ex_3.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 dtime;
    long double tol, *x;
    int n;
    long double ex3_fun( long double * );
    void ex3_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 = 4;
	x = a1d_allo_dbl( n );
    vec_null( x, n );
	tol = 1.0e-4;
	
	time_0 = clock();
    cauchy( ex3_fun, ex3_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);
}
/*
	Wood function
*/
long double ex3_fun( x )
long double *x;
{
   long double f, t1, t3, t5, t6, t8, t10, t11, t12, t13, t14, 
               x1, x2, x3, x4;
   
   n_fun++;
   
   x1 = x[0];
   x2 = x[1];
   x3 = x[2];
   x4 = x[3];
   t1 = x1*x1;
   t3 = pow(x2-t1,2.0);
   t5 = pow(1.0-x1,2.0);
   t6 = x3*x3;
   t8 = pow(x4-t6,2.0);
   t10 = pow(1.0-x3,2.0);
   t11 = x2-1.0;
   t12 = t11*t11;
   t13 = x4-1.0;
   t14 = t13*t13;
   f = 100.0*t3+t5+90.0*t8+t10+0.101E2*t12+0.101E2*t14+0.198E2*t11*t13;
     
   return( f );
}
void ex3_dfun( df, x )
long double *df, *x;
{
   long double t1, t6, x1, x2, x3, x4;
   n_grad++;
   
   x1 = x[0];
   x2 = x[1];
   x3 = x[2];
   x4 = x[3];
   t1 = x1*x1;
   t6 = x3*x3;
   df[0] = -400.0*(x2-t1)*x1-2.0+2.0*x1;
   df[1] = 0.2202E3*x2-200.0*t1-0.4E2+0.198E2*x4;
   df[2] = -360.0*(x4-t6)*x3-2.0+2.0*x3;
   df[3] = 0.2002E3*x4-180.0*t6-0.4E2+0.198E2*x2;
}
/*
***  Norm(grad f) <= eps

Solution x:  9.999592e-01  9.999183e-01  1.000041e+00  1.000082e+00

 # of function evaluations: 7562
 # of gradient evaluations: 1146
 Solution time: 3.645000e+01

*/