Major corrections to gradient descent code and associated plotting.
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Karthik
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cf5d3fd209
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@ -15,7 +15,7 @@ function plotLive(psi,Params,Transf,Observ,SimulationMode)
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n = abs(psi).^2;
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switch SimulationMode
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case {'ImaginaryTimeEvolution', 'EnergyMinimization'}
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case 'ImaginaryTimeEvolution'
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%Plotting
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fig = figure(1);
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fig.WindowState = 'maximized';
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@ -77,6 +77,68 @@ function plotLive(psi,Params,Transf,Observ,SimulationMode)
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title('Chemical Potential', 'FontSize', 14);
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grid on
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case 'EnergyMinimization'
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%Plotting
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fig = figure(1);
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fig.WindowState = 'maximized';
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clf
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% set(gcf,'Position', [100, 100, 1600, 900])
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t = tiledlayout(2, 3, 'TileSpacing', 'compact', 'Padding', 'compact'); % 2x3 grid
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nexttile;
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nxz = squeeze(trapz(n*dy,2));
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nyz = squeeze(trapz(n*dx,1));
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nxy = squeeze(trapz(n*dz,3));
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plotxz = pcolor(x,z,nxz');
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set(plotxz, 'EdgeColor', 'none');
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cbar1 = colorbar;
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cbar1.Label.Interpreter = 'latex';
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% cbar1.Ticks = []; % Disable the ticks
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colormap(gca, Helper.Colormaps.plasma())
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xlabel('$x$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
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ylabel('$z$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
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title('$|\Psi(x,z)|^2$', 'Interpreter', 'latex', 'FontSize', 14)
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nexttile;
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plotyz = pcolor(y,z,nyz');
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set(plotyz, 'EdgeColor', 'none');
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cbar1 = colorbar;
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cbar1.Label.Interpreter = 'latex';
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% cbar1.Ticks = []; % Disable the ticks
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colormap(gca, Helper.Colormaps.plasma())
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xlabel('$y$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
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ylabel('$z$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
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title('$|\Psi(y,z)|^2$', 'Interpreter', 'latex', 'FontSize', 14)
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nexttile;
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plotxy = pcolor(x,y,nxy');
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set(plotxy, 'EdgeColor', 'none');
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cbar1 = colorbar;
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cbar1.Label.Interpreter = 'latex';
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% cbar1.Ticks = []; % Disable the ticks
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colormap(gca, Helper.Colormaps.plasma())
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xlabel('$x$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
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ylabel('$y$ ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14)
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title('$|\Psi(x,y)|^2$', 'Interpreter', 'latex', 'FontSize', 14)
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nexttile;
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plot(Observ.theta,'-b')
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ylabel('$\theta_{opt}$', 'FontSize', 14); xlabel('Time steps', 'FontSize', 14);
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title('Optimal angle', 'FontSize', 14);
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grid on
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nexttile;
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plot(Observ.EVec,'-b')
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ylabel('$E_{tot}$', 'FontSize', 14); xlabel('Time steps', 'FontSize', 14);
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title('Total Energy', 'FontSize', 14);
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grid on
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nexttile;
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plot(Observ.mucVec,'-b')
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ylabel('$\mu$', 'FontSize', 14); xlabel('Time steps', 'FontSize', 14);
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title('Chemical Potential', 'FontSize', 14);
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grid on
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case 'RealTimeEvolution'
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%Plotting
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@ -94,6 +94,7 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
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i = 1;
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Observ.residual = 1;
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Observ.res = 1;
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Observ.theta = 0;
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% Initialize the PrematureExitFlag to false
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PrematureExitFlag = false;
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@ -109,24 +110,23 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
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% Compute gradient
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J = compute_gradient(psi, Params, Transf, VDk, V);
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% Calculate chemical potential
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muchem = real(psi(:)' * J(:)) / sum(abs(psi(:)).^2);
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muchem = real(inner_product(psi, J, Transf)) / inner_product(psi, psi, Transf);
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% Calculate residual
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residual = J - (muchem * psi);
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% Compute energy difference between the last two saved energy values
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if i == 1
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energydifference = NaN;
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elseif mod(i,100) == 0 && length(Observ.EVec) > 1
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% Energy convergence check every 100 steps
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if mod(i,100) == 0 && length(Observ.EVec) > 1
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energydifference = abs(Observ.EVec(end) - Observ.EVec(end-1));
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end
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% Convergence check - if energy difference is below set tolerance, then exit
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if energydifference <= epsilon
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disp('Tolerance reached: Energy difference is below the specified epsilon.');
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PrematureExitFlag = true; % Set flag to indicate premature exit
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PrematureExitFlag = true;
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break;
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elseif i >= this.MaxIterationsForGD % If set maximum number of iterations reached, then exit
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end
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end
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if i >= this.MaxIterationsForGD
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disp('Maximum number of iterations for CGD reached.');
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PrematureExitFlag = true; % Set flag to indicate premature exit
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PrematureExitFlag = true;
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break;
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end
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@ -135,33 +135,34 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
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d = -residual;
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else % Compute beta via Polak-Ribiere and create new direction
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residual_new = residual;
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beta = compute_beta(residual_new, residual_old);
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beta = compute_beta(residual_new, residual_old, Transf);
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d = -residual_new + beta * p_old;
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end
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residual_old = residual;
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p = d - (real(d(:)' * psi(:) * Transf.dx * Transf.dy * Transf.dz) .* psi);
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proj = inner_product(d, psi, Transf);
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p = d - (proj * psi);
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p_old = p;
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% Compute optimal theta to generate psi in the direction of minimum in the energy landscape
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theta = compute_optimal_theta(p, muchem, psi, Params, Transf, VDk, V);
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% Update solution
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gamma = 1 / sqrt(sum(abs(p(:)).^2) * Transf.dx * Transf.dy * Transf.dz);
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psi = (cos(theta).*psi) + (gamma*sin(theta).*p);
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gamma = 1 / sqrt(inner_product(p, p, Transf));
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psi = (cos(theta).*psi) + (sin(theta).*(p*gamma));
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% Normalize psi
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Norm = sum(abs(psi(:)).^2) * Transf.dx * Transf.dy * Transf.dz;
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psi = sqrt(Params.N) * psi / sqrt(Norm);
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psi = sqrt(Params.N) * psi / sqrt(abs(inner_product(psi, psi, Transf)));
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i = i + 1;
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% Calculate chemical potential with new psi
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muchem = real(psi(:)' * J(:)) / sum(abs(psi(:)).^2);
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J = compute_gradient(psi, Params, Transf, VDk, V);
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muchem = real(inner_product(psi, J, Transf)) / inner_product(psi, psi, Transf);
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if mod(i,100) == 0
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% Collect Energy value
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E = this.Calculator.calculateTotalEnergy(psi,Params,Transf,VDk,V);
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E = E/Norm;
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E = this.Calculator.calculateTotalEnergy(psi,Params,Transf,VDk,V) / inner_product(psi, psi, Transf);
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Observ.EVec = [Observ.EVec E];
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% Collect Chemical potential value
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@ -172,12 +173,14 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
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Observ.residual = [Observ.residual res];
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Observ.res_idx = Observ.res_idx + 1;
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% Collect calculated thetas
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Observ.theta = [Observ.theta theta];
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% Live plotter
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if this.PlotLive
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Plotter.plotLive(psi,Params,Transf,Observ,this.SimulationMode)
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drawnow
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end
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save(sprintf(strcat(this.SaveDirectory, '/Run_%03i/psi_gs.mat'),Params.njob),'psi','muchem','Observ','Transf','Params','VDk','V');
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end
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end
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@ -190,13 +193,11 @@ function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
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end
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% Change in Energy
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E = this.Calculator.calculateTotalEnergy(psi,Params,Transf,VDk,V);
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E = E/Norm;
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E = this.Calculator.calculateTotalEnergy(psi,Params,Transf,VDk,V) / inner_product(psi, psi, Transf);
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Observ.EVec = [Observ.EVec E];
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disp('Saving data...');
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save(sprintf(strcat(this.SaveDirectory, '/Run_%03i/psi_gs.mat'),Params.njob),'psi','muchem','Observ','Transf','Params','VDk','V');
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disp('Save complete!');
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disp('Completed and saved!');
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end
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end
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@ -261,15 +262,19 @@ function theta = compute_optimal_theta(p, muchem, psi, Params, Transf, VDk, V)
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Hpsi = compute_gradient(psi, Params, Transf, VDk, V);
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Hp = compute_gradient(p, Params, Transf, VDk, V);
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g = compute_g(psi, p, Params, VDk);
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gamma = 1 / sqrt(sum(abs(p(:)).^2) * Transf.dx * Transf.dy * Transf.dz);
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numerator = gamma * real(p(:)' * Hpsi(:) * Transf.dx * Transf.dy * Transf.dz);
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denominator = muchem - (gamma^2 * (real(p(:)' * Hp(:) * Transf.dx * Transf.dy * Transf.dz) + real(g(:)' * p(:) * Transf.dx * Transf.dy * Transf.dz)));
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gamma = 1 / sqrt(inner_product(p, p, Transf));
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numerator = gamma * real(inner_product(p, Hpsi, Transf));
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denominator = muchem - (gamma^2 * (real(inner_product(p, Hp, Transf)) + real(inner_product(g, p, Transf))));
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theta = numerator / denominator;
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end
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% Optimal step size via Polak-Ribiere
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function beta = compute_beta(residual_new, residual_old)
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beta = (residual_new(:)' * (residual_new(:) - residual_old(:))) / sum(abs(residual_old(:)).^2);
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beta = max(0,beta);
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function beta = compute_beta(residual_new, residual_old, Transf)
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beta = inner_product(residual_new, (residual_new - residual_old), Transf) / inner_product(residual_old, residual_old, Transf);
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beta = max(0, real(beta));
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end
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function s = inner_product(u, v, Transf)
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s = sum(conj(u(:)) .* v(:)) * Transf.dx * Transf.dy * Transf.dz;
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end
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