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Dear MKL experts,

My project needs performing the inverse of the complex symmetric dense matrix. I do it using three different pairs of subroutines, GETRF/GETRI, SYTRF/SYTRI, and SYTRF_ROOK/SYTRI_ROOK, in order to pick best one.It is supposed that the subroutines for symmetric matrix are faster than the subroutines for full matrix from the computational math theory, as it is documented in the INTEL programmer reference manual.

GETRF(...)

for real flavors,

If m = n, The approximate number of floating-point operation is (2/3)n^{3}

The number of operations for complex flavors is four times greater, (8/3)n^{3}.

GETRI(...)

The total number of floating-point operations is approximately (4/3)n^{3}for real flavors and (16/3)n^{3}for complex flavors.

SYTRF(...)

The total number of floating-point operations is approximately (1/3)n^{3}for real flavors or (4/3)n^{3}for complex flavors.

SYTRI(...)

The total number of floating-point operations is approximately (2/3)n^{3}for real flavors and (8/3)n^{3}for complex flavors.SYTRF_ROOK(...)

[No information of floating-point operations]

SYTRI_ROOK(...)

The total number of floating-point operations is approximately (2/3)n^{3}for real flavors and (8/3)n^{3}for complex flavors.

In reality, it is GETRF/GETRI are much faster for larger size dense matrix. My test results are summarized in the below.

Matrix Size GETRF SYTRF SYTRF_ROOK

1000x1000 0.015 0.016 0.047

2000x2000 0.142 0.141 0.281

5000x5000 1.486 1.406 2.595

10000x10000 9.907 9.283 16.282

Matrix Size GETRI SYTRI SYTRI_ROOK

1000x1000 0.064 0.563 0.595

2000x2000 0.312 4.908 4.938

5000x5000 4.437 74.600 74.490

10000x10000 26.972 625.908 615.346

We can learn GETRF/GETRI is 15 to 20 faster than those subroutines for symmetric ones.

Why? Please give me some advice. My test code is attached as the following.

Thanks.

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Additional information:

OS: Windows 8.0 Home

Compiler: Intel Parallel Studio 2018.3 + MKL 2018.3 with VS 2015 community edition

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