diff --git a/cmake/lapack.cmake b/cmake/lapack.cmake index 04dd49cfbe..6d22971a5c 100644 --- a/cmake/lapack.cmake +++ b/cmake/lapack.cmake @@ -70,7 +70,7 @@ set(SLASRC slaqgb.f slaqge.f slaqp2.f slaqps.f slaqp2rk.f slaqp3rk.f slaqsb.f slaqsp.f slaqsy.f slaqr0.f slaqr1.f slaqr2.f slaqr3.f slaqr4.f slaqr5.f slaqtr.f slar1v.f slar2v.f ilaslr.f ilaslc.f - slarf.f slarfb.f slarfb_gett.f slarfg.f slarfgp.f slarft.f slarfx.f slarfy.f slargv.f + slarf.f slarfb.f slarfb_gett.f slarfg.f slarfgp.f slarft.f slarft_lvl2.f slarfx.f slarfy.f slargv.f slarf1f.f slarf1l.f slarrv.f slartv.f slarz.f slarzb.f slarzt.f slasy2.f slasyf.f slasyf_rook.f slasyf_rk.f slasyf_aa.f @@ -177,7 +177,7 @@ set(CLASRC claqr0.f claqr1.f claqr2.f claqr3.f claqr4.f claqr5.f claqz0.f claqz1.f claqz2.f claqz3.f claqsp.f claqsy.f clar1v.f clar2v.f ilaclr.f ilaclc.f - clarf.f clarfb.f clarfb_gett.f clarfg.f clarfgp.f clarft.f + clarf.f clarfb.f clarfb_gett.f clarfg.f clarfgp.f clarft.f clarft_lvl2.f clarf1f.f clarf1l.f clarfx.f clarfy.f clargv.f clarnv.f clarrv.f clartg.f90 clartv.f clarz.f clarzb.f clarzt.f clascl.f claset.f clasr.f classq.f90 @@ -262,7 +262,7 @@ set(DLASRC dlaqgb.f dlaqge.f dlaqp2.f dlaqp2rk.f dlaqp3rk.f dlaqps.f dlaqsb.f dlaqsp.f dlaqsy.f dlaqr0.f dlaqr1.f dlaqr2.f dlaqr3.f dlaqr4.f dlaqr5.f dlaqtr.f dlar1v.f dlar2v.f iladlr.f iladlc.f - dlarf.f dlarfb.f dlarfb_gett.f dlarfg.f dlarfgp.f dlarft.f dlarfx.f dlarfy.f + dlarf.f dlarfb.f dlarfb_gett.f dlarfg.f dlarfgp.f dlarft.f dlarft_lvl2.f dlarfx.f dlarfy.f dlarf1f.f dlarf1l.f dlargv.f dlarrv.f dlartv.f dlarz.f dlarzb.f dlarzt.f dlasy2.f dlasyf.f dlasyf_rook.f dlasyf_rk.f dlasyf_aa.f @@ -372,7 +372,7 @@ set(ZLASRC zlaqr0.f zlaqr1.f zlaqr2.f zlaqr3.f zlaqr4.f zlaqr5.f zlaqsp.f zlaqsy.f zlar1v.f zlar2v.f ilazlr.f ilazlc.f zlarcm.f zlarf.f zlarfb.f zlarfb_gett.f - zlarfg.f zlarfgp.f zlarft.f zlarf1f.f zlarf1l.f + zlarfg.f zlarfgp.f zlarft.f zlarft_lvl2.f zlarf1f.f zlarf1l.f zlarfx.f zlarfy.f zlargv.f zlarnv.f zlarrv.f zlartg.f90 zlartv.f zlarz.f zlarzb.f zlarzt.f zlascl.f zlaset.f zlasr.f zlassq.f90 zlasyf.f zlasyf_rook.f zlasyf_rk.f zlasyf_aa.f diff --git a/lapack-netlib/SRC/Makefile b/lapack-netlib/SRC/Makefile index ebf3431a92..2200a4628d 100644 --- a/lapack-netlib/SRC/Makefile +++ b/lapack-netlib/SRC/Makefile @@ -154,7 +154,7 @@ SLASRC_O = \ slaqgb.o slaqge.o slaqp2.o slaqp2rk.o slaqp3rk.o slaqps.o slaqsb.o slaqsp.o slaqsy.o \ slaqr0.o slaqr1.o slaqr2.o slaqr3.o slaqr4.o slaqr5.o \ slaqtr.o slar1v.o slar2v.o ilaslr.o ilaslc.o \ - slarf.o slarfb.o slarfb_gett.o slarfg.o slarfgp.o slarft.o slarfx.o slarfy.o slargv.o \ + slarf.o slarfb.o slarfb_gett.o slarfg.o slarfgp.o slarft.o slarft_lvl2.o slarfx.o slarfy.o slargv.o \ slarf1f.o slarf1l.o slarrv.o slartv.o \ slarz.o slarzb.o slarzt.o slaswp.o slasy2.o slasyf.o slasyf_rook.o \ slasyf_rk.o \ @@ -270,7 +270,7 @@ CLASRC_O = \ claqr0.o claqr1.o claqr2.o claqr3.o claqr4.o claqr5.o \ claqsp.o claqsy.o clar1v.o clar2v.o ilaclr.o ilaclc.o \ claqz0.o claqz1.o claqz2.o claqz3.o \ - clarf.o clarfb.o clarfb_gett.o clarfg.o clarft.o clarfgp.o \ + clarf.o clarfb.o clarfb_gett.o clarfg.o clarft.o clarft_lvl2.o clarfgp.o \ clarf1f.o clarf1l.o \ clarfx.o clarfy.o clargv.o clarnv.o clarrv.o clartg.o clartv.o \ clarz.o clarzb.o clarzt.o clascl.o claset.o clasr.o classq.o \ @@ -364,7 +364,7 @@ DLASRC_O = \ dlaqgb.o dlaqge.o dlaqp2.o dlaqp2rk.o dlaqp3rk.o dlaqps.o dlaqsb.o dlaqsp.o dlaqsy.o \ dlaqr0.o dlaqr1.o dlaqr2.o dlaqr3.o dlaqr4.o dlaqr5.o \ dlaqtr.o dlar1v.o dlar2v.o iladlr.o iladlc.o \ - dlarf.o dlarfb.o dlarfb_gett.o dlarfg.o dlarfgp.o dlarft.o dlarfx.o dlarfy.o \ + dlarf.o dlarfb.o dlarfb_gett.o dlarfg.o dlarfgp.o dlarft.o dlarft_lvl2.o dlarfx.o dlarfy.o \ dlarf1f.o dlarf1l.o dlargv.o dlarrv.o dlartv.o \ dlarz.o dlarzb.o dlarzt.o dlaswp.o dlasy2.o \ dlasyf.o dlasyf_rook.o dlasyf_rk.o \ @@ -479,7 +479,7 @@ ZLASRC_O = \ zlaqsp.o zlaqsy.o zlar1v.o zlar2v.o ilazlr.o ilazlc.o \ zlaqz0.o zlaqz1.o zlaqz2.o zlaqz3.o \ zlarcm.o zlarf.o zlarfb.o zlarfb_gett.o \ - zlarfg.o zlarft.o zlarfgp.o zlarf1f.o zlarf1l.o \ + zlarfg.o zlarft.o zlarft_lvl2.o zlarfgp.o zlarf1f.o zlarf1l.o \ zlarfx.o zlarfy.o zlargv.o zlarnv.o zlarrv.o zlartg.o zlartv.o \ zlarz.o zlarzb.o zlarzt.o zlascl.o zlaset.o zlasr.o \ zlassq.o zlaswp.o zlasyf.o zlasyf_rook.o zlasyf_rk.o zlasyf_aa.o \ diff --git a/lapack-netlib/SRC/clarft.f b/lapack-netlib/SRC/clarft.f index de8b97bf9c..3bf2448ba8 100644 --- a/lapack-netlib/SRC/clarft.f +++ b/lapack-netlib/SRC/clarft.f @@ -5,7 +5,6 @@ * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * -*> \htmlonly *> Download CLARFT + dependencies *> *> [TGZ] @@ -13,7 +12,6 @@ *> [ZIP] *> *> [TXT] -*> \endhtmlonly * * Definition: * =========== @@ -161,6 +159,7 @@ * ===================================================================== RECURSIVE SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, $ TAU, T, LDT ) + IMPLICIT NONE * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- @@ -179,11 +178,12 @@ RECURSIVE SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, * .. Parameters .. * COMPLEX ONE, NEG_ONE, ZERO - PARAMETER(ONE=1.0E+0, ZERO = 0.0E+0, NEG_ONE=-1.0E+0) + PARAMETER(ONE=(1.0E+0,0.0E+0), ZERO = (0.0E+0,0.0E+0), + $ NEG_ONE=(-1.0E+0,0.0E+0)) * * .. Local Scalars .. * - INTEGER I,J,L + INTEGER I,J,L,NX LOGICAL QR,LQ,QL,DIRF,COLV * * .. External Subroutines .. @@ -193,7 +193,8 @@ RECURSIVE SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, * .. External Functions.. * LOGICAL LSAME - EXTERNAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV * * .. Intrinsic Functions.. * @@ -219,6 +220,14 @@ RECURSIVE SUBROUTINE CLARFT( DIRECT, STOREV, N, K, V, LDV, RETURN END IF * +* Determine when to cross over into the level 2 based implementation +* + NX = ILAENV(3, "CLARFT", DIRECT // STOREV, N, K, -1, -1) + IF(K.LT.NX) THEN + CALL CLARFT_LVL2(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) + RETURN + END IF +* * Beginning of executable statements * L = K / 2 diff --git a/lapack-netlib/SRC/clarft_lvl2.f b/lapack-netlib/SRC/clarft_lvl2.f new file mode 100644 index 0000000000..3b0aea1132 --- /dev/null +++ b/lapack-netlib/SRC/clarft_lvl2.f @@ -0,0 +1,328 @@ +*> \brief \b CLARFT_LVL2: Level 2 BLAS version for terminating case of CLARFT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> Download CLARFT_LVL2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +* +* Definition: +* =========== +* +* SUBROUTINE CLARFT_LVL2( DIRECT, STOREV, N, K, V, LDV, TAU, +* T, LDT ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, STOREV +* INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. +* COMPLEX T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CLARFT_LVL2 forms the triangular factor T of a complex block reflector H +*> of order n, which is defined as a product of k elementary reflectors. +*> +*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; +*> +*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. +*> +*> If STOREV = 'C', the vector which defines the elementary reflector +*> H(i) is stored in the i-th column of the array V, and +*> +*> H = I - V * T * V**H +*> +*> If STOREV = 'R', the vector which defines the elementary reflector +*> H(i) is stored in the i-th row of the array V, and +*> +*> H = I - V**H * T * V +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies the order in which the elementary reflectors are +*> multiplied to form the block reflector: +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Specifies how the vectors which define the elementary +*> reflectors are stored (see also Further Details): +*> = 'C': columnwise +*> = 'R': rowwise +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the block reflector H. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the triangular factor T (= the number of +*> elementary reflectors). K >= 1. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is COMPLEX array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,N) if STOREV = 'R' +*> The matrix V. See further details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is COMPLEX array, dimension (K) +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is COMPLEX array, dimension (LDT,K) +*> The k by k triangular factor T of the block reflector. +*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is +*> lower triangular. The rest of the array is not used. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup larft +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CLARFT_LVL2( DIRECT, STOREV, N, K, V, LDV, TAU, + $ T, LDT ) +* +* -- 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 DIRECT, STOREV + INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. + COMPLEX T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ONE, ZERO + PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), + $ ZERO = ( 0.0E+0, 0.0E+0 ) ) +* .. +* .. Local Scalars .. + INTEGER I, J, PREVLASTV, LASTV +* .. +* .. External Subroutines .. + EXTERNAL CGEMM, CGEMV, CTRMV +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( LSAME( DIRECT, 'F' ) ) THEN + PREVLASTV = N + DO I = 1, K + PREVLASTV = MAX( PREVLASTV, I ) + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = 1, I + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * CONJG( V( I , J ) ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) +* + CALL CGEMV( 'Conjugate transpose', J-I, I-1, + $ -TAU( I ), V( I+1, 1 ), LDV, + $ V( I+1, I ), 1, + $ ONE, T( 1, I ), 1 ) + ELSE +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( J , I ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H +* + CALL CGEMM( 'N', 'C', I-1, 1, J-I, -TAU( I ), + $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, + $ ONE, T( 1, I ), LDT ) + END IF +* +* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) +* + CALL CTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, + $ T, + $ LDT, T( 1, I ), 1 ) + T( I, I ) = TAU( I ) + IF( I.GT.1 ) THEN + PREVLASTV = MAX( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + END DO + ELSE + PREVLASTV = 1 + DO I = K, 1, -1 + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = I, K + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( I.LT.K ) THEN + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * CONJG( V( N-K+I , J ) ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) +* + CALL CGEMV( 'Conjugate transpose', N-K+I-J, K-I, + $ -TAU( I ), V( J, I+1 ), LDV, V( J, I ), + $ 1, ONE, T( I+1, I ), 1 ) + ELSE +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( J, N-K+I ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H +* + CALL CGEMM( 'N', 'C', K-I, 1, N-K+I-J, + $ -TAU( I ), + $ V( I+1, J ), LDV, V( I, J ), LDV, + $ ONE, T( I+1, I ), LDT ) + END IF +* +* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) +* + CALL CTRMV( 'Lower', 'No transpose', 'Non-unit', + $ K-I, + $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) + IF( I.GT.1 ) THEN + PREVLASTV = MIN( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + T( I, I ) = TAU( I ) + END IF + END DO + END IF + RETURN +* +* End of CLARFT_LVL2 +* + END diff --git a/lapack-netlib/SRC/dlarft.f b/lapack-netlib/SRC/dlarft.f index c27bb1a806..fa2ea0d134 100644 --- a/lapack-netlib/SRC/dlarft.f +++ b/lapack-netlib/SRC/dlarft.f @@ -5,7 +5,6 @@ * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * -*> \htmlonly *> Download DLARFT + dependencies *> *> [TGZ] @@ -13,7 +12,6 @@ *> [ZIP] *> *> [TXT] -*> \endhtmlonly * * Definition: * =========== @@ -161,6 +159,7 @@ * ===================================================================== RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, $ TAU, T, LDT ) + IMPLICIT NONE * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- @@ -183,7 +182,7 @@ RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, * * .. Local Scalars .. * - INTEGER I,J,L + INTEGER I,J,L,NX LOGICAL QR,LQ,QL,DIRF,COLV * * .. External Subroutines .. @@ -193,7 +192,8 @@ RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, * .. External Functions.. * LOGICAL LSAME - EXTERNAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV * * The general scheme used is inspired by the approach inside DGEQRT3 * which was (at the time of writing this code): @@ -215,6 +215,14 @@ RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, RETURN END IF * +* Determine when to cross over into the level 2 based implementation +* + NX = ILAENV(3, "DLARFT", DIRECT // STOREV, N, K, -1, -1) + IF(K.LT.NX) THEN + CALL DLARFT_LVL2(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) + RETURN + END IF +* * Beginning of executable statements * L = K / 2 diff --git a/lapack-netlib/SRC/dlarft_lvl2.f b/lapack-netlib/SRC/dlarft_lvl2.f new file mode 100644 index 0000000000..9614df466d --- /dev/null +++ b/lapack-netlib/SRC/dlarft_lvl2.f @@ -0,0 +1,326 @@ +*> \brief \b DLARFT_LVL2: Level 2 BLAS version for terminating case of DLARFT. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> Download DLARFT_LVL2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +* +* Definition: +* =========== +* +* SUBROUTINE DLARFT_LVL2( DIRECT, STOREV, N, K, V, LDV, TAU, +* T, LDT ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, STOREV +* INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARFT_LVL2 forms the triangular factor T of a real block reflector H +*> of order n, which is defined as a product of k elementary reflectors. +*> +*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; +*> +*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. +*> +*> If STOREV = 'C', the vector which defines the elementary reflector +*> H(i) is stored in the i-th column of the array V, and +*> +*> H = I - V * T * V**T +*> +*> If STOREV = 'R', the vector which defines the elementary reflector +*> H(i) is stored in the i-th row of the array V, and +*> +*> H = I - V**T * T * V +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies the order in which the elementary reflectors are +*> multiplied to form the block reflector: +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Specifies how the vectors which define the elementary +*> reflectors are stored (see also Further Details): +*> = 'C': columnwise +*> = 'R': rowwise +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the block reflector H. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the triangular factor T (= the number of +*> elementary reflectors). K >= 1. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is DOUBLE PRECISION array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,N) if STOREV = 'R' +*> The matrix V. See further details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is DOUBLE PRECISION array, dimension (K) +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is DOUBLE PRECISION array, dimension (LDT,K) +*> The k by k triangular factor T of the block reflector. +*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is +*> lower triangular. The rest of the array is not used. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup larft +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLARFT_LVL2( DIRECT, STOREV, N, K, V, LDV, TAU, + $ T, LDT ) +* +* -- 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 DIRECT, STOREV + INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J, PREVLASTV, LASTV +* .. +* .. External Subroutines .. + EXTERNAL DGEMV, DTRMV +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( LSAME( DIRECT, 'F' ) ) THEN + PREVLASTV = N + DO I = 1, K + PREVLASTV = MAX( I, PREVLASTV ) + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = 1, I + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( I , J ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) +* + CALL DGEMV( 'Transpose', J-I, I-1, -TAU( I ), + $ V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE, + $ T( 1, I ), 1 ) + ELSE +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( J , I ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T +* + CALL DGEMV( 'No transpose', I-1, J-I, -TAU( I ), + $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, ONE, + $ T( 1, I ), 1 ) + END IF +* +* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) +* + CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, + $ T, + $ LDT, T( 1, I ), 1 ) + T( I, I ) = TAU( I ) + IF( I.GT.1 ) THEN + PREVLASTV = MAX( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + END DO + ELSE + PREVLASTV = 1 + DO I = K, 1, -1 + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = I, K + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( I.LT.K ) THEN + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( N-K+I , J ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) +* + CALL DGEMV( 'Transpose', N-K+I-J, K-I, + $ -TAU( I ), + $ V( J, I+1 ), LDV, V( J, I ), 1, ONE, + $ T( I+1, I ), 1 ) + ELSE +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( J, N-K+I ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T +* + CALL DGEMV( 'No transpose', K-I, N-K+I-J, + $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV, + $ ONE, T( I+1, I ), 1 ) + END IF +* +* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) +* + CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', + $ K-I, + $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) + IF( I.GT.1 ) THEN + PREVLASTV = MIN( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + T( I, I ) = TAU( I ) + END IF + END DO + END IF + RETURN +* +* End of DLARFT_LVL2 +* + END diff --git a/lapack-netlib/SRC/ilaenv.f b/lapack-netlib/SRC/ilaenv.f index e74a2b35ec..e108108d7f 100644 --- a/lapack-netlib/SRC/ilaenv.f +++ b/lapack-netlib/SRC/ilaenv.f @@ -5,7 +5,6 @@ * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * -*> \htmlonly *> Download ILAENV + dependencies *> *> [TGZ] @@ -13,7 +12,6 @@ *> [ZIP] *> *> [TXT] -*> \endhtmlonly * * Definition: * =========== @@ -159,6 +157,7 @@ *> * ===================================================================== INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) + IMPLICIT NONE * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- @@ -667,6 +666,10 @@ INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) IF( C3.EQ.'HD3' ) THEN NX = 128 END IF + ELSE IF( C2.EQ.'LA' ) THEN + IF( C3.EQ.'RFT' ) THEN + NX = 64 + END IF END IF ILAENV = NX RETURN diff --git a/lapack-netlib/SRC/slarft.f b/lapack-netlib/SRC/slarft.f index ad3a4d924c..3e0eac751e 100644 --- a/lapack-netlib/SRC/slarft.f +++ b/lapack-netlib/SRC/slarft.f @@ -5,7 +5,6 @@ * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * -*> \htmlonly *> Download SLARFT + dependencies *> *> [TGZ] @@ -13,7 +12,6 @@ *> [ZIP] *> *> [TXT] -*> \endhtmlonly * * Definition: * =========== @@ -161,6 +159,7 @@ * ===================================================================== RECURSIVE SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, $ TAU, T, LDT ) + IMPLICIT NONE * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- @@ -183,7 +182,7 @@ RECURSIVE SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, * * .. Local Scalars .. * - INTEGER I,J,L + INTEGER I,J,L,NX LOGICAL QR,LQ,QL,DIRF,COLV * * .. External Subroutines .. @@ -193,7 +192,8 @@ RECURSIVE SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, * .. External Functions.. * LOGICAL LSAME - EXTERNAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV * * The general scheme used is inspired by the approach inside DGEQRT3 * which was (at the time of writing this code): @@ -215,6 +215,14 @@ RECURSIVE SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, RETURN END IF * +* Determine when to cross over into the level 2 based implementation +* + NX = ILAENV(3, "SLARFT", DIRECT // STOREV, N, K, -1, -1) + IF(K.LT.NX) THEN + CALL SLARFT_LVL2(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) + RETURN + END IF +* * Beginning of executable statements * L = K / 2 diff --git a/lapack-netlib/SRC/slarft_lvl2.f b/lapack-netlib/SRC/slarft_lvl2.f new file mode 100644 index 0000000000..7107a91d5d --- /dev/null +++ b/lapack-netlib/SRC/slarft_lvl2.f @@ -0,0 +1,326 @@ +*> \brief \b SLARFT_LVL2: Level 2 BLAS version for terminating case of SLARFT. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> Download SLARFT_LVL2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +* +* Definition: +* =========== +* +* SUBROUTINE SLARFT_LVL2( DIRECT, STOREV, N, K, V, LDV, TAU, +* T, LDT ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, STOREV +* INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. +* REAL T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLARFT_LVL2 forms the triangular factor T of a real block reflector H +*> of order n, which is defined as a product of k elementary reflectors. +*> +*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; +*> +*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. +*> +*> If STOREV = 'C', the vector which defines the elementary reflector +*> H(i) is stored in the i-th column of the array V, and +*> +*> H = I - V * T * V**T +*> +*> If STOREV = 'R', the vector which defines the elementary reflector +*> H(i) is stored in the i-th row of the array V, and +*> +*> H = I - V**T * T * V +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies the order in which the elementary reflectors are +*> multiplied to form the block reflector: +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Specifies how the vectors which define the elementary +*> reflectors are stored (see also Further Details): +*> = 'C': columnwise +*> = 'R': rowwise +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the block reflector H. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the triangular factor T (= the number of +*> elementary reflectors). K >= 1. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is REAL array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,N) if STOREV = 'R' +*> The matrix V. See further details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is REAL array, dimension (K) +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is REAL array, dimension (LDT,K) +*> The k by k triangular factor T of the block reflector. +*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is +*> lower triangular. The rest of the array is not used. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup larft +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE SLARFT_LVL2( DIRECT, STOREV, N, K, V, LDV, TAU, + $ T, LDT ) +* +* -- 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 DIRECT, STOREV + INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. + REAL T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, ZERO + PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J, PREVLASTV, LASTV +* .. +* .. External Subroutines .. + EXTERNAL SGEMV, STRMV +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( LSAME( DIRECT, 'F' ) ) THEN + PREVLASTV = N + DO I = 1, K + PREVLASTV = MAX( I, PREVLASTV ) + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = 1, I + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( I , J ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) +* + CALL SGEMV( 'Transpose', J-I, I-1, -TAU( I ), + $ V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE, + $ T( 1, I ), 1 ) + ELSE +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( J , I ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T +* + CALL SGEMV( 'No transpose', I-1, J-I, -TAU( I ), + $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, + $ ONE, T( 1, I ), 1 ) + END IF +* +* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) +* + CALL STRMV( 'Upper', 'No transpose', 'Non-unit', I-1, + $ T, + $ LDT, T( 1, I ), 1 ) + T( I, I ) = TAU( I ) + IF( I.GT.1 ) THEN + PREVLASTV = MAX( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + END DO + ELSE + PREVLASTV = 1 + DO I = K, 1, -1 + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = I, K + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( I.LT.K ) THEN + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( N-K+I , J ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) +* + CALL SGEMV( 'Transpose', N-K+I-J, K-I, + $ -TAU( I ), + $ V( J, I+1 ), LDV, V( J, I ), 1, ONE, + $ T( I+1, I ), 1 ) + ELSE +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( J, N-K+I ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T +* + CALL SGEMV( 'No transpose', K-I, N-K+I-J, + $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV, + $ ONE, T( I+1, I ), 1 ) + END IF +* +* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) +* + CALL STRMV( 'Lower', 'No transpose', 'Non-unit', + $ K-I, + $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) + IF( I.GT.1 ) THEN + PREVLASTV = MIN( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + T( I, I ) = TAU( I ) + END IF + END DO + END IF + RETURN +* +* End of SLARFT_LVL2 +* + END diff --git a/lapack-netlib/SRC/zlarft.f b/lapack-netlib/SRC/zlarft.f index 900795afad..efd52037d3 100644 --- a/lapack-netlib/SRC/zlarft.f +++ b/lapack-netlib/SRC/zlarft.f @@ -5,7 +5,6 @@ * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * -*> \htmlonly *> Download ZLARFT + dependencies *> *> [TGZ] @@ -13,7 +12,6 @@ *> [ZIP] *> *> [TXT] -*> \endhtmlonly * * Definition: * =========== @@ -161,6 +159,7 @@ * ===================================================================== RECURSIVE SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, $ TAU, T, LDT ) + IMPLICIT NONE * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- @@ -179,11 +178,12 @@ RECURSIVE SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, * .. Parameters .. * COMPLEX*16 ONE, NEG_ONE, ZERO - PARAMETER(ONE=1.0D+0, ZERO = 0.0D+0, NEG_ONE=-1.0D+0) + PARAMETER(ONE=(1.0D+0,0.0D+0), ZERO = (0.0D+0,0.0D+0), + $ NEG_ONE=(-1.0D+0,0.0D+0)) * * .. Local Scalars .. * - INTEGER I,J,L + INTEGER I,J,L,NX LOGICAL QR,LQ,QL,DIRF,COLV * * .. External Subroutines .. @@ -193,7 +193,8 @@ RECURSIVE SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, * .. External Functions.. * LOGICAL LSAME - EXTERNAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV * * .. Intrinsic Functions.. * @@ -219,6 +220,14 @@ RECURSIVE SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, RETURN END IF * +* Determine when to cross over into the level 2 based implementation +* + NX = ILAENV(3, "ZLARFT", DIRECT // STOREV, N, K, -1, -1) + IF(K.LT.NX) THEN + CALL ZLARFT_LVL2(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) + RETURN + END IF +* * Beginning of executable statements * L = K / 2 diff --git a/lapack-netlib/SRC/zlarft_lvl2.f b/lapack-netlib/SRC/zlarft_lvl2.f new file mode 100644 index 0000000000..808c7fdb25 --- /dev/null +++ b/lapack-netlib/SRC/zlarft_lvl2.f @@ -0,0 +1,327 @@ +*> \brief \b ZLARFT_LVL2: Level 2 BLAS version for terminating case of ZLARFT. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> Download ZLARFT_LVL2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +* +* Definition: +* =========== +* +* SUBROUTINE ZLARFT_LVL2( DIRECT, STOREV, N, K, V, LDV, TAU, +* T, LDT ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, STOREV +* INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. +* COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLARFT_LVL2 forms the triangular factor T of a complex block reflector H +*> of order n, which is defined as a product of k elementary reflectors. +*> +*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; +*> +*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. +*> +*> If STOREV = 'C', the vector which defines the elementary reflector +*> H(i) is stored in the i-th column of the array V, and +*> +*> H = I - V * T * V**H +*> +*> If STOREV = 'R', the vector which defines the elementary reflector +*> H(i) is stored in the i-th row of the array V, and +*> +*> H = I - V**H * T * V +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies the order in which the elementary reflectors are +*> multiplied to form the block reflector: +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Specifies how the vectors which define the elementary +*> reflectors are stored (see also Further Details): +*> = 'C': columnwise +*> = 'R': rowwise +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the block reflector H. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the triangular factor T (= the number of +*> elementary reflectors). K >= 1. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is COMPLEX*16 array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,N) if STOREV = 'R' +*> The matrix V. See further details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is COMPLEX*16 array, dimension (K) +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is COMPLEX*16 array, dimension (LDT,K) +*> The k by k triangular factor T of the block reflector. +*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is +*> lower triangular. The rest of the array is not used. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup larft +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZLARFT_LVL2( DIRECT, STOREV, N, K, V, LDV, TAU, + $ T, LDT ) +* +* -- 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 DIRECT, STOREV + INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. + COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ONE, ZERO + PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), + $ ZERO = ( 0.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + INTEGER I, J, PREVLASTV, LASTV +* .. +* .. External Subroutines .. + EXTERNAL ZGEMV, ZTRMV, ZGEMM +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( LSAME( DIRECT, 'F' ) ) THEN + PREVLASTV = N + DO I = 1, K + PREVLASTV = MAX( PREVLASTV, I ) + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = 1, I + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * CONJG( V( I , J ) ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) +* + CALL ZGEMV( 'Conjugate transpose', J-I, I-1, + $ -TAU( I ), V( I+1, 1 ), LDV, + $ V( I+1, I ), 1, ONE, T( 1, I ), 1 ) + ELSE +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( J , I ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H +* + CALL ZGEMM( 'N', 'C', I-1, 1, J-I, -TAU( I ), + $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, + $ ONE, T( 1, I ), LDT ) + END IF +* +* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) +* + CALL ZTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, + $ T, + $ LDT, T( 1, I ), 1 ) + T( I, I ) = TAU( I ) + IF( I.GT.1 ) THEN + PREVLASTV = MAX( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + END DO + ELSE + PREVLASTV = 1 + DO I = K, 1, -1 + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = I, K + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( I.LT.K ) THEN + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( LASTV, I ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * CONJG( V( N-K+I , J ) ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) +* + CALL ZGEMV( 'Conjugate transpose', N-K+I-J, K-I, + $ -TAU( I ), V( J, I+1 ), LDV, V( J, I ), + $ 1, ONE, T( I+1, I ), 1 ) + ELSE +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( I, LASTV ).NE.ZERO ) EXIT + END DO + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( J, N-K+I ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H +* + CALL ZGEMM( 'N', 'C', K-I, 1, N-K+I-J, + $ -TAU( I ), + $ V( I+1, J ), LDV, V( I, J ), LDV, + $ ONE, T( I+1, I ), LDT ) + END IF +* +* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) +* + CALL ZTRMV( 'Lower', 'No transpose', 'Non-unit', + $ K-I, + $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) + IF( I.GT.1 ) THEN + PREVLASTV = MIN( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + T( I, I ) = TAU( I ) + END IF + END DO + END IF + RETURN +* +* End of ZLARFT_LVL2 +* + END