example1.c

柯西方法解方程

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "math_util.h"
int n_fun, n_grad;
main()
{
    long double epsilon, *x;
    int n;
    long double ex1_fun( long double * );
    void ex1_dfun( long double *, long double * );
    void cauchy( long double(*)(long double *), 
                 void(*)(long double *, long double *), 
                 long double *, int, long double );
    
    n_fun = 0;
	   n_grad = 0;

	   n = 2;                  /* Number of unknown parameters */

	   x = a1d_allo_dbl( n );  /* Allocate storage for the vector x */

    x[0] = -2.9;            /* Initial guess */
    x[1] = 2.0;

	   epsilon = 1.0e-4;       /*Solution error */
	
    cauchy( ex1_fun, ex1_dfun, x, n, epsilon );
    
    printf("\nSolution x: ");
    print_vec_dbl( x, n );
    printf("\n");
    printf(" # of function evaluations: %d\n",n_fun);
    printf(" # of gradient evaluations: %d\n",n_grad);

    a1d_free_dbl( x );   /* Free storage for the vector x */
}
/*
	Rosenbrock's function
*/
long double ex1_fun( x )
long double *x;
{
   long double f;
   
   n_fun++;
   
   f = 100*(x[1]-x[0]*x[0])*(x[1]-x[0]*x[0]) + 
       (1.0-x[0])*(1.0-x[0]);
   
   return( f );
}
void ex1_dfun( df, x )
long double *df, *x;
{
   n_grad++;
   
   df[0] = -400.0*x[0]*(x[1]-x[0]*x[0])-2.0*(1.0-x[0]);
   df[1] = 200.0*(x[1]-x[0]*x[0]);
}
/*
***  Norm(grad f) <= eps

Solution x:  1.000024e+00  1.000048e+00

 # of function evaluations: 4208
 # of gradient evaluations: 579
 Solution time: 7.166667e+00

*/