Is there a function/subroutine in MKL to specify that the product (matrix multiplication) of two different matrices would be symmetric so that matrix multiplication happens faster. I am aware of DSYR2K but that routine only helps when we are multiplying A*A' which would result in a symmetric matrix.

E.G. I want to multiply H*Q*H' where Q is positive definite and H is any arbitrary rectangular matrix. These types of matrix multiplications arise quite a lot in statistics and inverse problems. I know before hand that output of HQH' would be a symmetric matrix. Hence, when I multiply HQ= H*Q; B=HQ *H'; I want to tell MKL that B is a symmetric matrix to reduce the cost of matrix multiplication.