## MB01TD

### Computation of A B in B, with A and B upper quasi-triangular matrices with the same structure

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

Purpose

      To compute the matrix product A * B, where A and B are upper
      quasi-triangular matrices (that is, block upper triangular with
      1-by-1 or 2-by-2 diagonal blocks) with the same structure.
      The result is returned in the array B.

Specification

          SUBROUTINE MB01TD( N, A, LDA, B, LDB, DWORK, INFO )
    C     .. Scalar Arguments ..
          INTEGER           INFO, LDA, LDB, N
    C     .. Array Arguments ..
          DOUBLE PRECISION  A(LDA,*), B(LDB,*), DWORK(*)

Arguments

Input/Output Parameters

      N       (input) INTEGER
              The order of the matrices A and B.  N >= 0.

      A       (input) DOUBLE PRECISION array, dimension (LDA,N)
              The leading N-by-N part of this array must contain the
              upper quasi-triangular matrix A. The elements below the
              subdiagonal are not referenced.

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

      B       (input/output) DOUBLE PRECISION array, dimension (LDB,N)
              On entry, the leading N-by-N part of this array must
              contain the upper quasi-triangular matrix B, with the same
              structure as matrix A.
              On exit, the leading N-by-N part of this array contains
              the computed product A * B, with the same structure as
              on entry.
              The elements below the subdiagonal are not referenced.

      LDB     INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

Workspace

      DWORK   DOUBLE PRECISION array, dimension (N-1)

Error Indicator

      INFO    INTEGER
              = 0:  successful exit;
              < 0:  if INFO = -i, the i-th argument had an illegal
                    value;
              = 1:  if the matrices A and B have not the same structure,
                    and/or A and B are not upper quasi-triangular.

Method

      The matrix product A * B is computed column by column, using
      BLAS 2 and BLAS 1 operations.

Further Comments

      This routine can be used, for instance, for computing powers of
      a real Schur form matrix.

Example

Program Text

    *     MB01TD EXAMPLE PROGRAM TEXT
    *
    *     .. Parameters ..
          INTEGER          NIN, NOUT
          PARAMETER        ( NIN = 5, NOUT = 6 )
          INTEGER          NMAX
          PARAMETER        ( NMAX = 20 )
          INTEGER          LDA, LDB
          PARAMETER        ( LDA = NMAX, LDB = NMAX )
          INTEGER          LDWORK
          PARAMETER        ( LDWORK = NMAX-1 )
    *     .. Local Scalars ..
          INTEGER          I, INFO, J, N
    *     .. Local Arrays ..
          DOUBLE PRECISION A(LDA,NMAX), B(LDB,NMAX), DWORK(LDWORK)
    *     .. External Subroutines ..
          EXTERNAL         MB01TD
    *     .. Executable Statements ..
    *
          WRITE ( NOUT, FMT = 99999 )
    *     Skip the heading in the data file and read in the data.
          READ ( NIN, FMT = '()' )
          READ ( NIN, FMT = * ) N
          IF ( N.LT.0 .OR. N.GT.NMAX ) THEN
             WRITE ( NOUT, FMT = 99995 ) N
          ELSE
             READ ( NIN, FMT = * ) ( ( A(I,J), J = 1,N ), I = 1,N )
             READ ( NIN, FMT = * ) ( ( B(I,J), J = 1,N ), I = 1,N )
    *        Compute the matrix product A*B.
             CALL MB01TD( N, A, LDA, B, LDB, DWORK, INFO )
    *
             IF ( INFO.NE.0 ) THEN
                WRITE ( NOUT, FMT = 99998 ) INFO
             ELSE
                WRITE ( NOUT, FMT = 99997 )
                DO 20 I = 1, N
                   WRITE ( NOUT, FMT = 99996 ) ( B(I,J), J = 1,N )
       20       CONTINUE
             END IF
          END IF
          STOP
    *
    99999 FORMAT (' MB01TD EXAMPLE PROGRAM RESULTS',/1X)
    99998 FORMAT (' INFO on exit from MB01TD = ',I2)
    99997 FORMAT (' The matrix product A*B is ')
    99996 FORMAT (20(1X,F8.4))
    99995 FORMAT (/' N is out of range.',/' N = ',I5)
          END

Program Data

     MB01TD EXAMPLE PROGRAM DATA
       5
       1.    2.    6.    3.    5.
      -2.   -1.   -1.    0.   -2.
       0.    0.    1.    5.    1.
       0.    0.    0.    0.   -4.
       0.    0.    0.   20.    4.
       5.    5.    1.    5.    1.
      -2.    1.    3.    0.   -4.
       0.    0.    4.   20.    4.
       0.    0.    0.    3.    5.
       0.    0.    0.    1.   -2.

Program Results

     MB01TD EXAMPLE PROGRAM RESULTS

     The matrix product A*B is
       1.0000   7.0000  31.0000 139.0000  22.0000
      -8.0000 -11.0000  -9.0000 -32.0000   2.0000
       0.0000   0.0000   4.0000  36.0000  27.0000
       0.0000   0.0000   0.0000  -4.0000   8.0000
       0.0000   0.0000   0.0000  64.0000  92.0000

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