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* Changed the average domain position parameter values in the CaM frame order system tests. This is in the base script used by all scripts in test_suite/system_tests/scripts/frame_order/cam/. The translation vector coordinates are now set, as well as the CoM Euler angle rotations. These come from the log file of the test_suite/shared_data/frame_order/cam/superimpose.py script, and are needed due to the simplification of the average domain position mechanics now mimicking the Kabsch superimposition algorithm.
* The CaM frame order system test mesg_opt_debug() method now prints out the translation vector. This is printed out at the end of all CaM frame order system tests to help with debugging when the test fails.
* Change for how the CaM frame order system test scripts handle the average domain position rotation. The trick of pre-rotating the 3D coordinates was used to solve the {α, β, γ} -> {0, β', γ'} angle conversion problem in the rotor models no longer works now that the average domain position mechanics has been simplified. Instead, high precision optimised bβ' and gγ' values are now set, and the ave_pos_alpha value set to None. The high precision parameters were obtained with the frame_order.py script located in the directory test_suite/shared_data/frame_order/cam/free_rotor. The free rotor target function was modified so that the translation vector is hard-coded to [-20.859750185691549, -2.450606987447843, -2.191854570352916] and the axis θ and φ angles to 0.96007997859534299767 and 4.0322755062196229403. These parameters were then commented out for the model in the module specific_analyses.frame_order.parameters so only bβ' and gγ' were optimised. Iterative optimisation was used with increasing precision, ending up with high precision using 10,000 Sobol' points.
* Updated a number of the CaM frame order system tests for the higher precision data. The new data results in chi-squared values at the real solution to be much closer to zero.
* Change for how the CaM frame order free-rotor pseudo-ellipse test script handle the average position.
* Added FIXME comments to the 2<sup>nd</sup> free-rotor CaM frame order model system test scripts. These explain the steps required to obtain the correct bβ' and gγ' average domain position rotation angles.
* Large increase in precision for the CaM frame order isotropic cone model test data set. The higher precision is because the number structures in the distribution is now 20 million rather than 1 million and the numpy.float128 data averaging has been used.
* Large increase in precision for the CaM frame order free-rotor, isotropic cone model test data set. The higher precision is because the number structures in the distribution is now 20 million rather than 1 million and the numpy.float128 data averaging has been used.
* Large increase in precision for the CaM frame order torsionless pseudo-ellipse model test data set. In addition, the θ<sub>x</sub> and θ<sub>y</sub> angles have also been swapped so that the new constraint of 0 ≤ θ<sub>x</sub> ≤ θ<sub>y</sub> ≤ π built into the analysis is satisfied. The higher precision is because the number structures in the distribution is now 20 million rather than 1 million and the numpy.float128 data averaging has been used. The algorithm for finding suitable random domain positions within the motional limits has been changed as well by extracting the θ and φ tilt angles from the random rotation, dropping the torsion angle σ, and reconstructing the rotation from just the tilt angles. This increases the speed of the data generation script by minimally 5 orders of magnitude.
* Changed the parameter values for the Frame_order.test_cam_pseudo_ellipse_torsionless* system tests. The θ<sub>x</sub> and θ<sub>y</sub> angles are now swapped. The chi-squared values are now also lower in the 3 system tests as the data is now of much higher precision.
* Speedup for the frame order analyses when only one domain is aligned. When only one domain is aligned, the reverse Ln3Ln<sup>3+ </sup> to spin vectors for the PCS are no longer calculated. For most analyses, this should significantly reduce the number of mathematical operations required for the quasi-random Sobol' point numerical integration.* Support for the 3 vector system for double motions has been added to the frame order analysis. This is used for the quasi-random Sobol' numeric integration of the PCS. The lanthanide to atom vector is the sum of three parts: the 1<sup>st</sup> pivot to atom vector rotated by the 1<sup>st</sup> mode of motion; the 2<sup>nd</sup> pivot to 1<sup>st</sup> pivot vector rotated by the 2<sup>nd</sup> mode of motion (together with the rotated 1<sup>st</sup> pivot to atom vectors); and the lanthanide to second pivot vector. All these vectors are passed into the lib.frame_order.double_rotor.pcs_numeric_int_double_rotor() function, which passes them to the pcs_pivot_motion_double_rotor() function where they are rotated and reconstructed into the Ln3Ln<sup>3+ </sup> to atom vectors.
* Fully implemented the double rotor frame order model for PCS data. Sobol' quasi-random points for the numerical integration are now generated separately for both torsion angles, and two separate sets of rotation matrices for both angles for each Sobol' point are now pre-calculated in the create_sobol_data() target function method. The calc_vectors() target function method has also been modified as the lanthanide to pivot vector is to the second pivot in the double rotor model rather than the first. The target function itself has been fixed as the two pivots were mixed up - the 2<sup>nd</sup> pivot is optimised and the inter-pivot distance along the z-axis gives the position of the 1<sup>st</sup> pivot. For the lib.frame_order.double_rotor module, the second set of Sobol' point rotation matrices corresponding to sigma2, the rotation about the second pivot, is now passed into the pcs_numeric_int_double_rotor() function. These rotations are frame shifted into the eigenframe of the motion, and then correctly passed into pcs_pivot_motion_double_rotor(). The elimination of Sobol' points outside of the distribution has been fixed in the base pcs_numeric_int_double_rotor() function and now both torsion angles are being checked.
* Fix for the unpacking of the double rotor frame order parameters in the target function. This is for when the pivot point is being optimised.
* Added a script for profiling the target function calls of the pseudo-ellipse frame order model.
* Added a timeit script and log file showing how numpy.cos() is 10 times slower than math.cos(). This is for single floats.
* Shifted the calculation of the θ_max <sup>max</sup> cone opening for the pseudo-ellipse outside of all loops. This is infrastructure change for potentially eliminating all of the looping for the PCS numeric integration in the future. It however slightly speeds up the pseudo-ellipse frame order model. Using 500 target function calls in the profiling_pseudo_ellipse.py script in test_suite/shared_data/frame_order/timings/, the time spent in the pcs_pivot_motion_full_qrint() function decreases from 20.849 to 20.719 seconds.* Converted the torsionless pseudo-ellipse model to also use the tmax_pseudo_ellipse_array() function. This allows the calculation of the pseudo-elliptic cone opening θ_max <sup>max</sup> to be shifted outside of all loops.
* Created a profiling script and log file for the isotropic cone frame order model. This shows where the slow points of the model are, using 2000 target function calls.
* Increased the function call number to 500 in the pseudo-ellipse frame order model profiling script. The profiling log file has also been added to show where the slowness is - specifically that the numeric PCS integration takes almost the same amount of time as the RDC frame order matrix construction using the scipy.integrate.quad() function.
* The geometric representation part of the [http://www.nmr-relax.com/manual/frame_order_pdb_model.html frame_order.pdb_model user function] now checks parameters. This calls the specific_analyses.frame_order.checks.check_parameters Check object to make sure that all necessary parameters for the model exist.
* Completed the Frame_order.test_pdb_model_rotor system test. This now sets the rotor axis to the z-axis (with a printout to be sure), sets the torsion angle to zero for simplicity, creates a new data pipe and loads the PDB representation file, then checks all of the key atom coordinates.
* Fixes for the unit tests of the lib.frame_order_matrix_ops module for the free rotor isotropic cone. The S1 order parameter has been eliminated due to angles > π/2.0 causing the frame order matrix to be incorrectly predicted. Therefore all unit tests have been converted to use the cone opening angle θ instead. In addition, the test_compile_2nd_matrix_iso_cone_free_rotor_disorder had been modified to pass with the incorrect frame order matrix by comparing to the half cone frame order matrix rather than the identity frame order matrix.
* Fix for inverted axes in the new Frame_order.test_pdb_model_rotor system test.
* Huge bug fix for the [http://www.nmr-relax.com/manual/frame_order_pdb_model.html frame_order.pdb_model user function] - the single axis direction was incorrect. In the PDB representation of the frame order motion for the rotor and isotropic cone models (rotor, free rotor, isotropic cone, free rotor isotropic cone, and torsionless isotropic cone), the X and Z axes were swapped. This is because the eigenframe of the motion was being incorrectly constructed via the lib.geometry.rotations.two_vect_to_R() function. For better control, the specific_analyses.frame_order.geometric.frame_from_axis() function has been created. This constructs a full motional eigenframe from the Z-axis. The problem was detected via the new Frame_order.test_pdb_model_rotor system test.
* Simplification for all of the Frame_order.test_pdb_model_* system tests. The model setup in all of these tests has been merged into the common setup_model() method. This not only removes a large quantity of repetitive code, but the new method can also be used for constructing future tests, for example for checking the [http://www.nmr-relax.com/manual/frame_order_simulate.html frame_order.simulate user function].
* Created an initial version of the Frame_order.test_simulate_rotor_z_axis system test. This is to check the [http://www.nmr-relax.com/manual/frame_order_simulate.html frame_order.simulate user function] rotor model along the z-axis. It currently fails due to a bug in the user function.
* Fixes for the Frame_order.test_simulate_rotor_z_axis system test. Now 6 atoms are being created at X, -X, Y, -Y, Z, and -Z, 100 Angstrom from the origin. This is required so that the CoM is at the origin, to allow the CoM-pivot vector to be unchanged at [1, 0, 0] so that the axis α angle of π/2 creates an axis parallel to Z. The origin to atom distance check has also been loosened due to the PDB truncation artifact.
* Fix for the Frame_order.test_pdb_model_free_rotor_xz_plane_tilt system test. This was broken while implementing the Frame_order.test_simulate_rotor_z_axis system test. Instead of shifting the 6 atom structure so its CoM is the pivot of the motion when creating the atoms, now the Frame_order.test_simulate_rotor_z_axis system test sets the average domain translation vector to the pivot to achieve the same result. This preserves the z-axis orientation of the rotor models.
* Created the Frame_order.test_simulate_free_rotor_z_axis system test. This is to check the [http://www.nmr-relax.com/manual/frame_order_simulate.html frame_order.simulate user function] for the free rotor model along the z-axis.
