Nuclear norm coding issue

So I have a Nuclear norm program thats supposed to output a graph but my issue is that when ever I decide to make the dimensions n and m smaller than 30 and 30 the code gives this error message and gives out a graph that isnt fully correct.

Following error message -

Index exceeds the number of array elements (3).

Error in Untitle234d (line 131)

plot([1 : 50:(m*n)], SuccessRate(2:9));

Here is my code

% Number of Monte Carlo simulations

MC = 10;

% Fix the dimentions of a groundtruth table X*

n = 10; m = 10;

% Fix the rank of k

k = 3;

% Use (41) to generate X*

U = randn(m, k); V = randn(n, k);

X = U*V';

% Define the success threshold(epsilon) and initialise variables for

% calculating the success rates

epsilon = 0.2;

CountS = 0; CountT = 0;

SuccessRate = 0;

for p = 1 : 50 : (m*n) % Number of observations

for mc = 1 : MC % Monte Carlo simulations

M_p = cell(p, 1); % Cell array of empty matrices

y = zeros(p, 1); % Vector of measurements

for i_p = 1 : p % Generate measurement matrices in the cell array

% Get e_i

rp_i = randperm(m);

% Generate a vector of random values

e_i = zeros(m, 1);

e_i(rp_i(1)) = 1;

% Generate e_i as a vector of zeros with a single 1 at a random index

% Get e_j

rp_j = randperm(n);

e_j = zeros(n, 1);

e_j(rp_j(1)) = 1;

% Get the M matrix

M_p{i_p} = e_i .* e_j';

y(i_p) = trace(M_p{i_p}*X);

end

cvx_begin % (48)

variable Xe(n,n);

minimize(norm_nuc(Xe));

subject to

for i_p = 1 : p

trace(Xe*M_p{i_p}) == y(i_p);

end

cvx_end

end

% If the recreation was successful, increment the success counter

if ((norm(Xe-X, 'fro')/norm(X, 'fro')) <= epsilon)

CountS = CountS + 1;

end

% Increment the trial counter

CountT = CountT + 1;

% Define the success rate for the current p value

SuccessRate = [SuccessRate (CountS/CountT)];

end

% Plot the success rate as a fuction of p. Then, on the same axes, plot the

% line @ p0 = 3k(m + n - k) + 1

hold on

plot([1 : 50:(m*n)], SuccessRate(2:9));

p0 = 3*k*(m + n - k) + 1;

xline(p0);

hold off;

Answer 1

[Image Analyst]

In

plot([1 : 50:(m*n)], SuccessRate(2:9))

SuccessRate(2:9) has 8 elements. Does x have 8 elements? What does this show

lengthX = length([1 : 50:(m*n)]);

If it's not 8, it won't work. What does it give for lengthX?