141 lines
5.4 KiB
Matlab
141 lines
5.4 KiB
Matlab
function [fitResults, rawCurves] = fitSingleGaussianCurvesToRadialSpectralDistribution(S_k_all, k_rho_vals, varargin)
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%% fitSingleGaussianCurvesToRadialSpectralDistribution
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% Fits a single-Gaussian model to multiple radial spectral curves (S(k_rho)),
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% truncating each curve to user-specified k_rho range.
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%
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% Inputs:
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% S_k_all - 1xN cell array of radial spectral curves
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% k_rho_vals - vector of corresponding k_rho values
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%
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% Optional name-value pairs:
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% 'KRhoRange' - [k_min, k_max] (default: [min(k_rho_vals), max(k_rho_vals)])
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% 'ResidualThreshold' - threshold for residual validation (default: 0.3)
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%
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% Outputs:
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% fitResults - struct array with fields:
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% .pFit, .kFit, .xFit, .yFit, .kFine, .isValid, .residual, .maxAbs, .R2, .fitMaxKRho
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% rawCurves - struct array of truncated raw curves for plotting
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% --- Parse optional inputs ---
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p = inputParser;
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addParameter(p, 'KRhoRange', [min(k_rho_vals), max(k_rho_vals)], @(x) isnumeric(x) && numel(x)==2);
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addParameter(p, 'ResidualThreshold', 0.3, @(x) isnumeric(x) && isscalar(x));
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parse(p, varargin{:});
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opts = p.Results;
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Ncurves = numel(S_k_all);
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fitResults = struct('pFit',[],'kFit',[],'xFit',[],'yFit',[],...
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'kFine',[],'isValid',[],'residual',[],'maxAbs',[],'R2',[],'fitMaxKRho',[]);
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rawCurves = struct('x', cell(1, Ncurves), 'k', cell(1, Ncurves));
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for k = 1:Ncurves
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% --- Truncate curve to k_rho and amplitude ranges ---
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xRaw = S_k_all{k};
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% --- Normalize and smooth ---
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xNorm = xRaw / max(xRaw);
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xSmooth = smooth(xNorm, 5, 'moving');
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mask = (k_rho_vals(:) >= opts.KRhoRange(1)) & (k_rho_vals(:) <= opts.KRhoRange(2));
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x = xSmooth(mask);
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kVals = k_rho_vals(mask);
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rawCurves(k).x = x;
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rawCurves(k).k = kVals;
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if any(isnan(xRaw))
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warning('Curve %d has NaNs, skipping.', k);
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fitResults(k) = fillNaNStructRadial();
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continue;
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elseif numel(x) < 5
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warning('Curve %d has too few points after truncation, skipping.', k);
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fitResults(k) = fillNaNStructRadial();
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continue;
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elseif isempty(x)
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warning('Curve %d is empty after truncation.', k);
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fitResults(k) = fillZeroStructRadial(kVals, opts.KRhoRange(2));
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continue;
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end
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try
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%% Single Gaussian fit with offset: A*exp(-(k-mu)^2/(2*sigma^2)) + C
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singleGauss = @(p,k) p(1) * exp(-0.5*((k - p(2))/max(p(3),1e-6)).^2) + p(4);
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% Initial guess
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[~, idxMax] = max(x);
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A_guess = x(idxMax) - min(x); % amplitude above baseline
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mu_guess = kVals(idxMax);
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sigma_guess = 0.1 * (opts.KRhoRange(2)-opts.KRhoRange(1));
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C_guess = min(x); % baseline offset
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p0 = [A_guess, mu_guess, sigma_guess, C_guess];
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lb = [0, opts.KRhoRange(1), 1e-6, -Inf];
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ub = [2*max(x), opts.KRhoRange(2), opts.KRhoRange(2), Inf];
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optsLSQ = optimoptions('lsqcurvefit','Display','off', ...
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'MaxFunctionEvaluations',1e4,'MaxIterations',1e4);
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pFit = lsqcurvefit(singleGauss, p0, kVals(:), x(:), lb, ub, optsLSQ);
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% --- Post-fit diagnostics ---
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r = x(:) - singleGauss(pFit, kVals(:));
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residualRMS = sqrt(mean(r.^2));
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maxAbsR = max(abs(r));
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kFine = linspace(min(kVals), max(kVals), 500);
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yFit = singleGauss(pFit, kFine);
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fitMaxKRho = pFit(2);
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SS_res = sum(r.^2);
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SS_tot = sum((x(:) - mean(x(:))).^2);
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R2 = 1 - SS_res/SS_tot;
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% Store results
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fitResults(k).pFit = pFit;
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fitResults(k).kFit = kVals;
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fitResults(k).xFit = x;
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fitResults(k).kFine = kFine;
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fitResults(k).yFit = yFit;
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fitResults(k).isValid = residualRMS <= opts.ResidualThreshold;
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fitResults(k).residual = residualRMS;
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fitResults(k).maxAbs = maxAbsR;
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fitResults(k).R2 = R2;
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fitResults(k).fitMaxKRho = fitMaxKRho;
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catch
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warning('Curve %d fit failed completely.', k);
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fitResults(k) = fillNaNStructRadial();
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end
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end
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end
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%% --- Helper: NaN struct for failed fits ---
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function s = fillNaNStructRadial()
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s = struct( ...
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'pFit', nan(1,3), ...
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'kFit', nan, ...
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'xFit', nan, ...
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'yFit', nan, ...
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'kFine', nan, ...
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'isValid', false, ...
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'residual', nan, ...
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'maxAbs', nan, ...
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'R2', nan, ...
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'fitMaxKRho', nan ...
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);
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end
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%% --- Helper: Zero struct for empty curves ---
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function s = fillZeroStructRadial(kVals, MaxKRho)
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s = struct( ...
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'pFit', zeros(1,3), ...
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'kFit', kVals, ...
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'xFit', zeros(size(kVals)), ...
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'yFit', zeros(size(kVals)), ...
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'kFine', zeros(1,500), ...
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'isValid', false, ...
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'residual', zeros(size(kVals)), ...
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'maxAbs', zeros(size(kVals)), ...
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'R2', zeros(size(kVals)), ...
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'fitMaxKRho', MaxKRho ...
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);
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end
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