Plot first element of vector in A^x * v in Matlab (matrix powers)

Question

I want to plot A^x * v, where A is a square matrix represent an adjacency matrix in a graph, x is the number of steps, and v is the initial vector.

My goal is to plot the first element of each resulting vector; that is, I want A*v[1], A^2*v[1], A^2*v[1]

I tried

x = 1:1:50 
y = A^x*v
plot(y(1),x)

But got

Error using  ^ 
Inputs must be a scalar and a square matrix.
To compute elementwise POWER, use POWER (.^) instead.

I understand the error, but don't understand how else to approach this problem, just going off Matlab's plot examples.

Thanks in advance for the help!

You need to do a for loop over the x's rather than trying to do all of the exponents at once. I don't know a way to vectorize that operation. — Justin Peel, Feb 25 '13 at 03:29
When `A` is not a square matrix, `A^n` is not defined. Thats why the error comes. — Autonomous, Feb 25 '13 at 03:46

Simon · Accepted Answer · 2013-02-25T04:28:47.887

4

If you want an almost one liner:

x = 1:1:50;
f = @(z) z(1);
plot(x, arrayfun(@(n) f(A^n*v), x))

The error in what you tried comes from A^x: x cannot be a vector, it must be a scalar because A is a square matrix. See the help of mpower for more info.

edited Feb 25 '13 at 04:28

answered Feb 25 '13 at 03:55

Simon

31,675
9
80
92

score 2 · Answer 2 · answered Feb 25 '13 at 07:48

2

How about saving some of the computations?
To get the first element you don't need to compute the entire product A*v.

x = 1:1:50;
f = (n) A(1,:) * ( A^(n-1) ) * v; % returns a scalar - no redundant computation
plot( x, arrayfun( f, x ) );

answered Feb 25 '13 at 07:48

Shai

111,146
38
238
371

score 1 · Answer 3 · edited May 23 '17 at 11:43

1

A modification to @Simon's answer, using subsref rather than anonymous function.

x = 1:1:50;
s.type = '()';
s.subs = {1};
plot( x, arrayfun( @(n) subsref( (A^n)*v, s ), x ) );

Plot first element of vector in A^x * v in Matlab (matrix powers)

3 Answers3