function [fitResults, rawCurves] = fitTwoGaussianCurves(S_theta_all, theta_vals, varargin)
%% fitTwoGaussianCurves
% Fits a two-Gaussian model to multiple spectral curves from θ=0 up to
% the first secondary peak ≥50% of the primary peak, within 0–π/2 radians.
%
% Author: Karthik
% Date: 2025-10-06
% Version: 1.1
%
% Inputs:
%   S_theta_all - 1xN cell array of spectral curves
%   theta_vals  - vector of corresponding theta values (radians)
%
% Optional name-value pairs:
%   'MaxTheta'           - Maximum theta for search (default: pi/2)
%   'ResidualThreshold'     - Max relative deviation allowed (default: 0.3)
%   'PositionThreshold'  - Minimum angular separation between main and
%                          secondary peaks (default: 0.1 rad)
%   'AmplitudeThreshold' - Minimum fraction of primary peak amplitude for secondary peak (default: 0.5)
%
% Output:
%   fitResults - struct array with fields:
%       .pFit, .thetaFit, .xFit, .yFit, .thetaFine, .isValid, .fitMaxTheta

    % --- Parse optional inputs ---
    p = inputParser;
    addParameter(p, 'MaxTheta', pi/2, @(x) isnumeric(x) && isscalar(x));
    addParameter(p, 'ResidualThreshold', 0.3, @(x) isnumeric(x) && isscalar(x));
    addParameter(p, 'PositionThreshold', 0.1, @(x) isnumeric(x) && isscalar(x));
    addParameter(p, 'AmplitudeThreshold', 0.5, @(x) isnumeric(x) && isscalar(x));
    addParameter(p, 'RecenterCurves', true, @islogical);
    parse(p, varargin{:});
    opts = p.Results;

    Ncurves = numel(S_theta_all);
    fitResults = struct('pFit',[],'thetaFit',[],'xFit',[],'yFit',[],...
                    'thetaFine',[],'isValid',[],'fitMaxTheta',[]);

    rawCurves = struct('x', cell(1, Ncurves), 'theta', cell(1, Ncurves));
    
    if opts.RecenterCurves
        % --- Preprocess curves: shift first peak to zero without wrapping ---
        S_theta_all_shifted = cell(size(S_theta_all));
        for k = 1:Ncurves
            curve = S_theta_all{k};
    
            idx_range = find(theta_vals >= 0 & theta_vals <= opts.MaxTheta);
            if isempty(idx_range)
                [~, peak_idx] = max(curve);
            else
                [~, local_max_idx] = max(curve(idx_range));
                peak_idx = idx_range(local_max_idx);
            end
    
            S_theta_all_shifted{k} = curve(peak_idx:end);
        end
    
        % --- Pad curves to same length ---
        Npoints_shifted = max(cellfun(@numel, S_theta_all_shifted));
        for k = 1:Ncurves
            len = numel(S_theta_all_shifted{k});
            if len < Npoints_shifted
                S_theta_all_shifted{k} = [S_theta_all_shifted{k}, nan(1, Npoints_shifted-len)];
            end
        end
    
        theta_recentered = theta_vals(1:Npoints_shifted) - theta_vals(1);
    else
        S_theta_all_shifted = S_theta_all;
        theta_recentered    = theta_vals;
    end

    for k = 1:Ncurves

        x        = S_theta_all_shifted{k};
        theta    = theta_recentered;

        validIdx = ~isnan(x);
        x        = x(validIdx);
        theta    = theta(validIdx);

        mask     = theta>=0 & theta<=opts.MaxTheta;
        x        = x(mask);
        theta    = theta(mask);
        
        x        = x / x(1);

        % --- Store raw data for plotting ---
        rawCurves(k).x     = x;
        rawCurves(k).theta = theta;

        try
            % --- Filter 1: Ensure curve covers full 0–MaxTheta range ---
            thetaRange = max(theta) - min(theta);
            if thetaRange < 0.9 * opts.MaxTheta
                warning('Curve %d excluded: does not span full 0–MaxTheta range.', k);
                fitResults(k)           = fillZeroStruct(theta, opts.MaxTheta);
                continue;
            end

            if numel(theta) < 8
                warning('Curve %d too short (<8 points), skipping.', k);
                fitResults(k)           = fillNaNStruct();
                continue;
            end
    
            xSmooth        = smooth(x, 5, 'moving');
            curveAmp       = max(xSmooth) - min(xSmooth);
    
            %% 1) Attempt primary detection via findpeaks
            minProm        = opts.AmplitudeThreshold * curveAmp;
            [pk, locIdx]   = findpeaks(xSmooth, 'MinPeakProminence', minProm);
            thetaPeaks     = theta(locIdx);
    
            foundSecondary = false;
            fitMaxTheta    = [];
            secondaryAmp   = [];
    
            secondaryIdx = find(thetaPeaks > opts.PositionThreshold, 1, 'first');
            if ~isempty(secondaryIdx)
                foundSecondary = true;
                fitMaxTheta    = thetaPeaks(secondaryIdx);
                secondaryAmp   = pk(secondaryIdx);
            end
    
            %% 2) If secondary found, fit constrained two-Gaussian directly
            if foundSecondary
                twoGauss = @(p,theta) ...
                    1.0 * exp(-0.5*((theta - p(1))/max(p(2),1e-6)).^2) + ...
                    p(3) * exp(-0.5*((theta - p(4))/max(p(5),1e-6)).^2);
    
                mu1_guess    = 0;
                sigma1_guess = 0.1 * fitMaxTheta;
                A2_guess     = secondaryAmp;
                mu2_guess    = fitMaxTheta;
                sigma2_guess = fitMaxTheta / 3;
                p0           = [mu1_guess, sigma1_guess, A2_guess, mu2_guess, sigma2_guess];
    
                lb           = [0, 1e-6, 0, max(fitMaxTheta - 0.1, 0), 1e-6];
                ub           = [fitMaxTheta/4, fitMaxTheta, 2, min(fitMaxTheta + 0.1, opts.MaxTheta), fitMaxTheta];
    
                optsLSQ      = optimoptions('lsqcurvefit','Display','off', ...
                                       'MaxFunctionEvaluations',1e4,'MaxIterations',1e4);
    
                try
                    pFit     = lsqcurvefit(twoGauss, p0, theta, x, lb, ub, optsLSQ);

                    % --- Handle missing or weak secondary peak, discard poor fits ---
                    if pFit(3) <= opts.AmplitudeThreshold
                        % amplitude too small → discard secondary
                        pFit(3) = 0;
                        pFit(4:5) = NaN;
                    else
                        % --- Compute RMS of fit vs raw curve in [0, pi/4] ---
                        maskRMS = theta >= 0 & theta <= pi/4;
                        if any(maskRMS)
                            x_raw_subset = x(maskRMS);
                            y_fit_subset = twoGauss(pFit, theta(maskRMS));
                            rms_val      = sqrt(mean((x_raw_subset - y_fit_subset).^2));
                            if rms_val > opts.ResidualThreshold
                                % residual too large → discard secondary
                                pFit(3)   = NaN;
                                pFit(4:5) = NaN;
                            end
                        end
                    end
                    
                    % --- Map to canonical format with primary amplitude = 1 ---
                    pCanonical = [1.0, pFit(1), pFit(2), pFit(3), pFit(4), pFit(5)];
            
                    thetaFine                 = linspace(0, opts.MaxTheta, 500);
                    yFit                      = 1.0*exp(-0.5*((thetaFine - pCanonical(2))/max(pCanonical(3),1e-6)).^2) + ...
                                                 pCanonical(4)*exp(-0.5*((thetaFine - pCanonical(5))/max(pCanonical(6),1e-6)).^2);
            
                    fitResults(k).pFit        = pCanonical;
                    fitResults(k).thetaFit    = theta;
                    fitResults(k).xFit        = x;
                    fitResults(k).thetaFine   = thetaFine;
                    fitResults(k).yFit        = yFit;
                    fitResults(k).isValid     = true;
                    fitResults(k).fitMaxTheta = fitMaxTheta;
                    continue; % success → next curve
                catch
                    warning('Curve %d constrained fit failed, switching to generic fit.', k);
                end
            end
    
            %% 3) Generic two-Gaussian fallback (no or failed secondary detection)
            try
                twoGaussFree = @(p,th) ...
                    p(1)*exp(-0.5*((th - p(2))/max(p(3),1e-6)).^2) + ...
                    p(4)*exp(-0.5*((th - p(5))/max(p(6),1e-6)).^2);
    
                p0  = [1, 0, 0.1, 0.3, opts.MaxTheta/3, 0.1];
                lb  = [0, 0, 1e-6, 0, opts.PositionThreshold, 1e-6];
                ub  = [2, opts.MaxTheta/2, opts.MaxTheta, 2, opts.MaxTheta, opts.MaxTheta];
    
                optsLSQfree = optimoptions('lsqcurvefit', 'Display', 'off', ...
                    'MaxFunctionEvaluations', 2e4, 'MaxIterations', 2e4);
    
                pFree    = lsqcurvefit(twoGaussFree, p0, theta(:), xSmooth(:), lb, ub, optsLSQfree);
                
                % --- Handle missing secondary peak ---
                if pFree(4) <= 1e-3
                    pFree(4)   = 0;     % secondary amplitude = 0
                    pFree(5:6) = NaN;   % secondary position & width = NaN
                end
                
                fitMaxTheta = max(pFree(5), pFree(2));
                thetaFine   = linspace(0, opts.MaxTheta, 500);
                yFit        = twoGaussFree(pFree, thetaFine);

                fitResults(k).pFit        = pFree;
                fitResults(k).thetaFit    = theta;
                fitResults(k).xFit        = x;
                fitResults(k).thetaFine   = thetaFine;
                fitResults(k).yFit        = yFit;
                fitResults(k).isValid     = true;
                fitResults(k).fitMaxTheta = fitMaxTheta;
            catch
                warning('Curve %d: generic two-Gaussian fit failed.', k);
                fitResults(k) = fillNaNStruct();
            end
    
        catch
            warning('Curve %d fit failed completely.', k);
            fitResults(k)           = fillNaNStruct();
        end
    end
end

% --- Helper: return struct with NaNs (fit failed) ---
function s = fillNaNStruct()
    s = struct( ...
        'pFit',        nan(1,5), ...
        'thetaFit',    nan, ...
        'xFit',        nan, ...
        'yFit',        nan, ...
        'thetaFine',   nan, ...
        'isValid',     false, ...
        'fitMaxTheta', nan ...
     );
end


% --- Helper: return struct with zeros (no secondary peak found) ---
function s = fillZeroStruct(theta, fitMaxTheta)
    s = struct( ...
        'pFit',        zeros(1,5), ...
        'thetaFit',    theta, ...
        'xFit',        zeros(size(theta)), ...
        'yFit',        zeros(size(theta)), ...
        'thetaFine',   zeros(1,500), ...
        'isValid',     false, ...
        'fitMaxTheta', fitMaxTheta ...
    );
end