Include Files

Description

The

mkl_graph_mxm

routine computes a (masked) graph matrix-matrix product defined as

where

A

,

B

and

C

are input and output matrices respectively,

accum

is an optional binary operator to be used as an accumulator for the output matrix, and

M

is an optional mask for the output matrix. Possible modifications of the operations, including matrix modifiers

opA

and

opB

are defined through the operation descriptor

desc

.

The routine supports both single-stage and multistage execution modes via the

request

parameter. See Graph Operations for a description of the two modes. You can specify a specific method to be used for computations via the

method

parameter. Use

MKL_GRAPH_METHOD_AUTO

for an automatic choice.

The operation can be done in-place meaning that the output matrix can be aliased with any of the input matrices or the mask. However, in this case the original data will be replaced.

In the masked case, by default, the pattern of the output matrix (entries present) will be the intersection of the pattern of the mask and the pattern of the non-masked product of matrices

A

and

B

. If

MKL_GRAPH_MODIFIER_OUTPUT

is set to

MKL_GRAPH_KEEP_MASK_STRUCTURE

in the descriptor

desc

, the pattern of the output matrix will be exactly the pattern of the mask. The edges missing in the non-masked product are given value zero in the output data type.

For user control of output storage allocation, use multistage execution.

For maximum performance, the following configurations are recommended. For masked multiplication with a sparse mask, multiply CSR times CSC using

MKL_GRAPH_METHOD_DOT

or

MKL_GRAPH_METHOD_ATUO

. Use CSR format for the mask and for the output of multistage execution. For non-masked multiplication, or when the mask is dense, multiply matching formats (CSR times CSR or CSC times CSC). Use the same format for the mask and for multistage output, and use

MKL_GRAPH_METHOD_GUSTAVSON

or

MKL_GRAPH_METHOD_ATUO

. A “dense” mask means the mask has all possible entries present. It must still be stored in CSR or CSC format using

mkl_graph_matrix_set_csr

or

mkl_graph_matrix_set_csc

. For the purpose of these recommendations a transpose flag in the descriptor effectively switches the format, so a CSR input with a transpose flag set is equivalent to CSC when selecting a recommended configuration.