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/* minpack/qrfac.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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__1 = 1;
/*< subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa) >*/
/* Subroutine */ int qrfac_(integer *m, integer *n, doublereal *a, integer *
lda, logical *pivot, integer *ipvt, integer *lipvt, doublereal *rdiag,
doublereal *acnorm, doublereal *wa)
{
/* Initialized data */
static doublereal one = 1.; /* constant */
static doublereal p05 = .05; /* constant */
static doublereal zero = 0.; /* constant */
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1, d__2, d__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k, jp1;
doublereal sum;
integer kmax;
doublereal temp;
integer minmn;
extern doublereal enorm_(integer *, doublereal *);
doublereal epsmch;
extern doublereal dpmpar_(integer *);
doublereal ajnorm;
(void)lipvt;
/*< integer m,n,lda,lipvt >*/
/*< integer ipvt(lipvt) >*/
/*< logical pivot >*/
/*< double precision a(lda,n),rdiag(n),acnorm(n),wa(n) >*/
/* ********** */
/* subroutine qrfac */
/* this subroutine uses householder transformations with column */
/* pivoting (optional) to compute a qr factorization of the */
/* m by n matrix a. that is, qrfac determines an orthogonal */
/* matrix q, a permutation matrix p, and an upper trapezoidal */
/* matrix r with diagonal elements of nonincreasing magnitude, */
/* such that a*p = q*r. the householder transformation for */
/* column k, k = 1,2,...,min(m,n), is of the form */
/* t */
/* i - (1/u(k))*u*u */
/* where u has zeros in the first k-1 positions. the form of */
/* this transformation and the method of pivoting first */
/* appeared in the corresponding linpack subroutine. */
/* the subroutine statement is */
/* subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa) */
/* where */
/* m is a positive integer input variable set to the number */
/* of rows of a. */
/* n is a positive integer input variable set to the number */
/* of columns of a. */
/* a is an m by n array. on input a contains the matrix for */
/* which the qr factorization is to be computed. on output */
/* the strict upper trapezoidal part of a contains the strict */
/* upper trapezoidal part of r, and the lower trapezoidal */
/* part of a contains a factored form of q (the non-trivial */
/* elements of the u vectors described above). */
/* lda is a positive integer input variable not less than m */
/* which specifies the leading dimension of the array a. */
/* pivot is a logical input variable. if pivot is set true, */
/* then column pivoting is enforced. if pivot is set false, */
/* then no column pivoting is done. */
/* ipvt is an integer output array of length lipvt. ipvt */
/* defines the permutation matrix p such that a*p = q*r. */
/* column j of p is column ipvt(j) of the identity matrix. */
/* if pivot is false, ipvt is not referenced. */
/* lipvt is a positive integer input variable. if pivot is false, */
/* then lipvt may be as small as 1. if pivot is true, then */
/* lipvt must be at least n. */
/* rdiag is an output array of length n which contains the */
/* diagonal elements of r. */
/* acnorm is an output array of length n which contains the */
/* norms of the corresponding columns of the input matrix a. */
/* if this information is not needed, then acnorm can coincide */
/* with rdiag. */
/* wa is a work array of length n. if pivot is false, then wa */
/* can coincide with rdiag. */
/* subprograms called */
/* minpack-supplied ... dpmpar,enorm */
/* fortran-supplied ... dmax1,dsqrt,min0 */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
/*< integer i,j,jp1,k,kmax,minmn >*/
/*< double precision ajnorm,epsmch,one,p05,sum,temp,zero >*/
/*< double precision dpmpar,enorm >*/
/*< data one,p05,zero /1.0d0,5.0d-2,0.0d0/ >*/
/* Parameter adjustments */
--wa;
--acnorm;
--rdiag;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipvt;
/* Function Body */
/* epsmch is the machine precision. */
/*< epsmch = dpmpar(1) >*/
epsmch = dpmpar_(&c__1);
/* compute the initial column norms and initialize several arrays. */
/*< do 10 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< acnorm(j) = enorm(m,a(1,j)) >*/
acnorm[j] = enorm_(m, &a[j * a_dim1 + 1]);
/*< rdiag(j) = acnorm(j) >*/
rdiag[j] = acnorm[j];
/*< wa(j) = rdiag(j) >*/
wa[j] = rdiag[j];
/*< if (pivot) ipvt(j) = j >*/
if (*pivot) {
ipvt[j] = j;
}
/*< 10 continue >*/
/* L10: */
}
/* reduce a to r with householder transformations. */
/*< minmn = min0(m,n) >*/
minmn = min(*m,*n);
/*< do 110 j = 1, minmn >*/
i__1 = minmn;
for (j = 1; j <= i__1; ++j) {
/*< if (.not.pivot) go to 40 >*/
if (! (*pivot)) {
goto L40;
}
/* bring the column of largest norm into the pivot position. */
/*< kmax = j >*/
kmax = j;
/*< do 20 k = j, n >*/
i__2 = *n;
for (k = j; k <= i__2; ++k) {
/*< if (rdiag(k) .gt. rdiag(kmax)) kmax = k >*/
if (rdiag[k] > rdiag[kmax]) {
kmax = k;
}
/*< 20 continue >*/
/* L20: */
}
/*< if (kmax .eq. j) go to 40 >*/
if (kmax == j) {
goto L40;
}
/*< do 30 i = 1, m >*/
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< temp = a(i,j) >*/
temp = a[i__ + j * a_dim1];
/*< a(i,j) = a(i,kmax) >*/
a[i__ + j * a_dim1] = a[i__ + kmax * a_dim1];
/*< a(i,kmax) = temp >*/
a[i__ + kmax * a_dim1] = temp;
/*< 30 continue >*/
/* L30: */
}
/*< rdiag(kmax) = rdiag(j) >*/
rdiag[kmax] = rdiag[j];
/*< wa(kmax) = wa(j) >*/
wa[kmax] = wa[j];
/*< k = ipvt(j) >*/
k = ipvt[j];
/*< ipvt(j) = ipvt(kmax) >*/
ipvt[j] = ipvt[kmax];
/*< ipvt(kmax) = k >*/
ipvt[kmax] = k;
/*< 40 continue >*/
L40:
/* compute the householder transformation to reduce the */
/* j-th column of a to a multiple of the j-th unit vector. */
/*< ajnorm = enorm(m-j+1,a(j,j)) >*/
i__2 = *m - j + 1;
ajnorm = enorm_(&i__2, &a[j + j * a_dim1]);
/*< if (ajnorm .eq. zero) go to 100 >*/
if (ajnorm == zero) {
goto L100;
}
/*< if (a(j,j) .lt. zero) ajnorm = -ajnorm >*/
if (a[j + j * a_dim1] < zero) {
ajnorm = -ajnorm;
}
/*< do 50 i = j, m >*/
i__2 = *m;
for (i__ = j; i__ <= i__2; ++i__) {
/*< a(i,j) = a(i,j)/ajnorm >*/
a[i__ + j * a_dim1] /= ajnorm;
/*< 50 continue >*/
/* L50: */
}
/*< a(j,j) = a(j,j) + one >*/
a[j + j * a_dim1] += one;
/* apply the transformation to the remaining columns */
/* and update the norms. */
/*< jp1 = j + 1 >*/
jp1 = j + 1;
/*< if (n .lt. jp1) go to 100 >*/
if (*n < jp1) {
goto L100;
}
/*< do 90 k = jp1, n >*/
i__2 = *n;
for (k = jp1; k <= i__2; ++k) {
/*< sum = zero >*/
sum = zero;
/*< do 60 i = j, m >*/
i__3 = *m;
for (i__ = j; i__ <= i__3; ++i__) {
/*< sum = sum + a(i,j)*a(i,k) >*/
sum += a[i__ + j * a_dim1] * a[i__ + k * a_dim1];
/*< 60 continue >*/
/* L60: */
}
/*< temp = sum/a(j,j) >*/
temp = sum / a[j + j * a_dim1];
/*< do 70 i = j, m >*/
i__3 = *m;
for (i__ = j; i__ <= i__3; ++i__) {
/*< a(i,k) = a(i,k) - temp*a(i,j) >*/
a[i__ + k * a_dim1] -= temp * a[i__ + j * a_dim1];
/*< 70 continue >*/
/* L70: */
}
/*< if (.not.pivot .or. rdiag(k) .eq. zero) go to 80 >*/
if (! (*pivot) || rdiag[k] == zero) {
goto L80;
}
/*< temp = a(j,k)/rdiag(k) >*/
temp = a[j + k * a_dim1] / rdiag[k];
/*< rdiag(k) = rdiag(k)*dsqrt(dmax1(zero,one-temp**2)) >*/
/* Computing MAX */
/* Computing 2nd power */
d__3 = temp;
d__1 = zero, d__2 = one - d__3 * d__3;
rdiag[k] *= sqrt((max(d__1,d__2)));
/*< if (p05*(rdiag(k)/wa(k))**2 .gt. epsmch) go to 80 >*/
/* Computing 2nd power */
d__1 = rdiag[k] / wa[k];
if (p05 * (d__1 * d__1) > epsmch) {
goto L80;
}
/*< rdiag(k) = enorm(m-j,a(jp1,k)) >*/
i__3 = *m - j;
rdiag[k] = enorm_(&i__3, &a[jp1 + k * a_dim1]);
/*< wa(k) = rdiag(k) >*/
wa[k] = rdiag[k];
/*< 80 continue >*/
L80:
/*< 90 continue >*/
/* L90: */
;
}
/*< 100 continue >*/
L100:
/*< rdiag(j) = -ajnorm >*/
rdiag[j] = -ajnorm;
/*< 110 continue >*/
/* L110: */
}
/*< return >*/
return 0;
/* last card of subroutine qrfac. */
/*< end >*/
} /* qrfac_ */
#ifdef __cplusplus
}
#endif
|
