evaluating matrix quadratic form

[tracyx]

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

[mecej4]

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

[Royi]

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.

[Spencer_P_Intel]

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.

[Sigolaev__Yuriy]

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