Language Reference |
ROOT Function |
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.
Copyright © SAS Institute, Inc. All Rights Reserved.