## 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.

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

```
Example

Program Text

```*     MB01TD EXAMPLE PROGRAM TEXT
*     Copyright (c) 2002-2017 NICONET e.V.
*
*     .. 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
```