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I am writing a for loop to calculate the value of four different variables. The first variable is M. M increases from 10^2 to 10^5,
M = [10^2,10^3,10^4,10^5];
The other three variables needed for the table are shown in the code below.
confmc
confcv
confmcSize/confcvSize
I first create a for loop to iterate through the four different values of M. I then create the table outside of the for loop.
How could I adjust the implementation so that the table displays all four values of M?
randn('state',100)
%%%%%% Problem and method parameters %%%%%%%%%
S = 5; E = 6; sigma = 0.3; r = 0.05; T = 1;
Dt = 1e-2; N = T/Dt; M = [10^2,10^3,10^4,10^5];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for k=1:numel(M)
%%%%%%%%% Geom Asian exact mean %%%%%%%%%%%%
sigsqT= sigma^2*T*(N+1)*(2*N+1)/(6*N*N);
muT = 0.5*sigsqT + (r - 0.5*sigma^2)*T*(N+1)/(2*N);
d1 = (log(S/E) + (muT + 0.5*sigsqT))/(sqrt(sigsqT));
d2 = d1 - sqrt(sigsqT);
N1 = 0.5*(1+erf(d1/sqrt(2)));
N2 = 0.5*(1+erf(d2/sqrt(2)));
geo = exp(-r*T)*( S*exp(muT)*N1 - E*N2 );
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Spath = S*cumprod(exp((r-0.5*sigma^2)*Dt+sigma*sqrt(Dt)*randn(M(k),N)),2);
% Standard Monte Carlo
arithave = mean(Spath,2);
Parith = exp(-r*T)*max(arithave-E,0); % payoffs
Pmean = mean(Parith);
Pstd = std(Parith);
confmc = [Pmean-1.96*Pstd/sqrt(M(k)), Pmean+1.96*Pstd/sqrt(M(k))];
confmcSize = [(Pmean+1.96*Pstd/sqrt(M(k)))-(Pmean-1.96*Pstd/sqrt(M(k)))];
% Control Variate
geoave = exp((1/N)*sum(log(Spath),2));
Pgeo = exp(-r*T)*max(geoave-E,0); % geo payoffs
Z = Parith + geo - Pgeo; % control variate version
Zmean = mean(Z);
Zstd = std(Z);
confcv = [Zmean-1.96*Zstd/sqrt(M(k)), Zmean+1.96*Zstd/sqrt(M(k))];
confcvSize = [(Zmean+1.96*Zstd/sqrt(M(k)))-(Zmean-1.96*Zstd/sqrt(M(k)))];
end
T = table(M,confmc,confcv,confmcSize/confcvSize)
The current code returns
T =
1×4 table
M confmc confcv Var4
_____ ____________________ ____________________ ______
1e+05 0.096756 0.1007 0.097306 0.097789 8.1622
How could I change my implementation so that all four values of M are computed?
I just modified few things.Take a look at the following code.
randn('state',100)
%%%%%% Problem and method parameters %%%%%%%%%
S = 5; E = 6; sigma = 0.3; r = 0.05; T = 1;
Dt = 1e-2; N = T/Dt; M = [10^2,10^3,10^4,10^5];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
confmc = zeros(numel(M), 2);
confcv = zeros(numel(M), 2);
confmcSize = zeros(numel(M), 1);
confcvSize = zeros(numel(M), 1);
for k=1:numel(M)
%%%%%%%%% Geom Asian exact mean %%%%%%%%%%%%
sigsqT= sigma^2*T*(N+1)*(2*N+1)/(6*N*N);
muT = 0.5*sigsqT + (r - 0.5*sigma^2)*T*(N+1)/(2*N);
d1 = (log(S/E) + (muT + 0.5*sigsqT))/(sqrt(sigsqT));
d2 = d1 - sqrt(sigsqT);
N1 = 0.5*(1+erf(d1/sqrt(2)));
N2 = 0.5*(1+erf(d2/sqrt(2)));
geo = exp(-r*T)*( S*exp(muT)*N1 - E*N2 );
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Spath = S*cumprod(exp((r-0.5*sigma^2)*Dt+sigma*sqrt(Dt)*randn(M(k),N)),2);
% Standard Monte Carlo
arithave = mean(Spath,2);
Parith = exp(-r*T)*max(arithave-E,0); % payoffs
Pmean = mean(Parith);
Pstd = std(Parith);
confmc(k,:) = [Pmean-1.96*Pstd/sqrt(M(k)), Pmean+1.96*Pstd/sqrt(M(k))];
confmcSize(k,1) = [(Pmean+1.96*Pstd/sqrt(M(k)))-(Pmean-1.96*Pstd/sqrt(M(k)))];
% Control Variate
geoave = exp((1/N)*sum(log(Spath),2));
Pgeo = exp(-r*T)*max(geoave-E,0); % geo payoffs
Z = Parith + geo - Pgeo; % control variate version
Zmean = mean(Z);
Zstd = std(Z);
confcv(k,:) = [Zmean-1.96*Zstd/sqrt(M(k)), Zmean+1.96*Zstd/sqrt(M(k))];
confcvSize(k,1) = [(Zmean+1.96*Zstd/sqrt(M(k)))-(Zmean-1.96*Zstd/sqrt(M(k)))];
end
T = table(M',confmc,confcv,confmcSize./confcvSize)
In short, I just used a matrix instead of a vector or scalar as the members of the table. In your code, the variables (confmc, confcv, confmcSize, confcvSize) were getting overwritten.
This is my Approximate entropy Calculator in MATLAB. https://en.wikipedia.org/wiki/Approximate_entropy
I'm not sure why it isn't working. It's returning a negative value.Can anyone help me with this? R1 being the data.
FindSize = size(R1);
N = FindSize(1);
% N = input ('insert number of data values');
%if you want to put your own N in, take away the % from the line above
and
%insert the % before the N = FindSize(1)
%m = input ('insert m: integer representing length of data, embedding
dimension ');
m = 2;
%r = input ('insert r: positive real number for filtering, threshold
');
r = 0.2*std(R1);
for x1= R1(1:N-m+1,1)
D1 = pdist2(x1,x1);
C11 = (D1 <= r)/(N-m+1);
c1 = C11(1);
end
for i1 = 1:N-m+1
s1 = sum(log(c1));
end
phi1 = (s1/(N-m+1));
for x2= R1(1:N-m+2,1)
D2 = pdist2(x2,x2);
C21 = (D2 <= r)/(N-m+2);
c2 = C21(1);
end
for i2 = 1:N-m+2
s2 = sum(log(c2));
end
phi2 = (s2/(N-m+2));
Ap = phi1 - phi2;
Apen = Ap(1)
Following the documentation provided by the Wikipedia article, I developed this small function that calculates the approximate entropy:
function res = approximate_entropy(U,m,r)
N = numel(U);
res = zeros(1,2);
for i = [1 2]
off = m + i - 1;
off_N = N - off;
off_N1 = off_N + 1;
x = zeros(off_N1,off);
for j = 1:off
x(:,j) = U(j:off_N+j);
end
C = zeros(off_N1,1);
for j = 1:off_N1
dist = abs(x - repmat(x(j,:),off_N1,1));
C(j) = sum(~any((dist > r),2)) / off_N1;
end
res(i) = sum(log(C)) / off_N1;
end
res = res(1) - res(2);
end
I first tried to replicate the computation shown the article, and the result I obtain matches the result shown in the example:
U = repmat([85 80 89],1,17);
approximate_entropy(U,2,3)
ans =
-1.09965411068114e-05
Then I created another example that shows a case in which approximate entropy produces a meaningful result (the entropy of the first sample is always less than the entropy of the second one):
% starting variables...
s1 = repmat([10 20],1,10);
s1_m = mean(s1);
s1_s = std(s1);
s2_m = 0;
s2_s = 0;
% datasample will not always return a perfect M and S match
% so let's repeat this until equality is achieved...
while ((s1_m ~= s2_m) && (s1_s ~= s2_s))
s2 = datasample([10 20],20,'Replace',true,'Weights',[0.5 0.5]);
s2_m = mean(s2);
s2_s = std(s2);
end
m = 2;
r = 3;
ae1 = approximate_entropy(s1,m,r)
ae2 = approximate_entropy(s2,m,r)
ae1 =
0.00138568170752751
ae2 =
0.680090884817465
Finally, I tried with your sample data:
fid = fopen('O1.txt','r');
U = cell2mat(textscan(fid,'%f'));
fclose(fid);
m = 2;
r = 0.2 * std(U);
approximate_entropy(U,m,r)
ans =
1.08567461184858
I am using PCA on a set of facial images in MatLab.
Creating an average face and randomizing others are working fine.
In my function vectorComparison I want to see the difference on each principal component vector when using the standard deviation. But when I use eig_face_index = 1 I see less of a difference than when I use 2, or 3 etc.
The higher indexes also seem to add more color, which could be due to noise in the eigenfaces, as I am using RGB space.
Why does my initial vector show the least difference. Shouldn't it be the other way around?
Here is all of the code I am using:
main.m
clear;clc;close all;
[imvecs,img] = loadImages();
meanval = meanValue(imvecs);
[T, D] = covarianceMatrix(imvecs, meanval);
[eigvecs, eigvals] = findEigVecs(imvecs, T, D);
eigenfaces = createEigenFaces(eigvecs, imvecs, img);
%%
[mean_image] = createAverageFace(meanval, img);
%%
[stdev_vec] = createRandomFace(eigvals, eigvecs, imvecs, meanval, img);
%%
vectorComparison(meanval, eigvecs, stdev_vec, img, mean_image);
loadImages.m
function [imvecs,img] = loadImages()
images = dir('D:My\Path\*.png');
imgPath = 'D:My\Path\';
img=imread([imgPath images(1).name]);
n=length(images);
for i = 1:n
img = imread([imgPath images(i).name]);
imvecs{i} = double(img(:));
end
return
meanValue.m
function meanval = meanValue(imvecs, imageNr)
%Creates the mean value from our images.
sumvec=imvecs{1};
for i = 2:(size(imvecs,2))
sumvec = sumvec + imvecs{i};
end
meanval = sumvec ./(size(imvecs,2));
return
covarianceMatrix.m
function [T, D] = covarianceMatrix(imvecs, meanval)
D = [];
for i = 1:size(imvecs,2),
diff = imvecs{i} - meanval;
D = [D, diff];
end
%Dimensionality reduction
T = (D' * D) ./ (size(imvecs,2));
return
findEigVecs.m
function [eigvecs, eigvals] = findEigVecs(imvecs, T, D)
[U,eigvals,V] = svd( T );
eigvecs = [];
for i = 1:size(imvecs,2),
eigvec = D * U(:,i);
eigvec = eigvec ./ sum(eigvec);
eigvecs = [eigvecs, eigvec];
end
return
createEigenFaces.m
function [eigenfaces] = createEigenFaces(eigvecs, imvecs, img)
for i = 1:size(imvecs,2),
eigface = reshape(eigvecs( : , i), size(img));
eigface = eigface - min(min(min((eigface))));
eigface = eigface ./ max(max(max((eigface))));
eigenfaces{i}=eigface;
%figure;imagesc(eigface);
end
return
createAverageFace.m
function [mean_image] = createAverageFace(meanval, img)
mean_image = reshape(meanval, size(img));
figure;imagesc(mean_image./255);
title('Average Face')
return
createRandomFace.m
function [stdev_vec] = createRandomFace(eigvals, eigvecs, imvecs, meanval, img)
stdev_vec = sqrt(diag(eigvals));
t = (100 * rand(size(imvecs,2),1) - 50) .* stdev_vec;
new_face1 = meanval + (eigvecs * t);
new_face1 = reshape(new_face1, size(img));
figure;imagesc(new_face1./255);
title('Random Face')
return
vectorComparison.m
function [] = vectorComparison(meanval, eigvecs, stdev_vec, img, mean_image)
t = zeros(17,1);
eig_face_index = 1;
t(eig_face_index) = 1000;
t = t.*stdev_vec;
new_face1 = meanval + (eigvecs * t);
new_face1 = reshape(new_face1, size(img));
new_face2 = meanval - (eigvecs * t);
new_face2 = reshape(new_face2, size(img));
figure;
title('PCA Comparison')
subplot(3,1,1), subimage(new_face1./255)
subplot(3,1,2), subimage(mean_image./255)
subplot(3,1,3), subimage(new_face2./255)
return
I found what was wrong here.
In my function findEigVals I make each vector a unit vector (length 1) by deviding by the sum of the vector itself. This is possible as long as the content of the vector does range positive entries.
However, as we cannot know if we have a vector in pos or neg direction (both equally valid), we cannot use sum here.
Instead we need to replace this with norm, matlab's way of stating normalization.
function [eigvecs, eigvals] = findEigVecs(imvecs, T, D)
[U,eigvals,V] = svd( T );
eigvecs = [];
for i = 1:size(imvecs,2),
eigvec = D * U(:,i);
eigvec = eigvec ./ norm(eigvec);
eigvecs = [eigvecs, eigvec];
end
return
If anyone is using a version of the code above, note that the random face function will give too strong values in rgb-space.
Replace the createRandomFace with the following:
stdev_vec = sqrt(diag(eigvals));
min_range = 0;
max_range = 2;
t = ((max_range - min_range)*rand(n,1)) .* stdev_vec + min_range;
new_face1 = meanval + (eigvecs * t);
new_face1 = reshape(new_face1, size(img));
figure;imagesc(new_face1./255);
I'm trying to implement this paper 'Salient Object detection by composition' here is the link: http://research.microsoft.com/en-us/people/yichenw/iccv11_salientobjectdetection.pdf
I have implemented the algorithm but it takes a long time to execute and display the output. I'm using 4 for loops in the code(Using for loops is the only way I could think of to implement this algorithm.) I have searched online for MATLAB code, but couldn't find anything. So can anyone please suggest any faster way to implement the algorithm. Also in the paper they(the authors) say that they have implemented the code using MATLAB and it runs quickly. So there definitely is a way to write the code more efficiently.
I appreciate any hint or code to execute this algorithm efficiently.
clc
clear all
close all
%%instructions to run segment.cpp
%to run this code
%we need an output image
%segment sigma K min input output
%sigma: used for gaussian smoothing of the image
%K: scale of observation; larger K means larger components in segmentation
%min: minimum component size enforced by post processing
%%
%calculating composition cost for each segment
I_org = imread('segment\1.ppm');
I = imread('segment\output1.ppm');
[rows,cols,dims] = size(I);
pixels = zeros(rows*cols,dims);
red_channel = I(:,:,1);
green_channel = I(:,:,2);
blue_channel = I(:,:,3);
[unique_pixels,count_pixels] = countPixels(I);
no_segments = size(count_pixels,1);
area_segments = count_pixels ./ (rows * cols);
appearance_distance = zeros(no_segments,no_segments);
spatial_distance = zeros(no_segments,no_segments);
thresh = multithresh(I_org,11);
thresh_values = [0 thresh];
for i = 1:no_segments
leave_pixel = unique_pixels(i,:);
mask_image = ((I(:,:,1) == leave_pixel(1)) & (I(:,:,2) == leave_pixel(2)) & (I(:,:,3) == leave_pixel(3)));
I_i(:,:,1) = I_org(:,:,1) .* uint8((mask_image));
I_i(:,:,2) = I_org(:,:,2) .* uint8((mask_image));
I_i(:,:,3) = I_org(:,:,3) .* uint8((mask_image));
LAB_trans = makecform('srgb2lab');
I_i_LAB = applycform(I_i,LAB_trans);
L_i_LAB = imhist(I_i_LAB(:,:,1));
A_i_LAB = imhist(I_i_LAB(:,:,2));
B_i_LAB = imhist(I_i_LAB(:,:,3));
for j = i:no_segments
leave_pixel = unique_pixels(j,:);
mask_image = ((I(:,:,1) == leave_pixel(1)) & (I(:,:,2) == leave_pixel(2)) & (I(:,:,3) == leave_pixel(3)));
I_j(:,:,1) = I_org(:,:,1) .* uint8((mask_image));
I_j(:,:,2) = I_org(:,:,2) .* uint8((mask_image));
I_j(:,:,3) = I_org(:,:,3) .* uint8((mask_image));
I_j_LAB = applycform(I_j,LAB_trans);
L_j_LAB = imhist(I_j_LAB(:,:,1));
A_j_LAB = imhist(I_j_LAB(:,:,2));
B_j_LAB = imhist(I_j_LAB(:,:,3));
appearance_distance(i,j) = sum(min(L_i_LAB,L_j_LAB) + min(A_i_LAB,A_j_LAB) + min(B_i_LAB,B_j_LAB));
spatial_distance(i,j) = ModHausdorffDist(I_i,I_j) / max(rows,cols);
end
end
spatial_distance = spatial_distance ./ max(max(spatial_distance));
max_apperance_distance = max(max(appearance_distance));
composition_cost = ((1 - spatial_distance) .* appearance_distance) + (spatial_distance * max_apperance_distance);
%%
%input parameters for computation
window_size = 9; %rows and colums are considered to be same
window = ones(window_size);
additional_elements = (window_size - 1)/2;
I_temp(:,:,1) = [zeros(additional_elements,cols);I(:,:,1);zeros(additional_elements,cols)];
I_new(:,:,1) = [zeros(rows + (window_size - 1),additional_elements) I_temp(:,:,1) zeros(rows + (window_size - 1),additional_elements)];
I_temp(:,:,2) = [zeros(additional_elements,cols);I(:,:,2);zeros(additional_elements,cols)];
I_new(:,:,2) = [zeros(rows + (window_size - 1),additional_elements) I_temp(:,:,2) zeros(rows + (window_size - 1),additional_elements)];
I_temp(:,:,3) = [zeros(additional_elements,cols);I(:,:,3);zeros(additional_elements,cols)];
I_new(:,:,3) = [zeros(rows + (window_size - 1),additional_elements) I_temp(:,:,3) zeros(rows + (window_size - 1),additional_elements)];
cost = zeros(rows,cols);
for i = additional_elements + 1:rows
for j = additional_elements+1:cols
I_windowed(:,:,1) = I_new(i-additional_elements:i+additional_elements,i-additional_elements:i+additional_elements,1);
I_windowed(:,:,2) = I_new(i-additional_elements:i+additional_elements,i-additional_elements:i+additional_elements,2);
I_windowed(:,:,3) = I_new(i-additional_elements:i+additional_elements,i-additional_elements:i+additional_elements,3);
[unique_pixels_w,count_pixels_w] = countPixels(I_windowed);
unique_pixels_w = setdiff(unique_pixels_w,[0 0 0],'rows');
inside_segment = setdiff(unique_pixels,unique_pixels_w);
outside_segments = setdiff(unique_pixels,inside_segment);
area_segment = count_pixels_w;
for k = 1:size(inside_pixels,1)
current_segment = inside_segment(k,:);
cost_curr_seg = sort(composition_cost(ismember(unique_pixels,current_segment,'rows'),:));
for l = 1:size(cost_curr_seg,2)
if(ismember(unique_pixels(l,:),outside_segments,'rows') && count_pixels(l) > 0)
composed_area = min(area_segment(k),count_pixels(l));
cost(i,j) = cost(i,j) + cost_curr_seg(l) * composed_area;
area_segment(k) = area_segment(k) - composed_area;
count_pixels(l) = count_pixels(l) - composed_area;
if area_segment(k) == 0
break
end
end
end
if area(k) > 0
cost(i,j) = cost(i,j) + max_apperance_distance * area_segment(k);
end
end
end
end
cost = cost / window_size;
The code for the countPixels function:
function [unique_rows,counts] = countPixels(I)
[rows,cols,dims] = size(I);
pixels_I = zeros(rows*cols,dims);
count = 1;
for i = 1:rows
for j = 1:cols
pixels_I(count,:) = reshape(I(i,j,:),[1,3]);
count = count + 1;
end
end
[unique_rows,~,ind] = unique(pixels_I,'rows');
counts = histc(ind,unique(ind));
end
I'm trying to make a time stepping code using the 4th order Runge-Kutta method but am running into issues indexing one of my values properly. My code is:
clc;
clear all;
L = 32; M = 32; N = 32; % No. of elements
Lx = 2; Ly = 2; Lz = 2; % Size of each element
dx = Lx/L; dy = Ly/M; dz = Lz/N; % Step size
Tt = 1;
t0 = 0; % Initial condition
T = 50; % Final time
dt = (Tt-t0)/T; % Determining time step interval
% Wave characteristics
H = 2; % Wave height
a = H/2; % Amplitude
Te = 6; % Period
omega = 2*pi/Te; % Wave rotational frequency
d = 25; % Water depth
x = 0; % Location of cylinder axis
u0(1:L,1:M,1:N,1) = 0; % Setting up solution space matrix (u values)
v0(1:L,1:M,1:N,1) = 0; % Setting up solution space matrix (v values)
w0(1:L,1:M,1:N,1) = 0; % Setting up solution space matrix (w values)
[k,L] = disp(d,omega); % Solving for k and wavelength using Newton-Raphson function
%u = zeros(1,50);
%v = zeros(1,50);
%w = zeros(1,50);
time = 1:1:50;
for t = 1:T
for i = 1:L
for j = 1:M
for k = 1:N
eta(i,j,k,t) = a*cos(omega*time(1,t);
u(i,j,k,1) = u0(i,j,k,1);
v(i,j,k,1) = v0(i,j,k,1);
w(i,j,k,1) = w0(i,j,k,1);
umag(i,j,k,t) = a*omega*(cosh(k*(d+eta(i,j,k,t))))/sinh(k*d);
vmag(i,j,k,t) = 0;
wmag(i,j,k,t) = -a*omega*(sinh(k*(d+eta(i,j,k,t))))/sinh(k*d);
uRHS(i,j,k,t) = umag(i,j,k,t)*cos(k*x-omega*t);
vRHS(i,j,k,t) = vmag(i,j,k,t)*sin(k*x-omega*t);
wRHS(i,j,k,t) = wmag(i,j,k,t)*sin(k*x-omega*t);
k1x(i,j,k,t) = dt*uRHS(i,j,k,t);
k2x(i,j,k,t) = dt*(0.5*k1x(i,j,k,t) + dt*uRHS(i,j,k,t));
k3x(i,j,k,t) = dt*(0.5*k2x(i,j,k,t) + dt*uRHS(i,j,k,t));
k4x(i,j,k,t) = dt*(k3x(i,j,k,t) + dt*uRHS(i,j,k,t));
u(i,j,k,t+1) = u(i,j,k,t) + (1/6)*(k1x(i,j,k,t) + 2*k2x(i,j,k,t) + 2*k3x(i,j,k,t) + k4x(i,j,k,t));
k1y(i,j,k,t) = dt*vRHS(i,j,k,t);
k2y(i,j,k,t) = dt*(0.5*k1y(i,j,k,t) + dt*vRHS(i,j,k,t));
k3y(i,j,k,t) = dt*(0.5*k2y(i,j,k,t) + dt*vRHS(i,j,k,t));
k4y(i,j,k,t) = dt*(k3y(i,j,k,t) + dt*vRHS(i,j,k,t));
v(i,j,k,t+1) = v(i,j,k,t) + (1/6)*(k1y(i,j,k,t) + 2*k2y(i,j,k,t) + 2*k3y(i,j,k,t) + k4y(i,j,k,t));
k1z(i,j,k,t) = dt*wRHS(i,j,k,t);
k2z(i,j,k,t) = dt*(0.5*k1z(i,j,k,t) + dt*wRHS(i,j,k,t));
k3z(i,j,k,t) = dt*(0.5*k2z(i,j,k,t) + dt*wRHS(i,j,k,t));
k4z(i,j,k,t) = dt*(k3z(i,j,k,t) + dt*wRHS(i,j,k,t));
w(i,j,k,t+1) = w(i,j,k,t) + (1/6)*(k1z(i,j,k,t) + 2*k2z(i,j,k,t) + 2*k3z(i,j,k,t) + k4z(i,j,k,t));
a(i,j,k,t+1) = ((u(i,j,k,t+1))^2 + (v(i,j,k,t+1))^2 + (w(i,j,k,t+1))^2)^0.5;
end
end
end
end
At the moment, the values seem to be fine for the first iteration but then I have the error Index exceeds matrix dimension in the line calculating eta. I understand that I am not correctly indexing the eta value but am not sure how to correct this.
My goal is to update the value of eta for each loop of t and then use that new eta value for the rest of the calculations.
I'm still quite new to programming and am trying to understand indexing, especially in 3 or 4 dimensional matrices and would really appreciate any advice in correctly calculating this value.
Thanks in advance for any advice!
You declare
time = 1:1:50;
which is just a row vector but access it here
eta(i,j,k,t) = a*cos(omega*time(i,j,k,t));
as if it were an array with 4 dimensions.
To correctly access element x of time you need to use syntax
time(1,x);
(as it is a 1 x 50 array)