Chol

chol(A)

A is a square matrix

Produces an upper triangular matrix R from the diagonal and upper triangle of matrix A, satisfying the equation R'*R=A.

chol(A, mode)

A is a square matrix,

mode is a string of 'up' or 'low'

chol(A, 'low') produces a lower triangular matrix L from the diagonal and lower triangle of matrix A, satisfying the equation L*L'=A. chol(A, 'up') is same as chol(A).

Input

Output

chol([1,1,1,1,1;1,2,3,4,5;1,3,6,10,15;1,4,10,20,35;1,5,15,35,70])

chol([1,1,1,1,1;1,2,3,4,5;1,3,6,10,15;1,4,10,20,35;1,5,15,35,70], 'up')

chol([1,1,1,1,1;1,2,3,4,5;1,3,6,10,15;1,4,10,20,35;1,5,15,35,70], 'low')