WUT_Computer_Science/ENUME/projectC/adamspc.asv

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