chol

Purpose

Computes the Cholesky decomposition of a symmetric, positive definite square matrix.

Format

u = chol(x)
Parameters:x (NxN matrix) – Symmetric, positive definite square matrix.
Returns:u (NxN matrix) – containing the Cholesky decomposition of x.

Examples

// 'moment' calculates x'*x with options for handling missing data

x = moment(rndn(100, 4), 0);

u = chol(x);

// u'u is equivalent to u'*u
upu = u'u;

    95.2801   8.6983   3.7248    1.5449      9.7612   0.8911   0.3816   0.1583
x =  8.6983  83.4547  -6.1455  -12.5551  u = 0.0000   9.0918  -0.7133  -1.3964
     3.7248  -6.1455  87.6666   -3.0284      0.0000   0.0000   9.3280  -0.4379
     1.5449 -12.5551  -3.0284   90.8311      0.0000   0.0000   0.0000   9.4162

     95.2801   8.6983   3.7248   1.5449
upu = 8.6983  83.4547  -6.1455 -12.5551
      3.7248  -6.1455  87.6666  -3.0284
      1.5449 -12.5551  -3.0284  90.8311

Remarks

u is the “square root” matrix of x. That is, it is an upper triangular matrix such that \(x = u'u\).

chol() does not check to see that the matrix is symmetric. chol() will look only at the upper half of the matrix including the principal diagonal.

If the matrix x is symmetric but not positive definite, either an error message or an error code will be generated, depending on the lowest order bit of the trap flag:

trap 0 Print error message and terminate program.
trap 1 Print error message and terminate program.

See scalerr() and trap for more details about error codes.

See also

Functions crout(), solpd()