

  test_fdfridge(gsl_multifit_fdfsolver_lmniel, xtol, gtol, ftol,

                wnlin_epsrel, 1.0, &wnlin_problem2, wnlin_W);

}

/*

test_fdf()

  Test a weighted nonlinear least squares problem

Inputs: T        - solver to use

        xtol     - tolerance in x

        gtol     - tolerance in gradient

        ftol     - tolerance in residual vector

        epsrel   - relative error tolerance in solution

        x0_scale - to test robustness against starting points,

                   the standard starting point in 'problem' is

                   multiplied by this scale factor:

                   x0 <- x0 * x0_scale

                   If x0 = 0, then all components of x0 are set to

                   x0_scale

        problem  - contains the nonlinear problem and solution point

        wts      - weight vector (NULL for unweighted)

*/

static void

test_fdf(const gsl_multifit_fdfsolver_type * T, const double xtol,

         const double gtol, const double ftol,

         const double epsrel, const double x0_scale,

         test_fdf_problem *problem,

         const double *wts)

{

  gsl_multifit_function_fdf *fdf = problem->fdf;

  const size_t n = fdf->n;

  const size_t p = fdf->p;

  const size_t max_iter = 1500;

  gsl_vector *x0 = gsl_vector_alloc(p);

  gsl_vector_view x0v = gsl_vector_view_array(problem->x0, p);

  gsl_multifit_fdfsolver *s = gsl_multifit_fdfsolver_alloc (T, n, p);

  const char *pname = problem->name;

  char sname[2048];

  int status, info;

  sprintf(sname, "%s/scale=%g%s",

    gsl_multifit_fdfsolver_name(s), x0_scale,

    problem->fdf->df ? "" : "/fdiff");

  /* scale starting point x0 */

  gsl_vector_memcpy(x0, &x0v.vector);

  test_scale_x0(x0, x0_scale);

  if (wts)

    {

      gsl_vector_const_view wv = gsl_vector_const_view_array(wts, n);

      gsl_multifit_fdfsolver_wset(s, fdf, x0, &wv.vector);

    }

  else

    gsl_multifit_fdfsolver_set(s, fdf, x0);

  status = gsl_multifit_fdfsolver_driver(s, max_iter, xtol, gtol,

                                         ftol, &info;;

  gsl_test(status, "%s/%s did not converge, status=%s",

           sname, pname, gsl_strerror(status));

  /* check solution */

  test_fdf_checksol(sname, pname, epsrel, s, problem);

  if (wts == NULL)

    {

      /* test again with weighting matrix W = I */

      gsl_vector *wv = gsl_vector_alloc(n);

      sprintf(sname, "%s/scale=%g%s/weights",

        gsl_multifit_fdfsolver_name(s), x0_scale,

        problem->fdf->df ? "" : "/fdiff");

      gsl_vector_memcpy(x0, &x0v.vector);

      test_scale_x0(x0, x0_scale);

      gsl_vector_set_all(wv, 1.0);

      gsl_multifit_fdfsolver_wset(s, fdf, x0, wv);

      status = gsl_multifit_fdfsolver_driver(s, max_iter, xtol, gtol,

                                             ftol, &info;;

      gsl_test(status, "%s/%s did not converge, status=%s",

               sname, pname, gsl_strerror(status));

      test_fdf_checksol(sname, pname, epsrel, s, problem);

      gsl_vector_free(wv);

    }

  gsl_multifit_fdfsolver_free(s);

  gsl_vector_free(x0);

}

/*

test_fdfridge()

  Test a nonlinear least squares problem

Inputs: T        - solver to use

        xtol     - tolerance in x

        gtol     - tolerance in gradient

        ftol     - tolerance in residual vector

        epsrel   - relative error tolerance in solution

        x0_scale - to test robustness against starting points,

                   the standard starting point in 'problem' is

                   multiplied by this scale factor:

                   x0 <- x0 * x0_scale

                   If x0 = 0, then all components of x0 are set to

                   x0_scale

        problem  - contains the nonlinear problem and solution point

        wts      - weight vector

*/

static void

test_fdfridge(const gsl_multifit_fdfsolver_type * T, const double xtol,

              const double gtol, const double ftol,

              const double epsrel, const double x0_scale,

              test_fdf_problem *problem, const double *wts)

{

  gsl_multifit_function_fdf *fdf = problem->fdf;

  const size_t n = fdf->n;

  const size_t p = fdf->p;

  const size_t max_iter = 1500;

  gsl_vector *x0 = gsl_vector_alloc(p);

  gsl_vector_view x0v = gsl_vector_view_array(problem->x0, p);

  gsl_multifit_fdfridge *w = gsl_multifit_fdfridge_alloc (T, n, p);

  const char *pname = problem->name;

  char sname[2048];

  int status, info;

  double lambda = 0.0;

  sprintf(sname, "ridge/%s", gsl_multifit_fdfridge_name(w));

  /* scale starting point x0 */

  gsl_vector_memcpy(x0, &x0v.vector);

  test_scale_x0(x0, x0_scale);

  /* test undamped case with lambda = 0 */

  if (wts)

    {

      gsl_vector_const_view wv = gsl_vector_const_view_array(wts, n);

      gsl_multifit_fdfridge_wset(w, fdf, x0, lambda, &wv.vector);

    }

  else

    gsl_multifit_fdfridge_set(w, fdf, x0, lambda);

  status = gsl_multifit_fdfridge_driver(w, max_iter, xtol, gtol,

                                        ftol, &info;;

  gsl_test(status, "%s/%s did not converge, status=%s",

           sname, pname, gsl_strerror(status));

  /* check solution */

  test_fdf_checksol(sname, pname, epsrel, w->s, problem);

  /* test for self consisent solution with L = \lambda I */

  {

    const double eps = 1.0e-10;

    gsl_matrix *L = gsl_matrix_calloc(p, p);

    gsl_vector_view diag = gsl_matrix_diagonal(L);

    gsl_multifit_fdfridge *w2 = gsl_multifit_fdfridge_alloc (T, n, p);

    gsl_vector *y0 = gsl_vector_alloc(p);

    size_t i;

    /* pick some value for lambda and set L = \lambda I */

    lambda = 5.0;

    gsl_vector_set_all(&diag.vector, lambda);

    /* scale initial vector */

    gsl_vector_memcpy(x0, &x0v.vector);

    test_scale_x0(x0, x0_scale);

    gsl_vector_memcpy(y0, x0);

    if (wts)

      {

        gsl_vector_const_view wv = gsl_vector_const_view_array(wts, n);

        gsl_multifit_fdfridge_wset(w, fdf, x0, lambda, &wv.vector);

        gsl_multifit_fdfridge_wset3(w2, fdf, y0, L, &wv.vector);

      }

    else

      {

        gsl_multifit_fdfridge_set(w, fdf, x0, lambda);

        gsl_multifit_fdfridge_set3(w2, fdf, y0, L);

      }

    /* solve with scalar lambda routine */

    status = gsl_multifit_fdfridge_driver(w, max_iter, xtol, gtol,

                                          ftol, &info;;

    gsl_test(status, "%s/lambda/%s did not converge, status=%s",

             sname, pname, gsl_strerror(status));

    /* solve with general matrix routine */

    status = gsl_multifit_fdfridge_driver(w2, max_iter, xtol, gtol,

                                          ftol, &info;;

    gsl_test(status, "%s/L/%s did not converge, status=%s",

             sname, pname, gsl_strerror(status));

    /* test x = y */

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

      {

        double xi = gsl_vector_get(w->s->x, i);

        double yi = gsl_vector_get(w2->s->x, i);

        if (fabs(xi) < eps)

          {

            gsl_test_abs(yi, xi, eps, "%s/%s ridge lambda=%g i=%zu",

                         sname, pname, lambda, i);

          }

        else

          {

            gsl_test_rel(yi, xi, eps, "%s/%s ridge lambda=%g i=%zu",

                         sname, pname, lambda, i);

          }

      }

    gsl_matrix_free(L);

    gsl_vector_free(y0);

    gsl_multifit_fdfridge_free(w2);

  }

  gsl_multifit_fdfridge_free(w);

  gsl_vector_free(x0);

}

static void

test_fdf_checksol(const char *sname, const char *pname,

                  const double epsrel, gsl_multifit_fdfsolver *s,

                  test_fdf_problem *problem)

{

  gsl_multifit_function_fdf *fdf = problem->fdf;

  const double *sigma = problem->sigma;

  gsl_vector *f = gsl_multifit_fdfsolver_residual(s);

  gsl_vector *x = gsl_multifit_fdfsolver_position(s);

  double sumsq;

  /* check solution vector x and sumsq = ||f||^2 */

  gsl_blas_ddot(f, f, &sumsq);

  (problem->checksol)(x->data, sumsq, epsrel, sname, pname);

#if 1

  /* check variances */

  if (sigma)

    {

      const size_t n = fdf->n;

      const size_t p = fdf->p;

      size_t i;

      gsl_matrix * J = gsl_matrix_alloc(n, p);

      gsl_matrix * covar = gsl_matrix_alloc (p, p);

      gsl_multifit_fdfsolver_jac (s, J);

      gsl_multifit_covar(J, 0.0, covar);

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

        {

          double ei = sqrt(sumsq/(n-p))*sqrt(gsl_matrix_get(covar,i,i));

          gsl_test_rel (ei, sigma[i], epsrel, 

                        "%s/%s, sigma(%d)", sname, pname, i) ;

        }

      gsl_matrix_free (J);

      gsl_matrix_free (covar);

    }

#endif

}

static void

test_scale_x0(gsl_vector *x0, const double scale)

{

  double nx = gsl_blas_dnrm2(x0);

  if (nx == 0.0)

    gsl_vector_set_all(x0, scale);

  else

    gsl_vector_scale(x0, scale);

} /* test_scale_x0() */