To mimic the error found in the QR algorithm, we have to test with matrices that have duplicate eigenvalues and introduce numerical precision errors.

To do this, a list of perturbed eigenvalues is passed to the eigenvectors method. The perturbation is achieved by adding a random +/- offset on an order of magnitude smaller than the default matrix error. This should allow the math to work out fine while causing the floating point comparison to fail.

array_search seems to fail in most cases when looking for a float in an array of floats. And even if it does find a match, if the key is 0, php evaluates `!0` to true.

To find a match, we can instead loop through and compare the numbers with `Arithmetic::almostEqual` and then explicitly check if `$key === false`

Calculates the Moore-Penrose inverse of the matrix using SVD

Just an alias for inverse

If it isn't, create a permutation matrix, P, such that SP is diagonal.
Multiply V by its inverse to balance the eqn.

After diagonalizing S and ensuring its values are positive,
check that its values are sorted. If not, permute it

The method of diagonalization permuted columns. However, if the row count exceeds the column count, there's a chance the column permutation won't diagonalize S. To address this, the diagonalization has been refactored to sort on the bigger dimension.

Not available in php 7.0

to getStandardBasisIndex

Because 0 can be a singular value, the S matrix can have zero-entries along the diagonal.
To allow this, we first check if the vector magnitude is 0 before calling getStandardBasisIndex

Since we're checking for non-zero components using Arithmetic::almostEqual, it seems appropriate to pass in the error of the matrix

Adds the case from the pseudoinverse test

If the diagonal has duplicate eigenvalues that are floats, the sort operation can shuffle them around. The strict equivalence then fails when it technically should not.

Instead, we can compare the diagonal entries to the sorted entries using `AlmostEqual` with the matrix error for tolerance.

Previously was just using the default error of `Support::isZero`