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lapack/SRC/clarf1f.f
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Mark Gates 8caa3ff67b implicit none in SRC/c
2025-08-26 23:27:57 -04:00

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*> \brief \b CLARF1F applies an elementary reflector to a general rectangular
* matrix assuming v(1) = 1.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> Download CLARF1F + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clarf1f.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clarf1f.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clarf1f.f">
*> [TXT]</a>
*
* Definition:
* ===========
*
* SUBROUTINE CLARF1F( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
*
* .. Scalar Arguments ..
* CHARACTER SIDE
* INTEGER INCV, LDC, M, N
* COMPLEX TAU
* ..
* .. Array Arguments ..
* COMPLEX C( LDC, * ), V( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLARF1F 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 assuming v(1) = 1.
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is CHARACTER*1
*> = 'L': form H * C
*> = 'R': form C * H
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix C.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix C.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*> V is 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.
*> \endverbatim
*>
*> \param[in] INCV
*> \verbatim
*> INCV is INTEGER
*> The increment between elements of v. INCV <> 0.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX
*> The value tau in the representation of H.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is 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'.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of the array C. LDC >= max(1,M).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension
*> (N) if SIDE = 'L'
*> or (M) if SIDE = 'R'
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup larf1f
*
* =====================================================================
SUBROUTINE CLARF1F( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
IMPLICIT NONE
*
* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER SIDE
INTEGER INCV, LDC, M, N
COMPLEX TAU
* ..
* .. Array Arguments ..
COMPLEX C( LDC, * ), V( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. 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 CAXPY, CGEMV, CGER, CSCAL
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILACLR, ILACLC
EXTERNAL LSAME, ILACLR, ILACLC
* ..
* .. Executable Statements ..
*
APPLYLEFT = LSAME( SIDE, 'L' )
LASTV = 1
LASTC = 0
IF( TAU.NE.ZERO ) THEN
! Set up variables for scanning V. LASTV begins pointing to the end
! of V up to V(1).
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.1 .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
IF( LASTC.EQ.0 ) THEN
RETURN
END IF
IF( APPLYLEFT ) THEN
*
* Form H * C
*
IF( LASTV.EQ.1 ) THEN
*
* C(1,1:lastc) := ( 1 - tau ) * C(1,1:lastc)
*
CALL CSCAL( LASTC, ONE - TAU, C, LDC )
ELSE
*
* w(1:lastc,1) := C(2:lastv,1:lastc)**H * v(2:lastv,1)
*
CALL CGEMV( 'Conjugate transpose', LASTV - 1, LASTC, ONE,
$ C( 2, 1 ), LDC, V( 1 + INCV ), INCV, ZERO,
$ WORK, 1 )
*
* w(1:lastc,1) += v(1,1) * C(1,1:lastc)**H
*
DO I = 1, LASTC
WORK( I ) = WORK( I ) + CONJG( C( 1, I ) )
END DO
*
* C(1, 1:lastc) += - tau * v(1,1) * w(1:lastc,1)**H
*
DO I = 1, LASTC
C( 1, I ) = C( 1, I ) - TAU * CONJG( WORK( I ) )
END DO
*
* C(2:lastv,1:lastc) += - tau * v(2:lastv,1) * w(1:lastc,1)**H
*
CALL CGERC( LASTV - 1, LASTC, -TAU, V( 1 + INCV ), INCV,
$ WORK, 1, C( 2, 1 ), LDC )
END IF
ELSE
*
* Form C * H
*
IF( LASTV.EQ.1 ) THEN
*
* C(1:lastc,1) := ( 1 - tau ) * C(1:lastc,1)
*
CALL CSCAL( LASTC, ONE - TAU, C, 1 )
ELSE
*
* w(1:lastc,1) := C(1:lastc,2:lastv) * v(2:lastv,1)
*
CALL CGEMV( 'No transpose', LASTC, LASTV - 1, ONE,
$ C( 1, 2 ), LDC, V( 1 + INCV ), INCV, ZERO,
$ WORK, 1 )
*
* w(1:lastc,1) += v(1,1) * C(1:lastc,1)
*
CALL CAXPY( LASTC, ONE, C, 1, WORK, 1 )
*
* C(1:lastc,1) += - tau * v(1,1) * w(1:lastc,1)
*
CALL CAXPY( LASTC, -TAU, WORK, 1, C, 1 )
*
* C(1:lastc,2:lastv) += - tau * w(1:lastc,1) * v(2:lastv)**H
*
CALL CGERC( LASTC, LASTV - 1, -TAU, WORK, 1,
$ V( 1 + INCV ), INCV, C( 1, 2 ), LDC )
END IF
END IF
RETURN
*
* End of CLARF1F
*
END
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