HP MLIB User's Guide Vol. 1 7th Ed.

Chapter 3 Basic Matrix Operations 231
Strassen matrix-matrix multiply DGEMMS/ZGEMMS
Actual character arguments in a subroutine call can be longer than the
corresponding dummy arguments. Therefore, readability of the CALL
statement can be improved, for example, by coding the transa and transb
arguments as ’NORMAL’ or ’NONTRANS’ for ’N’, ’TRANSPOSE’ for ’T’, or
’CTRANS’ for ’C’. Refer to “Example 2.”
Example 1 Form the REAL*8 matrix product C = AB, where A is a 900-by-600 real matrix
stored in an array A whose dimensions are 1000 by 1000, B is a 600-by-800 real
matrix stored in an array B of dimension 1000 by 1000, and C is a 900-by-800
real matrix stored in an array C, also of dimension 1000 by 1000.
CHARACTER*1 TRANSA,TRANSB
INTEGER*4 M,N,K,LDA,LDB,LDC
REAL*8 ALPHA,BETA,A(1000,1000),B(1000,1000),
& C(1000,1000)
TRANSA = ’N’
TRANSB = ’N’
M = 900
N = 800
K = 600
ALPHA = 1.0
BETA = 0.0
LDA = 1000
LDB = 1000
LDC = 1000
CALL DGEMMS (TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,
& BETA,C,LDC)
Example 2 Form the COMPLEX*16 matrix product , where ρ is a complex
scalar, A is a 600-by-900 complex matrix stored in an array A whose dimensions
are 1000 by 1000, B is a 600-by-800 complex matrix stored in an array B of
dimension 1000 by 1000, and C is a 900-by-800 complex matrix stored in an
array C, also of dimension 1000 by 1000.
INTEGER*4 M,N,K,LDA,LDB,LDC
COMPLEX*16 RHO,A(1000,1000),B(1000,1000),C(1000,1000)
M = 900
N = 800
K = 600
LDA = 1000
LDB = 1000
LDC = 1000
CALL ZGEMMS (’CONJ’,’NORMAL’,M,N,K,RHO,A,LDA,B,LDB,
& (0.5D0,0.0D0),C,LDC)
C
1
2
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C ρA*B+=