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/* slaqp2.f -- translated by f2c (version 20061008).
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 "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
/* Subroutine */ int slaqp2_(integer *m, integer *n, integer *offset, real *a,
integer *lda, integer *jpvt, real *tau, real *vn1, real *vn2, real *
work)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real r__1, r__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, mn;
real aii;
integer pvt;
real temp, temp2;
extern doublereal snrm2_(integer *, real *, integer *);
real tol3z;
integer offpi;
extern /* Subroutine */ int slarf_(char *, integer *, integer *, real *,
integer *, real *, real *, integer *, real *);
integer itemp;
extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *,
integer *);
extern doublereal slamch_(char *);
extern integer isamax_(integer *, real *, integer *);
extern /* Subroutine */ int slarfp_(integer *, real *, real *, integer *,
real *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLAQP2 computes a QR factorization with column pivoting of */
/* the block A(OFFSET+1:M,1:N). */
/* The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix A. N >= 0. */
/* OFFSET (input) INTEGER */
/* The number of rows of the matrix A that must be pivoted */
/* but no factorized. OFFSET >= 0. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, the upper triangle of block A(OFFSET+1:M,1:N) is */
/* the triangular factor obtained; the elements in block */
/* A(OFFSET+1:M,1:N) below the diagonal, together with the */
/* array TAU, represent the orthogonal matrix Q as a product of */
/* elementary reflectors. Block A(1:OFFSET,1:N) has been */
/* accordingly pivoted, but no factorized. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* JPVT (input/output) INTEGER array, dimension (N) */
/* On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted */
/* to the front of A*P (a leading column); if JPVT(i) = 0, */
/* the i-th column of A is a free column. */
/* On exit, if JPVT(i) = k, then the i-th column of A*P */
/* was the k-th column of A. */
/* TAU (output) REAL array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors. */
/* VN1 (input/output) REAL array, dimension (N) */
/* The vector with the partial column norms. */
/* VN2 (input/output) REAL array, dimension (N) */
/* The vector with the exact column norms. */
/* WORK (workspace) REAL array, dimension (N) */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
/* X. Sun, Computer Science Dept., Duke University, USA */
/* Partial column norm updating strategy modified by */
/* Z. Drmac and Z. Bujanovic, Dept. of Mathematics, */
/* University of Zagreb, Croatia. */
/* June 2006. */
/* For more details see LAPACK Working Note 176. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--jpvt;
--tau;
--vn1;
--vn2;
--work;
/* Function Body */
/* Computing MIN */
i__1 = *m - *offset;
mn = min(i__1,*n);
tol3z = sqrt(slamch_("Epsilon"));
/* Compute factorization. */
i__1 = mn;
for (i__ = 1; i__ <= i__1; ++i__) {
offpi = *offset + i__;
/* Determine ith pivot column and swap if necessary. */
i__2 = *n - i__ + 1;
pvt = i__ - 1 + isamax_(&i__2, &vn1[i__], &c__1);
if (pvt != i__) {
sswap_(m, &a[pvt * a_dim1 + 1], &c__1, &a[i__ * a_dim1 + 1], &
c__1);
itemp = jpvt[pvt];
jpvt[pvt] = jpvt[i__];
jpvt[i__] = itemp;
vn1[pvt] = vn1[i__];
vn2[pvt] = vn2[i__];
}
/* Generate elementary reflector H(i). */
if (offpi < *m) {
i__2 = *m - offpi + 1;
slarfp_(&i__2, &a[offpi + i__ * a_dim1], &a[offpi + 1 + i__ *
a_dim1], &c__1, &tau[i__]);
} else {
slarfp_(&c__1, &a[*m + i__ * a_dim1], &a[*m + i__ * a_dim1], &
c__1, &tau[i__]);
}
if (i__ < *n) {
/* Apply H(i)' to A(offset+i:m,i+1:n) from the left. */
aii = a[offpi + i__ * a_dim1];
a[offpi + i__ * a_dim1] = 1.f;
i__2 = *m - offpi + 1;
i__3 = *n - i__;
slarf_("Left", &i__2, &i__3, &a[offpi + i__ * a_dim1], &c__1, &
tau[i__], &a[offpi + (i__ + 1) * a_dim1], lda, &work[1]);
a[offpi + i__ * a_dim1] = aii;
}
/* Update partial column norms. */
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
if (vn1[j] != 0.f) {
/* NOTE: The following 4 lines follow from the analysis in */
/* Lapack Working Note 176. */
/* Computing 2nd power */
r__2 = (r__1 = a[offpi + j * a_dim1], dabs(r__1)) / vn1[j];
temp = 1.f - r__2 * r__2;
temp = dmax(temp,0.f);
/* Computing 2nd power */
r__1 = vn1[j] / vn2[j];
temp2 = temp * (r__1 * r__1);
if (temp2 <= tol3z) {
if (offpi < *m) {
i__3 = *m - offpi;
vn1[j] = snrm2_(&i__3, &a[offpi + 1 + j * a_dim1], &
c__1);
vn2[j] = vn1[j];
} else {
vn1[j] = 0.f;
vn2[j] = 0.f;
}
} else {
vn1[j] *= sqrt(temp);
}
}
/* L10: */
}
/* L20: */
}
return 0;
/* End of SLAQP2 */
} /* slaqp2_ */
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