VoseCholesky | Vose Software







Example model

This function does a Cholesky decomposition of the input matrix. The input matrix, that should be a symmetric, positive-definite matrix, is decomposed into a lower Triangle matrix L and the transpose LT of the lower Triangle matrix. The lower Triangle matrix is called the Cholesky triangle of the original, positive-definite matrix.

The Cholesky decomposition is mainly used to solve linear equations Ax = b numerically. The way this is done is by first computing the Cholesky decomposition A = L LT, then solving Ly = b for y and then solving  LTx = y for x. Another important use of the Cholesky decomposition (this is the use focussed on in ModelRisk) is in Monte Carlo simulations to simulate systems with multiple correlated variables. In this case (and thus in ModelRisk too) the output of the decomposition is only the lower Triangle matrix L and a null matrix as upper Triangle matrix because all the correlation from the decomposed matrix is in the lower Triangle matrix L.

For example, if one wants to do a Cholesky decomposition of the matrix:

one has to type: =VoseCholesky(A) where A refers to the input matrix here above. The output (this function is an array function and the output matrix must be of the same size as the input matrix) generated is then: