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310 lines
8.3 KiB
310 lines
8.3 KiB
*> \brief \b DTZRZF
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DTZRZF + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtzrzf.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtzrzf.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtzrzf.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
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*> to upper triangular form by means of orthogonal transformations.
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*>
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*> The upper trapezoidal matrix A is factored as
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*>
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*> A = ( R 0 ) * Z,
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*>
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*> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
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*> triangular matrix.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix A. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix A. N >= M.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (LDA,N)
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*> On entry, the leading M-by-N upper trapezoidal part of the
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*> array A must contain the matrix to be factorized.
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*> On exit, the leading M-by-M upper triangular part of A
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*> contains the upper triangular matrix R, and elements M+1 to
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*> N of the first M rows of A, with the array TAU, represent the
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*> orthogonal matrix Z as a product of M elementary reflectors.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,M).
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*> \endverbatim
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*>
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*> \param[out] TAU
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*> \verbatim
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*> TAU is DOUBLE PRECISION array, dimension (M)
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*> The scalar factors of the elementary reflectors.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK. LWORK >= max(1,M).
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*> For optimum performance LWORK >= M*NB, where NB is
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*> the optimal blocksize.
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*>
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*> If LWORK = -1, then a workspace query is assumed; the routine
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*> only calculates the optimal size of the WORK array, returns
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*> this value as the first entry of the WORK array, and no error
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*> message related to LWORK is issued by XERBLA.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup doubleOTHERcomputational
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*
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*> \par Contributors:
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* ==================
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*>
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*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> The N-by-N matrix Z can be computed by
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*>
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*> Z = Z(1)*Z(2)* ... *Z(M)
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*>
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*> where each N-by-N Z(k) is given by
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*>
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*> Z(k) = I - tau(k)*v(k)*v(k)**T
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*>
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*> with v(k) is the kth row vector of the M-by-N matrix
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*>
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*> V = ( I A(:,M+1:N) )
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*>
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*> I is the M-by-M identity matrix, A(:,M+1:N)
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*> is the output stored in A on exit from DTZRZF,
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*> and tau(k) is the kth element of the array TAU.
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*>
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE DTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY
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INTEGER I, IB, IWS, KI, KK, LDWORK, LWKMIN, LWKOPT,
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$ M1, MU, NB, NBMIN, NX
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, DLARZB, DLARZT, DLATRZ
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. External Functions ..
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INTEGER ILAENV
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EXTERNAL ILAENV
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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LQUERY = ( LWORK.EQ.-1 )
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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.M ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -4
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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IF( M.EQ.0 .OR. M.EQ.N ) THEN
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LWKOPT = 1
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LWKMIN = 1
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ELSE
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*
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* Determine the block size.
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*
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NB = ILAENV( 1, 'DGERQF', ' ', M, N, -1, -1 )
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LWKOPT = M*NB
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LWKMIN = MAX( 1, M )
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END IF
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WORK( 1 ) = LWKOPT
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*
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IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
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INFO = -7
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END IF
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DTZRZF', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.EQ.0 ) THEN
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RETURN
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ELSE IF( M.EQ.N ) THEN
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DO 10 I = 1, N
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TAU( I ) = ZERO
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10 CONTINUE
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RETURN
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END IF
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*
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NBMIN = 2
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NX = 1
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IWS = M
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IF( NB.GT.1 .AND. NB.LT.M ) THEN
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*
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* Determine when to cross over from blocked to unblocked code.
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*
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NX = MAX( 0, ILAENV( 3, 'DGERQF', ' ', M, N, -1, -1 ) )
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IF( NX.LT.M ) THEN
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*
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* Determine if workspace is large enough for blocked code.
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*
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LDWORK = M
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IWS = LDWORK*NB
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IF( LWORK.LT.IWS ) THEN
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*
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* Not enough workspace to use optimal NB: reduce NB and
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* determine the minimum value of NB.
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*
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NB = LWORK / LDWORK
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NBMIN = MAX( 2, ILAENV( 2, 'DGERQF', ' ', M, N, -1,
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$ -1 ) )
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END IF
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END IF
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END IF
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*
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IF( NB.GE.NBMIN .AND. NB.LT.M .AND. NX.LT.M ) THEN
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*
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* Use blocked code initially.
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* The last kk rows are handled by the block method.
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*
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M1 = MIN( M+1, N )
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KI = ( ( M-NX-1 ) / NB )*NB
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KK = MIN( M, KI+NB )
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*
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DO 20 I = M - KK + KI + 1, M - KK + 1, -NB
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IB = MIN( M-I+1, NB )
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*
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* Compute the TZ factorization of the current block
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* A(i:i+ib-1,i:n)
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*
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CALL DLATRZ( IB, N-I+1, N-M, A( I, I ), LDA, TAU( I ),
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$ WORK )
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IF( I.GT.1 ) THEN
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*
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* Form the triangular factor of the block reflector
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* H = H(i+ib-1) . . . H(i+1) H(i)
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*
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CALL DLARZT( 'Backward', 'Rowwise', N-M, IB, A( I, M1 ),
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$ LDA, TAU( I ), WORK, LDWORK )
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*
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* Apply H to A(1:i-1,i:n) from the right
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*
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CALL DLARZB( 'Right', 'No transpose', 'Backward',
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$ 'Rowwise', I-1, N-I+1, IB, N-M, A( I, M1 ),
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$ LDA, WORK, LDWORK, A( 1, I ), LDA,
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$ WORK( IB+1 ), LDWORK )
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END IF
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20 CONTINUE
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MU = I + NB - 1
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ELSE
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MU = M
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END IF
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*
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* Use unblocked code to factor the last or only block
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*
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IF( MU.GT.0 )
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$ CALL DLATRZ( MU, N, N-M, A, LDA, TAU, WORK )
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*
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WORK( 1 ) = LWKOPT
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*
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RETURN
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*
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* End of DTZRZF
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*
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END
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