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SUBROUTINE ZLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
$ LDV, T, LDT, C, LDC, WORK, LDWORK )
*
* -- LAPACK routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
CHARACTER DIRECT, SIDE, STOREV, TRANS
INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
* ..
* .. Array Arguments ..
COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ),
$ WORK( LDWORK, * )
* ..
*
* Purpose
* =======
*
* ZLARZB applies a complex block reflector H or its transpose H**H
* to a complex distributed M-by-N C from the left or the right.
*
* Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
*
* Arguments
* =========
*
* SIDE (input) CHARACTER*1
* = 'L': apply H or H' from the Left
* = 'R': apply H or H' from the Right
*
* TRANS (input) CHARACTER*1
* = 'N': apply H (No transpose)
* = 'C': apply H' (Conjugate transpose)
*
* DIRECT (input) CHARACTER*1
* Indicates how H is formed from a product of elementary
* reflectors
* = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
* = 'B': H = H(k) . . . H(2) H(1) (Backward)
*
* STOREV (input) CHARACTER*1
* Indicates how the vectors which define the elementary
* reflectors are stored:
* = 'C': Columnwise (not supported yet)
* = 'R': Rowwise
*
* M (input) INTEGER
* The number of rows of the matrix C.
*
* N (input) INTEGER
* The number of columns of the matrix C.
*
* K (input) INTEGER
* The order of the matrix T (= the number of elementary
* reflectors whose product defines the block reflector).
*
* L (input) INTEGER
* The number of columns of the matrix V containing the
* meaningful part of the Householder reflectors.
* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*
* V (input) COMPLEX*16 array, dimension (LDV,NV).
* If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
*
* LDV (input) INTEGER
* The leading dimension of the array V.
* If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
*
* T (input) COMPLEX*16 array, dimension (LDT,K)
* The triangular K-by-K matrix T in the representation of the
* block reflector.
*
* LDT (input) INTEGER
* The leading dimension of the array T. LDT >= K.
*
* C (input/output) COMPLEX*16 array, dimension (LDC,N)
* On entry, the M-by-N matrix C.
* On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
*
* LDC (input) INTEGER
* The leading dimension of the array C. LDC >= max(1,M).
*
* WORK (workspace) COMPLEX*16 array, dimension (LDWORK,K)
*
* LDWORK (input) INTEGER
* The leading dimension of the array WORK.
* If SIDE = 'L', LDWORK >= max(1,N);
* if SIDE = 'R', LDWORK >= max(1,M).
*
* Further Details
* ===============
*
* Based on contributions by
* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ONE
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
CHARACTER TRANST
INTEGER I, INFO, J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZCOPY, ZGEMM, ZLACGV, ZTRMM
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
* Check for currently supported options
*
INFO = 0
IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
INFO = -3
ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZLARZB', -INFO )
RETURN
END IF
*
IF( LSAME( TRANS, 'N' ) ) THEN
TRANST = 'C'
ELSE
TRANST = 'N'
END IF
*
IF( LSAME( SIDE, 'L' ) ) THEN
*
* Form H * C or H' * C
*
* W( 1:n, 1:k ) = conjg( C( 1:k, 1:n )' )
*
DO 10 J = 1, K
CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
10 CONTINUE
*
* W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
* conjg( C( m-l+1:m, 1:n )' ) * V( 1:k, 1:l )'
*
IF( L.GT.0 )
$ CALL ZGEMM( 'Transpose', 'Conjugate transpose', N, K, L,
$ ONE, C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK,
$ LDWORK )
*
* W( 1:n, 1:k ) = W( 1:n, 1:k ) * T' or W( 1:m, 1:k ) * T
*
CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
$ LDT, WORK, LDWORK )
*
* C( 1:k, 1:n ) = C( 1:k, 1:n ) - conjg( W( 1:n, 1:k )' )
*
DO 30 J = 1, N
DO 20 I = 1, K
C( I, J ) = C( I, J ) - WORK( J, I )
20 CONTINUE
30 CONTINUE
*
* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
* conjg( V( 1:k, 1:l )' ) * conjg( W( 1:n, 1:k )' )
*
IF( L.GT.0 )
$ CALL ZGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
$ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC )
*
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
*
* Form C * H or C * H'
*
* W( 1:m, 1:k ) = C( 1:m, 1:k )
*
DO 40 J = 1, K
CALL ZCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
40 CONTINUE
*
* W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
* C( 1:m, n-l+1:n ) * conjg( V( 1:k, 1:l )' )
*
IF( L.GT.0 )
$ CALL ZGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
$ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
*
* W( 1:m, 1:k ) = W( 1:m, 1:k ) * conjg( T ) or
* W( 1:m, 1:k ) * conjg( T' )
*
DO 50 J = 1, K
CALL ZLACGV( K-J+1, T( J, J ), 1 )
50 CONTINUE
CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
$ LDT, WORK, LDWORK )
DO 60 J = 1, K
CALL ZLACGV( K-J+1, T( J, J ), 1 )
60 CONTINUE
*
* C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
*
DO 80 J = 1, K
DO 70 I = 1, M
C( I, J ) = C( I, J ) - WORK( I, J )
70 CONTINUE
80 CONTINUE
*
* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
* W( 1:m, 1:k ) * conjg( V( 1:k, 1:l ) )
*
DO 90 J = 1, L
CALL ZLACGV( K, V( 1, J ), 1 )
90 CONTINUE
IF( L.GT.0 )
$ CALL ZGEMM( 'No transpose', 'No transpose', M, L, K, -ONE,
$ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC )
DO 100 J = 1, L
CALL ZLACGV( K, V( 1, J ), 1 )
100 CONTINUE
*
END IF
*
RETURN
*
* End of ZLARZB
*
END
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