Rewriting of gradient descent algorithm - follows Santo Roccuzzo's implementation.
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Karthik
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7aa4c7801b
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@ -17,7 +17,7 @@ classdef DipolarGas < handle & matlab.mixin.Copyable
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EnergyTolerance;
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ResidualTolerance;
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NoiseScaleFactor;
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MaxIterationsForCGD;
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MaxIterationsForGD;
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Calculator;
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@ -70,7 +70,7 @@ classdef DipolarGas < handle & matlab.mixin.Copyable
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@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
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addParameter(p, 'NoiseScaleFactor', 4,...
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@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
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addParameter(p, 'MaxIterationsForCGD', 100,...
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addParameter(p, 'MaxIterationsForGD', 100,...
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@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
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addParameter(p, 'IncludeDDICutOff', true,...
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@ -107,7 +107,7 @@ classdef DipolarGas < handle & matlab.mixin.Copyable
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this.EnergyTolerance = p.Results.EnergyTolerance;
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this.ResidualTolerance = p.Results.ResidualTolerance;
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this.NoiseScaleFactor = p.Results.NoiseScaleFactor;
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this.MaxIterationsForCGD = p.Results.MaxIterationsForCGD;
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this.MaxIterationsForGD = p.Results.MaxIterationsForGD;
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this.IncludeDDICutOff = p.Results.IncludeDDICutOff;
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this.UseApproximationForLHY = p.Results.UseApproximationForLHY;
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@ -1,20 +1,14 @@
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function [psi] = minimizeEnergyFunctional(this,psi,Params,Transf,VDk,V,Observ)
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function [psi] = runGradientDescent(this,psi,Params,Transf,VDk,V,Observ)
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format long;
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% Define the function handle
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f = @(X) this.Calculator.calculateTotalEnergy(X, Params, Transf, VDk, V)/Params.N;
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% Convergence Criteria:
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Epsilon = 1E-5;
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% Iteration Counter:
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i = 1;
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Observ.residual = 1;
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Observ.res = 1;
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epsilon = 1E-8;
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alpha = 1E-4;
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beta = 0.9;
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% Initialize the PrematureExitFlag to false
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PrematureExitFlag = false;
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Observ.residual = 1;
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psi_old = psi; % Previous psi value (for heavy-ball method)
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if this.PlotLive
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Plotter.plotLive(psi,Params,Transf,Observ)
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@ -22,56 +16,40 @@ function [psi] = minimizeEnergyFunctional(this,psi,Params,Transf,VDk,V,Observ)
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end
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% Minimization Loop
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while true
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for idx = 1:this.MaxIterationsForGD
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% Compute gradient
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J = compute_gradient(psi, Params, Transf, VDk, V);
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J = compute_gradient(psi, Params, Transf, VDk, V);
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% Check stopping criterion (Gradient norm)
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if norm(J(:)) < Epsilon
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disp('Tolerance reached: Gradient norm is below the specified epsilon.');
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PrematureExitFlag = true; % Set flag to indicate premature exit
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break;
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elseif i >= this.MaxIterationsForCGD
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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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% Calculate chemical potential and norm
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muchem = sum(real(conj(psi) .* J)) / sum(abs(psi).^2);
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% Calculate residual and check convergence
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residual = sum(abs(J - muchem * psi).^2) * Transf.dx * Transf.dy * Transf.dz;
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if residual < epsilon
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fprintf('Convergence reached at iteration %d\n', idx);
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break;
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end
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% Initialize search direction if first iteration
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if i == 1
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S = -J;
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else
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% Update search direction
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S = update_search_direction(S, J, J_old);
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end
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% Step Size Optimization (Line Search)
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alpha = optimize_step_size(f, psi, S, Params, Transf, VDk, V);
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% Update solution
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psi = psi + alpha * S;
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% Update psi using heavy-ball method
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psi_new = (1 + beta) * psi - alpha * J - beta * psi_old;
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psi_old = psi;
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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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Norm = sum(abs(psi_new(:)).^2) * Transf.dx * Transf.dy * Transf.dz;
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psi = sqrt(Params.N) * psi_new / sqrt(Norm);
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% Store old gradient
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J_old = J;
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i = i + 1;
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muchem = this.Calculator.calculateChemicalPotential(psi,Params,Transf,VDk,V);
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if mod(i,10) == 0
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if mod(idx,500) == 0
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% Change in Energy
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% Collect 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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Observ.EVec = [Observ.EVec E];
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% Chemical potential
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% Collect chemical potentials
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Observ.mucVec = [Observ.mucVec muchem];
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% Normalized residuals
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res = this.Calculator.calculateNormalizedResiduals(psi,Params,Transf,VDk,V,muchem);
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% Collect residuals
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Observ.residual = [Observ.residual res];
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Observ.res_idx = Observ.res_idx + 1;
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@ -84,12 +62,12 @@ function [psi] = minimizeEnergyFunctional(this,psi,Params,Transf,VDk,V,Observ)
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end
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end
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% Check if loop ended prematurely
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if PrematureExitFlag
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disp('Optimizer ended prematurely without convergence to a minimum.');
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% Check if max iterations were hit without convergence
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last_iteration_number = idx;
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if last_iteration_number == this.MaxIterationsForGD
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fprintf('Max iterations reached without convergence. Final chemical potential: %.6f, Residual: %.6f\n', muchem, residual);
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else
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disp('Minimum found!');
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fprintf('Number of Iterations for Convergence: %d\n\n', i);
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fprintf('Converged in %d iterations. Final chemical potential: %.6f\n', last_iteration_number, muchem);
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end
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% Change in Energy
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@ -131,42 +109,4 @@ function J = compute_gradient(psi, Params, Transf, VDk, V)
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J = H(psi);
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end
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% Line Search (Step Size Optimization)
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function alpha = optimize_step_size(f, X, S, Params, Transf, VDk, V)
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alpha = 1; % Initial step size
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rho = 0.5; % Step size reduction factor
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c = 1E-4; % Armijo condition constant
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max_iter = 100; % Max iterations for backtracking
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tol = 1E-4; % Tolerance for stopping
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grad = compute_gradient(X, Params, Transf, VDk, V); % Compute gradient once
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f_X = f(X); % Evaluate f(X) once
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for k = 1:max_iter
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% Evaluate Armijo condition with precomputed f(X) and grad
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if f(X + alpha * S) <= f_X + c * alpha * (S(:)' * grad(:))
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break;
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else
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alpha = rho * alpha; % Reduce the step size
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end
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% Early stopping if step size becomes too small
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if alpha < tol
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break;
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end
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end
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end
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% Update Search Direction
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function S_new = update_search_direction(S, J_new, J_old)
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% (Fletcher-Reeves method)
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% beta = (norm(J_new(:))^2) / (norm(J_old(:))^2);
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% S_new = -J_new + beta * S;
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% (Polak-Ribiere method)
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beta = max(0, (J_new(:)' * (J_new(:) - J_old(:))) / (norm(J_old(:))^2));
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S_new = -J_new + beta * S;
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end
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