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* Definition:
* ===========
*
* SUBROUTINE CTPLQT2( M, N, L, A, LDA, B, LDB, T, LDT, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDB, LDT, N, M, L
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CTPLQT2 computes a LQ a 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 total 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 lower trapezoidal part of B.
*> MIN(M,N) >= L >= 0. See Further Details.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LDT,M)
*> The N-by-N upper triangular factor T of the block reflector.
*> See Further Details.
*> \endverbatim
*>
*> \param[in] LDT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= max(1,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 December 2016
*
*> \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 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
*> N-by-N 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,
*>
*> W = [ 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 (M+N)-by-(M+N) block reflector H is then given by
*>
*> H = I - W**T * T * W
*>
*> where W^H is the conjugate transpose of W and T is the upper triangular
*> factor of the block reflector.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE CTPLQT2( M, N, L, A, LDA, B, LDB, T, LDT, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDB, LDT, N, M, L
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE, ZERO
PARAMETER( ZERO = ( 0.0E+0, 0.0E+0 ),ONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, J, P, MP, NP
COMPLEX ALPHA
* ..
* .. External Subroutines ..
EXTERNAL CLARFG, CGEMV, CGERC, CTRMV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. 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) ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
INFO = -7
ELSE IF( LDT.LT.MAX( 1, M ) ) THEN
INFO = -9
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CTPLQT2', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. M.EQ.0 ) RETURN
*
DO I = 1, M
*
* Generate elementary reflector H(I) to annihilate B(I,:)
*
P = N-L+MIN( L, I )
CALL CLARFG( P+1, A( I, I ), B( I, 1 ), LDB, T( 1, I ) )
T(1,I)=CONJG(T(1,I))
IF( I.LT.M ) THEN
DO J = 1, P
B( I, J ) = CONJG(B(I,J))
END DO
*
* W(M-I:1) := C(I+1:M,I:N) * C(I,I:N) [use W = T(M,:)]
*
DO J = 1, M-I
T( M, J ) = (A( I+J, I ))
END DO
CALL CGEMV( 'N', M-I, P, ONE, B( I+1, 1 ), LDB,
$ B( I, 1 ), LDB, ONE, T( M, 1 ), LDT )
*
* C(I+1:M,I:N) = C(I+1:M,I:N) + alpha * C(I,I:N)*W(M-1:1)^H
*
ALPHA = -(T( 1, I ))
DO J = 1, M-I
A( I+J, I ) = A( I+J, I ) + ALPHA*(T( M, J ))
END DO
CALL CGERC( M-I, P, (ALPHA), T( M, 1 ), LDT,
$ B( I, 1 ), LDB, B( I+1, 1 ), LDB )
DO J = 1, P
B( I, J ) = CONJG(B(I,J))
END DO
END IF
END DO
*
DO I = 2, M
*
* T(I,1:I-1) := C(I:I-1,1:N)**H * (alpha * C(I,I:N))
*
ALPHA = -(T( 1, I ))
DO J = 1, I-1
T( I, J ) = ZERO
END DO
P = MIN( I-1, L )
NP = MIN( N-L+1, N )
MP = MIN( P+1, M )
DO J = 1, N-L+P
B(I,J)=CONJG(B(I,J))
END DO
*
* Triangular part of B2
*
DO J = 1, P
T( I, J ) = (ALPHA*B( I, N-L+J ))
END DO
CALL CTRMV( 'L', 'N', 'N', P, B( 1, NP ), LDB,
$ T( I, 1 ), LDT )
*
* Rectangular part of B2
*
CALL CGEMV( 'N', I-1-P, L, ALPHA, B( MP, NP ), LDB,
$ B( I, NP ), LDB, ZERO, T( I,MP ), LDT )
*
* B1
*
CALL CGEMV( 'N', I-1, N-L, ALPHA, B, LDB, B( I, 1 ), LDB,
$ ONE, T( I, 1 ), LDT )
*
*
* T(1:I-1,I) := T(1:I-1,1:I-1) * T(I,1:I-1)
*
DO J = 1, I-1
T(I,J)=CONJG(T(I,J))
END DO
CALL CTRMV( 'L', 'C', 'N', I-1, T, LDT, T( I, 1 ), LDT )
DO J = 1, I-1
T(I,J)=CONJG(T(I,J))
END DO
DO J = 1, N-L+P
B(I,J)=CONJG(B(I,J))
END DO
*
* T(I,I) = tau(I)
*
T( I, I ) = T( 1, I )
T( 1, I ) = ZERO
END DO
DO I=1,M
DO J= I+1,M
T(I,J)=(T(J,I))
T(J,I)=ZERO
END DO
END DO
*
* End of CTPLQT2
*
END
|
