Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: Guide and Reference

Performance and Accuracy Considerations

This section describes some key points about performance and accuracy in the matrix operations subroutines.

In General

1. The matrix operation subroutines use algorithms that are tuned specifically to the workstation processors they run on. The techniques involve using any one of several computational methods, based on certain operation counts and sizes of data.
2. The short-precision multiplication subroutines provide increased accuracy by partially accumulating results in long precision.
3. Strassen's method is not stable for certain row or column scalings of the input matrices A and B. Therefore, for matrices A and B with divergent exponent values, Strassen's method may give inaccurate results. For these cases, you should use the _GEMUL or _GEMM subroutines.
4. There are ESSL-specific rules that apply to the results of computations on the workstation processors using the ANSI/IEEE standards. For details, see What Data Type Standards Are Used by ESSL, and What Exceptions Should You Know About?.

For Large Matrices

If you are using large square matrices in your matrix multiplication operations, you get better performance by using SGEMMS, DGEMMS, CGEMMS, and ZGEMMS. These subroutines use Winograd's variation of Strassen's algorithm for both real and complex matrices.

For Combined Operations

If you want to perform a combined matrix multiplication and addition with scaling, SGEMM, DGEMM, CGEMM, and ZGEMM provide better performance than if you perform the parts of the computation separately in your program. See references [32] and [35].