diff --git a/lapack-netlib/SRC/zgebrd.f b/lapack-netlib/SRC/zgebrd.f index f1791c6a4..c1a6169a7 100644 --- a/lapack-netlib/SRC/zgebrd.f +++ b/lapack-netlib/SRC/zgebrd.f @@ -122,7 +122,8 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The length of the array WORK. LWORK >= max(1,M,N). +*> The length of the array WORK. +*> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= MAX(M,N), otherwise. *> For optimum performance LWORK >= (M+N)*NB, where NB *> is the optimal blocksize. *> @@ -147,7 +148,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16GEcomputational +*> \ingroup gebrd * *> \par Further Details: * ===================== @@ -223,8 +224,8 @@ * .. * .. Local Scalars .. LOGICAL LQUERY - INTEGER I, IINFO, J, LDWRKX, LDWRKY, LWKOPT, MINMN, NB, - $ NBMIN, NX, WS + INTEGER I, IINFO, J, LDWRKX, LDWRKY, LWKMIN, LWKOPT, + $ MINMN, NB, NBMIN, NX, WS * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEBD2, ZGEMM, ZLABRD @@ -241,9 +242,17 @@ * Test the input parameters * INFO = 0 - NB = MAX( 1, ILAENV( 1, 'ZGEBRD', ' ', M, N, -1, -1 ) ) - LWKOPT = ( M+N )*NB + MINMN = MIN( M, N ) + IF( MINMN.EQ.0 ) THEN + LWKMIN = 1 + LWKOPT = 1 + ELSE + LWKMIN = MAX( M, N ) + NB = MAX( 1, ILAENV( 1, 'ZGEBRD', ' ', M, N, -1, -1 ) ) + LWKOPT = ( M+N )*NB + END IF WORK( 1 ) = DBLE( LWKOPT ) +* LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 @@ -251,7 +260,7 @@ INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 - ELSE IF( LWORK.LT.MAX( 1, M, N ) .AND. .NOT.LQUERY ) THEN + ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN INFO = -10 END IF IF( INFO.LT.0 ) THEN @@ -263,7 +272,6 @@ * * Quick return if possible * - MINMN = MIN( M, N ) IF( MINMN.EQ.0 ) THEN WORK( 1 ) = 1 RETURN @@ -282,7 +290,7 @@ * Determine when to switch from blocked to unblocked code. * IF( NX.LT.MINMN ) THEN - WS = ( M+N )*NB + WS = LWKOPT IF( LWORK.LT.WS ) THEN * * Not enough work space for the optimal NB, consider using diff --git a/lapack-netlib/SRC/zgehrd.f b/lapack-netlib/SRC/zgehrd.f index e18493cf9..0f4424ded 100644 --- a/lapack-netlib/SRC/zgehrd.f +++ b/lapack-netlib/SRC/zgehrd.f @@ -89,7 +89,7 @@ *> *> \param[out] WORK *> \verbatim -*> WORK is COMPLEX*16 array, dimension (LWORK) +*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> @@ -120,7 +120,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16GEcomputational +*> \ingroup gehrd * *> \par Further Details: * ===================== @@ -173,7 +173,7 @@ INTEGER IHI, ILO, INFO, LDA, LWORK, N * .. * .. Array Arguments .. - COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) + COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== @@ -182,7 +182,7 @@ INTEGER NBMAX, LDT, TSIZE PARAMETER ( NBMAX = 64, LDT = NBMAX+1, $ TSIZE = LDT*NBMAX ) - COMPLEX*16 ZERO, ONE + COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. @@ -190,7 +190,7 @@ LOGICAL LQUERY INTEGER I, IB, IINFO, IWT, J, LDWORK, LWKOPT, NB, $ NBMIN, NH, NX - COMPLEX*16 EI + COMPLEX*16 EI * .. * .. External Subroutines .. EXTERNAL ZAXPY, ZGEHD2, ZGEMM, ZLAHR2, ZLARFB, ZTRMM, @@ -221,12 +221,18 @@ INFO = -8 END IF * + NH = IHI - ILO + 1 IF( INFO.EQ.0 ) THEN * * Compute the workspace requirements * - NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) - LWKOPT = N*NB + TSIZE + IF( NH.LE.1 ) THEN + LWKOPT = 1 + ELSE + NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, + $ -1 ) ) + LWKOPT = N*NB + TSIZE + END IF WORK( 1 ) = LWKOPT ENDIF * @@ -248,7 +254,6 @@ * * Quick return if possible * - NH = IHI - ILO + 1 IF( NH.LE.1 ) THEN WORK( 1 ) = 1 RETURN @@ -268,7 +273,7 @@ * * Determine if workspace is large enough for blocked code * - IF( LWORK.LT.N*NB+TSIZE ) THEN + IF( LWORK.LT.LWKOPT ) THEN * * Not enough workspace to use optimal NB: determine the * minimum value of NB, and reduce NB or force use of diff --git a/lapack-netlib/SRC/zgelq.f b/lapack-netlib/SRC/zgelq.f index de7c9a378..86610e801 100644 --- a/lapack-netlib/SRC/zgelq.f +++ b/lapack-netlib/SRC/zgelq.f @@ -98,7 +98,7 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. +*> The dimension of the array WORK. LWORK >= 1. *> If LWORK = -1 or -2, then a workspace query is assumed. The routine *> only calculates the sizes of the T and WORK arrays, returns these *> values as the first entries of the T and WORK arrays, and no error @@ -166,6 +166,8 @@ *> the LQ factorization. *> \endverbatim *> +*> \ingroup gelq +*> * ===================================================================== SUBROUTINE ZGELQ( M, N, A, LDA, T, TSIZE, WORK, LWORK, $ INFO ) diff --git a/lapack-netlib/SRC/zgelqf.f b/lapack-netlib/SRC/zgelqf.f index 6c295eece..e988ea818 100644 --- a/lapack-netlib/SRC/zgelqf.f +++ b/lapack-netlib/SRC/zgelqf.f @@ -93,7 +93,8 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,M). +*> The dimension of the array WORK. +*> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise. *> For optimum performance LWORK >= M*NB, where NB is the *> optimal blocksize. *> @@ -118,7 +119,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16GEcomputational +*> \ingroup gelqf * *> \par Further Details: * ===================== @@ -174,9 +175,8 @@ * Test the input arguments * INFO = 0 + K = MIN( M, N ) NB = ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) - LWKOPT = M*NB - WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 @@ -184,19 +184,25 @@ INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 - ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN - INFO = -7 + ELSE IF( .NOT.LQUERY ) THEN + IF( LWORK.LE.0 .OR. ( N.GT.0 .AND. LWORK.LT.MAX( 1, M ) ) ) + $ INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGELQF', -INFO ) RETURN ELSE IF( LQUERY ) THEN + IF( K.EQ.0 ) THEN + LWKOPT = 1 + ELSE + LWKOPT = M*NB + END IF + WORK( 1 ) = LWKOPT RETURN END IF * * Quick return if possible * - K = MIN( M, N ) IF( K.EQ.0 ) THEN WORK( 1 ) = 1 RETURN diff --git a/lapack-netlib/SRC/zgemlq.f b/lapack-netlib/SRC/zgemlq.f index 41cd1c059..11489087a 100644 --- a/lapack-netlib/SRC/zgemlq.f +++ b/lapack-netlib/SRC/zgemlq.f @@ -109,16 +109,17 @@ *> *> \param[out] WORK *> \verbatim -*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the minimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. +*> The dimension of the array WORK. LWORK >= 1. *> If LWORK = -1, then a workspace query is assumed. The routine *> only calculates the size of the WORK array, returns this -*> value as WORK(1), and no error message related to WORK +*> value as WORK(1), and no error message related to WORK *> is issued by XERBLA. *> \endverbatim *> @@ -142,7 +143,7 @@ *> *> \verbatim *> -*> These details are particular for this LAPACK implementation. Users should not +*> These details are particular for this LAPACK implementation. Users should not *> take them for granted. These details may change in the future, and are not likely *> true for another LAPACK implementation. These details are relevant if one wants *> to try to understand the code. They are not part of the interface. @@ -158,11 +159,13 @@ *> block sizes MB and NB returned by ILAENV, ZGELQ will use either *> ZLASWLQ (if the matrix is wide-and-short) or ZGELQT to compute *> the LQ factorization. -*> This version of ZGEMLQ will use either ZLAMSWLQ or ZGEMLQT to +*> This version of ZGEMLQ will use either ZLAMSWLQ or ZGEMLQT to *> multiply matrix Q by another matrix. *> Further Details in ZLAMSWLQ or ZGEMLQT. *> \endverbatim *> +*> \ingroup gemlq +*> * ===================================================================== SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, $ C, LDC, WORK, LWORK, INFO ) @@ -184,7 +187,7 @@ * .. * .. Local Scalars .. LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY - INTEGER MB, NB, LW, NBLCKS, MN + INTEGER MB, NB, LW, NBLCKS, MN, MINMNK, LWMIN * .. * .. External Functions .. LOGICAL LSAME @@ -200,7 +203,7 @@ * * Test the input arguments * - LQUERY = LWORK.EQ.-1 + LQUERY = ( LWORK.EQ.-1 ) NOTRAN = LSAME( TRANS, 'N' ) TRAN = LSAME( TRANS, 'C' ) LEFT = LSAME( SIDE, 'L' ) @@ -215,6 +218,13 @@ LW = M * MB MN = N END IF +* + MINMNK = MIN( M, N, K ) + IF( MINMNK.EQ.0 ) THEN + LWMIN = 1 + ELSE + LWMIN = MAX( 1, LW ) + END IF * IF( ( NB.GT.K ) .AND. ( MN.GT.K ) ) THEN IF( MOD( MN - K, NB - K ) .EQ. 0 ) THEN @@ -243,7 +253,7 @@ INFO = -9 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -11 - ELSE IF( ( LWORK.LT.MAX( 1, LW ) ) .AND. ( .NOT.LQUERY ) ) THEN + ELSE IF( ( LWORK.LT.LWMIN ) .AND. ( .NOT.LQUERY ) ) THEN INFO = -13 END IF * @@ -260,7 +270,7 @@ * * Quick return if possible * - IF( MIN( M, N, K ).EQ.0 ) THEN + IF( MINMNK.EQ.0 ) THEN RETURN END IF * diff --git a/lapack-netlib/SRC/zgemqr.f b/lapack-netlib/SRC/zgemqr.f index c83eaff2f..d14d74fe2 100644 --- a/lapack-netlib/SRC/zgemqr.f +++ b/lapack-netlib/SRC/zgemqr.f @@ -111,16 +111,17 @@ *> *> \param[out] WORK *> \verbatim -*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the minimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. +*> The dimension of the array WORK. LWORK >= 1. *> If LWORK = -1, then a workspace query is assumed. The routine *> only calculates the size of the WORK array, returns this -*> value as WORK(1), and no error message related to WORK +*> value as WORK(1), and no error message related to WORK *> is issued by XERBLA. *> \endverbatim *> @@ -144,7 +145,7 @@ *> *> \verbatim *> -*> These details are particular for this LAPACK implementation. Users should not +*> These details are particular for this LAPACK implementation. Users should not *> take them for granted. These details may change in the future, and are not likely *> true for another LAPACK implementation. These details are relevant if one wants *> to try to understand the code. They are not part of the interface. @@ -166,6 +167,8 @@ *> *> \endverbatim *> +*> \ingroup gemqr +*> * ===================================================================== SUBROUTINE ZGEMQR( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, $ C, LDC, WORK, LWORK, INFO ) @@ -187,7 +190,7 @@ * .. * .. Local Scalars .. LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY - INTEGER MB, NB, LW, NBLCKS, MN + INTEGER MB, NB, LW, NBLCKS, MN, MINMNK, LWMIN * .. * .. External Functions .. LOGICAL LSAME @@ -203,7 +206,7 @@ * * Test the input arguments * - LQUERY = LWORK.EQ.-1 + LQUERY = ( LWORK.EQ.-1 ) NOTRAN = LSAME( TRANS, 'N' ) TRAN = LSAME( TRANS, 'C' ) LEFT = LSAME( SIDE, 'L' ) @@ -218,6 +221,13 @@ LW = MB * NB MN = N END IF +* + MINMNK = MIN( M, N, K ) + IF( MINMNK.EQ.0 ) THEN + LWMIN = 1 + ELSE + LWMIN = MAX( 1, LW ) + END IF * IF( ( MB.GT.K ) .AND. ( MN.GT.K ) ) THEN IF( MOD( MN - K, MB - K ).EQ.0 ) THEN @@ -246,12 +256,12 @@ INFO = -9 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -11 - ELSE IF( ( LWORK.LT.MAX( 1, LW ) ) .AND. ( .NOT.LQUERY ) ) THEN + ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -13 END IF * IF( INFO.EQ.0 ) THEN - WORK( 1 ) = LW + WORK( 1 ) = LWMIN END IF * IF( INFO.NE.0 ) THEN @@ -263,7 +273,7 @@ * * Quick return if possible * - IF( MIN( M, N, K ).EQ.0 ) THEN + IF( MINMNK.EQ.0 ) THEN RETURN END IF * @@ -276,7 +286,7 @@ $ NB, C, LDC, WORK, LWORK, INFO ) END IF * - WORK( 1 ) = LW + WORK( 1 ) = LWMIN * RETURN * diff --git a/lapack-netlib/SRC/zgeqlf.f b/lapack-netlib/SRC/zgeqlf.f index 94721540c..a27612c64 100644 --- a/lapack-netlib/SRC/zgeqlf.f +++ b/lapack-netlib/SRC/zgeqlf.f @@ -88,7 +88,8 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,N). +*> The dimension of the array WORK. +*> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise. *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. *> @@ -113,7 +114,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16GEcomputational +*> \ingroup geqlf * *> \par Further Details: * ===================== @@ -188,8 +189,9 @@ END IF WORK( 1 ) = LWKOPT * - IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN - INFO = -7 + IF( .NOT.LQUERY ) THEN + IF( LWORK.LE.0 .OR. ( M.GT.0 .AND. LWORK.LT.MAX( 1, N ) ) ) + $ INFO = -7 END IF END IF * diff --git a/lapack-netlib/SRC/zgeqp3rk.f b/lapack-netlib/SRC/zgeqp3rk.f index 247a3c379..01dcce0de 100644 --- a/lapack-netlib/SRC/zgeqp3rk.f +++ b/lapack-netlib/SRC/zgeqp3rk.f @@ -428,7 +428,8 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. -*. LWORK >= N+NRHS-1 +*> LWORK >= 1, if MIN(M,N) = 0, and +*> LWORK >= N+NRHS-1, otherwise. *> For optimal performance LWORK >= NB*( N+NRHS+1 ), *> where NB is the optimal block size for ZGEQP3RK returned *> by ILAENV. Minimal block size MINNB=2. diff --git a/lapack-netlib/SRC/zgeqr.f b/lapack-netlib/SRC/zgeqr.f index 20a80d083..7df9c2403 100644 --- a/lapack-netlib/SRC/zgeqr.f +++ b/lapack-netlib/SRC/zgeqr.f @@ -99,7 +99,7 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. +*> The dimension of the array WORK. LWORK >= 1. *> If LWORK = -1 or -2, then a workspace query is assumed. The routine *> only calculates the sizes of the T and WORK arrays, returns these *> values as the first entries of the T and WORK arrays, and no error @@ -168,6 +168,8 @@ *> *> \endverbatim *> +*> \ingroup geqr +*> * ===================================================================== SUBROUTINE ZGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK, $ INFO ) @@ -188,7 +190,7 @@ * .. * .. Local Scalars .. LOGICAL LQUERY, LMINWS, MINT, MINW - INTEGER MB, NB, MINTSZ, NBLCKS + INTEGER MB, NB, MINTSZ, NBLCKS, LWMIN, LWREQ * .. * .. External Functions .. LOGICAL LSAME @@ -244,8 +246,10 @@ * * Determine if the workspace size satisfies minimal size * + LWMIN = MAX( 1, N ) + LWREQ = MAX( 1, N*NB ) LMINWS = .FALSE. - IF( ( TSIZE.LT.MAX( 1, NB*N*NBLCKS + 5 ) .OR. LWORK.LT.NB*N ) + IF( ( TSIZE.LT.MAX( 1, NB*N*NBLCKS + 5 ) .OR. LWORK.LT.LWREQ ) $ .AND. ( LWORK.GE.N ) .AND. ( TSIZE.GE.MINTSZ ) $ .AND. ( .NOT.LQUERY ) ) THEN IF( TSIZE.LT.MAX( 1, NB*N*NBLCKS + 5 ) ) THEN @@ -253,7 +257,7 @@ NB = 1 MB = M END IF - IF( LWORK.LT.NB*N ) THEN + IF( LWORK.LT.LWREQ ) THEN LMINWS = .TRUE. NB = 1 END IF @@ -268,7 +272,7 @@ ELSE IF( TSIZE.LT.MAX( 1, NB*N*NBLCKS + 5 ) $ .AND. ( .NOT.LQUERY ) .AND. ( .NOT.LMINWS ) ) THEN INFO = -6 - ELSE IF( ( LWORK.LT.MAX( 1, N*NB ) ) .AND. ( .NOT.LQUERY ) + ELSE IF( ( LWORK.LT.LWREQ ) .AND. ( .NOT.LQUERY ) $ .AND. ( .NOT.LMINWS ) ) THEN INFO = -8 END IF @@ -282,9 +286,9 @@ T( 2 ) = MB T( 3 ) = NB IF( MINW ) THEN - WORK( 1 ) = MAX( 1, N ) + WORK( 1 ) = LWMIN ELSE - WORK( 1 ) = MAX( 1, NB*N ) + WORK( 1 ) = LWREQ END IF END IF IF( INFO.NE.0 ) THEN @@ -309,7 +313,7 @@ $ LWORK, INFO ) END IF * - WORK( 1 ) = MAX( 1, NB*N ) + WORK( 1 ) = LWREQ * RETURN * diff --git a/lapack-netlib/SRC/zgeqrfp.f b/lapack-netlib/SRC/zgeqrfp.f index 73bcde667..3562de36e 100644 --- a/lapack-netlib/SRC/zgeqrfp.f +++ b/lapack-netlib/SRC/zgeqrfp.f @@ -97,7 +97,8 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,N). +*> The dimension of the array WORK. +*> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise. *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. *> @@ -122,7 +123,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16GEcomputational +*> \ingroup geqrfp * *> \par Further Details: * ===================== @@ -162,8 +163,8 @@ * * .. Local Scalars .. LOGICAL LQUERY - INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB, - $ NBMIN, NX + INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKMIN, LWKOPT, + $ NB, NBMIN, NX * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEQR2P, ZLARFB, ZLARFT @@ -181,8 +182,16 @@ * INFO = 0 NB = ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) - LWKOPT = N*NB + K = MIN( M, N ) + IF( K.EQ.0 ) THEN + LWKMIN = 1 + LWKOPT = 1 + ELSE + LWKMIN = N + LWKOPT = N*NB + END IF WORK( 1 ) = LWKOPT +* LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 @@ -190,7 +199,7 @@ INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 - ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN + ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN @@ -202,7 +211,6 @@ * * Quick return if possible * - K = MIN( M, N ) IF( K.EQ.0 ) THEN WORK( 1 ) = 1 RETURN @@ -210,7 +218,7 @@ * NBMIN = 2 NX = 0 - IWS = N + IWS = LWKMIN IF( NB.GT.1 .AND. NB.LT.K ) THEN * * Determine when to cross over from blocked to unblocked code. diff --git a/lapack-netlib/SRC/zgesvj.f b/lapack-netlib/SRC/zgesvj.f index 6cd2335f2..2be45d826 100644 --- a/lapack-netlib/SRC/zgesvj.f +++ b/lapack-netlib/SRC/zgesvj.f @@ -200,23 +200,25 @@ *> \verbatim *> LDV is INTEGER *> The leading dimension of the array V, LDV >= 1. -*> If JOBV = 'V', then LDV >= max(1,N). -*> If JOBV = 'A', then LDV >= max(1,MV) . +*> If JOBV = 'V', then LDV >= MAX(1,N). +*> If JOBV = 'A', then LDV >= MAX(1,MV) . *> \endverbatim *> *> \param[in,out] CWORK *> \verbatim -*> CWORK is COMPLEX*16 array, dimension (max(1,LWORK)) +*> CWORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> Used as workspace. -*> If on entry LWORK = -1, then a workspace query is assumed and -*> no computation is done; CWORK(1) is set to the minial (and optimal) -*> length of CWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER. -*> Length of CWORK, LWORK >= M+N. +*> Length of CWORK. +*> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M+N, otherwise. +*> +*> If on entry LWORK = -1, then a workspace query is assumed and +*> no computation is done; CWORK(1) is set to the minial (and optimal) +*> length of CWORK. *> \endverbatim *> *> \param[in,out] RWORK @@ -247,15 +249,17 @@ *> RWORK(6) = the largest absolute value over all sines of the *> Jacobi rotation angles in the last sweep. It can be *> useful for a post festum analysis. -*> If on entry LRWORK = -1, then a workspace query is assumed and -*> no computation is done; RWORK(1) is set to the minial (and optimal) -*> length of RWORK. *> \endverbatim *> *> \param[in] LRWORK *> \verbatim *> LRWORK is INTEGER -*> Length of RWORK, LRWORK >= MAX(6,N). +*> Length of RWORK. +*> LRWORK >= 1, if MIN(M,N) = 0, and LRWORK >= MAX(6,N), otherwise. +*> +*> If on entry LRWORK = -1, then a workspace query is assumed and +*> no computation is done; RWORK(1) is set to the minial (and optimal) +*> length of RWORK. *> \endverbatim *> *> \param[out] INFO @@ -276,7 +280,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16GEcomputational +*> \ingroup gesvj * *> \par Further Details: * ===================== @@ -367,23 +371,25 @@ * * .. Local Parameters .. DOUBLE PRECISION ZERO, HALF, ONE - PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0) - COMPLEX*16 CZERO, CONE - PARAMETER ( CZERO = (0.0D0, 0.0D0), CONE = (1.0D0, 0.0D0) ) - INTEGER NSWEEP - PARAMETER ( NSWEEP = 30 ) + PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0) + COMPLEX*16 CZERO, CONE + PARAMETER ( CZERO = (0.0D0, 0.0D0), CONE = (1.0D0, 0.0D0) ) + INTEGER NSWEEP + PARAMETER ( NSWEEP = 30 ) * .. * .. Local Scalars .. - COMPLEX*16 AAPQ, OMPQ - DOUBLE PRECISION AAPP, AAPP0, AAPQ1, AAQQ, APOAQ, AQOAP, BIG, - $ BIGTHETA, CS, CTOL, EPSLN, MXAAPQ, - $ MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, ROOTTOL, - $ SKL, SFMIN, SMALL, SN, T, TEMP1, THETA, THSIGN, TOL - INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, - $ ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, N2, N34, - $ N4, NBL, NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND - LOGICAL APPLV, GOSCALE, LOWER, LQUERY, LSVEC, NOSCALE, ROTOK, - $ RSVEC, UCTOL, UPPER + COMPLEX*16 AAPQ, OMPQ + DOUBLE PRECISION AAPP, AAPP0, AAPQ1, AAQQ, APOAQ, AQOAP, BIG, + $ BIGTHETA, CS, CTOL, EPSLN, MXAAPQ, + $ MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, ROOTTOL, + $ SKL, SFMIN, SMALL, SN, T, TEMP1, THETA, THSIGN, + $ TOL + INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, + $ ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, N2, N34, + $ N4, NBL, NOTROT, p, PSKIPPED, q, ROWSKIP, + $ SWBAND, MINMN, LWMIN, LRWMIN + LOGICAL APPLV, GOSCALE, LOWER, LQUERY, LSVEC, NOSCALE, + $ ROTOK, RSVEC, UCTOL, UPPER * .. * .. * .. Intrinsic Functions .. @@ -422,7 +428,16 @@ UPPER = LSAME( JOBA, 'U' ) LOWER = LSAME( JOBA, 'L' ) * - LQUERY = ( LWORK .EQ. -1 ) .OR. ( LRWORK .EQ. -1 ) + MINMN = MIN( M, N ) + IF( MINMN.EQ.0 ) THEN + LWMIN = 1 + LRWMIN = 1 + ELSE + LWMIN = M+N + LRWMIN = MAX( 6, N ) + END IF +* + LQUERY = ( LWORK.EQ.-1 ) .OR. ( LRWORK.EQ.-1 ) IF( .NOT.( UPPER .OR. LOWER .OR. LSAME( JOBA, 'G' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( LSVEC .OR. UCTOL .OR. LSAME( JOBU, 'N' ) ) ) THEN @@ -442,9 +457,9 @@ INFO = -11 ELSE IF( UCTOL .AND. ( RWORK( 1 ).LE.ONE ) ) THEN INFO = -12 - ELSE IF( ( LWORK.LT.( M+N ) ) .AND. ( .NOT.LQUERY ) ) THEN + ELSE IF( LWORK.LT.LWMIN .AND. ( .NOT.LQUERY ) ) THEN INFO = -13 - ELSE IF( ( LRWORK.LT.MAX( N, 6 ) ) .AND. ( .NOT.LQUERY ) ) THEN + ELSE IF( LRWORK.LT.LRWMIN .AND. ( .NOT.LQUERY ) ) THEN INFO = -15 ELSE INFO = 0 @@ -454,15 +469,15 @@ IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGESVJ', -INFO ) RETURN - ELSE IF ( LQUERY ) THEN - CWORK(1) = M + N - RWORK(1) = MAX( N, 6 ) + ELSE IF( LQUERY ) THEN + CWORK( 1 ) = LWMIN + RWORK( 1 ) = LRWMIN RETURN END IF * * #:) Quick return for void matrix * - IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )RETURN + IF( MINMN.EQ.0 ) RETURN * * Set numerical parameters * The stopping criterion for Jacobi rotations is diff --git a/lapack-netlib/SRC/zgetri.f b/lapack-netlib/SRC/zgetri.f index 41782841c..f3806a77c 100644 --- a/lapack-netlib/SRC/zgetri.f +++ b/lapack-netlib/SRC/zgetri.f @@ -107,7 +107,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16GEcomputational +*> \ingroup getri * * ===================================================================== SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) @@ -152,7 +152,7 @@ * INFO = 0 NB = ILAENV( 1, 'ZGETRI', ' ', N, -1, -1, -1 ) - LWKOPT = N*NB + LWKOPT = MAX( 1, N*NB ) WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( N.LT.0 ) THEN diff --git a/lapack-netlib/SRC/zgetsls.f b/lapack-netlib/SRC/zgetsls.f index 17c6d5146..26311c611 100644 --- a/lapack-netlib/SRC/zgetsls.f +++ b/lapack-netlib/SRC/zgetsls.f @@ -127,7 +127,7 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. +*> The dimension of the array WORK. LWORK >= 1. *> If LWORK = -1 or -2, then a workspace query is assumed. *> If LWORK = -1, the routine calculates optimal size of WORK for the *> optimal performance and returns this value in WORK(1). @@ -154,7 +154,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16GEsolve +*> \ingroup getsls * * ===================================================================== SUBROUTINE ZGETSLS( TRANS, M, N, NRHS, A, LDA, B, LDB, @@ -192,7 +192,7 @@ * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, ZLANGE - EXTERNAL LSAME, DLABAD, DLAMCH, ZLANGE + EXTERNAL LSAME, DLAMCH, ZLANGE * .. * .. External Subroutines .. EXTERNAL ZGEQR, ZGEMQR, ZLASCL, ZLASET, @@ -229,7 +229,10 @@ * * Determine the optimum and minimum LWORK * - IF( M.GE.N ) THEN + IF( MIN( M, N, NRHS ).EQ.0 ) THEN + WSIZEO = 1 + WSIZEM = 1 + ELSE IF( M.GE.N ) THEN CALL ZGEQR( M, N, A, LDA, TQ, -1, WORKQ, -1, INFO2 ) TSZO = INT( TQ( 1 ) ) LWO = INT( WORKQ( 1 ) ) @@ -297,7 +300,6 @@ * SMLNUM = DLAMCH( 'S' ) / DLAMCH( 'P' ) BIGNUM = ONE / SMLNUM - CALL DLABAD( SMLNUM, BIGNUM ) * * Scale A, B if max element outside range [SMLNUM,BIGNUM] * diff --git a/lapack-netlib/SRC/zgetsqrhrt.f b/lapack-netlib/SRC/zgetsqrhrt.f index 5f0167937..e7ce993aa 100644 --- a/lapack-netlib/SRC/zgetsqrhrt.f +++ b/lapack-netlib/SRC/zgetsqrhrt.f @@ -131,13 +131,15 @@ *> \param[in] LWORK *> \verbatim *> The dimension of the array WORK. -*> LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ), +*> If MIN(M,N) = 0, LWORK >= 1, else +*> LWORK >= MAX( 1, LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ), *> where *> NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)), *> NB1LOCAL = MIN(NB1,N). *> LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL, *> LW1 = NB1LOCAL * N, -*> LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ), +*> LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ). +*> *> If LWORK = -1, then a workspace query is assumed. *> The routine only calculates the optimal size of the WORK *> array, returns this value as the first entry of the WORK @@ -160,7 +162,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup comlpex16OTHERcomputational +*> \ingroup getsqrhrt * *> \par Contributors: * ================== @@ -212,7 +214,7 @@ * Test the input arguments * INFO = 0 - LQUERY = LWORK.EQ.-1 + LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. M.LT.N ) THEN @@ -225,7 +227,7 @@ INFO = -5 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -7 - ELSE IF( LDT.LT.MAX( 1, MIN( NB2, N ) ) ) THEN + ELSE IF( LDT.LT.MAX( 1, MIN( NB2, N ) ) ) THEN INFO = -9 ELSE * @@ -263,8 +265,9 @@ LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ) * LWORKOPT = MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ) + LWORKOPT = MAX( 1, LWORKOPT ) * - IF( ( LWORK.LT.MAX( 1, LWORKOPT ) ).AND.(.NOT.LQUERY) ) THEN + IF( LWORK.LT.LWORKOPT .AND. .NOT.LQUERY ) THEN INFO = -11 END IF * diff --git a/lapack-netlib/SRC/zgges3.f b/lapack-netlib/SRC/zgges3.f index 8b3e44f88..8235c2543 100644 --- a/lapack-netlib/SRC/zgges3.f +++ b/lapack-netlib/SRC/zgges3.f @@ -215,7 +215,8 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. +*> The dimension of the array WORK. LWORK >= MAX(1,2*N) +*> For good performance, LWORK must generally be larger. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns @@ -260,7 +261,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16GEeigen +*> \ingroup gges3 * * ===================================================================== SUBROUTINE ZGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, @@ -300,7 +301,8 @@ LOGICAL CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL, $ LQUERY, WANTST INTEGER I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, - $ ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK, LWKOPT + $ ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK, LWKOPT, + $ LWKMIN DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL, $ PVSR, SMLNUM * .. @@ -309,9 +311,8 @@ DOUBLE PRECISION DIF( 2 ) * .. * .. External Subroutines .. - EXTERNAL DLABAD, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHD3, - $ ZLAQZ0, ZLACPY, ZLASCL, ZLASET, ZTGSEN, ZUNGQR, - $ ZUNMQR + EXTERNAL XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHD3, ZLAQZ0, + $ ZLACPY, ZLASCL, ZLASET, ZTGSEN, ZUNGQR, ZUNMQR * .. * .. External Functions .. LOGICAL LSAME @@ -353,6 +354,8 @@ * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) + LWKMIN = MAX( 1, 2*N ) +* IF( IJOBVL.LE.0 ) THEN INFO = -1 ELSE IF( IJOBVR.LE.0 ) THEN @@ -369,7 +372,7 @@ INFO = -14 ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN INFO = -16 - ELSE IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN + ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN INFO = -18 END IF * @@ -377,28 +380,32 @@ * IF( INFO.EQ.0 ) THEN CALL ZGEQRF( N, N, B, LDB, WORK, WORK, -1, IERR ) - LWKOPT = MAX( 1, N + INT ( WORK( 1 ) ) ) + LWKOPT = MAX( LWKMIN, N + INT( WORK( 1 ) ) ) CALL ZUNMQR( 'L', 'C', N, N, N, B, LDB, WORK, A, LDA, WORK, $ -1, IERR ) - LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) ) + LWKOPT = MAX( LWKOPT, N + INT( WORK( 1 ) ) ) IF( ILVSL ) THEN CALL ZUNGQR( N, N, N, VSL, LDVSL, WORK, WORK, -1, IERR ) LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) ) END IF CALL ZGGHD3( JOBVSL, JOBVSR, N, 1, N, A, LDA, B, LDB, VSL, $ LDVSL, VSR, LDVSR, WORK, -1, IERR ) - LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) ) + LWKOPT = MAX( LWKOPT, N + INT( WORK( 1 ) ) ) CALL ZLAQZ0( 'S', JOBVSL, JOBVSR, N, 1, N, A, LDA, B, LDB, $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, -1, $ RWORK, 0, IERR ) - LWKOPT = MAX( LWKOPT, INT ( WORK( 1 ) ) ) + LWKOPT = MAX( LWKOPT, INT( WORK( 1 ) ) ) IF( WANTST ) THEN CALL ZTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB, $ ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, SDIM, $ PVSL, PVSR, DIF, WORK, -1, IDUM, 1, IERR ) - LWKOPT = MAX( LWKOPT, INT ( WORK( 1 ) ) ) + LWKOPT = MAX( LWKOPT, INT( WORK( 1 ) ) ) + END IF + IF( N.EQ.0 ) THEN + WORK( 1 ) = 1 + ELSE + WORK( 1 ) = DCMPLX( LWKOPT ) END IF - WORK( 1 ) = DCMPLX( LWKOPT ) END IF * IF( INFO.NE.0 ) THEN @@ -420,7 +427,6 @@ EPS = DLAMCH( 'P' ) SMLNUM = DLAMCH( 'S' ) BIGNUM = ONE / SMLNUM - CALL DLABAD( SMLNUM, BIGNUM ) SMLNUM = SQRT( SMLNUM ) / EPS BIGNUM = ONE / SMLNUM * diff --git a/lapack-netlib/SRC/zggev3.f b/lapack-netlib/SRC/zggev3.f index 2d6c74582..0cc073470 100644 --- a/lapack-netlib/SRC/zggev3.f +++ b/lapack-netlib/SRC/zggev3.f @@ -174,7 +174,8 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. +*> The dimension of the array WORK. LWORK >= MAX(1,2*N). +*> For good performance, LWORK must generally be larger. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns @@ -208,7 +209,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16GEeigen +*> \ingroup ggev3 * * ===================================================================== SUBROUTINE ZGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, @@ -243,7 +244,7 @@ CHARACTER CHTEMP INTEGER ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, ILO, $ IN, IRIGHT, IROWS, IRWRK, ITAU, IWRK, JC, JR, - $ LWKOPT + $ LWKMIN, LWKOPT DOUBLE PRECISION ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, $ SMLNUM, TEMP COMPLEX*16 X @@ -252,9 +253,8 @@ LOGICAL LDUMMA( 1 ) * .. * .. External Subroutines .. - EXTERNAL DLABAD, XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHD3, - $ ZLAQZ0, ZLACPY, ZLASCL, ZLASET, ZTGEVC, ZUNGQR, - $ ZUNMQR + EXTERNAL XERBLA, ZGEQRF, ZGGBAK, ZGGBAL, ZGGHD3, ZLAQZ0, + $ ZLACPY, ZLASCL, ZLASET, ZTGEVC, ZUNGQR, ZUNMQR * .. * .. External Functions .. LOGICAL LSAME @@ -301,6 +301,7 @@ * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) + LWKMIN = MAX( 1, 2*N ) IF( IJOBVL.LE.0 ) THEN INFO = -1 ELSE IF( IJOBVR.LE.0 ) THEN @@ -315,7 +316,7 @@ INFO = -11 ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN INFO = -13 - ELSE IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN + ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN INFO = -15 END IF * @@ -323,7 +324,7 @@ * IF( INFO.EQ.0 ) THEN CALL ZGEQRF( N, N, B, LDB, WORK, WORK, -1, IERR ) - LWKOPT = MAX( 1, N+INT( WORK( 1 ) ) ) + LWKOPT = MAX( LWKMIN, N+INT( WORK( 1 ) ) ) CALL ZUNMQR( 'L', 'C', N, N, N, B, LDB, WORK, A, LDA, WORK, $ -1, IERR ) LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) ) @@ -348,7 +349,11 @@ $ RWORK, 0, IERR ) LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) ) END IF - WORK( 1 ) = DCMPLX( LWKOPT ) + IF( N.EQ.0 ) THEN + WORK( 1 ) = 1 + ELSE + WORK( 1 ) = DCMPLX( LWKOPT ) + END IF END IF * IF( INFO.NE.0 ) THEN @@ -368,7 +373,6 @@ EPS = DLAMCH( 'E' )*DLAMCH( 'B' ) SMLNUM = DLAMCH( 'S' ) BIGNUM = ONE / SMLNUM - CALL DLABAD( SMLNUM, BIGNUM ) SMLNUM = SQRT( SMLNUM ) / EPS BIGNUM = ONE / SMLNUM * diff --git a/lapack-netlib/SRC/zgghd3.f b/lapack-netlib/SRC/zgghd3.f index b29cdc70a..08343688d 100644 --- a/lapack-netlib/SRC/zgghd3.f +++ b/lapack-netlib/SRC/zgghd3.f @@ -176,14 +176,14 @@ *> *> \param[out] WORK *> \verbatim -*> WORK is COMPLEX*16 array, dimension (LWORK) +*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The length of the array WORK. LWORK >= 1. +*> The length of the array WORK. LWORK >= 1. *> For optimum performance LWORK >= 6*N*NB, where NB is the *> optimal blocksize. *> @@ -208,7 +208,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16OTHERcomputational +*> \ingroup gghd3 * *> \par Further Details: * ===================== @@ -275,7 +275,12 @@ * INFO = 0 NB = ILAENV( 1, 'ZGGHD3', ' ', N, ILO, IHI, -1 ) - LWKOPT = MAX( 6*N*NB, 1 ) + NH = IHI - ILO + 1 + IF( NH.LE.1 ) THEN + LWKOPT = 1 + ELSE + LWKOPT = 6*N*NB + END IF WORK( 1 ) = DCMPLX( LWKOPT ) INITQ = LSAME( COMPQ, 'I' ) WANTQ = INITQ .OR. LSAME( COMPQ, 'V' ) @@ -325,7 +330,6 @@ * * Quick return if possible * - NH = IHI - ILO + 1 IF( NH.LE.1 ) THEN WORK( 1 ) = CONE RETURN @@ -883,6 +887,7 @@ IF ( JCOL.LT.IHI ) $ CALL ZGGHRD( COMPQ2, COMPZ2, N, JCOL, IHI, A, LDA, B, LDB, Q, $ LDQ, Z, LDZ, IERR ) +* WORK( 1 ) = DCMPLX( LWKOPT ) * RETURN diff --git a/lapack-netlib/SRC/zggqrf.f b/lapack-netlib/SRC/zggqrf.f index 0388b0874..d8636d663 100644 --- a/lapack-netlib/SRC/zggqrf.f +++ b/lapack-netlib/SRC/zggqrf.f @@ -173,7 +173,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16OTHERcomputational +*> \ingroup ggqrf * *> \par Further Details: * ===================== @@ -250,7 +250,7 @@ NB2 = ILAENV( 1, 'ZGERQF', ' ', N, P, -1, -1 ) NB3 = ILAENV( 1, 'ZUNMQR', ' ', N, M, P, -1 ) NB = MAX( NB1, NB2, NB3 ) - LWKOPT = MAX( N, M, P )*NB + LWKOPT = MAX( 1, MAX( N, M, P )*NB ) WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( N.LT.0 ) THEN diff --git a/lapack-netlib/SRC/zggrqf.f b/lapack-netlib/SRC/zggrqf.f index be912c772..69c14af24 100644 --- a/lapack-netlib/SRC/zggrqf.f +++ b/lapack-netlib/SRC/zggrqf.f @@ -172,7 +172,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16OTHERcomputational +*> \ingroup ggrqf * *> \par Further Details: * ===================== @@ -249,7 +249,7 @@ NB2 = ILAENV( 1, 'ZGEQRF', ' ', P, N, -1, -1 ) NB3 = ILAENV( 1, 'ZUNMRQ', ' ', M, N, P, -1 ) NB = MAX( NB1, NB2, NB3 ) - LWKOPT = MAX( N, M, P )*NB + LWKOPT = MAX( 1, MAX( N, M, P )*NB ) WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN diff --git a/lapack-netlib/SRC/zggsvd3.f b/lapack-netlib/SRC/zggsvd3.f index 71257a7c0..40624f5be 100644 --- a/lapack-netlib/SRC/zggsvd3.f +++ b/lapack-netlib/SRC/zggsvd3.f @@ -277,7 +277,7 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. +*> The dimension of the array WORK. LWORK >= 1. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns @@ -332,7 +332,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16GEsing +*> \ingroup ggsvd3 * *> \par Contributors: * ================== diff --git a/lapack-netlib/SRC/zggsvp3.f b/lapack-netlib/SRC/zggsvp3.f index f39ccdad3..7b465aaee 100644 --- a/lapack-netlib/SRC/zggsvp3.f +++ b/lapack-netlib/SRC/zggsvp3.f @@ -233,7 +233,7 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. +*> The dimension of the array WORK. LWORK >= 1. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns @@ -256,7 +256,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16OTHERcomputational +*> \ingroup ggsvp3 * *> \par Further Details: * ===================== diff --git a/lapack-netlib/SRC/zheevd.f b/lapack-netlib/SRC/zheevd.f index ba52f9e72..8e86b9e88 100644 --- a/lapack-netlib/SRC/zheevd.f +++ b/lapack-netlib/SRC/zheevd.f @@ -116,8 +116,7 @@ *> *> \param[out] RWORK *> \verbatim -*> RWORK is DOUBLE PRECISION array, -*> dimension (LRWORK) +*> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) *> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. *> \endverbatim *> @@ -180,7 +179,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEeigen +*> \ingroup heevd * *> \par Further Details: * ===================== diff --git a/lapack-netlib/SRC/zheevr.f b/lapack-netlib/SRC/zheevr.f index 1452e04a3..fe6e1a85f 100644 --- a/lapack-netlib/SRC/zheevr.f +++ b/lapack-netlib/SRC/zheevr.f @@ -272,7 +272,8 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The length of the array WORK. LWORK >= max(1,2*N). +*> The length of the array WORK. +*> If N <= 1, LWORK >= 1, else LWORK >= 2*N. *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the max of the blocksize for ZHETRD and for *> ZUNMTR as returned by ILAENV. @@ -294,7 +295,8 @@ *> \param[in] LRWORK *> \verbatim *> LRWORK is INTEGER -*> The length of the array RWORK. LRWORK >= max(1,24*N). +*> The length of the array RWORK. +*> If N <= 1, LRWORK >= 1, else LRWORK >= 24*N. *> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK @@ -313,7 +315,8 @@ *> \param[in] LIWORK *> \verbatim *> LIWORK is INTEGER -*> The dimension of the array IWORK. LIWORK >= max(1,10*N). +*> The dimension of the array IWORK. +*> If N <= 1, LIWORK >= 1, else LIWORK >= 10*N. *> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK @@ -338,7 +341,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEeigen +*> \ingroup heevr * *> \par Contributors: * ================== @@ -417,9 +420,15 @@ LQUERY = ( ( LWORK.EQ.-1 ) .OR. ( LRWORK.EQ.-1 ) .OR. $ ( LIWORK.EQ.-1 ) ) * - LRWMIN = MAX( 1, 24*N ) - LIWMIN = MAX( 1, 10*N ) - LWMIN = MAX( 1, 2*N ) + IF( N.LE.1 ) THEN + LWMIN = 1 + LRWMIN = 1 + LIWMIN = 1 + ELSE + LWMIN = 2*N + LRWMIN = 24*N + LIWMIN = 10*N + END IF * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN @@ -454,7 +463,7 @@ NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) NB = MAX( NB, ILAENV( 1, 'ZUNMTR', UPLO, N, -1, -1, -1 ) ) LWKOPT = MAX( ( NB+1 )*N, LWMIN ) - WORK( 1 ) = LWKOPT + WORK( 1 ) = LWKOPT RWORK( 1 ) = LRWMIN IWORK( 1 ) = LIWMIN * @@ -483,7 +492,7 @@ END IF * IF( N.EQ.1 ) THEN - WORK( 1 ) = 2 + WORK( 1 ) = 1 IF( ALLEIG .OR. INDEIG ) THEN M = 1 W( 1 ) = DBLE( A( 1, 1 ) ) @@ -710,7 +719,7 @@ * * Set WORK(1) to optimal workspace size. * - WORK( 1 ) = LWKOPT + WORK( 1 ) = LWKOPT RWORK( 1 ) = LRWMIN IWORK( 1 ) = LIWMIN * diff --git a/lapack-netlib/SRC/zheevr_2stage.f b/lapack-netlib/SRC/zheevr_2stage.f index 5c576e633..b1cc7175f 100644 --- a/lapack-netlib/SRC/zheevr_2stage.f +++ b/lapack-netlib/SRC/zheevr_2stage.f @@ -265,7 +265,7 @@ *> indicating the nonzero elements in Z. The i-th eigenvector *> is nonzero only in elements ISUPPZ( 2*i-1 ) through *> ISUPPZ( 2*i ). This is an output of ZSTEMR (tridiagonal -*> matrix). The support of the eigenvectors of A is typically +*> matrix). The support of the eigenvectors of A is typically *> 1:N because of the unitary transformations applied by ZUNMTR. *> Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 *> \endverbatim @@ -279,12 +279,13 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. +*> The dimension of the array WORK. +*> If N <= 1, LWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LWORK must be queried. *> LWORK = MAX(1, 26*N, dimension) where *> dimension = max(stage1,stage2) + (KD+1)*N + N -*> = N*KD + N*max(KD+1,FACTOPTNB) -*> + max(2*KD*KD, KD*NTHREADS) +*> = N*KD + N*max(KD+1,FACTOPTNB) +*> + max(2*KD*KD, KD*NTHREADS) *> + (KD+1)*N + N *> where KD is the blocking size of the reduction, *> FACTOPTNB is the blocking used by the QR or LQ @@ -310,7 +311,8 @@ *> \param[in] LRWORK *> \verbatim *> LRWORK is INTEGER -*> The length of the array RWORK. LRWORK >= max(1,24*N). +*> The length of the array RWORK. +*> If N <= 1, LRWORK >= 1, else LRWORK >= 24*N. *> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK @@ -329,7 +331,8 @@ *> \param[in] LIWORK *> \verbatim *> LIWORK is INTEGER -*> The dimension of the array IWORK. LIWORK >= max(1,10*N). +*> The dimension of the array IWORK. +*> If N <= 1, LIWORK >= 1, else LIWORK >= 10*N. *> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK @@ -354,7 +357,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEeigen +*> \ingroup heevr_2stage * *> \par Contributors: * ================== @@ -382,7 +385,7 @@ *> http://doi.acm.org/10.1145/2063384.2063394 *> *> A. Haidar, J. Kurzak, P. Luszczek, 2013. -*> An improved parallel singular value algorithm and its implementation +*> An improved parallel singular value algorithm and its implementation *> for multicore hardware, In Proceedings of 2013 International Conference *> for High Performance Computing, Networking, Storage and Analysis (SC '13). *> Denver, Colorado, USA, 2013. @@ -390,11 +393,11 @@ *> http://doi.acm.org/10.1145/2503210.2503292 *> *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. -*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure +*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure *> calculations based on fine-grained memory aware tasks. *> International Journal of High Performance Computing Applications. *> Volume 28 Issue 2, Pages 196-209, May 2014. -*> http://hpc.sagepub.com/content/28/2/196 +*> http://hpc.sagepub.com/content/28/2/196 *> *> \endverbatim * @@ -472,9 +475,16 @@ IB = ILAENV2STAGE( 2, 'ZHETRD_2STAGE', JOBZ, N, KD, -1, -1 ) LHTRD = ILAENV2STAGE( 3, 'ZHETRD_2STAGE', JOBZ, N, KD, IB, -1 ) LWTRD = ILAENV2STAGE( 4, 'ZHETRD_2STAGE', JOBZ, N, KD, IB, -1 ) - LWMIN = N + LHTRD + LWTRD - LRWMIN = MAX( 1, 24*N ) - LIWMIN = MAX( 1, 10*N ) +* + IF( N.LE.1 ) THEN + LWMIN = 1 + LRWMIN = 1 + LIWMIN = 1 + ELSE + LWMIN = N + LHTRD + LWTRD + LRWMIN = 24*N + LIWMIN = 10*N + END IF * INFO = 0 IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN @@ -535,7 +545,7 @@ END IF * IF( N.EQ.1 ) THEN - WORK( 1 ) = 2 + WORK( 1 ) = 1 IF( ALLEIG .OR. INDEIG ) THEN M = 1 W( 1 ) = DBLE( A( 1, 1 ) ) @@ -643,9 +653,9 @@ * * Call ZHETRD_2STAGE to reduce Hermitian matrix to tridiagonal form. * - CALL ZHETRD_2STAGE( JOBZ, UPLO, N, A, LDA, RWORK( INDRD ), + CALL ZHETRD_2STAGE( JOBZ, UPLO, N, A, LDA, RWORK( INDRD ), $ RWORK( INDRE ), WORK( INDTAU ), - $ WORK( INDHOUS ), LHTRD, + $ WORK( INDHOUS ), LHTRD, $ WORK( INDWK ), LLWORK, IINFO ) * * If all eigenvalues are desired diff --git a/lapack-netlib/SRC/zhesv_aa.f b/lapack-netlib/SRC/zhesv_aa.f index df8498c7a..b3d4b3725 100644 --- a/lapack-netlib/SRC/zhesv_aa.f +++ b/lapack-netlib/SRC/zhesv_aa.f @@ -128,7 +128,7 @@ *> LWORK is INTEGER *> The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for best *> performance LWORK >= max(1,N*NB), where NB is the optimal -*> blocksize for ZHETRF. +*> blocksize for ZHETRF_AA. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns @@ -154,7 +154,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEsolve +*> \ingroup hesv_aa * * ===================================================================== SUBROUTINE ZHESV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, @@ -177,7 +177,7 @@ * * .. Local Scalars .. LOGICAL LQUERY - INTEGER LWKOPT, LWKOPT_HETRF, LWKOPT_HETRS + INTEGER LWKMIN, LWKOPT, LWKOPT_HETRF, LWKOPT_HETRS * .. * .. External Functions .. LOGICAL LSAME @@ -196,6 +196,7 @@ * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) + LWKMIN = MAX( 1, 2*N, 3*N-2 ) IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN @@ -206,17 +207,17 @@ INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 - ELSE IF( LWORK.LT.MAX(2*N, 3*N-2) .AND. .NOT.LQUERY ) THEN + ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN INFO = -10 END IF * IF( INFO.EQ.0 ) THEN CALL ZHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, -1, INFO ) - LWKOPT_HETRF = INT( WORK(1) ) + LWKOPT_HETRF = INT( WORK( 1 ) ) CALL ZHETRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, $ -1, INFO ) - LWKOPT_HETRS = INT( WORK(1) ) - LWKOPT = MAX( LWKOPT_HETRF, LWKOPT_HETRS ) + LWKOPT_HETRS = INT( WORK( 1 ) ) + LWKOPT = MAX( LWKMIN, LWKOPT_HETRF, LWKOPT_HETRS ) WORK( 1 ) = LWKOPT END IF * diff --git a/lapack-netlib/SRC/zhesv_aa_2stage.f b/lapack-netlib/SRC/zhesv_aa_2stage.f index 79c01c546..c503b5554 100644 --- a/lapack-netlib/SRC/zhesv_aa_2stage.f +++ b/lapack-netlib/SRC/zhesv_aa_2stage.f @@ -100,14 +100,14 @@ *> *> \param[out] TB *> \verbatim -*> TB is COMPLEX*16 array, dimension (LTB) +*> TB is COMPLEX*16 array, dimension (MAX(1,LTB)). *> On exit, details of the LU factorization of the band matrix. *> \endverbatim *> *> \param[in] LTB *> \verbatim *> LTB is INTEGER -*> The size of the array TB. LTB >= 4*N, internally +*> The size of the array TB. LTB >= MAX(1,4*N), internally *> used to select NB such that LTB >= (3*NB+1)*N. *> *> If LTB = -1, then a workspace query is assumed; the @@ -147,14 +147,15 @@ *> *> \param[out] WORK *> \verbatim -*> WORK is COMPLEX*16 workspace of size LWORK +*> WORK is COMPLEX*16 workspace of size (MAX(1,LWORK)). +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The size of WORK. LWORK >= N, internally used to select NB -*> such that LWORK >= N*NB. +*> The size of WORK. LWORK >= MAX(1,N), internally used to +*> select NB such that LWORK >= N*NB. *> *> If LWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the WORK array, @@ -178,7 +179,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEsolve +*> \ingroup hesv_aa_2stage * * ===================================================================== SUBROUTINE ZHESV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, @@ -208,7 +209,7 @@ * * .. Local Scalars .. LOGICAL UPPER, TQUERY, WQUERY - INTEGER LWKOPT + INTEGER LWKOPT, LWKMIN * .. * .. External Functions .. LOGICAL LSAME @@ -229,6 +230,7 @@ UPPER = LSAME( UPLO, 'U' ) WQUERY = ( LWORK.EQ.-1 ) TQUERY = ( LTB.EQ.-1 ) + LWKMIN = MAX( 1, N ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN @@ -237,18 +239,19 @@ INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 - ELSE IF( LTB.LT.( 4*N ) .AND. .NOT.TQUERY ) THEN + ELSE IF( LTB.LT.MAX( 1, 4*N ) .AND. .NOT.TQUERY ) THEN INFO = -7 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -11 - ELSE IF( LWORK.LT.N .AND. .NOT.WQUERY ) THEN + ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.WQUERY ) THEN INFO = -13 END IF * IF( INFO.EQ.0 ) THEN CALL ZHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, -1, IPIV, $ IPIV2, WORK, -1, INFO ) - LWKOPT = INT( WORK(1) ) + LWKOPT = MAX( LWKMIN, INT( WORK( 1 ) ) ) + WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN diff --git a/lapack-netlib/SRC/zhesvx.f b/lapack-netlib/SRC/zhesvx.f index 485c81df6..64aa16674 100644 --- a/lapack-netlib/SRC/zhesvx.f +++ b/lapack-netlib/SRC/zhesvx.f @@ -234,8 +234,8 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The length of WORK. LWORK >= max(1,2*N), and for best -*> performance, when FACT = 'N', LWORK >= max(1,2*N,N*NB), where +*> The length of WORK. LWORK >= MAX(1,2*N), and for best +*> performance, when FACT = 'N', LWORK >= MAX(1,2*N,N*NB), where *> NB is the optimal blocksize for ZHETRF. *> *> If LWORK = -1, then a workspace query is assumed; the routine @@ -276,7 +276,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEsolve +*> \ingroup hesvx * * ===================================================================== SUBROUTINE ZHESVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, @@ -307,7 +307,7 @@ * .. * .. Local Scalars .. LOGICAL LQUERY, NOFACT - INTEGER LWKOPT, NB + INTEGER LWKOPT, LWKMIN, NB DOUBLE PRECISION ANORM * .. * .. External Functions .. @@ -329,6 +329,7 @@ INFO = 0 NOFACT = LSAME( FACT, 'N' ) LQUERY = ( LWORK.EQ.-1 ) + LWKMIN = MAX( 1, 2*N ) IF( .NOT.NOFACT .AND. .NOT.LSAME( FACT, 'F' ) ) THEN INFO = -1 ELSE IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) @@ -346,12 +347,12 @@ INFO = -11 ELSE IF( LDX.LT.MAX( 1, N ) ) THEN INFO = -13 - ELSE IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN + ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN INFO = -18 END IF * IF( INFO.EQ.0 ) THEN - LWKOPT = MAX( 1, 2*N ) + LWKOPT = LWKMIN IF( NOFACT ) THEN NB = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 ) LWKOPT = MAX( LWKOPT, N*NB ) diff --git a/lapack-netlib/SRC/zhetrd_2stage.f b/lapack-netlib/SRC/zhetrd_2stage.f index b9d2f0eb1..ab444894b 100644 --- a/lapack-netlib/SRC/zhetrd_2stage.f +++ b/lapack-netlib/SRC/zhetrd_2stage.f @@ -4,23 +4,23 @@ * * =========== DOCUMENTATION =========== * -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ * *> \htmlonly -*> Download ZHETRD_2STAGE + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> +*> Download ZHETRD_2STAGE + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> *> [TXT] -*> \endhtmlonly +*> \endhtmlonly * * Definition: * =========== * -* SUBROUTINE ZHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU, +* SUBROUTINE ZHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU, * HOUS2, LHOUS2, WORK, LWORK, INFO ) * * IMPLICIT NONE @@ -34,7 +34,7 @@ * COMPLEX*16 A( LDA, * ), TAU( * ), * HOUS2( * ), WORK( * ) * .. -* +* * *> \par Purpose: * ============= @@ -52,11 +52,11 @@ *> \param[in] VECT *> \verbatim *> VECT is CHARACTER*1 -*> = 'N': No need for the Housholder representation, +*> = 'N': No need for the Housholder representation, *> in particular for the second stage (Band to *> tridiagonal) and thus LHOUS2 is of size max(1, 4*N); -*> = 'V': the Householder representation is needed to -*> either generate Q1 Q2 or to apply Q1 Q2, +*> = 'V': the Householder representation is needed to +*> either generate Q1 Q2 or to apply Q1 Q2, *> then LHOUS2 is to be queried and computed. *> (NOT AVAILABLE IN THIS RELEASE). *> \endverbatim @@ -86,7 +86,7 @@ *> triangular part of A is not referenced. *> On exit, if UPLO = 'U', the band superdiagonal *> of A are overwritten by the corresponding elements of the -*> internal band-diagonal matrix AB, and the elements above +*> internal band-diagonal matrix AB, and the elements above *> the KD superdiagonal, with the array TAU, represent the unitary *> matrix Q1 as a product of elementary reflectors; if UPLO *> = 'L', the diagonal and band subdiagonal of A are over- @@ -117,13 +117,13 @@ *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (N-KD) -*> The scalar factors of the elementary reflectors of +*> The scalar factors of the elementary reflectors of *> the first stage (see Further Details). *> \endverbatim *> *> \param[out] HOUS2 *> \verbatim -*> HOUS2 is COMPLEX*16 array, dimension (LHOUS2) +*> HOUS2 is COMPLEX*16 array, dimension (MAX(1,LHOUS2)) *> Stores the Householder representation of the stage2 *> band to tridiagonal. *> \endverbatim @@ -132,6 +132,8 @@ *> \verbatim *> LHOUS2 is INTEGER *> The dimension of the array HOUS2. +*> LHOUS2 >= 1. +*> *> If LWORK = -1, or LHOUS2 = -1, *> then a query is assumed; the routine *> only calculates the optimal size of the HOUS2 array, returns @@ -143,23 +145,26 @@ *> *> \param[out] WORK *> \verbatim -*> WORK is COMPLEX*16 array, dimension (LWORK) +*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. LWORK = MAX(1, dimension) -*> If LWORK = -1, or LHOUS2=-1, +*> The dimension of the array WORK. +*> If N = 0, LWORK >= 1, else LWORK = MAX(1, dimension). +*> +*> If LWORK = -1, or LHOUS2 = -1, *> then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> LWORK = MAX(1, dimension) where *> dimension = max(stage1,stage2) + (KD+1)*N -*> = N*KD + N*max(KD+1,FACTOPTNB) -*> + max(2*KD*KD, KD*NTHREADS) -*> + (KD+1)*N +*> = N*KD + N*max(KD+1,FACTOPTNB) +*> + max(2*KD*KD, KD*NTHREADS) +*> + (KD+1)*N *> where KD is the blocking size of the reduction, *> FACTOPTNB is the blocking used by the QR or LQ *> algorithm, usually FACTOPTNB=128 is a good choice @@ -177,12 +182,12 @@ * Authors: * ======== * -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -*> \ingroup complex16HEcomputational +*> \ingroup hetrd_2stage * *> \par Further Details: * ===================== @@ -202,7 +207,7 @@ *> http://doi.acm.org/10.1145/2063384.2063394 *> *> A. Haidar, J. Kurzak, P. Luszczek, 2013. -*> An improved parallel singular value algorithm and its implementation +*> An improved parallel singular value algorithm and its implementation *> for multicore hardware, In Proceedings of 2013 International Conference *> for High Performance Computing, Networking, Storage and Analysis (SC '13). *> Denver, Colorado, USA, 2013. @@ -210,16 +215,16 @@ *> http://doi.acm.org/10.1145/2503210.2503292 *> *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. -*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure +*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure *> calculations based on fine-grained memory aware tasks. *> International Journal of High Performance Computing Applications. *> Volume 28 Issue 2, Pages 196-209, May 2014. -*> http://hpc.sagepub.com/content/28/2/196 +*> http://hpc.sagepub.com/content/28/2/196 *> *> \endverbatim *> * ===================================================================== - SUBROUTINE ZHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU, + SUBROUTINE ZHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU, $ HOUS2, LHOUS2, WORK, LWORK, INFO ) * IMPLICIT NONE @@ -265,10 +270,13 @@ * KD = ILAENV2STAGE( 1, 'ZHETRD_2STAGE', VECT, N, -1, -1, -1 ) IB = ILAENV2STAGE( 2, 'ZHETRD_2STAGE', VECT, N, KD, -1, -1 ) - LHMIN = ILAENV2STAGE( 3, 'ZHETRD_2STAGE', VECT, N, KD, IB, -1 ) - LWMIN = ILAENV2STAGE( 4, 'ZHETRD_2STAGE', VECT, N, KD, IB, -1 ) -* WRITE(*,*),'ZHETRD_2STAGE N KD UPLO LHMIN LWMIN ',N, KD, UPLO, -* $ LHMIN, LWMIN + IF( N.EQ.0 ) THEN + LHMIN = 1 + LWMIN = 1 + ELSE + LHMIN = ILAENV2STAGE( 3, 'ZHETRD_2STAGE', VECT, N, KD, IB, -1 ) + LWMIN = ILAENV2STAGE( 4, 'ZHETRD_2STAGE', VECT, N, KD, IB, -1 ) + END IF * IF( .NOT.LSAME( VECT, 'N' ) ) THEN INFO = -1 @@ -309,14 +317,14 @@ LWRK = LWORK-LDAB*N ABPOS = 1 WPOS = ABPOS + LDAB*N - CALL ZHETRD_HE2HB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB, + CALL ZHETRD_HE2HB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB, $ TAU, WORK( WPOS ), LWRK, INFO ) IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHETRD_HE2HB', -INFO ) RETURN END IF - CALL ZHETRD_HB2ST( 'Y', VECT, UPLO, N, KD, - $ WORK( ABPOS ), LDAB, D, E, + CALL ZHETRD_HB2ST( 'Y', VECT, UPLO, N, KD, + $ WORK( ABPOS ), LDAB, D, E, $ HOUS2, LHOUS2, WORK( WPOS ), LWRK, INFO ) IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHETRD_HB2ST', -INFO ) @@ -324,7 +332,6 @@ END IF * * - HOUS2( 1 ) = LHMIN WORK( 1 ) = LWMIN RETURN * diff --git a/lapack-netlib/SRC/zhetrd_hb2st.F b/lapack-netlib/SRC/zhetrd_hb2st.F index 1d39ac942..247497ab6 100644 --- a/lapack-netlib/SRC/zhetrd_hb2st.F +++ b/lapack-netlib/SRC/zhetrd_hb2st.F @@ -18,7 +18,7 @@ * Definition: * =========== * -* SUBROUTINE ZHETRD_HB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB, +* SUBROUTINE ZHETRD_HB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB, * D, E, HOUS, LHOUS, WORK, LWORK, INFO ) * * #if defined(_OPENMP) @@ -53,12 +53,12 @@ *> \param[in] STAGE1 *> \verbatim *> STAGE1 is CHARACTER*1 -*> = 'N': "No": to mention that the stage 1 of the reduction +*> = 'N': "No": to mention that the stage 1 of the reduction *> from dense to band using the zhetrd_he2hb routine -*> was not called before this routine to reproduce AB. -*> In other term this routine is called as standalone. -*> = 'Y': "Yes": to mention that the stage 1 of the -*> reduction from dense to band using the zhetrd_he2hb +*> was not called before this routine to reproduce AB. +*> In other term this routine is called as standalone. +*> = 'Y': "Yes": to mention that the stage 1 of the +*> reduction from dense to band using the zhetrd_he2hb *> routine has been called to produce AB (e.g., AB is *> the output of zhetrd_he2hb. *> \endverbatim @@ -66,10 +66,10 @@ *> \param[in] VECT *> \verbatim *> VECT is CHARACTER*1 -*> = 'N': No need for the Housholder representation, +*> = 'N': No need for the Housholder representation, *> and thus LHOUS is of size max(1, 4*N); -*> = 'V': the Householder representation is needed to -*> either generate or to apply Q later on, +*> = 'V': the Householder representation is needed to +*> either generate or to apply Q later on, *> then LHOUS is to be queried and computed. *> (NOT AVAILABLE IN THIS RELEASE). *> \endverbatim @@ -132,34 +132,39 @@ *> *> \param[out] HOUS *> \verbatim -*> HOUS is COMPLEX*16 array, dimension LHOUS, that -*> store the Householder representation. +*> HOUS is COMPLEX*16 array, dimension (MAX(1,LHOUS)) +*> Stores the Householder representation. *> \endverbatim *> *> \param[in] LHOUS *> \verbatim *> LHOUS is INTEGER -*> The dimension of the array HOUS. LHOUS = MAX(1, dimension) -*> If LWORK = -1, or LHOUS=-1, +*> The dimension of the array HOUS. +*> If N = 0 or KD <= 1, LHOUS >= 1, else LHOUS = MAX(1, dimension). +*> +*> If LWORK = -1, or LHOUS = -1, *> then a query is assumed; the routine *> only calculates the optimal size of the HOUS array, returns *> this value as the first entry of the HOUS array, and no error *> message related to LHOUS is issued by XERBLA. *> LHOUS = MAX(1, dimension) where *> dimension = 4*N if VECT='N' -*> not available now if VECT='H' +*> not available now if VECT='H' *> \endverbatim *> *> \param[out] WORK *> \verbatim -*> WORK is COMPLEX*16 array, dimension LWORK. +*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. LWORK = MAX(1, dimension) -*> If LWORK = -1, or LHOUS=-1, +*> The dimension of the array WORK. +*> If N = 0 or KD <= 1, LWORK >= 1, else LWORK = MAX(1, dimension). +*> +*> If LWORK = -1, or LHOUS = -1, *> then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error @@ -188,7 +193,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16OTHERcomputational +*> \ingroup hetrd_hb2st * *> \par Further Details: * ===================== @@ -208,7 +213,7 @@ *> http://doi.acm.org/10.1145/2063384.2063394 *> *> A. Haidar, J. Kurzak, P. Luszczek, 2013. -*> An improved parallel singular value algorithm and its implementation +*> An improved parallel singular value algorithm and its implementation *> for multicore hardware, In Proceedings of 2013 International Conference *> for High Performance Computing, Networking, Storage and Analysis (SC '13). *> Denver, Colorado, USA, 2013. @@ -216,16 +221,16 @@ *> http://doi.acm.org/10.1145/2503210.2503292 *> *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. -*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure +*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure *> calculations based on fine-grained memory aware tasks. *> International Journal of High Performance Computing Applications. *> Volume 28 Issue 2, Pages 196-209, May 2014. -*> http://hpc.sagepub.com/content/28/2/196 +*> http://hpc.sagepub.com/content/28/2/196 *> *> \endverbatim *> * ===================================================================== - SUBROUTINE ZHETRD_HB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB, + SUBROUTINE ZHETRD_HB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB, $ D, E, HOUS, LHOUS, WORK, LWORK, INFO ) * * @@ -259,11 +264,11 @@ * .. * .. Local Scalars .. LOGICAL LQUERY, WANTQ, UPPER, AFTERS1 - INTEGER I, M, K, IB, SWEEPID, MYID, SHIFT, STT, ST, + INTEGER I, M, K, IB, SWEEPID, MYID, SHIFT, STT, ST, $ ED, STIND, EDIND, BLKLASTIND, COLPT, THED, $ STEPERCOL, GRSIZ, THGRSIZ, THGRNB, THGRID, - $ NBTILES, TTYPE, TID, NTHREADS, DEBUG, - $ ABDPOS, ABOFDPOS, DPOS, OFDPOS, AWPOS, + $ NBTILES, TTYPE, TID, NTHREADS, + $ ABDPOS, ABOFDPOS, DPOS, OFDPOS, AWPOS, $ INDA, INDW, APOS, SIZEA, LDA, INDV, INDTAU, $ SIZEV, SIZETAU, LDV, LHMIN, LWMIN DOUBLE PRECISION ABSTMP @@ -277,7 +282,7 @@ * .. * .. External Functions .. LOGICAL LSAME - INTEGER ILAENV2STAGE + INTEGER ILAENV2STAGE EXTERNAL LSAME, ILAENV2STAGE * .. * .. Executable Statements .. @@ -285,7 +290,6 @@ * Determine the minimal workspace size required. * Test the input parameters * - DEBUG = 0 INFO = 0 AFTERS1 = LSAME( STAGE1, 'Y' ) WANTQ = LSAME( VECT, 'V' ) @@ -294,9 +298,14 @@ * * Determine the block size, the workspace size and the hous size. * - IB = ILAENV2STAGE( 2, 'ZHETRD_HB2ST', VECT, N, KD, -1, -1 ) - LHMIN = ILAENV2STAGE( 3, 'ZHETRD_HB2ST', VECT, N, KD, IB, -1 ) - LWMIN = ILAENV2STAGE( 4, 'ZHETRD_HB2ST', VECT, N, KD, IB, -1 ) + IB = ILAENV2STAGE( 2, 'ZHETRD_HB2ST', VECT, N, KD, -1, -1 ) + IF( N.EQ.0 .OR. KD.LE.1 ) THEN + LHMIN = 1 + LWMIN = 1 + ELSE + LHMIN = ILAENV2STAGE( 3, 'ZHETRD_HB2ST', VECT, N, KD, IB, -1 ) + LWMIN = ILAENV2STAGE( 4, 'ZHETRD_HB2ST', VECT, N, KD, IB, -1 ) + END IF * IF( .NOT.AFTERS1 .AND. .NOT.LSAME( STAGE1, 'N' ) ) THEN INFO = -1 @@ -358,7 +367,7 @@ ABDPOS = KD + 1 ABOFDPOS = KD ELSE - APOS = INDA + APOS = INDA AWPOS = INDA + KD + 1 DPOS = APOS OFDPOS = DPOS + 1 @@ -366,11 +375,11 @@ ABOFDPOS = 2 ENDIF -* -* Case KD=0: -* The matrix is diagonal. We just copy it (convert to "real" for -* complex because D is double and the imaginary part should be 0) -* and store it in D. A sequential code here is better or +* +* Case KD=0: +* The matrix is diagonal. We just copy it (convert to "real" for +* complex because D is double and the imaginary part should be 0) +* and store it in D. A sequential code here is better or * in a parallel environment it might need two cores for D and E * IF( KD.EQ.0 ) THEN @@ -385,17 +394,17 @@ WORK( 1 ) = 1 RETURN END IF -* -* Case KD=1: -* The matrix is already Tridiagonal. We have to make diagonal +* +* Case KD=1: +* The matrix is already Tridiagonal. We have to make diagonal * and offdiagonal elements real, and store them in D and E. -* For that, for real precision just copy the diag and offdiag -* to D and E while for the COMPLEX case the bulge chasing is -* performed to convert the hermetian tridiagonal to symmetric -* tridiagonal. A simpler conversion formula might be used, but then +* For that, for real precision just copy the diag and offdiag +* to D and E while for the COMPLEX case the bulge chasing is +* performed to convert the hermetian tridiagonal to symmetric +* tridiagonal. A simpler conversion formula might be used, but then * updating the Q matrix will be required and based if Q is generated -* or not this might complicate the story. -* +* or not this might complicate the story. +* IF( KD.EQ.1 ) THEN DO 50 I = 1, N D( I ) = DBLE( AB( ABDPOS, I ) ) @@ -444,7 +453,7 @@ C END IF RETURN END IF * -* Main code start here. +* Main code start here. * Reduce the hermitian band of A to a tridiagonal matrix. * THGRSIZ = N @@ -453,7 +462,7 @@ C END IF NBTILES = CEILING( REAL(N)/REAL(KD) ) STEPERCOL = CEILING( REAL(SHIFT)/REAL(GRSIZ) ) THGRNB = CEILING( REAL(N-1)/REAL(THGRSIZ) ) -* +* CALL ZLACPY( "A", KD+1, N, AB, LDAB, WORK( APOS ), LDA ) CALL ZLASET( "A", KD, N, ZERO, ZERO, WORK( AWPOS ), LDA ) * @@ -462,7 +471,7 @@ C END IF * #if defined(_OPENMP) !$OMP PARALLEL PRIVATE( TID, THGRID, BLKLASTIND ) -!$OMP$ PRIVATE( THED, I, M, K, ST, ED, STT, SWEEPID ) +!$OMP$ PRIVATE( THED, I, M, K, ST, ED, STT, SWEEPID ) !$OMP$ PRIVATE( MYID, TTYPE, COLPT, STIND, EDIND ) !$OMP$ SHARED ( UPLO, WANTQ, INDV, INDTAU, HOUS, WORK) !$OMP$ SHARED ( N, KD, IB, NBTILES, LDA, LDV, INDA ) @@ -471,7 +480,7 @@ C END IF #endif * * main bulge chasing loop -* +* DO 100 THGRID = 1, THGRNB STT = (THGRID-1)*THGRSIZ+1 THED = MIN( (STT + THGRSIZ -1), (N-1)) @@ -482,7 +491,7 @@ C END IF ST = STT DO 130 SWEEPID = ST, ED DO 140 K = 1, GRSIZ - MYID = (I-SWEEPID)*(STEPERCOL*GRSIZ) + MYID = (I-SWEEPID)*(STEPERCOL*GRSIZ) $ + (M-1)*GRSIZ + K IF ( MYID.EQ.1 ) THEN TTYPE = 1 @@ -508,17 +517,17 @@ C END IF ENDIF * * Call the kernel -* +* #if defined(_OPENMP) && _OPENMP >= 201307 - IF( TTYPE.NE.1 ) THEN + IF( TTYPE.NE.1 ) THEN !$OMP TASK DEPEND(in:WORK(MYID+SHIFT-1)) !$OMP$ DEPEND(in:WORK(MYID-1)) !$OMP$ DEPEND(out:WORK(MYID)) TID = OMP_GET_THREAD_NUM() - CALL ZHB2ST_KERNELS( UPLO, WANTQ, TTYPE, + CALL ZHB2ST_KERNELS( UPLO, WANTQ, TTYPE, $ STIND, EDIND, SWEEPID, N, KD, IB, - $ WORK ( INDA ), LDA, + $ WORK ( INDA ), LDA, $ HOUS( INDV ), HOUS( INDTAU ), LDV, $ WORK( INDW + TID*KD ) ) !$OMP END TASK @@ -526,20 +535,20 @@ C END IF !$OMP TASK DEPEND(in:WORK(MYID+SHIFT-1)) !$OMP$ DEPEND(out:WORK(MYID)) TID = OMP_GET_THREAD_NUM() - CALL ZHB2ST_KERNELS( UPLO, WANTQ, TTYPE, + CALL ZHB2ST_KERNELS( UPLO, WANTQ, TTYPE, $ STIND, EDIND, SWEEPID, N, KD, IB, - $ WORK ( INDA ), LDA, + $ WORK ( INDA ), LDA, $ HOUS( INDV ), HOUS( INDTAU ), LDV, $ WORK( INDW + TID*KD ) ) !$OMP END TASK ENDIF #else - CALL ZHB2ST_KERNELS( UPLO, WANTQ, TTYPE, + CALL ZHB2ST_KERNELS( UPLO, WANTQ, TTYPE, $ STIND, EDIND, SWEEPID, N, KD, IB, - $ WORK ( INDA ), LDA, + $ WORK ( INDA ), LDA, $ HOUS( INDV ), HOUS( INDTAU ), LDV, $ WORK( INDW ) ) -#endif +#endif IF ( BLKLASTIND.GE.(N-1) ) THEN STT = STT + 1 EXIT @@ -554,14 +563,14 @@ C END IF !$OMP END MASTER !$OMP END PARALLEL #endif -* +* * Copy the diagonal from A to D. Note that D is REAL thus only * the Real part is needed, the imaginary part should be zero. * DO 150 I = 1, N D( I ) = DBLE( WORK( DPOS+(I-1)*LDA ) ) 150 CONTINUE -* +* * Copy the off diagonal from A to E. Note that E is REAL thus only * the Real part is needed, the imaginary part should be zero. * @@ -575,11 +584,10 @@ C END IF 170 CONTINUE ENDIF * - HOUS( 1 ) = LHMIN WORK( 1 ) = LWMIN RETURN * * End of ZHETRD_HB2ST * END - + diff --git a/lapack-netlib/SRC/zhetrd_he2hb.f b/lapack-netlib/SRC/zhetrd_he2hb.f index e1b2e1794..3e3bfa374 100644 --- a/lapack-netlib/SRC/zhetrd_he2hb.f +++ b/lapack-netlib/SRC/zhetrd_he2hb.f @@ -123,8 +123,8 @@ *> *> \param[out] WORK *> \verbatim -*> WORK is COMPLEX*16 array, dimension (LWORK) -*> On exit, if INFO = 0, or if LWORK=-1, +*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, or if LWORK = -1, *> WORK(1) returns the size of LWORK. *> \endverbatim *> @@ -132,7 +132,9 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK which should be calculated -*> by a workspace query. LWORK = MAX(1, LWORK_QUERY) +*> by a workspace query. +*> If N <= KD+1, LWORK >= 1, else LWORK = MAX(1, LWORK_QUERY). +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error @@ -158,7 +160,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEcomputational +*> \ingroup hetrd_he2hb * *> \par Further Details: * ===================== @@ -293,8 +295,12 @@ INFO = 0 UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) - LWMIN = ILAENV2STAGE( 4, 'ZHETRD_HE2HB', '', N, KD, -1, -1 ) - + IF( N.LE.KD+1 ) THEN + LWMIN = 1 + ELSE + LWMIN = ILAENV2STAGE( 4, 'ZHETRD_HE2HB', '', N, KD, -1, -1 ) + END IF +* IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN diff --git a/lapack-netlib/SRC/zhetrf.f b/lapack-netlib/SRC/zhetrf.f index 78d4f71b8..433887108 100644 --- a/lapack-netlib/SRC/zhetrf.f +++ b/lapack-netlib/SRC/zhetrf.f @@ -107,7 +107,7 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The length of WORK. LWORK >=1. For best performance +*> The length of WORK. LWORK >= 1. For best performance *> LWORK >= N*NB, where NB is the block size returned by ILAENV. *> \endverbatim *> @@ -130,7 +130,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEcomputational +*> \ingroup hetrf * *> \par Further Details: * ===================== @@ -227,7 +227,7 @@ * Determine the block size * NB = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 ) - LWKOPT = N*NB + LWKOPT = MAX( 1, N*NB ) WORK( 1 ) = LWKOPT END IF * @@ -346,6 +346,7 @@ END IF * 40 CONTINUE +* WORK( 1 ) = LWKOPT RETURN * diff --git a/lapack-netlib/SRC/zhetrf_aa.f b/lapack-netlib/SRC/zhetrf_aa.f index 537c16e8c..381c87d51 100644 --- a/lapack-netlib/SRC/zhetrf_aa.f +++ b/lapack-netlib/SRC/zhetrf_aa.f @@ -101,8 +101,10 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The length of WORK. LWORK >= MAX(1,2*N). For optimum performance -*> LWORK >= N*(1+NB), where NB is the optimal blocksize. +*> The length of WORK. +*> LWORK >= 1, if N >= 1, and LWORK >= 2*N, otherwise. +*> For optimum performance LWORK >= N*(1+NB), where NB is +*> the optimal blocksize, returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns @@ -125,10 +127,10 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEcomputational +*> \ingroup hetrf_aa * * ===================================================================== - SUBROUTINE ZHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO) + SUBROUTINE ZHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- @@ -152,7 +154,7 @@ * * .. Local Scalars .. LOGICAL LQUERY, UPPER - INTEGER J, LWKOPT + INTEGER J, LWKMIN, LWKOPT INTEGER NB, MJ, NJ, K1, K2, J1, J2, J3, JB COMPLEX*16 ALPHA * .. @@ -178,18 +180,25 @@ INFO = 0 UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) + IF( N.LE.1 ) THEN + LWKMIN = 1 + LWKOPT = 1 + ELSE + LWKMIN = 2*N + LWKOPT = (NB+1)*N + END IF +* IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 - ELSE IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN + ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN INFO = -7 END IF * IF( INFO.EQ.0 ) THEN - LWKOPT = (NB+1)*N WORK( 1 ) = LWKOPT END IF * @@ -202,11 +211,11 @@ * * Quick return * - IF ( N.EQ.0 ) THEN + IF( N.EQ.0 ) THEN RETURN ENDIF IPIV( 1 ) = 1 - IF ( N.EQ.1 ) THEN + IF( N.EQ.1 ) THEN A( 1, 1 ) = DBLE( A( 1, 1 ) ) RETURN END IF diff --git a/lapack-netlib/SRC/zhetrf_aa_2stage.f b/lapack-netlib/SRC/zhetrf_aa_2stage.f index 477602b5e..bab13a99d 100644 --- a/lapack-netlib/SRC/zhetrf_aa_2stage.f +++ b/lapack-netlib/SRC/zhetrf_aa_2stage.f @@ -87,14 +87,14 @@ *> *> \param[out] TB *> \verbatim -*> TB is COMPLEX*16 array, dimension (LTB) +*> TB is COMPLEX*16 array, dimension (MAX(1,LTB)) *> On exit, details of the LU factorization of the band matrix. *> \endverbatim *> *> \param[in] LTB *> \verbatim *> LTB is INTEGER -*> The size of the array TB. LTB >= 4*N, internally +*> The size of the array TB. LTB >= MAX(1,4*N), internally *> used to select NB such that LTB >= (3*NB+1)*N. *> *> If LTB = -1, then a workspace query is assumed; the @@ -121,14 +121,14 @@ *> *> \param[out] WORK *> \verbatim -*> WORK is COMPLEX*16 workspace of size LWORK +*> WORK is COMPLEX*16 workspace of size (MAX(1,LWORK)) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The size of WORK. LWORK >= N, internally used to select NB -*> such that LWORK >= N*NB. +*> The size of WORK. LWORK >= MAX(1,N), internally used to +*> select NB such that LWORK >= N*NB. *> *> If LWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the WORK array, @@ -152,7 +152,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16SYcomputational +*> \ingroup hetrf_aa_2stage * * ===================================================================== SUBROUTINE ZHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, @@ -182,7 +182,7 @@ * .. Local Scalars .. LOGICAL UPPER, TQUERY, WQUERY INTEGER I, J, K, I1, I2, TD - INTEGER LDTB, NB, KB, JB, NT, IINFO + INTEGER LWKOPT, LDTB, NB, KB, JB, NT, IINFO COMPLEX*16 PIV * .. * .. External Functions .. @@ -212,9 +212,9 @@ INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 - ELSE IF ( LTB .LT. 4*N .AND. .NOT.TQUERY ) THEN + ELSE IF( LTB.LT.MAX( 1, 4*N ) .AND. .NOT.TQUERY ) THEN INFO = -6 - ELSE IF ( LWORK .LT. N .AND. .NOT.WQUERY ) THEN + ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.WQUERY ) THEN INFO = -10 END IF * @@ -228,10 +228,10 @@ NB = ILAENV( 1, 'ZHETRF_AA_2STAGE', UPLO, N, -1, -1, -1 ) IF( INFO.EQ.0 ) THEN IF( TQUERY ) THEN - TB( 1 ) = (3*NB+1)*N + TB( 1 ) = MAX( 1, (3*NB+1)*N ) END IF IF( WQUERY ) THEN - WORK( 1 ) = N*NB + WORK( 1 ) = MAX( 1, N*NB ) END IF END IF IF( TQUERY .OR. WQUERY ) THEN @@ -240,7 +240,7 @@ * * Quick return * - IF ( N.EQ.0 ) THEN + IF( N.EQ.0 ) THEN RETURN ENDIF * @@ -392,7 +392,7 @@ CALL ZGETRF( N-(J+1)*NB, NB, $ WORK, N, $ IPIV( (J+1)*NB+1 ), IINFO ) -c IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN +c IF( IINFO.NE.0 .AND. INFO.EQ.0 ) THEN c INFO = IINFO+(J+1)*NB c END IF * @@ -587,7 +587,7 @@ c END IF CALL ZGETRF( N-(J+1)*NB, NB, $ A( (J+1)*NB+1, J*NB+1 ), LDA, $ IPIV( (J+1)*NB+1 ), IINFO ) -c IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN +c IF( IINFO.NE.0 .AND. INFO.EQ.0 ) THEN c INFO = IINFO+(J+1)*NB c END IF * diff --git a/lapack-netlib/SRC/zhetrf_rk.f b/lapack-netlib/SRC/zhetrf_rk.f index 73dd9f9d0..7c505fa4d 100644 --- a/lapack-netlib/SRC/zhetrf_rk.f +++ b/lapack-netlib/SRC/zhetrf_rk.f @@ -177,14 +177,14 @@ *> *> \param[out] WORK *> \verbatim -*> WORK is COMPLEX*16 array, dimension ( MAX(1,LWORK) ). +*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The length of WORK. LWORK >=1. For best performance +*> The length of WORK. LWORK >= 1. For best performance *> LWORK >= N*NB, where NB is the block size returned *> by ILAENV. *> @@ -229,7 +229,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEcomputational +*> \ingroup hetrf_rk * *> \par Further Details: * ===================== @@ -310,7 +310,7 @@ * Determine the block size * NB = ILAENV( 1, 'ZHETRF_RK', UPLO, N, -1, -1, -1 ) - LWKOPT = N*NB + LWKOPT = MAX( 1, N*NB ) WORK( 1 ) = LWKOPT END IF * diff --git a/lapack-netlib/SRC/zhetrf_rook.f b/lapack-netlib/SRC/zhetrf_rook.f index e9de47248..a56349092 100644 --- a/lapack-netlib/SRC/zhetrf_rook.f +++ b/lapack-netlib/SRC/zhetrf_rook.f @@ -122,7 +122,7 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The length of WORK. LWORK >=1. For best performance +*> The length of WORK. LWORK >= 1. For best performance *> LWORK >= N*NB, where NB is the block size returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine @@ -150,7 +150,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEcomputational +*> \ingroup hetrf_rook * *> \par Further Details: * ===================== diff --git a/lapack-netlib/SRC/zhetri2.f b/lapack-netlib/SRC/zhetri2.f index 384745c3a..1d932b866 100644 --- a/lapack-netlib/SRC/zhetri2.f +++ b/lapack-netlib/SRC/zhetri2.f @@ -88,16 +88,16 @@ *> *> \param[out] WORK *> \verbatim -*> WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3) +*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. -*> WORK is size >= (N+NB+1)*(NB+3) +*> If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3). *> If LWORK = -1, then a workspace query is assumed; the routine -*> calculates: +*> calculates: *> - the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, *> - and no error message related to LWORK is issued by XERBLA. @@ -120,7 +120,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEcomputational +*> \ingroup hetri2 * * ===================================================================== SUBROUTINE ZHETRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) @@ -159,9 +159,13 @@ INFO = 0 UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) +* * Get blocksize +* NBMAX = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 ) - IF ( NBMAX .GE. N ) THEN + IF( N.EQ.0 ) THEN + MINSIZE = 1 + ELSE IF( NBMAX.GE.N ) THEN MINSIZE = N ELSE MINSIZE = (N+NBMAX+1)*(NBMAX+3) @@ -173,28 +177,29 @@ INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 - ELSE IF (LWORK .LT. MINSIZE .AND. .NOT.LQUERY ) THEN + ELSE IF( LWORK.LT.MINSIZE .AND. .NOT.LQUERY ) THEN INFO = -7 END IF -* -* Quick return if possible -* * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHETRI2', -INFO ) RETURN ELSE IF( LQUERY ) THEN - WORK(1)=MINSIZE + WORK( 1 ) = MINSIZE RETURN END IF +* +* Quick return if possible +* IF( N.EQ.0 ) $ RETURN - IF( NBMAX .GE. N ) THEN + IF( NBMAX.GE.N ) THEN CALL ZHETRI( UPLO, N, A, LDA, IPIV, WORK, INFO ) ELSE CALL ZHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NBMAX, INFO ) END IF +* RETURN * * End of ZHETRI2 diff --git a/lapack-netlib/SRC/zhetrs_aa.f b/lapack-netlib/SRC/zhetrs_aa.f index 06ac1fd28..b7a1f7f07 100644 --- a/lapack-netlib/SRC/zhetrs_aa.f +++ b/lapack-netlib/SRC/zhetrs_aa.f @@ -106,7 +106,13 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,3*N-2). +*> The dimension of the array WORK. +*> If MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2. +*> +*> If LWORK = -1, then a workspace query is assumed; the routine +*> only calculates the minimal size of the WORK array, returns +*> this value as the first entry of the WORK array, and no error +*> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO @@ -124,7 +130,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup complex16HEcomputational +*> \ingroup hetrs_aa * * ===================================================================== SUBROUTINE ZHETRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, @@ -152,7 +158,7 @@ * .. * .. Local Scalars .. LOGICAL LQUERY, UPPER - INTEGER K, KP, LWKOPT + INTEGER K, KP, LWKMIN * .. * .. External Functions .. LOGICAL LSAME @@ -162,13 +168,19 @@ EXTERNAL ZGTSV, ZSWAP, ZTRSM, ZLACGV, ZLACPY, XERBLA * .. * .. Intrinsic Functions .. - INTRINSIC MAX + INTRINSIC MIN, MAX * .. * .. Executable Statements .. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) + IF( MIN( N, NRHS ).EQ.0 ) THEN + LWKMIN = 1 + ELSE + LWKMIN = 3*N-2 + END IF +* IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN @@ -179,21 +191,20 @@ INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 - ELSE IF( LWORK.LT.MAX( 1, 3*N-2 ) .AND. .NOT.LQUERY ) THEN + ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHETRS_AA', -INFO ) RETURN ELSE IF( LQUERY ) THEN - LWKOPT = (3*N-2) - WORK( 1 ) = LWKOPT + WORK( 1 ) = LWKMIN RETURN END IF * * Quick return if possible * - IF( N.EQ.0 .OR. NRHS.EQ.0 ) + IF( MIN( N, NRHS ).EQ.0 ) $ RETURN * IF( UPPER ) THEN diff --git a/lapack-netlib/SRC/zlamswlq.f b/lapack-netlib/SRC/zlamswlq.f index 4abefa434..59a0a5558 100644 --- a/lapack-netlib/SRC/zlamswlq.f +++ b/lapack-netlib/SRC/zlamswlq.f @@ -127,17 +127,20 @@ *> *> \param[out] WORK *> \verbatim -*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the minimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. -*> If SIDE = 'L', LWORK >= max(1,NB) * MB; -*> if SIDE = 'R', LWORK >= max(1,M) * MB. +*> If MIN(M,N,K) = 0, LWORK >= 1. +*> If SIDE = 'L', LWORK >= max(1,NB*MB). +*> If SIDE = 'R', LWORK >= max(1,M*MB). +*> *> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns +*> only calculates the minimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim @@ -189,92 +192,103 @@ *> SIAM J. Sci. Comput, vol. 34, no. 1, 2012 *> \endverbatim *> +*> \ingroup lamswlq +*> * ===================================================================== SUBROUTINE ZLAMSWLQ( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, - $ LDT, C, LDC, WORK, LWORK, INFO ) + $ LDT, C, LDC, WORK, LWORK, INFO ) * * -- LAPACK computational 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, TRANS - INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC + CHARACTER SIDE, TRANS + INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC * .. * .. Array Arguments .. - COMPLEX*16 A( LDA, * ), WORK( * ), C(LDC, * ), - $ T( LDT, * ) + COMPLEX*16 A( LDA, * ), WORK( * ), C( LDC, * ), + $ T( LDT, * ) * .. * * ===================================================================== * * .. * .. Local Scalars .. - LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY - INTEGER I, II, KK, LW, CTR + LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY + INTEGER I, II, KK, LW, CTR, MINMNK, LWMIN * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME +* .. * .. External Subroutines .. - EXTERNAL ZTPMLQT, ZGEMLQT, XERBLA + EXTERNAL ZTPMLQT, ZGEMLQT, XERBLA * .. * .. Executable Statements .. * * Test the input arguments * - LQUERY = LWORK.LT.0 + INFO = 0 + LQUERY = ( LWORK.EQ.-1 ) NOTRAN = LSAME( TRANS, 'N' ) TRAN = LSAME( TRANS, 'C' ) LEFT = LSAME( SIDE, 'L' ) RIGHT = LSAME( SIDE, 'R' ) - IF (LEFT) THEN + IF( LEFT ) THEN LW = N * MB ELSE LW = M * MB END IF * - INFO = 0 + MINMNK = MIN( M, N, K ) + IF( MINMNK.EQ.0 ) THEN + LWMIN = 1 + ELSE + LWMIN = MAX( 1, LW ) + END IF +* IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN - INFO = -1 + INFO = -1 ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN - INFO = -2 + INFO = -2 ELSE IF( K.LT.0 ) THEN INFO = -5 ELSE IF( M.LT.K ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 - ELSE IF( K.LT.MB .OR. MB.LT.1) THEN + ELSE IF( K.LT.MB .OR. MB.LT.1 ) THEN INFO = -6 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN INFO = -9 - ELSE IF( LDT.LT.MAX( 1, MB) ) THEN + ELSE IF( LDT.LT.MAX( 1, MB ) ) THEN INFO = -11 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -13 - ELSE IF(( LWORK.LT.MAX(1,LW)).AND.(.NOT.LQUERY)) THEN + INFO = -13 + ELSE IF( LWORK.LT.LWMIN .AND. (.NOT.LQUERY) ) THEN INFO = -15 END IF * + IF( INFO.EQ.0 ) THEN + WORK( 1 ) = LWMIN + END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLAMSWLQ', -INFO ) - WORK(1) = LW RETURN - ELSE IF (LQUERY) THEN - WORK(1) = LW + ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * - IF( MIN(M,N,K).EQ.0 ) THEN + IF( MINMNK.EQ.0 ) THEN RETURN END IF * IF((NB.LE.K).OR.(NB.GE.MAX(M,N,K))) THEN CALL ZGEMLQT( SIDE, TRANS, M, N, K, MB, A, LDA, - $ T, LDT, C, LDC, WORK, INFO) + $ T, LDT, C, LDC, WORK, INFO ) RETURN END IF * @@ -403,7 +417,7 @@ * END IF * - WORK(1) = LW + WORK( 1 ) = LWMIN RETURN * * End of ZLAMSWLQ diff --git a/lapack-netlib/SRC/zlamtsqr.f b/lapack-netlib/SRC/zlamtsqr.f index 5030cb75f..03770c06e 100644 --- a/lapack-netlib/SRC/zlamtsqr.f +++ b/lapack-netlib/SRC/zlamtsqr.f @@ -128,22 +128,24 @@ *> *> \param[out] WORK *> \verbatim -*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> +*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the minimal LWORK. *> \endverbatim +*> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. +*> If MIN(M,N,K) = 0, LWORK >= 1. +*> If SIDE = 'L', LWORK >= max(1,N*NB). +*> If SIDE = 'R', LWORK >= max(1,MB*NB). *> -*> If SIDE = 'L', LWORK >= max(1,N)*NB; -*> if SIDE = 'R', LWORK >= max(1,MB)*NB. *> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns +*> only calculates the minimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. -*> *> \endverbatim +*> *> \param[out] INFO *> \verbatim *> INFO is INTEGER @@ -191,46 +193,50 @@ *> SIAM J. Sci. Comput, vol. 34, no. 1, 2012 *> \endverbatim *> +*> \ingroup lamtsqr +*> * ===================================================================== SUBROUTINE ZLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, - $ LDT, C, LDC, WORK, LWORK, INFO ) + $ LDT, C, LDC, WORK, LWORK, INFO ) * * -- LAPACK computational 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, TRANS - INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC + CHARACTER SIDE, TRANS + INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC * .. * .. Array Arguments .. - COMPLEX*16 A( LDA, * ), WORK( * ), C(LDC, * ), - $ T( LDT, * ) + COMPLEX*16 A( LDA, * ), WORK( * ), C( LDC, * ), + $ T( LDT, * ) * .. * * ===================================================================== * * .. * .. Local Scalars .. - LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY - INTEGER I, II, KK, LW, CTR, Q + LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY + INTEGER I, II, KK, LW, CTR, Q, MINMNK, LWMIN * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME +* .. * .. External Subroutines .. - EXTERNAL ZGEMQRT, ZTPMQRT, XERBLA + EXTERNAL ZGEMQRT, ZTPMQRT, XERBLA * .. * .. Executable Statements .. * * Test the input arguments * - LQUERY = LWORK.LT.0 + INFO = 0 + LQUERY = ( LWORK.EQ.-1 ) NOTRAN = LSAME( TRANS, 'N' ) TRAN = LSAME( TRANS, 'C' ) LEFT = LSAME( SIDE, 'L' ) RIGHT = LSAME( SIDE, 'R' ) - IF (LEFT) THEN + IF( LEFT ) THEN LW = N * NB Q = M ELSE @@ -238,11 +244,17 @@ Q = N END IF * - INFO = 0 + MINMNK = MIN( M, N, K ) + IF( MINMNK.EQ.0 ) THEN + LWMIN = 1 + ELSE + LWMIN = MAX( 1, LW ) + END IF +* IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN - INFO = -1 + INFO = -1 ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN - INFO = -2 + INFO = -2 ELSE IF( M.LT.K ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN @@ -253,38 +265,38 @@ INFO = -7 ELSE IF( LDA.LT.MAX( 1, Q ) ) THEN INFO = -9 - ELSE IF( LDT.LT.MAX( 1, NB) ) THEN + ELSE IF( LDT.LT.MAX( 1, NB ) ) THEN INFO = -11 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -13 - ELSE IF(( LWORK.LT.MAX(1,LW)).AND.(.NOT.LQUERY)) THEN + INFO = -13 + ELSE IF( LWORK.LT.LWMIN .AND. (.NOT.LQUERY) ) THEN INFO = -15 END IF * -* Determine the block size if it is tall skinny or short and wide -* - IF( INFO.EQ.0) THEN - WORK(1) = LW + IF( INFO.EQ.0 ) THEN + WORK( 1 ) = LWMIN END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLAMTSQR', -INFO ) RETURN - ELSE IF (LQUERY) THEN - RETURN + ELSE IF( LQUERY ) THEN + RETURN END IF * * Quick return if possible * - IF( MIN(M,N,K).EQ.0 ) THEN + IF( MINMNK.EQ.0 ) THEN RETURN END IF +* +* Determine the block size if it is tall skinny or short and wide * IF((MB.LE.K).OR.(MB.GE.MAX(M,N,K))) THEN CALL ZGEMQRT( SIDE, TRANS, M, N, K, NB, A, LDA, - $ T, LDT, C, LDC, WORK, INFO) + $ T, LDT, C, LDC, WORK, INFO ) RETURN - END IF + END IF * IF(LEFT.AND.NOTRAN) THEN * @@ -410,7 +422,7 @@ * END IF * - WORK(1) = LW + WORK( 1 ) = LWMIN RETURN * * End of ZLAMTSQR diff --git a/lapack-netlib/SRC/zlaswlq.f b/lapack-netlib/SRC/zlaswlq.f index be4c48539..735207132 100644 --- a/lapack-netlib/SRC/zlaswlq.f +++ b/lapack-netlib/SRC/zlaswlq.f @@ -96,22 +96,23 @@ *> The leading dimension of the array T. LDT >= MB. *> \endverbatim *> -*> *> \param[out] WORK *> \verbatim -*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> +*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the minimal LWORK. *> \endverbatim *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= MB*M. +*> The dimension of the array WORK. +*> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= MB*M, otherwise. +*> *> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns +*> only calculates the minimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. -*> *> \endverbatim +*> *> \param[out] INFO *> \verbatim *> INFO is INTEGER @@ -159,33 +160,37 @@ *> SIAM J. Sci. Comput, vol. 34, no. 1, 2012 *> \endverbatim *> +*> \ingroup laswlq +*> * ===================================================================== SUBROUTINE ZLASWLQ( M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, - $ INFO) + $ INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. -- * * .. Scalar Arguments .. - INTEGER INFO, LDA, M, N, MB, NB, LWORK, LDT + INTEGER INFO, LDA, M, N, MB, NB, LWORK, LDT * .. * .. Array Arguments .. - COMPLEX*16 A( LDA, * ), WORK( * ), T( LDT, *) + COMPLEX*16 A( LDA, * ), WORK( * ), T( LDT, * ) * .. * * ===================================================================== * * .. * .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, II, KK, CTR + LOGICAL LQUERY + INTEGER I, II, KK, CTR, MINMN, LWMIN * .. * .. EXTERNAL FUNCTIONS .. LOGICAL LSAME EXTERNAL LSAME +* .. * .. EXTERNAL SUBROUTINES .. EXTERNAL ZGELQT, ZTPLQT, XERBLA +* .. * .. INTRINSIC FUNCTIONS .. INTRINSIC MAX, MIN, MOD * .. @@ -196,12 +201,19 @@ INFO = 0 * LQUERY = ( LWORK.EQ.-1 ) +* + MINMN = MIN( M, N ) + IF( MINMN.EQ.0 ) THEN + LWMIN = 1 + ELSE + LWMIN = M*MB + END IF * IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. N.LT.M ) THEN INFO = -2 - ELSE IF( MB.LT.1 .OR. ( MB.GT.M .AND. M.GT.0 )) THEN + ELSE IF( MB.LT.1 .OR. ( MB.GT.M .AND. M.GT.0 ) ) THEN INFO = -3 ELSE IF( NB.LE.0 ) THEN INFO = -4 @@ -209,60 +221,61 @@ INFO = -6 ELSE IF( LDT.LT.MB ) THEN INFO = -8 - ELSE IF( ( LWORK.LT.M*MB) .AND. (.NOT.LQUERY) ) THEN + ELSE IF( LWORK.LT.LWMIN .AND. (.NOT.LQUERY) ) THEN INFO = -10 END IF - IF( INFO.EQ.0) THEN - WORK(1) = MB*M +* + IF( INFO.EQ.0 ) THEN + WORK( 1 ) = LWMIN END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLASWLQ', -INFO ) RETURN - ELSE IF (LQUERY) THEN - RETURN + ELSE IF( LQUERY ) THEN + RETURN END IF * * Quick return if possible * - IF( MIN(M,N).EQ.0 ) THEN - RETURN + IF( MINMN.EQ.0 ) THEN + RETURN END IF * * The LQ Decomposition * - IF((M.GE.N).OR.(NB.LE.M).OR.(NB.GE.N)) THEN - CALL ZGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO) + IF( (M.GE.N) .OR. (NB.LE.M) .OR. (NB.GE.N) ) THEN + CALL ZGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO ) RETURN - END IF + END IF * - KK = MOD((N-M),(NB-M)) - II=N-KK+1 + KK = MOD((N-M),(NB-M)) + II = N-KK+1 * -* Compute the LQ factorization of the first block A(1:M,1:NB) +* Compute the LQ factorization of the first block A(1:M,1:NB) * - CALL ZGELQT( M, NB, MB, A(1,1), LDA, T, LDT, WORK, INFO) - CTR = 1 + CALL ZGELQT( M, NB, MB, A(1,1), LDA, T, LDT, WORK, INFO ) + CTR = 1 * - DO I = NB+1, II-NB+M , (NB-M) + DO I = NB+1, II-NB+M, (NB-M) * -* Compute the QR factorization of the current block A(1:M,I:I+NB-M) +* Compute the QR factorization of the current block A(1:M,I:I+NB-M) * - CALL ZTPLQT( M, NB-M, 0, MB, A(1,1), LDA, A( 1, I ), - $ LDA, T(1, CTR * M + 1), - $ LDT, WORK, INFO ) - CTR = CTR + 1 - END DO + CALL ZTPLQT( M, NB-M, 0, MB, A(1,1), LDA, A( 1, I ), + $ LDA, T(1, CTR * M + 1), + $ LDT, WORK, INFO ) + CTR = CTR + 1 + END DO * * Compute the QR factorization of the last block A(1:M,II:N) * - IF (II.LE.N) THEN + IF( II.LE.N ) THEN CALL ZTPLQT( M, KK, 0, MB, A(1,1), LDA, A( 1, II ), - $ LDA, T(1, CTR * M + 1), LDT, - $ WORK, INFO ) - END IF + $ LDA, T(1, CTR * M + 1), LDT, + $ WORK, INFO ) + END IF * - WORK( 1 ) = M * MB + WORK( 1 ) = LWMIN RETURN * * End of ZLASWLQ diff --git a/lapack-netlib/SRC/zlatrs3.f b/lapack-netlib/SRC/zlatrs3.f index 231a17274..27eac839b 100644 --- a/lapack-netlib/SRC/zlatrs3.f +++ b/lapack-netlib/SRC/zlatrs3.f @@ -158,7 +158,11 @@ *> \endverbatim *> *> \param[in] LWORK +*> \verbatim *> LWORK is INTEGER +*> The dimension of the array WORK. +*> +*> If MIN(N,NRHS) = 0, LWORK >= 1, else *> LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS, 32)), where *> NBA = (N + NB - 1)/NB and NB is the optimal block size. *> @@ -166,6 +170,7 @@ *> only calculates the optimal dimensions of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. +*> \endverbatim *> *> \param[out] INFO *> \verbatim @@ -182,7 +187,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \ingroup doubleOTHERauxiliary +*> \ingroup latrs3 *> \par Further Details: * ===================== * \verbatim @@ -257,7 +262,7 @@ LOGICAL LQUERY, NOTRAN, NOUNIT, UPPER INTEGER AWRK, I, IFIRST, IINC, ILAST, II, I1, I2, J, $ JFIRST, JINC, JLAST, J1, J2, K, KK, K1, K2, - $ LANRM, LDS, LSCALE, NB, NBA, NBX, RHS + $ LANRM, LDS, LSCALE, NB, NBA, NBX, RHS, LWMIN DOUBLE PRECISION ANRM, BIGNUM, BNRM, RSCAL, SCAL, SCALOC, $ SCAMIN, SMLNUM, TMAX * .. @@ -296,15 +301,24 @@ * row. WORK( I + KK * LDS ) is the scale factor of the vector * segment associated with the I-th block row and the KK-th vector * in the block column. +* LSCALE = NBA * MAX( NBA, MIN( NRHS, NBRHS ) ) LDS = NBA +* * The second part stores upper bounds of the triangular A. There are * a total of NBA x NBA blocks, of which only the upper triangular * part or the lower triangular part is referenced. The upper bound of * the block A( I, J ) is stored as WORK( AWRK + I + J * NBA ). +* LANRM = NBA * NBA AWRK = LSCALE - WORK( 1 ) = LSCALE + LANRM +* + IF( MIN( N, NRHS ).EQ.0 ) THEN + LWMIN = 1 + ELSE + LWMIN = LSCALE + LANRM + END IF + WORK( 1 ) = LWMIN * * Test the input parameters. * @@ -326,7 +340,7 @@ INFO = -8 ELSE IF( LDX.LT.MAX( 1, N ) ) THEN INFO = -10 - ELSE IF( .NOT.LQUERY .AND. LWORK.LT.WORK( 1 ) ) THEN + ELSE IF( .NOT.LQUERY .AND. LWORK.LT.LWMIN ) THEN INFO = -14 END IF IF( INFO.NE.0 ) THEN diff --git a/lapack-netlib/SRC/zlatsqr.f b/lapack-netlib/SRC/zlatsqr.f index 8c938aebc..24d00f28a 100644 --- a/lapack-netlib/SRC/zlatsqr.f +++ b/lapack-netlib/SRC/zlatsqr.f @@ -101,15 +101,18 @@ *> *> \param[out] WORK *> \verbatim -*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the minimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= NB*N. +*> The dimension of the array WORK. +*> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= NB*N, otherwise. +*> *> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns +*> only calculates the minimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim @@ -161,33 +164,37 @@ *> SIAM J. Sci. Comput, vol. 34, no. 1, 2012 *> \endverbatim *> +*> \ingroup latsqr +*> * ===================================================================== SUBROUTINE ZLATSQR( M, N, MB, NB, A, LDA, T, LDT, WORK, - $ LWORK, INFO) + $ LWORK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. -- * * .. Scalar Arguments .. - INTEGER INFO, LDA, M, N, MB, NB, LDT, LWORK + INTEGER INFO, LDA, M, N, MB, NB, LDT, LWORK * .. * .. Array Arguments .. - COMPLEX*16 A( LDA, * ), WORK( * ), T(LDT, *) + COMPLEX*16 A( LDA, * ), WORK( * ), T( LDT, * ) * .. * * ===================================================================== * * .. * .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, II, KK, CTR + LOGICAL LQUERY + INTEGER I, II, KK, CTR, LWMIN, MINMN * .. * .. EXTERNAL FUNCTIONS .. LOGICAL LSAME EXTERNAL LSAME +* .. * .. EXTERNAL SUBROUTINES .. - EXTERNAL ZGEQRT, ZTPQRT, XERBLA + EXTERNAL ZGEQRT, ZTPQRT, XERBLA +* .. * .. INTRINSIC FUNCTIONS .. INTRINSIC MAX, MIN, MOD * .. @@ -198,6 +205,13 @@ INFO = 0 * LQUERY = ( LWORK.EQ.-1 ) +* + MINMN = MIN( M, N ) + IF( MINMN.EQ.0 ) THEN + LWMIN = 1 + ELSE + LWMIN = N*NB + END IF * IF( M.LT.0 ) THEN INFO = -1 @@ -205,64 +219,65 @@ INFO = -2 ELSE IF( MB.LT.1 ) THEN INFO = -3 - ELSE IF( NB.LT.1 .OR. ( NB.GT.N .AND. N.GT.0 )) THEN + ELSE IF( NB.LT.1 .OR. ( NB.GT.N .AND. N.GT.0 ) ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -6 ELSE IF( LDT.LT.NB ) THEN INFO = -8 - ELSE IF( LWORK.LT.(N*NB) .AND. (.NOT.LQUERY) ) THEN + ELSE IF( LWORK.LT.LWMIN .AND. (.NOT.LQUERY) ) THEN INFO = -10 END IF - IF( INFO.EQ.0) THEN - WORK(1) = NB*N +* + IF( INFO.EQ.0 ) THEN + WORK( 1 ) = LWMIN END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLATSQR', -INFO ) RETURN - ELSE IF (LQUERY) THEN - RETURN + ELSE IF( LQUERY ) THEN + RETURN END IF * * Quick return if possible * - IF( MIN(M,N).EQ.0 ) THEN - RETURN + IF( MINMN.EQ.0 ) THEN + RETURN END IF * * The QR Decomposition * - IF ((MB.LE.N).OR.(MB.GE.M)) THEN - CALL ZGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO) - RETURN - END IF - KK = MOD((M-N),(MB-N)) - II=M-KK+1 + IF( (MB.LE.N) .OR. (MB.GE.M) ) THEN + CALL ZGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO ) + RETURN + END IF + KK = MOD((M-N),(MB-N)) + II = M-KK+1 * -* Compute the QR factorization of the first block A(1:MB,1:N) +* Compute the QR factorization of the first block A(1:MB,1:N) * - CALL ZGEQRT( MB, N, NB, A(1,1), LDA, T, LDT, WORK, INFO ) - CTR = 1 + CALL ZGEQRT( MB, N, NB, A(1,1), LDA, T, LDT, WORK, INFO ) + CTR = 1 * - DO I = MB+1, II-MB+N , (MB-N) + DO I = MB+1, II-MB+N, (MB-N) * -* Compute the QR factorization of the current block A(I:I+MB-N,1:N) +* Compute the QR factorization of the current block A(I:I+MB-N,1:N) * - CALL ZTPQRT( MB-N, N, 0, NB, A(1,1), LDA, A( I, 1 ), LDA, - $ T(1, CTR * N + 1), - $ LDT, WORK, INFO ) - CTR = CTR + 1 - END DO + CALL ZTPQRT( MB-N, N, 0, NB, A(1,1), LDA, A( I, 1 ), LDA, + $ T(1, CTR * N + 1), + $ LDT, WORK, INFO ) + CTR = CTR + 1 + END DO * -* Compute the QR factorization of the last block A(II:M,1:N) +* Compute the QR factorization of the last block A(II:M,1:N) * - IF (II.LE.M) THEN - CALL ZTPQRT( KK, N, 0, NB, A(1,1), LDA, A( II, 1 ), LDA, - $ T(1,CTR * N + 1), LDT, - $ WORK, INFO ) - END IF + IF( II.LE.M ) THEN + CALL ZTPQRT( KK, N, 0, NB, A(1,1), LDA, A( II, 1 ), LDA, + $ T(1,CTR * N + 1), LDT, + $ WORK, INFO ) + END IF * - work( 1 ) = N*NB + WORK( 1 ) = LWMIN RETURN * * End of ZLATSQR