1 files changed, 413 insertions, 0 deletions
diff --git a/gsl-1.9/multiroots/dogleg.c b/gsl-1.9/multiroots/dogleg.c
new file mode 100644
index 0000000..4a120ef
--- /dev/null
+++ b/gsl-1.9/multiroots/dogleg.c
@@ -0,0 +1,413 @@
+/* multiroots/dogleg.c
+ * 
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000 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.
+ */
+
+#include "enorm.c"
+
+static void compute_diag (const gsl_matrix * J, gsl_vector * diag);
+static void update_diag (const gsl_matrix * J, gsl_vector * diag);
+static double compute_delta (gsl_vector * diag, gsl_vector * x);
+static void compute_df (const gsl_vector * f_trial, const gsl_vector * f, gsl_vector * df);
+static void compute_wv (const gsl_vector * qtdf, const gsl_vector *rdx, const gsl_vector *dx, const gsl_vector *diag, double pnorm, gsl_vector * w, gsl_vector * v);
+
+static double scaled_enorm (const gsl_vector * d, const gsl_vector * f);
+
+static double scaled_enorm (const gsl_vector * d, const gsl_vector * f) {
+  double e2 = 0 ;
+  size_t i, n = f->size ;
+  for (i = 0; i < n ; i++) {
+    double fi= gsl_vector_get(f, i);
+    double di= gsl_vector_get(d, i);
+    double u = di * fi;
+    e2 += u * u ;
+  }
+  return sqrt(e2);
+}
+
+static double enorm_sum (const gsl_vector * a, const gsl_vector * b);
+
+static double enorm_sum (const gsl_vector * a, const gsl_vector * b) {
+  double e2 = 0 ;
+  size_t i, n = a->size ;
+  for (i = 0; i < n ; i++) {
+    double ai= gsl_vector_get(a, i);
+    double bi= gsl_vector_get(b, i);
+    double u = ai + bi;
+    e2 += u * u ;
+  }
+  return sqrt(e2);
+}
+
+static void
+compute_wv (const gsl_vector * qtdf, const gsl_vector *rdx, const gsl_vector *dx, const gsl_vector *diag, double pnorm, gsl_vector * w, gsl_vector * v)
+{
+  size_t i, n = qtdf->size;
+
+  for (i = 0; i < n; i++)
+    {
+      double qtdfi = gsl_vector_get (qtdf, i);
+      double rdxi = gsl_vector_get (rdx, i);
+      double dxi = gsl_vector_get (dx, i);
+      double diagi = gsl_vector_get (diag, i);
+
+      gsl_vector_set (w, i, (qtdfi - rdxi) / pnorm);
+      gsl_vector_set (v, i, diagi * diagi * dxi / pnorm);
+    }
+}
+
+
+static void
+compute_df (const gsl_vector * f_trial, const gsl_vector * f, gsl_vector * df)
+{
+  size_t i, n = f->size;
+
+  for (i = 0; i < n; i++)
+    {
+      double dfi = gsl_vector_get (f_trial, i) - gsl_vector_get (f, i);
+      gsl_vector_set (df, i, dfi);
+    }
+}
+
+static void
+compute_diag (const gsl_matrix * J, gsl_vector * diag)
+{
+  size_t i, j, n = diag->size;
+
+  for (j = 0; j < n; j++)
+    {
+      double sum = 0;
+      for (i = 0; i < n; i++)
+        {
+          double Jij = gsl_matrix_get (J, i, j);
+          sum += Jij * Jij;
+        }
+      if (sum == 0)
+        sum = 1.0;
+
+      gsl_vector_set (diag, j, sqrt (sum));
+    }
+}
+
+static void
+update_diag (const gsl_matrix * J, gsl_vector * diag)
+{
+  size_t i, j, n = diag->size;
+
+  for (j = 0; j < n; j++)
+    {
+      double cnorm, diagj, sum = 0;
+      for (i = 0; i < n; i++)
+        {
+          double Jij = gsl_matrix_get (J, i, j);
+          sum += Jij * Jij;
+        }
+      if (sum == 0)
+        sum = 1.0;
+
+      cnorm = sqrt (sum);
+      diagj = gsl_vector_get (diag, j);
+
+      if (cnorm > diagj)
+        gsl_vector_set (diag, j, cnorm);
+    }
+}
+
+static double
+compute_delta (gsl_vector * diag, gsl_vector * x)
+{
+  double Dx = scaled_enorm (diag, x);
+  double factor = 100;
+
+  return (Dx > 0) ? factor * Dx : factor;
+}
+
+static double
+compute_actual_reduction (double fnorm, double fnorm1)
+{
+  double actred;
+
+  if (fnorm1 < fnorm)
+    {
+      double u = fnorm1 / fnorm;
+      actred = 1 - u * u;
+    }
+  else
+    {
+      actred = -1;
+    }
+
+  return actred;
+}
+
+static double
+compute_predicted_reduction (double fnorm, double fnorm1)
+{
+  double prered;
+
+  if (fnorm1 < fnorm)
+    {
+      double u = fnorm1 / fnorm;
+      prered = 1 - u * u;
+    }
+  else
+    {
+      prered = 0;
+    }
+
+  return prered;
+}
+
+static void 
+compute_qtf (const gsl_matrix * q, const gsl_vector * f, gsl_vector * qtf)
+{
+  size_t i, j, N = f->size ;
+
+  for (j = 0; j < N; j++)
+    {
+      double sum = 0;
+      for (i = 0; i < N; i++)
+        sum += gsl_matrix_get (q, i, j) * gsl_vector_get (f, i);
+
+      gsl_vector_set (qtf, j, sum);
+    }
+}
+
+static void 
+compute_rdx (const gsl_matrix * r, const gsl_vector * dx, gsl_vector * rdx)
+{
+  size_t i, j, N = dx->size ;
+
+  for (i = 0; i < N; i++)
+    {
+      double sum = 0;
+
+      for (j = i; j < N; j++)
+        {
+          sum += gsl_matrix_get (r, i, j) * gsl_vector_get (dx, j);
+        }
+
+      gsl_vector_set (rdx, i, sum);
+    }
+}
+
+
+static void
+compute_trial_step (gsl_vector *x, gsl_vector * dx, gsl_vector * x_trial)
+{
+  size_t i, N = x->size;
+
+  for (i = 0; i < N; i++)
+    {
+      double pi = gsl_vector_get (dx, i);
+      double xi = gsl_vector_get (x, i);
+      gsl_vector_set (x_trial, i, xi + pi);
+    }
+}
+
+static int
+newton_direction (const gsl_matrix * r, const gsl_vector * qtf, gsl_vector * p)
+{
+  const size_t N = r->size2;
+  size_t i;
+  int status;
+
+  status = gsl_linalg_R_solve (r, qtf, p);
+
+#ifdef DEBUG
+  printf("rsolve status = %d\n", status);
+#endif
+
+  for (i = 0; i < N; i++)
+    {
+      double pi = gsl_vector_get (p, i);
+      gsl_vector_set (p, i, -pi);
+    }
+
+  return status;
+}
+
+static void
+gradient_direction (const gsl_matrix * r, const gsl_vector * qtf,
+                    const gsl_vector * diag, gsl_vector * g)
+{
+  const size_t M = r->size1;
+  const size_t N = r->size2;
+
+  size_t i, j;
+
+  for (j = 0; j < M; j++)
+    {
+      double sum = 0;
+      double dj;
+
+      for (i = 0; i < N; i++)
+        {
+          sum += gsl_matrix_get (r, i, j) * gsl_vector_get (qtf, i);
+        }
+
+      dj = gsl_vector_get (diag, j);
+      gsl_vector_set (g, j, -sum / dj);
+    }
+}
+
+static void
+minimum_step (double gnorm, const gsl_vector * diag, gsl_vector * g)
+{
+  const size_t N = g->size;
+  size_t i;
+
+  for (i = 0; i < N; i++)
+    {
+      double gi = gsl_vector_get (g, i);
+      double di = gsl_vector_get (diag, i);
+      gsl_vector_set (g, i, (gi / gnorm) / di);
+    }
+}
+
+static void
+compute_Rg (const gsl_matrix * r, const gsl_vector * gradient, gsl_vector * Rg)
+{
+  const size_t N = r->size2;
+  size_t i, j;
+
+  for (i = 0; i < N; i++)
+    {
+      double sum = 0;
+
+      for (j = i; j < N; j++)
+        {
+          double gj = gsl_vector_get (gradient, j);
+          double rij = gsl_matrix_get (r, i, j);
+          sum += rij * gj;
+        }
+
+      gsl_vector_set (Rg, i, sum);
+    }
+}
+
+static void
+scaled_addition (double alpha, gsl_vector * newton, double beta, gsl_vector * gradient, gsl_vector * p)
+{
+  const size_t N = p->size;
+  size_t i;
+
+  for (i = 0; i < N; i++)
+    {
+      double ni = gsl_vector_get (newton, i);
+      double gi = gsl_vector_get (gradient, i);
+      gsl_vector_set (p, i, alpha * ni + beta * gi);
+    }
+}
+
+static int
+dogleg (const gsl_matrix * r, const gsl_vector * qtf,
+        const gsl_vector * diag, double delta,
+        gsl_vector * newton, gsl_vector * gradient, gsl_vector * p)
+{
+  double qnorm, gnorm, sgnorm, bnorm, temp;
+
+  newton_direction (r, qtf, newton);
+
+#ifdef DEBUG
+  printf("newton = "); gsl_vector_fprintf(stdout, newton, "%g"); printf("\n");
+#endif
+
+  qnorm = scaled_enorm (diag, newton);
+
+  if (qnorm <= delta)
+    {
+      gsl_vector_memcpy (p, newton);
+#ifdef DEBUG
+      printf("took newton (qnorm = %g  <=   delta = %g)\n", qnorm, delta);
+#endif
+      return GSL_SUCCESS;
+    }
+
+  gradient_direction (r, qtf, diag, gradient);
+
+#ifdef DEBUG
+  printf("grad = "); gsl_vector_fprintf(stdout, gradient, "%g"); printf("\n");
+#endif
+
+  gnorm = enorm (gradient);
+
+  if (gnorm == 0)
+    {
+      double alpha = delta / qnorm;
+      double beta = 0;
+      scaled_addition (alpha, newton, beta, gradient, p);
+#ifdef DEBUG
+      printf("took scaled newton because gnorm = 0\n");
+#endif
+      return GSL_SUCCESS;
+    }
+
+  minimum_step (gnorm, diag, gradient);
+
+  compute_Rg (r, gradient, p);  /* Use p as temporary space to compute Rg */
+
+#ifdef DEBUG
+  printf("mingrad = "); gsl_vector_fprintf(stdout, gradient, "%g"); printf("\n");
+  printf("Rg = "); gsl_vector_fprintf(stdout, p, "%g"); printf("\n");
+#endif
+
+  temp = enorm (p);
+  sgnorm = (gnorm / temp) / temp;
+
+  if (sgnorm > delta)
+    {
+      double alpha = 0;
+      double beta = delta;
+      scaled_addition (alpha, newton, beta, gradient, p);
+#ifdef DEBUG
+      printf("took gradient\n");
+#endif
+      return GSL_SUCCESS;
+    }
+
+  bnorm = enorm (qtf);
+
+  {
+    double bg = bnorm / gnorm;
+    double bq = bnorm / qnorm;
+    double dq = delta / qnorm;
+    double dq2 = dq * dq;
+    double sd = sgnorm / delta;
+    double sd2 = sd * sd;
+
+    double t1 = bg * bq * sd;
+    double u = t1 - dq;
+    double t2 = t1 - dq * sd2 + sqrt (u * u + (1-dq2) * (1 - sd2));
+
+    double alpha = dq * (1 - sd2) / t2;
+    double beta = (1 - alpha) * sgnorm;
+
+#ifdef DEBUG
+    printf("bnorm = %g\n", bnorm);
+    printf("gnorm = %g\n", gnorm);
+    printf("qnorm = %g\n", qnorm);
+    printf("delta = %g\n", delta);
+    printf("alpha = %g   beta = %g\n", alpha, beta);
+    printf("took scaled combination of newton and gradient\n");
+#endif
+
+    scaled_addition (alpha, newton, beta, gradient, p);
+  }
+
+  return GSL_SUCCESS;
+}