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OpenBLAS/lapack-netlib/SRC/dtplqt.f

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*> \brief \b DTPLQT
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DTPQRT + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtplqt.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtplqt.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtplqt.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DTPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DTPLQT computes a blocked LQ factorization of a real
*> "triangular-pentagonal" matrix C, which is composed of a
*> triangular block A and pentagonal block B, using the compact
*> WY representation for Q.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix B, and the order of the
*> triangular matrix A.
*> M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix B.
*> N >= 0.
*> \endverbatim
*>
*> \param[in] L
*> \verbatim
*> L is INTEGER
*> The number of rows of the lower trapezoidal part of B.
*> MIN(M,N) >= L >= 0. See Further Details.
*> \endverbatim
*>
*> \param[in] MB
*> \verbatim
*> MB is INTEGER
*> The block size to be used in the blocked QR. M >= MB >= 1.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,M)
*> On entry, the lower triangular M-by-M matrix A.
*> On exit, the elements on and below the diagonal of the array
*> contain the lower triangular matrix L.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB,N)
*> On entry, the pentagonal M-by-N matrix B. The first N-L columns
*> are rectangular, and the last L columns are lower trapezoidal.
*> On exit, B contains the pentagonal matrix V. See Further Details.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,M).
*> \endverbatim
*>
*> \param[out] T
*> \verbatim
*> T is DOUBLE PRECISION array, dimension (LDT,N)
*> The lower triangular block reflectors stored in compact form
*> as a sequence of upper triangular blocks. See Further Details.
*> \endverbatim
*>
*> \param[in] LDT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= MB.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (MB*M)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date June 2017
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> The input matrix C is a M-by-(M+N) matrix
*>
*> C = [ A ] [ B ]
*>
*>
*> where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
*> matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
*> upper trapezoidal matrix B2:
*> [ B ] = [ B1 ] [ B2 ]
*> [ B1 ] <- M-by-(N-L) rectangular
*> [ B2 ] <- M-by-L lower trapezoidal.
*>
*> The lower trapezoidal matrix B2 consists of the first L columns of a
*> M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
*> B is rectangular M-by-N; if M=L=N, B is lower triangular.
*>
*> The matrix W stores the elementary reflectors H(i) in the i-th row
*> above the diagonal (of A) in the M-by-(M+N) input matrix C
*> [ C ] = [ A ] [ B ]
*> [ A ] <- lower triangular M-by-M
*> [ B ] <- M-by-N pentagonal
*>
*> so that W can be represented as
*> [ W ] = [ I ] [ V ]
*> [ I ] <- identity, M-by-M
*> [ V ] <- M-by-N, same form as B.
*>
*> Thus, all of information needed for W is contained on exit in B, which
*> we call V above. Note that V has the same form as B; that is,
*> [ V ] = [ V1 ] [ V2 ]
*> [ V1 ] <- M-by-(N-L) rectangular
*> [ V2 ] <- M-by-L lower trapezoidal.
*>
*> The rows of V represent the vectors which define the H(i)'s.
*>
*> The number of blocks is B = ceiling(M/MB), where each
*> block is of order MB except for the last block, which is of order
*> IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block
*> reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
*> for the last block) T's are stored in the MB-by-N matrix T as
*>
*> T = [T1 T2 ... TB].
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DTPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
$ INFO )
*
* -- LAPACK computational routine (version 3.7.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2017
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
* ..
*
* =====================================================================
*
* ..
* .. Local Scalars ..
INTEGER I, IB, LB, NB, IINFO
* ..
* .. External Subroutines ..
EXTERNAL DTPLQT2, DTPRFB, XERBLA
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( L.LT.0 .OR. (L.GT.MIN(M,N) .AND. MIN(M,N).GE.0)) THEN
INFO = -3
ELSE IF( MB.LT.1 .OR. (MB.GT.M .AND. M.GT.0)) THEN
INFO = -4
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -6
ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
INFO = -8
ELSE IF( LDT.LT.MB ) THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DTPLQT', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 ) RETURN
*
DO I = 1, M, MB
*
* Compute the QR factorization of the current block
*
IB = MIN( M-I+1, MB )
NB = MIN( N-L+I+IB-1, N )
IF( I.GE.L ) THEN
LB = 0
ELSE
LB = NB-N+L-I+1
END IF
*
CALL DTPLQT2( IB, NB, LB, A(I,I), LDA, B( I, 1 ), LDB,
$ T(1, I ), LDT, IINFO )
*
* Update by applying H**T to B(I+IB:M,:) from the right
*
IF( I+IB.LE.M ) THEN
CALL DTPRFB( 'R', 'N', 'F', 'R', M-I-IB+1, NB, IB, LB,
$ B( I, 1 ), LDB, T( 1, I ), LDT,
$ A( I+IB, I ), LDA, B( I+IB, 1 ), LDB,
$ WORK, M-I-IB+1)
END IF
END DO
RETURN
*
* End of DTPLQT
*
END
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