From 4d3d13070bb12b22ba1e24c8086d2098b567336b Mon Sep 17 00:00:00 2001 From: Elizaveta Tokmasheva Date: Thu, 30 Nov 2023 17:59:08 +0700 Subject: [PATCH] handle and document corner cases of lwork in lapack, double complex precision --- SRC/zgebrd.f | 22 ++++++--- SRC/zgehrd.f | 11 +++-- SRC/zgelq.f | 2 +- SRC/zgelqf.f | 16 ++++--- SRC/zgemlq.f | 20 ++++++--- SRC/zgemqr.f | 20 ++++++--- SRC/zgeqlf.f | 8 ++-- SRC/zgeqp3rk.f | 3 +- SRC/zgeqr.f | 16 ++++--- SRC/zgeqrfp.f | 22 ++++++--- SRC/zgesvj.f | 81 ++++++++++++++++++++-------------- SRC/zgetri.f | 2 +- SRC/zgetsls.f | 7 ++- SRC/zgetsqrhrt.f | 13 +++--- SRC/zgges3.f | 25 +++++++---- SRC/zggev3.f | 16 ++++--- SRC/zgghd3.f | 12 +++-- SRC/zggqrf.f | 2 +- SRC/zggrqf.f | 2 +- SRC/zggsvd3.f | 2 +- SRC/zggsvp3.f | 2 +- SRC/zhesv_aa.f | 4 +- SRC/zhesv_aa_2stage.f | 23 +++++----- SRC/zhesvx.f | 11 ++--- SRC/zhetrf.f | 2 +- SRC/zhetrf_aa.f | 18 +++++--- SRC/zhetrf_aa_2stage.f | 26 +++++------ SRC/zhetrf_rk.f | 4 +- SRC/zhetrf_rook.f | 2 +- SRC/zhetri2.f | 20 +++++---- SRC/zhetrs_aa.f | 23 +++++++--- TESTING/LIN/zchkhe_aa_2stage.f | 6 +-- TESTING/LIN/zdrvhe_aa_2stage.f | 4 +- 33 files changed, 278 insertions(+), 169 deletions(-) diff --git a/SRC/zgebrd.f b/SRC/zgebrd.f index 089fc1095c..d85721b8ab 100644 --- a/SRC/zgebrd.f +++ b/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. *> @@ -223,8 +224,8 @@ SUBROUTINE ZGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, * .. * .. 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 @@ SUBROUTINE ZGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, * 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 = MAX( 1, ( M+N )*NB ) + END IF WORK( 1 ) = DBLE( LWKOPT ) +* LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 @@ -251,7 +260,7 @@ SUBROUTINE ZGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, 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 @@ SUBROUTINE ZGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, * * Quick return if possible * - MINMN = MIN( M, N ) IF( MINMN.EQ.0 ) THEN WORK( 1 ) = 1 RETURN diff --git a/SRC/zgehrd.f b/SRC/zgehrd.f index 6ddb9551cb..05f385c976 100644 --- a/SRC/zgehrd.f +++ b/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 *> @@ -225,8 +225,13 @@ SUBROUTINE ZGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) * * Compute the workspace requirements * - NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) - LWKOPT = N*NB + TSIZE + IF( N.EQ.0 ) THEN + LWKOPT = 1 + ELSE + NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, + $ -1 ) ) + LWKOPT = N*NB + TSIZE + END IF WORK( 1 ) = LWKOPT ENDIF * diff --git a/SRC/zgelq.f b/SRC/zgelq.f index 22ca6ca76a..86610e8019 100644 --- a/SRC/zgelq.f +++ b/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 diff --git a/SRC/zgelqf.f b/SRC/zgelqf.f index 4d6e7d995b..3ca3b89088 100644 --- a/SRC/zgelqf.f +++ b/SRC/zgelqf.f @@ -93,6 +93,7 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER +*> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise. *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is the *> optimal blocksize. @@ -174,9 +175,8 @@ SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) * 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 @@ SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) 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/SRC/zgemlq.f b/SRC/zgemlq.f index 1c29aa886e..11489087a4 100644 --- a/SRC/zgemlq.f +++ b/SRC/zgemlq.f @@ -109,13 +109,14 @@ *> *> \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 @@ -186,7 +187,7 @@ SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, * .. * .. 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 @@ -202,7 +203,7 @@ SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, * * Test the input arguments * - LQUERY = LWORK.EQ.-1 + LQUERY = ( LWORK.EQ.-1 ) NOTRAN = LSAME( TRANS, 'N' ) TRAN = LSAME( TRANS, 'C' ) LEFT = LSAME( SIDE, 'L' ) @@ -217,6 +218,13 @@ SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, 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 @@ -245,7 +253,7 @@ SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, 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 * @@ -262,7 +270,7 @@ SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, * * Quick return if possible * - IF( MIN( M, N, K ).EQ.0 ) THEN + IF( MINMNK.EQ.0 ) THEN RETURN END IF * diff --git a/SRC/zgemqr.f b/SRC/zgemqr.f index f299ece847..ca2742c759 100644 --- a/SRC/zgemqr.f +++ b/SRC/zgemqr.f @@ -111,13 +111,14 @@ *> *> \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 @@ -189,7 +190,7 @@ SUBROUTINE ZGEMQR( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, * .. * .. 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 @@ -205,7 +206,7 @@ SUBROUTINE ZGEMQR( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, * * Test the input arguments * - LQUERY = LWORK.EQ.-1 + LQUERY = ( LWORK.EQ.-1 ) NOTRAN = LSAME( TRANS, 'N' ) TRAN = LSAME( TRANS, 'C' ) LEFT = LSAME( SIDE, 'L' ) @@ -220,6 +221,13 @@ SUBROUTINE ZGEMQR( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, 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 @@ -248,7 +256,7 @@ SUBROUTINE ZGEMQR( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, 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 * @@ -265,7 +273,7 @@ SUBROUTINE ZGEMQR( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, * * Quick return if possible * - IF( MIN( M, N, K ).EQ.0 ) THEN + IF( MINMNK.EQ.0 ) THEN RETURN END IF * diff --git a/SRC/zgeqlf.f b/SRC/zgeqlf.f index 89c5b1b08c..a27612c640 100644 --- a/SRC/zgeqlf.f +++ b/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. *> @@ -188,8 +189,9 @@ SUBROUTINE ZGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) 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/SRC/zgeqp3rk.f b/SRC/zgeqp3rk.f index f8ef986c70..c1ce752877 100755 --- a/SRC/zgeqp3rk.f +++ b/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/SRC/zgeqr.f b/SRC/zgeqr.f index 704bcbc6cd..7f37a4c7ff 100644 --- a/SRC/zgeqr.f +++ b/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 @@ -190,7 +190,7 @@ SUBROUTINE ZGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK, * .. * .. Local Scalars .. LOGICAL LQUERY, LMINWS, MINT, MINW - INTEGER MB, NB, MINTSZ, NBLCKS + INTEGER MB, NB, MINTSZ, NBLCKS, LWMIN, LWREQ * .. * .. External Functions .. LOGICAL LSAME @@ -246,8 +246,10 @@ SUBROUTINE ZGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK, * * 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 @@ -255,7 +257,7 @@ SUBROUTINE ZGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK, NB = 1 MB = M END IF - IF( LWORK.LT.NB*N ) THEN + IF( LWORK.LT.LWREQ ) THEN LMINWS = .TRUE. NB = 1 END IF @@ -284,9 +286,9 @@ SUBROUTINE ZGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK, 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 @@ -311,7 +313,7 @@ SUBROUTINE ZGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK, $ LWORK, INFO ) END IF * - WORK( 1 ) = MAX( 1, NB*N ) + WORK( 1 ) = LWREQ * RETURN * diff --git a/SRC/zgeqrfp.f b/SRC/zgeqrfp.f index 6fe06d962d..3562de36ec 100644 --- a/SRC/zgeqrfp.f +++ b/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. *> @@ -162,8 +163,8 @@ SUBROUTINE ZGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO ) * * .. 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 @@ SUBROUTINE ZGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO ) * 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 @@ SUBROUTINE ZGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO ) 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 @@ SUBROUTINE ZGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO ) * * Quick return if possible * - K = MIN( M, N ) IF( K.EQ.0 ) THEN WORK( 1 ) = 1 RETURN @@ -210,7 +218,7 @@ SUBROUTINE ZGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO ) * 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/SRC/zgesvj.f b/SRC/zgesvj.f index ea0b162f95..82ee5e22d1 100644 --- a/SRC/zgesvj.f +++ b/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 >= MAX(1,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 @@ -367,23 +371,25 @@ SUBROUTINE ZGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, * * .. 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 +428,18 @@ SUBROUTINE ZGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, 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 + CWORK(1) = LWMIN + RWORK(1) = LRWMIN +* + 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 +459,9 @@ SUBROUTINE ZGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, 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 +471,13 @@ SUBROUTINE ZGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, 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 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/SRC/zgetri.f b/SRC/zgetri.f index 9aab294975..f3806a77c2 100644 --- a/SRC/zgetri.f +++ b/SRC/zgetri.f @@ -152,7 +152,7 @@ SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) * 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/SRC/zgetsls.f b/SRC/zgetsls.f index b9adbc8325..26311c611b 100644 --- a/SRC/zgetsls.f +++ b/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). @@ -229,7 +229,10 @@ SUBROUTINE ZGETSLS( TRANS, M, N, NRHS, A, LDA, B, LDB, * * 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 ) ) diff --git a/SRC/zgetsqrhrt.f b/SRC/zgetsqrhrt.f index 807a96fbef..e7ce993aa3 100644 --- a/SRC/zgetsqrhrt.f +++ b/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 @@ -212,7 +214,7 @@ SUBROUTINE ZGETSQRHRT( M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK, * 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 @@ SUBROUTINE ZGETSQRHRT( M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK, 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 @@ SUBROUTINE ZGETSQRHRT( M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK, 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/SRC/zgges3.f b/SRC/zgges3.f index c316c66945..daf407102c 100644 --- a/SRC/zgges3.f +++ b/SRC/zgges3.f @@ -215,7 +215,7 @@ *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER -*> The dimension of the array WORK. +*> The dimension of the array WORK. LWORK >= MAX(1,2*N) *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns @@ -300,7 +300,8 @@ SUBROUTINE ZGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, 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 * .. @@ -352,6 +353,8 @@ SUBROUTINE ZGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) + LWKMIN = MAX( 1, 2*N ) +* IF( IJOBVL.LE.0 ) THEN INFO = -1 ELSE IF( IJOBVR.LE.0 ) THEN @@ -368,7 +371,7 @@ SUBROUTINE ZGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, 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 * @@ -376,28 +379,32 @@ SUBROUTINE ZGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, * 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 diff --git a/SRC/zggev3.f b/SRC/zggev3.f index f8729e91d2..0cc0734708 100644 --- a/SRC/zggev3.f +++ b/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 @@ -243,7 +244,7 @@ SUBROUTINE ZGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, 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 @@ -300,6 +301,7 @@ SUBROUTINE ZGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) + LWKMIN = MAX( 1, 2*N ) IF( IJOBVL.LE.0 ) THEN INFO = -1 ELSE IF( IJOBVR.LE.0 ) THEN @@ -314,7 +316,7 @@ SUBROUTINE ZGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, 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 * @@ -322,7 +324,7 @@ SUBROUTINE ZGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, * 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 ) ) ) @@ -347,7 +349,11 @@ SUBROUTINE ZGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, $ 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 diff --git a/SRC/zgghd3.f b/SRC/zgghd3.f index 0da8972966..159984e099 100644 --- a/SRC/zgghd3.f +++ b/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. *> @@ -275,7 +275,12 @@ SUBROUTINE ZGGHD3( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, * INFO = 0 NB = ILAENV( 1, 'ZGGHD3', ' ', N, ILO, IHI, -1 ) - LWKOPT = MAX( 6*N*NB, 1 ) + NH = IHI - ILO + 1 + IF( N.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 @@ SUBROUTINE ZGGHD3( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, * * Quick return if possible * - NH = IHI - ILO + 1 IF( NH.LE.1 ) THEN WORK( 1 ) = CONE RETURN diff --git a/SRC/zggqrf.f b/SRC/zggqrf.f index 79104606c0..d8636d6635 100644 --- a/SRC/zggqrf.f +++ b/SRC/zggqrf.f @@ -250,7 +250,7 @@ SUBROUTINE ZGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, 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/SRC/zggrqf.f b/SRC/zggrqf.f index 8e4e45f003..69c14af245 100644 --- a/SRC/zggrqf.f +++ b/SRC/zggrqf.f @@ -249,7 +249,7 @@ SUBROUTINE ZGGRQF( M, P, N, A, LDA, TAUA, B, LDB, TAUB, WORK, 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/SRC/zggsvd3.f b/SRC/zggsvd3.f index d97265d44c..40624f5beb 100644 --- a/SRC/zggsvd3.f +++ b/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 diff --git a/SRC/zggsvp3.f b/SRC/zggsvp3.f index c21a146fa8..7b465aaeea 100644 --- a/SRC/zggsvp3.f +++ b/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 diff --git a/SRC/zhesv_aa.f b/SRC/zhesv_aa.f index 30f9e41a31..4a16376bf7 100644 --- a/SRC/zhesv_aa.f +++ b/SRC/zhesv_aa.f @@ -206,7 +206,7 @@ SUBROUTINE ZHESV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, 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.MAX( 1, 2*N, 3*N-2 ) .AND. .NOT.LQUERY ) THEN INFO = -10 END IF * @@ -216,7 +216,7 @@ SUBROUTINE ZHESV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, 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 = MAX( 1, LWKOPT_HETRF, LWKOPT_HETRS ) WORK( 1 ) = LWKOPT END IF * diff --git a/SRC/zhesv_aa_2stage.f b/SRC/zhesv_aa_2stage.f index b68d7a5f33..158791ccf2 100644 --- a/SRC/zhesv_aa_2stage.f +++ b/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 @@ -142,19 +142,20 @@ *> \param[in] LDB *> \verbatim *> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,N). +*> The leading dimension of the array B. LDB >= MAX(1,N). *> \endverbatim *> *> \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, @@ -208,7 +209,7 @@ SUBROUTINE ZHESV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, * * .. Local Scalars .. LOGICAL UPPER, TQUERY, WQUERY - INTEGER LWKOPT + INTEGER LWKOPT, LWKMIN * .. * .. External Functions .. LOGICAL LSAME @@ -229,6 +230,7 @@ SUBROUTINE ZHESV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, 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 @@ SUBROUTINE ZHESV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, 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/SRC/zhesvx.f b/SRC/zhesvx.f index db9ca6d521..64aa166749 100644 --- a/SRC/zhesvx.f +++ b/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 @@ -307,7 +307,7 @@ SUBROUTINE ZHESVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, * .. * .. Local Scalars .. LOGICAL LQUERY, NOFACT - INTEGER LWKOPT, NB + INTEGER LWKOPT, LWKMIN, NB DOUBLE PRECISION ANORM * .. * .. External Functions .. @@ -329,6 +329,7 @@ SUBROUTINE ZHESVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, 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 @@ SUBROUTINE ZHESVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, 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/SRC/zhetrf.f b/SRC/zhetrf.f index cb5429839a..a8df90ffe9 100644 --- a/SRC/zhetrf.f +++ b/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 *> diff --git a/SRC/zhetrf_aa.f b/SRC/zhetrf_aa.f index acca14627a..55217521e6 100644 --- a/SRC/zhetrf_aa.f +++ b/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 @@ -128,7 +130,7 @@ *> \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, -- @@ -189,7 +191,11 @@ SUBROUTINE ZHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO) END IF * IF( INFO.EQ.0 ) THEN - LWKOPT = (NB+1)*N + IF( N.LE.1 ) THEN + LWKOPT = 1 + ELSE + LWKOPT = (NB+1)*N + END IF WORK( 1 ) = LWKOPT END IF * @@ -202,11 +208,11 @@ SUBROUTINE ZHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO) * * 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/SRC/zhetrf_aa_2stage.f b/SRC/zhetrf_aa_2stage.f index 631f7deb6f..6d6676436e 100644 --- a/SRC/zhetrf_aa_2stage.f +++ b/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, @@ -182,7 +182,7 @@ SUBROUTINE ZHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, * .. 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 @@ SUBROUTINE ZHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, 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 @@ SUBROUTINE ZHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, 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 @@ SUBROUTINE ZHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, * * Quick return * - IF ( N.EQ.0 ) THEN + IF( N.EQ.0 ) THEN RETURN ENDIF * @@ -392,7 +392,7 @@ SUBROUTINE ZHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, 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 @@ SUBROUTINE ZHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, 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/SRC/zhetrf_rk.f b/SRC/zhetrf_rk.f index f0c3b68bb2..01b3e412dc 100644 --- a/SRC/zhetrf_rk.f +++ b/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. *> diff --git a/SRC/zhetrf_rook.f b/SRC/zhetrf_rook.f index 9cae55366c..a563490927 100644 --- a/SRC/zhetrf_rook.f +++ b/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 diff --git a/SRC/zhetri2.f b/SRC/zhetri2.f index 0748a6e989..3d4b896bc4 100644 --- a/SRC/zhetri2.f +++ b/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. @@ -161,7 +161,9 @@ SUBROUTINE ZHETRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) 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) @@ -173,20 +175,20 @@ SUBROUTINE ZHETRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) 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 diff --git a/SRC/zhetrs_aa.f b/SRC/zhetrs_aa.f index b203665d0c..a75fcd9cbb 100644 --- a/SRC/zhetrs_aa.f +++ b/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 @@ -152,7 +158,7 @@ SUBROUTINE ZHETRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, * .. * .. Local Scalars .. LOGICAL LQUERY, UPPER - INTEGER K, KP, LWKOPT + INTEGER K, KP, LWKMIN * .. * .. External Functions .. LOGICAL LSAME @@ -162,13 +168,19 @@ SUBROUTINE ZHETRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, 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 @@ -179,15 +191,14 @@ SUBROUTINE ZHETRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, 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 * diff --git a/TESTING/LIN/zchkhe_aa_2stage.f b/TESTING/LIN/zchkhe_aa_2stage.f index 802bc9e7cc..51082f1d0b 100644 --- a/TESTING/LIN/zchkhe_aa_2stage.f +++ b/TESTING/LIN/zchkhe_aa_2stage.f @@ -431,9 +431,9 @@ SUBROUTINE ZCHKHE_AA_2STAGE( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, * block factorization, LWORK is the length of AINV. * SRNAMT = 'ZHETRF_AA_2STAGE' - LWORK = MIN(N*NB, 3*NMAX*NMAX) - CALL ZHETRF_AA_2STAGE( UPLO, N, AFAC, LDA, - $ AINV, (3*NB+1)*N, + LWORK = MIN( MAX( 1, N*NB ), 3*NMAX*NMAX ) + CALL ZHETRF_AA_2STAGE( UPLO, N, AFAC, LDA, + $ AINV, MAX( 1, (3*NB+1)*N ), $ IWORK, IWORK( 1+N ), $ WORK, LWORK, $ INFO ) diff --git a/TESTING/LIN/zdrvhe_aa_2stage.f b/TESTING/LIN/zdrvhe_aa_2stage.f index 9401867e0c..fcd7744912 100644 --- a/TESTING/LIN/zdrvhe_aa_2stage.f +++ b/TESTING/LIN/zdrvhe_aa_2stage.f @@ -400,9 +400,9 @@ SUBROUTINE ZDRVHE_AA_2STAGE( * Factor the matrix and solve the system using ZHESV_AA. * SRNAMT = 'ZHESV_AA_2STAGE ' - LWORK = MIN(N*NB, 3*NMAX*NMAX) + LWORK = MIN( MAX( 1, N*NB ), 3*NMAX*NMAX ) CALL ZHESV_AA_2STAGE( UPLO, N, NRHS, AFAC, LDA, - $ AINV, (3*NB+1)*N, + $ AINV, MAX( 1, (3*NB+1)*N ), $ IWORK, IWORK( 1+N ), $ X, LDA, WORK, LWORK, INFO ) *