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

Author: martin-frbg

lapack-netlib/SRC/zgebrd.f

@@ -122,7 +122,8 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The length of the array WORK.  LWORK >= max(1,M,N).
+*>          The length of the array WORK.
+*>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= MAX(M,N), otherwise.
 *>          For optimum performance LWORK >= (M+N)*NB, where NB
 *>          is the optimal blocksize.
 *>
@@ -147,7 +148,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complex16GEcomputational
+*> \ingroup gebrd
 *
 *> \par Further Details:
 *  =====================
@@ -223,8 +224,8 @@ SUBROUTINE ZGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LQUERY
-      INTEGER            I, IINFO, J, LDWRKX, LDWRKY, LWKOPT, MINMN, NB,
-     $                   NBMIN, NX, WS
+      INTEGER            I, IINFO, J, LDWRKX, LDWRKY, LWKMIN, LWKOPT,
+     $                   MINMN, NB, NBMIN, NX, WS
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           XERBLA, ZGEBD2, ZGEMM, ZLABRD
@@ -241,17 +242,25 @@ SUBROUTINE ZGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
 *     Test the input parameters
 *
       INFO = 0
-      NB = MAX( 1, ILAENV( 1, 'ZGEBRD', ' ', M, N, -1, -1 ) )
-      LWKOPT = ( M+N )*NB
+      MINMN = MIN( M, N )
+      IF( MINMN.EQ.0 ) THEN
+         LWKMIN = 1
+         LWKOPT = 1
+      ELSE
+         LWKMIN = MAX( M, N )
+         NB = MAX( 1, ILAENV( 1, 'ZGEBRD', ' ', M, N, -1, -1 ) )
+         LWKOPT = ( M+N )*NB
+      END IF
       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 ZGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
 *
 *     Quick return if possible
 *
-      MINMN = MIN( M, N )
       IF( MINMN.EQ.0 ) THEN
          WORK( 1 ) = 1
          RETURN
@@ -282,7 +290,7 @@ SUBROUTINE ZGEBRD( 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/zgehrd.f

@@ -89,7 +89,7 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX*16 array, dimension (LWORK)
+*>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *> \endverbatim
 *>
@@ -120,7 +120,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complex16GEcomputational
+*> \ingroup gehrd
 *
 *> \par Further Details:
 *  =====================
@@ -173,7 +173,7 @@ SUBROUTINE ZGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
       INTEGER            IHI, ILO, INFO, LDA, LWORK, N
 *     ..
 *     .. Array Arguments ..
-      COMPLEX*16        A( LDA, * ), TAU( * ), WORK( * )
+      COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
 *     ..
 *
 *  =====================================================================
@@ -182,15 +182,15 @@ SUBROUTINE ZGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
       INTEGER            NBMAX, LDT, TSIZE
       PARAMETER          ( NBMAX = 64, LDT = NBMAX+1,
      $                     TSIZE = LDT*NBMAX )
-      COMPLEX*16        ZERO, ONE
+      COMPLEX*16         ZERO, ONE
       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
      $                     ONE = ( 1.0D+0, 0.0D+0 ) )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LQUERY
       INTEGER            I, IB, IINFO, IWT, J, LDWORK, LWKOPT, NB,
      $                   NBMIN, NH, NX
-      COMPLEX*16        EI
+      COMPLEX*16         EI
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           ZAXPY, ZGEHD2, ZGEMM, ZLAHR2, ZLARFB, ZTRMM,
@@ -221,12 +221,18 @@ SUBROUTINE ZGEHRD( 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, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) )
-         LWKOPT = N*NB + TSIZE
+         IF( NH.LE.1 ) THEN
+            LWKOPT = 1
+         ELSE
+            NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI,
+     $                              -1 ) )
+            LWKOPT = N*NB + TSIZE
+         END IF
          WORK( 1 ) = LWKOPT
       ENDIF
 *
@@ -248,7 +254,6 @@ SUBROUTINE ZGEHRD( 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 ZGEHRD( 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

lapack-netlib/SRC/zgelq.f

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

lapack-netlib/SRC/zgelqf.f

@@ -93,7 +93,8 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.  LWORK >= max(1,M).
+*>          The dimension of the array WORK.
+*>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
 *>          For optimum performance LWORK >= M*NB, where NB is the
 *>          optimal blocksize.
 *>
@@ -118,7 +119,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complex16GEcomputational
+*> \ingroup gelqf
 *
 *> \par Further Details:
 *  =====================
@@ -174,29 +175,34 @@ SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *     Test the input arguments
 *
       INFO = 0
+      K = MIN( M, N )
       NB = ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 )
-      LWKOPT = M*NB
-      WORK( 1 ) = LWKOPT
       LQUERY = ( LWORK.EQ.-1 )
       IF( M.LT.0 ) THEN
          INFO = -1
       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( 'ZGELQF', -INFO )
          RETURN
       ELSE IF( LQUERY ) THEN
+         IF( K.EQ.0 ) THEN
+            LWKOPT = 1
+         ELSE
+            LWKOPT = M*NB
+         END IF
+         WORK( 1 ) = LWKOPT
          RETURN
       END IF
 *
 *     Quick return if possible
 *
-      K = MIN( M, N )
       IF( K.EQ.0 ) THEN
          WORK( 1 ) = 1
          RETURN

lapack-netlib/SRC/zgemlq.f

@@ -109,16 +109,17 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>         (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
+*>          (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
+*>          On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
 *> \endverbatim
 *>
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.
+*>          The dimension of the array WORK. LWORK >= 1.
 *>          If LWORK = -1, then a workspace query is assumed. The routine
 *>          only calculates the size of the WORK array, returns this
-*>          value as WORK(1), and no error message related to WORK 
+*>          value as WORK(1), and no error message related to WORK
 *>          is issued by XERBLA.
 *> \endverbatim
 *>
@@ -142,7 +143,7 @@
 *>
 *> \verbatim
 *>
-*> These details are particular for this LAPACK implementation. Users should not 
+*> These details are particular for this LAPACK implementation. Users should not
 *> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
@@ -158,11 +159,13 @@
 *>  block sizes MB and NB returned by ILAENV, ZGELQ will use either
 *>  ZLASWLQ (if the matrix is wide-and-short) or ZGELQT to compute
 *>  the LQ factorization.
-*>  This version of ZGEMLQ will use either ZLAMSWLQ or ZGEMLQT to 
+*>  This version of ZGEMLQ will use either ZLAMSWLQ or ZGEMLQT to
 *>  multiply matrix Q by another matrix.
 *>  Further Details in ZLAMSWLQ or ZGEMLQT.
 *> \endverbatim
 *>
+*> \ingroup gemlq
+*>
 *  =====================================================================
       SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
      $                   C, LDC, WORK, LWORK, INFO )
@@ -184,7 +187,7 @@ SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LEFT, RIGHT, TRAN, NOTRAN, LQUERY
-      INTEGER            MB, NB, LW, NBLCKS, MN
+      INTEGER            MB, NB, LW, NBLCKS, MN, MINMNK, LWMIN
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -200,7 +203,7 @@ SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
 *
 *     Test the input arguments
 *
-      LQUERY  = LWORK.EQ.-1
+      LQUERY  = ( LWORK.EQ.-1 )
       NOTRAN  = LSAME( TRANS, 'N' )
       TRAN    = LSAME( TRANS, 'C' )
       LEFT    = LSAME( SIDE, 'L' )
@@ -215,6 +218,13 @@ SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
         LW = M * MB
         MN = N
       END IF
+*
+      MINMNK = MIN( M, N, K )
+      IF( MINMNK.EQ.0 ) THEN
+        LWMIN = 1
+      ELSE
+        LWMIN = MAX( 1, LW )
+      END IF
 *
       IF( ( NB.GT.K ) .AND. ( MN.GT.K ) ) THEN
         IF( MOD( MN - K, NB - K ) .EQ. 0 ) THEN
@@ -243,7 +253,7 @@ SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
         INFO = -9
       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
         INFO = -11
-      ELSE IF( ( LWORK.LT.MAX( 1, LW ) ) .AND. ( .NOT.LQUERY ) ) THEN
+      ELSE IF( ( LWORK.LT.LWMIN ) .AND. ( .NOT.LQUERY ) ) THEN
         INFO = -13
       END IF
 *
@@ -260,7 +270,7 @@ SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
 *
 *     Quick return if possible
 *
-      IF( MIN( M, N, K ).EQ.0 ) THEN
+      IF( MINMNK.EQ.0 ) THEN
         RETURN
       END IF
 *