Language Reference

ROOT Function

performs the Cholesky decomposition of a matrix

ROOT( matrix)

where matrix is a symmetric positive-definite matrix.

The ROOT function performs the Cholesky decomposition of a matrix (for example, ) such that

where is upper triangular. The matrix must be symmetric and positive definite.

For example, consider the following statements:

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

These statements produce the following result:

  
                   U 
  
            5         0         1 
            0         2         3 
            0         0         7
 

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 in the following code.

  
    b = {5, 2, 53}; 
    /* want to solve xpx * t = b. 
       First solve U` z = b, 
       then solve U t = z */ 
    z = trisolv(2,U,b); 
    t = trisolv(1,U,z);
 

The solution is as follows:

  
                   T 
  
                   0 
                  -1 
                   1
 

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