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fix: removing unecessary files

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PolishPigeon 2022-01-08 03:25:41 +01:00
parent 3ae8bd014c
commit 73aa7654d6
3 changed files with 1 additions and 111 deletions
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2
ENUME/projectC/adamspc.m
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@ -1,6 +1,6 @@
function x = adamspc(functs, init, interval, stepsize)
% obtain first five steps from RK4
[x, derivs] = rk4(functs, init, interval, stepsize, 5);
[x, derivs] = RK4(functs, init, interval, stepsize, 5);
x = x(2:end, :);
% define coefficient tables

49
ENUME/projectC/rk4.m
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@ -1,49 +0,0 @@
% solve ODE system using RK4 with constant step size
function [x, derivativesTable] = RK4(equations, initialValues, interval, stepSize, maxSteps)
x = initialValues;
derivativesTable = buildDerivatiesTable(x, equations);
% Calculate stepCount
stepCount = ceil((interval(2) - interval(1)) / stepSize);
if nargin == 5
stepCount = min(stepCount, maxSteps - 1);
end % IF we include max steps in our function input
% (nargin is number of arguments in input)
% then choose smaller number between maxSteps and stepCount and choose
% it for stepCount
[x, derivativesTable] = rk4Loop(x, stepCount, stepSize, equations, derivativesTable);
% append arguments to output
x = [interval(1):stepSize:(stepCount * stepSize); x];
end
function derivativesTable = buildDerivatiesTable(x, equations)
derivativesTable = zeros(size(x));
for eqnum = 1:size(equations, 1)
derivativesTable(eqnum, 1) = equations{eqnum}(x(:, 1));
end
end
function [x, derivativesTable] = rk4Loop(x, stepCount, stepSize, equations, derivativesTable)
for step = 1 : stepCount
[x, derivativesTable] = rk4stepLoop(x, step, equations, stepSize, derivativesTable);
end
end
function [x, derivativesTable] = rk4stepLoop(x, step, equations, stepSize, derivativesTable)
stepValue = x(:, step);
[x, derivativesTable] = equationsLoop(x, equations, stepValue, stepSize, step, derivativesTable);
end
function [x, derivativesTable] = equationsLoop(x, equations, stepValue, stepSize, step, derivativesTable)
for equationNumber = 1 : 2
Phi = RK4Phi(equations{equationNumber}, stepValue, stepSize);
x(equationNumber, step + 1) = x(equationNumber, step) + stepSize * Phi;
derivativesTable(equationNumber, step + 1) = equations{equationNumber}(x(:, step + 1));
end
end

61
ENUME/projectC/rk4auto.m
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@ -1,61 +0,0 @@
% automatic step size variant of RK4
function [x, sizes, errors] = RK4Automatic(equations, initialValues, interval, initialStepSize, relativeEpsilon, absoluteEpsilon)
% set start points of output
args = interval(1);
x = initialValues;
% initialize output plots
sizes = double.empty();
errors = double.empty();
% integrate function until end of interval reached
stepsize = initialStepSize;
step = 0;
while 1
% obtain the preceding function values
step = step + 1;
stepval = x(:, step);
% advance output function
for eqnum = 1:size(equations, 1)
% generic single-step iteration
phi = RK4Phi(equations{eqnum}, stepval, stepsize);
x(eqnum, step + 1) = x(eqnum, step) + stepsize * phi;
end
% stop algorithm if function integrated over the whole interval
args(step + 1) = args(step) + stepsize;
if args(end) >= interval(2); break; end
% also calculate next step using two half-steps
for substep = 1:2
for eqnum = 1:size(equations, 1)
phi = RK4Phi(equations{eqnum}, stepval, stepsize / 2);
stepval(eqnum) = stepval(eqnum) + (stepsize / 2) * phi;
end
end
% calculate step correction factor
alpha = Inf;
for eqnum = 1:size(equations, 1)
% calculate approximation error
delta = abs(stepval(eqnum) - x(eqnum, step + 1)) / 15;
errors(step) = delta;
% calculate equation-specific alpha
epsilon = abs(stepval(eqnum)) * relativeEpsilon + absoluteEpsilon;
eqalpha = epsilon / delta;
% minimum alpha wins
if eqalpha < alpha; alpha = eqalpha; end
end
alpha = alpha ^ (1/5);
% correct step size with safety factor
stepsize = 0.9 * alpha * stepsize;
sizes(step) = stepsize;
end
% append arguments to output
x = [args; x];
end