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chkder.c
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chkder.c
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#include "cminpack.h"
#include <math.h>
#include "cminpackP.h"
#define log10e ((real)0.434294481903251827651128918916605082)
#define factor ((real)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_ */