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306 lines
9.0 KiB
306 lines
9.0 KiB
*> \brief \b CUNGTSQR
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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 CUNGTSQR + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cuntsqr.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/cungtsqr.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/cungtsqr.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 CUNGTSQR( M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK,
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* $ INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB
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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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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> CUNGTSQR generates an M-by-N complex matrix Q_out with orthonormal
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*> columns, which are the first N columns of a product of comlpex unitary
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*> matrices of order M which are returned by CLATSQR
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*>
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*> Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
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*>
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*> See the documentation for CLATSQR.
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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] MB
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*> \verbatim
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*> MB is INTEGER
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*> The row block size used by CLATSQR to return
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*> arrays A and T. MB > N.
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*> (Note that if MB > M, then M is used instead of MB
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*> as the row block size).
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*> \endverbatim
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*>
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*> \param[in] NB
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*> \verbatim
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*> NB is INTEGER
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*> The column block size used by CLATSQR to return
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*> arrays A and T. NB >= 1.
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*> (Note that if NB > N, then N is used instead of NB
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*> as the column block size).
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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 array, dimension (LDA,N)
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*>
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*> On entry:
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*>
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*> The elements on and above the diagonal are not accessed.
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*> The elements below the diagonal represent the unit
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*> lower-trapezoidal blocked matrix V computed by CLATSQR
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*> that defines the input matrices Q_in(k) (ones on the
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*> diagonal are not stored) (same format as the output A
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*> below the diagonal in CLATSQR).
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*>
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*> On exit:
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*>
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*> The array A contains an M-by-N orthonormal matrix Q_out,
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*> i.e the columns of A are orthogonal unit vectors.
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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[in] T
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*> \verbatim
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*> T is COMPLEX array,
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*> dimension (LDT, N * NIRB)
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*> where NIRB = Number_of_input_row_blocks
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*> = MAX( 1, CEIL((M-N)/(MB-N)) )
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*> Let NICB = Number_of_input_col_blocks
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*> = CEIL(N/NB)
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*>
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*> The upper-triangular block reflectors used to define the
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*> input matrices Q_in(k), k=(1:NIRB*NICB). The block
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*> reflectors are stored in compact form in NIRB block
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*> reflector sequences. Each of NIRB block reflector sequences
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*> is stored in a larger NB-by-N column block of T and consists
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*> of NICB smaller NB-by-NB upper-triangular column blocks.
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*> (same format as the output T in CLATSQR).
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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.
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*> LDT >= max(1,min(NB1,N)).
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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(2,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 >= (M+NB)*N.
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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 complexOTHERcomputational
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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 2019, 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 CUNGTSQR( M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK,
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$ 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, MB, NB
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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, CZERO
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PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ),
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$ CZERO = ( 0.0E+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 IINFO, LDC, LWORKOPT, LC, LW, NBLOCAL, J
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* ..
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* .. External Subroutines ..
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EXTERNAL CCOPY, CLAMTSQR, CLASET, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CMPLX, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters
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*
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LQUERY = LWORK.EQ.-1
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INFO = 0
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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( MB.LE.N ) THEN
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INFO = -3
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ELSE IF( NB.LT.1 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -6
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ELSE IF( LDT.LT.MAX( 1, MIN( NB, N ) ) ) THEN
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INFO = -8
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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 C(LDC, N) and WORK(LWORK)
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* in the call to CLAMTSQR. See the documentation for CLAMTSQR.
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*
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IF( LWORK.LT.2 .AND. (.NOT.LQUERY) ) THEN
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INFO = -10
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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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NBLOCAL = MIN( NB, N )
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*
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* LWORK = -1, then set the size for the array C(LDC,N)
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* in CLAMTSQR call and set the optimal size of the work array
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* WORK(LWORK) in CLAMTSQR call.
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*
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LDC = M
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LC = LDC*N
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LW = N * NBLOCAL
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*
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LWORKOPT = LC+LW
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*
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IF( ( LWORK.LT.MAX( 1, LWORKOPT ) ).AND.(.NOT.LQUERY) ) THEN
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INFO = -10
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END IF
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END IF
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*
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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( 'CUNGTSQR', -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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* (1) Form explicitly the tall-skinny M-by-N left submatrix Q1_in
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* of M-by-M orthogonal matrix Q_in, which is implicitly stored in
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* the subdiagonal part of input array A and in the input array T.
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* Perform by the following operation using the routine CLAMTSQR.
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*
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* Q1_in = Q_in * ( I ), where I is a N-by-N identity matrix,
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* ( 0 ) 0 is a (M-N)-by-N zero matrix.
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*
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* (1a) Form M-by-N matrix in the array WORK(1:LDC*N) with ones
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* on the diagonal and zeros elsewhere.
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*
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CALL CLASET( 'F', M, N, CZERO, CONE, WORK, LDC )
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*
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* (1b) On input, WORK(1:LDC*N) stores ( I );
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* ( 0 )
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*
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* On output, WORK(1:LDC*N) stores Q1_in.
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*
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CALL CLAMTSQR( 'L', 'N', M, N, N, MB, NBLOCAL, A, LDA, T, LDT,
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$ WORK, LDC, WORK( LC+1 ), LW, IINFO )
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*
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* (2) Copy the result from the part of the work array (1:M,1:N)
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* with the leading dimension LDC that starts at WORK(1) into
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* the output array A(1:M,1:N) column-by-column.
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*
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DO J = 1, N
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CALL CCOPY( M, WORK( (J-1)*LDC + 1 ), 1, A( 1, J ), 1 )
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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 CUNGTSQR
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*
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END
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