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/* covar.f -- translated by f2c (version 20050501).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "cminpack.h"
#include <math.h>
#define real __cminpack_real__
/* covar1 estimates the variance-covariance matrix:
C = sigma**2 (JtJ)**+
where (JtJ)**+ is the inverse of JtJ or the pseudo-inverse of JtJ (in case J does not have full rank),
and sigma**2 = fsumsq / (m - k)
where fsumsq is the residual sum of squares and k is the rank of J.
*/
__cminpack_attr__
int __cminpack_func__(covar1)(int m, int n, real fsumsq, real *r, int ldr,
const int *ipvt, real tol, real *wa)
{
/* Local variables */
int i, j, k, l, ii, jj;
int sing;
real temp, tolr;
/* ********** */
/* subroutine covar */
/* given an m by n matrix a, the problem is to determine */
/* the covariance matrix corresponding to a, defined as */
/* t */
/* inverse(a *a) . */
/* this subroutine completes the solution of the problem */
/* if it is provided with the necessary information from the */
/* qr factorization, with column pivoting, of a. that is, if */
/* a*p = q*r, where p is a permutation matrix, q has orthogonal */
/* columns, and r is an upper triangular matrix with diagonal */
/* elements of nonincreasing magnitude, then covar expects */
/* the full upper triangle of r and the permutation matrix p. */
/* the covariance matrix is then computed as */
/* t t */
/* p*inverse(r *r)*p . */
/* if a is nearly rank deficient, it may be desirable to compute */
/* the covariance matrix corresponding to the linearly independent */
/* columns of a. to define the numerical rank of a, covar uses */
/* the tolerance tol. if l is the largest integer such that */
/* abs(r(l,l)) .gt. tol*abs(r(1,1)) , */
/* then covar computes the covariance matrix corresponding to */
/* the first l columns of r. for k greater than l, column */
/* and row ipvt(k) of the covariance matrix are set to zero. */
/* the subroutine statement is */
/* subroutine covar(n,r,ldr,ipvt,tol,wa) */
/* where */
/* n is a positive integer input variable set to the order of r. */
/* r is an n by n array. on input the full upper triangle must */
/* contain the full upper triangle of the matrix r. on output */
/* r contains the square symmetric covariance matrix. */
/* ldr is a positive integer input variable not less than n */
/* which specifies the leading dimension of the array r. */
/* ipvt is an integer input array of length n which defines the */
/* permutation matrix p such that a*p = q*r. column j of p */
/* is column ipvt(j) of the identity matrix. */
/* tol is a nonnegative input variable used to define the */
/* numerical rank of a in the manner described above. */
/* wa is a work array of length n. */
/* subprograms called */
/* fortran-supplied ... dabs */
/* argonne national laboratory. minpack project. august 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
tolr = tol * fabs(r[0]);
/* form the inverse of r in the full upper triangle of r. */
l = -1;
for (k = 0; k < n; ++k) {
if (fabs(r[k + k * ldr]) <= tolr) {
break;
}
r[k + k * ldr] = 1. / r[k + k * ldr];
if (k > 0) {
for (j = 0; j < k; ++j) {
temp = r[k + k * ldr] * r[j + k * ldr];
r[j + k * ldr] = 0.;
for (i = 0; i <= j; ++i) {
r[i + k * ldr] -= temp * r[i + j * ldr];
}
}
}
l = k;
}
/* form the full upper triangle of the inverse of (r transpose)*r */
/* in the full upper triangle of r. */
if (l >= 0) {
for (k = 0; k <= l; ++k) {
if (k > 0) {
for (j = 0; j < k; ++j) {
temp = r[j + k * ldr];
for (i = 0; i <= j; ++i) {
r[i + j * ldr] += temp * r[i + k * ldr];
}
}
}
temp = r[k + k * ldr];
for (i = 0; i <= k; ++i) {
r[i + k * ldr] *= temp;
}
}
}
/* form the full lower triangle of the covariance matrix */
/* in the strict lower triangle of r and in wa. */
for (j = 0; j < n; ++j) {
jj = ipvt[j]-1;
sing = j > l;
for (i = 0; i <= j; ++i) {
if (sing) {
r[i + j * ldr] = 0.;
}
ii = ipvt[i]-1;
if (ii > jj) {
r[ii + jj * ldr] = r[i + j * ldr];
}
else if (ii < jj) {
r[jj + ii * ldr] = r[i + j * ldr];
}
}
wa[jj] = r[j + j * ldr];
}
/* symmetrize the covariance matrix in r. */
temp = fsumsq / (m - (l + 1));
for (j = 0; j < n; ++j) {
for (i = 0; i < j; ++i) {
r[j + i * ldr] *= temp;
r[i + j * ldr] = r[j + i * ldr];
}
r[j + j * ldr] = temp * wa[j];
}
/* last card of subroutine covar. */
if (l == (n - 1)) {
return 0;
}
return l + 1;
} /* covar_ */
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