Changes

* Changes to profiling script of [[NS CPMG 2-site expanded]]. The model does not have R_2A⁰ and R_2B⁰, but only r2R₂. [https://gna.org/task/?7807 Task #7807]: Speed-up of dispersion models for clustered analysis.

* Large extension of specific_analyses.relax_disp.data(), by adding several helper plotting functions. This is to prepare for plotting R_1ρ/R2 R₂ as function of effective field in rotating frame: w_eff. R_2 R₂ = R_1ρ / sin^2(theta) - R_1 / tan^2(theta) = (R_1ρ - R_1 * cos^2(theta) ) / sin^2(theta). [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].

* Added the back calculated R2 R₂ as function of effective field in rotating frame: w_eff. R_1ρ R_2 is defined as: R_2 = R_1ρ / sin^2(theta) - R_1 / tan^2(theta) = (R_1ρ - R_1 * cos^2(theta) ) / sin^2(theta). This is described more at: http://wiki.nmr-relax.com/DPL94#Equation_-_re-writed_forms. [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].* Added an intermediate attempt to show the back calculated data in the graph for R_1ρ/R2 R₂ as function of the effective field in rotating frame: w_eff. The graph is aiming for the representation of Figure 2 in Kjaergaard et al 2013. (http://dx.doi.org/10.1021/bi4001062). The figure can be seen at https://gna.org/support/download.php?file_id=20208. It becomes clear, that it is not necessary interpolate through the spin-lock offset, but it is sufficient to interpolate through the spin-lock field strengths. The necessary step was the extraction of the effective field in rotating frame, w_eff. In earlier attempt is shown at: http://wiki.nmr-relax.com/File:Matplotlib_52_N_R1_rho_R2eff_w_eff.png This though show lines for 6 offset values. The question is how to show the single line of interpolation. [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].

* Made both interpolation functions of the spin-lock field strength and spin-lock offset return the offset data. This is make it possible to switch between the interpolating functions, when plotting R_1ρ graphs. This is necessary to produce the R2 R₂ as function of effective field in rotating frame w_eff, and to produce R_1ρ as function of theta, when ramping the spin-lock offset. These graphs can be seen at: http://wiki.nmr-relax.com/Matplotlib_DPL94_R1rho_R2eff. [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].* Changed interpolation function from offset to spin lock field strength, to plot R_1ρ/R2 R₂ as function of effective field. [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].* Improved axis label for plotting R_1ρ/R2 R₂ as function of effective field w_eff. [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].* Added sub-title to the plot of R_1ρ/R2 R₂ as function of effective field. This is to add information about how the effective field has been interpolated. [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].* Added functionality to plot R_1ρ/R2 R₂ as function of effective field w_eff, for the [[R2eff]] model. Also renamed a function, to better reflect is functionality. The hard-coding of which models to plot, has been removed. If the exp-type is R_1ρ, then the plotting will commence. [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].

* Skip production of plotting R_1ρ/R2 R₂ as function of effective field w_eff, when spin.isotope is not present. This can happen when it is 'exp_fit' model curve fitting. [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].

* Ensured production of plotting R_1ρ/R2 R₂ as function of effective field w_eff, when spin.isotope is not present. The offset in radians would be set to 0.0 instead. This can happen when it is 'exp_fit' model curve fitting. [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].

* Fix for interpolation graph when plotting R_1ρ/R2 R₂ as function of offset (ppm). Missed to extract the offset value from list. [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].

* Added system test Relax_disp.test_kteilum_fmpoulsen_makke_check_graphs to check all CPMG graph combinations of: y_axis_types = [Y_AXIS_R2_EFF, Y_AXIS_R2_R1RHO]; x_axis_types = [X_AXIS_DISP, X_AXIS_THETA, X_AXIS_W_EFF]; interpolate_types = [INTERPOLATE_DISP]. This is a total of 6 graphs. The graphs will in most cases be totally equal, since the theta angle is calculated to 90 degrees, and R1 is returned as 0.0, then R2R₂=(R_1ρ - R1 cos^2(theta)) / sin^2(theta) = R_1ρ = R_2eff for CPMG models. [https://gna.org/support/?3124 Sr #3124]: Grace graphs production for R_1ρ analysis with R_2eff as function of Ω_eff. [https://gna.org/support/?3138 Sr #3138]: Interpolating theta through spin-lock offset [Omega], rather than spin-lock field strength [w1].

* Moved the auto-analyses plotting and writing of r2R₂, r2a and r2b for CPMG models into test of has_cpmg_exp_type(). [https://gna.org/support/?3135 Sr #3135]: Optimisation of the R1 relaxation rate for the off-resonance R_1ρ relaxation dispersion models.

* Fix for the nested copying of r2R₂, if using a nested list. [https://gna.org/support/?3135 Sr #3135]: Optimisation of the R1 relaxation rate for the off-resonance R_1ρ relaxation dispersion models.

* Fix for comment, which mentions R2 R₂ parameter, when it relates to R1 fit.

* Implemented system test Relax_disp.verify_estimate_r2eff_err_compare_mc for testing R_2eff error as function of Monte Carlo simulation. Note, since the name does not start with "test", but with "verify", this test will not be issued in the system test suite. [https://gna.org/task/?7822 Task #7822]: Implement user function to estimate R2eff R_2eff and associated errors for exponential curve fitting.

* Modified system test test Relax_disp.test_estimate_r2eff_err_methods() to show the difference between using the direct function Jacobian, or the χ² function Jacobian. Added also the functionality to the estimate R2eff R_2eff module, to switch between using the different Jacobians. The results show, that R2eff R_2eff can be estimated better.