GitLab

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.

The routines "eigenvalues" and "solve_tridiagonal" are now
also tested directly with the new API (and not only via the
legacy API -> new API mapping)

Todo: adapt test generator script to contain some logic

PGI has problems with elpa_int_value_to_string() where we return a
variable-length string pointer. A workaround for now is to copy the string into
a non-pointer variable of the same length.

This closes issue #55

This prevented compilation with Intel 2018 Beta and solves issue #54. It
turns out you can only override type-bound procedures that are
accessible in the module where you override them, thus they have to be
private. A "deferred, private" type bound procedure could only be
overriden from the same module (or a submodule thereof).

Many thanks to Igor Vorobtsov from Intel for clarifying this.