circulant

(yet another, but fast) Circulent Matrix
2.5K Downloads
Updated 12 Feb 2019

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C = circulant(V) or circulant(V, 1) returns the circulant matrix C
based on the row/column vector V. C is a square matrix in which each
row/column is a formed by circularly shifting the preceeding row/column
forward by one element. The first row (or column) is equal to V.

C = circulant(V, -1) applies a backward shift, returning a symmetric
matrix, so that C equals TRANSPOSE(C). In this case, it does not matter
if V is a row or column vector.

Examples:
circulant([2 3 5]) % forward shift
% -> 2 3 5
% 5 2 3
% 3 5 2

circulant([2 3 5].') % column input
% -> 2 5 3
% 3 2 5
% 5 3 2

circulant([2 3 5], -1), circulant([2 ; 3 ; 5], -1) % backward shift
% for both row or column vectors, this returns a symmetric matrix:
% -> 2 3 5
% 3 5 2
% 5 2 3

The output has the same type as the input.

V = {'One' '2' 'III'}
circulant(A)
% -> 'One' '2' 'III'
% 'III' 'One' '2'
% '2' 'III' 'One'

Notes:
- This version is completely based on indexing and does not use loops,
repmat, hankel, toeplitz or bsxfun. It should therefore run pretty
fast on most Matlab versions.
- See http://en.wikipedia.org/wiki/Circulant_matrix for more info on
circulant matrices.

See also toeplitz, hankel
latsq, ballatsq (on the file Exchange)

Cite As

Jos (10584) (2024). circulant (https://www.mathworks.com/matlabcentral/fileexchange/22876-circulant), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2018b
Compatible with any release
Platform Compatibility
Windows macOS Linux
Categories
Find more on Creating and Concatenating Matrices in Help Center and MATLAB Answers
Acknowledgements

Inspired by: Circular Matrix computation, Circulant matrix

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Version Published Release Notes
2.2.0.0

modernised

1.3.0.0

Multiple acknowledgements added

1.2.0.0

v2.0 - bug fixed for forward shifted vectors !!

1.1.0.0

acknowledge both FEX ID 22814 and 22858

1.0.0.0