MATLAB: Create a vector of vector exponents

exponentmatrix manipulation

Hi,

Assume I have a vector v and a square matrix A

v = [1, 2, 3, 4, 5];
A = randn(5);

I want to create a matrix

m = [v*A; v*A^2; v*A^3; ..; v*A^n]

Where n is a user input and ^ results in the matrix product operator (not dot product .^)

I can do that easily with a loop. Is there a quicker way of doing this without using a loop?

Best Answer

No, a for-loop is fastest, but you want to implement it the right way, with a recursive update,

m=repmat(v*A,n,1); %pre-allocate
for i=2:n
    m(i,:) = m(i-1,:)*A;
end

That way, the process takes only n matrix multiplications.

Related Solutions

MATLAB: Put elements into corresponding locations of upper triangular matrix

Start with nested loops:

v = 1:6;
n = round((sqrt(8 * numel(v) + 1) - 1) / 2);
M = zeros(n, n);
c = 0;
for i2 = 1:n
  for i1 = 1:i2
    c         = c + 1;
    M(i1, i2) = v(c);
  end
end

In the next step you can vectorize the inner loop: Move the loop index inside the assignment:

n = round((sqrt(8 * numel(v) + 1) - 1) / 2);
M = zeros(n, n);
a = 1;
for k = 1:n
  b         = a + k - 1;
  M(1:k, k) = v(a:b);
  a         = b + 1;
end

Is this nicer? Questionable, but maybe faster.

Now use a built-in function:

n = round((sqrt(8 * numel(v) + 1) - 1) / 2);
M(triu(ones(n)) == 1) = v;

or better:

M(triu(true(n))) = v;

[EDITED] Some timings - what did you expect?

v = 1:5050;
tic; for k = 1:10000; y = SerialTriU(v); end, toc
Elapsed time is 0.772492 seconds.   % Two loops
Elapsed time is 2.448738 seconds.   % Inner loop vectorized
Elapsed time is 1.029641 seconds.   % TRIU(ONES)
Elapsed time is 0.659360 seconds.   % TRIU(TRUE)

MATLAB: Help.. how would i get 7* to 1*

You can run the for-loop in reverse order too

N = 7; 
for mm = N:-1:1 % equivalent to mm = flip(1:N)
    for nn = 1:mm
        fprintf('*');
    end
    fprintf('\n');
end

Best Answer

Related Solutions

MATLAB: Put elements into corresponding locations of upper triangular matrix

MATLAB: Help.. how would i get 7* to 1*

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