Qr

Qr decomposition

Syntax

qr(A)

A is a square matrix

Returns unitary Q, upper triangular R and a permutation matrix P so that A*P = Q*R.

Examples

Input

Output

qr([2+i, -3i, -4; 1+i, -1+i, 4+2i; 3+2i, -2+2i, 3-i])

<Q,R,P> =

qr([2+i, -3i, -4; 1+i, -1+i, 4+2i; 3+2i, -2+2i, 3-i])