Hi,
I have a large symmetric sparse matrix (10000*10000) and I want to reduce the matrix to condense form of last N elements. In order to do that I need to calculate the schur complement form of the matrix:
K=[A B; C D]; S = A - B * inv(D) * C
K is symmetric sparse (10000*10000) ; S is condense form which is usually dense (N*N) N: between 1 to 1000.
My first approach was: 1. Calculate X = inv(D) * C with Pardiso sparse solver. 2. Calculate A - B * X with dgemm function of Math Kernel Library.
But I found the performance is very depend on N variable (size of condensed matrix) which in part1 is number of RHS and inpart 2 is the number of columns for X matrix.
If N = 9: Part1 time:0.06 seconds + Part2 time: 0.03 seconds = Total time around 0.09 seconds.
But if N=400: Part1 time:2 seconds + Part2 time: 3 seconds = Total time around 5 seconds.which is too much for my program!!!
Note: for both cases size of K is constant 10000*10000.
So it seems that Pardiso is not doing very well with so many RHS and dgemm matrix is not doing great with X having large number of columns.
I am using latest version of MKL. My program is in FORTRAN on Windows. Is there any way to speed up the process?
I found out that there are some libraries like MUMPS that have functions for partial factorization and calculating condense form of the sparse matrix. Is this feature available in Pardiso or Math Kernel library as well? If yes, would you please tell me the function name.
Thank you in advance for your help.