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/* ../../../dependencies/lapack/src/zlaqps.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"
/* Table of constant values */
static doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;
/* Subroutine */ int zlaqps_(integer *m, integer *n, integer *offset, integer
*nb, integer *kb, doublecomplex *a, integer *lda, integer *jpvt,
doublecomplex *tau, doublereal *vn1, doublereal *vn2, doublecomplex *
auxv, doublecomplex *f, integer *ldf)
{
/* System generated locals */
integer a_dim1, a_offset, f_dim1, f_offset, i__1, i__2, i__3;
doublereal d__1, d__2;
doublecomplex z__1;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
double z_abs(doublecomplex *), sqrt(doublereal);
integer i_dnnt(doublereal *);
/* Local variables */
static integer j, k, rk;
static doublecomplex akk;
static integer pvt;
static doublereal temp, temp2;
static integer itemp;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, ftnlen, ftnlen), zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, ftnlen),
zswap_(integer *, doublecomplex *, integer *, doublecomplex *,
integer *);
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
extern integer idamax_(integer *, doublereal *, integer *);
static integer lsticc;
extern /* Subroutine */ int zlarfg_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *);
static integer lastrk;
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLAQPS computes a step of QR factorization with column pivoting */
/* of a complex M-by-N matrix A by using Blas-3. It tries to factorize */
/* NB columns from A starting from the row OFFSET+1, and updates all */
/* of the matrix with Blas-3 xGEMM. */
/* In some cases, due to catastrophic cancellations, it cannot */
/* factorize NB columns. Hence, the actual number of factorized */
/* columns is returned in KB. */
/* 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 A that have been factorized in */
/* previous steps. */
/* NB (input) INTEGER */
/* The number of columns to factorize. */
/* KB (output) INTEGER */
/* The number of columns actually factorized. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, block A(OFFSET+1:M,1:KB) is the triangular */
/* factor obtained and block A(1:OFFSET,1:N) has been */
/* accordingly pivoted, but no factorized. */
/* The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has */
/* been updated. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* JPVT (input/output) INTEGER array, dimension (N) */
/* JPVT(I) = K <==> Column K of the full matrix A has been */
/* permuted into position I in AP. */
/* TAU (output) COMPLEX*16 array, dimension (KB) */
/* The scalar factors of the elementary reflectors. */
/* VN1 (input/output) DOUBLE PRECISION array, dimension (N) */
/* The vector with the partial column norms. */
/* VN2 (input/output) DOUBLE PRECISION array, dimension (N) */
/* The vector with the exact column norms. */
/* AUXV (input/output) COMPLEX*16 array, dimension (NB) */
/* Auxiliar vector. */
/* F (input/output) COMPLEX*16 array, dimension (LDF,NB) */
/* Matrix F' = L*Y'*A. */
/* LDF (input) INTEGER */
/* The leading dimension of the array F. LDF >= max(1,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 */
/* ===================================================================== */
/* .. 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;
--auxv;
f_dim1 = *ldf;
f_offset = 1 + f_dim1;
f -= f_offset;
/* Function Body */
/* Computing MIN */
i__1 = *m, i__2 = *n + *offset;
lastrk = min(i__1,i__2);
lsticc = 0;
k = 0;
/* Beginning of while loop. */
L10:
if (k < *nb && lsticc == 0) {
++k;
rk = *offset + k;
/* Determine ith pivot column and swap if necessary */
i__1 = *n - k + 1;
pvt = k - 1 + idamax_(&i__1, &vn1[k], &c__1);
if (pvt != k) {
zswap_(m, &a[pvt * a_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
i__1 = k - 1;
zswap_(&i__1, &f[pvt + f_dim1], ldf, &f[k + f_dim1], ldf);
itemp = jpvt[pvt];
jpvt[pvt] = jpvt[k];
jpvt[k] = itemp;
vn1[pvt] = vn1[k];
vn2[pvt] = vn2[k];
}
/* Apply previous Householder reflectors to column K: */
/* A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'. */
if (k > 1) {
/* CC CALL ZGEMM( 'No transpose', 'Conjugate transpose', */
/* CC $ M-RK+1, 1, K-1, -CONE, A( RK, 1 ), LDA, */
/* CC $ F( K, 1 ), LDF, CONE, A( RK, K ), LDA ) */
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = k + j * f_dim1;
d_cnjg(&z__1, &f[k + j * f_dim1]);
f[i__2].r = z__1.r, f[i__2].i = z__1.i;
/* L20: */
}
i__1 = *m - rk + 1;
i__2 = k - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", &i__1, &i__2, &z__1, &a[rk + a_dim1], lda,
&f[k + f_dim1], ldf, &c_b2, &a[rk + k * a_dim1], &c__1, (
ftnlen)12);
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = k + j * f_dim1;
d_cnjg(&z__1, &f[k + j * f_dim1]);
f[i__2].r = z__1.r, f[i__2].i = z__1.i;
/* L30: */
}
}
/* Generate elementary reflector H(k). */
if (rk < *m) {
i__1 = *m - rk + 1;
zlarfg_(&i__1, &a[rk + k * a_dim1], &a[rk + 1 + k * a_dim1], &
c__1, &tau[k]);
} else {
zlarfg_(&c__1, &a[rk + k * a_dim1], &a[rk + k * a_dim1], &c__1, &
tau[k]);
}
i__1 = rk + k * a_dim1;
akk.r = a[i__1].r, akk.i = a[i__1].i;
i__1 = rk + k * a_dim1;
a[i__1].r = 1., a[i__1].i = 0.;
/* Compute Kth column of F: */
/* Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K). */
if (k < *n) {
i__1 = *m - rk + 1;
i__2 = *n - k;
zgemv_("Conjugate transpose", &i__1, &i__2, &tau[k], &a[rk + (k +
1) * a_dim1], lda, &a[rk + k * a_dim1], &c__1, &c_b1, &f[
k + 1 + k * f_dim1], &c__1, (ftnlen)19);
}
/* Padding F(1:K,K) with zeros. */
i__1 = k;
for (j = 1; j <= i__1; ++j) {
i__2 = j + k * f_dim1;
f[i__2].r = 0., f[i__2].i = 0.;
/* L40: */
}
/* Incremental updating of F: */
/* F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)' */
/* *A(RK:M,K). */
if (k > 1) {
i__1 = *m - rk + 1;
i__2 = k - 1;
i__3 = k;
z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i;
zgemv_("Conjugate transpose", &i__1, &i__2, &z__1, &a[rk + a_dim1]
, lda, &a[rk + k * a_dim1], &c__1, &c_b1, &auxv[1], &c__1,
(ftnlen)19);
i__1 = k - 1;
zgemv_("No transpose", n, &i__1, &c_b2, &f[f_dim1 + 1], ldf, &
auxv[1], &c__1, &c_b2, &f[k * f_dim1 + 1], &c__1, (ftnlen)
12);
}
/* Update the current row of A: */
/* A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'. */
if (k < *n) {
i__1 = *n - k;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", &c__1, &i__1, &k, &
z__1, &a[rk + a_dim1], lda, &f[k + 1 + f_dim1], ldf, &
c_b2, &a[rk + (k + 1) * a_dim1], lda, (ftnlen)12, (ftnlen)
19);
}
/* Update partial column norms. */
if (rk < lastrk) {
i__1 = *n;
for (j = k + 1; j <= i__1; ++j) {
if (vn1[j] != 0.) {
temp = z_abs(&a[rk + j * a_dim1]) / vn1[j];
/* Computing MAX */
d__1 = 0., d__2 = (temp + 1.) * (1. - temp);
temp = max(d__1,d__2);
/* Computing 2nd power */
d__1 = vn1[j] / vn2[j];
temp2 = temp * .05 * (d__1 * d__1) + 1.;
if (temp2 == 1.) {
vn2[j] = (doublereal) lsticc;
lsticc = j;
} else {
vn1[j] *= sqrt(temp);
}
}
/* L50: */
}
}
i__1 = rk + k * a_dim1;
a[i__1].r = akk.r, a[i__1].i = akk.i;
/* End of while loop. */
goto L10;
}
*kb = k;
rk = *offset + *kb;
/* Apply the block reflector to the rest of the matrix: */
/* A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - */
/* A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)'. */
/* Computing MIN */
i__1 = *n, i__2 = *m - *offset;
if (*kb < min(i__1,i__2)) {
i__1 = *m - rk;
i__2 = *n - *kb;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "Conjugate transpose", &i__1, &i__2, kb, &z__1,
&a[rk + 1 + a_dim1], lda, &f[*kb + 1 + f_dim1], ldf, &c_b2, &
a[rk + 1 + (*kb + 1) * a_dim1], lda, (ftnlen)12, (ftnlen)19);
}
/* Recomputation of difficult columns. */
L60:
if (lsticc > 0) {
itemp = i_dnnt(&vn2[lsticc]);
i__1 = *m - rk;
vn1[lsticc] = dznrm2_(&i__1, &a[rk + 1 + lsticc * a_dim1], &c__1);
vn2[lsticc] = vn1[lsticc];
lsticc = itemp;
goto L60;
}
return 0;
/* End of ZLAQPS */
} /* zlaqps_ */
|
