cholfact!

..  cholfact!(A [,LU=:U [,pivot=Val{false}]][;tol=-1.0]) -> Cholesky

``cholfact!`` is the same as :func:`cholfact`, but saves space by overwriting the input ``A``, instead of creating a copy. ``cholfact!`` can also reuse the symbolic factorization from a different matrix ``F`` with the same structure when used as: ``cholfact!(F::CholmodFactor, A)``.

Examples

The cholfact! function in Julia performs a Cholesky factorization of a given matrix A and overwrites the input matrix A with the factorization result. It returns a Cholesky factorization object of size n x n.

Here are some examples of how to use the cholfact! function:

Perform Cholesky factorization and overwrite input matrix:
```
julia> A = [4.0 12.0 -16.0; 12.0 37.0 -43.0; -16.0 -43.0 98.0];
julia> cholfact!(A)
Cholesky{Float64,Array{Float64,2}}
U factor:
3×3 UpperTriangular{Float64,Array{Float64,2}}:
2.0   6.0  -8.0 
 ⋅    1.0  -5.0 
 ⋅     ⋅    3.0 
```
In this example, the cholfact! function performs a Cholesky factorization of the matrix A and overwrites A with the result. The returned object is a Cholesky factorization of the upper triangular matrix.
Reuse symbolic factorization from a different matrix:
```
julia> F = cholfact(A);
julia> B = [1.0 2.0 3.0; 2.0 5.0 6.0; 3.0 6.0 9.0];
julia> cholfact!(F, B)
Cholesky{Float64,Array{Float64,2}}
U factor:
3×3 UpperTriangular{Float64,Array{Float64,2}}:
1.0  2.0  3.0
 ⋅   1.0  1.0
 ⋅    ⋅   0.0
```
This example demonstrates how to reuse the symbolic factorization from matrix A (stored in F) and perform a Cholesky factorization of a different matrix B. The input matrix B is overwritten with the factorization result.

Note: The LU and pivot arguments mentioned in the documentation are optional parameters that control the factorization method. The tol parameter specifies the tolerance level for rank-deficient factorizations.

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cholfact!

Examples

See Also

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