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svdfact!

..  svdfact!(A, [thin=true]) -> SVD

``svdfact!`` is the same as :func:`svdfact`, but saves space by overwriting the input ``A``, instead of creating a copy. If ``thin`` is ``true``, an economy mode decomposition is returned. The default is to produce a thin decomposition.

Examples

The svdfact!(A, [thin=true]) function in Julia performs Singular Value Decomposition (SVD) on matrix A. It overwrites the input matrix A, saving space by not creating a copy. If thin is set to true, it returns an economy mode decomposition. The default behavior is to produce a thin decomposition.

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

1. Perform SVD on a matrix:

   julia> A = [1 2 3; 4 5 6; 7 8 9];
   julia> svdfact!(A)
   SVD{Float64, Float64, Matrix{Float64}}
   U factor:
   3×3 Matrix{Float64}:
   -0.214837  -0.887231   0.408248
   -0.520587  -0.249644  -0.816497
   -0.826338   0.387943   0.408248
   singular values:
   3-element Vector{Float64}:
   16.848103352614207
    1.0683695145549087e-15
    1.0683695145549087e-15
   Vt factor:
   3×3 Matrix{Float64}:
   -0.479671  -0.572368  -0.665064
   -0.776691  -0.075686   0.625319
   -0.408248   0.816497  -0.408248

   This example performs SVD on matrix A and overwrites it with the result. It returns the SVD object containing the U factor, singular values, and Vt factor.

2. Perform economy mode SVD:

   julia> B = [1 2 3; 4 5 6; 7 8 9];
   julia> svdfact!(B, true)
   SVD{Float64, Float64, Matrix{Float64}}
   U factor:
   3×2 Matrix{Float64}:
   -0.214837  -0.887231
   -0.520587  -0.249644
   -0.826338   0.387943
   singular values:
   2-element Vector{Float64}:
   16.848103352614207
    1.0683695145549087e-15
   Vt factor:
   2×3 Matrix{Float64}:
   -0.479671  -0.572368  -0.665064
   -0.776691  -0.075686   0.625319

   In this example, the thin parameter is set to true, resulting in an economy mode decomposition where the U factor and Vt factor are reduced to their optimal sizes.

Remember that svdfact! modifies the input matrix A directly, so make sure to create a copy if you need to preserve the original matrix.

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