dlascl.f

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*> \brief \b DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          TYPE
*       INTEGER            INFO, KL, KU, LDA, M, N
*       DOUBLE PRECISION   CFROM, CTO
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLASCL multiplies the M by N real matrix A by the real scalar
*> CTO/CFROM.  This is done without over/underflow as long as the final
*> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
*> A may be full, upper triangular, lower triangular, upper Hessenberg,
*> or banded.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] TYPE
*> \verbatim
*>          TYPE is CHARACTER*1
*>          TYPE indices the storage type of the input matrix.
*>          = 'G':  A is a full matrix.
*>          = 'L':  A is a lower triangular matrix.
*>          = 'U':  A is an upper triangular matrix.
*>          = 'H':  A is an upper Hessenberg matrix.
*>          = 'B':  A is a symmetric band matrix with lower bandwidth KL
*>                  and upper bandwidth KU and with the only the lower
*>                  half stored.
*>          = 'Q':  A is a symmetric band matrix with lower bandwidth KL
*>                  and upper bandwidth KU and with the only the upper
*>                  half stored.
*>          = 'Z':  A is a band matrix with lower bandwidth KL and upper
*>                  bandwidth KU. See DGBTRF for storage details.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*>          KL is INTEGER
*>          The lower bandwidth of A.  Referenced only if TYPE = 'B',
*>          'Q' or 'Z'.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*>          KU is INTEGER
*>          The upper bandwidth of A.  Referenced only if TYPE = 'B',
*>          'Q' or 'Z'.
*> \endverbatim
*>
*> \param[in] CFROM
*> \verbatim
*>          CFROM is DOUBLE PRECISION
*> \endverbatim
*>
*> \param[in] CTO
*> \verbatim
*>          CTO is DOUBLE PRECISION
*>
*>          The matrix A is multiplied by CTO/CFROM. A(I,J) is computed
*>          without over/underflow if the final result CTO*A(I,J)/CFROM
*>          can be represented without over/underflow.  CFROM must be
*>          nonzero.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix A.  M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          The matrix to be multiplied by CTO/CFROM.  See TYPE for the
*>          storage type.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.
*>          If TYPE = 'G', 'L', 'U', 'H', LDA >= max(1,M);
*>             TYPE = 'B', LDA >= KL+1;
*>             TYPE = 'Q', LDA >= KU+1;
*>             TYPE = 'Z', LDA >= 2*KL+KU+1.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          0  - successful exit
*>          <0 - if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup OTHERauxiliary
*
*  =====================================================================
      SUBROUTINE dlascl( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
*
*  -- LAPACK auxiliary 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          TYPE
      INTEGER            INFO, KL, KU, LDA, M, N
      DOUBLE PRECISION   CFROM, CTO
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d0, one = 1.0d0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            DONE
      INTEGER            I, ITYPE, J, K1, K2, K3, K4
      DOUBLE PRECISION   BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME, DISNAN
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           lsame, dlamch, disnan
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max, min
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
*
      IF( lsame( TYPE, 'G' ) ) then
         itype = 0
      ELSE IF( lsame( TYPE, 'L' ) ) then
         itype = 1
      ELSE IF( lsame( TYPE, 'U' ) ) then
         itype = 2
      ELSE IF( lsame( TYPE, 'h' ) ) THEN
         ITYPE = 3
      ELSE IF( LSAME( TYPE, 'b' ) ) THEN
         ITYPE = 4
      ELSE IF( LSAME( TYPE, 'q' ) ) THEN
         ITYPE = 5
      ELSE IF( LSAME( TYPE, 'z' ) ) THEN
         ITYPE = 6
      ELSE
         ITYPE = -1
      END IF
*
.EQ.      IF( ITYPE-1 ) THEN
         INFO = -1
.EQ..OR.      ELSE IF( CFROMZERO  DISNAN(CFROM) ) THEN
         INFO = -4
      ELSE IF( DISNAN(CTO) ) THEN
         INFO = -5
.LT.      ELSE IF( M0 ) THEN
         INFO = -6
.LT..OR..EQ..AND..NE..OR.      ELSE IF( N0  ( ITYPE4  NM ) 
.EQ..AND..NE.     $         ( ITYPE5  NM ) ) THEN
         INFO = -7
.LE..AND..LT.      ELSE IF( ITYPE3  LDAMAX( 1, M ) ) THEN
         INFO = -9
.GE.      ELSE IF( ITYPE4 ) THEN
.LT..OR..GT.         IF( KL0  KLMAX( M-1, 0 ) ) THEN
            INFO = -2
.LT..OR..GT..OR.         ELSE IF( KU0  KUMAX( N-1, 0 ) 
.EQ..OR..EQ..AND..NE.     $            ( ( ITYPE4  ITYPE5 )  KLKU ) )
     $             THEN
            INFO = -3
.EQ..AND..LT..OR.         ELSE IF( ( ITYPE4  LDAKL+1 ) 
.EQ..AND..LT..OR.     $            ( ITYPE5  LDAKU+1 ) 
.EQ..AND..LT.     $            ( ITYPE6  LDA2*KL+KU+1 ) ) THEN
            INFO = -9
         END IF
      END IF
*
.NE.      IF( INFO0 ) THEN
         CALL XERBLA( 'dlascl', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
.EQ..OR..EQ.      IF( N0  M0 )
     $   RETURN
*
*     Get machine parameters
*
      SMLNUM = DLAMCH( 's' )
      BIGNUM = ONE / SMLNUM
*
      CFROMC = CFROM
      CTOC = CTO
*
   10 CONTINUE
      CFROM1 = CFROMC*SMLNUM
.EQ.      IF( CFROM1CFROMC ) THEN
!        CFROMC is an inf.  Multiply by a correctly signed zero for
!        finite CTOC, or a NaN if CTOC is infinite.
         MUL = CTOC / CFROMC
         DONE = .TRUE.
         CTO1 = CTOC
      ELSE
         CTO1 = CTOC / BIGNUM
.EQ.         IF( CTO1CTOC ) THEN
!           CTOC is either 0 or an inf.  In both cases, CTOC itself
!           serves as the correct multiplication factor.
            MUL = CTOC
            DONE = .TRUE.
            CFROMC = ONE
.GT..AND..NE.         ELSE IF( ABS( CFROM1 )ABS( CTOC )  CTOCZERO ) THEN
            MUL = SMLNUM
            DONE = .FALSE.
            CFROMC = CFROM1
.GT.         ELSE IF( ABS( CTO1 )ABS( CFROMC ) ) THEN
            MUL = BIGNUM
            DONE = .FALSE.
            CTOC = CTO1
         ELSE
            MUL = CTOC / CFROMC
            DONE = .TRUE.
         END IF
      END IF
*
.EQ.      IF( ITYPE0 ) THEN
*
*        Full matrix
*
         DO 30 J = 1, N
            DO 20 I = 1, M
               A( I, J ) = A( I, J )*MUL
   20       CONTINUE
   30    CONTINUE
*
.EQ.      ELSE IF( ITYPE1 ) THEN
*
*        Lower triangular matrix
*
         DO 50 J = 1, N
            DO 40 I = J, M
               A( I, J ) = A( I, J )*MUL
   40       CONTINUE
   50    CONTINUE
*
.EQ.      ELSE IF( ITYPE2 ) THEN
*
*        Upper triangular matrix
*
         DO 70 J = 1, N
            DO 60 I = 1, MIN( J, M )
               A( I, J ) = A( I, J )*MUL
   60       CONTINUE
   70    CONTINUE
*
.EQ.      ELSE IF( ITYPE3 ) THEN
*
*        Upper Hessenberg matrix
*
         DO 90 J = 1, N
            DO 80 I = 1, MIN( J+1, M )
               A( I, J ) = A( I, J )*MUL
   80       CONTINUE
   90    CONTINUE
*
.EQ.      ELSE IF( ITYPE4 ) THEN
*
*        Lower half of a symmetric band matrix
*
         K3 = KL + 1
         K4 = N + 1
         DO 110 J = 1, N
            DO 100 I = 1, MIN( K3, K4-J )
               A( I, J ) = A( I, J )*MUL
  100       CONTINUE
  110    CONTINUE
*
.EQ.      ELSE IF( ITYPE5 ) THEN
*
*        Upper half of a symmetric band matrix
*
         K1 = KU + 2
         K3 = KU + 1
         DO 130 J = 1, N
            DO 120 I = MAX( K1-J, 1 ), K3
               A( I, J ) = A( I, J )*MUL
  120       CONTINUE
  130    CONTINUE
*
.EQ.      ELSE IF( ITYPE6 ) THEN
*
*        Band matrix
*
         K1 = KL + KU + 2
         K2 = KL + 1
         K3 = 2*KL + KU + 1
         K4 = KL + KU + 1 + M
         DO 150 J = 1, N
            DO 140 I = MAX( K1-J, K2 ), MIN( K3, K4-J )
               A( I, J ) = A( I, J )*MUL
  140       CONTINUE
  150    CONTINUE
*
      END IF
*
.NOT.      IF( DONE )
     $   GO TO 10
*
      RETURN
*
*     End of DLASCL
*
      END