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/* dogleg.f -- translated by f2c (version 20020621).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#include "cminpack.h"
#include <math.h>
#include "cminpackP.h"
/* Table of constant values */
__cminpack_attr__
void __cminpack_func__(dogleg)(int n, const real *r, int lr,
const real *diag, const real *qtb, real delta, real *x,
real *wa1, real *wa2)
{
/* System generated locals */
real d1, d2, d3, d4;
/* Local variables */
int i, j, k, l, jj, jp1;
real sum, temp, alpha, bnorm;
real gnorm, qnorm, epsmch;
real sgnorm;
/* ********** */
/* subroutine dogleg */
/* given an m by n matrix a, an n by n nonsingular diagonal */
/* matrix d, an m-vector b, and a positive number delta, the */
/* problem is to determine the convex combination x of the */
/* gauss-newton and scaled gradient directions that minimizes */
/* (a*x - b) in the least squares sense, subject to the */
/* restriction that the euclidean norm of d*x be at most delta. */
/* this subroutine completes the solution of the problem */
/* if it is provided with the necessary information from the */
/* qr factorization of a. that is, if a = q*r, where q has */
/* orthogonal columns and r is an upper triangular matrix, */
/* then dogleg expects the full upper triangle of r and */
/* the first n components of (q transpose)*b. */
/* the subroutine statement is */
/* subroutine dogleg(n,r,lr,diag,qtb,delta,x,wa1,wa2) */
/* where */
/* n is a positive integer input variable set to the order of r. */
/* r is an input array of length lr which must contain the upper */
/* triangular matrix r stored by rows. */
/* lr is a positive integer input variable not less than */
/* (n*(n+1))/2. */
/* diag is an input array of length n which must contain the */
/* diagonal elements of the matrix d. */
/* qtb is an input array of length n which must contain the first */
/* n elements of the vector (q transpose)*b. */
/* delta is a positive input variable which specifies an upper */
/* bound on the euclidean norm of d*x. */
/* x is an output array of length n which contains the desired */
/* convex combination of the gauss-newton direction and the */
/* scaled gradient direction. */
/* wa1 and wa2 are work arrays of length n. */
/* subprograms called */
/* minpack-supplied ... dpmpar,enorm */
/* fortran-supplied ... dabs,dmax1,dmin1,dsqrt */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
/* Parameter adjustments */
--wa2;
--wa1;
--x;
--qtb;
--diag;
--r;
(void)lr;
/* Function Body */
/* epsmch is the machine precision. */
epsmch = __cminpack_func__(dpmpar)(1);
/* first, calculate the gauss-newton direction. */
jj = n * (n + 1) / 2 + 1;
for (k = 1; k <= n; ++k) {
j = n - k + 1;
jp1 = j + 1;
jj -= k;
l = jj + 1;
sum = 0.;
if (n >= jp1) {
for (i = jp1; i <= n; ++i) {
sum += r[l] * x[i];
++l;
}
}
temp = r[jj];
if (temp == 0.) {
l = j;
for (i = 1; i <= j; ++i) {
/* Computing MAX */
d2 = fabs(r[l]);
temp = max(temp,d2);
l = l + n - i;
}
temp = epsmch * temp;
if (temp == 0.) {
temp = epsmch;
}
}
x[j] = (qtb[j] - sum) / temp;
}
/* test whether the gauss-newton direction is acceptable. */
for (j = 1; j <= n; ++j) {
wa1[j] = 0.;
wa2[j] = diag[j] * x[j];
}
qnorm = __cminpack_enorm__(n, &wa2[1]);
if (qnorm <= delta) {
return;
}
/* the gauss-newton direction is not acceptable. */
/* next, calculate the scaled gradient direction. */
l = 1;
for (j = 1; j <= n; ++j) {
temp = qtb[j];
for (i = j; i <= n; ++i) {
wa1[i] += r[l] * temp;
++l;
}
wa1[j] /= diag[j];
}
/* calculate the norm of the scaled gradient and test for */
/* the special case in which the scaled gradient is zero. */
gnorm = __cminpack_enorm__(n, &wa1[1]);
sgnorm = 0.;
alpha = delta / qnorm;
if (gnorm != 0.) {
/* calculate the point along the scaled gradient */
/* at which the quadratic is minimized. */
for (j = 1; j <= n; ++j) {
wa1[j] = wa1[j] / gnorm / diag[j];
}
l = 1;
for (j = 1; j <= n; ++j) {
sum = 0.;
for (i = j; i <= n; ++i) {
sum += r[l] * wa1[i];
++l;
}
wa2[j] = sum;
}
temp = __cminpack_enorm__(n, &wa2[1]);
sgnorm = gnorm / temp / temp;
/* test whether the scaled gradient direction is acceptable. */
alpha = 0.;
if (sgnorm < delta) {
/* the scaled gradient direction is not acceptable. */
/* finally, calculate the point along the dogleg */
/* at which the quadratic is minimized. */
bnorm = __cminpack_enorm__(n, &qtb[1]);
temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / delta);
/* Computing 2nd power */
d1 = sgnorm / delta;
/* Computing 2nd power */
d2 = temp - delta / qnorm;
/* Computing 2nd power */
d3 = delta / qnorm;
/* Computing 2nd power */
d4 = sgnorm / delta;
temp = temp - delta / qnorm * (d1 * d1)
+ sqrt(d2 * d2
+ (1. - d3 * d3) * (1. - d4 * d4));
/* Computing 2nd power */
d1 = sgnorm / delta;
alpha = delta / qnorm * (1. - d1 * d1) / temp;
}
}
/* form appropriate convex combination of the gauss-newton */
/* direction and the scaled gradient direction. */
temp = (1. - alpha) * min(sgnorm,delta);
for (j = 1; j <= n; ++j) {
x[j] = temp * wa1[j] + alpha * x[j];
}
/* last card of subroutine dogleg. */
} /* dogleg_ */
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