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SUBROUTINE CLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
* -- LAPACK routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* -- April 2011 --
*
* .. Scalar Arguments ..
CHARACTER SIDE
INTEGER INCV, L, LDC, M, N
COMPLEX TAU
* ..
* .. Array Arguments ..
COMPLEX C( LDC, * ), V( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* CLARZ applies a complex elementary reflector H to a complex
* M-by-N matrix C, from either the left or the right. H is represented
* in the form
*
* H = I - tau * v * v**H
*
* where tau is a complex scalar and v is a complex vector.
*
* If tau = 0, then H is taken to be the unit matrix.
*
* To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
* tau.
*
* H is a product of k elementary reflectors as returned by CTZRZF.
*
* Arguments
* =========
*
* SIDE (input) CHARACTER*1
* = 'L': form H * C
* = 'R': form C * H
*
* M (input) INTEGER
* The number of rows of the matrix C.
*
* N (input) INTEGER
* The number of columns of the matrix C.
*
* L (input) INTEGER
* The number of entries of the vector V containing
* the meaningful part of the Householder vectors.
* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*
* V (input) COMPLEX array, dimension (1+(L-1)*abs(INCV))
* The vector v in the representation of H as returned by
* CTZRZF. V is not used if TAU = 0.
*
* INCV (input) INTEGER
* The increment between elements of v. INCV <> 0.
*
* TAU (input) COMPLEX
* The value tau in the representation of H.
*
* C (input/output) COMPLEX array, dimension (LDC,N)
* On entry, the M-by-N matrix C.
* On exit, C is overwritten by the matrix H * C if SIDE = 'L',
* or C * H if SIDE = 'R'.
*
* LDC (input) INTEGER
* The leading dimension of the array C. LDC >= max(1,M).
*
* WORK (workspace) COMPLEX array, dimension
* (N) if SIDE = 'L'
* or (M) if SIDE = 'R'
*
* Further Details
* ===============
*
* Based on contributions by
* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE, ZERO
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. External Subroutines ..
EXTERNAL CAXPY, CCOPY, CGEMV, CGERC, CGERU, CLACGV
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Executable Statements ..
*
IF( LSAME( SIDE, 'L' ) ) THEN
*
* Form H * C
*
IF( TAU.NE.ZERO ) THEN
*
* w( 1:n ) = conjg( C( 1, 1:n ) )
*
CALL CCOPY( N, C, LDC, WORK, 1 )
CALL CLACGV( N, WORK, 1 )
*
* w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )**H * v( 1:l ) )
*
CALL CGEMV( 'Conjugate transpose', L, N, ONE, C( M-L+1, 1 ),
$ LDC, V, INCV, ONE, WORK, 1 )
CALL CLACGV( N, WORK, 1 )
*
* C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
*
CALL CAXPY( N, -TAU, WORK, 1, C, LDC )
*
* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
* tau * v( 1:l ) * w( 1:n )**H
*
CALL CGERU( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
$ LDC )
END IF
*
ELSE
*
* Form C * H
*
IF( TAU.NE.ZERO ) THEN
*
* w( 1:m ) = C( 1:m, 1 )
*
CALL CCOPY( M, C, 1, WORK, 1 )
*
* w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
*
CALL CGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
$ V, INCV, ONE, WORK, 1 )
*
* C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
*
CALL CAXPY( M, -TAU, WORK, 1, C, 1 )
*
* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
* tau * w( 1:m ) * v( 1:l )**H
*
CALL CGERC( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
$ LDC )
*
END IF
*
END IF
*
RETURN
*
* End of CLARZ
*
END
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