2010-07-16 20:54:53 +08:00
|
|
|
/* dorglq.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
|
|
|
|
*/
|
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
#include "clapack.h"
|
|
|
|
|
2010-07-16 20:54:53 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
/* 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 dorglq_(integer *m, integer *n, integer *k, doublereal *
|
|
|
|
a, integer *lda, doublereal *tau, doublereal *work, integer *lwork,
|
|
|
|
integer *info)
|
|
|
|
{
|
|
|
|
/* System generated locals */
|
|
|
|
integer a_dim1, a_offset, i__1, i__2, i__3;
|
|
|
|
|
|
|
|
/* Local variables */
|
|
|
|
integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo;
|
|
|
|
extern /* Subroutine */ int dorgl2_(integer *, integer *, integer *,
|
|
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *),
|
|
|
|
dlarfb_(char *, char *, char *, char *, integer *, integer *,
|
|
|
|
integer *, doublereal *, integer *, doublereal *, integer *,
|
|
|
|
doublereal *, integer *, doublereal *, integer *), dlarft_(char *, char *, integer *, integer *,
|
|
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *), xerbla_(char *, integer *);
|
|
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
|
|
integer *, integer *);
|
|
|
|
integer ldwork, lwkopt;
|
|
|
|
logical lquery;
|
|
|
|
|
|
|
|
|
2010-07-16 20:54:53 +08:00
|
|
|
/* -- LAPACK routine (version 3.2) -- */
|
2010-05-12 01:44:00 +08:00
|
|
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
|
|
|
|
/* November 2006 */
|
|
|
|
|
|
|
|
/* .. Scalar Arguments .. */
|
|
|
|
/* .. */
|
|
|
|
/* .. Array Arguments .. */
|
|
|
|
/* .. */
|
|
|
|
|
|
|
|
/* Purpose */
|
|
|
|
/* ======= */
|
|
|
|
|
|
|
|
/* DORGLQ generates an M-by-N real matrix Q with orthonormal rows, */
|
|
|
|
/* which is defined as the first M rows of a product of K elementary */
|
|
|
|
/* reflectors of order N */
|
|
|
|
|
|
|
|
/* Q = H(k) . . . H(2) H(1) */
|
|
|
|
|
|
|
|
/* as returned by DGELQF. */
|
|
|
|
|
|
|
|
/* Arguments */
|
|
|
|
/* ========= */
|
|
|
|
|
|
|
|
/* M (input) INTEGER */
|
|
|
|
/* The number of rows of the matrix Q. M >= 0. */
|
|
|
|
|
|
|
|
/* N (input) INTEGER */
|
|
|
|
/* The number of columns of the matrix Q. N >= M. */
|
|
|
|
|
|
|
|
/* K (input) INTEGER */
|
|
|
|
/* The number of elementary reflectors whose product defines the */
|
|
|
|
/* matrix Q. M >= K >= 0. */
|
|
|
|
|
|
|
|
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
|
|
|
|
/* On entry, the i-th row must contain the vector which defines */
|
|
|
|
/* the elementary reflector H(i), for i = 1,2,...,k, as returned */
|
|
|
|
/* by DGELQF in the first k rows of its array argument A. */
|
|
|
|
/* On exit, the M-by-N matrix Q. */
|
|
|
|
|
|
|
|
/* LDA (input) INTEGER */
|
|
|
|
/* The first dimension of the array A. LDA >= max(1,M). */
|
|
|
|
|
|
|
|
/* TAU (input) DOUBLE PRECISION array, dimension (K) */
|
|
|
|
/* TAU(i) must contain the scalar factor of the elementary */
|
|
|
|
/* reflector H(i), as returned by DGELQF. */
|
|
|
|
|
|
|
|
/* WORK (workspace/output) DOUBLE PRECISION 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,M). */
|
|
|
|
/* For optimum performance LWORK >= M*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 has an illegal value */
|
|
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
|
|
/* .. Parameters .. */
|
|
|
|
/* .. */
|
|
|
|
/* .. 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;
|
|
|
|
nb = ilaenv_(&c__1, "DORGLQ", " ", m, n, k, &c_n1);
|
|
|
|
lwkopt = max(1,*m) * nb;
|
|
|
|
work[1] = (doublereal) lwkopt;
|
|
|
|
lquery = *lwork == -1;
|
|
|
|
if (*m < 0) {
|
|
|
|
*info = -1;
|
|
|
|
} else if (*n < *m) {
|
|
|
|
*info = -2;
|
|
|
|
} else if (*k < 0 || *k > *m) {
|
|
|
|
*info = -3;
|
|
|
|
} else if (*lda < max(1,*m)) {
|
|
|
|
*info = -5;
|
|
|
|
} else if (*lwork < max(1,*m) && ! lquery) {
|
|
|
|
*info = -8;
|
|
|
|
}
|
|
|
|
if (*info != 0) {
|
|
|
|
i__1 = -(*info);
|
|
|
|
xerbla_("DORGLQ", &i__1);
|
|
|
|
return 0;
|
|
|
|
} else if (lquery) {
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
|
|
|
|
/* Quick return if possible */
|
|
|
|
|
|
|
|
if (*m <= 0) {
|
|
|
|
work[1] = 1.;
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
|
|
|
|
nbmin = 2;
|
|
|
|
nx = 0;
|
|
|
|
iws = *m;
|
|
|
|
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, "DORGLQ", " ", m, n, k, &c_n1);
|
|
|
|
nx = max(i__1,i__2);
|
|
|
|
if (nx < *k) {
|
|
|
|
|
|
|
|
/* Determine if workspace is large enough for blocked code. */
|
|
|
|
|
|
|
|
ldwork = *m;
|
|
|
|
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, "DORGLQ", " ", m, n, k, &c_n1);
|
|
|
|
nbmin = max(i__1,i__2);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
if (nb >= nbmin && nb < *k && nx < *k) {
|
|
|
|
|
|
|
|
/* Use blocked code after the last block. */
|
|
|
|
/* The first kk rows 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);
|
|
|
|
|
|
|
|
/* Set A(kk+1:m,1:kk) to zero. */
|
|
|
|
|
|
|
|
i__1 = kk;
|
|
|
|
for (j = 1; j <= i__1; ++j) {
|
|
|
|
i__2 = *m;
|
|
|
|
for (i__ = kk + 1; i__ <= i__2; ++i__) {
|
|
|
|
a[i__ + j * a_dim1] = 0.;
|
|
|
|
/* L10: */
|
|
|
|
}
|
|
|
|
/* L20: */
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
kk = 0;
|
|
|
|
}
|
|
|
|
|
|
|
|
/* Use unblocked code for the last or only block. */
|
|
|
|
|
|
|
|
if (kk < *m) {
|
|
|
|
i__1 = *m - kk;
|
|
|
|
i__2 = *n - kk;
|
|
|
|
i__3 = *k - kk;
|
|
|
|
dorgl2_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
|
|
|
|
tau[kk + 1], &work[1], &iinfo);
|
|
|
|
}
|
|
|
|
|
|
|
|
if (kk > 0) {
|
|
|
|
|
|
|
|
/* Use blocked code */
|
|
|
|
|
|
|
|
i__1 = -nb;
|
|
|
|
for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
|
|
|
|
/* Computing MIN */
|
|
|
|
i__2 = nb, i__3 = *k - i__ + 1;
|
|
|
|
ib = min(i__2,i__3);
|
|
|
|
if (i__ + ib <= *m) {
|
|
|
|
|
|
|
|
/* Form the triangular factor of the block reflector */
|
|
|
|
/* H = H(i) H(i+1) . . . H(i+ib-1) */
|
|
|
|
|
|
|
|
i__2 = *n - i__ + 1;
|
|
|
|
dlarft_("Forward", "Rowwise", &i__2, &ib, &a[i__ + i__ *
|
|
|
|
a_dim1], lda, &tau[i__], &work[1], &ldwork);
|
|
|
|
|
|
|
|
/* Apply H' to A(i+ib:m,i:n) from the right */
|
|
|
|
|
|
|
|
i__2 = *m - i__ - ib + 1;
|
|
|
|
i__3 = *n - i__ + 1;
|
|
|
|
dlarfb_("Right", "Transpose", "Forward", "Rowwise", &i__2, &
|
|
|
|
i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], &
|
|
|
|
ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib +
|
|
|
|
1], &ldwork);
|
|
|
|
}
|
|
|
|
|
|
|
|
/* Apply H' to columns i:n of current block */
|
|
|
|
|
|
|
|
i__2 = *n - i__ + 1;
|
|
|
|
dorgl2_(&ib, &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
|
|
|
|
work[1], &iinfo);
|
|
|
|
|
|
|
|
/* Set columns 1:i-1 of current block to zero */
|
|
|
|
|
|
|
|
i__2 = i__ - 1;
|
|
|
|
for (j = 1; j <= i__2; ++j) {
|
|
|
|
i__3 = i__ + ib - 1;
|
|
|
|
for (l = i__; l <= i__3; ++l) {
|
|
|
|
a[l + j * a_dim1] = 0.;
|
|
|
|
/* L30: */
|
|
|
|
}
|
|
|
|
/* L40: */
|
|
|
|
}
|
|
|
|
/* L50: */
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
work[1] = (doublereal) iws;
|
|
|
|
return 0;
|
|
|
|
|
|
|
|
/* End of DORGLQ */
|
|
|
|
|
|
|
|
} /* dorglq_ */
|