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1609 lines (1363 loc) · 42.2 KB
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import { unwrapDenseMatrix, wrapDenseMatrix } from '../utils/matrix.js';
import { fraction as makeFrac, isFraction, numer, denom } from '../math/fraction.js';
import { bigNumber as makeBN, isBigNumber } from '../math/bignumber.js';
/** @param {any[]} matrix */
function validateSquareMatrix(matrix) {
matrix = unwrapDenseMatrix(matrix);
if (!Array.isArray(matrix) || matrix.length === 0) {
throw new Error('det() expects a non-empty matrix');
}
if (!matrix.every(Array.isArray)) {
throw new Error('det() expects a 2D matrix');
}
const size = matrix.length;
if (!matrix.every((row) => row.length === size)) {
throw new Error('det() expects a square matrix');
}
for (const row of matrix) {
for (const value of row) {
if (typeof value !== 'number' && typeof value !== 'bigint') {
throw new Error('det() matrix values must be numeric');
}
}
}
}
/** @param {any[]} matrix */
function determinant(matrix) {
matrix = unwrapDenseMatrix(matrix);
validateSquareMatrix(matrix);
if (matrix.length === 1) {
return matrix[0][0];
}
if (matrix.length === 2) {
return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
}
// Laplace expansion: sum of (-1)^col * M[0][col] * det(minor)
return matrix[0].reduce(
(/** @type {number} */ sum, /** @type {number} */ value, /** @type {number} */ columnIndex) => {
const minor = matrix
.slice(1)
.map((row) =>
row.filter((/** @type {any} */ _, /** @type {number} */ index) => index !== columnIndex)
);
const cofactor = columnIndex % 2 === 0 ? value : -value;
return sum + cofactor * determinant(minor);
},
0
);
}
/** @param {any} value */
function asMatrixData(value) {
const data = unwrapDenseMatrix(value);
if (!Array.isArray(data)) {
throw new Error('Expected matrix data');
}
return data;
}
/**
* @param {any[]} coefficients
* @param {number[]} constants
*/
function solveLinearSystem(coefficients, constants) {
const n = coefficients.length;
const augmented = coefficients.map((row, rowIndex) => [...row, constants[rowIndex]]);
for (let pivot = 0; pivot < n; pivot++) {
let maxRow = pivot;
let maxValue = Math.abs(augmented[pivot][pivot]);
for (let row = pivot + 1; row < n; row++) {
const current = Math.abs(augmented[row][pivot]);
if (current > maxValue) {
maxValue = current;
maxRow = row;
}
}
if (maxValue === 0) {
throw new Error('Linear system is singular');
}
if (maxRow !== pivot) {
[augmented[pivot], augmented[maxRow]] = [augmented[maxRow], augmented[pivot]];
}
const pivotValue = augmented[pivot][pivot];
for (let col = pivot; col <= n; col++) {
augmented[pivot][col] /= pivotValue;
}
for (let row = 0; row < n; row++) {
if (row === pivot) {
continue;
}
const factor = augmented[row][pivot];
for (let col = pivot; col <= n; col++) {
augmented[row][col] -= factor * augmented[pivot][col];
}
}
}
return augmented.map((row) => row[n]);
}
/** @param {any} input */
function lupDecomposition(input) {
const matrix = asMatrixData(input).map((row) => [...row]);
validateSquareMatrix(matrix);
const n = matrix.length;
const permutation = Array.from({ length: n }, (_, index) => index);
for (let pivot = 0; pivot < n; pivot++) {
let maxRow = pivot;
let maxValue = Math.abs(matrix[pivot][pivot]);
for (let row = pivot + 1; row < n; row++) {
const current = Math.abs(matrix[row][pivot]);
if (current > maxValue) {
maxValue = current;
maxRow = row;
}
}
if (maxValue === 0) {
throw new Error('Matrix is singular');
}
if (maxRow !== pivot) {
[matrix[pivot], matrix[maxRow]] = [matrix[maxRow], matrix[pivot]];
[permutation[pivot], permutation[maxRow]] = [permutation[maxRow], permutation[pivot]];
}
for (let row = pivot + 1; row < n; row++) {
matrix[row][pivot] /= matrix[pivot][pivot];
for (let col = pivot + 1; col < n; col++) {
matrix[row][col] -= matrix[row][pivot] * matrix[pivot][col];
}
}
}
const L = matrix.map((row, rowIndex) =>
row.map((value, colIndex) => {
if (rowIndex === colIndex) {
return 1;
}
if (rowIndex > colIndex) {
return value;
}
return 0;
})
);
const U = matrix.map((row, rowIndex) =>
row.map((value, colIndex) => (rowIndex <= colIndex ? value : 0))
);
return {
L: wrapDenseMatrix(L),
U: wrapDenseMatrix(U),
p: permutation,
};
}
/**
* @param {any} aInput
* @param {{ exprify: string; data: any; size: number[]; }} bInput
*/
function linearSolve(aInput, bInput) {
const { L, U, p } = lupDecomposition(aInput);
const a = asMatrixData(aInput);
const bData = asMatrixData(bInput);
const bVector = Array.isArray(bData[0]) ? bData.map((row) => row[0]) : bData;
if (a.length !== bVector.length) {
throw new Error('Right-hand side dimension mismatch');
}
const permutedB = p.map((index) => bVector[index]);
const y = new Array(a.length).fill(0);
for (let row = 0; row < a.length; row++) {
y[row] = permutedB[row];
for (let col = 0; col < row; col++) {
y[row] -= L.data[row][col] * y[col];
}
}
const x = new Array(a.length).fill(0);
for (let row = a.length - 1; row >= 0; row--) {
x[row] = y[row];
for (let col = row + 1; col < a.length; col++) {
x[row] -= U.data[row][col] * x[col];
}
x[row] /= U.data[row][row];
}
return wrapDenseMatrix(x.map((value) => [value]));
}
/**
* @param {any} aInput
* @param {any} qInput
*/
function solveLyapunov(aInput, qInput) {
const A = asMatrixData(aInput).map((row) => [...row]);
const Q = asMatrixData(qInput).map((row) => [...row]);
validateSquareMatrix(A);
validateSquareMatrix(Q);
const n = A.length;
if (Q.length !== n) {
throw new Error('A and Q must have the same dimensions');
}
const coefficients = [];
const constants = [];
for (let row = 0; row < n; row++) {
for (let col = 0; col < n; col++) {
const equation = new Array(n * n).fill(0);
for (let k = 0; k < n; k++) {
equation[k * n + col] += A[row][k];
equation[row * n + k] += A[col][k];
}
coefficients.push(equation);
constants.push(-Q[row][col]);
}
}
const solution = solveLinearSystem(coefficients, constants);
const X = [];
for (let row = 0; row < n; row++) {
X.push(solution.slice(row * n, (row + 1) * n));
}
return wrapDenseMatrix(X);
}
/**
* @param {any[]} coefficients
* @param {number} x
*/
function evaluatePolynomial(coefficients, x) {
return coefficients.reduce((sum, coefficient, index) => sum + coefficient * x ** index, 0);
}
/**
* @param {any[]} coefficients
* @param {number} root
*/
function syntheticDivide(coefficients, root) {
const descending = [...coefficients].reverse();
const quotient = [descending[0]];
for (let index = 1; index < descending.length - 1; index++) {
quotient.push(descending[index] + quotient[index - 1] * root);
}
const remainder = descending[descending.length - 1] + quotient[quotient.length - 1] * root;
return {
quotient: quotient.reverse(),
remainder,
};
}
/**
* @param {any[]} coefficients
*/
function solveQuadratic(coefficients) {
const [c, b, a] = coefficients;
const discriminant = b ** 2 - 4 * a * c;
if (discriminant < 0) {
throw new Error('Only real roots are supported');
}
const sqrtDisc = Math.sqrt(discriminant);
return [(-b + sqrtDisc) / (2 * a), (-b - sqrtDisc) / (2 * a)];
}
/**
* @param {any[]} coefficients
*/
function polynomialRoots(...coefficients) {
while (coefficients.length > 1 && coefficients[coefficients.length - 1] === 0) {
coefficients.pop();
}
const degree = coefficients.length - 1;
if (degree < 1) {
throw new Error('polynomialRoot() expects at least a linear polynomial');
}
if (degree === 1) {
const [b, a] = coefficients;
return [-b / a];
}
if (degree === 2) {
return solveQuadratic(coefficients);
}
// Rational root theorem: possible roots are divisors of the constant term
if (degree === 3) {
const constant = coefficients[0];
const candidates = [];
const limit = Math.abs(constant);
for (let divisor = 1; divisor <= Math.max(1, limit); divisor++) {
if (limit % divisor === 0) {
candidates.push(divisor, -divisor);
}
}
for (const candidate of candidates) {
if (evaluatePolynomial(coefficients, candidate) === 0) {
const reduced = syntheticDivide(coefficients, candidate);
const remainingRoots = solveQuadratic(reduced.quotient);
return [candidate, ...remainingRoots];
}
}
}
throw new Error('polynomialRoot() currently supports degree up to 3');
}
/**
* @param {any[]} a
* @param {any[]} b
*/
function dotProduct(a, b) {
return a.reduce((sum, value, index) => sum + value * b[index], 0);
}
/**
* @param {any[]} vector
*/
function vectorNorm(vector) {
return Math.sqrt(dotProduct(vector, vector));
}
/**
* @param {any[]} vector
* @param {number} scalar
*/
function scaleVector(vector, scalar) {
return vector.map((value) => value * scalar);
}
/**
* @param {any} a
* @param {any} b
*/
function subtractVectors(a, b) {
return a.map(
(/** @type {number} */ value, /** @type {string | number} */ index) => value - b[index]
);
}
/**
* @param {any[]} matrix
*/
function transpose(matrix) {
return matrix[0].map((/** @type {any} */ _, /** @type {string | number} */ colIndex) =>
matrix.map((row) => row[colIndex])
);
}
/**
* @param {any} input
*/
function qrDecomposition(input) {
const A = asMatrixData(input).map((row) => [...row]);
if (!A.length || !A.every((row) => row.length === A[0].length)) {
throw new Error('qr() expects a rectangular matrix');
}
const rowCount = A.length;
const colCount = A[0].length;
const columns = transpose(A);
const qColumns = [];
for (let col = 0; col < colCount; col++) {
let vector = [...columns[col]];
for (let existing = 0; existing < qColumns.length; existing++) {
const projection = dotProduct(qColumns[existing], columns[col]);
vector = subtractVectors(vector, scaleVector(qColumns[existing], projection));
}
const norm = vectorNorm(vector);
if (norm === 0) {
throw new Error('qr() requires linearly independent columns');
}
qColumns.push(scaleVector(vector, 1 / norm));
}
for (let basisIndex = 0; qColumns.length < rowCount && basisIndex < rowCount; basisIndex++) {
let candidate = Array.from({ length: rowCount }, (_, index) => (index === basisIndex ? 1 : 0));
for (const column of qColumns) {
const projection = dotProduct(column, candidate);
candidate = subtractVectors(candidate, scaleVector(column, projection));
}
const norm = vectorNorm(candidate);
if (norm > 1e-10) {
qColumns.push(scaleVector(candidate, 1 / norm));
}
}
const Q = Array.from({ length: rowCount }, (_, rowIndex) =>
qColumns.map((column) => column[rowIndex])
);
const fullR = Array.from({ length: rowCount }, () => Array(colCount).fill(0));
for (let row = 0; row < rowCount; row++) {
for (let col = 0; col < colCount; col++) {
fullR[row][col] = dotProduct(qColumns[row], columns[col]);
}
}
return {
Q: wrapDenseMatrix(Q),
R: wrapDenseMatrix(fullR),
};
}
/**
* @param {string} expression
*/
function splitTerms(expression) {
const normalized = expression.replace(/\s+/g, '');
if (!normalized) {
return [];
}
return normalized.replace(/-/g, '+-').split('+').filter(Boolean);
}
/**
* @param {string} expression
* @param {string} variable
*/
function parsePolynomial(expression, variable) {
const terms = splitTerms(expression);
const coefficients = new Map();
for (const term of terms) {
if (term.includes(variable)) {
const [rawCoeff, rawPower] = term.split(variable);
let coefficient;
if (rawCoeff === '' || rawCoeff === '+') {
coefficient = 1;
} else if (rawCoeff === '-') {
coefficient = -1;
} else {
const cleaned = rawCoeff.endsWith('*') ? rawCoeff.slice(0, -1) : rawCoeff;
coefficient = Number(cleaned);
}
if (!Number.isFinite(coefficient)) {
throw new Error('Unsupported algebra term');
}
let power = 1;
if (rawPower) {
if (!rawPower.startsWith('^')) {
throw new Error('Unsupported algebra term');
}
power = Number(rawPower.slice(1));
}
if (!Number.isInteger(power) || power < 0) {
throw new Error('Only non-negative integer powers are supported');
}
coefficients.set(power, (coefficients.get(power) || 0) + coefficient);
} else {
const constant = Number(term);
if (!Number.isFinite(constant)) {
throw new Error('Unsupported algebra term');
}
coefficients.set(0, (coefficients.get(0) || 0) + constant);
}
}
return coefficients;
}
/**
* @param {any[] | Map<any, any>} coefficients
* @param {string} variable
*/
function formatPolynomial(coefficients, variable) {
const ordered = [...coefficients.entries()]
.filter(([, coefficient]) => coefficient !== 0)
.sort((a, b) => b[0] - a[0]);
if (!ordered.length) {
return '0';
}
return ordered
.map(([power, coefficient], index) => {
const negative = coefficient < 0;
const absCoeff = Math.abs(coefficient);
let body;
if (power === 0) {
body = `${absCoeff}`;
} else if (power === 1) {
body = absCoeff === 1 ? variable : `${absCoeff} * ${variable}`;
} else {
body = absCoeff === 1 ? `${variable}^${power}` : `${absCoeff} * ${variable}^${power}`;
}
if (index === 0) {
return negative ? `-${body}` : body;
}
return negative ? `- ${body}` : `+ ${body}`;
})
.join(' ');
}
/**
* @param {string} expression
*/
function simplifyExpression(expression) {
const compact = expression.replace(/\s+/g, '');
const variableMatch = compact.match(/[a-zA-Z]+/);
const variable = variableMatch?.[0] || 'x';
const coefficients = parsePolynomial(expression, variable);
return formatPolynomial(coefficients, variable);
}
/**
* @param {string} expression
* @param {string} variable
*/
function derivativeExpression(expression, variable) {
const coefficients = parsePolynomial(expression, variable);
const derived = new Map();
for (const [power, coefficient] of coefficients.entries()) {
if (power === 0) {
continue;
}
derived.set(power - 1, (derived.get(power - 1) || 0) + coefficient * power);
}
return formatPolynomial(derived, variable);
}
/**
* @param {number} a
* @param {number} b
*/
function _gcd(a, b) {
a = Math.abs(a);
b = Math.abs(b);
while (b) {
[a, b] = [b, a % b];
}
return a;
}
/**
* @param {any} n
*/
function _gamma(n) {
if (n === 0) {
throw new Error('gamma(0) is undefined');
}
if (Number.isInteger(n) && n < 0) {
throw new Error('gamma() undefined for negative integers');
}
if (Number.isInteger(n) && n > 0) {
let r = 1;
for (let i = 2; i < n; i++) {
r *= i;
}
return r;
}
const g = 7;
const c = [
0.99999999999980993, 676.5203681218851, -1259.1392167224028, 771.32342877765313,
-176.61502916214059, 12.507343278686905, -0.13857109526572012, 9.9843695780195716e-6,
1.5056327351493116e-7,
];
// Euler's reflection formula: Gamma(z) = pi / (sin(pi*z) * Gamma(1-z))
if (n < 0.5) {
return Math.PI / (Math.sin(Math.PI * n) * _gamma(1 - n));
}
n -= 1;
let x = c[0];
for (let i = 1; i < g + 2; i++) {
x += c[i] / (n + i);
}
const t = n + g + 0.5;
return Math.sqrt(2 * Math.PI) * t ** (n + 0.5) * Math.exp(-t) * x;
}
/**
* @param {any} n
*/
function _identity(n) {
return Array.from({ length: n }, (_, i) =>
Array.from({ length: n }, (_, j) => (i === j ? 1 : 0))
);
}
/**
* @param {any[]} matrix
*/
function _inverse(matrix) {
const data = unwrapDenseMatrix(matrix);
validateSquareMatrix(matrix);
const n = data.length;
if (n === 2) {
const det = data[0][0] * data[1][1] - data[0][1] * data[1][0];
if (det === 0) {
throw new Error('Matrix is singular');
}
return wrapDenseMatrix([
[data[1][1] / det, -data[0][1] / det],
[-data[1][0] / det, data[0][0] / det],
]);
}
const result = Array.from({ length: n }, () => Array(n).fill(0));
for (let col = 0; col < n; col++) {
const b = Array.from({ length: n }, (_, i) => (i === col ? 1 : 0));
const x = linearSolve(data, wrapDenseMatrix(b.map((v) => [v])));
const xData = unwrapDenseMatrix(x);
for (let row = 0; row < n; row++) {
result[row][col] = xData[row][0];
}
}
return wrapDenseMatrix(result);
}
/**
* @param {any} matrix
*/
function _rref(matrix) {
const data = unwrapDenseMatrix(matrix).map((/** @type {any} */ row) => [...row]);
let lead = 0;
const rowCount = data.length;
const colCount = data[0].length;
for (let r = 0; r < rowCount; r++) {
if (lead >= colCount) {
break;
}
let i = r;
while (Math.abs(data[i][lead]) < 1e-12) {
i++;
if (i === rowCount) {
i = r;
lead++;
if (lead >= colCount) {
break;
}
}
}
if (lead >= colCount) {
break;
}
[data[r], data[i]] = [data[i], data[r]];
const pivot = data[r][lead];
for (let j = 0; j < colCount; j++) {
data[r][j] /= pivot;
}
for (let i = 0; i < rowCount; i++) {
if (i !== r) {
const factor = data[i][lead];
for (let j = 0; j < colCount; j++) {
data[i][j] -= factor * data[r][j];
}
}
}
lead++;
}
return wrapDenseMatrix(data);
}
/**
* @param {any[]} a
* @param {any[]} b
*/
function _cross(a, b) {
return [a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]];
}
/**
* @param {any} matrix
*/
function _eig2x2(matrix) {
const data = unwrapDenseMatrix(matrix);
validateSquareMatrix(matrix);
const [[a, b], [c, d]] = data;
const trace = a + d;
const det = a * d - b * c;
const disc = trace * trace - 4 * det;
if (disc < 0) {
throw new Error('Complex eigenvalues not supported');
}
const sqrtDisc = Math.sqrt(disc);
const lambda1 = (trace + sqrtDisc) / 2;
const lambda2 = (trace - sqrtDisc) / 2;
// Solve (A - lambda*I)v = 0: pick non-zero row to solve for v1:v2 ratio
const eigenvec = (/** @type {number} */ lambda) => {
if (Math.abs(b) > 1e-12) {
return [1, (lambda - a) / b];
}
if (Math.abs(c) > 1e-12) {
return [(lambda - d) / c, 1];
}
return [1, 0];
};
const v1 = eigenvec(lambda1);
const norm1 = Math.sqrt(v1[0] * v1[0] + v1[1] * v1[1]);
const v2 = eigenvec(lambda2);
const norm2 = Math.sqrt(v2[0] * v2[0] + v2[1] * v2[1]);
return {
values: [lambda1, lambda2],
vectors: wrapDenseMatrix([
[v1[0] / norm1, v2[0] / norm2],
[v1[1] / norm1, v2[1] / norm2],
]),
};
}
/**
* @param {any[]} matrix
*/
function _cholesky(matrix) {
const data = unwrapDenseMatrix(matrix);
validateSquareMatrix(matrix);
const n = data.length;
const L = Array.from({ length: n }, () => Array(n).fill(0));
for (let j = 0; j < n; j++) {
let sum = 0;
for (let k = 0; k < j; k++) {
sum += L[j][k] * L[j][k];
}
const val = data[j][j] - sum;
if (val <= 0) {
throw new Error('Matrix is not positive definite');
}
L[j][j] = Math.sqrt(val);
for (let i = j + 1; i < n; i++) {
sum = 0;
for (let k = 0; k < j; k++) {
sum += L[i][k] * L[j][k];
}
L[i][j] = (data[i][j] - sum) / L[j][j];
}
}
return wrapDenseMatrix(L);
}
/**
* @param {any} matrix
*/
function _svd(matrix) {
const data = unwrapDenseMatrix(matrix);
const m = data.length;
const n = data[0].length;
if (m !== 2 || n !== 2) {
throw new Error('svd() currently supports 2x2 matrices only');
}
const ata = [
[
data[0][0] * data[0][0] + data[1][0] * data[1][0],
data[0][0] * data[0][1] + data[1][0] * data[1][1],
],
[
data[0][1] * data[0][0] + data[1][1] * data[1][0],
data[0][1] * data[0][1] + data[1][1] * data[1][1],
],
];
const eigResult = _eig2x2(wrapDenseMatrix(ata));
const S = [
Math.sqrt(Math.max(0, eigResult.values[0])),
Math.sqrt(Math.max(0, eigResult.values[1])),
];
const vecData = unwrapDenseMatrix(eigResult.vectors);
const V = vecData;
const U = [
[
(data[0][0] * V[0][0] + data[0][1] * V[1][0]) / (S[0] || 1),
(data[0][0] * V[0][1] + data[0][1] * V[1][1]) / (S[1] || 1),
],
[
(data[1][0] * V[0][0] + data[1][1] * V[1][0]) / (S[0] || 1),
(data[1][0] * V[0][1] + data[1][1] * V[1][1]) / (S[1] || 1),
],
];
return {
U: wrapDenseMatrix(U),
S: wrapDenseMatrix([
[S[0], 0],
[0, S[1]],
]),
V: wrapDenseMatrix(V),
};
}
export const internalFunctions = {
fraction: (/** @type {number} */ n, /** @type {number} */ d) => makeFrac(n, d),
numer: (/** @type {any} */ v) => numer(v),
denom: (/** @type {any} */ v) => denom(v),
isFraction: (/** @type {any} */ v) => isFraction(v),
bignumber: (/** @type {any} */ n) => makeBN(n),
isBigNumber: (/** @type {any} */ v) => isBigNumber(v),
max: (/** @type {any[]} */ ...args) => {
if (!args.length) {
throw new Error('max() requires arguments');
}
return Math.max(...args);
},
min: (/** @type {any[]} */ ...args) => {
if (!args.length) {
throw new Error('min() requires arguments');
}
return Math.min(...args);
},
abs: (/** @type {number} */ x) => Math.abs(x),
round: (/** @type {number} */ x) => Math.round(x),
floor: (/** @type {number} */ x) => Math.floor(x),
ceil: (/** @type {number} */ x) => Math.ceil(x),
sqrt: (/** @type {number} */ x) => {
if (x < 0) {
throw new Error('sqrt() domain error');
}
return Math.sqrt(x);
},
pow: (/** @type {number} */ a, /** @type {number} */ b) => a ** b,
det: (/** @type {any[]} */ matrix) => determinant(matrix),
polynomialRoot: (/** @type {any} */ ...coefficients) => polynomialRoots(...coefficients),
lsolve: (
/** @type {any} */ a,
/** @type {{ exprify: string; data: any; size: number[]; }} */ b
) => linearSolve(a, b),
lup: (/** @type {any} */ matrix) => lupDecomposition(matrix),
lyap: (/** @type {any} */ a, /** @type {any} */ q) => solveLyapunov(a, q),
qr: (/** @type {any} */ matrix) => qrDecomposition(matrix),
transpose: (/** @type {any} */ matrix) => wrapDenseMatrix(transpose(unwrapDenseMatrix(matrix))),
inverse: (/** @type {any[]} */ matrix) => _inverse(matrix),
trace: (/** @type {any[]} */ matrix) => {
const data = unwrapDenseMatrix(matrix);
validateSquareMatrix(matrix);
return data.reduce(
(
/** @type {any} */ sum,
/** @type {{ [x: string]: any; }} */ row,
/** @type {string | number} */ i
) => sum + row[i],
0
);
},
rank: (/** @type {any} */ matrix) => {
const rrefData = unwrapDenseMatrix(_rref(matrix));
return rrefData.filter((/** @type {any[]} */ row) => row.some((v) => Math.abs(v) > 1e-10))
.length;
},
rref: (/** @type {any} */ matrix) => _rref(matrix),
minor: (/** @type {any[]} */ matrix, /** @type {any} */ i, /** @type {any} */ j) => {
const data = unwrapDenseMatrix(matrix);
validateSquareMatrix(matrix);
const sub = data
.filter((/** @type {any} */ _, /** @type {any} */ ri) => ri !== i)
.map((/** @type {any[]} */ row) => row.filter((_, cj) => cj !== j));
return determinant(sub);
},
cofactor: (/** @type {any} */ matrix, /** @type {any} */ i, /** @type {any} */ j) => {
const data = unwrapDenseMatrix(matrix);
const sub = data
.filter((/** @type {any} */ _, /** @type {any} */ ri) => ri !== i)
.map((/** @type {any[]} */ row) =>
row.filter((/** @type {any} */ _, /** @type {any} */ cj) => cj !== j)
);
return ((i + j) % 2 === 0 ? 1 : -1) * determinant(sub);
},
cross: (/** @type {any} */ a, /** @type {any} */ b) => {
const v1 = unwrapDenseMatrix(a);
const v2 = unwrapDenseMatrix(b);
if (!Array.isArray(v1) || !Array.isArray(v2) || v1.length !== 3 || v2.length !== 3) {
throw new Error('cross() requires two 3D vectors');
}
return _cross(v1, v2);
},
normalize: (/** @type {any} */ v) => {
const data = unwrapDenseMatrix(v);
if (!Array.isArray(data)) {
throw new Error('normalize() expects a vector');
}
const norm = vectorNorm(data);
if (norm === 0) {
throw new Error('Cannot normalize zero vector');
}
return scaleVector(data, 1 / norm);
},
angle: (/** @type {any} */ a, /** @type {any} */ b) => {
const v1 = unwrapDenseMatrix(a);
const v2 = unwrapDenseMatrix(b);
if (!Array.isArray(v1) || !Array.isArray(v2)) {
throw new Error('angle() expects vectors');
}
const dot = dotProduct(v1, v2);
const norms = vectorNorm(v1) * vectorNorm(v2);
if (norms === 0) {
throw new Error('Zero vector angle is undefined');
}
return Math.acos(Math.max(-1, Math.min(1, dot / norms)));
},
projection: (/** @type {any} */ a, /** @type {any} */ b) => {
const v1 = unwrapDenseMatrix(a);
const v2 = unwrapDenseMatrix(b);
if (!Array.isArray(v1) || !Array.isArray(v2)) {
throw new Error('projection() expects vectors');
}
const dot = dotProduct(v1, v2);
const normB = vectorNorm(v2);
if (normB === 0) {
throw new Error('Zero vector projection undefined');
}
return dot / normB;
},
identity: (/** @type {any} */ n) => wrapDenseMatrix(_identity(n)),
eye: (/** @type {any} */ n) => wrapDenseMatrix(_identity(n)),
zeros: (/** @type {any} */ n, /** @type {undefined} */ m) => {
if (m === undefined) {
m = n;
}
return wrapDenseMatrix(Array.from({ length: n }, () => Array(m).fill(0)));
},
ones: (/** @type {any} */ n, /** @type {undefined} */ m) => {