Author: tlinnet
Date: Wed Jun 25 02:14:48 2014
New Revision: 24301
URL: http://svn.gna.org/viewcvs/relax?rev=24301&view=rev
Log:
Got rid of the inner evolution of the magnetization.
If the looping over the number of CPMG elements is given by the index l, and
the initial magnetization has
been formed, then the number of times for propagation of magnetization is l =
power_si_mi_di-1.
If the magnetization matrix "Mint" has the index Mint_(i,k) and the evolution
matrix has the index Evol_(k,j), i=1, k=7, j=7
then the dot product is given by: Sum_{k=1}^{k} Mint_(1,k) * Evol_(k,j) =
D_(1, j).
The numpy einsum formula for this would be: einsum('ik,kj -> ij', Mint, Evol)
Following evolution will be: Sum_{k=1}^{k} D_(1, j) * Evol_(k,j) = Mint_(1,k)
* Evol_(k,j) * Evol_(k,j).
We can then realize, that the evolution matrix can be raised to the power l.
Evol_P = Evol**l.
It will then be: einsum('ik,kj -> ij', Mint, Evol_P)
- Get which power to raise the matrix to.
l = power_si_mi_di-1
- Raise the square evolution matrix to the power l.
evolution_matrix_T_pwer_i = matrix_power(evolution_matrix_T_i, l)
Mint_T_i = dot(Mint_T_i, evolution_matrix_T_pwer_i)
or
Mint_T_i = einsum('ik,kj -> ij', Mint_T_i, evolution_matrix_T_pwer_i)
Task #7807 (https://gna.org/task/index.php?7807): Speed-up of dispersion
models for Clustered analysis.
Modified:
branches/disp_spin_speed/lib/dispersion/ns_cpmg_2site_3d.py
Modified: branches/disp_spin_speed/lib/dispersion/ns_cpmg_2site_3d.py
URL:
http://svn.gna.org/viewcvs/relax/branches/disp_spin_speed/lib/dispersion/ns_cpmg_2site_3d.py?rev=24301&r1=24300&r2=24301&view=diff
==============================================================================
--- branches/disp_spin_speed/lib/dispersion/ns_cpmg_2site_3d.py (original)
+++ branches/disp_spin_speed/lib/dispersion/ns_cpmg_2site_3d.py Wed Jun 25
02:14:48 2014
@@ -56,6 +56,7 @@
# Python module imports.
from numpy import array, dot, fabs, float64, einsum, isfinite, log, min,
multiply, rollaxis, sum, tile
+from numpy.linalg import matrix_power
from numpy.ma import fix_invalid, masked_where
# relax module imports.
@@ -331,9 +332,23 @@
# This matrix is a propagator that will evolve the
magnetization with the matrix R for a delay tcp.
evolution_matrix_T_i = evolution_matrix_T_mat[0, si, mi, 0,
di]
- # Loop over the CPMG elements, propagating the magnetisation.
- for j in range(power_si_mi_di - 1):
- Mint_T_i = dot(Mint_T_i, evolution_matrix_T_i)
+ # If the looping over the number of CPMG elements is given
by the index l, and the initial magnetization has
+ # been formed, then the number of times for propagation of
magnetization is l = power_si_mi_di-1.
+ # If the magnetization matrix "Mint" has the index
Mint_(i,k) and the evolution matrix has the index Evol_(k,j), i=1, k=7, j=7
+ # then the dot product is given by: Sum_{k=1}^{k} Mint_(1,k)
* Evol_(k,j) = D_(1, j).
+ # The numpy einsum formula for this would be: einsum('ik,kj
-> ij', Mint, Evol)
+ #
+ # Following evolution will be: Sum_{k=1}^{k} D_(1, j) *
Evol_(k,j) = Mint_(1,k) * Evol_(k,j) * Evol_(k,j).
+ # We can then realize, that the evolution matrix can be
raised to the power l. Evol^l.
+
+ # Get which power to raise the matrix to.
+ l = power_si_mi_di-1
+
+ # Raise the square evolution matrix to the power l.
+ evolution_matrix_T_pwer_i =
matrix_power(evolution_matrix_T_i, l)
+
+ #Mint_T_i = dot(Mint_T_i, evolution_matrix_T_pwer_i)
+ Mint_T_i = einsum('ik,kj -> ij', Mint_T_i,
evolution_matrix_T_pwer_i)
# The next lines calculate the R2eff using a two-point
approximation, i.e. assuming that the decay is mono-exponential.
Mx = Mint_T_i[0][1] / pA
r24301 - /branches/disp_spin_speed/lib/dispersion/ns_cpmg_2site_3d.py