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diff --git a/gsl-1.9/ode-initval/rk4.c b/gsl-1.9/ode-initval/rk4.c
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+/* ode-initval/rk4.c
+ *
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
+ *
+ * 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 4th order, Classical */
+
+/* Author: G. Jungman
+ */
+
+/* Reference: Abramowitz & Stegun, section 25.5. equation 25.5.10
+
+ Error estimation by step doubling, 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_errno.h>
+#include <gsl/gsl_odeiv.h>
+
+#include "odeiv_util.h"
+
+typedef struct
+{
+ double *k;
+ double *k1;
+ double *y0;
+ double *ytmp;
+ double *y_onestep;
+}
+rk4_state_t;
+
+static void *
+rk4_alloc (size_t dim)
+{
+ rk4_state_t *state = (rk4_state_t *) malloc (sizeof (rk4_state_t));
+
+ if (state == 0)
+ {
+ GSL_ERROR_NULL ("failed to allocate space for rk4_state", GSL_ENOMEM);
+ }
+
+ state->k = (double *) malloc (dim * sizeof (double));
+
+ if (state->k == 0)
+ {
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for k", GSL_ENOMEM);
+ }
+
+ state->k1 = (double *) malloc (dim * sizeof (double));
+
+ if (state->k1 == 0)
+ {
+ free (state);
+ free (state->k);
+ GSL_ERROR_NULL ("failed to allocate space for k1", GSL_ENOMEM);
+ }
+
+ state->y0 = (double *) malloc (dim * sizeof (double));
+
+ if (state->y0 == 0)
+ {
+ free (state->k);
+ free (state->k1);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for y0", GSL_ENOMEM);
+ }
+
+ state->ytmp = (double *) malloc (dim * sizeof (double));
+
+ if (state->ytmp == 0)
+ {
+ free (state->y0);
+ free (state->k);
+ free (state->k1);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM);
+ }
+
+ state->y_onestep = (double *) malloc (dim * sizeof (double));
+
+ if (state->y_onestep == 0)
+ {
+ free (state->ytmp);
+ free (state->y0);
+ free (state->k);
+ free (state->k1);
+ free (state);
+ GSL_ERROR_NULL ("failed to allocate space for ytmp", GSL_ENOMEM);
+ }
+
+ return state;
+}
+
+static int
+rk4_step (double *y, const rk4_state_t *state,
+ const double h, const double t, const size_t dim,
+ const gsl_odeiv_system *sys)
+{
+ /* Makes a Runge-Kutta 4th order advance with step size h. */
+
+ /* initial values of variables y. */
+ const double *y0 = state->y0;
+
+ /* work space */
+ double *ytmp = state->ytmp;
+
+ /* Runge-Kutta coefficients. Contains values of coefficient k1
+ in the beginning
+ */
+ double *k = state->k;
+
+ size_t i;
+
+ /* k1 step */
+
+ for (i = 0; i < dim; i++)
+ {
+ y[i] += h / 6.0 * k[i];
+ ytmp[i] = y0[i] + 0.5 * h * k[i];
+ }
+
+ /* k2 step */
+ {
+ int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, k);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+ }
+
+ for (i = 0; i < dim; i++)
+ {
+ y[i] += h / 3.0 * k[i];
+ ytmp[i] = y0[i] + 0.5 * h * k[i];
+ }
+
+ /* k3 step */
+ {
+ int s = GSL_ODEIV_FN_EVAL (sys, t + 0.5 * h, ytmp, k);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+ }
+
+ for (i = 0; i < dim; i++)
+ {
+ y[i] += h / 3.0 * k[i];
+ ytmp[i] = y0[i] + h * k[i];
+ }
+
+ /* k4 step */
+ {
+ int s = GSL_ODEIV_FN_EVAL (sys, t + h, ytmp, k);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+ }
+
+ for (i = 0; i < dim; i++)
+ {
+ y[i] += h / 6.0 * k[i];
+ }
+
+ return GSL_SUCCESS;
+}
+
+
+static int
+rk4_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)
+{
+ rk4_state_t *state = (rk4_state_t *) vstate;
+
+ size_t i;
+
+ double *const k = state->k;
+ double *const k1 = state->k1;
+ double *const y0 = state->y0;
+ double *const y_onestep = state->y_onestep;
+
+ DBL_MEMCPY (y0, y, dim);
+
+ if (dydt_in != NULL)
+ {
+ DBL_MEMCPY (k, dydt_in, dim);
+ }
+ else
+ {
+ int s = GSL_ODEIV_FN_EVAL (sys, t, y0, k);
+
+ if (s != GSL_SUCCESS)
+ {
+ return s;
+ }
+ }
+
+ /* Error estimation is done by step doubling procedure */
+
+ /* Save first point derivatives*/
+
+ DBL_MEMCPY (k1, k, dim);
+
+ /* First traverse h with one step (save to y_onestep) */
+
+ DBL_MEMCPY (y_onestep, y, dim);
+
+ {
+ int s = rk4_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) */
+
+ DBL_MEMCPY (k, k1, dim);
+
+ {
+ int s = rk4_step (y, state, h/2.0, t, dim, sys);
+
+ if (s != GSL_SUCCESS)
+ {
+ /* Restore original values */
+ DBL_MEMCPY (y, y0, dim);
+ return s;
+ }
+ }
+
+ /* Update before second step */
+ {
+ int s = GSL_ODEIV_FN_EVAL (sys, t + h/2.0, y, k);
+
+ if (s != GSL_SUCCESS)
+ {
+ /* Restore original values */
+ DBL_MEMCPY (y, y0, dim);
+ return s;
+ }
+ }
+
+ /* Save original y0 to k1 for possible failures */
+ DBL_MEMCPY (k1, y0, dim);
+
+ /* Update y0 for second step */
+ DBL_MEMCPY (y0, y, dim);
+
+ {
+ int s = rk4_step (y, state, h/2.0, t + h/2.0, dim, sys);
+
+ if (s != GSL_SUCCESS)
+ {
+ /* Restore original values */
+ DBL_MEMCPY (y, k1, 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 values */
+ DBL_MEMCPY (y, k1, dim);
+ return s;
+ }
+ }
+
+ /* Error estimation
+
+ yerr = C * 0.5 * | y(onestep) - y(twosteps) | / (2^order - 1)
+
+ constant C is approximately 8.0 to ensure 90% of samples lie within
+ the error (assuming a gaussian distribution with prior p(sigma)=1/sigma.)
+
+ */
+
+ for (i = 0; i < dim; i++)
+ {
+ yerr[i] = 4.0 * (y[i] - y_onestep[i]) / 15.0;
+ }
+
+ return GSL_SUCCESS;
+}
+
+static int
+rk4_reset (void *vstate, size_t dim)
+{
+ rk4_state_t *state = (rk4_state_t *) vstate;
+
+ DBL_ZERO_MEMSET (state->k, dim);
+ DBL_ZERO_MEMSET (state->k1, dim);
+ DBL_ZERO_MEMSET (state->y0, dim);
+ DBL_ZERO_MEMSET (state->ytmp, dim);
+ DBL_ZERO_MEMSET (state->y_onestep, dim);
+
+ return GSL_SUCCESS;
+}
+
+static unsigned int
+rk4_order (void *vstate)
+{
+ rk4_state_t *state = (rk4_state_t *) vstate;
+ state = 0; /* prevent warnings about unused parameters */
+ return 4;
+}
+
+static void
+rk4_free (void *vstate)
+{
+ rk4_state_t *state = (rk4_state_t *) vstate;
+ free (state->k);
+ free (state->k1);
+ free (state->y0);
+ free (state->ytmp);
+ free (state->y_onestep);
+ free (state);
+}
+
+static const gsl_odeiv_step_type rk4_type = { "rk4", /* name */
+ 1, /* can use dydt_in */
+ 1, /* gives exact dydt_out */
+ &rk4_alloc,
+ &rk4_apply,
+ &rk4_reset,
+ &rk4_order,
+ &rk4_free
+};
+
+const gsl_odeiv_step_type *gsl_odeiv_step_rk4 = &rk4_type;
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