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
* 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