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Mathematica

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    $\begingroup$ Yes, I'm interested in matrix of size range from 200 to 2000. We are working on high harmonic generation from atoms, which requires large-scale simulations sometimes. $\endgroup$ Commented May 15, 2016 at 1:35
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    $\begingroup$ Are you aware of subroutines in BLAS or MKL that can perform matrix number multiplication? I only found xSCAL that does the vector number multiplication, but there are no counterparts for matrix. $\endgroup$ Commented May 15, 2016 at 1:56
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    $\begingroup$ @xslittlegrass BLAS is based on FORTRAN. Matrices in FORTRAN can be seen as vectors. (Unfolding is column-wise). So axpy is the one to apply. $\endgroup$ Commented May 15, 2016 at 8:40
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    $\begingroup$ @TheDoctor Here is one of the classical reference. $\endgroup$ Commented May 30, 2016 at 15:52
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    $\begingroup$ @xslittlegrass: this reference mentions that the time-dependent Schrodinger equation is integrated directly on a numerical grid. I would have thought that one could use Chebyshev-polynomial expansion and the fast-Fourier-transform algorithm, modified for atoms exposed to an intense laser field. See, e.g., Electronic wave propagation with Mathematica (DOI: dx.doi.org/10.1016/S0010-4655(00)00196-X) $\endgroup$ Commented Jun 10, 2016 at 7:56