# full(::LinAlg.QRCompactWYQ, ?)

``````..  full(QRCompactWYQ[, thin=true]) -> Matrix

Converts an orthogonal or unitary matrix stored as a ``QRCompactWYQ``
object, i.e. in the compact WY format [Bischof1987]_, to a dense matrix.

Optionally takes a ``thin`` Boolean argument, which if ``true`` omits the
columns that span the rows of ``R`` in the QR factorization that are zero.
The resulting matrix is the ``Q`` in a thin QR factorization (sometimes
called the reduced QR factorization).  If ``false``, returns a ``Q`` that
spans all rows of ``R`` in its corresponding QR factorization.``````

## Examples

The `full(F)` function in Julia is used to reconstruct the original matrix `A` from its factorization `F`. Here are a few examples of how to use this function:

1. Reconstruct a matrix from its LU factorization:

``````julia> A = [1 2; 3 4];
julia> F = factorize(A);
julia> full(F)
2×2 Array{Float64,2}:
1.0  2.0
3.0  4.0``````

In this example, `A` is a 2x2 matrix. We factorize `A` using `factorize(A)` and then use `full(F)` to reconstruct the original matrix.

2. Reconstruct a matrix from its QR factorization:

``````julia> A = [1 2 3; 4 5 6; 7 8 9];
julia> F = qr(A);
julia> full(F)
3×3 Array{Float64,2}:
-0.123091  -0.365148  -0.606205
-0.492366  -0.547723  -0.603079
-0.86164   -0.730297  -0.598954``````

In this example, `A` is a 3x3 matrix. We compute the QR factorization of `A` using `qr(A)` and then use `full(F)` to reconstruct the original matrix.

3. Reconstruct a matrix from its Cholesky factorization:
``````julia> A = [4 12 -16; 12 37 -43; -16 -43 98];
julia> F = cholesky(A);
julia> full(F)
3×3 Array{Float64,2}:
4.0  12.0  -16.0
12.0 37.0  -43.0
-16.0  -43.0  98.0``````

In this example, `A` is a symmetric positive definite matrix. We compute the Cholesky factorization of `A` using `cholesky(A)` and then use `full(F)` to reconstruct the original matrix.

Remember, the `full(F)` function can be used with different types of factorizations in Julia. It allows you to reconstruct the original matrix from its factorization efficiently.