Add specialized methods for complex-real BLAS multiplication. #6235
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This implements the method proposed by @stevengj for multiplying a complex matrix with a real matrix or vector. On my computer this gives around a 12x speed up for two 1000x1000 matrices over calling the generic algorithm which is what happens now and it is a double speed up over converting the real array to complex.
The only methods where (I can see that) this is feasible are
A_mul_B(Matrix{Complex},MatOrVec{Real})
,A_mul_Bt(Matrix{Complex},Matrix})
and by transposing the result alsoA_mul_Bt(Matrix{Real},Matrix{Complex})
andAt_mul_Bt(Matrix{Real},Matrix{Complex})
.A_mul_B(Matrix{Real},Vector{Complex})
could be written in terms of twodgemv
call withstride=2
, but in my benchmarks this is not faster than the generic algorithm.Finally, I tried to write methods for
dot
but it was not faster than the Julia version. Not surprisingly, it appears that it is mainly for level 3 operations that BLAS gives big speed gains.