/* test.c

 * 

 * Copyright (C) 2012-2014 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 <stdlib.h>

#include <math.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_randist.h>

#include <gsl/gsl_rng.h>

#include <gsl/gsl_matrix.h>

#include <gsl/gsl_vector.h>

#include <gsl/gsl_test.h>

#include <gsl/gsl_blas.h>

#include <gsl/gsl_spmatrix.h>

#include <gsl/gsl_spblas.h>

#include <gsl/gsl_splinalg.h>

/*

create_random_sparse()

  Create a random sparse matrix with approximately

M*N*density non-zero entries

Inputs: M       - number of rows

        N       - number of columns

        density - sparse density \in [0,1]

                  0 = no non-zero entries

                  1 = all m*n entries are filled

        r       - random number generator

Return: pointer to sparse matrix in triplet format (must be freed by caller)

Notes:

1) non-zero matrix entries are uniformly distributed in [0,1]

*/

static gsl_spmatrix *

create_random_sparse(const size_t M, const size_t N, const double density,

                     const gsl_rng *r)

{

  size_t nnzwanted = (size_t) floor(M * N * GSL_MIN(density, 1.0));

  gsl_spmatrix *m = gsl_spmatrix_alloc_nzmax(M, N,

                                             nnzwanted,

                                             GSL_SPMATRIX_TRIPLET);

  size_t i;

  /* set diagonal entries to try to ensure non-singularity */

  for (i = 0; i < GSL_MIN(M, N); ++i)

    {

      double x = gsl_rng_uniform(r);

      gsl_spmatrix_set(m, i, i, x);

    }

  while (gsl_spmatrix_nnz(m) < nnzwanted)

    {

      /* generate a random row and column */

      size_t i = gsl_rng_uniform(r) * M;

      size_t j = gsl_rng_uniform(r) * N;

      /* generate random m_{ij} and add it */

      double x = gsl_rng_uniform(r);

      gsl_spmatrix_set(m, i, j, x);

    }

  return m;

} /* create_random_sparse() */

static void

create_random_vector(gsl_vector *v, const gsl_rng *r)

{

  size_t i;

  for (i = 0; i < v->size; ++i)

    {

      double x = gsl_rng_uniform(r);

      gsl_vector_set(v, i, x);

    }

} /* create_random_vector() */

/*

test_poisson()

  Solve u''(x) = -pi^2 sin(pi*x), u(x) = sin(pi*x)

  epsrel is the relative error threshold with the exact solution

*/

static void

test_poisson(const size_t N, const double epsrel, const int compress)

{

  const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres;

  const size_t n = N - 2;                     /* subtract 2 to exclude boundaries */

  const double h = 1.0 / (N - 1.0);           /* grid spacing */

  const double tol = 1.0e-9;

  const size_t max_iter = 10;

  size_t iter = 0;

  gsl_spmatrix *A = gsl_spmatrix_alloc(n ,n); /* triplet format */

  gsl_spmatrix *B;

  gsl_vector *b = gsl_vector_alloc(n);        /* right hand side vector */

  gsl_vector *u = gsl_vector_calloc(n);       /* solution vector, u0 = 0 */

  gsl_splinalg_itersolve *w = gsl_splinalg_itersolve_alloc(T, n, 0);

  const char *desc = gsl_splinalg_itersolve_name(w);

  size_t i;

  int status;

  /* construct the sparse matrix for the finite difference equation */

  /* first row of matrix */

  gsl_spmatrix_set(A, 0, 0, -2.0);

  gsl_spmatrix_set(A, 0, 1, 1.0);

  /* loop over interior grid points */

  for (i = 1; i < n - 1; ++i)

    {

      gsl_spmatrix_set(A, i, i + 1, 1.0);

      gsl_spmatrix_set(A, i, i, -2.0);

      gsl_spmatrix_set(A, i, i - 1, 1.0);

    }

  /* last row of matrix */

  gsl_spmatrix_set(A, n - 1, n - 1, -2.0);

  gsl_spmatrix_set(A, n - 1, n - 2, 1.0);

  /* scale by h^2 */

  gsl_spmatrix_scale(A, 1.0 / (h * h));

  /* construct right hand side vector */

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

    {

      double xi = (i + 1) * h;

      double bi = -M_PI * M_PI * sin(M_PI * xi);

      gsl_vector_set(b, i, bi);

    }

  if (compress)

    B = gsl_spmatrix_compcol(A);

  else

    B = A;

  /* solve the system */

  do

    {

      status = gsl_splinalg_itersolve_iterate(B, b, tol, u, w);

    }

  while (status == GSL_CONTINUE && ++iter < max_iter);

  gsl_test(status, "%s poisson status s=%d N=%zu", desc, status, N);

  /* check solution against analytic */

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

    {

      double xi = (i + 1) * h;

      double u_gsl = gsl_vector_get(u, i);

      double u_exact = sin(M_PI * xi);

      gsl_test_rel(u_gsl, u_exact, epsrel, "%s poisson N=%zu i=%zu",

                   desc, N, i);

    }

  /* check that the residual satisfies ||r|| <= tol*||b|| */

  {

    gsl_vector *r = gsl_vector_alloc(n);

    double normr, normb;

    gsl_vector_memcpy(r, b);

    gsl_spblas_dgemv(CblasNoTrans, -1.0, A, u, 1.0, r);

    normr = gsl_blas_dnrm2(r);

    normb = gsl_blas_dnrm2(b);

    status = (normr <= tol*normb) != 1;

    gsl_test(status, "%s poisson residual N=%zu normr=%.12e normb=%.12e",

             desc, N, normr, normb);

    gsl_vector_free(r);

  }

  gsl_splinalg_itersolve_free(w);

  gsl_spmatrix_free(A);

  gsl_vector_free(b);

  gsl_vector_free(u);

  if (compress)

    gsl_spmatrix_free(B);

} /* test_poisson() */

/*

test_toeplitz()

  Test Toeplitz matrix T = A + B + C where:

A = diag(a,-1)

B = diag(b)

C = diag(c,1)

rhs = ones(n,1)

*/

static void

test_toeplitz(const size_t N, const double a, const double b,

              const double c)

{

  int status;

  const double tol = 1.0e-10;

  const size_t max_iter = 10;

  const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres;

  const char *desc;

  gsl_spmatrix *A;

  gsl_vector *rhs, *x;

  gsl_splinalg_itersolve *w;

  size_t i, iter = 0;

  if (N <= 1)

    return;

  A = gsl_spmatrix_alloc(N ,N);

  rhs = gsl_vector_alloc(N);

  x = gsl_vector_calloc(N);

  w = gsl_splinalg_itersolve_alloc(T, N, 0);

  desc = gsl_splinalg_itersolve_name(w);

  /* first row */

  gsl_spmatrix_set(A, 0, 0, b);

  gsl_spmatrix_set(A, 0, 1, c);

  /* interior rows */

  for (i = 1; i < N - 1; ++i)

    {

      gsl_spmatrix_set(A, i, i - 1, a);

      gsl_spmatrix_set(A, i, i, b);

      gsl_spmatrix_set(A, i, i + 1, c);

    }

  /* last row */

  gsl_spmatrix_set(A, N - 1, N - 2, a);

  gsl_spmatrix_set(A, N - 1, N - 1, b);

  /* set rhs vector */

  gsl_vector_set_all(rhs, 1.0);

  /* solve the system */

  do

    {

      status = gsl_splinalg_itersolve_iterate(A, rhs, tol, x, w);

    }

  while (status == GSL_CONTINUE && ++iter < max_iter);

  gsl_test(status, "%s toeplitz status s=%d N=%zu a=%f b=%f c=%f",

           desc, status, N, a, b, c);

  /* check that the residual satisfies ||r|| <= tol*||b|| */

  {

    gsl_vector *r = gsl_vector_alloc(N);

    double normr, normb;

    gsl_vector_memcpy(r, rhs);

    gsl_spblas_dgemv(CblasNoTrans, -1.0, A, x, 1.0, r);

    normr = gsl_blas_dnrm2(r);

    normb = gsl_blas_dnrm2(rhs);

    status = (normr <= tol*normb) != 1;

    gsl_test(status, "%s toeplitz residual N=%zu a=%f b=%f c=%f normr=%.12e normb=%.12e",

             desc, N, a, b, c, normr, normb);

    gsl_vector_free(r);

  }

  gsl_vector_free(x);

  gsl_vector_free(rhs);

  gsl_spmatrix_free(A);

  gsl_splinalg_itersolve_free(w);

} /* test_toeplitz() */

static void

test_random(const size_t N, const gsl_rng *r, const int compress)

{

  const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres;

  const double tol = 1.0e-8;

  int status;

  gsl_spmatrix *A = create_random_sparse(N, N, 0.3, r);

  gsl_spmatrix *B;

  gsl_vector *b = gsl_vector_alloc(N);

  gsl_vector *x = gsl_vector_calloc(N);

  /* these random matrices require all N iterations to converge */

  gsl_splinalg_itersolve *w = gsl_splinalg_itersolve_alloc(T, N, N);

  const char *desc = gsl_splinalg_itersolve_name(w);

  create_random_vector(b, r);

  if (compress)

    B = gsl_spmatrix_compcol(A);

  else

    B = A;

  status = gsl_splinalg_itersolve_iterate(B, b, tol, x, w);

  gsl_test(status, "%s random status s=%d N=%zu", desc, status, N);

  /* check that the residual satisfies ||r|| <= tol*||b|| */

  {

    gsl_vector *res = gsl_vector_alloc(N);

    double normr, normb;

    gsl_vector_memcpy(res, b);

    gsl_spblas_dgemv(CblasNoTrans, -1.0, A, x, 1.0, res);

    normr = gsl_blas_dnrm2(res);

    normb = gsl_blas_dnrm2(b);

    status = (normr <= tol*normb) != 1;

    gsl_test(status, "%s random residual N=%zu normr=%.12e normb=%.12e",

             desc, N, normr, normb);

    gsl_vector_free(res);

  }

  gsl_spmatrix_free(A);

  gsl_vector_free(b);

  gsl_vector_free(x);

  gsl_splinalg_itersolve_free(w);

  if (compress)

    gsl_spmatrix_free(B);

} /* test_random() */

int

main()

{

  gsl_rng *r = gsl_rng_alloc(gsl_rng_default);

  size_t n;

  test_poisson(7, 1.0e-1, 0);

  test_poisson(7, 1.0e-1, 1);

  test_poisson(543, 1.0e-5, 0);

  test_poisson(543, 1.0e-5, 1);

  test_poisson(1000, 1.0e-6, 0);

  test_poisson(1000, 1.0e-6, 1);

  test_poisson(5000, 1.0e-7, 0);

  test_poisson(5000, 1.0e-7, 1);

  test_toeplitz(15, 0.01, 1.0, 0.01);

  test_toeplitz(15, 1.0, 1.0, 0.01);

  test_toeplitz(50, 1.0, 2.0, 0.01);

  test_toeplitz(1000, 0.5, 1.0, 0.01);

  for (n = 1; n <= 100; ++n)

    {

      test_random(n, r, 0);

      test_random(n, r, 1);

    }

  gsl_rng_free(r);

  exit (gsl_test_summary());

} /* main() */