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OpenBLAS/lapack-netlib/SRC/ctpqrt.f

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*> \brief \b CTPQRT
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CTPQRT + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctpqrt.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctpqrt.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctpqrt.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CTPQRT computes a blocked QR factorization of a complex
*> "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.
*> M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix B, and the order of the
*> triangular matrix A.
*> N >= 0.
*> \endverbatim
*>
*> \param[in] L
*> \verbatim
*> L is INTEGER
*> The number of rows of the upper trapezoidal part of B.
*> MIN(M,N) >= L >= 0. See Further Details.
*> \endverbatim
*>
*> \param[in] NB
*> \verbatim
*> NB is INTEGER
*> The block size to be used in the blocked QR. N >= NB >= 1.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> On entry, the upper triangular N-by-N matrix A.
*> On exit, the elements on and above the diagonal of the array
*> contain the upper triangular matrix R.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX array, dimension (LDB,N)
*> On entry, the pentagonal M-by-N matrix B. The first M-L rows
*> are rectangular, and the last L rows are upper 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 COMPLEX array, dimension (LDT,N)
*> The upper 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 >= NB.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (NB*N)
*> \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 November 2013
*
*> \ingroup complexOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> The input matrix C is a (N+M)-by-N matrix
*>
*> C = [ A ]
*> [ B ]
*>
*> where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
*> matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
*> upper trapezoidal matrix B2:
*>
*> B = [ B1 ] <- (M-L)-by-N rectangular
*> [ B2 ] <- L-by-N upper trapezoidal.
*>
*> The upper trapezoidal matrix B2 consists of the first L rows of a
*> N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
*> B is rectangular M-by-N; if M=L=N, B is upper triangular.
*>
*> The matrix W stores the elementary reflectors H(i) in the i-th column
*> below the diagonal (of A) in the (N+M)-by-N input matrix C
*>
*> C = [ A ] <- upper triangular N-by-N
*> [ B ] <- M-by-N pentagonal
*>
*> so that W can be represented as
*>
*> W = [ I ] <- identity, N-by-N
*> [ 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 ] <- (M-L)-by-N rectangular
*> [ V2 ] <- L-by-N upper trapezoidal.
*>
*> The columns of V represent the vectors which define the H(i)'s.
*>
*> The number of blocks is B = ceiling(N/NB), where each
*> block is of order NB except for the last block, which is of order
*> IB = N - (B-1)*NB. For each of the B blocks, a upper triangular block
*> reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB
*> for the last block) T's are stored in the NB-by-N matrix T as
*>
*> T = [T1 T2 ... TB].
*> \endverbatim
*>
* =====================================================================
SUBROUTINE CTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
$ INFO )
*
* -- LAPACK computational routine (version 3.5.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2013
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
* ..
*
* =====================================================================
*
* ..
* .. Local Scalars ..
INTEGER I, IB, LB, MB, IINFO
* ..
* .. External Subroutines ..
EXTERNAL CTPQRT2, CTPRFB, 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( NB.LT.1 .OR. (NB.GT.N .AND. N.GT.0)) THEN
INFO = -4
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -6
ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
INFO = -8
ELSE IF( LDT.LT.NB ) THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CTPQRT', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 ) RETURN
*
DO I = 1, N, NB
*
* Compute the QR factorization of the current block
*
IB = MIN( N-I+1, NB )
MB = MIN( M-L+I+IB-1, M )
IF( I.GE.L ) THEN
LB = 0
ELSE
LB = MB-M+L-I+1
END IF
*
CALL CTPQRT2( MB, IB, LB, A(I,I), LDA, B( 1, I ), LDB,
$ T(1, I ), LDT, IINFO )
*
* Update by applying H**H to B(:,I+IB:N) from the left
*
IF( I+IB.LE.N ) THEN
CALL CTPRFB( 'L', 'C', 'F', 'C', MB, N-I-IB+1, IB, LB,
$ B( 1, I ), LDB, T( 1, I ), LDT,
$ A( I, I+IB ), LDA, B( 1, I+IB ), LDB,
$ WORK, IB )
END IF
END DO
RETURN
*
* End of CTPQRT
*
END
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