added lapack 3.7.0 with latest patches from git
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Werner Saar
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*> \brief \b ZTPLQT
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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 DTPQRT + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtplqt.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/dtplqt.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/dtplqt.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 ZTPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
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* INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 A( LDA, * ), B( LDB, * ), 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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*> DTPLQT computes a blocked LQ factorization of a complex
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*> "triangular-pentagonal" matrix C, which is composed of a
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*> triangular block A and pentagonal block B, using the compact
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*> WY representation for Q.
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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 B, and the order of the
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*> triangular matrix A.
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*> 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 B.
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*> N >= 0.
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*> \endverbatim
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*>
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*> \param[in] L
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*> \verbatim
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*> L is INTEGER
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*> The number of rows of the lower trapezoidal part of B.
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*> MIN(M,N) >= L >= 0. See Further Details.
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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 block size to be used in the blocked QR. M >= MB >= 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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*> On entry, the lower triangular N-by-N matrix A.
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*> On exit, the elements on and below the diagonal of the array
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*> contain the lower triangular matrix L.
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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,N).
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is COMPLEX*16 array, dimension (LDB,N)
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*> On entry, the pentagonal M-by-N matrix B. The first N-L columns
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*> are rectangular, and the last L columns are lower trapezoidal.
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*> On exit, B contains the pentagonal matrix V. See Further Details.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= 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*16 array, dimension (LDT,N)
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*> The lower triangular block reflectors stored in compact form
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*> as a sequence of upper triangular blocks. See Further Details.
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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 >= MB.
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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 COMPLEX*16 array, dimension (MB*M)
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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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*> \date December 2016
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*
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*> \ingroup doubleOTHERcomputational
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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 input matrix C is a M-by-(M+N) matrix
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*>
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*> C = [ A ] [ B ]
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*>
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*>
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*> where A is an lower triangular N-by-N matrix, and B is M-by-N pentagonal
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*> matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
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*> upper trapezoidal matrix B2:
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*> [ B ] = [ B1 ] [ B2 ]
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*> [ B1 ] <- M-by-(N-L) rectangular
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*> [ B2 ] <- M-by-L upper trapezoidal.
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*>
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*> The lower trapezoidal matrix B2 consists of the first L columns of a
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*> N-by-N lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
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*> B is rectangular M-by-N; if M=L=N, B is lower triangular.
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*>
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*> The matrix W stores the elementary reflectors H(i) in the i-th row
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*> above the diagonal (of A) in the M-by-(M+N) input matrix C
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*> [ C ] = [ A ] [ B ]
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*> [ A ] <- lower triangular N-by-N
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*> [ B ] <- M-by-N pentagonal
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*>
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*> so that W can be represented as
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*> [ W ] = [ I ] [ V ]
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*> [ I ] <- identity, N-by-N
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*> [ V ] <- M-by-N, same form as B.
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*>
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*> Thus, all of information needed for W is contained on exit in B, which
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*> we call V above. Note that V has the same form as B; that is,
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*> [ V ] = [ V1 ] [ V2 ]
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*> [ V1 ] <- M-by-(N-L) rectangular
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*> [ V2 ] <- M-by-L lower trapezoidal.
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*>
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*> The rows of V represent the vectors which define the H(i)'s.
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*>
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*> The number of blocks is B = ceiling(M/MB), where each
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*> block is of order MB except for the last block, which is of order
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*> IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block
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*> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
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*> for the last block) T's are stored in the MB-by-N matrix T as
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*>
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*> T = [T1 T2 ... TB].
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE ZTPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
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$ INFO )
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*
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* -- LAPACK computational routine (version 3.7.0) --
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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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* December 2016
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* ..
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* .. Local Scalars ..
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INTEGER I, IB, LB, NB, IINFO
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* ..
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* .. External Subroutines ..
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EXTERNAL ZTPLQT2, ZTPRFB, XERBLA
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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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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( L.LT.0 .OR. (L.GT.MIN(M,N) .AND. MIN(M,N).GE.0)) THEN
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INFO = -3
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ELSE IF( MB.LT.1 .OR. (MB.GT.M .AND. M.GT.0)) 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( LDB.LT.MAX( 1, M ) ) THEN
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INFO = -8
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ELSE IF( LDT.LT.MB ) THEN
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INFO = -10
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZTPLQT', -INFO )
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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 .OR. N.EQ.0 ) RETURN
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*
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DO I = 1, M, MB
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*
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* Compute the QR factorization of the current block
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*
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IB = MIN( M-I+1, MB )
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NB = MIN( N-L+I+IB-1, N )
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IF( I.GE.L ) THEN
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LB = 0
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ELSE
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LB = NB-N+L-I+1
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END IF
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*
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CALL ZTPLQT2( IB, NB, LB, A(I,I), LDA, B( I, 1 ), LDB,
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$ T(1, I ), LDT, IINFO )
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*
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* Update by applying H**T to B(I+IB:M,:) from the right
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*
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IF( I+IB.LE.M ) THEN
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CALL ZTPRFB( 'R', 'N', 'F', 'R', M-I-IB+1, NB, IB, LB,
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$ B( I, 1 ), LDB, T( 1, I ), LDT,
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$ A( I+IB, I ), LDA, B( I+IB, 1 ), LDB,
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$ WORK, M-I-IB+1)
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END IF
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END DO
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RETURN
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*
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* End of ZTPLQT
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*
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END
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