Generating a vector with a pattern?

How do I generate the following vector efficiently for large lengths?

A=[1^1 2^2 3^3 4^4 5^5 6^6]

Answer 1

[Vieniava]

check this out:

A=[1:6].^[1:6];

[Andrew Newell]

Stylistically better is

A = (1:6).^(1:6);

because brackets are used to construct arrays and 1:6 already is an array.

Answer 2

[the cyclist]

>> v = 1:6;
>> A = v.^v;

Stylistically even better? ;-)

[Andrew Newell]

Definitely!

[Walter Roberson]

Now how would we do tetration, v^^v?

http://en.wikipedia.org/wiki/Tetration

[Walter Roberson]

Nevermind; 4^4^4^4 is the largest that fits within realmax.

Answer 3

[Jan]

This job overflows fast for large lengths and computing 200^200 is a waste of time.

EDITED: With Matt Fig's further improvements:

function x = XpowerX(n)
v = 1:min(n,143);
x = inf(1,n);
x(v) = v.^v;

This much faster than the direct 1:n approach:

tic; for i = 1:15000; y = XpowerX(i); end; toc
% 1.8 sec

tic; for i = 1:15000; v = 1:i; y = v.^v; end; toc
% 60 sec

[Matt Fig]

How about:

v = 1:min(n,143);

x = inf(1,n);

x(v) = v.^v;

[Jan]

@Matt: Some percent faster. I insert it.