src/parsec/disk-image/parsec/parsec-benchmark/pkgs/libs/gsl/src/ode-initval/rk2simp.c - public/gem5-resources - Git at Google

 /* ode-initval/rk2simp.c
  *
  * Copyright (C) 2004 Tuomo Keskitalo
  *
  * 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 2 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.
  */

 /* Runge-Kutta 2, Gaussian implicit. Also known as implicit midpoint rule.

    Non-linear equations solved by linearization, LU-decomposition
    and matrix inversion. For reference, see eg.

    Ascher, U.M., Petzold, L.R., Computer methods for ordinary
    differential and differential-algebraic equations, SIAM,
    Philadelphia, 1998.
  */

 #include <config.h>
 #include <stdlib.h>
 #include <string.h>
 #include <gsl/gsl_math.h>
 #include <gsl/gsl_errno.h>
 #include <gsl/gsl_odeiv.h>
 #include <gsl/gsl_linalg.h>

 #include "odeiv_util.h"

 typedef struct
 {
   double *Y1;
   double *y0;
   double *y0_orig;
   double *ytmp;
   double *dfdy;                 /* Jacobian */
   double *dfdt;                 /* time derivatives, not used */
   double *y_onestep;
   gsl_permutation *p;
 }
 rk2simp_state_t;

 static void *
 rk2simp_alloc (size_t dim)
 {
   rk2simp_state_t *state =
     (rk2simp_state_t *) malloc (sizeof (rk2simp_state_t));

   if (state == 0)
     {
       GSL_ERROR_NULL ("failed to allocate space for rk2simp_state",
                       GSL_ENOMEM);
     }

   state->Y1 = (double *) malloc (dim * sizeof (double));

   if (state->Y1 == 0)
     {
       free (state);
       GSL_ERROR_NULL ("failed to allocate space for Y1", GSL_ENOMEM);
     }

   state->y0 = (double *) malloc (dim * sizeof (double));

   if (state->y0 == 0)
     {
       free (state->Y1);
       free (state);
       GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM);
     }

   state->y0_orig = (double *) malloc (dim * sizeof (double));

   if (state->y0_orig == 0)
     {
       free (state->Y1);
       free (state->y0);
       free (state);
       GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM);
     }

   state->ytmp = (double *) malloc (dim * sizeof (double));

   if (state->ytmp == 0)
     {
       free (state->Y1);
       free (state->y0);
       free (state->y0_orig);
       free (state);
       GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM);
     }

   state->dfdy = (double *) malloc (dim * dim * sizeof (double));

   if (state->dfdy == 0)
     {
       free (state->Y1);
       free (state->y0);
       free (state->y0_orig);
       free (state->ytmp);
       free (state);
       GSL_ERROR_NULL ("failed to allocate space for dfdy", GSL_ENOMEM);
     }

   state->dfdt = (double *) malloc (dim * sizeof (double));

   if (state->dfdt == 0)
     {
       free (state->Y1);
       free (state->y0);
       free (state->y0_orig);
       free (state->ytmp);
       free (state->dfdy);
       free (state);
       GSL_ERROR_NULL ("failed to allocate space for dfdt", GSL_ENOMEM);
     }

   state->y_onestep = (double *) malloc (dim * sizeof (double));

   if (state->y_onestep == 0)
     {
       free (state->Y1);
       free (state->y0);
       free (state->y0_orig);
       free (state->ytmp);
       free (state->dfdy);
       free (state->dfdt);
       free (state);
       GSL_ERROR_NULL ("failed to allocate space for y_onestep", GSL_ENOMEM);
     }

   state->p = gsl_permutation_alloc (dim);

   if (state->p == 0)
     {
       free (state->Y1);
       free (state->y0);
       free (state->y0_orig);
       free (state->ytmp);
       free (state->dfdy);
       free (state->dfdt);
       free (state);
       GSL_ERROR_NULL ("failed to allocate space for p", GSL_ENOMEM);
     }

   return state;
 }


 static int
 rk2simp_step (double *y, rk2simp_state_t * state,
               const double h, const double t,
               const size_t dim, const gsl_odeiv_system * sys)
 {
   /* Makes a Runge-Kutta 2nd order semi-implicit advance with step size h.
      y0 is initial values of variables y.

      The linearized semi-implicit equations to calculate are:

      Y1 = y0 + h/2 * (1 - h/2 * df/dy)^(-1) * f(t + h/2, y0)

      y = y0 + h * f(t + h/2, Y1)
    */

   const double *y0 = state->y0;
   double *Y1 = state->Y1;
   double *ytmp = state->ytmp;

   size_t i;
   int s, ps;

   gsl_matrix_view J = gsl_matrix_view_array (state->dfdy, dim, dim);

   /* First solve Y1.
      Calculate the inverse matrix (1 - h/2 * df/dy)^-1
    */

   /* Create matrix to J */

   s = GSL_ODEIV_JA_EVAL (sys, t, y0, state->dfdy, state->dfdt);

   if (s != GSL_SUCCESS)
     {
       return s;
     }

   gsl_matrix_scale (&J.matrix, -h / 2.0);
   gsl_matrix_add_diagonal(&J.matrix, 1.0);

   /* Invert it by LU-decomposition to invmat */

   s += gsl_linalg_LU_decomp (&J.matrix, state->p, &ps);

   if (s != GSL_SUCCESS)
     {
       return GSL_EFAILED;
     }

   /* Evaluate f(t + h/2, y0) */

   s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, y0, ytmp);

   if (s != GSL_SUCCESS)
     {
       return s;
     }

   /* Calculate Y1 = y0 + h/2 * ((1-h/2 * df/dy)^-1) ytmp */

   {
     gsl_vector_const_view y0_view = gsl_vector_const_view_array(y0, dim);
     gsl_vector_view ytmp_view = gsl_vector_view_array(ytmp, dim);
     gsl_vector_view Y1_view = gsl_vector_view_array(Y1, dim);

     s = gsl_linalg_LU_solve (&J.matrix, state->p,
                              &ytmp_view.vector, &Y1_view.vector);

     gsl_vector_scale (&Y1_view.vector, 0.5 * h);
     gsl_vector_add (&Y1_view.vector, &y0_view.vector);
   }

   /* And finally evaluation of f(t + h/2, Y1) and calculation of y */

   s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, Y1, ytmp);

   if (s != GSL_SUCCESS)
     {
       return s;
     }

   for (i = 0; i < dim; i++)
     {
       y[i] = y0[i] + h * ytmp[i];
     }

   return s;
 }

 static int
 rk2simp_apply (void *vstate, size_t dim, double t, double h,
                double y[], double yerr[], const double dydt_in[],
                double dydt_out[], const gsl_odeiv_system * sys)
 {
   rk2simp_state_t *state = (rk2simp_state_t *) vstate;

   size_t i;

   double *y0 = state->y0;
   double *y0_orig = state->y0_orig;
   double *y_onestep = state->y_onestep;

   /* Error estimation is done by step doubling procedure */

   DBL_MEMCPY (y0, y, dim);

   /* Save initial values in case of failure */
   DBL_MEMCPY (y0_orig, y, dim);

   /* First traverse h with one step (save to y_onestep) */
   DBL_MEMCPY (y_onestep, y, dim);

   {
     int s = rk2simp_step (y_onestep, state, h, t, dim, sys);

     if (s != GSL_SUCCESS)
       {
         return s;
       }
   }

   /* Then with two steps with half step length (save to y) */

   {
     int s = rk2simp_step (y, state, h / 2.0, t, dim, sys);

     if (s != GSL_SUCCESS)
       {
         /* Restore original y vector */
         DBL_MEMCPY (y, y0_orig, dim);
         return s;
       }
   }

   DBL_MEMCPY (y0, y, dim);

   {
     int s = rk2simp_step (y, state, h / 2.0, t + h / 2.0, dim, sys);

     if (s != GSL_SUCCESS)
       {
         /* Restore original y vector */
         DBL_MEMCPY (y, y0_orig, dim);
         return s;
       }
   }

   /* Derivatives at output */

   if (dydt_out != NULL)
     {
       int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out);

       if (s != GSL_SUCCESS)
         {
           /* Restore original y vector */
           DBL_MEMCPY (y, y0_orig, dim);
           return s;
         }
     }

   /* Error estimation */

   for (i = 0; i < dim; i++)
     {
       yerr[i] = 4.0 * (y[i] - y_onestep[i]) / 3.0;
     }

   return GSL_SUCCESS;
 }


 static int
 rk2simp_reset (void *vstate, size_t dim)
 {
   rk2simp_state_t *state = (rk2simp_state_t *) vstate;

   DBL_ZERO_MEMSET (state->Y1, dim);
   DBL_ZERO_MEMSET (state->y0, dim);
   DBL_ZERO_MEMSET (state->y0_orig, dim);
   DBL_ZERO_MEMSET (state->ytmp, dim);
   DBL_ZERO_MEMSET (state->dfdt, dim * dim);
   DBL_ZERO_MEMSET (state->dfdt, dim);
   DBL_ZERO_MEMSET (state->y_onestep, dim);

   return GSL_SUCCESS;
 }

 static unsigned int
 rk2simp_order (void *vstate)
 {
   rk2simp_state_t *state = (rk2simp_state_t *) vstate;
   state = 0;                    /* prevent warnings about unused parameters */
   return 2;
 }

 static void
 rk2simp_free (void *vstate)
 {
   rk2simp_state_t *state = (rk2simp_state_t *) vstate;
   free (state->Y1);
   free (state->y0);
   free (state->y0_orig);
   free (state->ytmp);
   free (state->dfdy);
   free (state->dfdt);
   free (state->y_onestep);
   gsl_permutation_free (state->p);
   free (state);
 }

 static const gsl_odeiv_step_type rk2simp_type = {
   "rk2simp",                    /* name */
   0,                            /* can use dydt_in? */
   1,                            /* gives exact dydt_out? */
   &rk2simp_alloc,
   &rk2simp_apply,
   &rk2simp_reset,
   &rk2simp_order,
   &rk2simp_free
 };

 const gsl_odeiv_step_type *gsl_odeiv_step_rk2simp = &rk2simp_type;
	/* ode-initval/rk2simp.c
	*
	* Copyright (C) 2004 Tuomo Keskitalo
	*
	* 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 2 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.
	*/

	/* Runge-Kutta 2, Gaussian implicit. Also known as implicit midpoint rule.

	Non-linear equations solved by linearization, LU-decomposition
	and matrix inversion. For reference, see eg.

	Ascher, U.M., Petzold, L.R., Computer methods for ordinary
	differential and differential-algebraic equations, SIAM,
	Philadelphia, 1998.
	*/

	#include <config.h>
	#include <stdlib.h>
	#include <string.h>
	#include <gsl/gsl_math.h>
	#include <gsl/gsl_errno.h>
	#include <gsl/gsl_odeiv.h>
	#include <gsl/gsl_linalg.h>

	#include "odeiv_util.h"

	typedef struct
	{
	double *Y1;
	double *y0;
	double *y0_orig;
	double *ytmp;
	double dfdy; / Jacobian */
	double dfdt; / time derivatives, not used */
	double *y_onestep;
	gsl_permutation *p;
	}
	rk2simp_state_t;

	static void *
	rk2simp_alloc (size_t dim)
	{
	rk2simp_state_t *state =
	(rk2simp_state_t *) malloc (sizeof (rk2simp_state_t));

	if (state == 0)
	{
	GSL_ERROR_NULL ("failed to allocate space for rk2simp_state",
	GSL_ENOMEM);
	}

	state->Y1 = (double ) malloc (dim sizeof (double));

	if (state->Y1 == 0)
	{
	free (state);
	GSL_ERROR_NULL ("failed to allocate space for Y1", GSL_ENOMEM);
	}

	state->y0 = (double ) malloc (dim sizeof (double));

	if (state->y0 == 0)
	{
	free (state->Y1);
	free (state);
	GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM);
	}

	state->y0_orig = (double ) malloc (dim sizeof (double));

	if (state->y0_orig == 0)
	{
	free (state->Y1);
	free (state->y0);
	free (state);
	GSL_ERROR_NULL ("failed to allocate space for y0_orig", GSL_ENOMEM);
	}

	state->ytmp = (double ) malloc (dim sizeof (double));

	if (state->ytmp == 0)
	{
	free (state->Y1);
	free (state->y0);
	free (state->y0_orig);
	free (state);
	GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM);
	}

	state->dfdy = (double ) malloc (dim dim * sizeof (double));

	if (state->dfdy == 0)
	{
	free (state->Y1);
	free (state->y0);
	free (state->y0_orig);
	free (state->ytmp);
	free (state);
	GSL_ERROR_NULL ("failed to allocate space for dfdy", GSL_ENOMEM);
	}

	state->dfdt = (double ) malloc (dim sizeof (double));

	if (state->dfdt == 0)
	{
	free (state->Y1);
	free (state->y0);
	free (state->y0_orig);
	free (state->ytmp);
	free (state->dfdy);
	free (state);
	GSL_ERROR_NULL ("failed to allocate space for dfdt", GSL_ENOMEM);
	}

	state->y_onestep = (double ) malloc (dim sizeof (double));

	if (state->y_onestep == 0)
	{
	free (state->Y1);
	free (state->y0);
	free (state->y0_orig);
	free (state->ytmp);
	free (state->dfdy);
	free (state->dfdt);
	free (state);
	GSL_ERROR_NULL ("failed to allocate space for y_onestep", GSL_ENOMEM);
	}

	state->p = gsl_permutation_alloc (dim);

	if (state->p == 0)
	{
	free (state->Y1);
	free (state->y0);
	free (state->y0_orig);
	free (state->ytmp);
	free (state->dfdy);
	free (state->dfdt);
	free (state);
	GSL_ERROR_NULL ("failed to allocate space for p", GSL_ENOMEM);
	}

	return state;
	}


	static int
	rk2simp_step (double y, rk2simp_state_t state,
	const double h, const double t,
	const size_t dim, const gsl_odeiv_system * sys)
	{
	/* Makes a Runge-Kutta 2nd order semi-implicit advance with step size h.
	y0 is initial values of variables y.

	The linearized semi-implicit equations to calculate are:

	Y1 = y0 + h/2 * (1 - h/2 * df/dy)^(-1) * f(t + h/2, y0)

	y = y0 + h * f(t + h/2, Y1)
	*/

	const double *y0 = state->y0;
	double *Y1 = state->Y1;
	double *ytmp = state->ytmp;

	size_t i;
	int s, ps;

	gsl_matrix_view J = gsl_matrix_view_array (state->dfdy, dim, dim);

	/* First solve Y1.
	Calculate the inverse matrix (1 - h/2 * df/dy)^-1
	*/

	/* Create matrix to J */

	s = GSL_ODEIV_JA_EVAL (sys, t, y0, state->dfdy, state->dfdt);

	if (s != GSL_SUCCESS)
	{
	return s;
	}

	gsl_matrix_scale (&J.matrix, -h / 2.0);
	gsl_matrix_add_diagonal(&J.matrix, 1.0);

	/* Invert it by LU-decomposition to invmat */

	s += gsl_linalg_LU_decomp (&J.matrix, state->p, &ps);

	if (s != GSL_SUCCESS)
	{
	return GSL_EFAILED;
	}

	/* Evaluate f(t + h/2, y0) */

	s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, y0, ytmp);

	if (s != GSL_SUCCESS)
	{
	return s;
	}

	/* Calculate Y1 = y0 + h/2 * ((1-h/2 * df/dy)^-1) ytmp */

	{
	gsl_vector_const_view y0_view = gsl_vector_const_view_array(y0, dim);
	gsl_vector_view ytmp_view = gsl_vector_view_array(ytmp, dim);
	gsl_vector_view Y1_view = gsl_vector_view_array(Y1, dim);

	s = gsl_linalg_LU_solve (&J.matrix, state->p,
	&ytmp_view.vector, &Y1_view.vector);

	gsl_vector_scale (&Y1_view.vector, 0.5 * h);
	gsl_vector_add (&Y1_view.vector, &y0_view.vector);
	}

	/* And finally evaluation of f(t + h/2, Y1) and calculation of y */

	s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, Y1, ytmp);

	if (s != GSL_SUCCESS)
	{
	return s;
	}

	for (i = 0; i < dim; i++)
	{
	y[i] = y0[i] + h * ytmp[i];
	}

	return s;
	}

	static int
	rk2simp_apply (void *vstate, size_t dim, double t, double h,
	double y[], double yerr[], const double dydt_in[],
	double dydt_out[], const gsl_odeiv_system * sys)
	{
	rk2simp_state_t state = (rk2simp_state_t ) vstate;

	size_t i;

	double *y0 = state->y0;
	double *y0_orig = state->y0_orig;
	double *y_onestep = state->y_onestep;

	/* Error estimation is done by step doubling procedure */

	DBL_MEMCPY (y0, y, dim);

	/* Save initial values in case of failure */
	DBL_MEMCPY (y0_orig, y, dim);

	/* First traverse h with one step (save to y_onestep) */
	DBL_MEMCPY (y_onestep, y, dim);

	{
	int s = rk2simp_step (y_onestep, state, h, t, dim, sys);

	if (s != GSL_SUCCESS)
	{
	return s;
	}
	}

	/* Then with two steps with half step length (save to y) */

	{
	int s = rk2simp_step (y, state, h / 2.0, t, dim, sys);

	if (s != GSL_SUCCESS)
	{
	/* Restore original y vector */
	DBL_MEMCPY (y, y0_orig, dim);
	return s;
	}
	}

	DBL_MEMCPY (y0, y, dim);

	{
	int s = rk2simp_step (y, state, h / 2.0, t + h / 2.0, dim, sys);

	if (s != GSL_SUCCESS)
	{
	/* Restore original y vector */
	DBL_MEMCPY (y, y0_orig, dim);
	return s;
	}
	}

	/* Derivatives at output */

	if (dydt_out != NULL)
	{
	int s = GSL_ODEIV_FN_EVAL (sys, t + h, y, dydt_out);

	if (s != GSL_SUCCESS)
	{
	/* Restore original y vector */
	DBL_MEMCPY (y, y0_orig, dim);
	return s;
	}
	}

	/* Error estimation */

	for (i = 0; i < dim; i++)
	{
	yerr[i] = 4.0 * (y[i] - y_onestep[i]) / 3.0;
	}

	return GSL_SUCCESS;
	}


	static int
	rk2simp_reset (void *vstate, size_t dim)
	{
	rk2simp_state_t state = (rk2simp_state_t ) vstate;

	DBL_ZERO_MEMSET (state->Y1, dim);
	DBL_ZERO_MEMSET (state->y0, dim);
	DBL_ZERO_MEMSET (state->y0_orig, dim);
	DBL_ZERO_MEMSET (state->ytmp, dim);
	DBL_ZERO_MEMSET (state->dfdt, dim * dim);
	DBL_ZERO_MEMSET (state->dfdt, dim);
	DBL_ZERO_MEMSET (state->y_onestep, dim);

	return GSL_SUCCESS;
	}

	static unsigned int
	rk2simp_order (void *vstate)
	{
	rk2simp_state_t state = (rk2simp_state_t ) vstate;
	state = 0; /* prevent warnings about unused parameters */
	return 2;
	}

	static void
	rk2simp_free (void *vstate)
	{
	rk2simp_state_t state = (rk2simp_state_t ) vstate;
	free (state->Y1);
	free (state->y0);
	free (state->y0_orig);
	free (state->ytmp);
	free (state->dfdy);
	free (state->dfdt);
	free (state->y_onestep);
	gsl_permutation_free (state->p);
	free (state);
	}

	static const gsl_odeiv_step_type rk2simp_type = {
	"rk2simp", /* name */
	0, /* can use dydt_in? */
	1, /* gives exact dydt_out? */
	&rk2simp_alloc,
	&rk2simp_apply,
	&rk2simp_reset,
	&rk2simp_order,
	&rk2simp_free
	};

	const gsl_odeiv_step_type *gsl_odeiv_step_rk2simp = &rk2simp_type;