1 files changed, 178 insertions, 0 deletions
diff --git a/gsl-1.9/roots/falsepos.c b/gsl-1.9/roots/falsepos.c
new file mode 100644
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+++ b/gsl-1.9/roots/falsepos.c
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+/* roots/falsepos.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.
+ */
+
+/* falsepos.c -- falsepos root finding algorithm 
+
+   The false position algorithm uses bracketing by linear interpolation.
+
+   If a linear interpolation step would decrease the size of the
+   bracket by less than a bisection step would then the algorithm
+   takes a bisection step instead.
+   
+   The last linear interpolation estimate of the root is used. If a
+   bisection step causes it to fall outside the brackets then it is
+   replaced by the bisection estimate (x_upper + x_lower)/2.
+
+*/
+
+#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_lower, f_upper;
+  }
+falsepos_state_t;
+
+static int falsepos_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper);
+static int falsepos_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper);
+
+static int
+falsepos_init (void * vstate, gsl_function * f, double * root, double x_lower, double x_upper)
+{
+  falsepos_state_t * state = (falsepos_state_t *) vstate;
+
+  double f_lower, f_upper ;
+
+  *root = 0.5 * (x_lower + x_upper);
+
+  SAFE_FUNC_CALL (f, x_lower, &f_lower);
+  SAFE_FUNC_CALL (f, x_upper, &f_upper);
+  
+  state->f_lower = f_lower;
+  state->f_upper = f_upper;
+
+  if ((f_lower < 0.0 && f_upper < 0.0) || (f_lower > 0.0 && f_upper > 0.0))
+    {
+      GSL_ERROR ("endpoints do not straddle y=0", GSL_EINVAL);
+    }
+
+  return GSL_SUCCESS;
+
+}
+
+static int
+falsepos_iterate (void * vstate, gsl_function * f, double * root, double * x_lower, double * x_upper)
+{
+  falsepos_state_t * state = (falsepos_state_t *) vstate;
+
+  double x_linear, f_linear;
+  double x_bisect, f_bisect;
+
+  double x_left = *x_lower ;
+  double x_right = *x_upper ;
+
+  double f_lower = state->f_lower; 
+  double f_upper = state->f_upper;
+
+  double w ;
+
+  if (f_lower == 0.0)
+    {
+      *root = x_left ;
+      *x_upper = x_left;
+      return GSL_SUCCESS;
+    }
+  
+  if (f_upper == 0.0)
+    {
+      *root = x_right ;
+      *x_lower = x_right;
+      return GSL_SUCCESS;
+    }
+      
+  /* Draw a line between f(*lower_bound) and f(*upper_bound) and
+     note where it crosses the X axis; that's where we will
+     split the interval. */
+  
+  x_linear = x_right - (f_upper * (x_left - x_right) / (f_lower - f_upper));
+
+  SAFE_FUNC_CALL (f, x_linear, &f_linear);
+      
+  if (f_linear == 0.0)
+    {
+      *root = x_linear;
+      *x_lower = x_linear;
+      *x_upper = x_linear;
+      return GSL_SUCCESS;
+    }
+      
+  /* Discard the half of the interval which doesn't contain the root. */
+  
+  if ((f_lower > 0.0 && f_linear < 0.0) || (f_lower < 0.0 && f_linear > 0.0))
+    {
+      *root = x_linear ;
+      *x_upper = x_linear;
+      state->f_upper = f_linear;
+      w = x_linear - x_left ;
+    }
+  else
+    {
+      *root = x_linear ;
+      *x_lower = x_linear;
+      state->f_lower = f_linear;
+      w = x_right - x_linear;
+    }
+
+  if (w < 0.5 * (x_right - x_left)) 
+    {
+      return GSL_SUCCESS ;
+    }
+
+  x_bisect = 0.5 * (x_left + x_right);
+
+  SAFE_FUNC_CALL (f, x_bisect, &f_bisect);
+
+  if ((f_lower > 0.0 && f_bisect < 0.0) || (f_lower < 0.0 && f_bisect > 0.0))
+    {
+      *x_upper = x_bisect;
+      state->f_upper = f_bisect;
+      if (*root > x_bisect)
+        *root = 0.5 * (x_left + x_bisect) ;
+    }
+  else
+    {
+      *x_lower = x_bisect;
+      state->f_lower = f_bisect;
+      if (*root < x_bisect)
+        *root = 0.5 * (x_bisect + x_right) ;
+    }
+
+  return GSL_SUCCESS;
+}
+
+
+static const gsl_root_fsolver_type falsepos_type =
+{"falsepos",                            /* name */
+ sizeof (falsepos_state_t),
+ &falsepos_init,
+ &falsepos_iterate};
+
+const gsl_root_fsolver_type  * gsl_root_fsolver_falsepos = &falsepos_type;