udfactor

Factors a positive semi-definite matrix, A, into an upper-unitriangular matrix, U, and diagonal matrix with elements in d such that:

U * diag(d) * U.' == A

This function is nearly identical to ldfactor. See that function for more.

Inputs

A	Positive, semi-definite matrix
tol	Division tolerance; when divisors are below this value, no division will actually take place.

Outputs

U	Upper unitriangular matrix
d	Vector of diagonals
nz	Number of zero diagonals found during factorization

Example

Generate a random covariance matrix.

Break it down to U and d.

P = randcov(3)
[U, d] = udfactor(P)

P =
    0.5052   -0.2311   -0.2059
   -0.2311    0.5124   -0.0714
   -0.2059   -0.0714    0.7502
U =
    1.0000   -0.4959   -0.2744
         0    1.0000   -0.0951
         0         0    1.0000
d =
    0.3243
    0.5056
    0.7502

Reconstruct the original matrix

U * diag(d) * U.'

ans =
    0.5052   -0.2311   -0.2059
   -0.2311    0.5124   -0.0714
   -0.2059   -0.0714    0.7502

Reference

Stengel, Robert F. Optimal Control and Estimation. New York: Dover Publications, Inc. 1994. Print. Page 360.

Docs

udfactor

Inputs

Outputs

Example

Reference

See Also

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