feat: beautyfying task2.m and finishing code part

ENUME/projectC/AdamsPCMethod.m

@@ -1,4 +1,4 @@
-function x = adamspc(functions, initialValues, interval, stepSize)
+function x = AdamsPCMethod(functions, initialValues, interval, stepSize)
     [x, derrivatives, explicitCoefficients, implicitCoefficients, stepCount] = initialize(functions, initialValues, interval, stepSize);
     x = adamsPcLoop(x, derrivatives, explicitCoefficients, implicitCoefficients, stepCount, functions, stepSize);
     % append arguments to output

ENUME/projectC/adamspc.asv

@@ -1,70 +0,0 @@
-function x = adamspc(functions, initialValues, interval, stepSize)
-    [x, derrivatives, explicitCoefficients, implicitCoefficients, stepCount] = initialize(functions, initialValues, interval, stepSize);
-    [stepSize, stepCount, x] = adamsPcLoop(x, derrivatives, explicitCoefficients, implicitCoefficients, stepCount, functions, stepSize);
-    % append arguments to output
-    x = [interval(1):stepSize:(stepCount * stepSize); x];
-end
-
-function [x, derrivatives, explicitCoefficients, implicitCoefficients, stepCount] = initialize(functions, initialValues, interval, stepSize)
-    % obtain first five steps from RK4
-    [x, derrivatives] = RK4(functions, initialValues, interval, stepSize, 5);
-    x = x(2:end, :);
-    
-    % define coefficient 
-    explicitCoefficients = [1901, -2774, 1616, -1274, 251] / 720; 
-    % Constants that can  be found on the Internet or in Mister Tatjewski
-    % book on page 177, notice how beta(3) = 1616 instead of 2616
-    % I have found on the internet different value for this parameter and
-    % got better results with it so I decided to stick with it
-    implicitCoefficients = [475, 1427, -798, 482, -173, 27] / 1440;  
-    % Constants that can  be found on the Internet or in Mister Tatjewski
-    % book on page 178
-    % build output based on preceding values
-    stepCount = ceil((interval(2) - interval(1)) / stepSize);
-end
-
-function [stepSize, stepCount, x] = adamsPcLoop(x, derrivatives, explicitCoefficients, implicitCoefficients, stepCount, functions, stepSize)
-    for step = 6: (stepCount + 1)    
-        % P
-        predictionOfX = adamsPredict(x, step, stepSize, explicitCoefficients, derrivatives);
-            
-
-            
-        % correct
-        x(:, step) = x(:, step - 1);
-        for equationNumber = 1:size(functions, 1)
-            for previous = 1:5
-                x(equationNumber, step) = x(equationNumber, step) ...
-                    + stepSize * implicitCoefficients(previous + 1) * derrivatives(equationNumber, step - previous);
-            end
-            x(equationNumber, step) = x(equationNumber, step) ...
-                + stepSize * implicitCoefficients(1) * derrivativePrediction(equationNumber);
-        end
-        
-        % evaluate
-        for equationNumber = 1:size(functions, 1)
-            derrivatives(equationNumber, step) = functions{equationNumber}(x(:, step));
-        end
-    end
-end
-
-function predictionOfX = adamsPredict(x, step, stepSize, explicitCoefficients, derrivatives)
-    predictionOfX = x(:, step - 1);
-    for equationNumber = 1 : 2
-        for previous = 1:5
-            predictionOfX(equationNumber) = predictionOfX(equationNumber) ...
-                + stepSize * explicitCoefficients(previous) * derrivatives(equationNumber, step - previous);
-        end
-    end
-end
-
-function evaluateAdamsValue = adamsEvaluate
-    evaluateAdamsValue = zeros(size(functions, 1), 1);
-    for equationNumber = 1:size(functions, 1)
-        evaluateAdamsValue(equationNumber) = functions{equationNumber}(predictionOfX);
-    end
-end
-
-function adamsCorrect
-
-end

ENUME/projectC/auxplot.m

@@ -1,37 +0,0 @@
-% coordinate arguments
-argsx = -1:0.1:1;
-argsy = -2:0.5:12;
-
-% available functions
-functs = {
-    "x_1", -67, 50, @(x, y) y + x * (0.5 - x^2 - y^2);    
-    "x_2", -115, 30, @(x, y) -x + y * (0.5 - x^2 - y^2)
-};
-
-% plot each function
-for funct = 1:size(functs, 1)
-    [functname, cama, camb, functh] = functs{funct, :};
-    
-    % evaluate values
-    vals = zeros(length(argsx), length(argsy));
-    for i = 1:size(argsx, 2)
-        for j = 1:size(argsy, 2)
-            vals(i, j) = functh(argsx(i), argsy(j));
-        end
-    end
-    
-    % plot
-    figure;
-    surf(argsx, argsy, vals');
-    title(strcat("Gradient of ", functname));
-    xlabel('x_1');
-    ylabel('x_2');
-    zlabel(strcat("d", functname, "/dt"));
-    xlim([argsx(1), argsx(end)]);
-    ylim([argsy(1), argsy(end)]);
-    view(cama, camb);
-    grid on;
-    set(gcf, 'PaperPosition', [0 0 6 4]);
-    set(gcf, 'PaperSize', [6 4]);
-    print(strcat('report/', functname, 'gradient'), '-dpdf');
-end

ENUME/projectC/task2.asv

@@ -0,0 +1,116 @@
+
+function task2()
+    [ordinaryDifferentialEquations, initialValues, interval, algorithms] = initialize();
+    solveAndPrintODEs(algorithms, ordinaryDifferentialEquations, initialValues, interval);
+    [result, sizes, errors] = solveAndPlotODEAutomatic(ordinaryDifferentialEquations, initialValues, interval);
+    plotStatistics(result, sizes, errors);
+    plotComparisonToMatlabFunction(ordinaryDifferentialEquations, interval, initialValues);
+end
+
+function [ordinaryDifferentialEquations, initialValues, interval, algorithms] = initialize()
+    ordinaryDifferentialEquations = {
+        @(x) x(2) + x(1) * (0.5 - x(1)^2 - x(2)^2);
+        @(x) -x(1) + x(2) * (0.5 - x(1)^2 - x(2)^2)
+    };
+    initialValues = [8; 9];
+    interval = [0; 15];
+    
+    algorithms = {
+        'RK4 algorithm', @RK4, [0.01, 0.011];
+        'Adams PC algorithm', @AdamsPCMethod, [0.002, 0.01305]
+    };
+end
+
+function solveAndPrintODEs(algorithms, ordinaryDifferentialEquations, initialValues, interval)
+    for algorithm = 1 : 2
+        [algorithmName, algorithmFunction, stepSizes] = algorithms{algorithm, :};
+        stepResults = solveForEachStep(stepSizes, ordinaryDifferentialEquations, initialValues, interval, algorithmFunction);
+        plotAgainstTime(ordinaryDifferentialEquations, algorithmName, stepResults);
+        plotAgainst(algorithmName, stepResults);
+
+    end
+end
+
+function stepResults = solveForEachStep(stepSizes, ordinaryDifferentialEquations, initialValues, interval, algorithmFunction)
+    stepResults = cell(size(stepSizes, 2), 3);
+    stepNames = {'Optimal Step Size', 'Slightly Larger Step Size'};
+    for stepNumber = 1:size(stepSizes, 2)
+        result = algorithmFunction(ordinaryDifferentialEquations, initialValues, interval, stepSizes(stepNumber));
+        stepResults(stepNumber, :) = {stepSizes(stepNumber), stepNames{stepNumber}, result};
+    end
+end
+
+function beginPlot()
+    figure; 
+    grid on; 
+    hold on;
+end
+
+function plotAgainstTime(ordinaryDifferentialEquations, algorithmName, stepResults)
+    for equationNumber = 1:size(ordinaryDifferentialEquations, 1)
+        beginPlot();
+
+        title([algorithmName, ', x_', num2str(equationNumber), ' ODE']);
+
+        for stepresult = stepResults'
+            plot(stepresult{3}(1, :), stepresult{3}(equationNumber + 1, :));
+        end
+
+        hold off;
+        legend(stepResults{:, 2});
+    end
+end
+
+function plotAgainst(algorithmName, stepResults)
+    beginPlot();
+    title([algorithmName, ' trajectory plot (x_2 compared to x_1)']);
+    for stepresult = stepResults'
+        plot(stepresult{3}(2, :), stepresult{3}(3, :));
+    end
+    hold off;
+    legend(stepResults{:, 2});
+%    %print(['report/', func2str(algfunc), 'traj'], '-dpdf');
+end
+
+function [result, sizes, errors] = solveAndPlotODEAutomatic(ordinaryDifferentialEquations, initialValues, interval)
+    [result, sizes, errors] = solveRKAutomatic(ordinaryDifferentialEquations, initialValues, interval);
+    plotTrajectory(result);
+end
+
+function [result, sizes, errors] = solveRKAutomatic(ordinaryDifferentialEquations, initialValues, interval)
+    initialStepSize = 1e-5;
+    relativeEpsilon = 1e-9;
+    absoluteEpsilon = 1e-9;
+    [result, sizes, errors] = RK4Automatic(ordinaryDifferentialEquations, initialValues, interval, initialStepSize, relativeEpsilon, absoluteEpsilon);
+end
+
+function plotTrajectory(result)
+    figure;
+    plot(result(2, :), result(3, :));
+    grid on;
+    title('RK4 auto-step trajectory plot (x_2 against x_1)');
+end
+
+function plotStatistics(result, sizes, errors)
+    stats = {
+        "RK4 auto-step step size", "rk4sizes", sizes;
+        "RK4 auto-step approximation error", "rk4errors", errors
+    };
+    for stat = stats'
+        figure;
+        plot(result(1, 2:(end - 1)), stat{3});
+        grid on;
+        title(stat{1});
+    end
+end
+
+function plotComparisonToMatlabFunction(ordinaryDifferentialEquations, interval, initialValues) 
+    % compare results with ODE45
+    odefun = @(t, x) [ ordinaryDifferentialEquations{1}(x); ordinaryDifferentialEquations{2}(x) ];
+    odeoptions = odeset('RelTol', 10e-10, 'AbsTol', 10e-10);
+    [~, x] = ode45(odefun, interval, initialValues, odeoptions);
+    figure;
+    plot(x(:, 1), x(:, 2));
+    grid on;
+    title('ODE45 trajectory plot (x_2 against x_1)');
+end

ENUME/projectC/task2.m

@@ -1,90 +1,116 @@
-% functions of the ODE system and initial values
-sysfuncts = {
-    @(x) x(2) + x(1) * (0.5 - x(1)^2 - x(2)^2);
-    @(x) -x(1) + x(2) * (0.5 - x(1)^2 - x(2)^2)
-};
-initvalues = [0; 12];
-interval = [0; 15];
 
-% define available algorithms
+function task2()
-algorithms = {
+    [ordinaryDifferentialEquations, initialValues, interval, algorithms] = initialize();
-    'RK4', @RK4, [0.01, 0.013408];
+    solveAndPrintODEs(algorithms, ordinaryDifferentialEquations, initialValues, interval);
-    'Adams PC', @adamspc, [0.002, 0.01305]
+    [result, sizes, errors] = solveAndPlotODEAutomatic(ordinaryDifferentialEquations, initialValues, interval);
-};
+    plotStatistics(result, sizes, errors);
+    plotComparisonToMatlabFunction(ordinaryDifferentialEquations, interval, initialValues);
+end
 
-% solve ODE using different algorithms and step sizes
+function [ordinaryDifferentialEquations, initialValues, interval, algorithms] = initialize()
-for alg = 1 : 2
+    ordinaryDifferentialEquations = {
-    [algname, algfunc, stepsizes] = algorithms{alg, :};
+        @(x) x(2) + x(1) * (0.5 - x(1)^2 - x(2)^2);
+        @(x) -x(1) + x(2) * (0.5 - x(1)^2 - x(2)^2)
+    };
+    initialValues = [8; 9];
+    interval = [0; 15];
     
-    % solve using the given algorithm for each step size
+    algorithms = {
-    stepresults = cell(size(stepsizes, 2), 3);
+        'RK4 algorithm', @RK4, [0.01, 0.011];
-    stepnames = {'optimal step', 'larger step'};
+        'Adams PC algorithm', @AdamsPCMethod, [0.002, 0.01305]
-    for stepno = 1:size(stepsizes, 2)
+    };
-        result = algfunc(sysfuncts, initvalues, interval, stepsizes(stepno));
+end
-        stepresults(stepno, :) = { ...
+
-            stepsizes(stepno), ...
+function solveAndPrintODEs(algorithms, ordinaryDifferentialEquations, initialValues, interval)
-            stepnames{stepno}, ...
+    for algorithm = 1 : 2
-            result};
+        [algorithmName, algorithmFunction, stepSizes] = algorithms{algorithm, :};
+        stepResults = solveForEachStep(stepSizes, ordinaryDifferentialEquations, initialValues, interval, algorithmFunction);
+        plotAgainstTime(ordinaryDifferentialEquations, algorithmName, stepResults);
+        plotAgainst(algorithmName, stepResults);
+
     end
-    
+end
-    % plot each component against time
+
-    for eqnum = 1:size(sysfuncts, 1)
+function stepResults = solveForEachStep(stepSizes, ordinaryDifferentialEquations, initialValues, interval, algorithmFunction)
-        % begin plot
+    stepResults = cell(size(stepSizes, 2), 3);
-        figure; grid on; hold on;
+    stepNames = {'Optimal Step Size', 'Slightly Larger Step Size'};
-        title([algname, ', x_', num2str(eqnum), ' against time']);
+    for stepNumber = 1:size(stepSizes, 2)
-        
+        result = algorithmFunction(ordinaryDifferentialEquations, initialValues, interval, stepSizes(stepNumber));
-        % plot component for each step size
+        stepResults(stepNumber, :) = {stepSizes(stepNumber), stepNames{stepNumber}, result};
-        for stepresult = stepresults'
+    end
-            plot(stepresult{3}(1, :), stepresult{3}(eqnum + 1, :));
+end
+
+function beginPlot()
+    figure; 
+    grid on; 
+    hold on;
+end
+
+function plotAgainstTime(ordinaryDifferentialEquations, algorithmName, stepResults)
+    for equationNumber = 1:size(ordinaryDifferentialEquations, 1)
+        beginPlot();
+
+        title([algorithmName, ', x_', num2str(equationNumber), ' ODE']);
+
+        for stepresult = stepResults'
+            plot(stepresult{3}(1, :), stepresult{3}(equationNumber + 1, :));
         end
-        
+
-        % finish plot
         hold off;
-        legend(stepresults{:, 2});
+        legend(stepResults{:, 2});
     end
-    
+end
-    % plot first two components against each other
+
-    figure; grid on; hold on;
+function plotAgainst(algorithmName, stepResults)
-    title([algname, ' trajectory plot (x_2 against x_1)']);
+    beginPlot();
-    
+    title([algorithmName, ' trajectory plot (x_2 compared to x_1)']);
-    % plot for each step size
+    for stepresult = stepResults'
-    for stepresult = stepresults'
         plot(stepresult{3}(2, :), stepresult{3}(3, :));
     end
-    
-    % finish plot
     hold off;
-    legend(stepresults{:, 2});
+    legend(stepResults{:, 2});
 %    %print(['report/', func2str(algfunc), 'traj'], '-dpdf');
 end
 
-% solve ODE using RK4 with automatic step size
+function [result, sizes, errors] = solveAndPlotODEAutomatic(ordinaryDifferentialEquations, initialValues, interval)
-[result, sizes, errors] = RK4Automatic(sysfuncts, initvalues, interval, ...
+    [result, sizes, errors] = solveRKAutomatic(ordinaryDifferentialEquations, initialValues, interval);
-    1e-5, 10e-10, 10e-10);
+    plotTrajectory(result);
-
-% plot trajectory
-figure;
-plot(result(2, :), result(3, :));
-grid on;
-title('RK4 auto-step trajectory plot (x_2 against x_1)');
-
-% plot statistics
-stats = {
-    "RK4 auto-step step size", "rk4sizes", sizes;
-    "RK4 auto-step approximation error", "rk4errors", errors
-};
-for stat = stats'
-    figure;
-    plot(result(1, 2:(end - 1)), stat{3});
-    grid on;
-    title(stat{1});
 end
 
-% compare results with ODE45
+function [result, sizes, errors] = solveRKAutomatic(ordinaryDifferentialEquations, initialValues, interval)
-odefun = @(t, x) [ sysfuncts{1}(x); sysfuncts{2}(x) ];
+    initialStepSize = 1e-5;
-odeoptions = odeset('RelTol', 10e-10, 'AbsTol', 10e-10);
+    relativeEpsilon = 1e-9;
-[t, x] = ode45(odefun, interval, initvalues, odeoptions);
+    absoluteEpsilon = 1e-9;
-figure;
+    [result, sizes, errors] = RK4Automatic(ordinaryDifferentialEquations, initialValues, interval, initialStepSize, relativeEpsilon, absoluteEpsilon);
-plot(x(:, 1), x(:, 2));
+end
-grid on;
+
-title('ODE45 trajectory plot (x_2 against x_1)');
+function plotTrajectory(result)
+    figure;
+    plot(result(2, :), result(3, :));
+    grid on;
+    title('RK4 with auto step trajectory plot (x_2 against x_1)');
+end
+
+function plotStatistics(result, sizes, errors)
+    stats = {
+        "RK4 with auto step step size", "rk4sizes", sizes;
+        "RK4 with auto step approximation error", "rk4errors", errors
+    };
+    for stat = stats'
+        figure;
+        plot(result(1, 2:(end - 1)), stat{3});
+        grid on;
+        title(stat{1});
+    end
+end
+
+function plotComparisonToMatlabFunction(ordinaryDifferentialEquations, interval, initialValues) 
+    % compare results with ODE45
+    odefun = @(t, x) [ ordinaryDifferentialEquations{1}(x); ordinaryDifferentialEquations{2}(x) ];
+    odeoptions = odeset('RelTol', 10e-10, 'AbsTol', 10e-10);
+    [~, x] = ode45(odefun, interval, initialValues, odeoptions);
+    figure;
+    plot(x(:, 1), x(:, 2));
+    grid on;
+    title('ODE45 trajectory plot (x_2 against x_1)');
+end