Merge pull request #4391 from martin-frbg/lapack942

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

lapack-netlib/SRC/cgebrd.f

@@ -123,7 +123,8 @@
 *> \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.
 *>
@@ -148,7 +149,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexGEcomputational
+*> \ingroup gebrd
 *
 *> \par Further Details:
 *  =====================
@@ -225,8 +226,8 @@
 *     ..
 *     .. 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           CGEBD2, CGEMM, CLABRD, XERBLA
@@ -236,16 +237,24 @@
 *     ..
 *     .. External Functions ..
       INTEGER            ILAENV
-      EXTERNAL           ILAENV
+      REAL               SROUNDUP_LWORK
+      EXTERNAL           ILAENV, SROUNDUP_LWORK
 *     ..
 *     .. Executable Statements ..
 *
 *     Test the input parameters
 *
       INFO = 0
-      NB = MAX( 1, ILAENV( 1, 'CGEBRD', ' ', M, N, -1, -1 ) )
-      LWKOPT = ( M+N )*NB
-      WORK( 1 ) = REAL( LWKOPT )
+      MINMN = MIN( M, N )
+      IF( MINMN.EQ.0 ) THEN
+         LWKMIN = 1
+         LWKOPT = 1
+      ELSE
+         LWKMIN = MAX( M, N )
+         NB = MAX( 1, ILAENV( 1, 'CGEBRD', ' ', M, N, -1, -1 ) )
+         LWKOPT = ( M+N )*NB
+      END IF
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
       LQUERY = ( LWORK.EQ.-1 )
       IF( M.LT.0 ) THEN
          INFO = -1
@@ -253,7 +262,7 @@
          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
@@ -265,7 +274,6 @@
 *
 *     Quick return if possible
 *
-      MINMN = MIN( M, N )
       IF( MINMN.EQ.0 ) THEN
          WORK( 1 ) = 1
          RETURN
@@ -284,7 +292,7 @@
 *        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
@@ -343,7 +351,7 @@
 *
       CALL CGEBD2( M-I+1, N-I+1, A( I, I ), LDA, D( I ), E( I ),
      $             TAUQ( I ), TAUP( I ), WORK, IINFO )
-      WORK( 1 ) = WS
+      WORK( 1 ) = SROUNDUP_LWORK( WS )
       RETURN
 *
 *     End of CGEBRD

lapack-netlib/SRC/cgehrd.f

@@ -89,7 +89,7 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX array, dimension (LWORK)
+*>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *> \endverbatim
 *>
@@ -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, 'CGEHRD', ' ', 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, 'DGEHRD', ' ', N, ILO, IHI,
+     $                              -1 ) )
+            LWKOPT = N*NB + TSIZE
+         END IF
+         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 CGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO )
-      WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+*
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
 *
       RETURN
 *

lapack-netlib/SRC/cgelq.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
@@ -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
 *

lapack-netlib/SRC/cgelqf.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.
 *>
@@ -175,9 +176,8 @@
 *     Test the input arguments
 *
       INFO = 0
+      K = MIN( M, N )
       NB = ILAENV( 1, 'CGELQF', ' ', 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( 'CGELQF', -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 CGELQ2( 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 CGELQF

lapack-netlib/SRC/cgemlq.f

@@ -110,16 +110,17 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>         (workspace) COMPLEX array, dimension (MAX(1,LWORK))
+*>          (workspace) COMPLEX 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
 *>
@@ -143,7 +144,7 @@
 *>
 *> \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.
@@ -159,11 +160,13 @@
 *>  block sizes MB and NB returned by ILAENV, CGELQ will use either
 *>  CLASWLQ (if the matrix is wide-and-short) or CGELQT to compute
 *>  the LQ factorization.
-*>  This version of CGEMLQ will use either CLAMSWLQ or CGEMLQT to 
+*>  This version of CGEMLQ will use either CLAMSWLQ or CGEMLQT to
 *>  multiply matrix Q by another matrix.
 *>  Further Details in CLAMSWLQ or CGEMLQT.
 *> \endverbatim
 *>
+*> \ingroup gemlq
+*>
 *  =====================================================================
       SUBROUTINE CGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
      $                   C, LDC, WORK, LWORK, INFO )
@@ -185,11 +188,12 @@
 *     ..
 *     .. 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 Subroutines ..
       EXTERNAL           CLAMSWLQ, CGEMLQT, XERBLA
@@ -201,7 +205,7 @@
 *
 *     Test the input arguments
 *
-      LQUERY  = LWORK.EQ.-1
+      LQUERY  = ( LWORK.EQ.-1 )
       NOTRAN  = LSAME( TRANS, 'N' )
       TRAN    = LSAME( TRANS, 'C' )
       LEFT    = LSAME( SIDE, 'L' )
@@ -216,6 +220,13 @@
         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
@@ -244,12 +255,12 @@
         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 ) = REAL( LW )
+        WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -261,7 +272,7 @@
 *
 *     Quick return if possible
 *
-      IF( MIN( M, N, K ).EQ.0 ) THEN
+      IF( MINMNK.EQ.0 ) THEN
         RETURN
       END IF
 *
@@ -274,7 +285,7 @@
      $                 MB, C, LDC, WORK, LWORK, INFO )
       END IF
 *
-      WORK( 1 ) = REAL( LW )
+      WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
 *
       RETURN
 *

lapack-netlib/SRC/cgemqr.f

@@ -111,16 +111,17 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>         (workspace) COMPLEX array, dimension (MAX(1,LWORK))
+*>          (workspace) COMPLEX 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.
@@ -166,6 +167,8 @@
 *>
 *> \endverbatim
 *>
+*> \ingroup gemqr
+*>
 *  =====================================================================
       SUBROUTINE CGEMQR( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
      $                   C, LDC, WORK, LWORK, INFO )
@@ -187,11 +190,12 @@
 *     ..
 *     .. 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 Subroutines ..
       EXTERNAL           CGEMQRT, CLAMTSQR, XERBLA
@@ -203,7 +207,7 @@
 *
 *     Test the input arguments
 *
-      LQUERY  = LWORK.EQ.-1
+      LQUERY  = ( LWORK.EQ.-1 )
       NOTRAN  = LSAME( TRANS, 'N' )
       TRAN    = LSAME( TRANS, 'C' )
       LEFT    = LSAME( SIDE, 'L' )
@@ -218,6 +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
@@ -251,7 +262,7 @@
       END IF
 *
       IF( INFO.EQ.0 ) THEN
-        WORK( 1 ) = LW
+        WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -263,7 +274,7 @@
 *
 *     Quick return if possible
 *
-      IF( MIN( M, N, K ).EQ.0 ) THEN
+      IF( MINMNK.EQ.0 ) THEN
         RETURN
       END IF
 *
@@ -276,7 +287,7 @@
      $                 NB, C, LDC, WORK, LWORK, INFO )
       END IF
 *
-      WORK( 1 ) = LW
+      WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
 *
       RETURN
 *

lapack-netlib/SRC/cgeqlf.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.
 *>
@@ -187,10 +188,11 @@
             NB = ILAENV( 1, 'CGEQLF', ' ', M, N, -1, -1 )
             LWKOPT = N*NB
          END IF
-         WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+         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
 *
@@ -277,7 +279,7 @@
       IF( MU.GT.0 .AND. NU.GT.0 )
      $   CALL CGEQL2( MU, NU, A, LDA, TAU, WORK, IINFO )
 *
-      WORK( 1 ) = SROUNDUP_LWORK(IWS)
+      WORK( 1 ) = SROUNDUP_LWORK( IWS )
       RETURN
 *
 *     End of CGEQLF

lapack-netlib/SRC/cgeqp3rk.f

@@ -428,7 +428,8 @@
 *> \verbatim
 *>          LWORK is INTEGER
 *>          The dimension of the array WORK.
-*.          LWORK >= N+NRHS-1
+*>          LWORK >= 1, if MIN(M,N) = 0, and
+*>          LWORK >= N+NRHS-1, otherwise.
 *>          For optimal performance LWORK >= NB*( N+NRHS+1 ),
 *>          where NB is the optimal block size for CGEQP3RK returned
 *>          by ILAENV. Minimal block size MINNB=2.
@@ -627,8 +628,9 @@
 *     .. External Functions ..
       LOGICAL            SISNAN
       INTEGER            ISAMAX, ILAENV
-      REAL               SLAMCH, SCNRM2
-      EXTERNAL           SISNAN, SLAMCH, SCNRM2, ISAMAX, ILAENV
+      REAL               SLAMCH, SCNRM2, SROUNDUP_LWORK
+      EXTERNAL           SISNAN, SLAMCH, SCNRM2, ISAMAX, ILAENV,
+     $                   SROUNDUP_LWORK
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          CMPLX, MAX, MIN
@@ -703,7 +705,7 @@
 *
             LWKOPT = 2*N + NB*( N+NRHS+1 )
          END IF
-         WORK( 1 ) = CMPLX( LWKOPT )
+         WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
 *
          IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN
             INFO = -15
@@ -726,7 +728,7 @@
          K = 0
          MAXC2NRMK = ZERO
          RELMAXC2NRMK = ZERO
-         WORK( 1 ) = CMPLX( LWKOPT )
+         WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
          RETURN
       END IF
 *
@@ -778,7 +780,7 @@
 *
 *        Array TAU is not set and contains undefined elements.
 *
-         WORK( 1 ) = CMPLX( LWKOPT )
+         WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
          RETURN
       END IF
 *
@@ -797,7 +799,7 @@
             TAU( J ) = CZERO
          END DO
 *
-         WORK( 1 ) = CMPLX( LWKOPT )
+         WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
          RETURN
 *
       END IF
@@ -828,7 +830,7 @@
          DO J = 1, MINMN
             TAU( J ) = CZERO
          END DO
-         WORK( 1 ) = CMPLX( LWKOPT )
+         WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
          RETURN
       END IF
 *
@@ -873,7 +875,7 @@
             TAU( J ) = CZERO
          END DO
 *
-         WORK( 1 ) = CMPLX( LWKOPT )
+         WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
          RETURN
       END IF
 *
@@ -991,7 +993,7 @@
 *
 *              Return from the routine.
 *
-               WORK( 1 ) = CMPLX( LWKOPT )
+               WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
 *
                RETURN
 *
@@ -1082,7 +1084,7 @@
 *
       END IF
 *
-      WORK( 1 ) = CMPLX( LWKOPT )
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
 *
       RETURN
 *

lapack-netlib/SRC/cgeqr.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
@@ -168,6 +168,8 @@
 *>
 *> \endverbatim
 *>
+*> \ingroup geqr
+*>
 *  =====================================================================
       SUBROUTINE CGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK,
      $                  INFO )
@@ -188,11 +190,12 @@
 *     ..
 *     .. 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           LSAME, SROUNDUP_LWORK
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CLATSQR, CGEQRT, XERBLA
@@ -244,8 +247,10 @@
 *
 *     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 +258,7 @@
           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 +273,7 @@
       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 +287,9 @@
         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 +314,7 @@
      $                LWORK, INFO )
       END IF
 *
-      WORK( 1 ) = MAX( 1, NB*N )
+      WORK( 1 ) = SROUNDUP_LWORK( LWREQ )
 *
       RETURN
 *

lapack-netlib/SRC/cgeqrfp.f

@@ -97,7 +97,8 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.  LWORK >= max(1,N).
+*>          The dimension of the array WORK.
+*>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise.
 *>          For optimum performance LWORK >= N*NB, where NB is
 *>          the optimal blocksize.
 *>
@@ -162,8 +163,8 @@
 *
 *     .. 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           CGEQR2P, CLARFB, CLARFT, XERBLA
@@ -182,8 +183,16 @@
 *
       INFO = 0
       NB = ILAENV( 1, 'CGEQRF', ' ', 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 +200,7 @@
          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
@@ -203,7 +212,6 @@
 *
 *     Quick return if possible
 *
-      K = MIN( M, N )
       IF( K.EQ.0 ) THEN
          WORK( 1 ) = 1
          RETURN
@@ -211,7 +219,7 @@
 *
       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 +281,7 @@
      $   CALL CGEQR2P( 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 CGEQRFP

lapack-netlib/SRC/cgesvdx.f

@@ -208,7 +208,7 @@
 *> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
-*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK;
+*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *> \endverbatim
 *>
 *> \param[in] LWORK
@@ -261,7 +261,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexGEsing
+*> \ingroup gesvdx
 *
 *  =====================================================================
       SUBROUTINE CGESVDX( JOBU, JOBVT, RANGE, M, N, A, LDA, VL, VU,
@@ -312,8 +312,8 @@
 *     .. External Functions ..
       LOGICAL            LSAME
       INTEGER            ILAENV
-      REAL               SLAMCH, CLANGE
-      EXTERNAL           LSAME, ILAENV, SLAMCH, CLANGE
+      REAL               SLAMCH, CLANGE, SROUNDUP_LWORK
+      EXTERNAL           LSAME, ILAENV, SLAMCH, CLANGE, SROUNDUP_LWORK
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          MAX, MIN, SQRT
@@ -448,7 +448,7 @@
             END IF
          END IF
          MAXWRK = MAX( MAXWRK, MINWRK )
-         WORK( 1 ) = CMPLX( REAL( MAXWRK ), ZERO )
+         WORK( 1 ) = SROUNDUP_LWORK( MAXWRK )
 *
          IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
             INFO = -19
@@ -464,7 +464,7 @@
 *
 *     Quick return if possible
 *
-      IF( M.EQ.0 .OR. N.EQ.0 ) THEN
+      IF( MINMN.EQ.0 ) THEN
          RETURN
       END IF
 *
@@ -846,7 +846,7 @@
 *
 *     Return optimal workspace in WORK(1)
 *
-      WORK( 1 ) = CMPLX( REAL( MAXWRK ), ZERO )
+      WORK( 1 ) = SROUNDUP_LWORK( MAXWRK )
 *
       RETURN
 *

lapack-netlib/SRC/cgesvj.f

@@ -208,15 +208,17 @@
 *> \verbatim
 *>          CWORK is COMPLEX array, dimension (max(1,LWORK))
 *>          Used as workspace.
-*>          If on entry LWORK = -1, then a workspace query is assumed and
-*>          no computation is done; CWORK(1) is set to the minial (and optimal)
-*>          length of CWORK.
 *> \endverbatim
 *>
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER.
-*>          Length of CWORK, LWORK >= M+N.
+*>          Length of CWORK.
+*>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M+N, otherwise.
+*>
+*>          If on entry LWORK = -1, then a workspace query is assumed and
+*>          no computation is done; CWORK(1) is set to the minial (and optimal)
+*>          length of CWORK.
 *> \endverbatim
 *>
 *> \param[in,out] RWORK
@@ -247,15 +249,17 @@
 *>          RWORK(6) = the largest absolute value over all sines of the
 *>                    Jacobi rotation angles in the last sweep. It can be
 *>                    useful for a post festum analysis.
-*>         If on entry LRWORK = -1, then a workspace query is assumed and
-*>         no computation is done; RWORK(1) is set to the minial (and optimal)
-*>         length of RWORK.
 *> \endverbatim
 *>
 *> \param[in] LRWORK
 *> \verbatim
 *>         LRWORK is INTEGER
-*>         Length of RWORK, LRWORK >= MAX(6,N).
+*>         Length of RWORK.
+*>         LRWORK >= 1, if MIN(M,N) = 0, and LRWORK >= MAX(6,N), otherwise
+*>
+*>         If on entry LRWORK = -1, then a workspace query is assumed and
+*>         no computation is done; RWORK(1) is set to the minial (and optimal)
+*>         length of RWORK.
 *> \endverbatim
 *>
 *> \param[out] INFO
@@ -276,7 +280,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexGEcomputational
+*> \ingroup gesvj
 *
 *> \par Further Details:
 *  =====================
@@ -374,16 +378,17 @@
       PARAMETER  ( NSWEEP = 30 )
 *     ..
 *     .. Local Scalars ..
-      COMPLEX AAPQ, OMPQ
-      REAL    AAPP, AAPP0, AAPQ1, AAQQ, APOAQ, AQOAP, BIG,
-     $        BIGTHETA, CS, CTOL, EPSLN, MXAAPQ,
-     $        MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, ROOTTOL,
-     $        SKL, SFMIN, SMALL, SN, T, TEMP1, THETA, THSIGN, TOL
-      INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1,
-     $        ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, N2, N34,
-     $        N4, NBL, NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND
-      LOGICAL APPLV, GOSCALE, LOWER, LQUERY, LSVEC, NOSCALE, ROTOK,
-     $        RSVEC, UCTOL, UPPER
+      COMPLEX    AAPQ, OMPQ
+      REAL       AAPP, AAPP0, AAPQ1, AAQQ, APOAQ, AQOAP, BIG,
+     $           BIGTHETA, CS, CTOL, EPSLN, MXAAPQ,
+     $           MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, ROOTTOL,
+     $           SKL, SFMIN, SMALL, SN, T, TEMP1, THETA, THSIGN, TOL
+      INTEGER    BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1,
+     $           ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, N2, N34,
+     $           N4, NBL, NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND,
+     $           MINMN, LWMIN, LRWMIN
+      LOGICAL    APPLV, GOSCALE, LOWER, LQUERY, LSVEC, NOSCALE, ROTOK,
+     $           RSVEC, UCTOL, UPPER
 *     ..
 *     ..
 *     .. Intrinsic Functions ..
@@ -398,8 +403,8 @@
       INTEGER            ISAMAX
       EXTERNAL           ISAMAX
 *     from LAPACK
-      REAL               SLAMCH
-      EXTERNAL           SLAMCH
+      REAL               SLAMCH, SROUNDUP_LWORK
+      EXTERNAL           SLAMCH, SROUNDUP_LWORK
       LOGICAL            LSAME
       EXTERNAL           LSAME
 *     ..
@@ -422,7 +427,16 @@
       UPPER = LSAME( JOBA, 'U' )
       LOWER = LSAME( JOBA, 'L' )
 *
-      LQUERY = ( LWORK .EQ. -1 ) .OR. ( LRWORK .EQ. -1 )
+      MINMN = MIN( M, N )
+      IF( MINMN.EQ.0 ) THEN
+         LWMIN  = 1
+         LRWMIN = 1
+      ELSE
+         LWMIN  = M + N
+         LRWMIN = MAX( 6, N )
+      END IF
+*
+      LQUERY = ( LWORK.EQ.-1 ) .OR. ( LRWORK.EQ.-1 )
       IF( .NOT.( UPPER .OR. LOWER .OR. LSAME( JOBA, 'G' ) ) ) THEN
          INFO = -1
       ELSE IF( .NOT.( LSVEC .OR. UCTOL .OR. LSAME( JOBU, 'N' ) ) ) THEN
@@ -442,9 +456,9 @@
          INFO = -11
       ELSE IF( UCTOL .AND. ( RWORK( 1 ).LE.ONE ) ) THEN
          INFO = -12
-      ELSE IF( LWORK.LT.( M+N ) .AND. ( .NOT.LQUERY ) ) THEN
+      ELSE IF( LWORK.LT.LWMIN .AND. ( .NOT.LQUERY ) ) THEN
          INFO = -13
-      ELSE IF( LRWORK.LT.MAX( N, 6 ) .AND. ( .NOT.LQUERY ) ) THEN
+      ELSE IF( LRWORK.LT.LRWMIN .AND. ( .NOT.LQUERY ) ) THEN
          INFO = -15
       ELSE
          INFO = 0
@@ -454,15 +468,15 @@
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGESVJ', -INFO )
          RETURN
-      ELSE IF ( LQUERY ) THEN
-         CWORK(1) = M + N
-         RWORK(1) = MAX( N, 6 )
+      ELSE IF( LQUERY ) THEN
+         CWORK( 1 ) = SROUNDUP_LWORK( LWMIN )
+         RWORK( 1 ) = SROUNDUP_LWORK( LRWMIN )
          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

lapack-netlib/SRC/cgetri.f

@@ -153,8 +153,8 @@
 *
       INFO = 0
       NB = ILAENV( 1, 'CGETRI', ' ', 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
@@ -252,7 +252,7 @@
      $      CALL CSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
    60 CONTINUE
 *
-      WORK( 1 ) = SROUNDUP_LWORK(IWS)
+      WORK( 1 ) = SROUNDUP_LWORK( IWS )
       RETURN
 *
 *     End of CGETRI

lapack-netlib/SRC/cgetsls.f

@@ -127,7 +127,7 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.
+*>          The dimension of the array WORK. LWORK >= 1.
 *>          If LWORK = -1 or -2, then a workspace query is assumed.
 *>          If LWORK = -1, the routine calculates optimal size of WORK for the
 *>          optimal performance and returns this value in WORK(1).
@@ -229,7 +229,10 @@
 *
 *     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 CGEQR( M, N, A, LDA, TQ, -1, WORKQ, -1, INFO2 )
          TSZO = INT( TQ( 1 ) )
          LWO  = INT( WORKQ( 1 ) )

lapack-netlib/SRC/cgetsqrhrt.f

@@ -131,13 +131,15 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          The dimension of the array WORK.
-*>          LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),
+*>          If MIN(M,N) = 0, LWORK >= 1, else
+*>          LWORK >= MAX( 1, LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),
 *>          where
 *>             NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)),
 *>             NB1LOCAL = MIN(NB1,N).
 *>             LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL,
 *>             LW1 = NB1LOCAL * N,
-*>             LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ),
+*>             LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ).
+*>
 *>          If LWORK = -1, then a workspace query is assumed.
 *>          The routine only calculates the optimal size of the WORK
 *>          array, returns this value as the first entry of the WORK
@@ -160,7 +162,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup comlpexOTHERcomputational
+*> \ingroup getsqrhrt
 *
 *> \par Contributors:
 *  ==================
@@ -200,6 +202,10 @@
       INTEGER            I, IINFO, J, LW1, LW2, LWT, LDWT, LWORKOPT,
      $                   NB1LOCAL, NB2LOCAL, NUM_ALL_ROW_BLOCKS
 *     ..
+*     .. External Functions ..
+      REAL               SROUNDUP_LWORK
+      EXTERNAL           SROUNDUP_LWORK
+*     ..
 *     .. External Subroutines ..
       EXTERNAL           CCOPY, CLATSQR, CUNGTSQR_ROW, CUNHR_COL,
      $                   XERBLA
@@ -212,7 +218,7 @@
 *     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
@@ -225,7 +231,7 @@
          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
 *
@@ -263,8 +269,9 @@
             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
 *
@@ -277,14 +284,14 @@
          CALL XERBLA( 'CGETSQRHRT', -INFO )
          RETURN
       ELSE IF ( LQUERY ) THEN
-         WORK( 1 ) = CMPLX( LWORKOPT )
+         WORK( 1 ) = SROUNDUP_LWORK( LWORKOPT )
          RETURN
       END IF
 *
 *     Quick return if possible
 *
       IF( MIN( M, N ).EQ.0 ) THEN
-         WORK( 1 ) = CMPLX( LWORKOPT )
+         WORK( 1 ) = SROUNDUP_LWORK( LWORKOPT )
          RETURN
       END IF
 *
@@ -341,9 +348,9 @@
          END IF
       END DO
 *
-      WORK( 1 ) = CMPLX( LWORKOPT )
+      WORK( 1 ) = SROUNDUP_LWORK( LWORKOPT )
       RETURN
 *
 *     End of CGETSQRHRT
 *
-      END
+      END

lapack-netlib/SRC/cgges3.f

@@ -215,7 +215,8 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.
+*>          The dimension of the array WORK. LWORK >= MAX(1,2*N).
+*>          For good performance, LWORK must generally be larger.
 *>
 *>          If LWORK = -1, then a workspace query is assumed; the routine
 *>          only calculates the optimal size of the WORK array, returns
@@ -260,7 +261,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexGEeigen
+*> \ingroup gges3
 *
 *  =====================================================================
       SUBROUTINE CGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B,
@@ -300,7 +301,8 @@
       LOGICAL            CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
      $                   LQUERY, WANTST
       INTEGER            I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
-     $                   ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK, LWKOPT
+     $                   ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK, LWKOPT,
+     $                   LWKMIN
       REAL               ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL,
      $                   PVSR, SMLNUM
 *     ..
@@ -310,13 +312,12 @@
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CGEQRF, CGGBAK, CGGBAL, CGGHD3, CLAQZ0, CLACPY,
-     $                   CLASCL, CLASET, CTGSEN, CUNGQR, CUNMQR, SLABAD,
-     $                   XERBLA
+     $                   CLASCL, CLASET, CTGSEN, CUNGQR, CUNMQR, XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
-      REAL               CLANGE, SLAMCH
-      EXTERNAL           LSAME, CLANGE, SLAMCH
+      REAL               CLANGE, SLAMCH, SROUNDUP_LWORK
+      EXTERNAL           LSAME, CLANGE, SLAMCH, SROUNDUP_LWORK
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          MAX, SQRT
@@ -353,6 +354,8 @@
 *
       INFO = 0
       LQUERY = ( LWORK.EQ.-1 )
+      LWKMIN = MAX( 1, 2*N )
+*
       IF( IJOBVL.LE.0 ) THEN
          INFO = -1
       ELSE IF( IJOBVR.LE.0 ) THEN
@@ -369,7 +372,7 @@
          INFO = -14
       ELSE IF( LDVSR.LT.1 .OR. ( ILVSR .AND. LDVSR.LT.N ) ) THEN
          INFO = -16
-      ELSE IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN
+      ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
          INFO = -18
       END IF
 *
@@ -377,29 +380,33 @@
 *
       IF( INFO.EQ.0 ) THEN
          CALL CGEQRF( N, N, B, LDB, WORK, WORK, -1, IERR )
-         LWKOPT = MAX( 1,  N + INT ( WORK( 1 ) ) )
+         LWKOPT = MAX( LWKMIN, N + INT( WORK( 1 ) ) )
          CALL CUNMQR( 'L', 'C', N, N, N, B, LDB, WORK, A, LDA, WORK,
      $                -1, IERR )
-         LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) )
+         LWKOPT = MAX( LWKOPT, N + INT( WORK( 1 ) ) )
          IF( ILVSL ) THEN
             CALL CUNGQR( N, N, N, VSL, LDVSL, WORK, WORK, -1,
      $                   IERR )
-            LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) )
+            LWKOPT = MAX( LWKOPT, N + INT( WORK( 1 ) ) )
          END IF
          CALL CGGHD3( JOBVSL, JOBVSR, N, 1, N, A, LDA, B, LDB, VSL,
      $                LDVSL, VSR, LDVSR, WORK, -1, IERR )
-         LWKOPT = MAX( LWKOPT, N + INT ( WORK( 1 ) ) )
+         LWKOPT = MAX( LWKOPT, N + INT( WORK( 1 ) ) )
          CALL CLAQZ0( 'S', JOBVSL, JOBVSR, N, 1, N, A, LDA, B, LDB,
      $                ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, -1,
      $                RWORK, 0, IERR )
-         LWKOPT = MAX( LWKOPT, INT ( WORK( 1 ) ) )
+         LWKOPT = MAX( LWKOPT, INT( WORK( 1 ) ) )
          IF( WANTST ) THEN
             CALL CTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB,
      $                   ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, SDIM,
      $                   PVSL, PVSR, DIF, WORK, -1, IDUM, 1, IERR )
-            LWKOPT = MAX( LWKOPT, INT ( WORK( 1 ) ) )
+            LWKOPT = MAX( LWKOPT, INT( WORK( 1 ) ) )
+         END IF
+         IF( N.EQ.0 ) THEN
+            WORK( 1 ) = 1
+         ELSE
+            WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
          END IF
-         WORK( 1 ) = CMPLX( LWKOPT )
       END IF
 
 *
@@ -422,7 +429,6 @@
       EPS = SLAMCH( 'P' )
       SMLNUM = SLAMCH( 'S' )
       BIGNUM = ONE / SMLNUM
-      CALL SLABAD( SMLNUM, BIGNUM )
       SMLNUM = SQRT( SMLNUM ) / EPS
       BIGNUM = ONE / SMLNUM
 *
@@ -585,7 +591,7 @@
 *
    30 CONTINUE
 *
-      WORK( 1 ) = CMPLX( LWKOPT )
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
 *
       RETURN
 *

lapack-netlib/SRC/cggev3.f

@@ -174,7 +174,8 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.
+*>          The dimension of the array WORK. LWORK >= MAX(1,2*N).
+*>          For good performance, LWORK must generally be larger.
 *>
 *>          If LWORK = -1, then a workspace query is assumed; the routine
 *>          only calculates the optimal size of the WORK array, returns
@@ -208,7 +209,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexGEeigen
+*> \ingroup ggev3
 *
 *  =====================================================================
       SUBROUTINE CGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA,
@@ -243,7 +244,7 @@
       CHARACTER          CHTEMP
       INTEGER            ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, ILO,
      $                   IN, IRIGHT, IROWS, IRWRK, ITAU, IWRK, JC, JR,
-     $                   LWKOPT
+     $                   LWKOPT, LWKMIN
       REAL               ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
      $                   SMLNUM, TEMP
       COMPLEX            X
@@ -253,13 +254,12 @@
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CGEQRF, CGGBAK, CGGBAL, CGGHD3, CLAQZ0, CLACPY,
-     $                   CLASCL, CLASET, CTGEVC, CUNGQR, CUNMQR, SLABAD,
-     $                   XERBLA
+     $                   CLASCL, CLASET, CTGEVC, CUNGQR, CUNMQR, XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
-      REAL               CLANGE, SLAMCH
-      EXTERNAL           LSAME, CLANGE, SLAMCH
+      REAL               CLANGE, SLAMCH, SROUNDUP_LWORK
+      EXTERNAL           LSAME, CLANGE, SLAMCH, SROUNDUP_LWORK
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, AIMAG, MAX, REAL, SQRT
@@ -301,6 +301,7 @@
 *
       INFO = 0
       LQUERY = ( LWORK.EQ.-1 )
+      LWKMIN = MAX( 1, 2*N )
       IF( IJOBVL.LE.0 ) THEN
          INFO = -1
       ELSE IF( IJOBVR.LE.0 ) THEN
@@ -315,7 +316,7 @@
          INFO = -11
       ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN
          INFO = -13
-      ELSE IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN
+      ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
          INFO = -15
       END IF
 *
@@ -323,7 +324,7 @@
 *
       IF( INFO.EQ.0 ) THEN
          CALL CGEQRF( N, N, B, LDB, WORK, WORK, -1, IERR )
-         LWKOPT = MAX( N,  N+INT( WORK( 1 ) ) )
+         LWKOPT = MAX( LWKMIN, N+INT( WORK( 1 ) ) )
          CALL CUNMQR( 'L', 'C', N, N, N, B, LDB, WORK, A, LDA, WORK,
      $                -1, IERR )
          LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) )
@@ -348,7 +349,11 @@
      $                   RWORK, 0, IERR )
             LWKOPT = MAX( LWKOPT, N+INT( WORK( 1 ) ) )
          END IF
-         WORK( 1 ) = CMPLX( LWKOPT )
+         IF( N.EQ.0 ) THEN
+            WORK( 1 ) = 1
+         ELSE
+            WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
+         END IF
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -368,7 +373,6 @@
       EPS = SLAMCH( 'E' )*SLAMCH( 'B' )
       SMLNUM = SLAMCH( 'S' )
       BIGNUM = ONE / SMLNUM
-      CALL SLABAD( SMLNUM, BIGNUM )
       SMLNUM = SQRT( SMLNUM ) / EPS
       BIGNUM = ONE / SMLNUM
 *
@@ -549,7 +553,7 @@
       IF( ILBSCL )
      $   CALL CLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR )
 *
-      WORK( 1 ) = CMPLX( LWKOPT )
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
       RETURN
 *
 *     End of CGGEV3

lapack-netlib/SRC/cgghd3.f

@@ -180,14 +180,14 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX array, dimension (LWORK)
+*>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *> \endverbatim
 *>
 *> \param[in]  LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The length of the array WORK.  LWORK >= 1.
+*>          The length of the array WORK. LWORK >= 1.
 *>          For optimum performance LWORK >= 6*N*NB, where NB is the
 *>          optimal blocksize.
 *>
@@ -212,7 +212,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexOTHERcomputational
+*> \ingroup gghd3
 *
 *> \par Further Details:
 *  =====================
@@ -265,7 +265,8 @@
 *     .. External Functions ..
       LOGICAL            LSAME
       INTEGER            ILAENV
-      EXTERNAL           ILAENV, LSAME
+      REAL               SROUNDUP_LWORK
+      EXTERNAL           ILAENV, LSAME, SROUNDUP_LWORK
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CGGHRD, CLARTG, CLASET, CUNM22, CROT, CGEMM,
@@ -280,8 +281,13 @@
 *
       INFO = 0
       NB = ILAENV( 1, 'CGGHD3', ' ', N, ILO, IHI, -1 )
-      LWKOPT = MAX( 6*N*NB, 1 )
-      WORK( 1 ) = CMPLX( LWKOPT )
+      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' )
       INITZ = LSAME( COMPZ, 'I' )
@@ -330,7 +336,6 @@
 *
 *     Quick return if possible
 *
-      NH = IHI - ILO + 1
       IF( NH.LE.1 ) THEN
          WORK( 1 ) = CONE
          RETURN
@@ -888,7 +893,8 @@
       IF ( JCOL.LT.IHI )
      $   CALL CGGHRD( COMPQ2, COMPZ2, N, JCOL, IHI, A, LDA, B, LDB, Q,
      $                LDQ, Z, LDZ, IERR )
-      WORK( 1 ) = CMPLX( LWKOPT )
+*
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
 *
       RETURN
 *

lapack-netlib/SRC/cggqrf.f

@@ -251,8 +251,8 @@
       NB2 = ILAENV( 1, 'CGERQF', ' ', N, P, -1, -1 )
       NB3 = ILAENV( 1, 'CUNMQR', ' ', 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
@@ -288,7 +288,7 @@
 *     RQ factorization of N-by-P matrix B: B = T*Z.
 *
       CALL CGERQF( N, P, B, LDB, TAUB, WORK, LWORK, INFO )
-      WORK( 1 ) = MAX( LOPT, INT( WORK( 1 ) ) )
+      WORK( 1 ) = SROUNDUP_LWORK( MAX( LOPT, INT( WORK( 1 ) ) ) )
 *
       RETURN
 *

lapack-netlib/SRC/cggrqf.f

@@ -250,8 +250,8 @@
       NB2 = ILAENV( 1, 'CGEQRF', ' ', P, N, -1, -1 )
       NB3 = ILAENV( 1, 'CUNMRQ', ' ', M, N, 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( M.LT.0 ) THEN
          INFO = -1
@@ -288,7 +288,7 @@
 *     QR factorization of P-by-N matrix B: B = Z*T
 *
       CALL CGEQRF( P, N, B, LDB, TAUB, WORK, LWORK, INFO )
-      WORK( 1 ) = MAX( LOPT, INT( WORK( 1 ) ) )
+      WORK( 1 ) = SROUNDUP_LWORK( MAX( LOPT, INT( WORK( 1 ) ) ) )
 *
       RETURN
 *

lapack-netlib/SRC/cggsvd3.f

@@ -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
@@ -333,7 +333,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexGEsing
+*> \ingroup ggsvd3
 *
 *> \par Contributors:
 *  ==================

lapack-netlib/SRC/cggsvp3.f

@@ -233,7 +233,7 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.
+*>          The dimension of the array WORK. LWORK >= 1.
 *>
 *>          If LWORK = -1, then a workspace query is assumed; the routine
 *>          only calculates the optimal size of the WORK array, returns
@@ -256,7 +256,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexOTHERcomputational
+*> \ingroup ggsvp3
 *
 *> \par Further Details:
 *  =====================

lapack-netlib/SRC/cheevd.f

@@ -116,8 +116,7 @@
 *>
 *> \param[out] RWORK
 *> \verbatim
-*>          RWORK is REAL array,
-*>                                         dimension (LRWORK)
+*>          RWORK is REAL array, dimension (MAX(1,LRWORK))
 *>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
 *> \endverbatim
 *>
@@ -282,8 +281,8 @@
             LROPT = LRWMIN
             LIOPT = LIWMIN
          END IF
-         WORK( 1 ) = SROUNDUP_LWORK(LOPT)
-         RWORK( 1 ) = LROPT
+         WORK( 1 ) = SROUNDUP_LWORK( LOPT )
+         RWORK( 1 ) = SROUNDUP_LWORK( LROPT )
          IWORK( 1 ) = LIOPT
 *
          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
@@ -378,8 +377,8 @@
          CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
       END IF
 *
-      WORK( 1 ) = SROUNDUP_LWORK(LOPT)
-      RWORK( 1 ) = LROPT
+      WORK( 1 ) = SROUNDUP_LWORK( LOPT )
+      RWORK( 1 ) = SROUNDUP_LWORK( LROPT )
       IWORK( 1 ) = LIOPT
 *
       RETURN

lapack-netlib/SRC/cheevr.f

@@ -272,7 +272,8 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The length of the array WORK.  LWORK >= max(1,2*N).
+*>          The length of the array WORK.
+*>          If N <= 1, LWORK >= 1, else LWORK >= 2*N.
 *>          For optimal efficiency, LWORK >= (NB+1)*N,
 *>          where NB is the max of the blocksize for CHETRD and for
 *>          CUNMTR as returned by ILAENV.
@@ -294,7 +295,8 @@
 *> \param[in] LRWORK
 *> \verbatim
 *>          LRWORK is INTEGER
-*>          The length of the array RWORK.  LRWORK >= max(1,24*N).
+*>          The length of the array RWORK.
+*>          If N <= 1, LRWORK >= 1, else LRWORK >= 24*N.
 *>
 *>          If LRWORK = -1, then a workspace query is assumed; the
 *>          routine only calculates the optimal sizes of the WORK, RWORK
@@ -313,7 +315,8 @@
 *> \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, RWORK
@@ -417,9 +420,15 @@
       LQUERY = ( ( LWORK.EQ.-1 ) .OR. ( LRWORK.EQ.-1 ) .OR.
      $         ( LIWORK.EQ.-1 ) )
 *
-      LRWMIN = MAX( 1, 24*N )
-      LIWMIN = MAX( 1, 10*N )
-      LWMIN = MAX( 1, 2*N )
+      IF( N.LE.1 ) THEN
+         LWMIN  = 1
+         LRWMIN = 1
+         LIWMIN = 1
+      ELSE
+         LWMIN  = 2*N
+         LRWMIN = 24*N
+         LIWMIN = 10*N
+      END IF
 *
       INFO = 0
       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
@@ -454,8 +463,8 @@
          NB = ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 )
          NB = MAX( NB, ILAENV( 1, 'CUNMTR', UPLO, N, -1, -1, -1 ) )
          LWKOPT = MAX( ( NB+1 )*N, LWMIN )
-         WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
-         RWORK( 1 ) = LRWMIN
+         WORK( 1 )  = SROUNDUP_LWORK( LWKOPT )
+         RWORK( 1 ) = SROUNDUP_LWORK( LRWMIN )
          IWORK( 1 ) = LIWMIN
 *
          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
@@ -483,7 +492,7 @@
       END IF
 *
       IF( N.EQ.1 ) THEN
-         WORK( 1 ) = 2
+         WORK( 1 ) = 1
          IF( ALLEIG .OR. INDEIG ) THEN
             M = 1
             W( 1 ) = REAL( A( 1, 1 ) )
@@ -710,8 +719,8 @@
 *
 *     Set WORK(1) to optimal workspace size.
 *
-      WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
-      RWORK( 1 ) = LRWMIN
+      WORK( 1 )  = SROUNDUP_LWORK( LWKOPT )
+      RWORK( 1 ) = SROUNDUP_LWORK( LRWMIN )
       IWORK( 1 ) = LIWMIN
 *
       RETURN

lapack-netlib/SRC/cheevr_2stage.f

@@ -265,7 +265,7 @@
 *>          indicating the nonzero elements in Z. The i-th eigenvector
 *>          is nonzero only in elements ISUPPZ( 2*i-1 ) through
 *>          ISUPPZ( 2*i ). This is an output of CSTEMR (tridiagonal
-*>          matrix). The support of the eigenvectors of A is typically 
+*>          matrix). The support of the eigenvectors of A is typically
 *>          1:N because of the unitary transformations applied by CUNMTR.
 *>          Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1
 *> \endverbatim
@@ -279,12 +279,13 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.  
+*>          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 + N
-*>                                             = N*KD + N*max(KD+1,FACTOPTNB) 
-*>                                               + max(2*KD*KD, KD*NTHREADS) 
+*>                                             = N*KD + N*max(KD+1,FACTOPTNB)
+*>                                               + max(2*KD*KD, KD*NTHREADS)
 *>                                               + (KD+1)*N + N
 *>                                   where KD is the blocking size of the reduction,
 *>                                   FACTOPTNB is the blocking used by the QR or LQ
@@ -310,7 +311,8 @@
 *> \param[in] LRWORK
 *> \verbatim
 *>          LRWORK is INTEGER
-*>          The length of the array RWORK.  LRWORK >= max(1,24*N).
+*>          The length of the array RWORK.
+*>          If N <= 1, LRWORK >= 1, else LRWORK >= 24*N.
 *>
 *>          If LRWORK = -1, then a workspace query is assumed; the
 *>          routine only calculates the optimal sizes of the WORK, RWORK
@@ -329,7 +331,8 @@
 *> \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, RWORK
@@ -354,7 +357,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexHEeigen
+*> \ingroup heevr_2stage
 *
 *> \par Contributors:
 *  ==================
@@ -382,7 +385,7 @@
 *>  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.
@@ -390,11 +393,11 @@
 *>  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
 *
@@ -443,8 +446,9 @@
 *     .. External Functions ..
       LOGICAL            LSAME
       INTEGER            ILAENV, ILAENV2STAGE
-      REAL               SLAMCH, CLANSY
-      EXTERNAL           LSAME, SLAMCH, CLANSY, ILAENV, ILAENV2STAGE
+      REAL               SLAMCH, CLANSY, SROUNDUP_LWORK
+      EXTERNAL           LSAME, SLAMCH, CLANSY, ILAENV, ILAENV2STAGE,
+     $                   SROUNDUP_LWORK 
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           SCOPY, SSCAL, SSTEBZ, SSTERF, XERBLA, CSSCAL,
@@ -472,9 +476,16 @@
       IB     = ILAENV2STAGE( 2, 'CHETRD_2STAGE', JOBZ, N, KD, -1, -1 )
       LHTRD  = ILAENV2STAGE( 3, 'CHETRD_2STAGE', JOBZ, N, KD, IB, -1 )
       LWTRD  = ILAENV2STAGE( 4, 'CHETRD_2STAGE', JOBZ, N, KD, IB, -1 )
-      LWMIN  = N + LHTRD + LWTRD
-      LRWMIN = MAX( 1, 24*N )
-      LIWMIN = MAX( 1, 10*N )
+*
+      IF( N.LE.1 ) THEN
+         LWMIN  = 1
+         LRWMIN = 1
+         LIWMIN = 1
+      ELSE
+         LWMIN  = N + LHTRD + LWTRD
+         LRWMIN = 24*N
+         LIWMIN = 10*N
+      END IF
 *
       INFO = 0
       IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
@@ -506,8 +517,8 @@
       END IF
 *
       IF( INFO.EQ.0 ) THEN
-         WORK( 1 )  = LWMIN
-         RWORK( 1 ) = LRWMIN
+         WORK( 1 )  = SROUNDUP_LWORK( LWMIN )
+         RWORK( 1 ) = SROUNDUP_LWORK( LRWMIN )
          IWORK( 1 ) = LIWMIN
 *
          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
@@ -535,7 +546,7 @@
       END IF
 *
       IF( N.EQ.1 ) THEN
-         WORK( 1 ) = 2
+         WORK( 1 ) = 1
          IF( ALLEIG .OR. INDEIG ) THEN
             M = 1
             W( 1 ) = REAL( A( 1, 1 ) )
@@ -643,9 +654,9 @@
 *
 *     Call CHETRD_2STAGE to reduce Hermitian matrix to tridiagonal form.
 *
-      CALL CHETRD_2STAGE( JOBZ, UPLO, N, A, LDA, RWORK( INDRD ), 
+      CALL CHETRD_2STAGE( JOBZ, UPLO, N, A, LDA, RWORK( INDRD ),
      $                    RWORK( INDRE ), WORK( INDTAU ),
-     $                    WORK( INDHOUS ), LHTRD, 
+     $                    WORK( INDHOUS ), LHTRD,
      $                    WORK( INDWK ), LLWORK, IINFO )
 *
 *     If all eigenvalues are desired
@@ -666,7 +677,7 @@
             CALL SCOPY( N-1, RWORK( INDRE ), 1, RWORK( INDREE ), 1 )
             CALL SCOPY( N, RWORK( INDRD ), 1, RWORK( INDRDD ), 1 )
 *
-            IF (ABSTOL .LE. TWO*N*EPS) THEN
+            IF ( ABSTOL .LE. TWO*N*EPS ) THEN
                TRYRAC = .TRUE.
             ELSE
                TRYRAC = .FALSE.
@@ -765,8 +776,8 @@
 *
 *     Set WORK(1) to optimal workspace size.
 *
-      WORK( 1 )  = LWMIN
-      RWORK( 1 ) = LRWMIN
+      WORK( 1 )  = SROUNDUP_LWORK( LWMIN )
+      RWORK( 1 ) = SROUNDUP_LWORK( LRWMIN )
       IWORK( 1 ) = LIWMIN
 *
       RETURN

lapack-netlib/SRC/cheevx.f

@@ -348,14 +348,14 @@
       IF( INFO.EQ.0 ) THEN
          IF( N.LE.1 ) THEN
             LWKMIN = 1
-            WORK( 1 ) = LWKMIN
+            LWKOPT = 1
          ELSE
             LWKMIN = 2*N
             NB = ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 )
             NB = MAX( NB, ILAENV( 1, 'CUNMTR', UPLO, N, -1, -1, -1 ) )
-            LWKOPT = MAX( 1, ( NB + 1 )*N )
-            WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+            LWKOPT = ( NB + 1 )*N
          END IF
+         WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
 *
          IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY )
      $      INFO = -17

lapack-netlib/SRC/chesv_aa.f

@@ -177,7 +177,7 @@
 *
 *     .. Local Scalars ..
       LOGICAL            LQUERY
-      INTEGER            LWKOPT, LWKOPT_HETRF, LWKOPT_HETRS
+      INTEGER            LWKMIN, LWKOPT, LWKOPT_HETRF, LWKOPT_HETRS
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -197,6 +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
@@ -207,18 +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 CHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
-         LWKOPT_HETRF = INT( WORK(1) )
+         LWKOPT_HETRF = INT( WORK( 1 ) )
          CALL CHETRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
      $                   -1, INFO )
-         LWKOPT_HETRS = INT( WORK(1) )
-         LWKOPT = MAX( LWKOPT_HETRF, LWKOPT_HETRS )
-         WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+         LWKOPT_HETRS = INT( WORK( 1 ) )
+         LWKOPT = MAX( LWKMIN, LWKOPT_HETRF, LWKOPT_HETRS )
+         WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -240,7 +241,7 @@
 *
       END IF
 *
-      WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
 *
       RETURN
 *

lapack-netlib/SRC/chesv_aa_2stage.f

@@ -99,14 +99,14 @@
 *>
 *> \param[out] TB
 *> \verbatim
-*>          TB is COMPLEX array, dimension (LTB)
+*>          TB is COMPLEX 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
@@ -146,14 +146,15 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX workspace of size LWORK
+*>          WORK is COMPLEX 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,
@@ -203,7 +204,7 @@
 *
 *     .. Local Scalars ..
       LOGICAL            UPPER, TQUERY, WQUERY
-      INTEGER            LWKOPT
+      INTEGER            LWKMIN, LWKOPT
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -225,6 +226,7 @@
       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
@@ -233,18 +235,19 @@
          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 CHETRF_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
@@ -254,7 +257,6 @@
          RETURN
       END IF
 *
-*
 *     Compute the factorization A = U**H*T*U or A = L*T*L**H.
 *
       CALL CHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2,
@@ -268,7 +270,7 @@
 *
       END IF
 *
-      WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
 *
       RETURN
 *

lapack-netlib/SRC/chesvx.f

@@ -307,7 +307,7 @@
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LQUERY, NOFACT
-      INTEGER            LWKOPT, NB
+      INTEGER            LWKMIN, LWKOPT, NB
       REAL               ANORM
 *     ..
 *     .. External Functions ..
@@ -329,6 +329,7 @@
       INFO = 0
       NOFACT = LSAME( FACT, 'N' )
       LQUERY = ( LWORK.EQ.-1 )
+      LWKMIN = MAX( 1, 2*N )
       IF( .NOT.NOFACT .AND. .NOT.LSAME( FACT, 'F' ) ) THEN
          INFO = -1
       ELSE IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) )
@@ -346,17 +347,17 @@
          INFO = -11
       ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
          INFO = -13
-      ELSE IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN
+      ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
          INFO = -18
       END IF
 *
       IF( INFO.EQ.0 ) THEN
-         LWKOPT = MAX( 1, 2*N )
+         LWKOPT = LWKMIN
          IF( NOFACT ) THEN
             NB = ILAENV( 1, 'CHETRF', UPLO, N, -1, -1, -1 )
             LWKOPT = MAX( LWKOPT, N*NB )
          END IF
-         WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+         WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -405,7 +406,7 @@
       IF( RCOND.LT.SLAMCH( 'Epsilon' ) )
      $   INFO = N + 1
 *
-      WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
 *
       RETURN
 *

lapack-netlib/SRC/chetrd_2stage.f

@@ -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 CHETRD_2STAGE + dependencies 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrd_2stage.f"> 
-*> [TGZ]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrd_2stage.f"> 
-*> [ZIP]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrd_2stage.f"> 
+*> Download CHETRD_2STAGE + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrd_2stage.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrd_2stage.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrd_2stage.f">
 *> [TXT]</a>
-*> \endhtmlonly 
+*> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE CHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU, 
+*       SUBROUTINE CHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
 *                                 HOUS2, LHOUS2, WORK, LWORK, INFO )
 *
 *       IMPLICIT NONE
@@ -34,7 +34,7 @@
 *       COMPLEX            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 unitary
 *>          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 COMPLEX 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 COMPLEX array, dimension (LHOUS2)
+*>          HOUS2 is COMPLEX 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
@@ -143,13 +145,16 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX array, dimension (LWORK)
+*>          WORK is COMPLEX 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. LWORK = MAX(1, dimension)
+*>          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
@@ -157,9 +162,9 @@
 *>          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 +182,12 @@
 *  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 complexHEcomputational
+*> \ingroup hetrd_2stage
 *
 *> \par Further Details:
 *  =====================
@@ -202,7 +207,7 @@
 *>  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 +215,16 @@
 *>  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 CHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU, 
+      SUBROUTINE CHETRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
      $                          HOUS2, LHOUS2, WORK, LWORK, INFO )
 *
       IMPLICIT NONE
@@ -250,7 +255,8 @@
 *     .. External Functions ..
       LOGICAL            LSAME
       INTEGER            ILAENV2STAGE
-      EXTERNAL           LSAME, ILAENV2STAGE
+      REAL               SROUNDUP_LWORK
+      EXTERNAL           LSAME, ILAENV2STAGE, SROUNDUP_LWORK
 *     ..
 *     .. Executable Statements ..
 *
@@ -265,10 +271,13 @@
 *
       KD     = ILAENV2STAGE( 1, 'CHETRD_2STAGE', VECT, N, -1, -1, -1 )
       IB     = ILAENV2STAGE( 2, 'CHETRD_2STAGE', VECT, N, KD, -1, -1 )
-      LHMIN  = ILAENV2STAGE( 3, 'CHETRD_2STAGE', VECT, N, KD, IB, -1 )
-      LWMIN  = ILAENV2STAGE( 4, 'CHETRD_2STAGE', VECT, N, KD, IB, -1 )
-*      WRITE(*,*),'CHETRD_2STAGE N KD UPLO LHMIN LWMIN ',N, KD, UPLO,
-*     $            LHMIN, LWMIN
+      IF( N.EQ.0 ) THEN
+         LHMIN = 1
+         LWMIN = 1
+      ELSE
+         LHMIN = ILAENV2STAGE( 3, 'CHETRD_2STAGE', VECT, N, KD, IB, -1 )
+         LWMIN = ILAENV2STAGE( 4, 'CHETRD_2STAGE', VECT, N, KD, IB, -1 )
+      END IF
 *
       IF( .NOT.LSAME( VECT, 'N' ) ) THEN
          INFO = -1
@@ -285,8 +294,8 @@
       END IF
 *
       IF( INFO.EQ.0 ) THEN
-         HOUS2( 1 ) = LHMIN
-         WORK( 1 )  = LWMIN
+         HOUS2( 1 ) = SROUNDUP_LWORK( LHMIN )
+         WORK( 1 )  = SROUNDUP_LWORK( LWMIN )
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -309,14 +318,14 @@
       LWRK  = LWORK-LDAB*N
       ABPOS = 1
       WPOS  = ABPOS + LDAB*N
-      CALL CHETRD_HE2HB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB, 
+      CALL CHETRD_HE2HB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB,
      $                   TAU, WORK( WPOS ), LWRK, INFO )
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CHETRD_HE2HB', -INFO )
          RETURN
       END IF
-      CALL CHETRD_HB2ST( 'Y', VECT, UPLO, N, KD, 
-     $                   WORK( ABPOS ), LDAB, D, E, 
+      CALL CHETRD_HB2ST( 'Y', VECT, UPLO, N, KD,
+     $                   WORK( ABPOS ), LDAB, D, E,
      $                   HOUS2, LHOUS2, WORK( WPOS ), LWRK, INFO )
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CHETRD_HB2ST', -INFO )
@@ -324,8 +333,7 @@
       END IF
 *
 *
-      HOUS2( 1 ) = LHMIN
-      WORK( 1 )  = LWMIN
+      WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       RETURN
 *
 *     End of CHETRD_2STAGE

lapack-netlib/SRC/chetrd_hb2st.F

@@ -132,15 +132,17 @@
 *>
 *> \param[out] HOUS
 *> \verbatim
-*>          HOUS is COMPLEX array, dimension LHOUS, that
-*>          store the Householder representation.
+*>          HOUS is COMPLEX array, dimension (MAX(1,LHOUS))
+*>          Stores the Householder representation.
 *> \endverbatim
 *>
 *> \param[in] LHOUS
 *> \verbatim
 *>          LHOUS is INTEGER
-*>          The dimension of the array HOUS. LHOUS = MAX(1, dimension)
-*>          If LWORK = -1, or LHOUS=-1,
+*>          The dimension of the array HOUS.
+*>          If N = 0 or KD <= 1, LHOUS >= 1, else LHOUS = MAX(1, dimension).
+*>
+*>          If LWORK = -1, or LHOUS = -1,
 *>          then a query is assumed; the routine
 *>          only calculates the optimal size of the HOUS array, returns
 *>          this value as the first entry of the HOUS array, and no error
@@ -152,14 +154,17 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX array, dimension LWORK.
+*>          WORK is COMPLEX 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. LWORK = MAX(1, dimension)
-*>          If LWORK = -1, or LHOUS=-1,
+*>          The dimension of the array WORK.
+*>          If N = 0 or KD <= 1, LWORK >= 1, else LWORK = MAX(1, dimension).
+*>
+*>          If LWORK = -1, or LHOUS = -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
@@ -262,7 +267,7 @@
       INTEGER            I, M, K, IB, SWEEPID, MYID, SHIFT, STT, ST,
      $                   ED, STIND, EDIND, BLKLASTIND, COLPT, THED,
      $                   STEPERCOL, GRSIZ, THGRSIZ, THGRNB, THGRID,
-     $                   NBTILES, TTYPE, TID, NTHREADS, DEBUG,
+     $                   NBTILES, TTYPE, TID, NTHREADS,
      $                   ABDPOS, ABOFDPOS, DPOS, OFDPOS, AWPOS,
      $                   INDA, INDW, APOS, SIZEA, LDA, INDV, INDTAU,
      $                   SICEV, SIZETAU, LDV, LHMIN, LWMIN
@@ -286,7 +291,6 @@
 *     Determine the minimal workspace size required.
 *     Test the input parameters
 *
-      DEBUG   = 0
       INFO    = 0
       AFTERS1 = LSAME( STAGE1, 'Y' )
       WANTQ   = LSAME( VECT, 'V' )
@@ -295,9 +299,14 @@
 *
 *     Determine the block size, the workspace size and the hous size.
 *
-      IB     = ILAENV2STAGE( 2, 'CHETRD_HB2ST', VECT, N, KD, -1, -1 )
-      LHMIN  = ILAENV2STAGE( 3, 'CHETRD_HB2ST', VECT, N, KD, IB, -1 )
-      LWMIN  = ILAENV2STAGE( 4, 'CHETRD_HB2ST', VECT, N, KD, IB, -1 )
+      IB       = ILAENV2STAGE( 2, 'CHETRD_HB2ST', VECT, N, KD, -1, -1 )
+      IF( N.EQ.0 .OR. KD.LE.1 ) THEN
+         LHMIN = 1
+         LWMIN = 1
+      ELSE
+         LHMIN = ILAENV2STAGE( 3, 'CHETRD_HB2ST', VECT, N, KD, IB, -1 )
+         LWMIN = ILAENV2STAGE( 4, 'CHETRD_HB2ST', VECT, N, KD, IB, -1 )
+      END IF
 *
       IF( .NOT.AFTERS1 .AND. .NOT.LSAME( STAGE1, 'N' ) ) THEN
          INFO = -1
@@ -318,8 +327,8 @@
       END IF
 *
       IF( INFO.EQ.0 ) THEN
-         HOUS( 1 ) = LHMIN
-         WORK( 1 ) = SROUNDUP_LWORK(LWMIN)
+         HOUS( 1 ) = SROUNDUP_LWORK( LHMIN )
+         WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -575,8 +584,7 @@ C                 END IF
   170     CONTINUE
       ENDIF
 *
-      HOUS( 1 ) = LHMIN
-      WORK( 1 ) = SROUNDUP_LWORK(LWMIN)
+      WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       RETURN
 *
 *     End of CHETRD_HB2ST

lapack-netlib/SRC/chetrd_he2hb.f

@@ -123,8 +123,8 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX array, dimension (LWORK)
-*>          On exit, if INFO = 0, or if LWORK=-1, 
+*>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
+*>          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, 'CHETRD_HE2HB', '', N, KD, -1, -1 )
-      
+      IF( N.LE.KD+1 ) THEN
+         LWMIN = 1
+      ELSE
+         LWMIN = ILAENV2STAGE( 4, 'CHETRD_HE2HB', '', 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( 'CHETRD_HE2HB', -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 CHETRD_HE2HB

lapack-netlib/SRC/chetrf.f

@@ -107,7 +107,7 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The length of WORK.  LWORK >=1.  For best performance
+*>          The length of WORK. LWORK >= 1. For best performance
 *>          LWORK >= N*NB, where NB is the block size returned by ILAENV.
 *> \endverbatim
 *>
@@ -228,8 +228,8 @@
 *        Determine the block size
 *
          NB = ILAENV( 1, 'CHETRF', UPLO, N, -1, -1, -1 )
-         LWKOPT = N*NB
-         WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+         LWKOPT = MAX( 1, N*NB )
+         WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -347,7 +347,7 @@
       END IF
 *
    40 CONTINUE
-      WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
       RETURN
 *
 *     End of CHETRF

lapack-netlib/SRC/chetrf_aa.f

@@ -101,8 +101,10 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The length of WORK.  LWORK >= 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 CHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
+      SUBROUTINE CHETRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
 *
 *  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
@@ -152,7 +154,7 @@
 *
 *     .. Local Scalars ..
       LOGICAL      LQUERY, UPPER
-      INTEGER      J, LWKOPT
+      INTEGER      J, LWKMIN, LWKOPT
       INTEGER      NB, MJ, NJ, K1, K2, J1, J2, J3, JB
       COMPLEX      ALPHA
 *     ..
@@ -179,19 +181,26 @@
       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.( 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
@@ -203,11 +212,11 @@
 *
 *     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
          A( 1, 1 ) = REAL( A( 1, 1 ) )
          RETURN
       END IF
@@ -460,7 +469,7 @@
       END IF
 *
    20 CONTINUE
-      WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
       RETURN
 *
 *     End of CHETRF_AA

lapack-netlib/SRC/chetrf_aa_2stage.f

@@ -87,14 +87,14 @@
 *>
 *> \param[out] TB
 *> \verbatim
-*>          TB is COMPLEX array, dimension (LTB)
+*>          TB is COMPLEX array, dimension (MAX(1,LTB))
 *>          On exit, details of the LU factorization of the band matrix.
 *> \endverbatim
 *>
 *> \param[in] LTB
 *> \verbatim
 *>          LTB is INTEGER
-*>          The size of the array TB. LTB >= 4*N, internally
+*>          The size of the array TB. LTB >= MAX(1,4*N), internally
 *>          used to select NB such that LTB >= (3*NB+1)*N.
 *>
 *>          If LTB = -1, then a workspace query is assumed; the
@@ -121,14 +121,14 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX workspace of size LWORK
+*>          WORK is COMPLEX 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,
@@ -152,7 +152,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexSYcomputational
+*> \ingroup hetrf_aa_2stage
 *
 *  =====================================================================
       SUBROUTINE CHETRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV,
@@ -188,7 +188,8 @@
 *     .. External Functions ..
       LOGICAL            LSAME
       INTEGER            ILAENV
-      EXTERNAL           LSAME, ILAENV
+      REAL               SROUNDUP_LWORK
+      EXTERNAL           LSAME, ILAENV, SROUNDUP_LWORK
       
 *     ..
 *     .. External Subroutines ..
@@ -213,9 +214,9 @@
          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
 *
@@ -229,10 +230,10 @@
       NB = ILAENV( 1, 'CHETRF_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 ) = N*NB
+            WORK( 1 ) = SROUNDUP_LWORK( MAX( 1, N*NB ) )
          END IF
       END IF
       IF( TQUERY .OR. WQUERY ) THEN
@@ -241,7 +242,7 @@
 *
 *     Quick return
 *
-      IF ( N.EQ.0 ) THEN
+      IF( N.EQ.0 ) THEN
          RETURN
       ENDIF
 *

lapack-netlib/SRC/chetrf_rk.f

@@ -177,14 +177,14 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX array, dimension ( MAX(1,LWORK) ).
+*>          WORK is COMPLEX 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.
 *>
@@ -311,8 +311,8 @@
 *        Determine the block size
 *
          NB = ILAENV( 1, 'CHETRF_RK', UPLO, N, -1, -1, -1 )
-         LWKOPT = N*NB
-         WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+         LWKOPT = MAX( 1, N*NB )
+         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 CHETRF_RK

lapack-netlib/SRC/chetrf_rook.f

@@ -122,7 +122,7 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The length of WORK.  LWORK >=1.  For best performance
+*>          The length of WORK.  LWORK >= 1.  For best performance
 *>          LWORK >= N*NB, where NB is the block size returned by ILAENV.
 *>
 *>          If LWORK = -1, then a workspace query is assumed; the routine
@@ -264,7 +264,7 @@
 *
          NB = ILAENV( 1, 'CHETRF_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
@@ -387,7 +387,7 @@
       END IF
 *
    40 CONTINUE
-      WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
       RETURN
 *
 *     End of CHETRF_ROOK

lapack-netlib/SRC/chetri2.f

@@ -88,16 +88,16 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX array, dimension (N+NB+1)*(NB+3)
+*>          WORK is COMPLEX 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 complexHEcomputational
+*> \ingroup hetri2
 *
 *  =====================================================================
       SUBROUTINE CHETRI2( 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           CHETRI2X, CHETRI, XERBLA
@@ -159,9 +160,13 @@
       INFO = 0
       UPPER = LSAME( UPLO, 'U' )
       LQUERY = ( LWORK.EQ.-1 )
+*
 *     Get blocksize
+*
       NBMAX = ILAENV( 1, 'CHETRF', 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( 'CHETRI2', -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 CHETRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
       ELSE
          CALL CHETRI2X( UPLO, N, A, LDA, IPIV, WORK, NBMAX, INFO )
       END IF
+*
       RETURN
 *
 *     End of CHETRI2

lapack-netlib/SRC/chetri_3.f

@@ -119,16 +119,17 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is COMPLEX array, dimension (N+NB+1)*(NB+3).
+*>          WORK is COMPLEX 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, 'CHETRI_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, 'CHETRI_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( 'CHETRI_3', -INFO )
          RETURN
       ELSE IF( LQUERY ) THEN
-         WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
          RETURN
       END IF
 *
@@ -237,7 +242,7 @@
 *
       CALL CHETRI_3X( UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO )
 *
-      WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
+      WORK( 1 ) = SROUNDUP_LWORK( LWKOPT )
 *
       RETURN
 *

lapack-netlib/SRC/chetrs_aa.f

@@ -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
@@ -151,24 +157,30 @@
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LQUERY, UPPER
-      INTEGER            K, KP, LWKOPT
+      INTEGER            K, KP, LWKMIN
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
       REAL               SROUNDUP_LWORK
-      EXTERNAL           LSAME,SROUNDUP_LWORK
+      EXTERNAL           LSAME, SROUNDUP_LWORK
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CLACPY, CLACGV, CGTSV, CSWAP, CTRSM, 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 +191,20 @@
          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( 'CHETRS_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

lapack-netlib/SRC/clamswlq.f

@@ -127,17 +127,20 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>         (workspace) COMPLEX array, dimension (MAX(1,LWORK))
+*>          (workspace) COMPLEX 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
@@ -193,91 +196,100 @@
 *>
 *  =====================================================================
       SUBROUTINE CLAMSWLQ( 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 ..
-      COMPLEX           A( LDA, * ), WORK( * ), C(LDC, * ),
-     $      T( LDT, * )
+      COMPLEX            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
       REAL               SROUNDUP_LWORK
       EXTERNAL           LSAME, SROUNDUP_LWORK
+*     ..
 *     .. External Subroutines ..
-      EXTERNAL    CTPMLQT, CGEMLQT, XERBLA
+      EXTERNAL           CTPMLQT, CGEMLQT, XERBLA
 *     ..
 *     .. Executable Statements ..
 *
 *     Test the input arguments
 *
-      LQUERY  = LWORK.LT.0
+      INFO = 0
+      LQUERY  = ( LWORK.EQ.-1 )
       NOTRAN  = LSAME( TRANS, 'N' )
       TRAN    = LSAME( TRANS, 'C' )
       LEFT    = LSAME( SIDE, 'L' )
       RIGHT   = LSAME( SIDE, 'R' )
-      IF (LEFT) THEN
+      IF( LEFT ) THEN
         LW = N * MB
       ELSE
         LW = M * MB
       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( 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( 'CLAMSWLQ', -INFO )
-        WORK(1) = SROUNDUP_LWORK(LW)
         RETURN
-      ELSE IF (LQUERY) THEN
-        WORK(1) = SROUNDUP_LWORK(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
 *
       IF((NB.LE.K).OR.(NB.GE.MAX(M,N,K))) THEN
         CALL CGEMLQT( SIDE, TRANS, M, N, K, MB, A, LDA,
-     $        T, LDT, C, LDC, WORK, INFO)
+     $        T, LDT, C, LDC, WORK, INFO )
         RETURN
       END IF
 *
@@ -404,7 +416,7 @@
 *
       END IF
 *
-      WORK(1) = SROUNDUP_LWORK(LW)
+      WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       RETURN
 *
 *     End of CLAMSWLQ

lapack-netlib/SRC/clamtsqr.f

@@ -128,22 +128,24 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>         (workspace) COMPLEX array, dimension (MAX(1,LWORK))
-*>
+*>          (workspace) COMPLEX 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
@@ -195,45 +197,47 @@
 *>
 *  =====================================================================
       SUBROUTINE CLAMTSQR( 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 ..
-      COMPLEX        A( LDA, * ), WORK( * ), C(LDC, * ),
-     $                T( LDT, * )
+      COMPLEX            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
       REAL               SROUNDUP_LWORK
       EXTERNAL           LSAME, SROUNDUP_LWORK
+*     ..
 *     .. External Subroutines ..
-      EXTERNAL   CGEMQRT, CTPMQRT, XERBLA
+      EXTERNAL           CGEMQRT, CTPMQRT, XERBLA
 *     ..
 *     .. Executable Statements ..
 *
 *     Test the input arguments
 *
-      LQUERY  = LWORK.LT.0
+      INFO = 0
+      LQUERY  = ( LWORK.EQ.-1 )
       NOTRAN  = LSAME( TRANS, 'N' )
       TRAN    = LSAME( TRANS, 'C' )
       LEFT    = LSAME( SIDE, 'L' )
       RIGHT   = LSAME( SIDE, 'R' )
-      IF (LEFT) THEN
+      IF( LEFT ) THEN
         LW = N * NB
         Q = M
       ELSE
@@ -241,11 +245,17 @@
         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
@@ -256,38 +266,38 @@
         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) = SROUNDUP_LWORK(LW)
+      IF( INFO.EQ.0 ) THEN
+        WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       END IF
 *
       IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CLAMTSQR', -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 CGEMQRT( 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
 *
@@ -412,7 +422,7 @@
 *
       END IF
 *
-      WORK(1) = SROUNDUP_LWORK(LW)
+      WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       RETURN
 *
 *     End of CLAMTSQR

lapack-netlib/SRC/claswlq.f

@@ -96,22 +96,24 @@
 *>          The leading dimension of the array T.  LDT >= MB.
 *> \endverbatim
 *>
-*>
 *> \param[out] WORK
 *> \verbatim
-*>         (workspace) COMPLEX array, dimension (MAX(1,LWORK))
-*>
+*>          (workspace) COMPLEX 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
@@ -163,33 +165,35 @@
 *>
 *  =====================================================================
       SUBROUTINE CLASWLQ( 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 ..
-      COMPLEX           A( LDA, * ), WORK( * ), T( LDT, *)
+      COMPLEX            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
       INTEGER            ILAENV
       REAL               SROUNDUP_LWORK
       EXTERNAL           LSAME, ILAENV, SROUNDUP_LWORK
+*     ..
 *     .. EXTERNAL SUBROUTINES ..
       EXTERNAL           CGELQT, CTPLQT, XERBLA
+*     ..
 *     .. INTRINSIC FUNCTIONS ..
       INTRINSIC          MAX, MIN, MOD
 *     ..
@@ -200,12 +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
@@ -213,60 +224,61 @@
         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) = SROUNDUP_LWORK(MB*M)
+*
+      IF( INFO.EQ.0 ) THEN
+        WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       END IF
 *
       IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CLASWLQ', -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
+      IF( (M.GE.N) .OR. (NB.LE.M) .OR. (NB.GE.N) ) THEN
         CALL CGELQT( 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 CGELQT( M, NB, MB, A(1,1), LDA, T, LDT, WORK, INFO)
-       CTR = 1
+      CALL CGELQT( 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 CTPLQT( M, NB-M, 0, MB, A(1,1), LDA, A( 1, I ),
+        CALL CTPLQT( 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
+        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 CTPLQT( M, KK, 0, MB, A(1,1), LDA, A( 1, II ),
      $                  LDA, T(1,CTR*M+1), LDT,
      $                  WORK, INFO )
-       END IF
+      END IF
 *
-      WORK( 1 ) = SROUNDUP_LWORK(M * MB)
+      WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       RETURN
 *
 *     End of CLASWLQ

lapack-netlib/SRC/clatrs3.f

@@ -152,13 +152,17 @@
 *>
 *> \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 size of
 *>          WORK.
 *> \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.
 *>
@@ -166,6 +170,7 @@
 *>          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
@@ -182,7 +187,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleOTHERauxiliary
+*> \ingroup latrs3
 *> \par Further Details:
 *  =====================
 *  \verbatim
@@ -257,15 +262,16 @@
       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
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
       INTEGER            ILAENV
-      REAL               SLAMCH, CLANGE, SLARMM
-      EXTERNAL           ILAENV, LSAME, SLAMCH, CLANGE, SLARMM
+      REAL               SLAMCH, CLANGE, SLARMM, SROUNDUP_LWORK
+      EXTERNAL           ILAENV, LSAME, SLAMCH, CLANGE, SLARMM,
+     $                   SROUNDUP_LWORK
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           CLATRS, CSSCAL, XERBLA
@@ -296,15 +302,24 @@
 *     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.
 *
@@ -326,7 +341,7 @@
          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
@@ -659,6 +674,9 @@
             END IF
          END DO
       END DO
+*
+      WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
+*
       RETURN
 *
 *     End of CLATRS3

lapack-netlib/SRC/clatsqr.f

@@ -101,15 +101,18 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>         (workspace) COMPLEX array, dimension (MAX(1,LWORK))
+*>          (workspace) COMPLEX 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
@@ -165,32 +168,34 @@
 *>
 *  =====================================================================
       SUBROUTINE CLATSQR( 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 ..
-      COMPLEX           A( LDA, * ), WORK( * ), T(LDT, *)
+      COMPLEX            A( LDA, * ), WORK( * ), T( LDT, * )
 *     ..
 *
 *  =====================================================================
 *
 *     ..
 *     .. Local Scalars ..
-      LOGICAL    LQUERY
-      INTEGER    I, II, KK, CTR
+      LOGICAL            LQUERY
+      INTEGER            I, II, KK, CTR, LWMIN, MINMN
 *     ..
 *     .. EXTERNAL FUNCTIONS ..
       LOGICAL            LSAME
       REAL               SROUNDUP_LWORK
       EXTERNAL           LSAME, SROUNDUP_LWORK
+*     ..
 *     .. EXTERNAL SUBROUTINES ..
-      EXTERNAL    CGEQRT, CTPQRT, XERBLA
+      EXTERNAL           CGEQRT, CTPQRT, XERBLA
+*     ..
 *     .. INTRINSIC FUNCTIONS ..
       INTRINSIC          MAX, MIN, MOD
 *     ..
@@ -201,6 +206,13 @@
       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
@@ -208,64 +220,65 @@
         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) = SROUNDUP_LWORK(NB*N)
+*
+      IF( INFO.EQ.0 ) THEN
+        WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       END IF
       IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CLATSQR', -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 CGEQRT( 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 CGEQRT( 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 CGEQRT( MB, N, NB, A(1,1), LDA, T, LDT, WORK, INFO )
-       CTR = 1
+      CALL CGEQRT( MB, N, NB, A(1,1), LDA, T, LDT, WORK, INFO )
+      CTR = 1
 *
-       DO I = MB+1, II-MB+N ,  (MB-N)
+      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 CTPQRT( MB-N, N, 0, NB, A(1,1), LDA, A( I, 1 ), LDA,
+        CALL CTPQRT( 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
+     $                 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 CTPQRT( KK, N, 0, NB, A(1,1), LDA, A( II, 1 ), LDA,
+      IF( II.LE.M ) THEN
+        CALL CTPQRT( KK, N, 0, NB, A(1,1), LDA, A( II, 1 ), LDA,
      $                 T(1, CTR * N + 1), LDT,
-     $                  WORK, INFO )
-       END IF
+     $                 WORK, INFO )
+      END IF
 *
-      WORK( 1 ) = SROUNDUP_LWORK(N*NB)
+      WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
       RETURN
 *
 *     End of CLATSQR

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 @@
 *     ..
 *     .. 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
@@ -241,9 +242,17 @@
 *     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
@@ -251,7 +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
@@ -263,7 +272,6 @@
 *
 *     Quick return if possible
 *
-      MINMN = MIN( M, N )
       IF( MINMN.EQ.0 ) THEN
          WORK( 1 ) = 1
          RETURN
@@ -282,7 +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

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 @@
       INTEGER            IHI, ILO, INFO, LDA, LWORK, N
 *     ..
 *     .. Array Arguments ..
-      DOUBLE PRECISION  A( LDA, * ), TAU( * ), WORK( * )
+      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
 *     ..
 *
 *  =====================================================================
@@ -182,7 +182,7 @@
       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 )
 *     ..
@@ -190,7 +190,7 @@
       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 @@
          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 @@
 *
 *     Quick return if possible
 *
-      NH = IHI - ILO + 1
       IF( NH.LE.1 ) THEN
          WORK( 1 ) = 1
          RETURN
@@ -268,7 +273,7 @@
 *
 *           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
@@ -344,6 +349,7 @@
 *     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:
 *  =====================
@@ -174,9 +175,8 @@
 *     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
@@ -184,19 +184,25 @@
          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( '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 @@
       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 @@
      $       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 @@
       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 @@
 *     ..
 *     .. 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 @@
 *
 *     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 @@
         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 @@
         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 @@
 *
 *     Quick return if possible
 *
-      IF( MIN( M, N, K ).EQ.0 ) THEN
+      IF( MINMNK.EQ.0 ) THEN
         RETURN
       END IF
 *
@@ -275,7 +285,7 @@
      $                 MB, C, LDC, WORK, LWORK, INFO )
       END IF
 *
-      WORK( 1 ) = LW
+      WORK( 1 ) = LWMIN
 *
       RETURN
 *

lapack-netlib/SRC/dgemqr.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.
@@ -160,12 +161,14 @@
 *>  block sizes MB and NB returned by ILAENV, DGEQR will use either
 *>  DLATSQR (if the matrix is tall-and-skinny) or DGEQRT to compute
 *>  the QR factorization.
-*>  This version of DGEMQR will use either DLAMTSQR or DGEMQRT to 
+*>  This version of DGEMQR will use either DLAMTSQR or DGEMQRT to
 *>  multiply matrix Q by another matrix.
 *>  Further Details in DLATMSQR or DGEMQRT.
 *>
 *> \endverbatim
 *>
+*> \ingroup gemqr
+*>
 *  =====================================================================
       SUBROUTINE DGEMQR( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
      $                   C, LDC, WORK, LWORK, INFO )
@@ -187,7 +190,7 @@
 *     ..
 *     .. 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
@@ -203,7 +206,7 @@
 *
 *     Test the input arguments
 *
-      LQUERY  = LWORK.EQ.-1
+      LQUERY  = ( LWORK.EQ.-1 )
       NOTRAN  = LSAME( TRANS, 'N' )
       TRAN    = LSAME( TRANS, 'T' )
       LEFT    = LSAME( SIDE, 'L' )
@@ -218,6 +221,13 @@
         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
@@ -246,12 +256,12 @@
         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 ) = LW
+        WORK( 1 ) = LWMIN
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -263,7 +273,7 @@
 *
 *     Quick return if possible
 *
-      IF( MIN( M, N, K ).EQ.0 ) THEN
+      IF( MINMNK.EQ.0 ) THEN
         RETURN
       END IF
 *
@@ -276,7 +286,7 @@
      $                 NB, C, LDC, WORK, LWORK, INFO )
       END IF
 *
-      WORK( 1 ) = LW
+      WORK( 1 ) = LWMIN
 *
       RETURN
 *

lapack-netlib/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.
 *>
@@ -113,7 +114,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEcomputational
+*> \ingroup geqlf
 *
 *> \par Further Details:
 *  =====================
@@ -188,8 +189,9 @@
          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
 *

lapack-netlib/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, 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 DGEQP3RK returned
 *>          by ILAENV. Minimal block size MINNB=2.

lapack-netlib/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
@@ -168,6 +168,8 @@
 *>
 *> \endverbatim
 *>
+*> \ingroup geqr
+*>
 *  =====================================================================
       SUBROUTINE DGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK,
      $                  INFO )
@@ -188,7 +190,7 @@
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LQUERY, LMINWS, MINT, MINW
-      INTEGER            MB, NB, MINTSZ, NBLCKS
+      INTEGER            MB, NB, MINTSZ, NBLCKS, LWMIN, LWREQ
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -244,8 +246,10 @@
 *
 *     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 +257,7 @@
           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 +272,7 @@
       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 +286,9 @@
         T( 2 ) = MB
         T( 3 ) = NB
         IF( MINW ) THEN
-          WORK( 1 ) = MAX( 1, N )
+          WORK( 1 ) = LWMIN
         ELSE
-          WORK( 1 ) = MAX( 1, NB*N )
+          WORK( 1 ) = LWREQ
         END IF
       END IF
       IF( INFO.NE.0 ) THEN
@@ -309,7 +313,7 @@
      $                LWORK, INFO )
       END IF
 *
-      WORK( 1 ) = MAX( 1, NB*N )
+      WORK( 1 ) = LWREQ
 *
       RETURN
 *

lapack-netlib/SRC/dgeqrfp.f

@@ -97,7 +97,8 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.  LWORK >= max(1,N).
+*>          The dimension of the array WORK.
+*>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise.
 *>          For optimum performance LWORK >= N*NB, where NB is
 *>          the optimal blocksize.
 *>
@@ -122,7 +123,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEcomputational
+*> \ingroup geqrfp
 *
 *> \par Further Details:
 *  =====================
@@ -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           DGEQR2P, DLARFB, DLARFT, XERBLA
@@ -181,8 +182,16 @@
 *
       INFO = 0
       NB = ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
-      LWKOPT = N*NB
+      K = MIN( M, N )
+      IF( K.EQ.0 ) THEN
+         LWKMIN = 1
+         LWKOPT = 1
+      ELSE
+         LWKMIN = N
+         LWKOPT = N*NB
+      END IF
       WORK( 1 ) = LWKOPT
+*
       LQUERY = ( LWORK.EQ.-1 )
       IF( M.LT.0 ) THEN
          INFO = -1
@@ -190,7 +199,7 @@
          INFO = -2
       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
          INFO = -4
-      ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
+      ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
          INFO = -7
       END IF
       IF( INFO.NE.0 ) THEN
@@ -202,7 +211,6 @@
 *
 *     Quick return if possible
 *
-      K = MIN( M, N )
       IF( K.EQ.0 ) THEN
          WORK( 1 ) = 1
          RETURN
@@ -210,7 +218,7 @@
 *
       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.

lapack-netlib/SRC/dgerqf.f

@@ -114,7 +114,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEcomputational
+*> \ingroup gerqf
 *
 *> \par Further Details:
 *  =====================
@@ -189,7 +189,7 @@
          END IF
          WORK( 1 ) = LWKOPT
 *
-         IF ( .NOT.LQUERY ) THEN
+         IF( .NOT.LQUERY ) THEN
             IF( LWORK.LE.0 .OR. ( N.GT.0 .AND. LWORK.LT.MAX( 1, M ) ) )
      $         INFO = -7
          END IF

lapack-netlib/SRC/dgesvj.f

@@ -208,7 +208,7 @@
 *>
 *> \param[in,out] WORK
 *> \verbatim
-*>          WORK is DOUBLE PRECISION array, dimension (LWORK)
+*>          WORK is DOUBLE PRECISION 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)
+*>          The length of the array 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 doubleGEcomputational
+*> \ingroup gesvj
 *
 *> \par Further Details:
 *  =====================
@@ -365,9 +370,9 @@
       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 ..
       DOUBLE PRECISION   FASTR( 5 )
@@ -408,6 +413,14 @@
       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
@@ -427,7 +440,7 @@
          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
@@ -437,11 +450,14 @@
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGESVJ', -INFO )
          RETURN
+      ELSE IF( LQUERY ) THEN
+         WORK( 1 ) = 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

lapack-netlib/SRC/dgetri.f

@@ -107,7 +107,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEcomputational
+*> \ingroup getri
 *
 *  =====================================================================
       SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
@@ -151,8 +151,9 @@
 *
       INFO = 0
       NB = ILAENV( 1, 'DGETRI', ' ', N, -1, -1, -1 )
-      LWKOPT = N*NB
+      LWKOPT = MAX( 1, N*NB )
       WORK( 1 ) = LWKOPT
+*
       LQUERY = ( LWORK.EQ.-1 )
       IF( N.LT.0 ) THEN
          INFO = -1

lapack-netlib/SRC/dgetsls.f

@@ -127,7 +127,7 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.
+*>          The dimension of the array WORK. LWORK >= 1.
 *>          If LWORK = -1 or -2, then a workspace query is assumed.
 *>          If LWORK = -1, the routine calculates optimal size of WORK for the
 *>          optimal performance and returns this value in WORK(1).
@@ -154,7 +154,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEsolve
+*> \ingroup getsls
 *
 *  =====================================================================
       SUBROUTINE DGETSLS( TRANS, M, N, NRHS, A, LDA, B, LDB,
@@ -189,7 +189,7 @@
 *     .. External Functions ..
       LOGICAL            LSAME
       DOUBLE PRECISION   DLAMCH, DLANGE
-      EXTERNAL           LSAME, DLABAD, DLAMCH, DLANGE
+      EXTERNAL           LSAME, DLAMCH, DLANGE
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           DGEQR, DGEMQR, DLASCL, DLASET,
@@ -226,7 +226,10 @@
 *
 *     Determine the optimum and minimum LWORK
 *
-       IF( M.GE.N ) THEN
+       IF( MIN( M, N, NRHS ).EQ.0 ) THEN
+         WSIZEM = 1
+         WSIZEO = 1
+       ELSE IF( M.GE.N ) THEN
          CALL DGEQR( M, N, A, LDA, TQ, -1, WORKQ, -1, INFO2 )
          TSZO = INT( TQ( 1 ) )
          LWO  = INT( WORKQ( 1 ) )
@@ -294,7 +297,6 @@
 *
        SMLNUM = DLAMCH( 'S' ) / DLAMCH( 'P' )
        BIGNUM = ONE / SMLNUM
-       CALL DLABAD( SMLNUM, BIGNUM )
 *
 *     Scale A, B if max element outside range [SMLNUM,BIGNUM]
 *

lapack-netlib/SRC/dgetsqrhrt.f

@@ -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
@@ -160,7 +163,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleOTHERcomputational
+*> \ingroup getsqrhrt
 *
 *> \par Contributors:
 *  ==================
@@ -212,7 +215,7 @@
 *     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
@@ -225,7 +228,7 @@
          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
 *
@@ -263,8 +266,9 @@
             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
 *
@@ -346,4 +350,4 @@
 *
 *     End of DGETSQRHRT
 *
-      END
+      END

lapack-netlib/SRC/dgges.f

@@ -234,8 +234,8 @@
 *> \verbatim
 *>          LWORK is INTEGER
 *>          The dimension of the array WORK.
-*>          If N = 0, LWORK >= 1, else LWORK >= 8*N+16.
-*>          For good performance , LWORK must generally be larger.
+*>          If N = 0, LWORK >= 1, else LWORK >= MAX(8*N,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
@@ -275,7 +275,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEeigen
+*> \ingroup gges
 *
 *  =====================================================================
       SUBROUTINE DGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
@@ -321,9 +321,8 @@
       DOUBLE PRECISION   DIF( 2 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLABAD,
-     $                   DLACPY, DLASCL, DLASET, DORGQR, DORMQR, DTGSEN,
-     $                   XERBLA
+      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLACPY,
+     $                   DLASCL, DLASET, DORGQR, DORMQR, DTGSEN, XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -431,7 +430,6 @@
       EPS = DLAMCH( 'P' )
       SAFMIN = DLAMCH( 'S' )
       SAFMAX = ONE / SAFMIN
-      CALL DLABAD( SAFMIN, SAFMAX )
       SMLNUM = SQRT( SAFMIN ) / EPS
       BIGNUM = ONE / SMLNUM
 *

lapack-netlib/SRC/dgges3.f

@@ -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
@@ -273,7 +275,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEeigen
+*> \ingroup gges3
 *
 *  =====================================================================
       SUBROUTINE DGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B,
@@ -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
       DOUBLE PRECISION   ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PVSL,
      $                   PVSR, SAFMAX, SAFMIN, SMLNUM
 *     ..
@@ -318,9 +321,8 @@
       DOUBLE PRECISION   DIF( 2 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHD3, DLAQZ0, DLABAD,
-     $                   DLACPY, DLASCL, DLASET, DORGQR, DORMQR, DTGSEN,
-     $                   XERBLA
+      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHD3, DLAQZ0, DLACPY,
+     $                   DLASCL, DLASET, DORGQR, DORMQR, DTGSEN, XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -362,6 +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
@@ -378,7 +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
 *
@@ -386,29 +394,33 @@
 *
       IF( INFO.EQ.0 ) THEN
          CALL DGEQRF( 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 DORMQR( '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 ) ) )
          IF( ILVSL ) THEN
             CALL DORGQR( N, N, N, VSL, LDVSL, WORK, WORK, -1, IERR )
-            LWKOPT = MAX( LWKOPT, 3*N+INT( WORK ( 1 ) ) )
+            LWKOPT = MAX( LWKOPT, 3*N+INT( WORK( 1 ) ) )
          END IF
          CALL DGGHD3( JOBVSL, JOBVSR, N, 1, N, A, LDA, B, LDB, VSL,
      $                LDVSL, VSR, LDVSR, WORK, -1, IERR )
-         LWKOPT = MAX( LWKOPT, 3*N+INT( WORK ( 1 ) ) )
+         LWKOPT = MAX( LWKOPT, 3*N+INT( WORK( 1 ) ) )
          CALL DLAQZ0( 'S', JOBVSL, JOBVSR, N, 1, N, A, LDA, B, LDB,
      $                ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR,
      $                WORK, -1, 0, IERR )
-         LWKOPT = MAX( LWKOPT, 2*N+INT( WORK ( 1 ) ) )
+         LWKOPT = MAX( LWKOPT, 2*N+INT( WORK( 1 ) ) )
          IF( WANTST ) THEN
             CALL DTGSEN( 0, ILVSL, ILVSR, BWORK, N, A, LDA, B, LDB,
      $                   ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR,
      $                   SDIM, PVSL, PVSR, DIF, WORK, -1, IDUM, 1,
      $                   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 ) = LWKOPT
          END IF
-         WORK( 1 ) = LWKOPT
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -430,7 +442,6 @@
       EPS = DLAMCH( 'P' )
       SAFMIN = DLAMCH( 'S' )
       SAFMAX = ONE / SAFMIN
-      CALL DLABAD( SAFMIN, SAFMAX )
       SMLNUM = SQRT( SAFMIN ) / EPS
       BIGNUM = ONE / SMLNUM
 *

lapack-netlib/SRC/dggev3.f

@@ -188,7 +188,9 @@
 *>
 *> \param[in] LWORK
 *> \verbatim
-*>          LWORK is INTEGER
+*>          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
@@ -217,7 +219,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEeigen
+*> \ingroup ggev3
 *
 *  =====================================================================
       SUBROUTINE DGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR,
@@ -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
       DOUBLE PRECISION   ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
      $                   SMLNUM, TEMP
 *     ..
@@ -256,9 +259,8 @@
       LOGICAL            LDUMMA( 1 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHD3, DLAQZ0, DLABAD,
-     $                   DLACPY, DLASCL, DLASET, DORGQR, DORMQR, DTGEVC,
-     $                   XERBLA
+      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHD3, DLAQZ0, DLACPY,
+     $                   DLASCL, DLASET, DORGQR, DORMQR, DTGEVC, XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -299,6 +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
@@ -313,7 +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
 *
@@ -321,13 +324,13 @@
 *
       IF( INFO.EQ.0 ) THEN
          CALL DGEQRF( 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 DORMQR( '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 ) ) )
          IF( ILVL ) THEN
             CALL DORGQR( 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 ) ) )
          END IF
          IF( ILV ) THEN
             CALL DGGHD3( JOBVL, JOBVR, N, 1, N, A, LDA, B, LDB, VL,
@@ -336,18 +339,21 @@
             CALL DLAQZ0( '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 DGGHD3( 'N', 'N', 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 ) ) )
             CALL DLAQZ0( '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 ) = LWKOPT
          END IF
-
-         WORK( 1 ) = LWKOPT
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -367,7 +373,6 @@
       EPS = DLAMCH( 'P' )
       SMLNUM = DLAMCH( 'S' )
       BIGNUM = ONE / SMLNUM
-      CALL DLABAD( SMLNUM, BIGNUM )
       SMLNUM = SQRT( SMLNUM ) / EPS
       BIGNUM = ONE / SMLNUM
 *

lapack-netlib/SRC/dgghd3.f

@@ -179,14 +179,14 @@
 *>
 *> \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
 *>
-*> \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.
 *>
@@ -211,7 +211,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleOTHERcomputational
+*> \ingroup gghd3
 *
 *> \par Further Details:
 *  =====================
@@ -275,7 +275,12 @@
 *
       INFO = 0
       NB = ILAENV( 1, 'DGGHD3', ' ', 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 ) = DBLE( LWKOPT )
       INITQ = LSAME( COMPQ, 'I' )
       WANTQ = INITQ .OR. LSAME( COMPQ, 'V' )
@@ -325,7 +330,6 @@
 *
 *     Quick return if possible
 *
-      NH = IHI - ILO + 1
       IF( NH.LE.1 ) THEN
          WORK( 1 ) = ONE
          RETURN
@@ -885,6 +889,7 @@
       IF ( JCOL.LT.IHI )
      $   CALL DGGHRD( COMPQ2, COMPZ2, N, JCOL, IHI, A, LDA, B, LDB, Q,
      $                LDQ, Z, LDZ, IERR )
+*
       WORK( 1 ) = DBLE( LWKOPT )
 *
       RETURN

lapack-netlib/SRC/dggqrf.f

@@ -173,7 +173,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleOTHERcomputational
+*> \ingroup ggqrf
 *
 *> \par Further Details:
 *  =====================
@@ -250,7 +250,7 @@
       NB2 = ILAENV( 1, 'DGERQF', ' ', N, P, -1, -1 )
       NB3 = ILAENV( 1, 'DORMQR', ' ', N, M, P, -1 )
       NB = MAX( NB1, NB2, NB3 )
-      LWKOPT = MAX( N, M, P )*NB
+      LWKOPT = MAX( 1, MAX( N, M, P )*NB )
       WORK( 1 ) = LWKOPT
       LQUERY = ( LWORK.EQ.-1 )
       IF( N.LT.0 ) THEN
@@ -287,6 +287,7 @@
 *     RQ factorization of N-by-P matrix B: B = T*Z.
 *
       CALL DGERQF( N, P, B, LDB, TAUB, WORK, LWORK, INFO )
+*
       WORK( 1 ) = MAX( LOPT, INT( WORK( 1 ) ) )
 *
       RETURN

lapack-netlib/SRC/dggrqf.f

@@ -172,7 +172,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleOTHERcomputational
+*> \ingroup ggrqf
 *
 *> \par Further Details:
 *  =====================
@@ -249,7 +249,7 @@
       NB2 = ILAENV( 1, 'DGEQRF', ' ', P, N, -1, -1 )
       NB3 = ILAENV( 1, 'DORMRQ', ' ', M, N, P, -1 )
       NB = MAX( NB1, NB2, NB3 )
-      LWKOPT = MAX( N, M, P )*NB
+      LWKOPT = MAX( 1, MAX( N, M, P )*NB )
       WORK( 1 ) = LWKOPT
       LQUERY = ( LWORK.EQ.-1 )
       IF( M.LT.0 ) THEN

lapack-netlib/SRC/dggsvd3.f

@@ -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
@@ -328,7 +328,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEsing
+*> \ingroup ggsvd3
 *
 *> \par Contributors:
 *  ==================

lapack-netlib/SRC/dggsvp3.f

@@ -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
@@ -250,7 +250,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleOTHERcomputational
+*> \ingroup ggsvp3
 *
 *> \par Further Details:
 *  =====================

lapack-netlib/SRC/dlamswlq.f

@@ -127,17 +127,20 @@
 *>
 *> \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.
-*>          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
@@ -189,29 +192,31 @@
 *>     SIAM J. Sci. Comput, vol. 34, no. 1, 2012
 *> \endverbatim
 *>
+*> \ingroup lamswlq
+*>
 *  =====================================================================
       SUBROUTINE DLAMSWLQ( 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 ..
-      DOUBLE PRECISION A( LDA, * ), WORK( * ), C(LDC, * ),
-     $      T( LDT, * )
+      DOUBLE PRECISION   A( LDA, * ), WORK( * ), C( LDC, * ),
+     $                   T( LDT, * )
 *     ..
 *
 * =====================================================================
 *
 *     ..
 *     .. Local Scalars ..
-      LOGICAL    LEFT, RIGHT, TRAN, NOTRAN, LQUERY
-      INTEGER    I, II, KK, CTR, LW
+      LOGICAL            LEFT, RIGHT, TRAN, NOTRAN, LQUERY
+      INTEGER            I, II, KK, CTR, LW, MINMNK, LWMIN
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -223,52 +228,60 @@
 *
 *     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 ) = LWMIN
+      END IF
       IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DLAMSWLQ', -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 +415,8 @@
 *
       END IF
 *
-      WORK(1) = LW
+      WORK( 1 ) = LWMIN
+*
       RETURN
 *
 *     End of DLAMSWLQ

lapack-netlib/SRC/dlamtsqr.f

@@ -128,22 +128,24 @@
 *>
 *> \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.
+*>          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
@@ -191,29 +193,31 @@
 *>     SIAM J. Sci. Comput, vol. 34, no. 1, 2012
 *> \endverbatim
 *>
+*> \ingroup lamtsqr
+*>
 *  =====================================================================
       SUBROUTINE DLAMTSQR( 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 ..
-      DOUBLE PRECISION A( LDA, * ), WORK( * ), C(LDC, * ),
-     $                T( LDT, * )
+      DOUBLE PRECISION   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
@@ -225,12 +229,13 @@
 *
 *     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 +243,17 @@
         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 +264,38 @@
         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 ) = LWMIN
       END IF
 *
       IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DLAMTSQR', -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 DGEMQRT( 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 +421,8 @@
 *
       END IF
 *
-      WORK(1) = LW
+      WORK( 1 ) = LWMIN
+*
       RETURN
 *
 *     End of DLAMTSQR

lapack-netlib/SRC/dlaswlq.f

@@ -99,19 +99,22 @@
 *>
 *> \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.  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
@@ -159,33 +162,37 @@
 *>     SIAM J. Sci. Comput, vol. 34, no. 1, 2012
 *> \endverbatim
 *>
+*> \ingroup laswlq
+*>
 *  =====================================================================
       SUBROUTINE DLASWLQ( 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 ..
-      DOUBLE PRECISION  A( LDA, * ), WORK( * ), T( LDT, *)
+      DOUBLE PRECISION   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
+*     ..
 *     .. EXTERNAL SUBROUTINES ..
       EXTERNAL           DGELQT, DTPLQT, XERBLA
+*     ..
 *     .. INTRINSIC FUNCTIONS ..
       INTRINSIC          MAX, MIN, MOD
 *     ..
@@ -196,12 +203,19 @@
       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.LT.0 ) THEN
         INFO = -4
@@ -209,60 +223,62 @@
         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 ) = LWMIN
       END IF
 *
       IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DLASWLQ', -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 DGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO)
+      IF( (M.GE.N) .OR. (NB.LE.M) .OR. (NB.GE.N) ) THEN
+        CALL DGELQT( 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 DGELQT( M, NB, MB, A(1,1), LDA, T, LDT, WORK, INFO)
-       CTR = 1
+      CALL DGELQT( 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 DTPLQT( 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 DTPLQT( 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 DTPLQT( 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 ) = LWMIN
 *
-      WORK( 1 ) = M * MB
       RETURN
 *
 *     End of DLASWLQ

lapack-netlib/SRC/dlatrs3.f

@@ -151,13 +151,17 @@
 *>
 *> \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 size of
 *>          WORK.
 *> \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 +169,7 @@
 *>          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 +186,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleOTHERauxiliary
+*> \ingroup latrs3
 *> \par Further Details:
 *  =====================
 *  \verbatim
@@ -253,7 +258,7 @@
       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
       DOUBLE PRECISION   ANRM, BIGNUM, BNRM, RSCAL, SCAL, SCALOC,
      $                   SCAMIN, SMLNUM, TMAX
 *     ..
@@ -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 ) = 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
@@ -649,6 +663,9 @@
             END IF
          END DO
       END DO
+*
+      WORK( 1 ) = LWMIN
+*
       RETURN
 *
 *     End of DLATRS3

lapack-netlib/SRC/dlatsqr.f

@@ -101,15 +101,18 @@
 *>
 *> \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.  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
@@ -161,27 +164,29 @@
 *>     SIAM J. Sci. Comput, vol. 34, no. 1, 2012
 *> \endverbatim
 *>
+*> \ingroup latsqr
+*>
 *  =====================================================================
       SUBROUTINE DLATSQR( 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 ..
-      DOUBLE PRECISION  A( LDA, * ), WORK( * ), T(LDT, *)
+      DOUBLE PRECISION   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
@@ -198,6 +203,13 @@
       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
@@ -205,65 +217,67 @@
         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 ) = LWMIN
       END IF
+*
       IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DLATSQR', -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 DGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO)
-         RETURN
-       END IF
+      IF( (MB.LE.N) .OR. (MB.GE.M) ) THEN
+        CALL DGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO )
+        RETURN
+      END IF
 *
-       KK = MOD((M-N),(MB-N))
-       II=M-KK+1
+      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 DGEQRT( MB, N, NB, A(1,1), LDA, T, LDT, WORK, INFO )
+      CALL DGEQRT( 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 DTPQRT( 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 DTPQRT( 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 DTPQRT( 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 DTPQRT( 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 ) = LWMIN
       RETURN
 *
 *     End of DLATSQR

lapack-netlib/SRC/dsyev_2stage.f

@@ -20,7 +20,7 @@
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE DSYEV_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, 
+*       SUBROUTINE DSYEV_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
 *                                INFO )
 *
 *       IMPLICIT NONE
@@ -97,7 +97,7 @@
 *>
 *> \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
 *>
@@ -105,12 +105,12 @@
 *> \verbatim
 *>          LWORK is INTEGER
 *>          The length of the array WORK. LWORK >= 1, when N <= 1;
-*>          otherwise  
+*>          otherwise
 *>          If JOBZ = 'N' and N > 1, LWORK must be queried.
 *>                                   LWORK = MAX(1, dimension) where
 *>                                   dimension = max(stage1,stage2) + (KD+1)*N + 2*N
-*>                                             = N*KD + N*max(KD+1,FACTOPTNB) 
-*>                                               + max(2*KD*KD, KD*NTHREADS) 
+*>                                             = N*KD + N*max(KD+1,FACTOPTNB)
+*>                                               + max(2*KD*KD, KD*NTHREADS)
 *>                                               + (KD+1)*N + 2*N
 *>                                   where KD is the blocking size of the reduction,
 *>                                   FACTOPTNB is the blocking used by the QR or LQ
@@ -143,7 +143,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYeigen
+*> \ingroup heev_2stage
 *
 *> \par Further Details:
 *  =====================
@@ -161,7 +161,7 @@
 *>  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.
@@ -169,16 +169,16 @@
 *>  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 DSYEV_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, 
+      SUBROUTINE DSYEV_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
      $                         INFO )
 *
       IMPLICIT NONE
@@ -305,7 +305,7 @@
       LLWORK  = LWORK - INDWRK + 1
 *
       CALL DSYTRD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK( INDE ),
-     $                    WORK( INDTAU ), WORK( INDHOUS ), LHTRD, 
+     $                    WORK( INDTAU ), WORK( INDHOUS ), LHTRD,
      $                    WORK( INDWRK ), LLWORK, IINFO )
 *
 *     For eigenvalues only, call DSTERF.  For eigenvectors, first call

lapack-netlib/SRC/dsyevd.f

@@ -96,8 +96,7 @@
 *>
 *> \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
 *>
@@ -160,7 +159,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYeigen
+*> \ingroup heevd
 *
 *> \par Contributors:
 *  ==================

lapack-netlib/SRC/dsyevr.f

@@ -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 DSYTRD and DORMTR
 *>          returned by ILAENV.
@@ -285,13 +286,14 @@
 *> \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,
@@ -315,7 +317,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYeigen
+*> \ingroup heevr
 *
 *> \par Contributors:
 *  ==================
@@ -390,8 +392,13 @@
 *
       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
@@ -450,7 +457,7 @@
       END IF
 *
       IF( N.EQ.1 ) THEN
-         WORK( 1 ) = 7
+         WORK( 1 ) = 1
          IF( ALLEIG .OR. INDEIG ) THEN
             M = 1
             W( 1 ) = A( 1, 1 )

lapack-netlib/SRC/dsyevr_2stage.f

@@ -263,7 +263,7 @@
 *>          indicating the nonzero elements in Z. The i-th eigenvector
 *>          is nonzero only in elements ISUPPZ( 2*i-1 ) through
 *>          ISUPPZ( 2*i ). This is an output of DSTEMR (tridiagonal
-*>          matrix). The support of the eigenvectors of A is typically 
+*>          matrix). The support of the eigenvectors of A is typically
 *>          1:N because of the orthogonal transformations applied by DORMTR.
 *>          Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1
 *> \endverbatim
@@ -277,12 +277,13 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK.  
+*>          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
-*>                                             = N*KD + N*max(KD+1,FACTOPTNB) 
-*>                                               + max(2*KD*KD, KD*NTHREADS) 
+*>                                             = N*KD + N*max(KD+1,FACTOPTNB)
+*>                                               + max(2*KD*KD, KD*NTHREADS)
 *>                                               + (KD+1)*N + 5*N
 *>                                   where KD is the blocking size of the reduction,
 *>                                   FACTOPTNB is the blocking used by the QR or LQ
@@ -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,
@@ -330,7 +332,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYeigen
+*> \ingroup heevr_2stage
 *
 *> \par Contributors:
 *  ==================
@@ -358,7 +360,7 @@
 *>  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.
@@ -366,11 +368,11 @@
 *>  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
 *
@@ -444,8 +446,14 @@
       IB     = ILAENV2STAGE( 2, 'DSYTRD_2STAGE', JOBZ, N, KD, -1, -1 )
       LHTRD  = ILAENV2STAGE( 3, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1 )
       LWTRD  = ILAENV2STAGE( 4, 'DSYTRD_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
@@ -484,7 +492,7 @@
 *         NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
 *         NB = MAX( NB, ILAENV( 1, 'DORMTR', UPLO, N, -1, -1, -1 ) )
 *         LWKOPT = MAX( ( NB+1 )*N, LWMIN )
-         WORK( 1 ) = LWMIN
+         WORK( 1 )  = LWMIN
          IWORK( 1 ) = LIWMIN
       END IF
 *
@@ -504,7 +512,7 @@
       END IF
 *
       IF( N.EQ.1 ) THEN
-         WORK( 1 ) = 7
+         WORK( 1 ) = 1
          IF( ALLEIG .OR. INDEIG ) THEN
             M = 1
             W( 1 ) = A( 1, 1 )
@@ -608,7 +616,7 @@
 *     Call DSYTRD_2STAGE to reduce symmetric matrix to tridiagonal form.
 *
 *
-      CALL DSYTRD_2STAGE( JOBZ, UPLO, N, A, LDA, WORK( INDD ), 
+      CALL DSYTRD_2STAGE( JOBZ, UPLO, N, A, LDA, WORK( INDD ),
      $                    WORK( INDE ), WORK( INDTAU ), WORK( INDHOUS ),
      $                    LHTRD, WORK( INDWK ), LLWORK, IINFO )
 *
@@ -727,7 +735,7 @@
 *
 *     Set WORK(1) to optimal workspace size.
 *
-      WORK( 1 ) = LWMIN
+      WORK( 1 )  = LWMIN
       IWORK( 1 ) = LIWMIN
 *
       RETURN

lapack-netlib/SRC/dsyevx.f

@@ -244,7 +244,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYeigen
+*> \ingroup heevx
 *
 *  =====================================================================
       SUBROUTINE DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
@@ -338,14 +338,14 @@
       IF( INFO.EQ.0 ) THEN
          IF( N.LE.1 ) THEN
             LWKMIN = 1
-            WORK( 1 ) = LWKMIN
+            LWKOPT = 1
          ELSE
             LWKMIN = 8*N
             NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
             NB = MAX( NB, ILAENV( 1, 'DORMTR', UPLO, N, -1, -1, -1 ) )
             LWKOPT = MAX( LWKMIN, ( NB + 3 )*N )
-            WORK( 1 ) = LWKOPT
          END IF
+         WORK( 1 ) = LWKOPT
 *
          IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY )
      $      INFO = -17

lapack-netlib/SRC/dsysv_aa.f

@@ -154,7 +154,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYsolve
+*> \ingroup hesv_aa
 *
 *  =====================================================================
       SUBROUTINE DSYSV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
@@ -177,7 +177,7 @@
 *
 *     .. Local Scalars ..
       LOGICAL            LQUERY
-      INTEGER            LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
+      INTEGER            LWKMIN, LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -196,6 +196,7 @@
 *
       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
@@ -206,17 +207,17 @@
          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 DSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
-         LWKOPT_SYTRF = INT( WORK(1) )
+         LWKOPT_SYTRF = INT( WORK( 1 ) )
          CALL DSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
      $                   -1, INFO )
-         LWKOPT_SYTRS = INT( WORK(1) )
-         LWKOPT = MAX( LWKOPT_SYTRF, LWKOPT_SYTRS )
+         LWKOPT_SYTRS = INT( WORK( 1 ) )
+         LWKOPT = MAX( LWKMIN, LWKOPT_SYTRF, LWKOPT_SYTRS )
          WORK( 1 ) = LWKOPT
       END IF
 *

lapack-netlib/SRC/dsysv_aa_2stage.f

@@ -101,14 +101,14 @@
 *>
 *> \param[out] TB
 *> \verbatim
-*>          TB is DOUBLE PRECISION array, dimension (LTB)
+*>          TB is DOUBLE PRECISION 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
@@ -148,14 +148,15 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is DOUBLE PRECISION workspace of size LWORK
+*>          WORK is DOUBLE PRECISION 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,
@@ -179,7 +180,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYsolve
+*> \ingroup hesv_aa_2stage
 *
 *  =====================================================================
       SUBROUTINE DSYSV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
@@ -205,7 +206,7 @@
 *
 *     .. Local Scalars ..
       LOGICAL            UPPER, TQUERY, WQUERY
-      INTEGER            LWKOPT
+      INTEGER            LWKMIN, LWKOPT
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -226,6 +227,7 @@
       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 +236,19 @@
          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 DSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, -1, IPIV,
      $                          IPIV2, WORK, -1, INFO )
-         LWKOPT = INT( WORK(1) )
+         LWKOPT = MAX( LWKMIN, INT( WORK( 1 ) ) )
+         WORK( 1 ) = LWKOPT
       END IF
 *
       IF( INFO.NE.0 ) THEN
@@ -255,7 +258,6 @@
          RETURN
       END IF
 *
-*
 *     Compute the factorization A = U**T*T*U or A = L*T*L**T.
 *
       CALL DSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2,

lapack-netlib/SRC/dsysvx.f

@@ -275,7 +275,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYsolve
+*> \ingroup hesvx
 *
 *  =====================================================================
       SUBROUTINE DSYSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B,
@@ -305,7 +305,7 @@
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LQUERY, NOFACT
-      INTEGER            LWKOPT, NB
+      INTEGER            LWKMIN, LWKOPT, NB
       DOUBLE PRECISION   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, 'DSYTRF', UPLO, N, -1, -1, -1 )
             LWKOPT = MAX( LWKOPT, N*NB )

lapack-netlib/SRC/dsytrd.f

@@ -139,7 +139,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYcomputational
+*> \ingroup hetrd
 *
 *> \par Further Details:
 *  =====================
@@ -247,7 +247,7 @@
 *        Determine the block size.
 *
          NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
-         LWKOPT = N*NB
+         LWKOPT = MAX( 1, N*NB )
          WORK( 1 ) = LWKOPT
       END IF
 *

lapack-netlib/SRC/dsytrd_2stage.f

@@ -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 DSYTRD_2STAGE + dependencies 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrd_2stage.f"> 
-*> [TGZ]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrd_2stage.f"> 
-*> [ZIP]</a> 
-*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrd_2stage.f"> 
+*> Download DSYTRD_2STAGE + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrd_2stage.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrd_2stage.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrd_2stage.f">
 *> [TXT]</a>
-*> \endhtmlonly 
+*> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE DSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU, 
+*       SUBROUTINE DSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
 *                                 HOUS2, LHOUS2, WORK, LWORK, INFO )
 *
 *       IMPLICIT NONE
@@ -34,7 +34,7 @@
 *       DOUBLE PRECISION   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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LHOUS2)
+*>          HOUS2 is DOUBLE PRECISION 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
@@ -143,23 +145,26 @@
 *>
 *> \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
 *>
 *> \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 +182,12 @@
 *  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 doubleSYcomputational
+*> \ingroup hetrd_2stage
 *
 *> \par Further Details:
 *  =====================
@@ -202,7 +207,7 @@
 *>  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 +215,16 @@
 *>  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 DSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU, 
+      SUBROUTINE DSYTRD_2STAGE( VECT, UPLO, N, A, LDA, D, E, TAU,
      $                          HOUS2, LHOUS2, WORK, LWORK, INFO )
 *
       IMPLICIT NONE
@@ -265,10 +270,13 @@
 *
       KD     = ILAENV2STAGE( 1, 'DSYTRD_2STAGE', VECT, N, -1, -1, -1 )
       IB     = ILAENV2STAGE( 2, 'DSYTRD_2STAGE', VECT, N, KD, -1, -1 )
-      LHMIN  = ILAENV2STAGE( 3, 'DSYTRD_2STAGE', VECT, N, KD, IB, -1 )
-      LWMIN  = ILAENV2STAGE( 4, 'DSYTRD_2STAGE', VECT, N, KD, IB, -1 )
-*      WRITE(*,*),'DSYTRD_2STAGE N KD UPLO LHMIN LWMIN ',N, KD, UPLO,
-*     $            LHMIN, LWMIN
+      IF( N.EQ.0 ) THEN
+         LHMIN = 1
+         LWMIN = 1
+      ELSE
+         LHMIN = ILAENV2STAGE( 3, 'DSYTRD_2STAGE', VECT, N, KD, IB, -1 )
+         LWMIN = ILAENV2STAGE( 4, 'DSYTRD_2STAGE', VECT, N, KD, IB, -1 )
+      END IF
 *
       IF( .NOT.LSAME( VECT, 'N' ) ) THEN
          INFO = -1
@@ -309,14 +317,14 @@
       LWRK  = LWORK-LDAB*N
       ABPOS = 1
       WPOS  = ABPOS + LDAB*N
-      CALL DSYTRD_SY2SB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB, 
+      CALL DSYTRD_SY2SB( UPLO, N, KD, A, LDA, WORK( ABPOS ), LDAB,
      $                   TAU, WORK( WPOS ), LWRK, INFO )
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DSYTRD_SY2SB', -INFO )
          RETURN
       END IF
-      CALL DSYTRD_SB2ST( 'Y', VECT, UPLO, N, KD, 
-     $                   WORK( ABPOS ), LDAB, D, E, 
+      CALL DSYTRD_SB2ST( 'Y', VECT, UPLO, N, KD,
+     $                   WORK( ABPOS ), LDAB, D, E,
      $                   HOUS2, LHOUS2, WORK( WPOS ), LWRK, INFO )
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DSYTRD_SB2ST', -INFO )
@@ -324,8 +332,7 @@
       END IF
 *
 *
-      HOUS2( 1 ) = LHMIN
-      WORK( 1 )  = LWMIN
+      WORK( 1 ) = LWMIN
       RETURN
 *
 *     End of DSYTRD_2STAGE

lapack-netlib/SRC/dsytrd_sb2st.F

@@ -18,7 +18,7 @@
 *  Definition:
 *  ===========
 *
-*       SUBROUTINE DSYTRD_SB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB, 
+*       SUBROUTINE DSYTRD_SB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB,
 *                               D, E, HOUS, LHOUS, WORK, LWORK, INFO )
 *
 *       #if defined(_OPENMP)
@@ -53,12 +53,12 @@
 *> \param[in] STAGE1
 *> \verbatim
 *>          STAGE1 is CHARACTER*1
-*>          = 'N':  "No": to mention that the stage 1 of the reduction  
+*>          = 'N':  "No": to mention that the stage 1 of the reduction
 *>                  from dense to band using the dsytrd_sy2sb routine
-*>                  was not called before this routine to reproduce AB. 
-*>                  In other term this routine is called as standalone. 
-*>          = 'Y':  "Yes": to mention that the stage 1 of the 
-*>                  reduction from dense to band using the dsytrd_sy2sb 
+*>                  was not called before this routine to reproduce AB.
+*>                  In other term this routine is called as standalone.
+*>          = 'Y':  "Yes": to mention that the stage 1 of the
+*>                  reduction from dense to band using the dsytrd_sy2sb
 *>                  routine has been called to produce AB (e.g., AB is
 *>                  the output of dsytrd_sy2sb.
 *> \endverbatim
@@ -66,10 +66,10 @@
 *> \param[in] VECT
 *> \verbatim
 *>          VECT is CHARACTER*1
-*>          = 'N':  No need for the Housholder representation, 
+*>          = 'N':  No need for the Housholder representation,
 *>                  and thus LHOUS is of size max(1, 4*N);
-*>          = 'V':  the Householder representation is needed to 
-*>                  either generate or to apply Q later on, 
+*>          = 'V':  the Householder representation is needed to
+*>                  either generate or to apply Q later on,
 *>                  then LHOUS is to be queried and computed.
 *>                  (NOT AVAILABLE IN THIS RELEASE).
 *> \endverbatim
@@ -132,34 +132,39 @@
 *>
 *> \param[out] HOUS
 *> \verbatim
-*>          HOUS is DOUBLE PRECISION array, dimension LHOUS, that
-*>          store the Householder representation.
+*>          HOUS is DOUBLE PRECISION array, dimension (MAX(1,LHOUS))
+*>          Stores the Householder representation.
 *> \endverbatim
 *>
 *> \param[in] LHOUS
 *> \verbatim
 *>          LHOUS is INTEGER
-*>          The dimension of the array HOUS. LHOUS = MAX(1, dimension)
-*>          If LWORK = -1, or LHOUS=-1,
+*>          The dimension of the array HOUS.
+*>          If N = 0 or KD <= 1, LHOUS >= 1, else LHOUS = MAX(1, dimension).
+*>
+*>          If LWORK = -1, or LHOUS = -1,
 *>          then a query is assumed; the routine
 *>          only calculates the optimal size of the HOUS array, returns
 *>          this value as the first entry of the HOUS array, and no error
 *>          message related to LHOUS is issued by XERBLA.
 *>          LHOUS = MAX(1, dimension) where
 *>          dimension = 4*N if VECT='N'
-*>          not available now if VECT='H'     
+*>          not available now if VECT='H'
 *> \endverbatim
 *>
 *> \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
 *>
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The dimension of the array WORK. LWORK = MAX(1, dimension)
-*>          If LWORK = -1, or LHOUS=-1,
+*>          The dimension of the array WORK.
+*>          If N = 0 or KD <= 1, LWORK >= 1, else LWORK = MAX(1, dimension).
+*>
+*>          If LWORK = -1, or LHOUS = -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
@@ -188,7 +193,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup real16OTHERcomputational
+*> \ingroup hetrd_hb2st
 *
 *> \par Further Details:
 *  =====================
@@ -208,7 +213,7 @@
 *>  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.
@@ -216,16 +221,16 @@
 *>  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 DSYTRD_SB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB, 
+      SUBROUTINE DSYTRD_SB2ST( STAGE1, VECT, UPLO, N, KD, AB, LDAB,
      $                         D, E, HOUS, LHOUS, WORK, LWORK, INFO )
 *
 #if defined(_OPENMP)
@@ -258,11 +263,11 @@
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LQUERY, WANTQ, UPPER, AFTERS1
-      INTEGER            I, M, K, IB, SWEEPID, MYID, SHIFT, STT, ST, 
+      INTEGER            I, M, K, IB, SWEEPID, MYID, SHIFT, STT, ST,
      $                   ED, STIND, EDIND, BLKLASTIND, COLPT, THED,
      $                   STEPERCOL, GRSIZ, THGRSIZ, THGRNB, THGRID,
-     $                   NBTILES, TTYPE, TID, NTHREADS, DEBUG,
-     $                   ABDPOS, ABOFDPOS, DPOS, OFDPOS, AWPOS, 
+     $                   NBTILES, TTYPE, TID, NTHREADS,
+     $                   ABDPOS, ABOFDPOS, DPOS, OFDPOS, AWPOS,
      $                   INDA, INDW, APOS, SIZEA, LDA, INDV, INDTAU,
      $                   SIDEV, SIZETAU, LDV, LHMIN, LWMIN
 *     ..
@@ -274,7 +279,7 @@
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
-      INTEGER            ILAENV2STAGE 
+      INTEGER            ILAENV2STAGE
       EXTERNAL           LSAME, ILAENV2STAGE
 *     ..
 *     .. Executable Statements ..
@@ -282,7 +287,6 @@
 *     Determine the minimal workspace size required.
 *     Test the input parameters
 *
-      DEBUG   = 0
       INFO    = 0
       AFTERS1 = LSAME( STAGE1, 'Y' )
       WANTQ   = LSAME( VECT, 'V' )
@@ -291,9 +295,14 @@
 *
 *     Determine the block size, the workspace size and the hous size.
 *
-      IB     = ILAENV2STAGE( 2, 'DSYTRD_SB2ST', VECT, N, KD, -1, -1 )
-      LHMIN  = ILAENV2STAGE( 3, 'DSYTRD_SB2ST', VECT, N, KD, IB, -1 )
-      LWMIN  = ILAENV2STAGE( 4, 'DSYTRD_SB2ST', VECT, N, KD, IB, -1 )
+      IB       = ILAENV2STAGE( 2, 'DSYTRD_SB2ST', VECT, N, KD, -1, -1 )
+      IF( N.EQ.0 .OR. KD.LE.1 ) THEN
+         LHMIN = 1
+         LWMIN = 1
+      ELSE
+         LHMIN = ILAENV2STAGE( 3, 'DSYTRD_SB2ST', VECT, N, KD, IB, -1 )
+         LWMIN = ILAENV2STAGE( 4, 'DSYTRD_SB2ST', VECT, N, KD, IB, -1 )
+      END IF
 *
       IF( .NOT.AFTERS1 .AND. .NOT.LSAME( STAGE1, 'N' ) ) THEN
          INFO = -1
@@ -355,7 +364,7 @@
           ABDPOS   = KD + 1
           ABOFDPOS = KD
       ELSE
-          APOS     = INDA 
+          APOS     = INDA
           AWPOS    = INDA + KD + 1
           DPOS     = APOS
           OFDPOS   = DPOS + 1
@@ -363,11 +372,11 @@
           ABOFDPOS = 2
 
       ENDIF
-*      
-*     Case KD=0: 
-*     The matrix is diagonal. We just copy it (convert to "real" for 
-*     real because D is double and the imaginary part should be 0) 
-*     and store it in D. A sequential code here is better or 
+*
+*     Case KD=0:
+*     The matrix is diagonal. We just copy it (convert to "real" for
+*     real because D is double and the imaginary part should be 0)
+*     and store it in D. A sequential code here is better or
 *     in a parallel environment it might need two cores for D and E
 *
       IF( KD.EQ.0 ) THEN
@@ -382,17 +391,17 @@
           WORK( 1 ) = 1
           RETURN
       END IF
-*      
-*     Case KD=1: 
-*     The matrix is already Tridiagonal. We have to make diagonal 
+*
+*     Case KD=1:
+*     The matrix is already Tridiagonal. We have to make diagonal
 *     and offdiagonal elements real, and store them in D and E.
-*     For that, for real precision just copy the diag and offdiag 
-*     to D and E while for the COMPLEX case the bulge chasing is  
-*     performed to convert the hermetian tridiagonal to symmetric 
-*     tridiagonal. A simpler conversion formula might be used, but then 
+*     For that, for real precision just copy the diag and offdiag
+*     to D and E while for the COMPLEX case the bulge chasing is
+*     performed to convert the hermetian tridiagonal to symmetric
+*     tridiagonal. A simpler conversion formula might be used, but then
 *     updating the Q matrix will be required and based if Q is generated
-*     or not this might complicate the story. 
-*      
+*     or not this might complicate the story.
+*
       IF( KD.EQ.1 ) THEN
           DO 50 I = 1, N
               D( I ) = ( AB( ABDPOS, I ) )
@@ -413,7 +422,7 @@
           RETURN
       END IF
 *
-*     Main code start here. 
+*     Main code start here.
 *     Reduce the symmetric band of A to a tridiagonal matrix.
 *
       THGRSIZ   = N
@@ -422,7 +431,7 @@
       NBTILES   = CEILING( REAL(N)/REAL(KD) )
       STEPERCOL = CEILING( REAL(SHIFT)/REAL(GRSIZ) )
       THGRNB    = CEILING( REAL(N-1)/REAL(THGRSIZ) )
-*      
+*
       CALL DLACPY( "A", KD+1, N, AB, LDAB, WORK( APOS ), LDA )
       CALL DLASET( "A", KD,   N, ZERO, ZERO, WORK( AWPOS ), LDA )
 *
@@ -431,7 +440,7 @@
 *
 #if defined(_OPENMP)
 !$OMP PARALLEL PRIVATE( TID, THGRID, BLKLASTIND )
-!$OMP$         PRIVATE( THED, I, M, K, ST, ED, STT, SWEEPID ) 
+!$OMP$         PRIVATE( THED, I, M, K, ST, ED, STT, SWEEPID )
 !$OMP$         PRIVATE( MYID, TTYPE, COLPT, STIND, EDIND )
 !$OMP$         SHARED ( UPLO, WANTQ, INDV, INDTAU, HOUS, WORK)
 !$OMP$         SHARED ( N, KD, IB, NBTILES, LDA, LDV, INDA )
@@ -440,7 +449,7 @@
 #endif
 *
 *     main bulge chasing loop
-*      
+*
       DO 100 THGRID = 1, THGRNB
           STT  = (THGRID-1)*THGRSIZ+1
           THED = MIN( (STT + THGRSIZ -1), (N-1))
@@ -451,7 +460,7 @@
                   ST = STT
                   DO 130 SWEEPID = ST, ED
                       DO 140 K = 1, GRSIZ
-                          MYID  = (I-SWEEPID)*(STEPERCOL*GRSIZ) 
+                          MYID  = (I-SWEEPID)*(STEPERCOL*GRSIZ)
      $                           + (M-1)*GRSIZ + K
                           IF ( MYID.EQ.1 ) THEN
                               TTYPE = 1
@@ -477,16 +486,16 @@
                           ENDIF
 *
 *                         Call the kernel
-*                             
+*
 #if defined(_OPENMP) &&  _OPENMP >= 201307
-                          IF( TTYPE.NE.1 ) THEN      
+                          IF( TTYPE.NE.1 ) THEN
 !$OMP TASK DEPEND(in:WORK(MYID+SHIFT-1))
 !$OMP$     DEPEND(in:WORK(MYID-1))
 !$OMP$     DEPEND(out:WORK(MYID))
                               TID      = OMP_GET_THREAD_NUM()
-                              CALL DSB2ST_KERNELS( UPLO, WANTQ, TTYPE, 
+                              CALL DSB2ST_KERNELS( UPLO, WANTQ, TTYPE,
      $                             STIND, EDIND, SWEEPID, N, KD, IB,
-     $                             WORK ( INDA ), LDA, 
+     $                             WORK ( INDA ), LDA,
      $                             HOUS( INDV ), HOUS( INDTAU ), LDV,
      $                             WORK( INDW + TID*KD ) )
 !$OMP END TASK
@@ -494,20 +503,20 @@
 !$OMP TASK DEPEND(in:WORK(MYID+SHIFT-1))
 !$OMP$     DEPEND(out:WORK(MYID))
                               TID      = OMP_GET_THREAD_NUM()
-                              CALL DSB2ST_KERNELS( UPLO, WANTQ, TTYPE, 
+                              CALL DSB2ST_KERNELS( UPLO, WANTQ, TTYPE,
      $                             STIND, EDIND, SWEEPID, N, KD, IB,
-     $                             WORK ( INDA ), LDA, 
+     $                             WORK ( INDA ), LDA,
      $                             HOUS( INDV ), HOUS( INDTAU ), LDV,
      $                             WORK( INDW + TID*KD ) )
 !$OMP END TASK
                           ENDIF
 #else
-                          CALL DSB2ST_KERNELS( UPLO, WANTQ, TTYPE, 
+                          CALL DSB2ST_KERNELS( UPLO, WANTQ, TTYPE,
      $                         STIND, EDIND, SWEEPID, N, KD, IB,
-     $                         WORK ( INDA ), LDA, 
+     $                         WORK ( INDA ), LDA,
      $                         HOUS( INDV ), HOUS( INDTAU ), LDV,
      $                         WORK( INDW ) )
-#endif 
+#endif
                           IF ( BLKLASTIND.GE.(N-1) ) THEN
                               STT = STT + 1
                               EXIT
@@ -522,14 +531,14 @@
 !$OMP END MASTER
 !$OMP END PARALLEL
 #endif
-*      
+*
 *     Copy the diagonal from A to D. Note that D is REAL thus only
 *     the Real part is needed, the imaginary part should be zero.
 *
       DO 150 I = 1, N
           D( I ) = ( WORK( DPOS+(I-1)*LDA ) )
   150 CONTINUE
-*      
+*
 *     Copy the off diagonal from A to E. Note that E is REAL thus only
 *     the Real part is needed, the imaginary part should be zero.
 *
@@ -543,11 +552,10 @@
   170     CONTINUE
       ENDIF
 *
-      HOUS( 1 ) = LHMIN
       WORK( 1 ) = LWMIN
       RETURN
 *
 *     End of DSYTRD_SB2ST
 *
       END
-      
+

lapack-netlib/SRC/dsytrd_sy2sb.f

@@ -123,8 +123,8 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is DOUBLE PRECISION array, dimension (LWORK)
-*>          On exit, if INFO = 0, or if LWORK=-1, 
+*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+*>          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
@@ -158,7 +160,7 @@
 *> \author Univ. of Colorado Denver 
 *> \author NAG Ltd. 
 *
-*> \ingroup doubleSYcomputational
+*> \ingroup hetrd_he2hb
 *
 *> \par Further Details:
 *  =====================
@@ -293,8 +295,12 @@
       INFO   = 0
       UPPER  = LSAME( UPLO, 'U' )
       LQUERY = ( LWORK.EQ.-1 )
-      LWMIN  = ILAENV2STAGE( 4, 'DSYTRD_SY2SB', '', N, KD, -1, -1 )
-      
+      IF( N.LE.KD+1 ) THEN
+         LWMIN = 1
+      ELSE
+         LWMIN = ILAENV2STAGE( 4, 'DSYTRD_SY2SB', ' ', N, KD, -1, -1 )
+      END IF
+*
       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
          INFO = -1
       ELSE IF( N.LT.0 ) THEN

lapack-netlib/SRC/dsytrf.f

@@ -107,7 +107,7 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The length of WORK.  LWORK >=1.  For best performance
+*>          The length of WORK.  LWORK >= 1.  For best performance
 *>          LWORK >= N*NB, where NB is the block size returned by ILAENV.
 *>
 *>          If LWORK = -1, then a workspace query is assumed; the routine
@@ -135,7 +135,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYcomputational
+*> \ingroup hetrf
 *
 *> \par Further Details:
 *  =====================
@@ -352,6 +352,7 @@
       END IF
 *
    40 CONTINUE
+*
       WORK( 1 ) = LWKOPT
       RETURN
 *

lapack-netlib/SRC/dsytrf_aa.f

@@ -101,8 +101,10 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          The length of WORK.  LWORK >= MAX(1,2*N). For optimum performance
-*>          LWORK >= N*(1+NB), where NB is the optimal blocksize.
+*>          The length of WORK.
+*>          LWORK >= 1, if N <= 1, and LWORK >= 2*N, otherwise.
+*>          For optimum performance LWORK >= N*(1+NB), where NB is
+*>          the optimal blocksize, returned by ILAENV.
 *>
 *>          If LWORK = -1, then a workspace query is assumed; the routine
 *>          only calculates the optimal size of the WORK array, returns
@@ -125,10 +127,10 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYcomputational
+*> \ingroup hetrf_aa
 *
 *  =====================================================================
-      SUBROUTINE DSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
+      SUBROUTINE DSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
 *
 *  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
@@ -152,7 +154,7 @@
 *
 *     .. Local Scalars ..
       LOGICAL            LQUERY, UPPER
-      INTEGER            J, LWKOPT
+      INTEGER            J, LWKMIN, LWKOPT
       INTEGER            NB, MJ, NJ, K1, K2, J1, J2, J3, JB
       DOUBLE PRECISION   ALPHA
 *     ..
@@ -179,18 +181,25 @@
       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 ) = LWKOPT
       END IF
 *
@@ -203,11 +212,11 @@
 *
 *     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
 *

lapack-netlib/SRC/dsytrf_aa_2stage.f

@@ -87,14 +87,14 @@
 *>
 *> \param[out] TB
 *> \verbatim
-*>          TB is DOUBLE PRECISION array, dimension (LTB)
+*>          TB is DOUBLE PRECISION array, dimension (MAX(1,LTB))
 *>          On exit, details of the LU factorization of the band matrix.
 *> \endverbatim
 *>
 *> \param[in] LTB
 *> \verbatim
 *>          LTB is INTEGER
-*>          The size of the array TB. LTB >= 4*N, internally
+*>          The size of the array TB. LTB >= MAX(1,4*N), internally
 *>          used to select NB such that LTB >= (3*NB+1)*N.
 *>
 *>          If LTB = -1, then a workspace query is assumed; the
@@ -121,14 +121,14 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is DOUBLE PRECISION workspace of size LWORK
+*>          WORK is DOUBLE PRECISION 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,
@@ -152,7 +152,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYcomputational
+*> \ingroup hetrf_aa_2stage
 *
 *  =====================================================================
       SUBROUTINE DSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV,
@@ -211,9 +211,9 @@
          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
 *
@@ -227,10 +227,10 @@
       NB = ILAENV( 1, 'DSYTRF_AA_2STAGE', UPLO, N, -1, -1, -1 )
       IF( INFO.EQ.0 ) THEN
          IF( TQUERY ) THEN
-            TB( 1 ) = (3*NB+1)*N
+            TB( 1 ) = MAX( 1, (3*NB+1)*N )
          END IF
          IF( WQUERY ) THEN
-            WORK( 1 ) = N*NB
+            WORK( 1 ) = MAX( 1, N*NB )
          END IF
       END IF
       IF( TQUERY .OR. WQUERY ) THEN
@@ -239,7 +239,7 @@
 *
 *     Quick return
 *
-      IF ( N.EQ.0 ) THEN
+      IF( N.EQ.0 ) THEN
          RETURN
       ENDIF
 *

lapack-netlib/SRC/dsytrf_rk.f

@@ -177,14 +177,14 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is DOUBLE PRECISION array, dimension ( MAX(1,LWORK) ).
+*>          WORK is DOUBLE PRECISION 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.
 *>
@@ -229,7 +229,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYcomputational
+*> \ingroup hetrf_rk
 *
 *> \par Further Details:
 *  =====================

lapack-netlib/SRC/dsytrf_rook.f

@@ -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
@@ -146,7 +146,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYcomputational
+*> \ingroup hetrf_rook
 *
 *> \par Further Details:
 *  =====================

lapack-netlib/SRC/dsytri2.f

@@ -88,16 +88,16 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is DOUBLE PRECISION array, dimension (N+NB+1)*(NB+3)
+*>          WORK is DOUBLE PRECISION 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 doubleSYcomputational
+*> \ingroup hetri2
 *
 *  =====================================================================
       SUBROUTINE DSYTRI2( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
@@ -159,9 +159,13 @@
       INFO = 0
       UPPER = LSAME( UPLO, 'U' )
       LQUERY = ( LWORK.EQ.-1 )
+*
 *     Get blocksize
+*
       NBMAX = ILAENV( 1, 'DSYTRI2', 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 +177,29 @@
          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( 'DSYTRI2', -INFO )
          RETURN
       ELSE IF( LQUERY ) THEN
-         WORK(1)=MINSIZE
+         WORK( 1 ) = MINSIZE
          RETURN
       END IF
+*
+*     Quick return if possible
+*
       IF( N.EQ.0 )
      $   RETURN
 
-      IF( NBMAX .GE. N ) THEN
+      IF( NBMAX.GE.N ) THEN
          CALL DSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
       ELSE
          CALL DSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NBMAX, INFO )
       END IF
+*
       RETURN
 *
 *     End of DSYTRI2

lapack-netlib/SRC/dsytri_3.f

@@ -119,16 +119,17 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is DOUBLE PRECISION array, dimension (N+NB+1)*(NB+3).
+*>          WORK is DOUBLE PRECISION 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
@@ -152,7 +153,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYcomputational
+*> \ingroup hetri_3
 *
 *> \par Contributors:
 *  ==================
@@ -208,8 +209,13 @@
 *
 *     Determine the block size
 *
-      NB = MAX( 1, ILAENV( 1, 'DSYTRI_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, 'DSYTRI_3', UPLO, N, -1, -1, -1 ) )
+         LWKOPT = ( N+NB+1 ) * ( NB+3 )
+      END IF
+      WORK( 1 ) = LWKOPT
 *
       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
          INFO = -1
@@ -217,7 +223,7 @@
          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
 *
@@ -225,7 +231,6 @@
          CALL XERBLA( 'DSYTRI_3', -INFO )
          RETURN
       ELSE IF( LQUERY ) THEN
-         WORK( 1 ) = LWKOPT
          RETURN
       END IF
 *

lapack-netlib/SRC/dsytrs_aa.f

@@ -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
@@ -123,7 +129,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleSYcomputational
+*> \ingroup hetrs_aa
 *
 *  =====================================================================
       SUBROUTINE DSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
@@ -151,7 +157,7 @@
 *     ..
 *     .. Local Scalars ..
       LOGICAL            LQUERY, UPPER
-      INTEGER            K, KP, LWKOPT
+      INTEGER            K, KP, LWKMIN
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -161,13 +167,19 @@
       EXTERNAL           DLACPY, DGTSV, DSWAP, DTRSM, 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
@@ -178,21 +190,20 @@
          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( 'DSYTRS_AA', -INFO )
          RETURN
       ELSE IF( LQUERY ) THEN
-         LWKOPT = (3*N-2)
-         WORK( 1 ) = LWKOPT
+         WORK( 1 ) = 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

lapack-netlib/SRC/sgebrd.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 @@
 *     ..
 *     .. 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

lapack-netlib/SRC/sgehrd.f

@@ -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
 *

lapack-netlib/SRC/sgelq.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
@@ -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

lapack-netlib/SRC/sgelqf.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.
 *>
@@ -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

lapack-netlib/SRC/sgemlq.f

@@ -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
 *

lapack-netlib/SRC/sgemqr.f

@@ -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
 *