Introducing analytical test
Introducing new test in which matrix and its eigendecomposition is known and thus can be easily created and checked directly, without the need to use scalapack or any other communication (apart from reducing error). The test is based on the fact, that if L_A and S_A are eigenvalues and eigenvectors of matrix A, respectively, and L_B and S_B eigenvalues and eigenvectors of B, then kron(L_A, L_B) and kron (S_A, S_B) are eigenvalues and eigenvectors of kron(A, B). Since it is easy to know exact eigendecomposition of a small matrix (e.g. 2x2), and kron operator has very simple structure, we can construct arbitrarily large matrix and its eigendecomposition. We only have to select small matrices such that the resulting matrix has unique and ordered eigenvalues, so that the checking of the result is than easy. Each element of matrix, eigenvector matrix and eigenvalue vector can be quickly computed independently, just using its global coordinates. The test is currently limited to matrices of size 2^n, but by storing eigendecompositions of more small matrices (e.g. 3x3 and 5x5) we could construct any matrix of size 2^n*3^m*5^o, which would probably be sufficient, since most often used sizes (150, 1000, 5000, 2000, 60000) are of this form.
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