From d859b687222b65558c346a8ad0682e16dc331927 Mon Sep 17 00:00:00 2001 From: RichardWaiteSTFC <55979119+RichardWaiteSTFC@users.noreply.github.com> Date: Fri, 16 Aug 2024 14:15:22 +0100 Subject: [PATCH] Add powder fitting tutorial (#199) * Average rather than sum over nQ points for 1D cuts Such that scale factor and constant background unchanged from 2D fit * Fix bug in eval cost func for bg bins with independent bg strategy * Add tutorial m file * Use varargout to avoid cell unpacking of fit result * Finish tutorial and output (html, .png etc.) * Fix typos, add clarification * Add test for calc bg cost function bug with 1D data Test test_calc_cost_func_of_background_indep fails on main * Use correct resolution parameters * Apply noise to simulated data after resolution convolution * Increase low energy range exlcluded now Ei larger * Update html and png --- +sw_tests/+unit_tests/unittest_sw_fitpowder.m | 22 ++ swfiles/sw_fitpowder.m | 22 +- tutorials/publish/tutorial39.m | 186 +++++++++ tutorials/publish/tutorial39/tutorial39.html | 374 ++++++++++++++++++ tutorials/publish/tutorial39/tutorial39.png | Bin 0 -> 4490 bytes tutorials/publish/tutorial39/tutorial39.txt | 305 ++++++++++++++ .../publish/tutorial39/tutorial39_01.png | Bin 0 -> 77711 bytes .../publish/tutorial39/tutorial39_02.png | Bin 0 -> 85171 bytes .../publish/tutorial39/tutorial39_03.png | Bin 0 -> 45986 bytes .../publish/tutorial39/tutorial39_04.png | Bin 0 -> 46576 bytes 10 files changed, 896 insertions(+), 13 deletions(-) create mode 100644 tutorials/publish/tutorial39.m create mode 100644 tutorials/publish/tutorial39/tutorial39.html create mode 100644 tutorials/publish/tutorial39/tutorial39.png create mode 100644 tutorials/publish/tutorial39/tutorial39.txt create mode 100644 tutorials/publish/tutorial39/tutorial39_01.png create mode 100644 tutorials/publish/tutorial39/tutorial39_02.png create mode 100644 tutorials/publish/tutorial39/tutorial39_03.png create mode 100644 tutorials/publish/tutorial39/tutorial39_04.png diff --git a/+sw_tests/+unit_tests/unittest_sw_fitpowder.m b/+sw_tests/+unit_tests/unittest_sw_fitpowder.m index 06e8a30e5..420d9bde3 100644 --- a/+sw_tests/+unit_tests/unittest_sw_fitpowder.m +++ b/+sw_tests/+unit_tests/unittest_sw_fitpowder.m @@ -338,6 +338,28 @@ function test_fit_background(testCase) 'abs_tol', 1e-4); end + function test_calc_cost_func_of_background_indep(testCase) + out = sw_fitpowder(testCase.swobj, testCase.data_1d_cuts, ... + testCase.fit_func, testCase.j1, "independent", 2); + out.y(1) = 10; % higher so other bins are background + bg_pars = out.params(2:end-1); + bg_pars(2:2:end) = 1; + out.estimate_constant_background(); % so ibg is set + cost = out.calc_cost_func_of_background(bg_pars); + testCase.verify_val(cost, 10); + end + + function test_calc_cost_func_of_background_planar(testCase) + out = sw_fitpowder(testCase.swobj, testCase.data_1d_cuts, ... + testCase.fit_func, testCase.j1, "planar", 2); + out.y(1) = 10; % higher so other bins are background + bg_pars = out.params(2:end-1); + bg_pars(end) = 1; + out.estimate_constant_background(); % so ibg is set + cost = out.calc_cost_func_of_background(bg_pars); + testCase.verify_val(cost, 10); + end + function test_set_errors_of_bg_bins(testCase) out = sw_fitpowder(testCase.swobj, testCase.data_2d, ... testCase.fit_func, testCase.j1); diff --git a/swfiles/sw_fitpowder.m b/swfiles/sw_fitpowder.m index 8f69b7106..8a3fda592 100644 --- a/swfiles/sw_fitpowder.m +++ b/swfiles/sw_fitpowder.m @@ -122,9 +122,8 @@ % >> fitpow.fix_bg_parameters(1:2); % fix slopes of background to 0 % >> fitpow.cost_function = "Rsq"; % or "chisq" % >> fitpow.optimizer = @ndbase.simplex; -% >> result = fitpow.fit('MaxIter', 1); % passes varargin to optimizer -% >> -% >> [pfit,cost_val,stat] = result{:}; +% >> [pfit,cost_val,stat] = fitpow.fit('MaxIter', 1); % passes varargin to optimizer +% >> % >> fitpow.plot_result(pfit, 26, 'EdgeAlpha', 0.9, 'LineWidth', 2) % ``` % @@ -469,22 +468,22 @@ function clear_cache(obj) function resid_sq_sum = calc_cost_func_of_background(obj, bg_params) bg = obj.calc_background(bg_params); - if obj.ndim == 1 + if obj.ndim == 1 && obj.background_strategy=="planar" % integrate nQ |Q| points for each cut bg = obj.rebin_powspec_to_1D_cuts(bg); end resid_sq_sum = obj.eval_cost(obj.y(obj.ibg), obj.e(obj.ibg), bg(obj.ibg)); end - function result = fit(obj, varargin) + function varargout = fit(obj, varargin) if obj.liveplot_interval > 0 figure("color","white"); obj.liveplot_counter = 0; end % setup cell for output of ndbase optimizer/minimizer - result = cell(1,nargout(obj.optimizer)); + varargout = cell(1,nargout(obj.optimizer)); % pass params and bounds as rows for ndbase optimisers - [result{:}] = obj.optimizer([], @obj.calc_cost_func, obj.params(:)', ... + [varargout{:}] = obj.optimizer([], @obj.calc_cost_func, obj.params(:)', ... 'lb', obj.bounds(:,1)', ... 'ub', obj.bounds(:,2)', ... varargin{:}); @@ -563,9 +562,6 @@ function estimate_constant_background(obj) else bg = mean(obj.y(obj.ibg)); end - if obj.background_strategy == "planar" && obj.ndim == 1 - bg = bg/obj.nQ; - end % set constant background assuming last bg parameter obj.set_bg_parameters(obj.nparams_bg, bg); % set constant background end @@ -682,13 +678,13 @@ function plot_1d_cuts_of_2d_data(obj, qmins, qmaxs, params) 'This function is only valid for 2D data'); cut = struct('x', obj.ebin_cens, 'qmin', qmin, 'qmax', qmax); ikeep = obj.modQ_cens > qmin & obj.modQ_cens <= qmax; - cut.y = sum(obj.y(:, ikeep), 2); - cut.e = sqrt(sum(obj.e(:, ikeep).^2, 2)); + cut.y = mean(obj.y(:, ikeep), 2, 'omitnan'); + cut.e = sqrt(sum(obj.e(:, ikeep).^2, 2))/sum(ikeep); end function ycalc = rebin_powspec_to_1D_cuts(obj, ycalc) % sum up successive nQ points along |Q| axis (dim=2) ycalc = reshape(ycalc, size(ycalc,1), obj.nQ, []); - ycalc = squeeze(sum(ycalc, 2, 'omitnan')); + ycalc = squeeze(mean(ycalc, 2, 'omitnan')); end function nbg_pars = get_nparams_in_background_func(obj) diff --git a/tutorials/publish/tutorial39.m b/tutorials/publish/tutorial39.m new file mode 100644 index 000000000..b52e514b8 --- /dev/null +++ b/tutorials/publish/tutorial39.m @@ -0,0 +1,186 @@ +%% Description +% This tutorial fits a spinwave model to simulated powder data. + +%% Define instrument resolution parameters for MARI +% This is a simplified parameterisation of the resolution of a +% Time-of-Flight spectrometer which will be used to broaden the simulated +% data. These parameters will depend on the instrument used - the instrument +% contact should be able to provide these. + +Ei = 20; % meV + +% Resolution for MARI with Gd chopper running at 200Hz and Ei=20meV (from PyChop) +eres = @(en) 2.1750e-04*sqrt((Ei-en).^3 .* ( (32.27217*(0.168+0.400*(Ei./(Ei-en)).^1.5)).^2 + (14.53577*(1.168+0.400*(Ei./(Ei-en)).^1.5)).^2) ); +% Q-resolution (parameters for MARI) +e2k = @(en) sqrt( en .* (2*1.67492728e-27*1.60217653e-22) )./1.05457168e-34./1e10; +L1 = 11.8; % Moderator to Sample distance in m +L2 = 4.0; % Sample to detector distance in m +ws = 0.05; % Width of sample in m +wm = 0.12; % Width of moderator in m +wd = 0.025; % Width of detector in m +ki = e2k(Ei); +a1 = ws/L1; % Angular width of sample seen from moderator +a2 = wm/L1; % Angular width of moderator seen from sample +a3 = wd/L2; % Angular width of detector seen from sample +a4 = ws/L2; % Angular width of sample seen from detector +dQ = 2.35 * sqrt( (ki*a1)^2/12 + (ki*a2)^2/12 + (ki*a3)^2/12 + (ki*a4)^2/12 ); + +%% Generate data +% Simulate a powder spectrum of a triangular AFM with constant background +% and normally distributed noise. This can also be done using the powder +% fitting class if an empty data array is passed. + + +% intialise spinw model +tri = sw_model('triAF',1); +scale = 1000; + +% calculate powder spectrum +E = linspace(0,4,80); +Q = linspace(0.1,3,60); +spec = tri.powspec(Q,'Evect',E,'nRand',2e2); +% scale data and add background +spec.swConv= scale*(spec.swConv + 0.1*mean(spec.swConv, 'all')); +% crop to kinematic range of instrument and apply some arbitrary resolution +spec = sw_instrument(spec, 'dQ', dQ, 'dE', eres, 'ThetaMin', 3.5, 'Ei', Ei); +% add noise +e = sqrt(spec.swConv); +spec.swConv = spec.swConv + e.*randn(size(spec.swConv)); + +% make xye struct containing data +data = struct('x', {{0.5*(E(1:end-1) + E(2:end)), Q}}, ... + 'y', spec.swConv', ... + 'e', e'); + +%% Initialise the sw_fitpowder class and plot data to inspect initial guess +% To initialise the powder fitting class (sw_fitpowder) object requires a +% spinw model with a magnetic strucutre and couplings added. +% Additional arguments are the data (can be xye structs for 2D data a cell +% array of xye structs for 1D data, or HORACE objects - see sw_fitpowder +% help for more details), a fit function which alters the matrices on the +% spinw object and a vector of initial guesses for the fit parameters. +% +% Optinally a background strategy can be specified as a 5th positional +% argument ("planar" background in energy transfer and |Q| or "independent" +% background for each 1D cut (1D only)). +% +% The class will call other spinw algorithms such as powspec and +% sw_instrument. The parameters used in these calls can be set by the user +% by modifying structs as shown below. +% +% Data can be cropped in |Q| and energy transfer - for example it is +% advisible not to include the low-energy transfer region close to the +% elastic line (relative to the resolution). + + +fit_func = @(obj, p) matparser(obj, 'param', p, 'mat', {'J_1'}, 'init', true); +J1 = 0.85; + +fitpow = sw_fitpowder(tri, data, fit_func, [J1]); +fitpow.set_caching(true); % will store last calculated spectra + +% set parameters passed to powspec +fitpow.powspec_args.dE = eres; % emergy resolution +fitpow.powspec_args.fastmode = true; +fitpow.powspec_args.neutron_output = true; +fitpow.powspec_args.nRand = 2e2; % low for speed (typically want > 1e3) +fitpow.powspec_args.hermit = true; +% set parameters passsed to sw_instrument +fitpow.sw_instrument_args = struct('dQ', dQ, 'ThetaMin', 3.5, 'Ei', Ei); + +% crop data +fitpow.crop_energy_range(1.5*eres(0), inf); % typically want to avoid elastic line +fitpow.crop_q_range(0.25, 3); +fitpow.powspec_args.dE = eres; +fitpow.powspec_args.fastmode = true; +fitpow.powspec_args.neutron_output = true; + +% estimate background and scale factor +fitpow.estimate_constant_background(); +fitpow.estimate_scale_factor(); + + +% plot data to inspect - any arguments after parameters are passed to +% contour plot (which shows the result the calculated intensity) +fitpow.plot_result(fitpow.params, 'EdgeAlpha', 0.9, 'LineWidth', 1 ,'EdgeColor', 'k'); + + +%% Fit and inspect the result +% It can be desirable to set bounds on fit parameters and fix some +% parameters initially to get a reasonable fit with as few degrees of +% freedom as possible. For example one might assume the background is +% constant in an initial fit. +% +% The cost function minimised in the fit can be chi-squared ("chisq") or +% the unweighted sum of the squared residuals ("Rsq"). Also the minimiser +% can be set to any callable as long as it shares the API of the ndbase +% minimisers. Typically users would be recommended ndbase.lm or +% ndbase.simplex. + +% set cost function and minimser +fitpow.cost_function = "Rsq"; % "Rsq" or "chisq" +fitpow.optimizer = @ndbase.simplex; % or e.g. ndbase.simplex + +% Fix background parameters (planar background of form +% default background is planar with parameters: +% [slope_energy, slope_modQ, intercept] +fitpow.fix_bg_parameters(1:2); % fix slopes to initial value (0) +fitpow.set_bg_parameter_bounds(3, 0.0, []) % Set lb of constant bg = 0 +% fit background +fitpow.fit_background(); +fitpow.fix_bg_parameters(3); % fix fitted constant bg + +% set bounds on first (and only in this case) model parameter +fitpow.set_model_parameter_bounds(1, 0, []) % Force J_1 to be AFM + +[pfit, cost_val, stat] = fitpow.fit(); + +% plot 2D colorfill +fitpow.plot_result(pfit, 10, 'EdgeAlpha', 0.9, 'LineWidth', 1 ,'EdgeColor', 'k') + +% make 1D plots +qcens = [0.8:0.4:1.6]; +dq = 0.05; +fitpow.plot_1d_cuts_of_2d_data(qcens-dq, qcens+dq, pfit) + + +%% Fit 1D cuts +% As discussed the sw_fitpowder class can be initialised with a cell array +% of xye structs correpsonding to 1D cuts at constant |Q|. +% Alternatively, having loaded in 2D data the sw_fitpowder class has a +% convenient method to take 1D cuts and replace the data. +% +% To evaluate the cost function for 1D cuts, the class averages the model +% over nQ points. Depending on the size of the 2D data and the value of nQ +% it can be much quicker to fit 1D cuts. +% +% The background for 1D cuts can be handled in two ways: +% +% - A planar background as in the 2D case +% +% - A linear background in energy transfer that's independent for each cut. +% +% The background parameters and bounds are reset if the background +% strategy is changed to independent. + +% set nQ before replacing data (reduced from default, 10, for speed) +fitpow.nQ = 5; +% change background strategyto independent (planar is default) +fitpow.replace_2D_data_with_1D_cuts(qcens-dq, qcens+dq, "independent"); + +% independent linear background for all cuts with parameters: +% [slope_energy, intercept] +fitpow.fix_bg_parameters(1); % fix slopes to initial value (0) for all cuts +% e.g. fitpow.fix_bg_parameters(1, 2) would fix the bg slope of the second cut +fitpow.set_bg_parameter_bounds(2, 0.0, []) % Set lb of constant bg = 0 +% fit background +fitpow.estimate_constant_background(); +fitpow.fit_background(); +fitpow.fix_bg_parameters(2); % fix fitted constant bg + +[pfit, cost_val, stat] = fitpow.fit(); + +fitpow.plot_result(pfit) + + + diff --git a/tutorials/publish/tutorial39/tutorial39.html b/tutorials/publish/tutorial39/tutorial39.html new file mode 100644 index 000000000..2fc5c99f2 --- /dev/null +++ b/tutorials/publish/tutorial39/tutorial39.html @@ -0,0 +1,374 @@ + + + + + Description

Description

This tutorial fits a spinwave model to simulated powder data.

Contents

Define instrument resolution parameters for MARI

This is a simplified parameterisation of the resolution of a Time-of-Flight spectrometer which will be used to broaden the simulated data. These parameters will depend on the instrument used - the instrument contact should be able to provide these.

Ei = 20; % meV
+
+% Resolution for MARI with Gd chopper running at 200Hz and Ei=20meV (from PyChop)
+eres = @(en) 2.1750e-04*sqrt((Ei-en).^3 .* ( (32.27217*(0.168+0.400*(Ei./(Ei-en)).^1.5)).^2 + (14.53577*(1.168+0.400*(Ei./(Ei-en)).^1.5)).^2) );
+% Q-resolution (parameters for MARI)
+e2k = @(en) sqrt( en .* (2*1.67492728e-27*1.60217653e-22) )./1.05457168e-34./1e10;
+L1 = 11.8;  % Moderator to Sample distance in m
+L2 = 4.0;   % Sample to detector distance in m
+ws = 0.05;  % Width of sample in m
+wm = 0.12;  % Width of moderator in m
+wd = 0.025; % Width of detector in m
+ki = e2k(Ei);
+a1 = ws/L1; % Angular width of sample seen from moderator
+a2 = wm/L1; % Angular width of moderator seen from sample
+a3 = wd/L2; % Angular width of detector seen from sample
+a4 = ws/L2; % Angular width of sample seen from detector
+dQ = 2.35 * sqrt( (ki*a1)^2/12 + (ki*a2)^2/12 + (ki*a3)^2/12 + (ki*a4)^2/12 );
+

Generate data

Simulate a powder spectrum of a triangular AFM with constant background and normally distributed noise. This can also be done using the powder fitting class if an empty data array is passed.

% intialise spinw model
+tri = sw_model('triAF',1);
+scale = 1000;
+
+% calculate powder spectrum
+E = linspace(0,4,80);
+Q = linspace(0.1,3,60);
+spec = tri.powspec(Q,'Evect',E,'nRand',2e2);
+% scale data and add background
+spec.swConv= scale*(spec.swConv + 0.1*mean(spec.swConv, 'all'));
+% crop to kinematic range of instrument and apply some arbitrary resolution
+spec = sw_instrument(spec, 'dQ', dQ, 'dE', eres, 'ThetaMin', 3.5, 'Ei', Ei);
+% add noise
+e = sqrt(spec.swConv);
+spec.swConv = spec.swConv + e.*randn(size(spec.swConv));
+
+% make xye struct containing data
+data = struct('x', {{0.5*(E(1:end-1) + E(2:end)), Q}}, ...
+              'y', spec.swConv', ...
+              'e', e');
+

Initialise the sw_fitpowder class and plot data to inspect initial guess

To initialise the powder fitting class (sw_fitpowder) object requires a spinw model with a magnetic strucutre and couplings added. Additional arguments are the data (can be xye structs for 2D data a cell array of xye structs for 1D data, or HORACE objects - see sw_fitpowder help for more details), a fit function which alters the matrices on the spinw object and a vector of initial guesses for the fit parameters.

Optinally a background strategy can be specified as a 5th positional argument ("planar" background in energy transfer and Q or "independent" background for each 1D cut (1D only)).

The class will call other spinw algorithms such as powspec and sw_instrument. The parameters used in these calls can be set by the user by modifying structs as shown below.

Data can be cropped in Q and energy transfer - for example it is advisible not to include the low-energy transfer region close to the elastic line (relative to the resolution).

fit_func =  @(obj, p) matparser(obj, 'param', p, 'mat', {'J_1'}, 'init', true);
+J1 = 0.85;
+
+fitpow = sw_fitpowder(tri, data,  fit_func, [J1]);
+fitpow.set_caching(true); % will store last calculated spectra
+
+% set parameters passed to powspec
+fitpow.powspec_args.dE = eres; % emergy resolution
+fitpow.powspec_args.fastmode = true;
+fitpow.powspec_args.neutron_output = true;
+fitpow.powspec_args.nRand = 2e2; % low for speed (typically want > 1e3)
+fitpow.powspec_args.hermit = true;
+% set parameters passsed to sw_instrument
+fitpow.sw_instrument_args = struct('dQ', dQ, 'ThetaMin', 3.5, 'Ei', Ei);
+
+% crop data
+fitpow.crop_energy_range(1.5*eres(0), inf); % typically want to avoid elastic line
+fitpow.crop_q_range(0.25, 3);
+fitpow.powspec_args.dE = eres;
+fitpow.powspec_args.fastmode = true;
+fitpow.powspec_args.neutron_output = true;
+
+% estimate background and scale factor
+fitpow.estimate_constant_background();
+fitpow.estimate_scale_factor();
+
+
+% plot data to inspect - any arguments after parameters are passed to
+% contour plot (which shows the result the calculated intensity)
+fitpow.plot_result(fitpow.params, 'EdgeAlpha', 0.9, 'LineWidth', 1 ,'EdgeColor', 'k');
+

Fit and inspect the result

It can be desirable to set bounds on fit parameters and fix some parameters initially to get a reasonable fit with as few degrees of freedom as possible. For example one might assume the background is constant in an initial fit.

The cost function minimised in the fit can be chi-squared ("chisq") or the unweighted sum of the squared residuals ("Rsq"). Also the minimiser can be set to any callable as long as it shares the API of the ndbase minimisers. Typically users would be recommended ndbase.lm or ndbase.simplex.

% set cost function and minimser
+fitpow.cost_function = "Rsq";  % "Rsq" or "chisq"
+fitpow.optimizer = @ndbase.simplex; % or e.g. ndbase.simplex
+
+% Fix background parameters (planar background of form
+% default background is planar with parameters:
+% [slope_energy, slope_modQ,  intercept]
+fitpow.fix_bg_parameters(1:2); % fix slopes to initial value (0)
+fitpow.set_bg_parameter_bounds(3, 0.0, []) % Set lb of constant bg = 0
+% fit background
+fitpow.fit_background();
+fitpow.fix_bg_parameters(3); % fix fitted constant bg
+
+% set bounds on first (and only in this case) model parameter
+fitpow.set_model_parameter_bounds(1, 0, []) % Force J_1 to be AFM
+
+[pfit, cost_val, stat] = fitpow.fit();
+
+% plot 2D colorfill
+fitpow.plot_result(pfit, 10,  'EdgeAlpha', 0.9, 'LineWidth', 1 ,'EdgeColor', 'k')
+
+% make 1D plots
+qcens = [0.8:0.4:1.6];
+dq = 0.05;
+fitpow.plot_1d_cuts_of_2d_data(qcens-dq, qcens+dq, pfit)
+

Fit 1D cuts

As discussed the sw_fitpowder class can be initialised with a cell array of xye structs correpsonding to 1D cuts at constant Q. Alternatively, having loaded in 2D data the sw_fitpowder class has a convenient method to take 1D cuts and replace the data.

To evaluate the cost function for 1D cuts, the class averages the model over nQ points. Depending on the size of the 2D data and the value of nQ it can be much quicker to fit 1D cuts.

The background for 1D cuts can be handled in two ways:

- A planar background as in the 2D case
- A linear background in energy transfer that's independent for each cut.

The background parameters and bounds are reset if the background strategy is changed to independent.

% set nQ before replacing data (reduced from default, 10, for speed)
+fitpow.nQ = 5;
+% change background strategyto independent (planar is default)
+fitpow.replace_2D_data_with_1D_cuts(qcens-dq, qcens+dq, "independent");
+
+% independent linear background for all cuts with parameters:
+% [slope_energy,  intercept]
+fitpow.fix_bg_parameters(1); % fix slopes to initial value (0) for all cuts
+% e.g. fitpow.fix_bg_parameters(1, 2) would fix the bg slope of the second cut
+fitpow.set_bg_parameter_bounds(2, 0.0, []) % Set lb of constant bg = 0
+% fit background
+fitpow.estimate_constant_background();
+fitpow.fit_background();
+fitpow.fix_bg_parameters(2); % fix fitted constant bg
+
+[pfit, cost_val, stat]  = fitpow.fit();
+
+fitpow.plot_result(pfit)
+
Warning: Clearing 2D data previously added. 
+Warning: Overwriting background parmaweters with 0. 
+Warning: Background strategy changed - background parameters and bounds
+will be cleared. 
+
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Description

This tutorial fits a spinwave model to simulated powder data.

Contents

Define instrument resolution parameters for MARI

This is a simplified parameterisation of the resolution of a Time-of-Flight spectrometer which will be used to broaden the simulated data. These parameters will depend on the instrument used - the instrument contact should be able to provide these.

Ei = 20; % meV
+
+% Resolution for MARI with Gd chopper running at 200Hz and Ei=20meV (from PyChop)
+eres = @(en) 2.1750e-04*sqrt((Ei-en).^3 .* ( (32.27217*(0.168+0.400*(Ei./(Ei-en)).^1.5)).^2 + (14.53577*(1.168+0.400*(Ei./(Ei-en)).^1.5)).^2) );
+% Q-resolution (parameters for MARI)
+e2k = @(en) sqrt( en .* (2*1.67492728e-27*1.60217653e-22) )./1.05457168e-34./1e10;
+L1 = 11.8;  % Moderator to Sample distance in m
+L2 = 4.0;   % Sample to detector distance in m
+ws = 0.05;  % Width of sample in m
+wm = 0.12;  % Width of moderator in m
+wd = 0.025; % Width of detector in m
+ki = e2k(Ei);
+a1 = ws/L1; % Angular width of sample seen from moderator
+a2 = wm/L1; % Angular width of moderator seen from sample
+a3 = wd/L2; % Angular width of detector seen from sample
+a4 = ws/L2; % Angular width of sample seen from detector
+dQ = 2.35 * sqrt( (ki*a1)^2/12 + (ki*a2)^2/12 + (ki*a3)^2/12 + (ki*a4)^2/12 );
+

Generate data

Simulate a powder spectrum of a triangular AFM with constant background and normally distributed noise. This can also be done using the powder fitting class if an empty data array is passed.

% intialise spinw model
+tri = sw_model('triAF',1);
+scale = 1000;
+
+% calculate powder spectrum
+E = linspace(0,4,80);
+Q = linspace(0.1,3,60);
+spec = tri.powspec(Q,'Evect',E,'nRand',2e2);
+% scale data and add background
+spec.swConv= scale*(spec.swConv + 0.1*mean(spec.swConv, 'all'));
+% crop to kinematic range of instrument and apply some arbitrary resolution
+spec = sw_instrument(spec, 'dQ', dQ, 'dE', eres, 'ThetaMin', 3.5, 'Ei', Ei);
+% add noise
+e = sqrt(spec.swConv);
+spec.swConv = spec.swConv + e.*randn(size(spec.swConv));
+
+% make xye struct containing data
+data = struct('x', {{0.5*(E(1:end-1) + E(2:end)), Q}}, ...
+              'y', spec.swConv', ...
+              'e', e');
+

Initialise the sw_fitpowder class and plot data to inspect initial guess

To initialise the powder fitting class (sw_fitpowder) object requires a spinw model with a magnetic strucutre and couplings added. Additional arguments are the data (can be xye structs for 2D data a cell array of xye structs for 1D data, or HORACE objects - see sw_fitpowder help for more details), a fit function which alters the matrices on the spinw object and a vector of initial guesses for the fit parameters.

Optinally a background strategy can be specified as a 5th positional argument ("planar" background in energy transfer and Q or "independent" background for each 1D cut (1D only)).

The class will call other spinw algorithms such as powspec and sw_instrument. The parameters used in these calls can be set by the user by modifying structs as shown below.

Data can be cropped in Q and energy transfer - for example it is advisible not to include the low-energy transfer region close to the elastic line (relative to the resolution).

fit_func =  @(obj, p) matparser(obj, 'param', p, 'mat', {'J_1'}, 'init', true);
+J1 = 0.85;
+
+fitpow = sw_fitpowder(tri, data,  fit_func, [J1]);
+fitpow.set_caching(true); % will store last calculated spectra
+
+% set parameters passed to powspec
+fitpow.powspec_args.dE = eres; % emergy resolution
+fitpow.powspec_args.fastmode = true;
+fitpow.powspec_args.neutron_output = true;
+fitpow.powspec_args.nRand = 2e2; % low for speed (typically want > 1e3)
+fitpow.powspec_args.hermit = true;
+% set parameters passsed to sw_instrument
+fitpow.sw_instrument_args = struct('dQ', dQ, 'ThetaMin', 3.5, 'Ei', Ei);
+
+% crop data
+fitpow.crop_energy_range(1.5*eres(0), inf); % typically want to avoid elastic line
+fitpow.crop_q_range(0.25, 3);
+fitpow.powspec_args.dE = eres;
+fitpow.powspec_args.fastmode = true;
+fitpow.powspec_args.neutron_output = true;
+
+% estimate background and scale factor
+fitpow.estimate_constant_background();
+fitpow.estimate_scale_factor();
+
+
+% plot data to inspect - any arguments after parameters are passed to
+% contour plot (which shows the result the calculated intensity)
+fitpow.plot_result(fitpow.params, 'EdgeAlpha', 0.9, 'LineWidth', 1 ,'EdgeColor', 'k');
+

Fit and inspect the result

It can be desirable to set bounds on fit parameters and fix some parameters initially to get a reasonable fit with as few degrees of freedom as possible. For example one might assume the background is constant in an initial fit.

The cost function minimised in the fit can be chi-squared ("chisq") or the unweighted sum of the squared residuals ("Rsq"). Also the minimiser can be set to any callable as long as it shares the API of the ndbase minimisers. Typically users would be recommended ndbase.lm or ndbase.simplex.

% set cost function and minimser
+fitpow.cost_function = "Rsq";  % "Rsq" or "chisq"
+fitpow.optimizer = @ndbase.simplex; % or e.g. ndbase.simplex
+
+% Fix background parameters (planar background of form
+% default background is planar with parameters:
+% [slope_energy, slope_modQ,  intercept]
+fitpow.fix_bg_parameters(1:2); % fix slopes to initial value (0)
+fitpow.set_bg_parameter_bounds(3, 0.0, []) % Set lb of constant bg = 0
+% fit background
+fitpow.fit_background();
+fitpow.fix_bg_parameters(3); % fix fitted constant bg
+
+% set bounds on first (and only in this case) model parameter
+fitpow.set_model_parameter_bounds(1, 0, []) % Force J_1 to be AFM
+
+[pfit, cost_val, stat] = fitpow.fit();
+
+% plot 2D colorfill
+fitpow.plot_result(pfit, 10,  'EdgeAlpha', 0.9, 'LineWidth', 1 ,'EdgeColor', 'k')
+
+% make 1D plots
+qcens = [0.8:0.4:1.6];
+dq = 0.05;
+fitpow.plot_1d_cuts_of_2d_data(qcens-dq, qcens+dq, pfit)
+

Fit 1D cuts

As discussed the sw_fitpowder class can be initialised with a cell array of xye structs correpsonding to 1D cuts at constant Q. Alternatively, having loaded in 2D data the sw_fitpowder class has a convenient method to take 1D cuts and replace the data.

To evaluate the cost function for 1D cuts, the class averages the model over nQ points. Depending on the size of the 2D data and the value of nQ it can be much quicker to fit 1D cuts.

The background for 1D cuts can be handled in two ways:

- A planar background as in the 2D case
- A linear background in energy transfer that's independent for each cut.

The background parameters and bounds are reset if the background strategy is changed to independent.

% set nQ before replacing data (reduced from default, 10, for speed)
+fitpow.nQ = 5;
+% change background strategyto independent (planar is default)
+fitpow.replace_2D_data_with_1D_cuts(qcens-dq, qcens+dq, "independent");
+
+% independent linear background for all cuts with parameters:
+% [slope_energy,  intercept]
+fitpow.fix_bg_parameters(1); % fix slopes to initial value (0) for all cuts
+% e.g. fitpow.fix_bg_parameters(1, 2) would fix the bg slope of the second cut
+fitpow.set_bg_parameter_bounds(2, 0.0, []) % Set lb of constant bg = 0
+% fit background
+fitpow.estimate_constant_background();
+fitpow.fit_background();
+fitpow.fix_bg_parameters(2); % fix fitted constant bg
+
+[pfit, cost_val, stat]  = fitpow.fit();
+
+fitpow.plot_result(pfit)
+
Warning: Clearing 2D data previously added. 
+Warning: Overwriting background parmaweters with 0. 
+Warning: Background strategy changed - background parameters and bounds
+will be cleared. 
+
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