topic Blas Level 2 is a tricky in Intel® oneAPI Math Kernel Library

evaluating matrix quadratic form

tracyx — Thu, 16 Feb 2012 01:09:27 GMT

What is the best way to evaluate the quadratic form X'*A*X where X is an mx1 matrix and A is a m x m symmetric matrix? Is there a routine to do this in MKL as this is a common problem?
Thanks, Tracy

evaluating matrix quadratic form

mecej4 — Thu, 16 Feb 2012 04:45:19 GMT

For dense A, a call to ?gemv to compute A X, followed by a call to ?dot.

The result of:

Royi — Fri, 26 Apr 2019 16:46:10 GMT

The result of:

X' * A * X

For symmetric A has such a nice structure (Result is symmetric) that it is a pity MKL doesn't have an optimized function for it.
Quadratic Forms are very common in Machine Learning, Optimization, etc... It would benefit many users.

In case of dense, there is no

Spencer_P_Intel — Fri, 26 Apr 2019 20:44:20 GMT

In case of dense, there is no single call solution as mecej4 mentioned.

However, if X and A are sparse matrices, then we added exactly this type of product to our Inspector-Executor Sparse BLAS routines. The structure is indeed quite nice. This type of product shows up a lot in multi-scale finite element methods as well where X could be a projection or elongation matrix. We call it the symmetric product with api -- mkl_sparse_sypr().

See reference documentation mkl_sparse_sypr for more details on how to use it.

Blas Level 2 is a tricky

Sigolaev__Yuriy — Sun, 28 Apr 2019 23:27:36 GMT

Blas Level 2 is a tricky thing. For example, my dsptrd faster dsptrd Intel MKL twice.

See https://software.intel.com/en-us/forums/intel-math-kernel-library/topic/288316