Changes

* Fix for the RDC and PCS averaging in the CaM frame order test data generation base script. For the double rotor model, or any multiple motional mode model, the averaging was incorrect. Instead of dividing by N, the values should be divided by N**^M, where M is the number of motional modes.* Huge increase in precision for the CaM frame order free rotor model test data. The higher precision is because the number structures in the distribution is now twenty million rather than one million, and the much higher precision numpy.float128 averaging of the updated data generation base script has been used. This data should allow for a much better estimate of the &beta ; and &gamma ; average domain position parameter values for the free rotor models which are affected by the collapse of the &alpha ; parameter to zero.* Huge increase in precision for the CaM frame order double rotor model test data. The higher precision is because the number structures in the distribution is now over twenty million (4500**²) rather than a quarter of a million (500**²). And the much higher precision numpy.float128 averaging of the updated data generation base script has been used.

* Large increase in precision for the 2nd 2^nd CaM frame order rotor model test data set. The higher precision is because the number structures in the distribution is now 20 million rather than 1,000,001 and the numpy.float128 data averaging has been used.* Parameter update for the 2nd 2^nd rotor CaM frame order test model optimisation script. The Euler angles for the rotation about the motional pivot have been replaced by the translation vector and Euler angle CoM rotation parameters.* Large increase in precision for the 2nd 2^nd CaM frame order free rotor model test data set. The higher precision is because the number structures in the distribution is now 20 million rather than 999,999 and the numpy.float128 data averaging has been used.

* 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 {aα, bβ, gγ} -> {0, bβ', gγ'} angle conversion problem in the rotor models no longer works now that the average domain position mechanics has been simplified. Instead, high precision optimised b' and g' 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 &theta ; and &phi ; 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 b' and g' were optimised. Iterative optimisation was used with increasing precision, ending up with high precision using 10,000 Sobol' points.

* Added FIXME comments to the 2nd 2^nd free-rotor CaM frame order model system test scripts. These explain the steps required to obtain the correct b' and g' average domain position rotation angles.

* Large increase in precision for the 2nd 2^nd 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.

* Fixes for the 2nd 2^nd frame order free-rotor system tests. The average domain position parameters are now set to the correct values, matching those in the relax log file frame_order_ave_pos_opt.log in test_suite/shared_data/frame_order/cam/free_rotor2.* Updated the 2nd 2^nd CaM free-rotor frame order system tests for the correct average domain position. The chi-squared values are now significantly lower.

* Preformed a frame order analysis on the 2nd 2^nd CaM free-rotor model test data. This is to check that everything is operating as expected.

* Attempt to speed up the pseudo-elliptic frame order models. The quasi-random numerical integration of the PCS for the pseudo-ellipse has been modified so that the torsion angle check for each Sobol' point is preformed before the tmax_pseudo_ellipse() function call. A new check that the tilt angle is less than cone_theta_y, the larger of the two cone angles, has also been added to avoid tmax_pseudo_ellipse() when the &theta ; tilt angle is outside of an isotropic cone defined by cone_theta_y.

* Updated the rotor CaM test data frame_order.py script for the parameter reduction. The rotor axis {θ, φ} polar angles have been replaced by the single axis &alpha ; angle. This now matches the script for the 2nd 2^nd rotor model.

* Updated the frame_order.py optimisation script for the small angle CaM rotor frame order test data. This now has the correct rotor torsion angle of 1 degree, and the spherical coordinates are now converted to the axis &alpha ; parameter.

* Constraints are now implemented in the frame order grid search. This is useful for the pseudo-elliptic models as the cone theta_x &theta;< theta_y sub>x</sub> < &theta;_y constraint halves the optimisation space.

* Important fix for the 2nd 2^nd rotor model of the CaM frame order test data. The tilt angle was not set, and therefore the old data matched the non-tilted 1st 1^st rotor model. All PCS and RDC data has been regenerated to the highest quality using 20,000,000 structures.

* Expanded the 2nd 2^nd CaM pseudo-ellipse test data frame_order.py optimisation script. The optimisation is now implemented as in the auto-analysis, with an iterative increase in accuracy of the quasi-random numerical integration together with an decrease of the function tolerance cutoff for optimisation. The accuracy of the initial chi-squared calculation is now much higher. And the accuracy of the initial grid search and the Monte Carlo simulations is now much lower. The results of the new optimisation have been added to the repository.

* Updated the CaM 2-site to rotor model frame_order.py optimisation script for the parameter reduction. The rotor frame order model axis spherical angles have now been converted to a single &alpha ; angle.

* Converted the 'free rotor' frame order model to the new axis_alpha parameter system. The axis_theta and axis_phi spherical coordinates are converted to the new reduced parameter set defined by a random point in space (the CoM of all atoms), the pivot point, and a single angle &alpha;. The &alpha ; parameter defines the rotor axis angle from the xy-plane.* Parameter conversion for all of the CaM free rotor test data frame_order.py optimisation scripts. The rotor axis spherical angles have been replaced by the axis &alpha ; angle defining the rotor with respect to the xy-plane.* Modified the CaM frame order base system test script to catch a bug in the free rotor model. The axis spherical angles are no longer set for the rotor or free rotor models, as they use the &alpha ; angle instead and the lack of the &theta ; and &phi ; parameters triggers the bug. The PDB representation of the frame order motions is also now tested for all frame order models, as it was turned off for the rigid, rotor and free rotor models and this is where the bug lies.* Fix for the failure of the [http://www.nmr-relax.com/manual/frame_order_pdb_model.html frame_order.pdb_model user function] for the free rotor frame order model. This is due to the recent parameter conversion to the axis &alpha ; angle.* Eliminated the average position &alpha ; Euler angle parameter from the free-rotor pseudo-ellipse model. As this frame order model is a free-rotor, the average domain position is therefore undefined and it can freely rotate about the rotor axis. One of the Euler angles for rotating to the average position can therefore be removed, just as in the free rotor and free rotor isotropic cone models.* Eliminated the free rotor psuedo-ellipse model ave_pos_alpha parameter from the target function. The average domain position &alpha ; Euler angle has already been removed from the specific analyses code and this change brings the target function into line with these changes.* Added the full optimisation results for the 2nd 2^nd rotor frame order model for the CaM test data. This is from the new frame_order.py optimisation script and the results demonstrate the stability of the rotor model.

* Fix for the free rotor PDB representation created by the [http://www.nmr-relax.com/manual/frame_order_pdb_model.html frame_order.pdb_model user function]. The simulation axes were being incorrectly generated from the &theta ; and &phi ; angles, which no longer exist as they have been replaced by the &alpha ; angle.

* Added the full optimisation results for the 2nd 2^nd free rotor frame order model. This is for the CaM test data using the new frame_order.py optimisation script.

* Updated the free rotor and 2nd 2^nd free rotor PDB representations using the represent_frame_order.py script. This is for the CaM frame order test data.

* Removed the 2nd 2^nd pivot point infrastructure from the frame order analysis. The 2nd 2^nd pivot is now defined via the pivot_disp parameter.* Added the 2nd 2^nd rotor axis torsion angle to the list of frame order parameters. This is for the double rotor model.

* Added a script for timing different ways to calculate PCSs and RDCs for multiple vectors. This uses the timeit module rather than profile to demonstrate the speed of 7 different ways to calculate the RDCs or PCSs for an array of vectors using numpy. In the frame order analysis, this is the bottleneck for the quasi-random numerical integration of the PCS. The log file shows a potential 1 order of magnitude speedup between the 1st 1^st technique, which is currently used in the frame order analysis, and the 7th 7^th and last technique. The first technique loops over each vector, calculating the PCS. The last expands the PCS/RDC equation of the projection of the vector into the alignment tensor, and calculates all PCSs simultaneously.

* Attempt at speeding up the torsionless pseudo-ellipse frame order model. The check if the Sobol' point is outside of an isotropic cone defined by the largest angle theta_y &theta;_y is now performed to avoid many unnecessary calls to the tmax_pseudo_ellipse() function. This however reveals a problem with the test suite data for this model.

* The rigid frame order matrix for the pseudo-ellipse models is now correctly handled. This allows the rigid case RDCs to be correctly calculated for both the pseudo-ellipse and torsionless pseudo-ellipse models. The previous catch of the theta_x &theta;_x cone angle of zero was incorrectly recreating the frame order matrix, which really should be the identity matrix. However truncation artifacts due to the quadratic SciPy integration still cause the model to be ill-conditioned near the rigid case. The rigid case is correctly handled, but a tiny shift of the parameters off zero cause a discontinuity.

* Large increase in precision for the CaM frame order torsionless pseudo-ellipse model test data set. In addition, the theta_x &theta;_x and theta_y &theta;_y angles have also been swapped so that the new constraint of 0 &le; &theta;<= theta_x sub>x<= theta_y /sub> &le; &theta;<= sub>y</sub> &le; &pi ; 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 &theta ; and &phi ; tilt angles from the random rotation, dropping the torsion angle &sigma;, 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 theta_x &theta;_x and theta_y &theta;_y 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.

* 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 1st 1^st pivot to atom vector rotated by the 1st 1^st mode of motion; the 2nd 2^nd pivot to 1st 1^st pivot vector rotated by the 2nd 2^nd mode of motion (together with the rotated 1st 1^st 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 Ln3+ 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 2nd 2^nd pivot is optimised and the inter-pivot distance along the z-axis gives the position of the 1st 1^st 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.

* Added the full optimisation results for the 2nd 2^nd free rotor isotropic cone frame order model. This is for the CaM test data using the new frame_order.py optimisation script.

* Attempt at implementing the 2nd 2^nd degree frame order matrix for the double rotor model. This is required for the RDC.

* Created an auxiliary function for automatically generating the pivots of the frame order analysis. This is the new specific_analyses.frame_order.data.generate_pivot() function. It will generate the 1st 1^st or 2nd 2^nd pivot, hence supporting both the single motion models and the double motion double rotor model.

* Fix for the pivots created by the specific_analyses.frame_order.data.generate_pivot() function. This is for the double rotor model where the 1st 1^st mode of motion is about the 2nd 2^nd pivot, and the 2nd 2^nd mode of motion about the 1st 1^st pivot.

* Updated the chi2 &chi;² check for the large angle double rotor frame order system tests. This is needed for the eigenframe fix.

* Speedup of the PCS component of the rigid frame order model. The lanthanide to atom vectors are now being calculated outside of the alignment tensor and spin loops, as well as the inverse vector lengths to the 5th 5^th power. This increases the speed by a factor of 1.216 (from 38.133 to 31.368 seconds for 23329 calls of the func_rigid() target function).

* Numpy <= &le; 1.6 fixes for the frame order PCS code. The numpy.linalg.norm function does not have an axis argument in numpy 1.6, therefore the lib.compat.norm() function is now used instead. This function was created exactly for this axis argument problem.

* Shifted the calculation of the theta_max &theta;_max 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 theta_max &theta;_max to be shifted outside of all loops.

* Updated the frame order optimisation results for the 2nd 2^nd CaM free rotor test data. The optimisation in the frame_order.py is now of higher precision with the number of Sobol' numeric integration points significantly increased, especially for the Monte Carlo simulations. The new frame order representation files have been added to the repository, as well as the intermediate state files.

* Updated the frame order optimisation results for the 2nd 2^nd CaM free rotor isotropic cone test data. The optimisation in the frame_order.py is now of higher precision with the number of Sobol' numeric integration points significantly increased, especially for the Monte Carlo simulations. The new frame order representation files have been added to the repository, as well as the intermediate state files.

* Updated the frame order optimisation results for the 2nd 2^nd CaM pseudo-elliptic cone test data. The optimisation in the frame_order.py is now of higher precision with the number of Sobol' numeric integration points significantly increased, especially for the Monte Carlo simulations. The new frame order representation files have been added to the repository, as well as the intermediate state files.

* Updated the frame order optimisation results for the 2nd 2^nd CaM rotor test data. The optimisation in the frame_order.py is now of higher precision with the number of Sobol' numeric integration points significantly increased, especially for the Monte Carlo simulations. The new frame order representation files have been added to the repository, as well as the intermediate state files.* Fixes for the CaM free-rotor pseudo-ellipse frame order model test data set. This is for the constraint 0 &le; &theta;<= theta_x sub>x<= theta_y /sub> &le; &theta;<= sub>y</sub> &le; &pi;, as the old data was created with theta_x &theta;_x > &theta;_y theta_y. The new data is also of high quality using 20 million structures and numpy.float128 data averaging.* Created the lib.frame_order.rotor_axis.convert_axis_alpha_to_spherical() function. This will convert the axis &alpha ; angle to the equivalent spherical angles &theta ; and &phi;.

* Redesign and expansion of the nested model parameter copying in the frame order auto-analysis. The nested parameter protocol used to allow the analysis to complete in under 1,000,000 years was no longer functional due to the switching to the axis &alpha ; parameter to decrease parameter number and redundancy. The copying of the average domain position for the free rotor models was also incorrect as the dropping of the &alpha ; Euler angle cause the translation parameters and &beta ; and &gamma ; angles to change drastically. The new protocol has been split into four methods for the average domain position, the pivot point, the motional eigenframe and the parameters of ordering. These use the fact that the free rotor and torsionless models are the two extrema of the models where the torsion angle is restricted. The pivot copying is a new addition.

* Updates and fixes for the frame order auto-analysis. The custom grid setup now works for the new reduced parameter set models and the double rotor model is now also included. The cone axis &alpha ; angle to spherical angle conversion has had a bug removed. And some of the printouts are now more detailed.

* Added support for axis permutations in the frame order auto-analysis. This is done by copying the data pipe of the already optimised pseudo-elliptic models, permuting the axes, and performing another optimisation using all RDC and PCS data. This allows the second solution for these pseudo-elliptic models to be found. The 2nd 2^nd pipe is included in the model selection step to allow the best solution for the model to be found.

* Redesigned the [http://www.nmr-relax.com/manual/frame_order_permute_axes.html frame_order.permute_axes user function] frontend. Previously only cyclic permutations were considered, however non-cyclic permutations are also allowed when accompanied by an axis inversion. Therefore 3 combinations exist with cone_theta_x <= &le; cone_theta_y, or 2 when the current combination is excluded.

* Fix for the [http://www.nmr-relax.com/manual/frame_order_permute_axes.html frame_order.permute_axes user function]. One of the 6 permutations had the x and y axes switched (the x <= &le; z <= &le; y condition, permutation A).* Visualisation files for all of the pseudo-ellipse permutations by [http://www.nmr-relax.com/manual/frame_order_permute_axes.html frame_order.permute_axes]. This includes the x <= &le; z <= &le; y and z <= &le; x <= &le; y conditions (the previous files were for x <= &le; y <= &le; z). In all permutation combinations, optimisation has been performed to demonstrate that these are all local minima. These all approximate the rotor when using the CaM frame order rotor model synthetic data.

* Created the other isotropic cone condition z <= &le; x = y. As there are no constraints in this model, this condition should not result in any major differences, just the size of the cone being different and the optimisation having to decrease the cone angle significantly to mimic the rotor.

* Bug fix for the lib.frame_order.pseudo_ellipse.tmax_pseudo_ellipse_array() function. The problem was that when theta_x &theta;_x or theta_y &theta;_y were zero, the floating point value of 0.0 would be returned. This is the incorrect behaviour as the returned value must be an array matching the dimensions of the &phi ; angle array argument.

* Fix for the [http://www.nmr-relax.com/manual/frame_order_count_sobol_points.html frame_order.count_sobol_points user function] for the rotor model. The &sigma ; angles unpacking required a dimensionality collapse in the Sobol' angle data structure.

* Fix for the frame order count_sobol_points() function. The torsion angle ranges from -&pi ; to &pi;, so the absolute value needs to be checked, just as in the lib.frame_order modules.

* Redesigned the [http://www.nmr-relax.com/manual/frame_order_sobol_setup.html frame_order.num_int_pts user function] frontend for the oversampling idea. The use of the quasi-random Sobol' sequence for numerical PCS integration will be modified to use the concept of oversampling. Instead of specifying the exact number of points in the Sobol' sequence and then removing points outside of the current parameter values, the algorithm will oversample as N * Ov * 10**^M, where N is the maximum number of Sobol' points to be used for the integration, Ov is the oversampling factor, and M is the number of dimensions or torsion-tilt angles used in the system. The aim is to try to use the maximum number of points N for all frame order models and all ranges of dynamics.

* Updated the chi2 &chi;² check in the Frame_order.test_rigid_data_to_free_rotor_model system test. This value has changed due to the first 1000 points of the Sobol' sequence being skipped.

* Updates for all of the Frame_order.test_cam_* system tests. The NUM_INT_PTS variable in the system tests scripts is now passed into the [http://www.nmr-relax.com/manual/frame_order_sobol_setup.html frame_order.sobol_setup user function] as the max_num argument. This number has also been changed so that the tests take a reasonable amount of time. All chi2 &chi;² value checks were updated. These were validated by increasing the number of integration points and watching the chi2 &chi;² value of the Frame_order.test_cam_*_pcs version of the system tests head to zero.* Another update for the chi2 &chi;² check in the Frame_order.test_rigid_data_to_free_rotor_model system test. The previous commit used an incorrect value for the chi2&chi;². This new value is now much closer to the original.

* Updated the chi2 &chi;² check in the Frame_order.test_cam_qr_int_pseudo_ellipse_free_rotor_rdc system test. This test is not normally run as it blacklisted and duplicates the coverage of other tests. However its chi-squared value check had not been updated for a while and hence the test fails when explicitly run.

* Updated all of the chi2 &chi;² value checks for the Frame_order.test_cam_quad_int_* system tests. This is only for those tests which use PCS data - the RDC only test chi2 &chi;² values are the same as in the Frame_order.test_cam_qr_int_* system tests. In all cases, the chi2 &chi;² value is lower for the more accurate SciPy quadratic integration as compared to the quasi-random Sobol' integration, as expected.

* Changed the chi2 &chi;² value checks in the Frame_order.test_cam_quad_int_double_rotor* system tests. These were the values for the quasi-random Sobol' integration and needed updating for the SciPy quadratic integration.

* The verbosity flag is now being respected by the frame order specific API calculate() method. This silences the method when executing the [http://www.nmr-relax.com/manual/dx_map.html dx.map user function]. The chi2 &chi;² value printout is suppressed and the verbosity argument is being sent into the frame order count_sobol_points() function.

* Zero values can now be handled in the pseudo-ellipse 1st 1^st degree frame order matrix function. This is in lib.frame_order.pseudo_ellipse.compile_1st_matrix_pseudo_ellipse().* Removed some unused code in the pseudo-ellipse 2nd 2^nd degree frame order matrix function. This is the compile_2nd_matrix_pseudo_ellipse() function in the lib.frame_order.pseudo_ellipse module. The change should make the RDC part of the frame order analysis for the pseudo-ellipse model slightly faster.

* Fix for the compile_1st_matrix_pseudo_ellipse() function. This function of the lib.frame_order.pseudo_ellipse module now can rotate the 1st 1^st degree frame order matrix out of its eigenframe and into the PDB frame.

* Redesign of the frame_order_solution.py script for calculating the frame order matrix elements. This script now loops over all models, all motional frame orientations, and all order parameters to generate the Grace graphs of all 1st 1^st and 2nd 2^nd degree frame order matrix elements. Therefore the script only needs to be executed once. The script also now calculates a point at zero (slightly shifted to 0.01 to avoid artifacts).* Added all of the Grace graphs produced by the frame_order_solution.py script. These are the graphs of the 1st 1^st and 2nd 2^nd degree frame order matrix elements, calculated using the functions in lib.frame_order.

* Implemented the compile_1st_matrix_rotor() function. This is for the lib.frame_order.rotor module. The function will calculate the 1st 1^st degree in-frame frame order matrix for the rotor model.* Created the Grace graphs for the rotor model 1st 1^st degree frame order matrix elements. These are the values calculated directly from the lib.frame_order modules. The graphs were previously all zeros.* Implemented the compile_1st_matrix_free_rotor() function. This is for the lib.frame_order.free_rotor module. The function will calculate the 1st 1^st degree in-frame frame order matrix for the free rotor model.* Created the Grace graphs for the free rotor model 1st 1^st degree frame order matrix elements. These are the values calculated directly from the lib.frame_order modules. The graphs were previously all zeros.* Implemented the compile_1st_matrix_iso_cone() function. This is for the lib.frame_order.iso_cone module. The function will calculate the 1st 1^st degree in-frame frame order matrix for the isotropic cone model.* Created the Grace graphs for the isotropic cone model 1st 1^st degree frame order matrix elements. These are the values calculated directly from the lib.frame_order modules. The graphs were previously all zeros.* Implemented the compile_1st_matrix_iso_cone_torsionless() function. This is for the lib.frame_order.iso_cone_torsionless module. The function will calculate the 1st 1^st degree in-frame frame order matrix for the torsionless isotropic cone model.* Created the Grace graphs for the torsionless isotropic cone 1st 1^st degree frame order matrix elements. These are the values calculated directly from the lib.frame_order modules. The graphs were previously all zeros.* Implemented the compile_1st_matrix_iso_cone_free_rotor() function. This is for the lib.frame_order.iso_cone_free_rotor module. The function will calculate the 1st 1^st degree in-frame frame order matrix for the free rotor isotropic cone model.* Created the Grace graphs for the free rotor isotropic cone 1st 1^st degree frame order matrix elements. These are the values calculated directly from the lib.frame_order modules. The graphs were previously all zeros.

* Simulation of the pseudo-ellipse frame order matrix elements. This is for a simulation of 1,000,000 states for each angle increment, and includes in-frame and out-of-frame and varying of &theta ; X, Y, and Z. The resultant Grace graphs have been added to the repository.

* Simplifications and fixes for the 1st 1^st degree frame order matrix calculation for the pseudo-ellipse. The compile_1st_matrix_pseudo_ellipse() function of the lib.frame_order.pseudo_ellipse module has been significantly simplified by shifting a lot of maths outside of the quadratic integration.* Updated all the calculated 1st 1^st degree frame order matrix graphs for the pseudo-ellipse. The changes are due to the fixes in the lib.frame_order.pseudo_ellipse module.

* Implemented the compile_1st_matrix_pseudo_ellipse_torsionless() function. This is for the lib.frame_order.pseudo_ellipse_torsionless module. The function will calculate the 1st 1^st degree in-frame frame order matrix for the torsionless pseudo-ellipse model.* Created the Grace graphs for the torsionless pseudo-ellipse model 1st 1^st degree frame order matrix. These are the values calculated directly from the lib.frame_order modules. The graphs were previously all zeros.* Added the isotropic cone model to the frame order matrix element simulation script. The generated in-frame and out-of-frame Grace graphs for the torsion angle cone_sigma_max, containing the matrix values for 1,000,000 simulation values have been added to the repository. The inside_iso_cone() method has been created to check for the theta_x &theta;_x and theta_z &theta;_z angle violations from the rotation_hypersphere() method.

* Simplification of some of the pseudo-ellipse 2nd 2^nd degree frame order matrix equations.* More simplifications of the pseudo-ellipse 2nd 2^nd degree frame order matrix equations.* Integer to float conversions in part_int_daeg2_pseudo_ellipse_13(). This avoid integer to float conversion during execution, saving a little time for the pseudo-ellipse 2nd 2^nd degree frame order matrix compilation.* Removal of many repetitive calculations in the pseudo-ellipse 2nd 2^nd degree frame order matrix equations.* Simplifications of pseudo-ellipse 1st 1^st degree frame order matrix functions. The xx, yy, and zz have been renamed to 00, 11, and 22 for consistency. And all sigma_max arguments have been dropped as they are not used.* Small numerical changes for the pseudo-ellipse 2nd 2^nd degree frame order matrix graphs. These are only for the first point close to zero and the changes are minimal, caused by the recent simplifications of the code.* Created the Grace graphs for the free rotor pseudo-ellipse model 1st 1^st degree frame order matrix. These are the values calculated directly from the lib.frame_order modules. The graphs were previously all zeros.* Implemented the compile_1st_matrix_pseudo_ellipse_free_rotor() function. This is for the lib.frame_order.pseudo_ellipse_free_rotor module. The function will calculate the 1st 1^st degree in-frame frame order matrix for the free_rotor pseudo-ellipse model.* Speedups and simplifications of the free rotor pseudo-ellipse 2nd 2^nd degree frame order matrix equations.

* Implemented the compile_1st_matrix_double_rotor() function. This is for the lib.frame_order.double_rotor module. The function will calculate the 1st 1^st degree frame order matrix for the double_rotor model.* Created the Grace graphs for the double rotor model 1st 1^st degree frame order matrix. These are the values calculated directly from the lib.frame_order modules. The graphs were previously all zeros.

* Fix for the pseudo-ellipse 1st 1^st degree frame order matrix Daeg22 element.* Updated all of the pseudo-ellipse 1st 1^st degree frame order matrix graphs for the recent fix.

* Added the isotropic cone model frame order matrix simulation graphs for the cone opening angle theta_x&theta;_x.

* Bug fix for the torsionless pseudo-ellipse 1st 1^st degree frame order matrix. The 11 element was of the wrong sign.* Fixes for the torsionless pseudo-ellipse 1st 1^st degree frame order matrix element graphs.

* Fixes for free rotor isotropic cone 1st 1^st degree frame order matrix graphs calculated using relax. The 1st 1^st degree function accepts the cone opening angle &theta ; rather than the order parameter S.

* Added support for the double rotor model to the frame order matrix element simulation script. The double rotation is constructed in the new rotation_double_xy_axes() method, and the checks for the violation of the two torsion angles in the inside_double_rotor() method. In the main loop, the &theta;, &phi ; and &sigma ; angles correspond to sigma1, sigma2, and nothing.

* The 1st 1^st angle for the calculated frame order matrix graphs is 0 for all non pseudo-ellipse models. This is for the frame_order_solution.py script. Only the pseudo-ellipse models where numerical integration is required fail for the angle of 0.0. Therefore the changing of the first angle from 0.0 to 0.01 only occurs for the pseudo-ellipse models. All graphs have been updated.* The 1st 1^st pseudo-ellipse torsion angle value in the frame order matrix graphs is now 0.0. Only the cone opening angles set to 0.0 cause a failure in the pseudo-ellipse models, so the torsion angle is now allowed to start at exactly zero.

* Redesign of the free rotor isotropic cone frame order model - the order parameter has been replaced. From the frame order matrix element graphs in test_suite/shared_data/frame_order/sim_vs_pred_matrix, specifically Sijkl_iso_cone_free_rotor_in_frame_theta_x_calc.agr, Sijkl_iso_cone_free_rotor_axis2_1_3_theta_x_calc.agr, and Sijkl_iso_cone_free_rotor_out_of_frame_theta_x_calc.agr, it is clear that the symmetry of the order parameter after 120 degrees causes the 2nd 2^nd degree frame order matrix to be incorrectly estimated. Therefore the S1 order parameter has been replaced with the original cone opening angle cone_theta. All parts of relax have been updated for this large conversion.* Updated the frame order matrix element graphs for the free rotor isotropic cone fixes. The cone S1 parameter has been converted back to the original cone &theta ; opening half-angle, allowing the 2nd 2^nd degree frame order matrix elements to be properly calculated for all motions.

* 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 > pi/2.0 causing the frame order matrix to be incorrectly predicted. Therefore all unit tests have been converted to use the cone opening angle &theta ; 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.

* 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 &alpha ; angle of pi/2 creates an axis parallel to Z. The origin to atom distance check has also been loosened due to the PDB truncation artifact.