handle and document corner cases of lwork in lapack, double precision

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.
 *>
@@ -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

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
 *>
@@ -225,8 +225,13 @@ SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
 *
 *        Compute the workspace requirements
 *
-         NB = MIN( NBMAX, ILAENV( 1, 'DGEHRD', ' ', N, ILO, IHI, -1 ) )
-         LWKOPT = N*NB + TSIZE
+         IF( N.EQ.0 ) THEN
+            LWKOPT = 1
+         ELSE
+            NB = MIN( NBMAX, ILAENV( 1, 'DGEHRD', ' ', N, ILO, IHI,
+     $                              -1 ) )
+            LWKOPT = N*NB + TSIZE
+         ENDIF
          WORK( 1 ) = LWKOPT
       END IF
 *
@@ -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

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

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.
 *>
@@ -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

SRC/dgelsd.f

@@ -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

SRC/dgemlq.f

@@ -111,13 +111,14 @@
 *>
 *> \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
@@ -188,7 +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
@@ -204,7 +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' )
@@ -219,6 +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
@@ -247,12 +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
@@ -264,7 +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
 *
@@ -277,7 +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
 *

SRC/dgemqr.f

@@ -111,13 +111,14 @@
 *>
 *> \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
@@ -189,7 +190,7 @@ SUBROUTINE DGEMQR( 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 DGEMQR( 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' )
@@ -220,6 +221,13 @@ SUBROUTINE DGEMQR( 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
@@ -248,12 +256,12 @@ SUBROUTINE DGEMQR( 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
@@ -265,7 +273,7 @@ SUBROUTINE DGEMQR( 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
 *
@@ -278,7 +286,7 @@ SUBROUTINE DGEMQR( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
      $                 NB, C, LDC, WORK, LWORK, INFO )
       END IF
 *
-      WORK( 1 ) = LW
+      WORK( 1 ) = LWMIN
 *
       RETURN
 *

SRC/dgeqlf.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 DGEQLF( 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
 *

SRC/dgeqp3rk.f

@@ -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,
+*>          LWORK >= (3*N + NRHS - 1), otherwise.
 *>          For optimal performance LWORK >= (2*N + NB*( N+NRHS+1 )),
 *>          where NB is the optimal block size for DGEQP3RK returned
 *>          by ILAENV. Minimal block size MINNB=2.

SRC/dgeqr.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