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/* lapack/double/dorgqr.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;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
/*< SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) >*/
/* Subroutine */ int dorgqr_(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=0, kk, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int dorg2r_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *),
dlarfb_(char *, char *, char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen,
ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK 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 .. */
/*< INTEGER INFO, K, LDA, LWORK, M, N >*/
/* .. */
/* .. Array Arguments .. */
/*< DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* DORGQR generates an M-by-N real matrix Q with orthonormal columns, */
/* which is defined as the first N columns of a product of K elementary */
/* reflectors of order M */
/* Q = H(1) H(2) . . . H(k) */
/* as returned by DGEQRF. */
/* 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. M >= N >= 0. */
/* K (input) INTEGER */
/* The number of elementary reflectors whose product defines the */
/* matrix Q. N >= K >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the i-th column must contain the vector which */
/* defines the elementary reflector H(i), for i = 1,2,...,k, as */
/* returned by DGEQRF in the first k columns 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 DGEQRF. */
/* WORK (workspace/output) DOUBLE PRECISION array, dimension (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 has an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/*< DOUBLE PRECISION ZERO >*/
/*< PARAMETER ( ZERO = 0.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< LOGICAL LQUERY >*/
/*< >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL DLARFB, DLARFT, DORG2R, XERBLA >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC MAX, MIN >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER ILAENV >*/
/*< EXTERNAL ILAENV >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/*< NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 ) >*/
nb = ilaenv_(&c__1, "DORGQR", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
/*< LWKOPT = MAX( 1, N )*NB >*/
lwkopt = max(1,*n) * nb;
/*< WORK( 1 ) = LWKOPT >*/
work[1] = (doublereal) lwkopt;
/*< LQUERY = ( LWORK.EQ.-1 ) >*/
lquery = *lwork == -1;
/*< IF( M.LT.0 ) THEN >*/
if (*m < 0) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( N.LT.0 .OR. N.GT.M ) THEN >*/
} else if (*n < 0 || *n > *m) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( K.LT.0 .OR. K.GT.N ) THEN >*/
} else if (*k < 0 || *k > *n) {
/*< INFO = -3 >*/
*info = -3;
/*< ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
} else if (*lda < max(1,*m)) {
/*< INFO = -5 >*/
*info = -5;
/*< ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN >*/
} else if (*lwork < max(1,*n) && ! lquery) {
/*< INFO = -8 >*/
*info = -8;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'DORGQR', -INFO ) >*/
i__1 = -(*info);
xerbla_("DORGQR", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< ELSE IF( LQUERY ) THEN >*/
} else if (lquery) {
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Quick return if possible */
/*< IF( N.LE.0 ) THEN >*/
if (*n <= 0) {
/*< WORK( 1 ) = 1 >*/
work[1] = 1.;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< NBMIN = 2 >*/
nbmin = 2;
/*< NX = 0 >*/
nx = 0;
/*< IWS = N >*/
iws = *n;
/*< IF( NB.GT.1 .AND. NB.LT.K ) THEN >*/
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code. */
/*< NX = MAX( 0, ILAENV( 3, 'DORGQR', ' ', M, N, K, -1 ) ) >*/
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "DORGQR", " ", m, n, k, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
/*< IF( NX.LT.K ) THEN >*/
if (nx < *k) {
/* Determine if workspace is large enough for blocked code. */
/*< LDWORK = N >*/
ldwork = *n;
/*< IWS = LDWORK*NB >*/
iws = ldwork * nb;
/*< IF( LWORK.LT.IWS ) THEN >*/
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
/*< NB = LWORK / LDWORK >*/
nb = *lwork / ldwork;
/*< NBMIN = MAX( 2, ILAENV( 2, 'DORGQR', ' ', M, N, K, -1 ) ) >*/
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "DORGQR", " ", m, n, k, &c_n1,
(ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN >*/
if (nb >= nbmin && nb < *k && nx < *k) {
/* Use blocked code after the last block. */
/* The first kk columns are handled by the block method. */
/*< KI = ( ( K-NX-1 ) / NB )*NB >*/
ki = (*k - nx - 1) / nb * nb;
/*< KK = MIN( K, KI+NB ) >*/
/* Computing MIN */
i__1 = *k, i__2 = ki + nb;
kk = min(i__1,i__2);
/* Set A(1:kk,kk+1:n) to zero. */
/*< DO 20 J = KK + 1, N >*/
i__1 = *n;
for (j = kk + 1; j <= i__1; ++j) {
/*< DO 10 I = 1, KK >*/
i__2 = kk;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
a[i__ + j * a_dim1] = 0.;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< 20 CONTINUE >*/
/* L20: */
}
/*< ELSE >*/
} else {
/*< KK = 0 >*/
kk = 0;
/*< END IF >*/
}
/* Use unblocked code for the last or only block. */
/*< >*/
if (kk < *n) {
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
dorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
tau[kk + 1], &work[1], &iinfo);
}
/*< IF( KK.GT.0 ) THEN >*/
if (kk > 0) {
/* Use blocked code */
/*< DO 50 I = KI + 1, 1, -NB >*/
i__1 = -nb;
for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
/*< IB = MIN( NB, K-I+1 ) >*/
/* Computing MIN */
i__2 = nb, i__3 = *k - i__ + 1;
ib = min(i__2,i__3);
/*< IF( I+IB.LE.N ) THEN >*/
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
/*< >*/
i__2 = *m - i__ + 1;
dlarft_("Forward", "Columnwise", &i__2, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7,
(ftnlen)10);
/* Apply H to A(i:m,i+ib:n) from the left */
/*< >*/
i__2 = *m - i__ + 1;
i__3 = *n - i__ - ib + 1;
dlarfb_("Left", "No transpose", "Forward", "Columnwise", &
i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[
1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &
work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)
7, (ftnlen)10);
/*< END IF >*/
}
/* Apply H to rows i:m of current block */
/*< >*/
i__2 = *m - i__ + 1;
dorg2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
work[1], &iinfo);
/* Set rows 1:i-1 of current block to zero */
/*< DO 40 J = I, I + IB - 1 >*/
i__2 = i__ + ib - 1;
for (j = i__; j <= i__2; ++j) {
/*< DO 30 L = 1, I - 1 >*/
i__3 = i__ - 1;
for (l = 1; l <= i__3; ++l) {
/*< A( L, J ) = ZERO >*/
a[l + j * a_dim1] = 0.;
/*< 30 CONTINUE >*/
/* L30: */
}
/*< 40 CONTINUE >*/
/* L40: */
}
/*< 50 CONTINUE >*/
/* L50: */
}
/*< END IF >*/
}
/*< WORK( 1 ) = IWS >*/
work[1] = (doublereal) iws;
/*< RETURN >*/
return 0;
/* End of DORGQR */
/*< END >*/
} /* dorgqr_ */
#ifdef __cplusplus
}
#endif
|
