numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/dgemlq.f | 8104B | -rw-r--r-- |
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*> \brief \b DGEMLQ * * Definition: * =========== * * SUBROUTINE DGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, * $ TSIZE, C, LDC, WORK, LWORK, INFO ) * * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, LDA, M, N, K, LDT, TSIZE, LWORK, LDC * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), T( * ), C(LDC, * ), WORK( * ) * .. * *> \par Purpose: * ============= *> *> \verbatim *> *> DGEMLQ overwrites the general real M-by-N matrix C with *> *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'T': Q**T * C C * Q**T *> where Q is a real orthogonal matrix defined as the product *> of blocked elementary reflectors computed by short wide LQ *> factorization (DGELQ) *> *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**T from the Left; *> = 'R': apply Q or Q**T from the Right. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q; *> = 'T': Transpose, apply Q**T. *> \endverbatim *> *> \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 C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension *> (LDA,M) if SIDE = 'L', *> (LDA,N) if SIDE = 'R' *> Part of the data structure to represent Q as returned by DGELQ. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,K). *> \endverbatim *> *> \param[in] T *> \verbatim *> T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)). *> Part of the data structure to represent Q as returned by DGELQ. *> \endverbatim *> *> \param[in] TSIZE *> \verbatim *> TSIZE is INTEGER *> The dimension of the array T. TSIZE >= 5. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the minimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= 1. *> If LWORK = -1, then a workspace query is assumed. The routine *> only calculates the size of the WORK array, returns this *> value as WORK(1), and no error message related to WORK *> 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. * *> \par Further Details * ==================== *> *> \verbatim *> *> These details are particular for this LAPACK implementation. Users should not *> take them for granted. These details may change in the future, and are not likely *> true for another LAPACK implementation. These details are relevant if one wants *> to try to understand the code. They are not part of the interface. *> *> In this version, *> *> T(2): row block size (MB) *> T(3): column block size (NB) *> T(6:TSIZE): data structure needed for Q, computed by *> DLASWLQ or DGELQT *> *> Depending on the matrix dimensions M and N, and row and column *> block sizes MB and NB returned by ILAENV, DGELQ will use either *> DLASWLQ (if the matrix is wide-and-short) or DGELQT to compute *> the LQ factorization. *> This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to *> multiply matrix Q by another matrix. *> Further Details in DLAMSWLQ or DGEMLQT. *> \endverbatim *> *> \ingroup gemlq *> * ===================================================================== SUBROUTINE DGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, $ C, LDC, WORK, LWORK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), T( * ), C( LDC, * ), WORK( * ) * .. * * ===================================================================== * * .. * .. Local Scalars .. LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY INTEGER MB, NB, LW, NBLCKS, MN, MINMNK, LWMIN * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DLAMSWLQ, DGEMLQT, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC INT, MAX, MIN, MOD * .. * .. Executable Statements .. * * Test the input arguments * LQUERY = ( LWORK.EQ.-1 ) NOTRAN = LSAME( TRANS, 'N' ) TRAN = LSAME( TRANS, 'T' ) LEFT = LSAME( SIDE, 'L' ) RIGHT = LSAME( SIDE, 'R' ) * MB = INT( T( 2 ) ) NB = INT( T( 3 ) ) IF( LEFT ) THEN LW = N * MB MN = M ELSE LW = M * MB MN = N END IF * MINMNK = MIN( M, N, K ) IF( MINMNK.EQ.0 ) THEN LWMIN = 1 ELSE LWMIN = MAX( 1, LW ) END IF * IF( ( NB.GT.K ) .AND. ( MN.GT.K ) ) THEN IF( MOD( MN - K, NB - K ) .EQ. 0 ) THEN NBLCKS = ( MN - K ) / ( NB - K ) ELSE NBLCKS = ( MN - K ) / ( NB - K ) + 1 END IF ELSE NBLCKS = 1 END IF * INFO = 0 IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN INFO = -1 ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.MN ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN INFO = -7 ELSE IF( TSIZE.LT.5 ) THEN INFO = -9 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -11 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -13 END IF * IF( INFO.EQ.0 ) THEN WORK( 1 ) = LWMIN END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGEMLQ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( MINMNK.EQ.0 ) THEN RETURN END IF * IF( ( LEFT .AND. M.LE.K ) .OR. ( RIGHT .AND. N.LE.K ) $ .OR. ( NB.LE.K ) .OR. ( NB.GE.MAX( M, N, K ) ) ) THEN CALL DGEMLQT( SIDE, TRANS, M, N, K, MB, A, LDA, $ T( 6 ), MB, C, LDC, WORK, INFO ) ELSE CALL DLAMSWLQ( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T( 6 ), $ MB, C, LDC, WORK, LWORK, INFO ) END IF * WORK( 1 ) = LWMIN * RETURN * * End of DGEMLQ * END