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⚡ Optimize Matrix Determinant Calculation (O(N!) -> O(N^3)) #7

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⚡ Optimize Matrix Determinant Calculation (O(N!) -> O(N^3)) #7

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35 changes: 31 additions & 4 deletions utils/matrixMath.ts
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Original file line number Diff line number Diff line change
Expand Up @@ -51,11 +51,38 @@ export const getDeterminant = (m: MatrixData): number | null => {
if (n === 1) return m[0][0];
if (n === 2) return m[0][0] * m[1][1] - m[0][1] * m[1][0];

// Simple recursion for example (Laplace expansion on row 0)
let det = 0;
for (let j = 0; j < n; j++) {
det += Math.pow(-1, j) * m[0][j] * getDeterminant(getMinor(m, 0, j))!;
// Gaussian elimination (O(N^3))
const tempM = m.map(row => [...row]); // Copy matrix to avoid side effects
let det = 1;

for (let i = 0; i < n; i++) {
// Pivot
let pivotIdx = i;
for (let j = i + 1; j < n; j++) {
if (Math.abs(tempM[j][i]) > Math.abs(tempM[pivotIdx][i])) {
pivotIdx = j;
}
}

// Swap rows if needed
if (pivotIdx !== i) {
[tempM[i], tempM[pivotIdx]] = [tempM[pivotIdx], tempM[i]];
det *= -1;
}

if (Math.abs(tempM[i][i]) < 1e-10) return 0; // Singular matrix

Comment on lines +73 to +74

Copilot AI Feb 4, 2026

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The singular-matrix check uses a fixed absolute threshold (1e-10). This is scale-dependent and can incorrectly return 0 for non-singular matrices with small pivots (or fail to detect singularity for very large-valued matrices). Consider using a relative tolerance based on the matrix scale (e.g., compare pivot to maxAbs in the column/row or to a norm times Number.EPSILON) and/or make the epsilon a named constant configurable by callers.

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det *= tempM[i][i];

// Elimination
for (let j = i + 1; j < n; j++) {
const factor = tempM[j][i] / tempM[i][i];
for (let k = i; k < n; k++) {
tempM[j][k] -= factor * tempM[i][k];
}
}
}

return det;
};

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