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Add failing RREF Case #475

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Add failing RREF Case #475

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3ec7c55
Add successful rref case and its failing counterpart
Aweptimum Nov 8, 2023
f386771
REF: scale by smallest non-zero element
Aweptimum Nov 9, 2023
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13 changes: 13 additions & 0 deletions src/LinearAlgebra/Reduction/RowEchelonForm.php
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Original file line number Diff line number Diff line change
Expand Up @@ -127,6 +127,19 @@ public static function gaussianElimination(NumericMatrix $A): array
$swaps = 0;
$ε = $A->getError();

// Scale the matrix by its smallest non-zero element
$min = PHP_INT_MAX;
for ($i = 0; $i < $m; $i++) {
for ($j = 0; $j < $n; $j++) {
$elem = \abs($A[$i][$j]);
if (Support::isNotZero($elem, $ε) and $elem < $min) {
$min = $elem;
}
}
}

$R = $A->scalarMultiply(1/$min)->getMatrix();

for ($k = 0; $k < $size; $k++) {
// Find column max
$i_max = $k;
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38 changes: 38 additions & 0 deletions tests/LinearAlgebra/Reduction/ReducedRowEchelonFormTest.php
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Expand Up @@ -1045,6 +1045,44 @@ public function dataProviderForRref(): array
[0, 0, 0, 0, 0],
],
],
// Large magnitude case
[
[
[-2.82878905765*10**6, 0, 0, 0, 0, 0],
[0, -2.82878905765*10**6, 0, 0, 0, 1729.7],
[0, 0, -2.82878905765*10**6, 0, -1729.7, 0],
[0, 0, 0, -2.82879105765*10**6, 0, 0],
[0, 0, -1729.7, 0, -1.05765, 0],
[0, 1729.7, 0, 0, 0, -1.05765]
],
[
[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1]
]
],
// Scaled version of large magnitude case
[
[
[-0.99999966687087, 0, 0, 0, 0, 0],
[0, -0.99999966687087, 0, 0, 0, 0.00061146285160793],
[0, 0, -0.99999966687087, 0, -0.00061146285160793, 0],
[0, 0, 0, -1.0000003738869, 0, 0],
[0, 0, -0.00061146285160793, 0, -3.7388694340557*10**-7, 0],
[0, 0.00061146285160793, 0, 0, 0, -3.7388694340557*10**-7]
],
[
[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1]
]
]
];
}

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