Hi,
The matrix_exponential() and square_matrix_power() functions are the
problem. If an equivalent for an array of matrices could be designed,
it could be added as a new function to
lib.linear_algebra.matrix_exponential and
lib.linear_algebra.matrix_power. This is a difficult problem.
Regards,
Edward
On 19 May 2014 10:46, Troels E. Linnet <NO-REPLY.INVALID-ADDRESS@xxxxxxx>
wrote:
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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Re: [task #7793] Speed-up of dispersion models