Diff of /src/foreign/levmar/lmdemo.c [000000] .. [efa19d]  Maximize  Restore

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+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Demonstration driver program for the Levenberg - Marquardt minimization
+//  algorithm
+//  Copyright (C) 2004-05  Manolis Lourakis (lourakis@ics.forth.gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  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.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+/******************************************************************************** 
+ * Levenberg-Marquardt minimization demo driver. Only the double precision versions
+ * are tested here. See the Meyer case for an example of verifying the jacobian 
+ ********************************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <float.h>
+
+#include "lm.h"
+
+
+/* Sample functions to be minimized with LM and their jacobians.
+ * More test functions at http://www.csit.fsu.edu/~burkardt/f_src/test_nls/test_nls.html
+ * Check also the CUTE problems collection at ftp://ftp.numerical.rl.ac.uk/pub/cute/;
+ * CUTE is searchable through http://numawww.mathematik.tu-darmstadt.de:8081/opti/select.html
+ * CUTE problems can also be solved through the AMPL web interface at http://www.ampl.com/TRYAMPL/startup.html
+ */
+
+#define ROSD 105.0
+
+/* Rosenbrock function, global minimum at (1, 1) */
+void ros(double *p, double *x, int m, int n, void *data)
+{
+register int i;
+
+  for(i=0; i<n; ++i)
+    x[i]=((1.0-p[0])*(1.0-p[0]) + ROSD*(p[1]-p[0]*p[0])*(p[1]-p[0]*p[0]));
+}
+
+void jacros(double *p, double *jac, int m, int n, void *data)
+{
+register int i, j;
+
+  for(i=j=0; i<n; ++i){
+    jac[j++]=(-2 + 2*p[0]-4*ROSD*(p[1]-p[0]*p[0])*p[0]);
+    jac[j++]=(2*ROSD*(p[1]-p[0]*p[0]));
+  }
+}
+
+
+#define MODROSLAM 1E02
+/* Modified Rosenbrock problem, global minimum at (1, 1) */
+void modros(double *p, double *x, int m, int n, void *data)
+{
+register int i;
+
+  for(i=0; i<n; i+=3){
+    x[i]=10*(p[1]-p[0]*p[0]);
+	  x[i+1]=1.0-p[0];
+	  x[i+2]=MODROSLAM;
+  }
+}
+
+void jacmodros(double *p, double *jac, int m, int n, void *data)
+{
+register int i, j;
+
+  for(i=j=0; i<n; i+=3){
+    jac[j++]=-20.0*p[0];
+	  jac[j++]=10.0;
+
+	  jac[j++]=-1.0;
+	  jac[j++]=0.0;
+
+	  jac[j++]=0.0;
+	  jac[j++]=0.0;
+  }
+}
+
+
+/* Powell's function, minimum at (0, 0) */
+void powell(double *p, double *x, int m, int n, void *data)
+{
+register int i;
+
+  for(i=0; i<n; i+=2){
+    x[i]=p[0];
+    x[i+1]=10.0*p[0]/(p[0]+0.1) + 2*p[1]*p[1];
+  }
+}
+
+void jacpowell(double *p, double *jac, int m, int n, void *data)
+{
+register int i, j;
+
+  for(i=j=0; i<n; i+=2){
+    jac[j++]=1.0;
+    jac[j++]=0.0;
+
+    jac[j++]=1.0/((p[0]+0.1)*(p[0]+0.1));
+    jac[j++]=4.0*p[1];
+  }
+}
+
+/* Wood's function, minimum at (1, 1, 1, 1) */
+void wood(double *p, double *x, int m, int n, void *data)
+{
+register int i;
+
+  for(i=0; i<n; i+=6){
+    x[i]=10.0*(p[1] - p[0]*p[0]);
+    x[i+1]=1.0 - p[0];
+    x[i+2]=sqrt(90.0)*(p[3] - p[2]*p[2]);
+    x[i+3]=1.0 - p[2];
+    x[i+4]=sqrt(10.0)*(p[1]+p[3] - 2.0);
+    x[i+5]=(p[1] - p[3])/sqrt(10.0);
+  }
+}
+
+/* Meyer's (reformulated) problem, minimum at (2.48, 6.18, 3.45) */
+void meyer(double *p, double *x, int m, int n, void *data)
+{
+register int i;
+double ui;
+
+	for(i=0; i<n; ++i){
+		ui=0.45+0.05*i;
+		x[i]=p[0]*exp(10.0*p[1]/(ui+p[2]) - 13.0);
+	}
+}
+
+void jacmeyer(double *p, double *jac, int m, int n, void *data)
+{
+register int i, j;
+double ui, tmp;
+
+  for(i=j=0; i<n; ++i){
+	  ui=0.45+0.05*i;
+	  tmp=exp(10.0*p[1]/(ui+p[2]) - 13.0);
+
+	  jac[j++]=tmp;
+	  jac[j++]=10.0*p[0]*tmp/(ui+p[2]);
+	  jac[j++]=-10.0*p[0]*p[1]*tmp/((ui+p[2])*(ui+p[2]));
+  }
+}
+
+/* helical valley function, minimum at (1.0, 0.0, 0.0) */
+#ifndef M_PI
+#define M_PI   3.14159265358979323846  /* pi */
+#endif
+
+void helval(double *p, double *x, int m, int n, void *data)
+{
+double theta;
+
+  if(p[0]<0.0)
+     theta=atan(p[1]/p[0])/(2.0*M_PI) + 0.5;
+  else if(0.0<p[0])
+     theta=atan(p[1]/p[0])/(2.0*M_PI);
+  else 
+    theta=(p[1]>=0)? 0.25 : -0.25;
+
+  x[0]=10.0*(p[2] - 10.0*theta);
+  x[1]=10.0*(sqrt(p[0]*p[0] + p[1]*p[1]) - 1.0);
+  x[2]=p[2];
+}
+
+void jachelval(double *p, double *jac, int m, int n, void *data)
+{
+register int i=0;
+double tmp;
+
+  tmp=p[0]*p[0] + p[1]*p[1];
+
+  jac[i++]=50.0*p[1]/(M_PI*tmp);
+  jac[i++]=-50.0*p[0]/(M_PI*tmp);
+  jac[i++]=10.0;
+
+  jac[i++]=10.0*p[0]/sqrt(tmp);
+  jac[i++]=10.0*p[1]/sqrt(tmp);
+  jac[i++]=0.0;
+
+  jac[i++]=0.0;
+  jac[i++]=0.0;
+  jac[i++]=1.0;
+}
+
+/* Boggs - Tolle problem 3 (linearly constrained), minimum at (-0.76744, 0.25581, 0.62791, -0.11628, 0.25581)
+ * constr1: p[0] + 3*p[1] = 0;
+ * constr2: p[2] + p[3] - 2*p[4] = 0;
+ * constr3: p[1] - p[4] = 0;
+ */
+void bt3(double *p, double *x, int m, int n, void *data)
+{
+register int i;
+double t1, t2, t3, t4;
+
+  t1=p[0]-p[1];
+  t2=p[1]+p[2]-2.0;
+  t3=p[3]-1.0;
+  t4=p[4]-1.0;
+
+  for(i=0; i<n; ++i)
+    x[i]=t1*t1 + t2*t2 + t3*t3 + t4*t4;
+}
+
+void jacbt3(double *p, double *jac, int m, int n, void *data)
+{
+register int i, j;
+double t1, t2, t3, t4;
+
+  t1=p[0]-p[1];
+  t2=p[1]+p[2]-2.0;
+  t3=p[3]-1.0;
+  t4=p[4]-1.0;
+
+  for(i=j=0; i<n; ++i){
+    jac[j++]=2.0*t1;
+    jac[j++]=2.0*(t2-t1);
+    jac[j++]=2.0*t2;
+    jac[j++]=2.0*t3;
+    jac[j++]=2.0*t4;
+  }
+}
+
+/* Hock - Schittkowski problem 28 (linearly constrained), minimum at (0.5, -0.5, 0.5)
+ * constr1: p[0] + 2*p[1] + 3*p[2] = 1;
+ */
+void hs28(double *p, double *x, int m, int n, void *data)
+{
+register int i;
+double t1, t2;
+
+  t1=p[0]+p[1];
+  t2=p[1]+p[2];
+
+  for(i=0; i<n; ++i)
+    x[i]=t1*t1 + t2*t2;
+}
+
+void jachs28(double *p, double *jac, int m, int n, void *data)
+{
+register int i, j;
+double t1, t2;
+
+  t1=p[0]+p[1];
+  t2=p[1]+p[2];
+
+  for(i=j=0; i<n; ++i){
+    jac[j++]=2.0*t1;
+    jac[j++]=2.0*(t1+t2);
+    jac[j++]=2.0*t2;
+  }
+}
+
+/* Hock - Schittkowski problem 48 (linearly constrained), minimum at (1.0, 1.0, 1.0, 1.0, 1.0)
+ * constr1: sum {i in 0..4} p[i] = 5;
+ * constr2: p[2] - 2*(p[3]+p[4]) = -3;
+ */
+void hs48(double *p, double *x, int m, int n, void *data)
+{
+register int i;
+double t1, t2, t3;
+
+  t1=p[0]-1.0;
+  t2=p[1]-p[2];
+  t3=p[3]-p[4];
+
+  for(i=0; i<n; ++i)
+    x[i]=t1*t1 + t2*t2 + t3*t3;
+}
+
+void jachs48(double *p, double *jac, int m, int n, void *data)
+{
+register int i, j;
+double t1, t2, t3;
+
+  t1=p[0]-1.0;
+  t2=p[1]-p[2];
+  t3=p[3]-p[4];
+
+  for(i=j=0; i<n; ++i){
+    jac[j++]=2.0*t1;
+    jac[j++]=2.0*t2;
+    jac[j++]=-2.0*t2;
+    jac[j++]=2.0*t3;
+    jac[j++]=-2.0*t3;
+  }
+}
+
+/* Hock - Schittkowski problem 51 (linearly constrained), minimum at (1.0, 1.0, 1.0, 1.0, 1.0)
+ * constr1: p[0] + 3*p[1] = 4;
+ * constr2: p[2] + p[3] - 2*p[4] = 0;
+ * constr3: p[1] - p[4] = 0;
+ */
+void hs51(double *p, double *x, int m, int n, void *data)
+{
+register int i;
+double t1, t2, t3, t4;
+
+  t1=p[0]-p[1];
+  t2=p[1]+p[2]-2.0;
+  t3=p[3]-1.0;
+  t4=p[4]-1.0;
+
+  for(i=0; i<n; ++i)
+    x[i]=t1*t1 + t2*t2 + t3*t3 + t4*t4;
+}
+
+void jachs51(double *p, double *jac, int m, int n, void *data)
+{
+register int i, j;
+double t1, t2, t3, t4;
+
+  t1=p[0]-p[1];
+  t2=p[1]+p[2]-2.0;
+  t3=p[3]-1.0;
+  t4=p[4]-1.0;
+
+  for(i=j=0; i<n; ++i){
+    jac[j++]=2.0*t1;
+    jac[j++]=2.0*(t2-t1);
+    jac[j++]=2.0*t2;
+    jac[j++]=2.0*t3;
+    jac[j++]=2.0*t4;
+  }
+}
+
+/* Hock - Schittkowski problem 01 (box constrained), minimum at (1.0, 1.0)
+ * constr1: p[1]>=-1.5;
+ */
+void hs01(double *p, double *x, int m, int n, void *data)
+{
+double t;
+
+  t=p[0]*p[0];
+  x[0]=10.0*(p[1]-t);
+  x[1]=1.0-p[0];
+}
+
+void jachs01(double *p, double *jac, int m, int n, void *data)
+{
+register int j=0;
+
+  jac[j++]=-20.0*p[0];
+  jac[j++]=10.0;
+
+  jac[j++]=-1.0;
+  jac[j++]=0.0;
+}
+
+/* Hock - Schittkowski MODIFIED problem 21 (box constrained), minimum at (2.0, 0.0)
+ * constr1: 2 <= p[0] <=50;
+ * constr2: -50 <= p[1] <=50;
+ *
+ * Original HS21 has the additional contraint 10*p[0] - p[1] >= 10; which is inactive
+ * at the solution, so it is dropped here.
+ */
+void hs21(double *p, double *x, int m, int n, void *data)
+{
+  x[0]=p[0]/10.0;
+  x[1]=p[1];
+}
+
+void jachs21(double *p, double *jac, int m, int n, void *data)
+{
+register int j=0;
+
+  jac[j++]=0.1;
+  jac[j++]=0.0;
+
+  jac[j++]=0.0;
+  jac[j++]=1.0;
+}
+
+/* Problem hatfldb (box constrained), minimum at (0.947214, 0.8, 0.64, 0.4096)
+ * constri: p[i]>=0.0; (i=1..4)
+ * constr5: p[1]<=0.8;
+ */
+void hatfldb(double *p, double *x, int m, int n, void *data)
+{
+register int i;
+
+  x[0]=p[0]-1.0;
+
+  for(i=1; i<m; ++i)
+     x[i]=p[i-1]-sqrt(p[i]);
+}
+
+void jachatfldb(double *p, double *jac, int m, int n, void *data)
+{
+register int j=0;
+
+  jac[j++]=1.0;
+  jac[j++]=0.0;
+  jac[j++]=0.0;
+  jac[j++]=0.0;
+
+  jac[j++]=1.0;
+  jac[j++]=-0.5/sqrt(p[1]);
+  jac[j++]=0.0;
+  jac[j++]=0.0;
+
+  jac[j++]=0.0;
+  jac[j++]=1.0;
+  jac[j++]=-0.5/sqrt(p[2]);
+  jac[j++]=0.0;
+
+  jac[j++]=0.0;
+  jac[j++]=0.0;
+  jac[j++]=1.0;
+  jac[j++]=-0.5/sqrt(p[3]);
+}
+
+/* Problem hatfldc (box constrained), minimum at (1.0, 1.0, 1.0, 1.0)
+ * constri: p[i]>=0.0; (i=1..4)
+ * constri+4: p[i]<=10.0; (i=1..4)
+ */
+void hatfldc(double *p, double *x, int m, int n, void *data)
+{
+register int i;
+
+  x[0]=p[0]-1.0;
+
+  for(i=1; i<m-1; ++i)
+     x[i]=p[i-1]-sqrt(p[i]);
+
+  x[m-1]=p[m-1]-1.0;
+}
+
+void jachatfldc(double *p, double *jac, int m, int n, void *data)
+{
+register int j=0;
+
+  jac[j++]=1.0;
+  jac[j++]=0.0;
+  jac[j++]=0.0;
+  jac[j++]=0.0;
+
+  jac[j++]=1.0;
+  jac[j++]=-0.5/sqrt(p[1]);
+  jac[j++]=0.0;
+  jac[j++]=0.0;
+
+  jac[j++]=0.0;
+  jac[j++]=1.0;
+  jac[j++]=-0.5/sqrt(p[2]);
+  jac[j++]=0.0;
+
+  jac[j++]=0.0;
+  jac[j++]=0.0;
+  jac[j++]=0.0;
+  jac[j++]=1.0;
+}
+
+/* Equilibrium combustion problem, constrained nonlinear equation from the book by Floudas et al.
+ * Minimum at (0.0034, 31.3265, 0.0684, 0.8595, 0.0370)
+ * constri: p[i]>=0.0001; (i=1..5)
+ * constri+5: p[i]<=100.0; (i=1..5)
+ */
+void combust(double *p, double *x, int m, int n, void *data)
+{
+  double R, R5, R6, R7, R8, R9, R10;
+
+  R=10;
+  R5=0.193;
+  R6=4.10622*1e-4;
+  R7=5.45177*1e-4;
+  R8=4.4975*1e-7;
+  R9=3.40735*1e-5;
+  R10=9.615*1e-7;
+
+  x[0]=p[0]*p[1]+p[0]-3*p[4];
+  x[1]=2*p[0]*p[1]+p[0]+3*R10*p[1]*p[1]+p[1]*p[2]*p[2]+R7*p[1]*p[2]+R9*p[1]*p[3]+R8*p[1]-R*p[4];
+  x[2]=2*p[1]*p[2]*p[2]+R7*p[1]*p[2]+2*R5*p[2]*p[2]+R6*p[2]-8*p[4];
+  x[3]=R9*p[1]*p[3]+2*p[3]*p[3]-4*R*p[4];
+  x[4]=p[0]*p[1]+p[0]+R10*p[1]*p[1]+p[1]*p[2]*p[2]+R7*p[1]*p[2]+R9*p[1]*p[3]+R8*p[1]+R5*p[2]*p[2]+R6*p[2]+p[3]*p[3]-1.0;
+}
+
+void jaccombust(double *p, double *jac, int m, int n, void *data)
+{
+register int j=0;
+  double R, R5, R6, R7, R8, R9, R10;
+
+  R=10;
+  R5=0.193;
+  R6=4.10622*1e-4;
+  R7=5.45177*1e-4;
+  R8=4.4975*1e-7;
+  R9=3.40735*1e-5;
+  R10=9.615*1e-7;
+
+  for(j=0; j<m*n; ++j) jac[j]=0.0;
+
+  j=0;
+  jac[j]=p[1]+1;
+  jac[j+1]=p[0];
+  jac[j+4]=-3;
+
+  j+=m;
+  jac[j]=2*p[1]+1;
+  jac[j+1]=2*p[0]+6*R10*p[1]+p[2]*p[2]+R7*p[2]+R9*p[3]+R8;
+  jac[j+2]=2*p[1]*p[2]+R7*p[1];
+  jac[j+3]=R9*p[1];
+  jac[j+4]=-R;
+
+  j+=m;
+  jac[j+1]=2*p[2]*p[2]+R7*p[2];
+  jac[j+2]=4*p[1]*p[2]+R7*p[1]+4*R5*p[2]+R6;
+  jac[j+4]=-8;
+
+  j+=m;
+  jac[j+1]=R9*p[3];
+  jac[j+3]=R9*p[1]+4*p[3];
+  jac[j+4]=-4*R;
+
+  j+=m;
+  jac[j]=p[1]+1;
+  jac[j+1]=p[0]+2*R10*p[1]+p[2]*p[2]+R7*p[2]+R9*p[3]+R8;
+  jac[j+2]=2*p[1]*p[2]+R7*p[1]+2*R5*p[2]+R6;
+  jac[j+3]=R9*p[1]+2*p[3];
+}
+
+
+
+int main()
+{
+register int i, j;
+int problem, ret;
+double p[5], // 6 is max(2, 3, 5)
+	   x[16]; // 16 is max(2, 3, 5, 6, 16)
+int m, n;
+double opts[LM_OPTS_SZ], info[LM_INFO_SZ];
+char *probname[]={
+    "Rosenbrock function",
+    "modified Rosenbrock problem",
+    "Powell's function",
+    "Wood's function",
+    "Meyer's (reformulated) problem",
+    "helical valley function",
+    "Boggs & Tolle's problem #3",
+    "Hock - Schittkowski problem #28",
+    "Hock - Schittkowski problem #48",
+    "Hock - Schittkowski problem #51",
+    "Hock - Schittkowski problem #01",
+    "Hock - Schittkowski (modified) problem #21",
+    "hatfldb problem",
+    "hatfldc problem",
+    "equilibrium combustion problem"
+};
+
+  opts[0]=LM_INIT_MU; opts[1]=1E-15; opts[2]=1E-15; opts[3]=1E-20;
+  opts[4]=LM_DIFF_DELTA; // relevant only if the finite difference jacobian version is used 
+
+  /* uncomment the appropriate line below to select a minimization problem */
+  problem=
+		  //0; // Rosenbrock function
+		  //1; // modified Rosenbrock problem
+		  //2; // Powell's function
+      //3; // Wood's function
+		  4; // Meyer's (reformulated) problem
+      //5; // helical valley function
+#ifdef HAVE_LAPACK
+      //6; // Boggs & Tolle's problem 3
+      //7; // Hock - Schittkowski problem 28
+      //8; // Hock - Schittkowski problem 48
+      //9; // Hock - Schittkowski problem 51
+#else // no LAPACK
+#ifdef _MSC_VER
+#pragma message("LAPACK not available, some test problems cannot be used")
+#else
+#warning LAPACK not available, some test problems cannot be used
+#endif // _MSC_VER
+
+#endif /* HAVE_LAPACK */
+      //10; // Hock - Schittkowski problem 01
+      //11; // Hock - Schittkowski (modified) problem 21
+      //12; // hatfldb problem
+      //13; // hatfldc problem
+      //14; // equilibrium combustion problem
+				
+  switch(problem){
+  default: fprintf(stderr, "unknown problem specified (#%d)! Note that some minimization problems require LAPACK.\n", problem);
+           exit(1);
+    break;
+  case 0:
+  /* Rosenbrock function */
+    m=2; n=2;
+    p[0]=-1.2; p[1]=1.0;
+    for(i=0; i<n; i++) x[i]=0.0;
+    ret=dlevmar_der(ros, jacros, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    //ret=dlevmar_dif(ros, p, x, m, n, 1000, opts, info, NULL, NULL, NULL);  // no jacobian
+  break;
+
+  case 1:
+  /* modified Rosenbrock problem */
+    m=2; n=3;
+    p[0]=-1.2; p[1]=1.0;
+    for(i=0; i<n; i++) x[i]=0.0;
+    ret=dlevmar_der(modros, jacmodros, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    //ret=dlevmar_dif(modros, p, x, m, n, 1000, opts, info, NULL, NULL, NULL);  // no jacobian
+  break;
+
+  case 2:
+  /* Powell's function */
+    m=2; n=2;
+    p[0]=3.0; p[1]=1.0;
+    for(i=0; i<n; i++) x[i]=0.0;
+    ret=dlevmar_der(powell, jacpowell, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    //ret=dlevmar_dif(powell, p, x, m, n, 1000, opts, info, NULL, NULL, NULL);		// no jacobian
+  break;
+
+  case 3:
+  /* Woods's function */
+    m=4; n=6;
+    p[0]=-3.0; p[1]=-1.0; p[2]=-3.0; p[3]=-1.0;
+    for(i=0; i<n; i++) x[i]=0.0;
+    ret=dlevmar_dif(wood, p, x, m, n, 1000, opts, info, NULL, NULL, NULL);  // no jacobian
+  break;
+
+  case 4:
+  /* Meyer's data fitting problem */
+    m=3; n=16;
+    p[0]=8.85; p[1]=4.0; p[2]=2.5;
+    x[0]=34.780;	x[1]=28.610; x[2]=23.650; x[3]=19.630;
+    x[4]=16.370;	x[5]=13.720; x[6]=11.540; x[7]=9.744;
+    x[8]=8.261;	x[9]=7.030; x[10]=6.005; x[11]=5.147;
+    x[12]=4.427;	x[13]=3.820; x[14]=3.307; x[15]=2.872;
+    //ret=dlevmar_der(meyer, jacmeyer, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+
+   { double *work, *covar;
+    work=malloc((LM_DIF_WORKSZ(m, n)+m*m)*sizeof(double));
+    if(!work){
+    	fprintf(stderr, "memory allocation request failed in main()\n");
+      exit(1);
+    }
+    covar=work+LM_DIF_WORKSZ(m, n);
+
+    ret=dlevmar_dif(meyer, p, x, m, n, 1000, opts, info, work, covar, NULL); // no jacobian, caller allocates work memory, covariance estimated
+
+    printf("Covariance of the fit:\n");
+    for(i=0; i<m; ++i){
+      for(j=0; j<m; ++j)
+        printf("%g ", covar[i*m+j]);
+      printf("\n");
+    }
+    printf("\n");
+
+    free(work);
+   }
+
+/* uncomment the following block to verify jacobian */
+/*
+   {
+    double err[16];
+    dlevmar_chkjac(meyer, jacmeyer, p, m, n, NULL, err); 
+    for(i=0; i<n; ++i) printf("gradient %d, err %g\n", i, err[i]);
+   }
+*/
+
+  break;
+
+  case 5:
+  /* helical valley function */
+    m=3; n=3;
+    p[0]=-1.0; p[1]=0.0; p[2]=0.0;
+    for(i=0; i<n; i++) x[i]=0.0;
+    ret=dlevmar_der(helval, jachelval, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    //ret=dlevmar_dif(helval, p, x, m, n, 1000, opts, info, NULL, NULL, NULL);  // no jacobian
+  break;
+
+#ifdef HAVE_LAPACK
+  case 6:
+  /* Boggs-Tolle problem 3 */
+    m=5; n=5;
+    p[0]=2.0; p[1]=2.0; p[2]=2.0;
+    p[3]=2.0; p[4]=2.0;
+    for(i=0; i<n; i++) x[i]=0.0;
+
+    {
+      double A[3*5]={1.0, 3.0, 0.0, 0.0, 0.0,  0.0, 0.0, 1.0, 1.0, -2.0,  0.0, 1.0, 0.0, 0.0, -1.0},
+             b[3]={0.0, 0.0, 0.0};
+
+    ret=dlevmar_lec_der(bt3, jacbt3, p, x, m, n, A, b, 3, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, analytic jacobian
+    //ret=dlevmar_lec_dif(bt3, p, x, m, n, A, b, 3, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, no jacobian
+    }
+  break;
+  case 7:
+  /* Hock - Schittkowski problem 28 */
+    m=3; n=3;
+    p[0]=-4.0; p[1]=1.0; p[2]=1.0;
+    for(i=0; i<n; i++) x[i]=0.0;
+
+    {
+      double A[1*3]={1.0, 2.0, 3.0},
+             b[1]={1.0};
+
+    ret=dlevmar_lec_der(hs28, jachs28, p, x, m, n, A, b, 1, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, analytic jacobian
+    //ret=dlevmar_lec_dif(hs28, p, x, m, n, A, b, 1, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, no jacobian
+    }
+  break;
+  case 8:
+  /* Hock - Schittkowski problem 48 */
+    m=5; n=5;
+    p[0]=3.0; p[1]=5.0; p[2]=-3.0;
+    p[3]=2.0; p[4]=-2.0;
+    for(i=0; i<n; i++) x[i]=0.0;
+
+    {
+      double A[2*5]={1.0, 1.0, 1.0, 1.0, 1.0,  0.0, 0.0, 1.0, -2.0, -2.0},
+             b[2]={5.0, -3.0};
+
+    ret=dlevmar_lec_der(hs48, jachs48, p, x, m, n, A, b, 2, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, analytic jacobian
+    //ret=dlevmar_lec_dif(hs48, p, x, m, n, A, b, 2, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, no jacobian
+    }
+  break;
+  case 9:
+  /* Hock - Schittkowski problem 51 */
+    m=5; n=5;
+    p[0]=2.5; p[1]=0.5; p[2]=2.0;
+    p[3]=-1.0; p[4]=0.5;
+    for(i=0; i<n; i++) x[i]=0.0;
+
+    {
+      double A[3*5]={1.0, 3.0, 0.0, 0.0, 0.0,  0.0, 0.0, 1.0, 1.0, -2.0,  0.0, 1.0, 0.0, 0.0, -1.0},
+             b[3]={4.0, 0.0, 0.0};
+
+    ret=dlevmar_lec_der(hs51, jachs51, p, x, m, n, A, b, 3, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, analytic jacobian
+    //ret=dlevmar_lec_dif(hs51, p, x, m, n, A, b, 3, 1000, opts, info, NULL, NULL, NULL); // lin. constraints, no jacobian
+    }
+  break;
+#endif /* HAVE_LAPACK */
+
+  case 10:
+  /* Hock - Schittkowski problem 01 */
+    m=2; n=2;
+    p[0]=-2.0; p[1]=1.0;
+    for(i=0; i<n; i++) x[i]=0.0;
+    //ret=dlevmar_der(hs01, jachs01, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    {
+      double lb[2], ub[2];
+
+      lb[0]=-DBL_MAX; lb[1]=-1.5;
+      ub[0]=ub[1]=DBL_MAX;
+
+      ret=dlevmar_bc_der(hs01, jachs01, p, x, m, n, lb, ub, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    }
+    break;
+  case 11:
+  /* Hock - Schittkowski (modified) problem 21 */
+    m=2; n=2;
+    p[0]=-1.0; p[1]=-1.0;
+    for(i=0; i<n; i++) x[i]=0.0;
+    //ret=dlevmar_der(hs21, jachs21, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    {
+      double lb[2], ub[2];
+
+      lb[0]=2.0; lb[1]=-50.0;
+      ub[0]=50.0; ub[1]=50.0;
+
+      ret=dlevmar_bc_der(hs21, jachs21, p, x, m, n, lb, ub, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    }
+    break;
+  case 12:
+  /* hatfldb problem */
+    m=4; n=4;
+    p[0]=p[1]=p[2]=p[3]=0.1;
+    for(i=0; i<n; i++) x[i]=0.0;
+    //ret=dlevmar_der(hatfldb, jachatfldb, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    {
+      double lb[4], ub[4];
+
+      lb[0]=lb[1]=lb[2]=lb[3]=0.0;
+
+      ub[0]=ub[2]=ub[3]=DBL_MAX;
+      ub[1]=0.8;
+
+      ret=dlevmar_bc_der(hatfldb, jachatfldb, p, x, m, n, lb, ub, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    }
+    break;
+  case 13:
+  /* hatfldc problem */
+    m=4; n=4;
+    p[0]=p[1]=p[2]=p[3]=0.9;
+    for(i=0; i<n; i++) x[i]=0.0;
+    //ret=dlevmar_der(hatfldc, jachatfldc, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    {
+      double lb[4], ub[4];
+
+      lb[0]=lb[1]=lb[2]=lb[3]=0.0;
+
+      ub[0]=ub[1]=ub[2]=ub[3]=10.0;
+
+      ret=dlevmar_bc_der(hatfldc, jachatfldc, p, x, m, n, lb, ub, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    }
+    break;
+  case 14:
+  /* equilibrium combustion problem */
+    m=5; n=5;
+    p[0]=p[1]=p[2]=p[3]=p[4]=0.0001;
+    for(i=0; i<n; i++) x[i]=0.0;
+    //ret=dlevmar_der(combust, jaccombust, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    {
+      double lb[5], ub[5];
+
+      lb[0]=lb[1]=lb[2]=lb[3]=lb[4]=0.0001;
+
+      ub[0]=ub[1]=ub[2]=ub[3]=ub[4]=100.0;
+
+      ret=dlevmar_bc_der(combust, jaccombust, p, x, m, n, lb, ub, 5000, opts, info, NULL, NULL, NULL); // with analytic jacobian
+    }
+    break;
+  } /* switch */
+  
+  printf("Results for %s:\n", probname[problem]);
+  printf("Levenberg-Marquardt returned %d in %g iter, reason %g\nSolution: ", ret, info[5], info[6]);
+  for(i=0; i<m; ++i)
+    printf("%.7g ", p[i]);
+  printf("\n\nMinimization info:\n");
+  for(i=0; i<LM_INFO_SZ; ++i)
+    printf("%g ", info[i]);
+  printf("\n");
+
+  return 0;
+}

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