#include "ESMF_LapackBlas.inc" !> \brief \b DGEQP3 ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DGEQP3 + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqp3.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqp3.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqp3.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO ) ! ! .. Scalar Arguments .. ! INTEGER INFO, LDA, LWORK, M, N ! .. ! .. Array Arguments .. ! INTEGER JPVT( * ) ! DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DGEQP3 computes a QR factorization with column pivoting of a !> matrix A: A*P = Q*R using Level 3 BLAS. !> \endverbatim ! ! Arguments: ! ========== ! !> \param[in] M !> \verbatim !> M is INTEGER !> The number of rows of the matrix A. M >= 0. !> \endverbatim !> !> \param[in] N !> \verbatim !> N is INTEGER !> The number of columns of the matrix A. N >= 0. !> \endverbatim !> !> \param[in,out] A !> \verbatim !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the M-by-N matrix A. !> On exit, the upper triangle of the array contains the !> min(M,N)-by-N upper trapezoidal matrix R; the elements below !> the diagonal, together with the array TAU, represent the !> orthogonal matrix Q as a product of min(M,N) elementary !> reflectors. !> \endverbatim !> !> \param[in] LDA !> \verbatim !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !> \endverbatim !> !> \param[in,out] JPVT !> \verbatim !> JPVT is INTEGER array, dimension (N) !> On entry, if JPVT(J).ne.0, the J-th column of A is permuted !> to the front of A*P (a leading column); if JPVT(J)=0, !> the J-th column of A is a free column. !> On exit, if JPVT(J)=K, then the J-th column of A*P was the !> the K-th column of A. !> \endverbatim !> !> \param[out] TAU !> \verbatim !> TAU is DOUBLE PRECISION array, dimension (min(M,N)) !> The scalar factors of the elementary reflectors. !> \endverbatim !> !> \param[out] WORK !> \verbatim !> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO=0, WORK(1) returns the optimal LWORK. !> \endverbatim !> !> \param[in] LWORK !> \verbatim !> LWORK is INTEGER !> The dimension of the array WORK. LWORK >= 3*N+1. !> For optimal performance LWORK >= 2*N+( N+1 )*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. !> \endverbatim !> !> \param[out] INFO !> \verbatim !> INFO is INTEGER !> = 0: successful exit. !> < 0: if INFO = -i, the i-th argument had an illegal value. !> \endverbatim ! ! Authors: ! ======== ! !> \author Univ. of Tennessee !> \author Univ. of California Berkeley !> \author Univ. of Colorado Denver !> \author NAG Ltd. ! !> \date November 2011 ! !> \ingroup doubleGEcomputational ! !> \par Further Details: ! ===================== !> !> \verbatim !> !> The matrix Q is represented as a product of elementary reflectors !> !> Q = H(1) H(2) . . . H(k), where k = min(m,n). !> !> Each H(i) has the form !> !> H(i) = I - tau * v * v**T !> !> where tau is a real/complex scalar, and v is a real/complex vector !> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in !> A(i+1:m,i), and tau in TAU(i). !> \endverbatim ! !> \par Contributors: ! ================== !> !> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain !> X. Sun, Computer Science Dept., Duke University, USA !> ! ===================================================================== SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO ) ! ! -- LAPACK computational routine (version 3.4.0) -- ! -- LAPACK is a software package provided by Univ. of Tennessee, -- ! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- ! November 2011 ! ! .. Scalar Arguments .. INTEGER INFO, LDA, LWORK, M, N ! .. ! .. Array Arguments .. INTEGER JPVT( * ) DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. INTEGER INB, INBMIN, IXOVER PARAMETER ( INB = 1, INBMIN = 2, IXOVER = 3 ) ! .. ! .. Local Scalars .. LOGICAL LQUERY INTEGER FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB, & & NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN ! .. ! .. External Subroutines .. EXTERNAL DGEQRF, DLAQP2, DLAQPS, DORMQR, DSWAP, XERBLA ! .. ! .. External Functions .. INTEGER ILAENV DOUBLE PRECISION DNRM2 EXTERNAL ILAENV, DNRM2 ! .. ! .. Intrinsic Functions .. INTRINSIC INT, MAX, MIN ! .. ! .. Executable Statements .. ! ! Test input arguments ! ==================== ! INFO = 0 LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 END IF ! IF( INFO.EQ.0 ) THEN MINMN = MIN( M, N ) IF( MINMN.EQ.0 ) THEN IWS = 1 LWKOPT = 1 ELSE IWS = 3*N + 1 NB = ILAENV( INB, 'DGEQRF', ' ', M, N, -1, -1 ) LWKOPT = 2*N + ( N + 1 )*NB END IF WORK( 1 ) = LWKOPT ! IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN INFO = -8 END IF END IF ! IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGEQP3', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF ! ! Quick return if possible. ! IF( MINMN.EQ.0 ) THEN RETURN END IF ! ! Move initial columns up front. ! NFXD = 1 DO 10 J = 1, N IF( JPVT( J ).NE.0 ) THEN IF( J.NE.NFXD ) THEN CALL DSWAP( M, A( 1, J ), 1, A( 1, NFXD ), 1 ) JPVT( J ) = JPVT( NFXD ) JPVT( NFXD ) = J ELSE JPVT( J ) = J END IF NFXD = NFXD + 1 ELSE JPVT( J ) = J END IF 10 CONTINUE NFXD = NFXD - 1 ! ! Factorize fixed columns ! ======================= ! ! Compute the QR factorization of fixed columns and update ! remaining columns. ! IF( NFXD.GT.0 ) THEN NA = MIN( M, NFXD ) !CC CALL DGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) CALL DGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO ) IWS = MAX( IWS, INT( WORK( 1 ) ) ) IF( NA.LT.N ) THEN !CC CALL DORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA, !CC $ TAU, A( 1, NA+1 ), LDA, WORK, INFO ) CALL DORMQR( 'Left', 'Transpose', M, N-NA, NA, A, LDA, TAU, & & A( 1, NA+1 ), LDA, WORK, LWORK, INFO ) IWS = MAX( IWS, INT( WORK( 1 ) ) ) END IF END IF ! ! Factorize free columns ! ====================== ! IF( NFXD.LT.MINMN ) THEN ! SM = M - NFXD SN = N - NFXD SMINMN = MINMN - NFXD ! ! Determine the block size. ! NB = ILAENV( INB, 'DGEQRF', ' ', SM, SN, -1, -1 ) NBMIN = 2 NX = 0 ! IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN ! ! Determine when to cross over from blocked to unblocked code. ! NX = MAX( 0, ILAENV( IXOVER, 'DGEQRF', ' ', SM, SN, -1, & & -1 ) ) ! ! IF( NX.LT.SMINMN ) THEN ! ! Determine if workspace is large enough for blocked code. ! MINWS = 2*SN + ( SN+1 )*NB IWS = MAX( IWS, MINWS ) IF( LWORK.LT.MINWS ) THEN ! ! Not enough workspace to use optimal NB: Reduce NB and ! determine the minimum value of NB. ! NB = ( LWORK-2*SN ) / ( SN+1 ) NBMIN = MAX( 2, ILAENV( INBMIN, 'DGEQRF', ' ', SM, SN, & & -1, -1 ) ) ! ! END IF END IF END IF ! ! Initialize partial column norms. The first N elements of work ! store the exact column norms. ! DO 20 J = NFXD + 1, N WORK( J ) = DNRM2( SM, A( NFXD+1, J ), 1 ) WORK( N+J ) = WORK( J ) 20 CONTINUE ! IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND. & & ( NX.LT.SMINMN ) ) THEN ! ! Use blocked code initially. ! J = NFXD + 1 ! ! Compute factorization: while loop. ! ! TOPBMN = MINMN - NX 30 CONTINUE IF( J.LE.TOPBMN ) THEN JB = MIN( NB, TOPBMN-J+1 ) ! ! Factorize JB columns among columns J:N. ! CALL DLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA, & & JPVT( J ), TAU( J ), WORK( J ), WORK( N+J ), & & WORK( 2*N+1 ), WORK( 2*N+JB+1 ), N-J+1 ) ! J = J + FJB GO TO 30 END IF ELSE J = NFXD + 1 END IF ! ! Use unblocked code to factor the last or only block. ! ! IF( J.LE.MINMN ) & & CALL DLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ), & & TAU( J ), WORK( J ), WORK( N+J ), & & WORK( 2*N+1 ) ) ! END IF ! WORK( 1 ) = IWS RETURN ! ! End of DGEQP3 ! END