File: chkder.c

package info (click to toggle)
cminpack 1.3.4-4
  • links: PTS, VCS
  • area: main
  • in suites: stretch
  • size: 3,296 kB
  • ctags: 2,315
  • sloc: ansic: 11,544; fortran: 6,260; makefile: 429; f90: 354; sh: 10
file content (159 lines) | stat: -rw-r--r-- 5,034 bytes parent folder | download | duplicates (4)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
#include "cminpack.h"
#include <math.h>
#include "cminpackP.h"

#define log10e 0.43429448190325182765
#define factor 100.

/* Table of constant values */

__cminpack_attr__
void __cminpack_func__(chkder)(int m, int n, const real *x, 
	real *fvec, real *fjac, int ldfjac, real *xp, 
	real *fvecp, int mode, real *err)
{
    /* Local variables */
    int i, j;
    real eps, epsf, temp, epsmch;
    real epslog;

/*     ********** */

/*     subroutine chkder */

/*     this subroutine checks the gradients of m nonlinear functions */
/*     in n variables, evaluated at a point x, for consistency with */
/*     the functions themselves. the user must call chkder twice, */
/*     first with mode = 1 and then with mode = 2. */

/*     mode = 1. on input, x must contain the point of evaluation. */
/*               on output, xp is set to a neighboring point. */

/*     mode = 2. on input, fvec must contain the functions and the */
/*                         rows of fjac must contain the gradients */
/*                         of the respective functions each evaluated */
/*                         at x, and fvecp must contain the functions */
/*                         evaluated at xp. */
/*               on output, err contains measures of correctness of */
/*                          the respective gradients. */

/*     the subroutine does not perform reliably if cancellation or */
/*     rounding errors cause a severe loss of significance in the */
/*     evaluation of a function. therefore, none of the components */
/*     of x should be unusually small (in particular, zero) or any */
/*     other value which may cause loss of significance. */

/*     the subroutine statement is */

/*       subroutine chkder(m,n,x,fvec,fjac,ldfjac,xp,fvecp,mode,err) */

/*     where */

/*       m is a positive integer input variable set to the number */
/*         of functions. */

/*       n is a positive integer input variable set to the number */
/*         of variables. */

/*       x is an input array of length n. */

/*       fvec is an array of length m. on input when mode = 2, */
/*         fvec must contain the functions evaluated at x. */

/*       fjac is an m by n array. on input when mode = 2, */
/*         the rows of fjac must contain the gradients of */
/*         the respective functions evaluated at x. */

/*       ldfjac is a positive integer input parameter not less than m */
/*         which specifies the leading dimension of the array fjac. */

/*       xp is an array of length n. on output when mode = 1, */
/*         xp is set to a neighboring point of x. */

/*       fvecp is an array of length m. on input when mode = 2, */
/*         fvecp must contain the functions evaluated at xp. */

/*       mode is an integer input variable set to 1 on the first call */
/*         and 2 on the second. other values of mode are equivalent */
/*         to mode = 1. */

/*       err is an array of length m. on output when mode = 2, */
/*         err contains measures of correctness of the respective */
/*         gradients. if there is no severe loss of significance, */
/*         then if err(i) is 1.0 the i-th gradient is correct, */
/*         while if err(i) is 0.0 the i-th gradient is incorrect. */
/*         for values of err between 0.0 and 1.0, the categorization */
/*         is less certain. in general, a value of err(i) greater */
/*         than 0.5 indicates that the i-th gradient is probably */
/*         correct, while a value of err(i) less than 0.5 indicates */
/*         that the i-th gradient is probably incorrect. */

/*     subprograms called */

/*       minpack supplied ... dpmpar */

/*       fortran supplied ... dabs,dlog10,dsqrt */

/*     argonne national laboratory. minpack project. march 1980. */
/*     burton s. garbow, kenneth e. hillstrom, jorge j. more */

/*     ********** */

/*     epsmch is the machine precision. */

    epsmch = __cminpack_func__(dpmpar)(1);

    eps = sqrt(epsmch);

    if (mode != 2) {

/*        mode = 1. */

        for (j = 0; j < n; ++j) {
            temp = eps * fabs(x[j]);
            if (temp == 0.) {
                temp = eps;
            }
            xp[j] = x[j] + temp;
        }
        return;
    }

/*        mode = 2. */

    epsf = factor * epsmch;
    epslog = log10e * log(eps);
    for (i = 0; i < m; ++i) {
	err[i] = 0.;
    }
    for (j = 0; j < n; ++j) {
	temp = fabs(x[j]);
	if (temp == 0.) {
	    temp = 1.;
	}
	for (i = 0; i < m; ++i) {
	    err[i] += temp * fjac[i + j * ldfjac];
	}
    }
    for (i = 0; i < m; ++i) {
	temp = 1.;
	if (fvec[i] != 0. && fvecp[i] != 0. &&
            fabs(fvecp[i] - fvec[i]) >= epsf * fabs(fvec[i]))
		 {
	    temp = eps * fabs((fvecp[i] - fvec[i]) / eps - err[i]) 
		    / (fabs(fvec[i]) +
                       fabs(fvecp[i]));
	}
	err[i] = 1.;
	if (temp > epsmch && temp < eps) {
	    err[i] = (log10e * log(temp) - epslog) / epslog;
	}
	if (temp >= eps) {
	    err[i] = 0.;
	}
    }

/*     last card of subroutine chkder. */

} /* chkder_ */