Strassen matrix-matrix multiply | DGEMMS/ZGEMMS |
Name DGEMMS/ZGEMMS
Strassen matrix-matrix multiply
Purpose These subprograms use Strassen’s method to compute the matrix-matrix product AB, where A is an m-by-kmatrix and B is a k-by-nmatrix. Strassen’s method is an algorithm for matrix multiplication that, under certain circumstances, uses fewer than mnk multiplications and additions. These subprograms have argument lists identical to the standard Level 3 BLAS subprograms DGEMM and ZGEMM in VECLIB and CGEMM and SGEMM in VECLIB8. So to convert a program to call a Strassen subprogram instead of a standard matrix multiply, it is only necessary to change the subprogram name. With consistent upper or lower case coding, a simple preprocessor directive can select standard or Strassen matrix multiply calls. Work area management is done by the subprograms.
By using Strassen’s method, these subprograms can be considerably faster than their VECLIB and VECLIB8 counterparts. Refer to “Notes” for details. In
addition to computing the matrix-matrix product AB, A can be replaced by AT or A*, where A is a k-by-mmatrix, and B can be replaced by BT or B*, where B
is an n-by-kmatrix. Here, AT and BT are the transposes and A* and B* are the conjugate-transposes of A and B, respectively. The product can be stored in the result matrix (which is always of size m-by-n) or optionally can be added to or subtracted from it. This is handled in a convenient, but general, way by two scalar arguments, α and β, which are used as multipliers of the matrix product and the result matrix. Specifically, these subprograms compute matrix products of the forms:
C ← αAB + βC, | C | ← α | T | B | + β , | C | ← α | A | ∗ | B | + β , |
| | A | C | | | C |
C ← αABT + βC, | C ← αATBT + βC, | C ← αA∗BT + βC, |
C ← αAB∗ + βC, | C ← αATB∗ + βC, | C ← αA∗B∗ + βC. |
Refer to “F_SGEMM/F_DGEMM/F_CGEMM/F_ZGEMM” on page 362 for a description of the equivalent BLAS Standard subprograms.
Usage | VECLIB: | |
| CHARACTER*1 | transa, transb |
| INTEGER*4 | m, n, k, lda, ldb, ldc |
| REAL*8 | alpha, beta, a(lda, *), b(ldb, *), c(ldc, n) |
CALL DGEMMS(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CHARACTER*1 | transa, transb |
INTEGER*4 | m, n, k, lda, ldb, ldc |
COMPLEX*16 | alpha, beta, a(lda, *), b(ldb, *), c(ldc, n) |
CALL ZGEMMS(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
