158 lines
4.4 KiB
FortranFixed
158 lines
4.4 KiB
FortranFixed
SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
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IMPLICIT NONE
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*
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* -- LAPACK auxiliary routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER SIDE
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INTEGER INCV, LDC, M, N
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COMPLEX*16 TAU
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* ..
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* .. Array Arguments ..
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COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* ZLARF applies a complex elementary reflector H to a complex M-by-N
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* matrix C, from either the left or the right. H is represented in the
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* form
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*
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* H = I - tau * v * v'
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*
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* where tau is a complex scalar and v is a complex vector.
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*
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* If tau = 0, then H is taken to be the unit matrix.
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*
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* To apply H' (the conjugate transpose of H), supply conjg(tau) instead
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* tau.
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*
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* Arguments
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* =========
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*
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* SIDE (input) CHARACTER*1
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* = 'L': form H * C
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* = 'R': form C * H
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*
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* M (input) INTEGER
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* The number of rows of the matrix C.
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*
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* N (input) INTEGER
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* The number of columns of the matrix C.
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*
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* V (input) COMPLEX*16 array, dimension
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* (1 + (M-1)*abs(INCV)) if SIDE = 'L'
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* or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
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* The vector v in the representation of H. V is not used if
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* TAU = 0.
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*
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* INCV (input) INTEGER
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* The increment between elements of v. INCV <> 0.
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*
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* TAU (input) COMPLEX*16
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* The value tau in the representation of H.
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*
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* C (input/output) COMPLEX*16 array, dimension (LDC,N)
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* On entry, the M-by-N matrix C.
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* On exit, C is overwritten by the matrix H * C if SIDE = 'L',
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* or C * H if SIDE = 'R'.
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*
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* LDC (input) INTEGER
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* The leading dimension of the array C. LDC >= max(1,M).
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*
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* WORK (workspace) COMPLEX*16 array, dimension
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* (N) if SIDE = 'L'
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* or (M) if SIDE = 'R'
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX*16 ONE, ZERO
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PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
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$ ZERO = ( 0.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL APPLYLEFT
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INTEGER I, LASTV, LASTC
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* ..
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* .. External Subroutines ..
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EXTERNAL ZGEMV, ZGERC
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAZLR, ILAZLC
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EXTERNAL LSAME, ILAZLR, ILAZLC
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* ..
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* .. Executable Statements ..
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*
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APPLYLEFT = LSAME( SIDE, 'L' )
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LASTV = 0
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LASTC = 0
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IF( TAU.NE.ZERO ) THEN
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! Set up variables for scanning V. LASTV begins pointing to the end
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! of V.
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IF( APPLYLEFT ) THEN
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LASTV = M
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ELSE
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LASTV = N
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END IF
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IF( INCV.GT.0 ) THEN
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I = 1 + (LASTV-1) * INCV
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ELSE
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I = 1
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END IF
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! Look for the last non-zero row in V.
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DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )
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LASTV = LASTV - 1
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I = I - INCV
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END DO
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IF( APPLYLEFT ) THEN
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! Scan for the last non-zero column in C(1:lastv,:).
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LASTC = ILAZLC(LASTV, N, C, LDC)
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ELSE
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! Scan for the last non-zero row in C(:,1:lastv).
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LASTC = ILAZLR(M, LASTV, C, LDC)
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END IF
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END IF
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! Note that lastc.eq.0 renders the BLAS operations null; no special
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! case is needed at this level.
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IF( APPLYLEFT ) THEN
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*
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* Form H * C
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*
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IF( LASTV.GT.0 ) THEN
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*
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* w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1)
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*
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CALL ZGEMV( 'Conjugate transpose', LASTV, LASTC, ONE,
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$ C, LDC, V, INCV, ZERO, WORK, 1 )
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*
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* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)'
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*
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CALL ZGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
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END IF
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ELSE
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*
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* Form C * H
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*
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IF( LASTV.GT.0 ) THEN
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*
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* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
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*
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CALL ZGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
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$ V, INCV, ZERO, WORK, 1 )
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*
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* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)'
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*
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CALL ZGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
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END IF
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END IF
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RETURN
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*
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* End of ZLARF
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*
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END
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