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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