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// mnożenie macierzy
function multiply(A, B) {
// pobierzmy potrzebne wymiary z obu macierzy
const rowsA = A.length;
const colsA = A[0].length;
const colsB = B[0].length;
// tworzymy nowÄ… macierz o odpowiednich wymiarach
const result = Array.from({ length: rowsA }, () => Array(colsB).fill(0));
// w pętli mnożymy elementy z oryginalnych macierzy
for (let i = 0; i < rowsA; i++) {
for (let j = 0; j < colsB; j++) {
for (let k = 0; k < colsA; k++) {
result[i][j] += A[i][k] * B[k][j];
}
}
}
return result;
}
// funkcja tworzÄ…ca macierz jednostkowÄ…
function identity(n) {
return Array.from({ length: n }, (_, i) =>
Array.from({ length: n }, (_, j) => (i === j ? 1 : 0)),
);
}
// potęgowanie macierzy
function power(matrix, exponent) {
// A^0 = I
if (exponent === 0) {
return identity(matrix.length);
}
if (exponent % 2 === 1) {
// obsługa nieparzystych wykładników
return multiply(matrix, power(matrix, exponent - 1));
} else {
// obsługa parzystych wykładników
const halfPower = power(matrix, Math.floor(exponent / 2));
return multiply(halfPower, halfPower);
}
}
const A = [
[1, 2],
[3, 4],
];
const B = [
[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
];
console.log(power(A, 0));
console.log(power(A, 1));
console.log(power(A, 2));
console.log(power(A, 3));
console.log(power(A, 4));
console.log(power(A, 5));
console.log(power(B, 2));
console.log(power(B, 3));
console.log(power(B, 4));
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