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Scilab help >> Linear Algebra > chol

chol

Cholesky factorization

Calling Sequence

`[R]=chol(X)`

Arguments

X

a symmetric positive definite real or complex matrix.

Description

If `X` is positive definite, then `R = chol(X)` produces an upper triangular matrix `R` such that `R'*R = X`.

`chol(X)` uses only the diagonal and upper triangle of `X`. The lower triangular is assumed to be the (complex conjugate) transpose of the upper.

References

Cholesky decomposition is based on the Lapack routines DPOTRF for real matrices and ZPOTRF for the complex case.

Examples

```W=rand(5,5)+%i*rand(5,5);
X=W*W';
R=chol(X);
norm(R'*R-X)```

• spchol — sparse cholesky factorization
• qr — QR decomposition
• svd — singular value decomposition
• bdiag — block diagonalization, generalized eigenvectors
• fullrf — full rank factorization