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Handle corner cases of LWORK (Reference-LAPACK PR 942)

This commit is contained in:
Martin Kroeker 2023-12-23 20:05:03 +01:00 committed by GitHub
parent 29d6024ec5
commit c082669ad4
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GPG Key ID: 4AEE18F83AFDEB23
43 changed files with 671 additions and 418 deletions
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28
lapack-netlib/SRC/sgebrd.f
View File

@ -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 @@
* ..
* .. 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 SGEBD2, SGEMM, SLABRD, XERBLA
@ -242,9 +243,16 @@
* Test the input parameters
*
INFO = 0
NB = MAX( 1, ILAENV( 1, 'SGEBRD', ' ', M, N, -1, -1 ) )
LWKOPT = ( M+N )*NB
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
MINMN = MIN( M, N )
IF( MINMN.EQ.0 ) THEN
LWKMIN = 1
LWKOPT = 1
ELSE
LWKMIN = MAX( M, N )
NB = MAX( 1, ILAENV( 1, 'SGEBRD', ' ', M, N, -1, -1 ) )
LWKOPT = ( M+N )*NB
ENDIF
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
LQUERY = ( LWORK.EQ.-1 )
IF( M.LT.0 ) THEN
INFO = -1
@ -252,7 +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
@ -264,7 +272,6 @@
*
* Quick return if possible
*
MINMN = MIN( M, N )
IF( MINMN.EQ.0 ) THEN
WORK( 1 ) = 1
RETURN
@ -283,7 +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
@ -342,7 +349,8 @@
*
CALL SGEBD2( M-I+1, N-I+1, A( I, I ), LDA, D( I ), E( I ),
$ TAUQ( I ), TAUP( I ), WORK, IINFO )
WORK( 1 ) = SROUNDUP_LWORK(WS)
*
WORK( 1 ) = SROUNDUP_LWORK( WS )
RETURN
*
* End of SGEBRD

26
lapack-netlib/SRC/sgehrd.f
View File

@ -89,7 +89,7 @@
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK)
*> WORK is REAL array, dimension (MAX(1,LWORK))
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
@ -173,7 +173,7 @@
INTEGER IHI, ILO, INFO, LDA, LWORK, N
* ..
* .. Array Arguments ..
REAL A( LDA, * ), TAU( * ), WORK( * )
REAL A( LDA, * ), TAU( * ), WORK( * )
* ..
*
* =====================================================================
@ -182,7 +182,7 @@
INTEGER NBMAX, LDT, TSIZE
PARAMETER ( NBMAX = 64, LDT = NBMAX+1,
$ TSIZE = LDT*NBMAX )
REAL ZERO, ONE
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0,
$ ONE = 1.0E+0 )
* ..
@ -190,7 +190,7 @@
LOGICAL LQUERY
INTEGER I, IB, IINFO, IWT, J, LDWORK, LWKOPT, NB,
$ NBMIN, NH, NX
REAL EI
REAL EI
* ..
* .. External Subroutines ..
EXTERNAL SAXPY, SGEHD2, SGEMM, SLAHR2, SLARFB, STRMM,
@ -222,13 +222,19 @@
INFO = -8
END IF
*
NH = IHI - ILO + 1
IF( INFO.EQ.0 ) THEN
*
* Compute the workspace requirements
*
NB = MIN( NBMAX, ILAENV( 1, 'SGEHRD', ' ', N, ILO, IHI, -1 ) )
LWKOPT = N*NB + TSIZE
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
IF( NH.LE.1 ) THEN
LWKOPT = 1
ELSE
NB = MIN( NBMAX, ILAENV( 1, 'SGEHRD', ' ', N, ILO, IHI,
$ -1 ) )
LWKOPT = N*NB + TSIZE
ENDIF
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
END IF
*
IF( INFO.NE.0 ) THEN
@ -249,7 +255,6 @@
*
* Quick return if possible
*
NH = IHI - ILO + 1
IF( NH.LE.1 ) THEN
WORK( 1 ) = 1
RETURN
@ -269,7 +274,7 @@
*
* 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
@ -345,7 +350,8 @@
* Use unblocked code to reduce the rest of the matrix
*
CALL SGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO )
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
*
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
RETURN
*

8
lapack-netlib/SRC/sgelq.f
View File

@ -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
@ -295,9 +295,9 @@
T( 2 ) = MB
T( 3 ) = NB
IF( MINW ) THEN
WORK( 1 ) = SROUNDUP_LWORK(LWMIN)
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
ELSE
WORK( 1 ) = SROUNDUP_LWORK(LWREQ)
WORK( 1 ) = SROUNDUP_LWORK( LWREQ )
END IF
END IF
IF( INFO.NE.0 ) THEN
@ -322,7 +322,7 @@
$ LWORK, INFO )
END IF
*
WORK( 1 ) = SROUNDUP_LWORK(LWREQ)
WORK( 1 ) = SROUNDUP_LWORK( LWREQ )
RETURN
*
* End of SGELQ

20
lapack-netlib/SRC/sgelqf.f
View File

@ -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.
*>
@ -175,9 +176,8 @@
* Test the input arguments
*
INFO = 0
K = MIN( M, N )
NB = ILAENV( 1, 'SGELQF', ' ', M, N, -1, -1 )
LWKOPT = M*NB
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
LQUERY = ( LWORK.EQ.-1 )
IF( M.LT.0 ) THEN
INFO = -1
@ -185,19 +185,25 @@
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( 'SGELQF', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
IF( K.EQ.0 ) THEN
LWKOPT = 1
ELSE
LWKOPT = M*NB
END IF
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
RETURN
END IF
*
* Quick return if possible
*
K = MIN( M, N )
IF( K.EQ.0 ) THEN
WORK( 1 ) = 1
RETURN
@ -267,7 +273,7 @@
$ CALL SGELQ2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
$ IINFO )
*
WORK( 1 ) = SROUNDUP_LWORK(IWS)
WORK( 1 ) = SROUNDUP_LWORK( IWS )
RETURN
*
* End of SGELQF

24
lapack-netlib/SRC/sgemlq.f
View File

@ -110,13 +110,14 @@
*>
*> \param[out] WORK
*> \verbatim
*> (workspace) REAL array, dimension (MAX(1,LWORK))
*> (workspace) DOUBLE PRECISION 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
@ -187,7 +188,7 @@
* ..
* .. 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
@ -207,7 +208,7 @@
*
* Test the input arguments
*
LQUERY = LWORK.EQ.-1
LQUERY = ( LWORK.EQ.-1 )
NOTRAN = LSAME( TRANS, 'N' )
TRAN = LSAME( TRANS, 'T' )
LEFT = LSAME( SIDE, 'L' )
@ -222,6 +223,13 @@
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
@ -250,12 +258,12 @@
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 ) = SROUNDUP_LWORK( LW )
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
END IF
*
IF( INFO.NE.0 ) THEN
@ -267,7 +275,7 @@
*
* Quick return if possible
*
IF( MIN( M, N, K ).EQ.0 ) THEN
IF( MINMNK.EQ.0 ) THEN
RETURN
END IF
*
@ -280,7 +288,7 @@
$ MB, C, LDC, WORK, LWORK, INFO )
END IF
*
WORK( 1 ) = SROUNDUP_LWORK( LW )
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
*
RETURN
*

22
lapack-netlib/SRC/sgemqr.f
View File

@ -189,12 +189,13 @@
* ..
* .. 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
EXTERNAL LSAME
REAL SROUNDUP_LWORK
EXTERNAL LSAME, SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. External Subroutines ..
EXTERNAL SGEMQRT, SLAMTSQR, XERBLA
@ -206,7 +207,7 @@
*
* Test the input arguments
*
LQUERY = LWORK.EQ.-1
LQUERY = ( LWORK.EQ.-1 )
NOTRAN = LSAME( TRANS, 'N' )
TRAN = LSAME( TRANS, 'T' )
LEFT = LSAME( SIDE, 'L' )
@ -221,6 +222,13 @@
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
@ -249,12 +257,12 @@
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 ) = SROUNDUP_LWORK(LW)
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
END IF
*
IF( INFO.NE.0 ) THEN
@ -266,7 +274,7 @@
*
* Quick return if possible
*
IF( MIN( M, N, K ).EQ.0 ) THEN
IF( MINMNK.EQ.0 ) THEN
RETURN
END IF
*
@ -279,7 +287,7 @@
$ NB, C, LDC, WORK, LWORK, INFO )
END IF
*
WORK( 1 ) = SROUNDUP_LWORK(LW)
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
*
RETURN
*

8
lapack-netlib/SRC/sgeqlf.f
View File

@ -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.
*>
@ -189,8 +190,9 @@
END IF
WORK( 1 ) = SROUNDUP_LWORK(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
*

24
lapack-netlib/SRC/sgeqp3rk.f
View File

@ -427,7 +427,8 @@
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK.
*. LWORK >= (3*N + NRHS - 1)
*> LWORK >= 1, if MIN(M,N) = 0, and
*> LWORK >= (3*N+NRHS-1), otherwise.
*> For optimal performance LWORK >= (2*N + NB*( N+NRHS+1 )),
*> where NB is the optimal block size for SGEQP3RK returned
*> by ILAENV. Minimal block size MINNB=2.
@ -618,8 +619,9 @@
* .. External Functions ..
LOGICAL SISNAN
INTEGER ISAMAX, ILAENV
REAL SLAMCH, SNRM2
EXTERNAL SISNAN, SLAMCH, SNRM2, ISAMAX, ILAENV
REAL SLAMCH, SNRM2, SROUNDUP_LWORK
EXTERNAL SISNAN, SLAMCH, SNRM2, ISAMAX, ILAENV,
$ SROUNDUP_LWORK
* ..
* .. Intrinsic Functions ..
INTRINSIC REAL, MAX, MIN
@ -696,7 +698,7 @@
*
LWKOPT = 2*N + NB*( N+NRHS+1 )
END IF
WORK( 1 ) = REAL( LWKOPT )
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN
INFO = -15
@ -719,7 +721,7 @@
K = 0
MAXC2NRMK = ZERO
RELMAXC2NRMK = ZERO
WORK( 1 ) = REAL( LWKOPT )
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
RETURN
END IF
*
@ -772,7 +774,7 @@
*
* Array TAU is not set and contains undefined elements.
*
WORK( 1 ) = REAL( LWKOPT )
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
RETURN
END IF
*
@ -791,7 +793,7 @@
TAU( J ) = ZERO
END DO
*
WORK( 1 ) = REAL( LWKOPT )
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
RETURN
*
END IF
@ -822,7 +824,7 @@
DO J = 1, MINMN
TAU( J ) = ZERO
END DO
WORK( 1 ) = REAL( LWKOPT )
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
RETURN
END IF
*
@ -867,7 +869,7 @@
TAU( J ) = ZERO
END DO
*
WORK( 1 ) = REAL( LWKOPT )
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
RETURN
END IF
*
@ -985,7 +987,7 @@
*
* Return from the routine.
*
WORK( 1 ) = REAL( LWKOPT )
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
RETURN
*
@ -1072,7 +1074,7 @@
*
END IF
*
WORK( 1 ) = REAL( LWKOPT )
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
RETURN
*

22
lapack-netlib/SRC/sgeqr.f
View File

@ -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 SGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK,
$ INFO )
@ -188,11 +190,13 @@
* ..
* .. Local Scalars ..
LOGICAL LQUERY, LMINWS, MINT, MINW
INTEGER MB, NB, MINTSZ, NBLCKS
INTEGER MB, NB, MINTSZ, NBLCKS, LWMIN, LWREQ
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
REAL SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. External Subroutines ..
EXTERNAL SLATSQR, SGEQRT, XERBLA
@ -244,8 +248,10 @@
*
* 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 +259,7 @@
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 +274,7 @@
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 +288,9 @@
T( 2 ) = MB
T( 3 ) = NB
IF( MINW ) THEN
WORK( 1 ) = MAX( 1, N )
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
ELSE
WORK( 1 ) = MAX( 1, NB*N )
WORK( 1 ) = SROUNDUP_LWORK( LWREQ )
END IF
END IF
IF( INFO.NE.0 ) THEN
@ -309,7 +315,7 @@
$ LWORK, INFO )
END IF
*
WORK( 1 ) = MAX( 1, NB*N )
WORK( 1 ) = SROUNDUP_LWORK( LWREQ )
*
RETURN
*

28
lapack-netlib/SRC/sgeqrfp.f
View File

@ -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 @@
*
* .. 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 SGEQR2P, SLARFB, SLARFT, XERBLA
@ -173,8 +174,9 @@
* ..
* .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
REAL SROUNDUP_LWORK
EXTERNAL ILAENV, SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. Executable Statements ..
*
@ -182,8 +184,16 @@
*
INFO = 0
NB = ILAENV( 1, 'SGEQRF', ' ', M, N, -1, -1 )
LWKOPT = N*NB
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
K = MIN( M, N )
IF( K.EQ.0 ) THEN
LWKMIN = 1
LWKOPT = 1
ELSE
LWKMIN = N
LWKOPT = N*NB
END IF
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
LQUERY = ( LWORK.EQ.-1 )
IF( M.LT.0 ) THEN
INFO = -1
@ -191,7 +201,7 @@
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
@ -211,7 +221,7 @@
*
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.
@ -273,7 +283,7 @@
$ CALL SGEQR2P( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
$ IINFO )
*
WORK( 1 ) = SROUNDUP_LWORK(IWS)
WORK( 1 ) = SROUNDUP_LWORK( IWS )
RETURN
*
* End of SGEQRFP

36
lapack-netlib/SRC/sgesvj.f
View File

@ -208,7 +208,7 @@
*>
*> \param[in,out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK)
*> WORK is REAL array, dimension (MAX(1,LWORK))
*> On entry,
*> If JOBU = 'C' :
*> WORK(1) = CTOL, where CTOL defines the threshold for convergence.
@ -239,7 +239,12 @@
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> length of WORK, WORK >= MAX(6,M+N)
*> Length of WORK.
*> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= MAX(6,M+N), otherwise.
*>
*> If on entry LWORK = -1, then a workspace query is assumed and
*> no computation is done; WORK(1) is set to the minial (and optimal)
*> length of WORK.
*> \endverbatim
*>
*> \param[out] INFO
@ -260,7 +265,7 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup realGEcomputational
*> \ingroup gesvj
*
*> \par Further Details:
* =====================
@ -351,9 +356,9 @@
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, LSVEC, NOSCALE, ROTOK,
$ RSVEC, UCTOL, UPPER
$ SWBAND, MINMN, LWMIN
LOGICAL APPLV, GOSCALE, LOWER, LQUERY, LSVEC, NOSCALE,
$ ROTOK, RSVEC, UCTOL, UPPER
* ..
* .. Local Arrays ..
REAL FASTR( 5 )
@ -369,8 +374,8 @@
INTEGER ISAMAX
EXTERNAL ISAMAX
* from LAPACK
REAL SLAMCH
EXTERNAL SLAMCH
REAL SLAMCH, SROUNDUP_LWORK
EXTERNAL SLAMCH, SROUNDUP_LWORK
LOGICAL LSAME
EXTERNAL LSAME
* ..
@ -394,6 +399,14 @@
UPPER = LSAME( JOBA, 'U' )
LOWER = LSAME( JOBA, 'L' )
*
MINMN = MIN( M, N )
IF( MINMN.EQ.0 ) THEN
LWMIN = 1
ELSE
LWMIN = MAX( 6, M+N )
END IF
*
LQUERY = ( LWORK.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
@ -413,7 +426,7 @@
INFO = -11
ELSE IF( UCTOL .AND. ( WORK( 1 ).LE.ONE ) ) THEN
INFO = -12
ELSE IF( LWORK.LT.MAX( M+N, 6 ) ) THEN
ELSE IF( LWORK.LT.LWMIN .AND. ( .NOT.LQUERY ) ) THEN
INFO = -13
ELSE
INFO = 0
@ -423,11 +436,14 @@
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SGESVJ', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
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

10
lapack-netlib/SRC/sgetri.f
View File

@ -137,8 +137,9 @@
* ..
* .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
REAL SROUNDUP_LWORK
EXTERNAL ILAENV, SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SGEMV, SSWAP, STRSM, STRTRI, XERBLA
@ -152,8 +153,9 @@
*
INFO = 0
NB = ILAENV( 1, 'SGETRI', ' ', N, -1, -1, -1 )
LWKOPT = N*NB
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
LWKOPT = MAX( 1, N*NB )
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
LQUERY = ( LWORK.EQ.-1 )
IF( N.LT.0 ) THEN
INFO = -1
@ -251,7 +253,7 @@
$ CALL SSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
60 CONTINUE
*
WORK( 1 ) = SROUNDUP_LWORK(IWS)
WORK( 1 ) = SROUNDUP_LWORK( IWS )
RETURN
*
* End of SGETRI

7
lapack-netlib/SRC/sgetsls.f
View File

@ -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).
@ -226,7 +226,10 @@
*
* 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 SGEQR( M, N, A, LDA, TQ, -1, WORKQ, -1, INFO2 )
TSZO = INT( TQ( 1 ) )
LWO = INT( WORKQ( 1 ) )

16
lapack-netlib/SRC/sgetsqrhrt.f
View File

@ -130,14 +130,17 @@
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> 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
@ -216,7 +219,7 @@
* 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
@ -229,7 +232,7 @@
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
*
@ -267,8 +270,9 @@
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
*
@ -350,4 +354,4 @@
*
* End of SGETSQRHRT
*
END
END

24
lapack-netlib/SRC/sgges3.f
View File

@ -234,6 +234,8 @@
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK.
*> If N = 0, LWORK >= 1, else LWORK >= 6*N+16.
*> 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
@ -309,7 +311,8 @@
LOGICAL CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
$ LQUERY, LST2SL, WANTST
INTEGER I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
$ ILO, IP, IRIGHT, IROWS, ITAU, IWRK, LWKOPT
$ ILO, IP, IRIGHT, IROWS, ITAU, IWRK, LWKOPT,
$ LWKMIN
REAL ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL,
$ PVSR, SAFMAX, SAFMIN, SMLNUM
* ..
@ -361,6 +364,12 @@
*
INFO = 0
LQUERY = ( LWORK.EQ.-1 )
IF( N.EQ.0 ) THEN
LWKMIN = 1
ELSE
LWKMIN = 6*N+16
END IF
*
IF( IJOBVL.LE.0 ) THEN
INFO = -1
ELSE IF( IJOBVR.LE.0 ) THEN
@ -377,7 +386,7 @@
INFO = -15
ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
INFO = -17
ELSE IF( LWORK.LT.6*N+16 .AND. .NOT.LQUERY ) THEN
ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
INFO = -19
END IF
*
@ -385,7 +394,7 @@
*
IF( INFO.EQ.0 ) THEN
CALL SGEQRF( N, N, B, LDB, WORK, WORK, -1, IERR )
LWKOPT = MAX( 6*N+16, 3*N+INT( WORK( 1 ) ) )
LWKOPT = MAX( LWKMIN, 3*N+INT( WORK( 1 ) ) )
CALL SORMQR( 'L', 'T', N, N, N, B, LDB, WORK, A, LDA, WORK,
$ -1, IERR )
LWKOPT = MAX( LWKOPT, 3*N+INT( WORK( 1 ) ) )
@ -407,7 +416,11 @@
$ IERR )
LWKOPT = MAX( LWKOPT, 2*N+INT( WORK( 1 ) ) )
END IF
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
IF( N.EQ.0 ) THEN
WORK( 1 ) = 1
ELSE
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
END IF
END IF
*
IF( INFO.NE.0 ) THEN
@ -421,6 +434,7 @@
*
IF( N.EQ.0 ) THEN
SDIM = 0
WORK( 1 ) = 1
RETURN
END IF
*
@ -657,7 +671,7 @@
*
40 CONTINUE
*
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
RETURN
*

27
lapack-netlib/SRC/sggev3.f
View File

@ -189,6 +189,8 @@
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK. LWORK >= MAX(1,8*N).
*> For good performance, LWORK should generally be larger.
*>
*> If LWORK = -1, then a workspace query is assumed; the routine
*> only calculates the optimal size of the WORK array, returns
@ -248,7 +250,8 @@
LOGICAL ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY
CHARACTER CHTEMP
INTEGER ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, ILO,
$ IN, IRIGHT, IROWS, ITAU, IWRK, JC, JR, LWKOPT
$ IN, IRIGHT, IROWS, ITAU, IWRK, JC, JR, LWKOPT,
$ LWKMIN
REAL ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
$ SMLNUM, TEMP
* ..
@ -298,6 +301,7 @@
*
INFO = 0
LQUERY = ( LWORK.EQ.-1 )
LWKMIN = MAX( 1, 8*N )
IF( IJOBVL.LE.0 ) THEN
INFO = -1
ELSE IF( IJOBVR.LE.0 ) THEN
@ -312,7 +316,7 @@
INFO = -12
ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN
INFO = -14
ELSE IF( LWORK.LT.MAX( 1, 8*N ) .AND. .NOT.LQUERY ) THEN
ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
INFO = -16
END IF
*
@ -320,28 +324,31 @@
*
IF( INFO.EQ.0 ) THEN
CALL SGEQRF( N, N, B, LDB, WORK, WORK, -1, IERR )
LWKOPT = MAX( 1, 8*N, 3*N+INT ( WORK( 1 ) ) )
LWKOPT = MAX( LWKMIN, 3*N+INT( WORK( 1 ) ) )
CALL SORMQR( 'L', 'T', N, N, N, B, LDB, WORK, A, LDA, WORK,
$ -1, IERR )
LWKOPT = MAX( LWKOPT, 3*N+INT ( WORK( 1 ) ) )
LWKOPT = MAX( LWKOPT, 3*N+INT( WORK( 1 ) ) )
CALL SGGHD3( JOBVL, JOBVR, N, 1, N, A, LDA, B, LDB, VL, LDVL,
$ VR, LDVR, WORK, -1, IERR )
LWKOPT = MAX( LWKOPT, 3*N+INT ( WORK( 1 ) ) )
LWKOPT = MAX( LWKOPT, 3*N+INT( WORK( 1 ) ) )
IF( ILVL ) THEN
CALL SORGQR( N, N, N, VL, LDVL, WORK, WORK, -1, IERR )
LWKOPT = MAX( LWKOPT, 3*N+INT ( WORK( 1 ) ) )
LWKOPT = MAX( LWKOPT, 3*N+INT( WORK( 1 ) ) )
CALL SLAQZ0( 'S', JOBVL, JOBVR, N, 1, N, A, LDA, B, LDB,
$ ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR,
$ WORK, -1, 0, IERR )
LWKOPT = MAX( LWKOPT, 2*N+INT ( WORK( 1 ) ) )
LWKOPT = MAX( LWKOPT, 2*N+INT( WORK( 1 ) ) )
ELSE
CALL SLAQZ0( 'E', JOBVL, JOBVR, N, 1, N, A, LDA, B, LDB,
$ ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR,
$ WORK, -1, 0, IERR )
LWKOPT = MAX( LWKOPT, 2*N+INT ( WORK( 1 ) ) )
LWKOPT = MAX( LWKOPT, 2*N+INT( WORK( 1 ) ) )
END IF
IF( N.EQ.0 ) THEN
WORK( 1 ) = 1
ELSE
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
END IF
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
END IF
*
IF( INFO.NE.0 ) THEN

15
lapack-netlib/SRC/sgghd3.f
View File

@ -179,14 +179,14 @@
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK)
*> WORK is REAL array, dimension (MAX(1,LWORK))
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \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.
*>
@ -276,7 +276,12 @@
*
INFO = 0
NB = ILAENV( 1, 'SGGHD3', ' ', 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 ) = SROUNDUP_LWORK( LWKOPT )
INITQ = LSAME( COMPQ, 'I' )
WANTQ = INITQ .OR. LSAME( COMPQ, 'V' )
@ -326,7 +331,6 @@
*
* Quick return if possible
*
NH = IHI - ILO + 1
IF( NH.LE.1 ) THEN
WORK( 1 ) = ONE
RETURN
@ -886,6 +890,7 @@
IF ( JCOL.LT.IHI )
$ CALL SGGHRD( COMPQ2, COMPZ2, N, JCOL, IHI, A, LDA, B, LDB, Q,
$ LDQ, Z, LDZ, IERR )
*
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
RETURN

9
lapack-netlib/SRC/sggqrf.f
View File

@ -236,8 +236,9 @@
* ..
* .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
REAL SROUNDUP_LWORK
EXTERNAL ILAENV, SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. Intrinsic Functions ..
INTRINSIC INT, MAX, MIN
@ -251,8 +252,9 @@
NB2 = ILAENV( 1, 'SGERQF', ' ', N, P, -1, -1 )
NB3 = ILAENV( 1, 'SORMQR', ' ', N, M, P, -1 )
NB = MAX( NB1, NB2, NB3 )
LWKOPT = MAX( N, M, P )*NB
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
LWKOPT = MAX( 1, MAX( N, M, P )*NB )
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
LQUERY = ( LWORK.EQ.-1 )
IF( N.LT.0 ) THEN
INFO = -1
@ -289,6 +291,7 @@
*
CALL SGERQF( N, P, B, LDB, TAUB, WORK, LWORK, INFO )
LWKOPT = MAX( LOPT, INT( WORK( 1 ) ) )
*
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
RETURN

2
lapack-netlib/SRC/sggrqf.f
View File

@ -250,7 +250,7 @@
NB2 = ILAENV( 1, 'SGEQRF', ' ', P, N, -1, -1 )
NB3 = ILAENV( 1, 'SORMRQ', ' ', 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 ) = SROUNDUP_LWORK(LWKOPT)
LQUERY = ( LWORK.EQ.-1 )
IF( M.LT.0 ) THEN

2
lapack-netlib/SRC/sggsvd3.f
View File

@ -278,7 +278,7 @@
*> \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

5
lapack-netlib/SRC/sggsvp3.f
View File

@ -227,7 +227,7 @@
*> \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
@ -300,8 +300,9 @@
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
REAL SROUNDUP_LWORK
EXTERNAL LSAME, SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. External Subroutines ..
EXTERNAL SGEQP3, SGEQR2, SGERQ2, SLACPY, SLAPMT,

64
lapack-netlib/SRC/slamswlq.f
View File

@ -127,17 +127,20 @@
*>
*> \param[out] WORK
*> \verbatim
*> (workspace) REAL array, dimension (MAX(1,LWORK))
*> (workspace) REAL 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
@ -189,33 +192,38 @@
*> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
*> \endverbatim
*>
*> \ingroup lamswlq
*>
* =====================================================================
SUBROUTINE SLAMSWLQ( 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 ..
REAL A( LDA, * ), WORK( * ), C(LDC, * ),
$ T( LDT, * )
REAL 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
REAL SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. External Subroutines ..
EXTERNAL STPMLQT, SGEMLQT, XERBLA
* ..
@ -223,52 +231,60 @@
*
* Test the input arguments
*
LQUERY = LWORK.LT.0
LQUERY = ( LWORK.EQ.-1 )
NOTRAN = LSAME( TRANS, 'N' )
TRAN = LSAME( TRANS, 'T' )
LEFT = LSAME( SIDE, 'L' )
RIGHT = LSAME( SIDE, 'R' )
IF (LEFT) THEN
IF( LEFT ) THEN
LW = N * MB
ELSE
LW = M * MB
END IF
*
MINMNK = MIN( M, N, K )
IF( MINMNK.EQ.0 ) THEN
LWMIN = 1
ELSE
LWMIN = MAX( 1, LW )
END IF
*
INFO = 0
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 ) = SROUNDUP_LWORK( LWMIN )
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SLAMSWLQ', -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
*
@ -402,7 +418,7 @@
*
END IF
*
WORK(1) = LW
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
RETURN
*
* End of SLAMSWLQ

76
lapack-netlib/SRC/slamtsqr.f
View File

@ -128,22 +128,24 @@
*>
*> \param[out] WORK
*> \verbatim
*> (workspace) REAL array, dimension (MAX(1,LWORK))
*>
*> (workspace) REAL 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
@ -191,33 +193,38 @@
*> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
*> \endverbatim
*>
*> \ingroup lamtsqr
*>
* =====================================================================
SUBROUTINE SLAMTSQR( 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 ..
REAL A( LDA, * ), WORK( * ), C(LDC, * ),
$ T( LDT, * )
REAL 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
REAL SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. External Subroutines ..
EXTERNAL SGEMQRT, STPMQRT, XERBLA
* ..
@ -225,12 +232,13 @@
*
* Test the input arguments
*
LQUERY = LWORK.LT.0
INFO = 0
LQUERY = ( LWORK.EQ.-1 )
NOTRAN = LSAME( TRANS, 'N' )
TRAN = LSAME( TRANS, 'T' )
LEFT = LSAME( SIDE, 'L' )
RIGHT = LSAME( SIDE, 'R' )
IF (LEFT) THEN
IF( LEFT ) THEN
LW = N * NB
Q = M
ELSE
@ -238,11 +246,17 @@
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 +267,38 @@
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 ) = SROUNDUP_LWORK( LWMIN )
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SLAMTSQR', -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 SGEMQRT( 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 +424,7 @@
*
END IF
*
WORK(1) = LW
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
RETURN
*
* End of SLAMTSQR

92
lapack-netlib/SRC/slaswlq.f
View File

@ -96,22 +96,24 @@
*> The leading dimension of the array T. LDT >= MB.
*> \endverbatim
*>
*>
*> \param[out] WORK
*> \verbatim
*> (workspace) REAL array, dimension (MAX(1,LWORK))
*>
*> (workspace) REAL 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
@ -163,32 +165,35 @@
*>
* =====================================================================
SUBROUTINE SLASWLQ( 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 ..
REAL A( LDA, * ), WORK( * ), T( LDT, *)
REAL 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
REAL SROUNDUP_LWORK
EXTERNAL LSAME, SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. EXTERNAL SUBROUTINES ..
EXTERNAL SGELQT, SGEQRT, STPLQT, STPQRT, XERBLA
* ..
* .. INTRINSIC FUNCTIONS ..
INTRINSIC MAX, MIN, MOD
* ..
@ -199,12 +204,19 @@
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
@ -212,60 +224,60 @@
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 ) = SROUNDUP_LWORK( LWMIN )
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SLASWLQ', -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 SGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO)
IF( (M.GE.N) .OR. (NB.LE.M) .OR. (NB.GE.N) ) THEN
CALL SGELQT( 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 SGELQT( M, NB, MB, A(1,1), LDA, T, LDT, WORK, INFO)
CTR = 1
CALL SGELQT( 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 STPLQT( 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 STPLQT( 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 STPLQT( 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 ) = SROUNDUP_LWORK(M * MB)
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
RETURN
*
* End of SLASWLQ

32
lapack-netlib/SRC/slatrs3.f
View File

@ -151,13 +151,16 @@
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK).
*> On exit, if INFO = 0, WORK(1) returns the optimal size of
*> WORK.
*> WORK is REAL 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.
*>
*> 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.
*>
@ -165,6 +168,7 @@
*> 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
@ -181,7 +185,7 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup doubleOTHERauxiliary
*> \ingroup latrs3
*> \par Further Details:
* =====================
* \verbatim
@ -253,7 +257,7 @@
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
REAL ANRM, BIGNUM, BNRM, RSCAL, SCAL, SCALOC,
$ SCAMIN, SMLNUM, TMAX
* ..
@ -264,7 +268,8 @@
EXTERNAL ILAENV, LSAME, SLAMCH, SLANGE, SLARMM
* ..
* .. External Subroutines ..
EXTERNAL SLATRS, SSCAL, XERBLA
REAL SROUNDUP_LWORK
EXTERNAL SLATRS, SSCAL, SROUNDUP_LWORK, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN
@ -292,15 +297,24 @@
* 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 ) = SROUNDUP_LWORK( LWMIN )
*
* Test the input parameters.
*
@ -322,7 +336,7 @@
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
@ -650,6 +664,8 @@
END DO
END DO
RETURN
*
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
*
* End of SLATRS3
*

95
lapack-netlib/SRC/slatsqr.f
View File

@ -101,15 +101,18 @@
*>
*> \param[out] WORK
*> \verbatim
*> (workspace) REAL array, dimension (MAX(1,LWORK))
*> (workspace) REAL 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 +164,39 @@
*> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
*> \endverbatim
*>
*> \ingroup latsqr
*>
* =====================================================================
SUBROUTINE SLATSQR( 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 ..
REAL A( LDA, * ), WORK( * ), T(LDT, *)
REAL 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
REAL SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. EXTERNAL SUBROUTINES ..
EXTERNAL SGEQRT, STPQRT, XERBLA
* ..
* .. INTRINSIC FUNCTIONS ..
INTRINSIC MAX, MIN, MOD
* ..
@ -198,6 +207,13 @@
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 +221,65 @@
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 ) = SROUNDUP_LWORK( LWMIN )
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SLATSQR', -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 SGEQRT( 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 SGEQRT( 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 SGEQRT( MB, N, NB, A(1,1), LDA, T, LDT, WORK, INFO )
CALL SGEQRT( MB, N, NB, A(1,1), LDA, T, LDT, WORK, INFO )
*
CTR = 1
DO I = MB+1, II-MB+N , (MB-N)
CTR = 1
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 STPQRT( 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 STPQRT( 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 STPQRT( 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 STPQRT( 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 ) = SROUNDUP_LWORK( LWMIN )
RETURN
*
* End of SLATSQR

7
lapack-netlib/SRC/ssyevd.f
View File

@ -96,8 +96,7 @@
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array,
*> dimension (LWORK)
*> WORK is REAL array, dimension (MAX(1,LWORK))
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
@ -251,7 +250,7 @@
$ N*ILAENV( 1, 'SSYTRD', UPLO, N, -1, -1, -1 ) )
LIOPT = LIWMIN
END IF
WORK( 1 ) = SROUNDUP_LWORK(LOPT)
WORK( 1 ) = SROUNDUP_LWORK( LOPT )
IWORK( 1 ) = LIOPT
*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
@ -335,7 +334,7 @@
IF( ISCALE.EQ.1 )
$ CALL SSCAL( N, ONE / SIGMA, W, 1 )
*
WORK( 1 ) = SROUNDUP_LWORK(LOPT)
WORK( 1 ) = SROUNDUP_LWORK( LOPT )
IWORK( 1 ) = LIOPT
*
RETURN

19
lapack-netlib/SRC/ssyevr.f
View File

@ -271,7 +271,8 @@
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK. LWORK >= max(1,26*N).
*> The dimension of the array WORK.
*> If N <= 1, LWORK >= 1, else LWORK >= 26*N.
*> For optimal efficiency, LWORK >= (NB+6)*N,
*> where NB is the max of the blocksize for SSYTRD and SORMTR
*> returned by ILAENV.
@ -292,7 +293,8 @@
*> \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 and
@ -392,8 +394,13 @@
*
LQUERY = ( ( LWORK.EQ.-1 ) .OR. ( LIWORK.EQ.-1 ) )
*
LWMIN = MAX( 1, 26*N )
LIWMIN = MAX( 1, 10*N )
IF( N.LE.1 ) THEN
LWMIN = 1
LIWMIN = 1
ELSE
LWMIN = 26*N
LIWMIN = 10*N
END IF
*
INFO = 0
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
@ -428,7 +435,7 @@
NB = ILAENV( 1, 'SSYTRD', UPLO, N, -1, -1, -1 )
NB = MAX( NB, ILAENV( 1, 'SORMTR', UPLO, N, -1, -1, -1 ) )
LWKOPT = MAX( ( NB+1 )*N, LWMIN )
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
IWORK( 1 ) = LIWMIN
*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
@ -677,7 +684,7 @@
*
* Set WORK(1) to optimal workspace size.
*
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
IWORK( 1 ) = LIWMIN
*
RETURN

22
lapack-netlib/SRC/ssyevr_2stage.f
View File

@ -278,6 +278,7 @@
*> \verbatim
*> LWORK is INTEGER
*> 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 + 5*N
@ -300,13 +301,14 @@
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
*> On exit, if INFO = 0, IWORK(1) returns the optimal LWORK.
*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
*> \endverbatim
*>
*> \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 size of the IWORK array,
@ -445,8 +447,14 @@
IB = ILAENV2STAGE( 2, 'SSYTRD_2STAGE', JOBZ, N, KD, -1, -1 )
LHTRD = ILAENV2STAGE( 3, 'SSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
LWTRD = ILAENV2STAGE( 4, 'SSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
LWMIN = MAX( 26*N, 5*N + LHTRD + LWTRD )
LIWMIN = MAX( 1, 10*N )
*
IF( N.LE.1 ) THEN
LWMIN = 1
LIWMIN = 1
ELSE
LWMIN = MAX( 26*N, 5*N + LHTRD + LWTRD )
LIWMIN = 10*N
END IF
*
INFO = 0
IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
@ -485,7 +493,7 @@
* NB = ILAENV( 1, 'SSYTRD', UPLO, N, -1, -1, -1 )
* NB = MAX( NB, ILAENV( 1, 'SORMTR', UPLO, N, -1, -1, -1 ) )
* LWKOPT = MAX( ( NB+1 )*N, LWMIN )
WORK( 1 ) = SROUNDUP_LWORK(LWMIN)
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
IWORK( 1 ) = LIWMIN
END IF
*
@ -505,7 +513,7 @@
END IF
*
IF( N.EQ.1 ) THEN
WORK( 1 ) = 26
WORK( 1 ) = 1
IF( ALLEIG .OR. INDEIG ) THEN
M = 1
W( 1 ) = A( 1, 1 )
@ -733,7 +741,7 @@
*
* Set WORK(1) to optimal workspace size.
*
WORK( 1 ) = SROUNDUP_LWORK(LWMIN)
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
IWORK( 1 ) = LIWMIN
*
RETURN

6
lapack-netlib/SRC/ssyevx.f
View File

@ -338,14 +338,14 @@
IF( INFO.EQ.0 ) THEN
IF( N.LE.1 ) THEN
LWKMIN = 1
WORK( 1 ) = SROUNDUP_LWORK(LWKMIN)
LWKOPT = 1
ELSE
LWKMIN = 8*N
NB = ILAENV( 1, 'SSYTRD', UPLO, N, -1, -1, -1 )
NB = MAX( NB, ILAENV( 1, 'SORMTR', UPLO, N, -1, -1, -1 ) )
LWKOPT = MAX( LWKMIN, ( NB + 3 )*N )
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
END IF
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY )
$ INFO = -17
@ -542,7 +542,7 @@
*
* Set WORK(1) to optimal workspace size.
*
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
RETURN
*

18
lapack-netlib/SRC/ssysv_aa.f
View File

@ -177,12 +177,13 @@
*
* .. Local Scalars ..
LOGICAL LQUERY
INTEGER LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
INTEGER LWKMIN, LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
REAL SROUNDUP_LWORK
EXTERNAL LSAME, SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, SSYTRS_AA, SSYTRF_AA
@ -196,6 +197,7 @@
*
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
@ -206,18 +208,18 @@
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 SSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
LWKOPT_SYTRF = INT( WORK(1) )
LWKOPT_SYTRF = INT( WORK( 1 ) )
CALL SSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
$ -1, INFO )
LWKOPT_SYTRS = INT( WORK(1) )
LWKOPT = MAX( LWKOPT_SYTRF, LWKOPT_SYTRS )
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
LWKOPT_SYTRS = INT( WORK( 1 ) )
LWKOPT = MAX( LWKMIN, LWKOPT_SYTRF, LWKOPT_SYTRS )
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
END IF
*
IF( INFO.NE.0 ) THEN
@ -239,7 +241,7 @@
*
END IF
*
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
RETURN
*

27
lapack-netlib/SRC/ssysv_aa_2stage.f
View File

@ -100,14 +100,14 @@
*>
*> \param[out] TB
*> \verbatim
*> TB is REAL array, dimension (LTB)
*> TB is REAL 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 REAL workspace of size LWORK
*> WORK is REAL 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,
@ -204,12 +205,13 @@
* ..
* .. Local Scalars ..
LOGICAL UPPER, TQUERY, WQUERY
INTEGER LWKOPT
INTEGER LWKMIN, LWKOPT
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
REAL SROUNDUP_LWORK
EXTERNAL LSAME, SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. External Subroutines ..
EXTERNAL SSYTRF_AA_2STAGE, SSYTRS_AA_2STAGE,
@ -226,6 +228,7 @@
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
@ -234,18 +237,19 @@
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 SSYTRF_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 ) = SROUNDUP_LWORK( LWKOPT )
END IF
*
IF( INFO.NE.0 ) THEN
@ -255,7 +259,6 @@
RETURN
END IF
*
*
* Compute the factorization A = U**T*T*U or A = L*T*L**T.
*
CALL SSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2,
@ -269,7 +272,7 @@
*
END IF
*
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
RETURN
*

7
lapack-netlib/SRC/ssysvx.f
View File

@ -305,7 +305,7 @@
* ..
* .. Local Scalars ..
LOGICAL LQUERY, NOFACT
INTEGER LWKOPT, NB
INTEGER LWKMIN, LWKOPT, NB
REAL ANORM
* ..
* .. External Functions ..
@ -327,6 +327,7 @@
INFO = 0
NOFACT = LSAME( FACT, 'N' )
LQUERY = ( LWORK.EQ.-1 )
LWKMIN = MAX( 1, 3*N )
IF( .NOT.NOFACT .AND. .NOT.LSAME( FACT, 'F' ) ) THEN
INFO = -1
ELSE IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) )
@ -344,12 +345,12 @@
INFO = -11
ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
INFO = -13
ELSE IF( LWORK.LT.MAX( 1, 3*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, 3*N )
LWKOPT = LWKMIN
IF( NOFACT ) THEN
NB = ILAENV( 1, 'SSYTRF', UPLO, N, -1, -1, -1 )
LWKOPT = MAX( LWKOPT, N*NB )

86
lapack-netlib/SRC/ssytrd_2stage.f
View File

@ -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 SSYTRD_2STAGE + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssytrd_2stage.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssytrd_2stage.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssytrd_2stage.f">
*> Download SSYTRD_2STAGE + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssytrd_2stage.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssytrd_2stage.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssytrd_2stage.f">
*> [TXT]</a>
*> \endhtmlonly
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
* SUBROUTINE SSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
* HOUS2, LHOUS2, WORK, LWORK, INFO )
*
* IMPLICIT NONE
@ -34,7 +34,7 @@
* REAL 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 orthogonal
*> 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 REAL 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 REAL array, dimension (LHOUS2)
*> HOUS2 is REAL 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
@ -149,17 +151,19 @@
*> \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 +181,12 @@
* 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 realSYcomputational
*> \ingroup hetrd_2stage
*
*> \par Further Details:
* =====================
@ -202,7 +206,7 @@
*> 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 +214,16 @@
*> 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 SSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
SUBROUTINE SSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
$ HOUS2, LHOUS2, WORK, LWORK, INFO )
*
IMPLICIT NONE
@ -265,10 +269,13 @@
*
KD = ILAENV2STAGE( 1, 'SSYTRD_2STAGE', VECT, N, -1, -1, -1 )
IB = ILAENV2STAGE( 2, 'SSYTRD_2STAGE', VECT, N, KD, -1, -1 )
LHMIN = ILAENV2STAGE( 3, 'SSYTRD_2STAGE', VECT, N, KD, IB, -1 )
LWMIN = ILAENV2STAGE( 4, 'SSYTRD_2STAGE', VECT, N, KD, IB, -1 )
* WRITE(*,*),'SSYTRD_2STAGE N KD UPLO LHMIN LWMIN ',N, KD, UPLO,
* $ LHMIN, LWMIN
IF( N.EQ.0 ) THEN
LHMIN = 1
LWMIN = 1
ELSE
LHMIN = ILAENV2STAGE( 3, 'SSYTRD_2STAGE', VECT, N, KD, IB, -1 )
LWMIN = ILAENV2STAGE( 4, 'SSYTRD_2STAGE', VECT, N, KD, IB, -1 )
END IF
*
IF( .NOT.LSAME( VECT, 'N' ) ) THEN
INFO = -1
@ -309,14 +316,14 @@
LWRK = LWORK-LDAB*N
ABPOS = 1
WPOS = ABPOS + LDAB*N
CALL SSYTRD_SY2SB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB,
CALL SSYTRD_SY2SB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB,
$ TAU, WORK( WPOS ), LWRK, INFO )
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SSYTRD_SY2SB', -INFO )
RETURN
END IF
CALL SSYTRD_SB2ST( 'Y', VECT, UPLO, N, KD,
$ WORK( ABPOS ), LDAB, D, E,
CALL SSYTRD_SB2ST( 'Y', VECT, UPLO, N, KD,
$ WORK( ABPOS ), LDAB, D, E,
$ HOUS2, LHOUS2, WORK( WPOS ), LWRK, INFO )
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SSYTRD_SB2ST', -INFO )
@ -324,8 +331,7 @@
END IF
*
*
HOUS2( 1 ) = LHMIN
WORK( 1 ) = LWMIN
WORK( 1 ) = LWMIN
RETURN
*
* End of SSYTRD_2STAGE

18
lapack-netlib/SRC/ssytrd_sy2sb.f
View File

@ -124,7 +124,7 @@
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK)
*> On exit, if INFO = 0, or if LWORK=-1,
*> 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
@ -294,8 +296,12 @@
INFO = 0
UPPER = LSAME( UPLO, 'U' )
LQUERY = ( LWORK.EQ.-1 )
LWMIN = ILAENV2STAGE( 4, 'SSYTRD_SY2SB', '', N, KD, -1, -1 )
IF( N.LE.KD+1 ) THEN
LWMIN = 1
ELSE
LWMIN = ILAENV2STAGE( 4, 'SSYTRD_SY2SB', '', N, KD, -1, -1 )
END IF
*
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
@ -314,7 +320,7 @@
CALL XERBLA( 'SSYTRD_SY2SB', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
WORK( 1 ) = SROUNDUP_LWORK(LWMIN)
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
RETURN
END IF
*
@ -507,7 +513,7 @@
END IF
*
WORK( 1 ) = SROUNDUP_LWORK(LWMIN)
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
RETURN
*
* End of SSYTRD_SY2SB

5
lapack-netlib/SRC/ssytrf.f
View File

@ -234,7 +234,7 @@
*
NB = ILAENV( 1, 'SSYTRF', UPLO, N, -1, -1, -1 )
LWKOPT = MAX( 1, N*NB )
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
END IF
*
IF( INFO.NE.0 ) THEN
@ -353,7 +353,8 @@
END IF
*
40 CONTINUE
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
*
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
RETURN
*
* End of SSYTRF

36
lapack-netlib/SRC/ssytrf_aa.f
View File

@ -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 SSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SUBROUTINE SSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
@ -142,19 +144,19 @@
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
REAL A( LDA, * ), WORK( * )
REAL A( LDA, * ), WORK( * )
* ..
*
* =====================================================================
* .. Parameters ..
REAL ZERO, ONE
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
*
* .. Local Scalars ..
LOGICAL LQUERY, UPPER
INTEGER J, LWKOPT
INTEGER J, LWKMIN, LWKOPT
INTEGER NB, MJ, NJ, K1, K2, J1, J2, J3, JB
REAL ALPHA
REAL ALPHA
* ..
* .. External Functions ..
LOGICAL LSAME
@ -180,19 +182,26 @@
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 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
END IF
*
IF( INFO.NE.0 ) THEN
@ -204,11 +213,11 @@
*
* 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
RETURN
END IF
*
@ -458,7 +467,8 @@
END IF
*
20 CONTINUE
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
*
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
RETURN
*
* End of SSYTRF_AA

18
lapack-netlib/SRC/ssytrf_aa_2stage.f
View File

@ -94,7 +94,7 @@
*> \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 REAL workspace of size LWORK
*> WORK is REAL 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,
@ -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, 'SSYTRF_AA_2STAGE', UPLO, N, -1, -1, -1 )
IF( INFO.EQ.0 ) THEN
IF( TQUERY ) THEN
TB( 1 ) = (3*NB+1)*N
TB( 1 ) = SROUNDUP_LWORK( MAX( 1, (3*NB+1)*N ) )
END IF
IF( WQUERY ) THEN
WORK( 1 ) = SROUNDUP_LWORK(N*NB)
WORK( 1 ) = SROUNDUP_LWORK( 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
*

8
lapack-netlib/SRC/ssytrf_rk.f
View File

@ -177,14 +177,14 @@
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension ( MAX(1,LWORK) ).
*> WORK is REAL 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.
*>
@ -312,7 +312,7 @@
*
NB = ILAENV( 1, 'SSYTRF_RK', UPLO, N, -1, -1, -1 )
LWKOPT = MAX( 1, N*NB )
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
END IF
*
IF( INFO.NE.0 ) THEN
@ -488,7 +488,7 @@
*
END IF
*
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
RETURN
*
* End of SSYTRF_RK

7
lapack-netlib/SRC/ssytrf_rook.f
View File

@ -118,7 +118,7 @@
*> \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
@ -260,7 +260,7 @@
*
NB = ILAENV( 1, 'SSYTRF_ROOK', UPLO, N, -1, -1, -1 )
LWKOPT = MAX( 1, N*NB )
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
END IF
*
IF( INFO.NE.0 ) THEN
@ -383,7 +383,8 @@
END IF
*
40 CONTINUE
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
*
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
RETURN
*
* End of SSYTRF_ROOK

32
lapack-netlib/SRC/ssytri2.f
View File

@ -88,16 +88,16 @@
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (N+NB+1)*(NB+3)
*> WORK is REAL 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 realSYcomputational
*> \ingroup hetri2
*
* =====================================================================
SUBROUTINE SSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
@ -147,7 +147,8 @@
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
REAL SROUNDUP_LWORK
EXTERNAL LSAME, ILAENV, SROUNDUP_LWORK
* ..
* .. External Subroutines ..
EXTERNAL SSYTRI, SSYTRI2X, XERBLA
@ -159,9 +160,13 @@
INFO = 0
UPPER = LSAME( UPLO, 'U' )
LQUERY = ( LWORK.EQ.-1 )
*
* Get blocksize
*
NBMAX = ILAENV( 1, 'SSYTRF', 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 +178,29 @@
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( 'SSYTRI2', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
WORK(1)=MINSIZE
WORK( 1 ) = SROUNDUP_LWORK( MINSIZE )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
IF( NBMAX .GE. N ) THEN
*
IF( NBMAX.GE.N ) THEN
CALL SSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
ELSE
CALL SSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NBMAX, INFO )
END IF
*
RETURN
*
* End of SSYTRI2

21
lapack-netlib/SRC/ssytri_3.f
View File

@ -119,16 +119,17 @@
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (N+NB+1)*(NB+3).
*> WORK is REAL 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 >= (N+NB+1)*(NB+3).
*> The length of WORK.
*> If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3).
*>
*> If LDWORK = -1, then a workspace query is assumed;
*> If LWORK = -1, then a workspace query is assumed;
*> the routine only calculates the optimal size of the optimal
*> size of the WORK array, returns this value as the first
*> entry of the WORK array, and no error message related to
@ -209,8 +210,13 @@
*
* Determine the block size
*
NB = MAX( 1, ILAENV( 1, 'SSYTRI_3', UPLO, N, -1, -1, -1 ) )
LWKOPT = ( N+NB+1 ) * ( NB+3 )
IF( N.EQ.0 ) THEN
LWKOPT = 1
ELSE
NB = MAX( 1, ILAENV( 1, 'SSYTRI_3', UPLO, N, -1, -1, -1 ) )
LWKOPT = ( N+NB+1 ) * ( NB+3 )
END IF
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
@ -218,7 +224,7 @@
INFO = -2
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF ( LWORK .LT. LWKOPT .AND. .NOT.LQUERY ) THEN
ELSE IF( LWORK.LT.LWKOPT .AND. .NOT.LQUERY ) THEN
INFO = -8
END IF
*
@ -226,7 +232,6 @@
CALL XERBLA( 'SSYTRI_3', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
RETURN
END IF
*
@ -237,7 +242,7 @@
*
CALL SSYTRI_3X( UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO )
*
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
*
RETURN
*

30
lapack-netlib/SRC/ssytrs_aa.f
View File

@ -105,7 +105,13 @@
*> \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
@ -141,7 +147,7 @@
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
REAL A( LDA, * ), B( LDB, * ), WORK( * )
REAL A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
* =====================================================================
@ -151,24 +157,31 @@
* ..
* .. Local Scalars ..
LOGICAL LQUERY, UPPER
INTEGER K, KP, LWKOPT
INTEGER K, KP, LWKMIN
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
REAL SROUNDUP_LWORK
EXTERNAL LSAME, SROUNDUP_LWORK
EXTERNAL SROUNDUP_LWORK
* ..
* .. External Subroutines ..
EXTERNAL SGTSV, SSWAP, SLACPY, STRSM, 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 +192,20 @@
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( 'SSYTRS_AA', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
LWKOPT = (3*N-2)
WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
WORK( 1 ) = SROUNDUP_LWORK( 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