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# Question: a matlab question which need to modify the code and...

###### Question details

A Matlab question, which need to modify the code and answer it, thanks! % experimental parameters
N = 1000;
Nex = 50;

% three matrix types

% dense matrix (no zeros)
Md = randn(N,N);

% upper triangular
Mt = triu(Md);

% randomly row-exchanged upper triangular (these are tricky array commands,
% but if you run a small sample, it is clear they do the right thing)
idx=randperm(N);
Mp = Mt(idx,:);

% exact solution of all ones
x = ones(N,1);

% right-side vectors
bd = Md*x;
bt = Mt*x;
bp = bt(idx);

% dense test
tic
for jj = 1:Nex
xd = Mdd;
end
dense_time=toc;

% upper tri test
tic
for jj = 1:Nex
xt = Mtt;
end
tri_time=toc;

% permuted upper tri test
tic
for jj = 1:Nex
xp = Mpp;
end
perm_tri_time=toc;

%Computing avgerage solve times
avg_tri_time = tri_time/(Nex);

avg_perm_time = perm_tri_time/(Nex);

avg_dense_time = dense_time/(Nex);

% You may find the following code helpful for displaying the results
% of this demo.
type_times = {'Dense',avg_dense_time,'Upper Triangular', ...
avg_tri_time,'permuted Upper Triangular', ...
avg_perm_time};
fprintf('
')
fprintf('Estimated time for a %s matrix is %f seconds.
',type_times{:})
###### Solution by an expert tutor 