[task #7793] Speed-up of dispersion models -- May 19, 2014 - 10:46

Follow-up Comment #18, task #7793 (project relax):

It remains still to figure out how to speed up the numerical models:

The problem is how to make a 3 dimensional array, which is a list which
contains matrices.

Each matrix is multiplied with for example a constant tcp.

############
# Loop over the time points, back calculating the R2eff values.
for i in range(num_points):
    # This matrix is a propagator that will evolve the magnetization with the
matrix R for a delay tcp.
    eR_tcp = matrix_exponential(R*tcp[i])

    # This is the propagator for an element of [delay tcp; 180 deg pulse; 2
times delay tcp; 180 deg pulse; delay tau], i.e. for 2 times tau-180-tau.
    prop_2 = dot(dot(eR_tcp, matrix_exponential(cR2*tcp[i])), eR_tcp)

    # Now create the total propagator that will evolve the magnetization under
the CPMG train, i.e. it applies the above tau-180-tau-tau-180-tau so many
times as required for the CPMG frequency under consideration.
    prop_total = square_matrix_power(prop_2, power[i])

    # Now we apply the above propagator to the initial magnetization vector -
resulting in the magnetization that remains after the full CPMG pulse train. 
It is called M of t (t is the time after the CPMG train).
    Moft = dot(prop_total, M0)

##########

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