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/* zgeqlf.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;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
/* Subroutine */ int zgeqlf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, k, ib, nb, ki, kk, mu, nu, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zgeql2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGEQLF computes a QL factorization of a complex M-by-N matrix A: */
/* A = Q * L. */
/* 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. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, */
/* if m >= n, the lower triangle of the subarray */
/* A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L; */
/* if m <= n, the elements on and below the (n-m)-th */
/* superdiagonal contain the M-by-N lower trapezoidal matrix L; */
/* the remaining elements, with the array TAU, represent the */
/* unitary matrix Q as a product of elementary reflectors */
/* (see Further Details). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* TAU (output) COMPLEX*16 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= max(1,N). */
/* For optimum performance LWORK >= N*NB, where NB is */
/* the optimal blocksize. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of elementary reflectors */
/* Q = H(k) . . . H(2) H(1), where k = min(m,n). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a complex scalar, and v is a complex vector with */
/* v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in */
/* A(1:m-k+i-1,n-k+i), and tau in TAU(i). */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info == 0) {
k = min(*m,*n);
if (k == 0) {
lwkopt = 1;
} else {
nb = ilaenv_(&c__1, "ZGEQLF", " ", m, n, &c_n1, &c_n1);
lwkopt = *n * nb;
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
if (*lwork < max(1,*n) && ! lquery) {
*info = -7;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEQLF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (k == 0) {
return 0;
}
nbmin = 2;
nx = 1;
iws = *n;
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "ZGEQLF", " ", m, n, &c_n1, &c_n1);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEQLF", " ", m, n, &c_n1, &
c_n1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially. */
/* The last kk columns are handled by the block method. */
ki = (k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = k, i__2 = ki + nb;
kk = min(i__1,i__2);
i__1 = k - kk + 1;
i__2 = -nb;
for (i__ = k - kk + ki + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__
+= i__2) {
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/* Compute the QL factorization of the current block */
/* A(1:m-k+i+ib-1,n-k+i:n-k+i+ib-1) */
i__3 = *m - k + i__ + ib - 1;
zgeql2_(&i__3, &ib, &a[(*n - k + i__) * a_dim1 + 1], lda, &tau[
i__], &work[1], &iinfo);
if (*n - k + i__ > 1) {
/* Form the triangular factor of the block reflector */
/* H = H(i+ib-1) . . . H(i+1) H(i) */
i__3 = *m - k + i__ + ib - 1;
zlarft_("Backward", "Columnwise", &i__3, &ib, &a[(*n - k +
i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */
i__3 = *m - k + i__ + ib - 1;
i__4 = *n - k + i__ - 1;
zlarfb_("Left", "Conjugate transpose", "Backward", "Columnwi"
"se", &i__3, &i__4, &ib, &a[(*n - k + i__) * a_dim1 +
1], lda, &work[1], &ldwork, &a[a_offset], lda, &work[
ib + 1], &ldwork);
}
/* L10: */
}
mu = *m - k + i__ + nb - 1;
nu = *n - k + i__ + nb - 1;
} else {
mu = *m;
nu = *n;
}
/* Use unblocked code to factor the last or only block */
if (mu > 0 && nu > 0) {
zgeql2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGEQLF */
} /* zgeqlf_ */
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