349 lines
10 KiB
Fortran
349 lines
10 KiB
Fortran
*> \brief \b CGETSQRHRT
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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 CGETSQRHRT + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgetsqrhrt.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/cgetsqrhrt.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/cgetsqrhrt.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 CGETSQRHRT( M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK,
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* $ LWORK, INFO )
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* IMPLICIT NONE
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDT, LWORK, M, N, NB1, NB2, MB1
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 A( LDA, * ), T( LDT, * ), 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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*> CGETSQRHRT computes a NB2-sized column blocked QR-factorization
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*> of a complex M-by-N matrix A with M >= N,
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*>
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*> A = Q * R.
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*>
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*> The routine uses internally a NB1-sized column blocked and MB1-sized
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*> row blocked TSQR-factorization and perfors the reconstruction
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*> of the Householder vectors from the TSQR output. The routine also
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*> converts the R_tsqr factor from the TSQR-factorization output into
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*> the R factor that corresponds to the Householder QR-factorization,
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*>
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*> A = Q_tsqr * R_tsqr = Q * R.
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*>
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*> The output Q and R factors are stored in the same format as in CGEQRT
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*> (Q is in blocked compact WY-representation). See the documentation
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*> of CGEQRT for more details on the format.
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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. M >= N >= 0.
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*> \endverbatim
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*>
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*> \param[in] MB1
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*> \verbatim
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*> MB1 is INTEGER
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*> The row block size to be used in the blocked TSQR.
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*> MB1 > N.
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*> \endverbatim
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*>
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*> \param[in] NB1
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*> \verbatim
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*> NB1 is INTEGER
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*> The column block size to be used in the blocked TSQR.
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*> N >= NB1 >= 1.
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*> \endverbatim
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*>
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*> \param[in] NB2
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*> \verbatim
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*> NB2 is INTEGER
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*> The block size to be used in the blocked QR that is
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*> output. NB2 >= 1.
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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 COMPLEX*16 array, dimension (LDA,N)
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*>
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*> On entry: an M-by-N matrix A.
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*>
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*> On exit:
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*> a) the elements on and above the diagonal
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*> of the array contain the N-by-N upper-triangular
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*> matrix R corresponding to the Householder QR;
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*> b) the elements below the diagonal represent Q by
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*> the columns of blocked V (compact WY-representation).
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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] T
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*> \verbatim
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*> T is COMPLEX array, dimension (LDT,N))
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*> The upper triangular block reflectors stored in compact form
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*> as a sequence of upper triangular blocks.
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*> \endverbatim
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*>
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*> \param[in] LDT
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*> \verbatim
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*> LDT is INTEGER
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*> The leading dimension of the array T. LDT >= NB2.
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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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*> (workspace) COMPLEX 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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*> The dimension of the array WORK.
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*> LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),
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*> where
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*> NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)),
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*> NB1LOCAL = MIN(NB1,N).
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*> LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL,
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*> LW1 = NB1LOCAL * N,
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*> LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ),
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*> If LWORK = -1, then a workspace query is assumed.
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*> The routine only calculates the optimal size of the WORK
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*> array, returns this value as the first entry of the WORK
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*> array, and no error message related to LWORK is issued
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*> 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 comlpexOTHERcomputational
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*
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*> \par Contributors:
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* ==================
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*>
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*> \verbatim
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*>
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*> November 2020, Igor Kozachenko,
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*> Computer Science Division,
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*> University of California, Berkeley
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*>
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE CGETSQRHRT( M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK,
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$ LWORK, INFO )
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IMPLICIT NONE
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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, LDT, LWORK, M, N, NB1, NB2, MB1
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* ..
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* .. Array Arguments ..
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COMPLEX A( LDA, * ), T( LDT, * ), 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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COMPLEX CONE
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PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY
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INTEGER I, IINFO, J, LW1, LW2, LWT, LDWT, LWORKOPT,
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$ NB1LOCAL, NB2LOCAL, NUM_ALL_ROW_BLOCKS
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* ..
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* .. External Subroutines ..
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EXTERNAL CCOPY, CLATSQR, CUNGTSQR_ROW, CUNHR_COL,
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$ XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CEILING, REAL, CMPLX, MAX, MIN
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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.0 .OR. M.LT.N ) THEN
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INFO = -2
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ELSE IF( MB1.LE.N ) THEN
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INFO = -3
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ELSE IF( NB1.LT.1 ) THEN
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INFO = -4
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ELSE IF( NB2.LT.1 ) THEN
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INFO = -5
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -7
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ELSE IF( LDT.LT.MAX( 1, MIN( NB2, N ) ) ) THEN
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INFO = -9
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ELSE
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*
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* Test the input LWORK for the dimension of the array WORK.
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* This workspace is used to store array:
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* a) Matrix T and WORK for CLATSQR;
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* b) N-by-N upper-triangular factor R_tsqr;
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* c) Matrix T and array WORK for CUNGTSQR_ROW;
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* d) Diagonal D for CUNHR_COL.
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*
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IF( LWORK.LT.N*N+1 .AND. .NOT.LQUERY ) THEN
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INFO = -11
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ELSE
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*
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* Set block size for column blocks
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*
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NB1LOCAL = MIN( NB1, N )
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*
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NUM_ALL_ROW_BLOCKS = MAX( 1,
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$ CEILING( REAL( M - N ) / REAL( MB1 - N ) ) )
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*
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* Length and leading dimension of WORK array to place
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* T array in TSQR.
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*
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LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL
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LDWT = NB1LOCAL
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*
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* Length of TSQR work array
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*
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LW1 = NB1LOCAL * N
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*
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* Length of CUNGTSQR_ROW work array.
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*
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LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) )
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*
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LWORKOPT = MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) )
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*
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IF( ( LWORK.LT.MAX( 1, LWORKOPT ) ).AND.(.NOT.LQUERY) ) THEN
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INFO = -11
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END IF
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*
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END IF
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END IF
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*
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* Handle error in the input parameters and return workspace query.
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CGETSQRHRT', -INFO )
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RETURN
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ELSE IF ( LQUERY ) THEN
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WORK( 1 ) = CMPLX( LWORKOPT )
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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( MIN( M, N ).EQ.0 ) THEN
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WORK( 1 ) = CMPLX( LWORKOPT )
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RETURN
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END IF
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*
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NB2LOCAL = MIN( NB2, N )
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*
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*
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* (1) Perform TSQR-factorization of the M-by-N matrix A.
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*
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CALL CLATSQR( M, N, MB1, NB1LOCAL, A, LDA, WORK, LDWT,
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$ WORK(LWT+1), LW1, IINFO )
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*
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* (2) Copy the factor R_tsqr stored in the upper-triangular part
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* of A into the square matrix in the work array
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* WORK(LWT+1:LWT+N*N) column-by-column.
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*
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DO J = 1, N
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CALL CCOPY( J, A( 1, J ), 1, WORK( LWT + N*(J-1)+1 ), 1 )
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END DO
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*
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* (3) Generate a M-by-N matrix Q with orthonormal columns from
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* the result stored below the diagonal in the array A in place.
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*
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CALL CUNGTSQR_ROW( M, N, MB1, NB1LOCAL, A, LDA, WORK, LDWT,
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$ WORK( LWT+N*N+1 ), LW2, IINFO )
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*
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* (4) Perform the reconstruction of Householder vectors from
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* the matrix Q (stored in A) in place.
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*
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CALL CUNHR_COL( M, N, NB2LOCAL, A, LDA, T, LDT,
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$ WORK( LWT+N*N+1 ), IINFO )
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*
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* (5) Copy the factor R_tsqr stored in the square matrix in the
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* work array WORK(LWT+1:LWT+N*N) into the upper-triangular
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* part of A.
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*
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* (6) Compute from R_tsqr the factor R_hr corresponding to
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* the reconstructed Householder vectors, i.e. R_hr = S * R_tsqr.
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* This multiplication by the sign matrix S on the left means
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* changing the sign of I-th row of the matrix R_tsqr according
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* to sign of the I-th diagonal element DIAG(I) of the matrix S.
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* DIAG is stored in WORK( LWT+N*N+1 ) from the CUNHR_COL output.
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*
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* (5) and (6) can be combined in a single loop, so the rows in A
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* are accessed only once.
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*
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DO I = 1, N
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IF( WORK( LWT+N*N+I ).EQ.-CONE ) THEN
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DO J = I, N
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A( I, J ) = -CONE * WORK( LWT+N*(J-1)+I )
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END DO
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ELSE
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CALL CCOPY( N-I+1, WORK(LWT+N*(I-1)+I), N, A( I, I ), LDA )
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END IF
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END DO
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*
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WORK( 1 ) = CMPLX( LWORKOPT )
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RETURN
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*
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* End of CGETSQRHRT
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*
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END |