relax SVN archive

Added the ns matrice, rr1rho_3d_rankN, to collect the multi dimensional 3D exchange matrix, of rank [NE][NS][NM][NO][ND][6][6].

Task #7807 (https://gna.org/task/index.php?7807): Speed-up of dispersion models for Clustered analysis.

Changed back from einsum to dot method, since dot method it faster for square matrixes.

Task #7807 (https://gna.org/task/index.php?7807): Speed-up of dispersion models for Clustered analysis.

Replaced the inner dot product with numpy einsum.

This though slows it down from 8.5 s to 13 s.
This is only as an intermediate step, how to figure to dot product inner parts of the big matrix.

Task #7807 (https://gna.org/task/index.php?7807): Speed-up of dispersion models for Clustered analysis.

Removed unused variables in NS CPMG 2site 3D, to clean up the code.

Task #7807 (https://gna.org/task/index.php?7807): Speed-up of dispersion models for Clustered analysis.

Implemeted systemtest: test_cpmg_synthetic_b14_to_ns3d_cluster

This is to cathc failures of the model, when data is clusted.

Task #7807 (https://gna.org/task/index.php?7807): Speed-up of dispersion models for Clustered analysis.

Moved the calculation the evolution matrix out of for loops.

The trick is that numpy.einsum allows for dot product of higher dimension:

- The the essential evolution matrix.
- This is a dot product of the outer [7][7] matrix of the Rexpo_mat and r180x_mat matrixes, which
- have the shape [NE][NS][NM][NO][ND][7][7].
- This can be achieved by using numpy einsum, and where ellipsis notation will use the last axis.
evolution_matrix_mat = einsum('...ij,...jk', Rexpo_mat, r180x_mat)
evolution_matrix_mat = einsum('...ij,...jk', evolution_matrix_mat, Rexpo_mat)
evolution_matrix_mat = einsum('...ij,...jk', evolution_matrix_mat, evolution_matrix_mat)

Task #7807 (https://gna.org/task/index.php?7807): Speed-up of dispersion models for Clustered analysis.

Made notation consistent for variables, using "_i" to clarify extracted data from matrix.

Task #7807 (https://gna.org/task/index.php?7807): Speed-up of dispersion models for Clustered analysis.

Implemented double speed of model NS CPMG 2site 3D:

This is done by moving the costly calculation of the matrix exponential out of the for loops.
The trick was to find a method to do dot product of higher dimensions.
Thiw was done with numpy.einsum:
Example at:
http://wiki.nmr-relax.com/Numpy_linalg#Ellipsis_broadcasting_in_numpy.einsum

Example:
dot_V_W = einsum('...ij,...jk', V, W_exp_diag)
Where V, and W_exp_diag has shape: [NE][NS][NM][NO][ND][7][7]

The profiling script shows a 2X speed up.

----BEFORE:
SINGLE
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 18.811 18.811 <string>:1(<module>)
1 0.002 0.002 18.811 18.811 pf_3d:407(single)
CLUSTER
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 18.315 18.315 <string>:1(<module>)
1 0.001 0.001 18.315 18.315 pf_3d:431(cluster)

-----AFTER:
SINGLE
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 8.818 8.818 <string>:1(<module>)
1 0.002 0.002 8.818 8.818 pf_3d:407(single)
CLUSTER
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 9.082 9.082 <string>:1(<module>)
1 0.001 0.001 9.082 9.082 pf_3d:431(cluster)

Task #7807 (https://gna.org/task/index.php?7807): Speed-up of dispersion models for Clustered analysis.

Inserted intermediate step, to check if the matrix propagator to evolve the magnetization is equal
when done for lower dimensional data of shape [7][7] and higher dimensional data of shape [NE][NS][NM][NO][ND][7][7].

A short example is shown at the wiki:
http://wiki.nmr-relax.com/Numpy_linalg#Ellipsis_broadcasting_in_numpy.einsum

Task #7807 (https://gna.org/task/index.php?7807): Speed-up of dispersion models for Clustered analysis.

Added function to compute the matrix exponential for higher dimensional data of shape [NE][NS][NM][NO][ND][7][7].

This is done by using numpy.einsum, to make the dot product of the last two axis.

Task #7807 (https://gna.org/task/index.php?7807): Speed-up of dispersion models for Clustered analysis.