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

lapack-netlib/SRC/dgebrd.f

@@ -122,7 +122,8 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The length of the array WORK.  LWORK >= max(1,M,N).
+*>          The length of the array WORK.
+*>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= MAX(M,N), otherwise.
 *>          For optimum performance LWORK >= (M+N)*NB, where NB
 *>          is the optimal blocksize.
 *>
@@ -147,7 +148,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEcomputational
+*> \ingroup gebrd
 *
 *> \par Further Details:
 *  =====================
@@ -223,8 +224,8 @@ SUBROUTINE DGEBRD( 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           DGEBD2, DGEMM, DLABRD, XERBLA
@@ -241,17 +242,25 @@ SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
 *     Test the input parameters
 *
       INFO = 0
-      NB = MAX( 1, ILAENV( 1, 'DGEBRD', ' ', 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, 'DGEBRD', ' ', M, N, -1, -1 ) )
+         LWKOPT = ( M+N )*NB
+      ENDIF
       WORK( 1 ) = DBLE( LWKOPT )
+*
       LQUERY = ( LWORK.EQ.-1 )
       IF( M.LT.0 ) THEN
          INFO = -1
       ELSE IF( N.LT.0 ) THEN
          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 DGEBRD( 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
@@ -282,7 +290,7 @@ SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
 *        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

lapack-netlib/SRC/dgehrd.f

@@ -89,7 +89,7 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is DOUBLE PRECISION array, dimension (LWORK)
+*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *> \endverbatim
 *>
@@ -120,7 +120,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEcomputational
+*> \ingroup gehrd
 *
 *> \par Further Details:
 *  =====================
@@ -173,7 +173,7 @@ SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
       INTEGER            IHI, ILO, INFO, LDA, LWORK, N
 *     ..
 *     .. Array Arguments ..
-      DOUBLE PRECISION  A( LDA, * ), TAU( * ), WORK( * )
+      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
 *     ..
 *
 *  =====================================================================
@@ -182,15 +182,15 @@ SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
       INTEGER            NBMAX, LDT, TSIZE
       PARAMETER          ( NBMAX = 64, LDT = NBMAX+1,
      $                     TSIZE = LDT*NBMAX )
-      DOUBLE PRECISION  ZERO, ONE
+      DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0D+0,
      $                     ONE = 1.0D+0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LQUERY
       INTEGER            I, IB, IINFO, IWT, J, LDWORK, LWKOPT, NB,
      $                   NBMIN, NH, NX
-      DOUBLE PRECISION  EI
+      DOUBLE PRECISION   EI
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DAXPY, DGEHD2, DGEMM, DLAHR2, DLARFB, DTRMM,
@@ -221,12 +221,18 @@ SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
          INFO = -8
       END IF
 *
+      NH = IHI - ILO + 1
       IF( INFO.EQ.0 ) THEN
 *
 *        Compute the workspace requirements
 *
-         NB = MIN( NBMAX, ILAENV( 1, 'DGEHRD', ' ', N, ILO, IHI, -1 ) )
-         LWKOPT = N*NB + TSIZE
+         IF( NH.LE.1 ) THEN
+            LWKOPT = 1
+         ELSE
+            NB = MIN( NBMAX, ILAENV( 1, 'DGEHRD', ' ', N, ILO, IHI,
+     $                              -1 ) )
+            LWKOPT = N*NB + TSIZE
+         ENDIF
          WORK( 1 ) = LWKOPT
       END IF
 *
@@ -248,7 +254,6 @@ SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
 *
 *     Quick return if possible
 *
-      NH = IHI - ILO + 1
       IF( NH.LE.1 ) THEN
          WORK( 1 ) = 1
          RETURN
@@ -268,7 +273,7 @@ SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
 *
 *           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
@@ -344,6 +349,7 @@ SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
 *     Use unblocked code to reduce the rest of the matrix
 *
       CALL DGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO )
+*
       WORK( 1 ) = LWKOPT
 *
       RETURN

lapack-netlib/SRC/dgelq.f

@@ -98,7 +98,7 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.
+*>          The dimension of the array WORK. LWORK >= 1.
 *>          If LWORK = -1 or -2, then a workspace query is assumed. The routine
 *>          only calculates the sizes of the T and WORK arrays, returns these
 *>          values as the first entries of the T and WORK arrays, and no error
@@ -166,6 +166,8 @@
 *>  the LQ factorization.
 *> \endverbatim
 *>
+*> \ingroup gelq
+*>
 *  =====================================================================
       SUBROUTINE DGELQ( M, N, A, LDA, T, TSIZE, WORK, LWORK,
      $                  INFO )

lapack-netlib/SRC/dgelqf.f

@@ -93,7 +93,8 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.  LWORK >= max(1,M).
+*>          The dimension of the array WORK.
+*>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
 *>          For optimum performance LWORK >= M*NB, where NB is the
 *>          optimal blocksize.
 *>
@@ -118,7 +119,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEcomputational
+*> \ingroup gelqf
 *
 *> \par Further Details:
 *  =====================
@@ -174,29 +175,34 @@ SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *     Test the input arguments
 *
       INFO = 0
+      K = MIN( M, N )
       NB = ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 )
-      LWKOPT = M*NB
-      WORK( 1 ) = LWKOPT
       LQUERY = ( LWORK.EQ.-1 )
       IF( M.LT.0 ) THEN
          INFO = -1
       ELSE IF( N.LT.0 ) THEN
          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( 'DGELQF', -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

lapack-netlib/SRC/dgelsd.f

@@ -188,7 +188,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEsolve
+*> \ingroup gelsd
 *
 *> \par Contributors:
 *  ==================
@@ -228,7 +228,7 @@ SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
       DOUBLE PRECISION   ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           DGEBRD, DGELQF, DGEQRF, DLABAD, DLACPY, DLALSD,
+      EXTERNAL           DGEBRD, DGELQF, DGEQRF, DLACPY, DLALSD,
      $                   DLASCL, DLASET, DORMBR, DORMLQ, DORMQR, XERBLA
 *     ..
 *     .. External Functions ..
@@ -276,7 +276,7 @@ SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
      $       LOG( TWO ) ) + 1, 0 )
 *
       IF( INFO.EQ.0 ) THEN
-         MAXWRK = 0
+         MAXWRK = 1
          LIWORK = 3*MINMN*NLVL + 11*MINMN
          MM = M
          IF( M.GE.N .AND. M.GE.MNTHR ) THEN
@@ -372,7 +372,6 @@ SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
       SFMIN = DLAMCH( 'S' )
       SMLNUM = SFMIN / EPS
       BIGNUM = ONE / SMLNUM
-      CALL DLABAD( SMLNUM, BIGNUM )
 *
 *     Scale A if max entry outside range [SMLNUM,BIGNUM].
 *

lapack-netlib/SRC/dgemlq.f

@@ -111,16 +111,17 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>         (workspace) DOUBLE PRECISION 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 
+*>          value as WORK(1), and no error message related to WORK
 *>          is issued by XERBLA.
 *> \endverbatim
 *>
@@ -144,7 +145,7 @@
 *>
 *> \verbatim
 *>
-*> These details are particular for this LAPACK implementation. Users should not 
+*> These details are particular for this LAPACK implementation. Users should not
 *> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
@@ -160,11 +161,13 @@
 *>  block sizes MB and NB returned by ILAENV, DGELQ will use either
 *>  DLASWLQ (if the matrix is wide-and-short) or DGELQT to compute
 *>  the LQ factorization.
-*>  This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to 
+*>  This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to
 *>  multiply matrix Q by another matrix.
 *>  Further Details in DLAMSWLQ or DGEMLQT.
 *> \endverbatim
 *>
+*> \ingroup gemlq
+*>
 *  =====================================================================
       SUBROUTINE DGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
      $                   C, LDC, WORK, LWORK, INFO )
@@ -186,7 +189,7 @@ SUBROUTINE DGEMLQ( 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 +205,7 @@ SUBROUTINE DGEMLQ( 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, 'T' )
       LEFT    = LSAME( SIDE, 'L' )
@@ -217,6 +220,13 @@ SUBROUTINE DGEMLQ( 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
@@ -245,12 +255,12 @@ SUBROUTINE DGEMLQ( 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
 *
       IF( INFO.EQ.0 ) THEN
-        WORK( 1 ) = LW
+        WORK( 1 ) = LWMIN
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -262,7 +272,7 @@ SUBROUTINE DGEMLQ( 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
 *
@@ -275,7 +285,7 @@ SUBROUTINE DGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
      $                 MB, C, LDC, WORK, LWORK, INFO )
       END IF
 *
-      WORK( 1 ) = LW
+      WORK( 1 ) = LWMIN
 *
       RETURN
 *