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matlabmatrixlinear-algebra
user3529945
user3529945

Reputation: 21

Using `diag()` Command to Construct Circulant Matrix

Here is the question: Write a MATLAB program which uses the diag command to generate n by n circulant matrices: given vector v = (v1 v2 v3 ....vn). Example of circulant matrices: 

A = [1 2 3 4 5;
     5 1 2 3 4;
     4 5 1 2 3;
     3 4 5 1 2;
     2 3 4 5 1]

note the wrap-around patter of successive rows.
Use diag command in MATLAB.

(here is what I started from, I am having trouble to construct the matrix using diag command. Please help).

n = length(v);
a = zeros(n);

for i = 1:n

Upvotes: 0

Views: 2295

Answers (4)

AnonSubmitter85
AnonSubmitter85

Reputation: 933

The simplest way to do this without any looping is to take advantage of the Fourier properties of circulant matrices and use the FFT:

V = ifft( fft( diag( fft(x) ), [], 1 ), [], 2 );

Upvotes: 0

Seul Ement
Seul Ement

Reputation: 225

Interestingly, since all the circulant matrices are made diagonal by the DFT, you can also do something like that

// given vector
v = [1 2 3 4 5];
n = numel(v);
// DFT matrix
F = dftmtx(n);
//circulant matrix
V = (F*diag(fft(v))*F')./n;

Upvotes: 3

guest1
guest1

Reputation: 11

function m = prgrm9( x )
%UNTITLED3 Summary of this function goes here
%   Detailed explanation goes here

m = diag(x(1)* ones(1,length(x)));

for i = 2: length(x)
   m = m + diag(x(i) * ones(1, length(x)-(i-1)),i-1)+ diag(x(i)*ones(1,i-1),i-(length(x)+1));
end

Upvotes: 1

Divakar
Divakar

Reputation: 221624

Code

%%// Given vector v
v = [1 2 3 4 5];

%%// Parameters
n = numel(v);
arr1 = [v1(2:end) v1];

%%// Construct circulant matrix
A1 = zeros(n);
for k = -(n-1):n-1
    A1 = A1+ arr1(k+n)*diag(ones(n-abs(k),1),k);
end

Upvotes: 1

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