The ROOT function performs the Cholesky decomposition of a symmetric and positive definite matrix, . The Cholesky decomposition factors into the product

where is upper triangular.

For example, the following statements compute the upper-triangular matrix, U, in the Cholesky decomposition of a matrix:

A = {25  0  5, 
      0  4  6, 
      5  6 59};
U = root(A);
print U;

If you need to solve a linear system and you already have a Cholesky decomposition of your matrix, then use the TRISOLV function as illustrated by the following statements:

b = {5, 2, 53};
/* Want to solve A * v = b.
   First solve U` z = b,
   then solve U v = z */
z = trisolv(2, U, b);
v = trisolv(1, U, z);
print v;

The ROOT function performs most of its computations in the memory allocated for returning the Cholesky decomposition.