SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) IMPLICIT NONE * * -- LAPACK auxiliary routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER SIDE INTEGER INCV, LDC, M, N COMPLEX TAU * .. * .. Array Arguments .. COMPLEX C( LDC, * ), V( * ), WORK( * ) * .. * * Purpose * ======= * * CLARF 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' * * 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' (the conjugate transpose of H), supply conjg(tau) instead * tau. * * 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. * * V (input) COMPLEX array, dimension * (1 + (M-1)*abs(INCV)) if SIDE = 'L' * or (1 + (N-1)*abs(INCV)) if SIDE = 'R' * The vector v in the representation of H. 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' * * ===================================================================== * * .. Parameters .. COMPLEX ONE, ZERO PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), \$ ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL APPLYLEFT INTEGER I, LASTV, LASTC * .. * .. External Subroutines .. EXTERNAL CGEMV, CGERC * .. * .. External Functions .. LOGICAL LSAME INTEGER ILACLR, ILACLC EXTERNAL LSAME, ILACLR, ILACLC * .. * .. Executable Statements .. * APPLYLEFT = LSAME( SIDE, 'L' ) LASTV = 0 LASTC = 0 IF( TAU.NE.ZERO ) THEN ! Set up variables for scanning V. LASTV begins pointing to the end ! of V. IF( APPLYLEFT ) THEN LASTV = M ELSE LASTV = N END IF IF( INCV.GT.0 ) THEN I = 1 + (LASTV-1) * INCV ELSE I = 1 END IF ! Look for the last non-zero row in V. DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) LASTV = LASTV - 1 I = I - INCV END DO IF( APPLYLEFT ) THEN ! Scan for the last non-zero column in C(1:lastv,:). LASTC = ILACLC(LASTV, N, C, LDC) ELSE ! Scan for the last non-zero row in C(:,1:lastv). LASTC = ILACLR(M, LASTV, C, LDC) END IF END IF ! Note that lastc.eq.0 renders the BLAS operations null; no special ! case is needed at this level. IF( APPLYLEFT ) THEN * * Form H * C * IF( LASTV.GT.0 ) THEN * * w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1) * CALL CGEMV( 'Conjugate transpose', LASTV, LASTC, ONE, \$ C, LDC, V, INCV, ZERO, WORK, 1 ) * * C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)' * CALL CGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) END IF ELSE * * Form C * H * IF( LASTV.GT.0 ) THEN * * w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) * CALL CGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, \$ V, INCV, ZERO, WORK, 1 ) * * C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)' * CALL CGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) END IF END IF RETURN * * End of CLARF * END