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Thanks, Tracy

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**?gemv**to compute A X, followed by a call to

**?dot**.

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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.

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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.

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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

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