AMATH-581-AS-COOL-AS-IT-GETS/CompiledToHW4.m at main · iluvjava/AMATH-581-AS-COOL-AS-IT-GETS · GitHub

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% Organized the solutions for HW4 and ready to put them into a template for
% submitting.
% Files Included:
% 1. This file
% 2. FiniteDiffMatrix
% 3. Parameters.m
%   3.1. PsiGuess.
% 4. Rhs.m
% 5. SolveForPsi.m
% 6. VectorizedInitialDistribution.m
%
% Pre submit checks: Completed.
% First Trial:
% Status: Failed.
%   Reason 1:
%       Grid discritization DeltaX is incorrect, it should be 20/63, because
%   there are 63 intervals, and 64 points for discritization.
%       ! ADDRESSED
%   Reason 2:
%       Use the modified A for both advancing the omega function, and
%       solving for the stream function.
%       (This might not be a contributing factor because of small 0.001 for diffusion)
%
%
% Second Trial:
%   Status: All Failed.
%   Reason:
%       1. Confirmed by reading the textbook, there is something wrong with
%       the grid points, and the boundary conditions is not addressed.
%       And this will also place my FFT for first submission even if that
%       FFT handles the boundary condition differently.
%
%       For FFT, we need a better soluton.
%
% Third Trial:
%   Status: All Failed.
%   Reason:
%       1. The boundary points ARE NOT Included! The matrix took care of
%       that already.

clear variables

n      = 64;
L      = 20;
DeltaX = L/n;
AA     = zeros(9, n^2, 5);  % To store all solutions.
xs     = -L/2 : DeltaX: L/2 - DeltaX;
ys     = -L/2 : DeltaX: L/2 - DeltaX;

Params   = Parameters(n, DeltaX);
Params.l = 20;  % For fft.
InitialDistribution = @(x, y) exp(-x.^2 - y.^2./20);
w_vec = VectorizeInitialDistribution(xs, ys, InitialDistribution);

for I = 1:5
    Tspan = 0: 0.5: 4;
    Params.SolveModes = I;
    % Setting Options for solving and stuff.

    % Solving
    ODEFun = @(t, w) Rhs(w, Params);
    [~, Ws] = ode45(ODEFun, Tspan, w_vec);
    AA(:, :, I) = Ws;
end

A1 = AA(:, :, 1);
A2 = AA(:, :, 2);
A3 = AA(:, :, 3);
A4 = AA(:, :, 4);
A5 = AA(:, :, 5);


%%
% Plotting the data out.
% figure(1); imagesc(reshape(A1(9, :), 64, 64)); colorbar; title("A1");
% figure(2); imagesc(reshape(A2(9, :), 64, 64)); colorbar; title("A2");
% figure(3); imagesc(reshape(A3(9, :), 64, 64)); colorbar; title("A3");
% figure(4); imagesc(reshape(A4(9, :), 64, 64)); colorbar; title("A4");
% figure(5); imagesc(reshape(A5(9, :), 64, 64)); colorbar; title("A5");

PlotSimulations(A1, 1);
PlotSimulations(A2, 2);
PlotSimulations(A3, 3);
PlotSimulations(A4, 4);
PlotSimulations(A5, 5);

%% Functions

function Argout = PlotSimulations(Dat, t)
    % Stitch all of them together.
    TotalMatrix = zeros(64*3, 64*3);
    figure(t);
    for I = 0: 8
        m = floor(I/3);
        n = mod(I, 3);
        TotalMatrix(m*64 + 1: (m + 1)*64, n*64 + 1: (n + 1)*64) ...
            = reshape(Dat(I + 1, :), 64, 64);
    end
    pcolor(TotalMatrix);
    shading interp;
    title(strcat("A", num2str(t)));
end


% function argout = TrimOffBoundary(dat, n)
%     m = size(dat, 1);
%     argout = zeros(m, (n - 1)^2);
%     for I = 1: m
%         argout(I, :) = Helper(dat(I, :), n);
%     end
%
%     function argOut = Helper(w, n)
%         % Trim off the first, last row of the vectorized matrix, and put them
%         % back to vector, for submission.
%         M = reshape(w, n, n);
%         M = M(1: end - 1, 1: end - 1);
%         argOut = reshape(M, (n - 1)^2, 1);
%     end
%
% end