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Add QR algorithm #472

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Add QR algorithm #472

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Commits on Nov 6, 2023

  1. Replace array_search with floating-point filter 

    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`
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    Aweptimum committed Nov 6, 2023
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  2. Make 8.2 linter happy

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    Aweptimum committed Nov 6, 2023
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  3. Add NumericaMatrix->upperHessenberg 

    Converts a matrix to hessenberg form using householder reflections
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    Aweptimum committed Nov 6, 2023
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  4. Test uppserHessenberg

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    Aweptimum committed Nov 6, 2023
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  5. Add qrAlgorithm

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    Aweptimum committed Nov 6, 2023
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  6. test QRAlgorithm eigenvalues

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    Aweptimum committed Nov 6, 2023
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  7. Shift QR by Wilkinson, refactor a bit 

    The Wilkinson shift accelerates the rate of convergence for the QR algorithm - it's in the static calcShift helper

Additionally, moved the iteration to an inner helper function to hide the $values parameter from the public method
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    Aweptimum committed Nov 6, 2023
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  8. Add qr method to Eigenvector 

    Just gets the eigenvalues from the qr algorithm and feeds them to the eigenvectors method
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    Aweptimum committed Nov 6, 2023
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  9. Test Eigenvector::qrAlgorithm

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    Aweptimum committed Nov 6, 2023
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  10. Add failing eigenvector cases to eigenvalues 

    They work, so the problem must be in the eigenvectors method
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    Aweptimum committed Nov 6, 2023
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