This is a type of 9 x 9 Sylvester matrix
1 2 3 4 0 0 0 0 0
0 1 2 3 4 0 0 0 0
0 0 1 2 3 4 0 0 0
0 0 0 1 2 3 4 0 0
0 0 0 0 1 2 3 4 0
0 0 0 0 0 1 2 3 4
5 6 7 8 9 10 11 0 0
0 5 6 7 8 9 10 11 0
0 0 5 6 7 8 9 10 11
while the code I used to generate it is :
- Code: Select all
SUBROUTINE MATINIT( AA, DESCA )
*
* MATINIT generates and distributes matrices A and B (depicted in
* figures 2.5 and 2.6) to a 2 x 3 process grid
*
* .. Array Arguments ..
INTEGER DESCA( * )
DOUBLE PRECISION AA( * ) , C (1,4), D(1,7)
* .. Parameters ..
INTEGER CTXT_, LLD_ ,I ,J, M
PARAMETER ( CTXT_ = 2, LLD_ = 9 )
* ..
* .. Local Scalars ..
INTEGER ICTXT, MXLLDA, MYCOL, MYROW, NPCOL, NPROW
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, PDELSET
* ..
* .. Executable Statements ..
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
C(1,1)=1.0D0
C(1,2)=2.0D0
C(1,3)=3.0D0
C(1,4)=4.0D0
D(1,1)=5.0D0
D(1,2)=6.0D0
D(1,3)=7.0D0
D(1,4)=8.0D0
D(1,5)=9.0D0
D(1,6)=10.0D0
D(1,7)=11.0D0
DO 30 I=1, 9
IF (I.LT.7) THEN
DO 50 J=0, 3
CALL PDELSET(AA ,I,I+J,DESCA,C(1,J+1))
50 CONTINUE
ELSE IF (I.GE.7) THEN
DO 60 M=0, 6
CALL PDELSET(AA,I,I-M,DESCA,D(1,7-M))
60 CONTINUE
END IF
30 CONTINUE
*
RETURN
END
I am asking actyually if there is any better way to generate a Sylvester matrix.. I want actually to generate a 30x30 or bigger Sylvester matrix which has a lot of zeros in it , a non dense matrix. My main problem is that i want to test the QR factorization on it and so I want try to make the algorithm cheaper avoiding the operations between the zero elements !
Thanks !!
