hessfact!

..  hessfact!(A)

``hessfact!`` is the same as :func:`hessfact`, but saves space by overwriting the input ``A``, instead of creating a copy.

Examples

The hessfact!(A) function in Julia is used to compute the Hessenberg factorization of a matrix. It is similar to the hessfact function, but it overwrites the input matrix A instead of creating a copy, which helps to save space.

Here are some examples of how to use hessfact!:

1. Compute the Hessenberg factorization of a matrix:

julia> A = [1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0];
julia> hessfact!(A)
3×3 Matrix{Float64}:
1.0  3.74  4.9
5.92  0.514  6.68
0.0  -6.2    0.515

In this example, the Hessenberg factorization of the matrix A is computed and stored in A itself.

2. Update an existing matrix with its Hessenberg factorization:
julia> B = [2.0 4.0; 6.0 8.0];
julia> hessfact!(B)
2×2 Matrix{Float64}:
2.0  6.32456
6.32456  7.67544

The function updates the matrix B with its Hessenberg factorization.

It is important to note that the hessfact!(A) function modifies the input matrix A in-place. Therefore, if you need to preserve the original matrix, make a copy before using hessfact!.

Please make sure to have a backup of your data before using the hessfact! function, as it overwrites the input matrix.