topic Fastest method to sum matrix in Intel® oneAPI Math Kernel Library

Fastest method to sum matrix

Tan__Elad — Tue, 25 Oct 2011 17:38:19 GMT

Hello,

I want to take the sum of a product of two symmetric matrices, meaning that if A and B are symmetric matrices than I want to compute
c=sum(A*B)
where c is a scalar and the multiplication is done element wise. Is there some way to do this by using an MKL routine or is the fastest method using the default compiler commands?

Elad

Fastest method to sum matrix

mecej4 — Tue, 25 Oct 2011 18:01:59 GMT

It seems to me that you really do not want a matrix product, but the scalar product of two vectors (i.e., 1-D arrays) that happen to be mis-arranged as square matrices. Look up the reshape function in your Fortran manual, so that you can cast the operation that is desired by you into an equivalent scalar product evaluation.

Fastest method to sum matrix

Tan__Elad — Tue, 25 Oct 2011 18:07:41 GMT

That seems like a good idea, do you think it will be worth my time to work with 1D arrays (which will make the code very unreadable) or just do a reshape every time (this product will occur a lot of times using matrices which are typically (1024,1024) big, so basically I'm asking if the reshape command is very time consuming)

Elad

Fastest method to sum matrix

Tan__Elad — Tue, 25 Oct 2011 19:18:12 GMT

Is there some routine other than reshape that converts a symmetrical matrix into a packed scheme?

Fastest method to sum matrix

mecej4 — Tue, 25 Oct 2011 23:01:29 GMT

Fortran has always allowed argument association between multidimensional arrays and one-dimensional arrays, as in the example below. Note that this will not work if you use subroutine arguments of assumed shape.

[fortran]program treshape
integer A(3,3)
data  A/11,12,13,21,22,23,31,32,33/
call sub(A,3*3)
end program treshape

subroutine sub(A,n)
integer A(n)
write(*,10)(i,A(i),i=1,n)
10 format(I4,2x,I4)
return
end subroutine sub
[/fortran]

Converting a dense matrix to packed or banded matrices is straightforward. Read the section on matrix storage schemes in the MKL manual.