1 files changed, 117 insertions, 0 deletions
diff --git a/gsl-1.9/roots/secant.c b/gsl-1.9/roots/secant.c
new file mode 100644
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+++ b/gsl-1.9/roots/secant.c
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+/* roots/secant.c
+ * 
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000 Reid Priedhorsky, Brian Gough
+ * 
+ * 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.
+ */
+
+/* secant.c -- secant root finding algorithm 
+
+   The secant algorithm is a variant of the Newton algorithm with the
+   derivative term replaced by a numerical estimate from the last two
+   function evaluations.
+
+   x[i+1] = x[i] - f(x[i]) / f'_est
+
+   where f'_est = (f(x[i]) - f(x[i-1])) / (x[i] - x[i-1])
+
+   The exact derivative is used for the initial value of f'_est.
+
+*/
+
+#include <config.h>
+
+#include <stddef.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <math.h>
+#include <float.h>
+
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_roots.h>
+
+#include "roots.h"
+
+typedef struct
+  {
+    double f;
+    double df;
+  }
+secant_state_t;
+
+static int secant_init (void * vstate, gsl_function_fdf * fdf, double * root);
+static int secant_iterate (void * vstate, gsl_function_fdf * fdf, double * root);
+
+static int
+secant_init (void * vstate, gsl_function_fdf * fdf, double * root)
+{
+  secant_state_t * state = (secant_state_t *) vstate;
+
+  const double x = *root;
+
+  GSL_FN_FDF_EVAL_F_DF (fdf, x, &(state->f), &(state->df));
+  
+  return GSL_SUCCESS;
+
+}
+
+static int
+secant_iterate (void * vstate, gsl_function_fdf * fdf, double * root)
+{
+  secant_state_t * state = (secant_state_t *) vstate;
+  
+  const double x = *root ;
+  const double f = state->f;
+  const double df = state->df;
+
+  double x_new, f_new, df_new;
+
+  if (state->df == 0.0)
+    {
+      GSL_ERROR("derivative is zero", GSL_EZERODIV);
+    }
+
+  x_new = x - (f / df);
+
+  f_new = GSL_FN_FDF_EVAL_F(fdf, x_new) ;
+  df_new = (f_new - f) / (x_new - x) ;
+
+  *root = x_new ;
+
+  state->f = f_new ;
+  state->df = df_new ;
+
+  if (!finite (f_new))
+    {
+      GSL_ERROR ("function value is not finite", GSL_EBADFUNC);
+    }
+
+  if (!finite (df_new))
+    {
+      GSL_ERROR ("derivative value is not finite", GSL_EBADFUNC);
+    }
+      
+  return GSL_SUCCESS;
+}
+
+
+static const gsl_root_fdfsolver_type secant_type =
+{"secant",                              /* name */
+ sizeof (secant_state_t),
+ &secant_init,
+ &secant_iterate};
+
+const gsl_root_fdfsolver_type  * gsl_root_fdfsolver_secant = &secant_type;