..  hessfact!(A)

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


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.

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