MB01QD - SLICOT Library Routine Documentation

## MB01QD

### Matrix scaling (lower level routine)

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

      To multiply 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, (block) upper triangular, (block) lower triangular,
      (block) upper Hessenberg, or banded.

Specification

          SUBROUTINE MB01QD( TYPE, M, N, KL, KU, CFROM, CTO, NBL, NROWS, A,
         $                   LDA, INFO )
    C     .. Scalar Arguments ..
          CHARACTER          TYPE
          INTEGER            INFO, KL, KU, LDA, M, N, NBL
          DOUBLE PRECISION   CFROM, CTO
    C     .. Array Arguments ..
          INTEGER            NROWS ( * )
          DOUBLE PRECISION   A( LDA, * )

Arguments

Mode Parameters

      TYPE    CHARACTER*1
              TYPE indices the storage type of the input matrix.
              = 'G':  A is a full matrix.
              = 'L':  A is a (block) lower triangular matrix.
              = 'U':  A is a (block) upper triangular matrix.
              = 'H':  A is a (block) 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.

Input/Output Parameters

      M       (input) INTEGER
              The number of rows of the matrix A.  M >= 0.

      N       (input) INTEGER
              The number of columns of the matrix A.  N >= 0.

      KL      (input) INTEGER
              The lower bandwidth of A.  Referenced only if TYPE = 'B',
              'Q' or 'Z'.

      KU      (input) INTEGER
              The upper bandwidth of A.  Referenced only if TYPE = 'B',
              'Q' or 'Z'.

      CFROM   (input) DOUBLE PRECISION
      CTO     (input) 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.

      NBL     (input) INTEGER
              The number of diagonal blocks of the matrix A, if it has a
              block structure.  To specify that matrix A has no block
              structure, set NBL = 0.  NBL >= 0.

      NROWS   (input) INTEGER array, dimension max(1,NBL)
              NROWS(i) contains the number of rows and columns of the
              i-th diagonal block of matrix A.  The sum of the values
              NROWS(i),  for  i = 1: NBL,  should be equal to min(M,N).
              The array  NROWS  is not referenced if NBL = 0.

      A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
              The matrix to be multiplied by CTO/CFROM.  See TYPE for
              the storage type.

      LDA     (input) INTEGER
              The leading dimension of the array A.  LDA >= max(1,M).

Error Indicator

      INFO    INTEGER
              Not used in this implementation.

Method

      Matrix A is multiplied by the real scalar CTO/CFROM, taking into
      account the specified storage mode of the matrix.
      MB01QD is a version of the LAPACK routine DLASCL, modified for
      dealing with block triangular, or block Hessenberg matrices.
      For efficiency, no tests of the input scalar parameters are
      performed.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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