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diff --git a/eigen/lapack/clarf.f b/eigen/lapack/clarf.f new file mode 100644 index 0000000..ca0328f --- /dev/null +++ b/eigen/lapack/clarf.f @@ -0,0 +1,232 @@ +*> \brief \b CLARF +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download CLARF + dependencies +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clarf.f"> +*> [TGZ]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clarf.f"> +*> [ZIP]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clarf.f"> +*> [TXT]</a> +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE CLARF( 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 +*> +*> 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**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. +*> \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. +* +*> \date November 2011 +* +*> \ingroup complexOTHERauxiliary +* +* ===================================================================== + SUBROUTINE CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. 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 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)**H * 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)**H +* + 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)**H +* + CALL CGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) + END IF + END IF + RETURN +* +* End of CLARF +* + END |