ex_2.c

柯西方法解方程

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include "math_util.h"
int n_fun, n_grad;
main()
{
    clock_t time_0, time_1;
    long double tol, *x, dtime;
    int n;
    long double ex2_fun( long double * );
    void ex2_dfun( long double *, long double * );
    long double line_search( long double(*)(), long double, long double *,
                             long double *, int, long double );
    void cauchy( long double(*)(), void(*)(), long double *, int, 
                 long double );
    
	n_fun = 0;
	n_grad = 0;
	n = 2;
	x = a1d_allo_dbl( n );
	x[0] = 0.50;
	x[1] = 0.50;
	tol = 1.0e-4;
	
	time_0 = clock();
    cauchy( ex2_fun, ex2_dfun, x, n, tol );
	time_1 = clock();
    dtime = (long double)(time_1-time_0)/((long double)CLOCKS_PER_SEC);    
    
    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);
    printf(" Solution time: %Le",dtime);
}
/*
	Easson function
*/
long double ex2_fun( x )
long double *x;
{
   long double f, t1, t2, t8, t11, x1, x2;
   
   n_fun++;
   
   x1 = x[0];
   x2 = x[1];
   t1 = x1*x1;
   t2 = x2*x2;
   t8 = t1*t1;
   t11 = t2*t2;
   f = 6.0/5.0+t1/10+(1.0+t2)/t1/10+(t1*t2+100.0)/t8/t11/10;
     
   return( f );
}
void ex2_dfun( df, x )
long double *df, *x;
{
   long double t1, t3, t5, t10, t11, t15, t19, x1, x2;
   n_grad++;
   
   x1 = x[0];
   x2 = x[1];
   t1 = x2*x2;
   t3 = x1*x1;
   t5 = 1/t3/x1;
   t10 = t3*t1+100.0;
   t11 = t3*t3;
   t15 = t1*t1;
   t19 = 1/t3;
   df[0] = x1/5-(t1+1.0)*t5/5+t5/t1/5-2.0/5.0*t10/t11/x1/t15;
   df[1] = x2*t19/5+t19/t1/x2/5-2.0/5.0*t10/t11/t15/x2;
}
/*
***  Norm(grad f) <= eps

Solution x:  1.743450e+00  2.029806e+00

 # of function evaluations: 5045
 # of gradient evaluations: 418
 Solution time: 8.783333e+00

*/