From b24d232f0aa6e259a4a08efc1307363e17d3e61c Mon Sep 17 00:00:00 2001 From: utkarsh Date: Fri, 2 Oct 2020 16:40:48 +0530 Subject: [PATCH] Added Matrix Exponentiation (Recursive) --- Maths/MatrixExponentiationRecursive.js | 84 ++++++++++++++++++++++++++ 1 file changed, 84 insertions(+) create mode 100644 Maths/MatrixExponentiationRecursive.js diff --git a/Maths/MatrixExponentiationRecursive.js b/Maths/MatrixExponentiationRecursive.js new file mode 100644 index 0000000000..6ee00aa250 --- /dev/null +++ b/Maths/MatrixExponentiationRecursive.js @@ -0,0 +1,84 @@ +/* + Source: + https://en.wikipedia.org/wiki/Exponentiation_by_squaring + + Complexity: + O(d^3 log n) + where: d is the dimension of the square matrix + n is the power the matrix is raised to +*/ + +const Identity = (n) => { + // Input: n: int + // Output: res: Identity matrix of size n x n + // Complexity: O(n^2) + const res = [] + for (let i = 0; i < n; i++) { + res[i] = [] + for (let j = 0; j < n; j++) { + res[i][j] = i === j ? 1 : 0 + } + } + return res +} + +const MatMult = (matA, matB) => { + // Input: matA: 2D Array of Numbers of size n x n + // matB: 2D Array of Numbers of size n x n + // Output: matA x matB: 2D Array of Numbers of size n x n + // Complexity: O(n^3) + const n = matA.length + const matC = [] + for (let i = 0; i < n; i++) { + matC[i] = [] + for (let j = 0; j < n; j++) { + matC[i][j] = 0 + } + } + for (let i = 0; i < n; i++) { + for (let j = 0; j < n; j++) { + for (let k = 0; k < n; k++) { + matC[i][j] += matA[i][k] * matB[k][j] + } + } + } + return matC +} + +const MatrixExponentiationRecursive = (mat, m) => { + // Input: mat: 2D Array of Numbers of size n x n + // Output: mat^n: 2D Array of Numbers of size n x n + // Complexity: O(n^3 log m) + if (m === 0) { + // return identity matrix of size n x n + return Identity(mat.length) + } else if (m % 2 === 1) { + // tmp = mat ^ m-1 + const tmp = MatrixExponentiationRecursive(mat, m - 1) + /// return tmp * mat = (mat ^ m-1) * mat = mat ^ m + return MatMult(tmp, mat) + } else { + // tmp = mat ^ m/2 + const tmp = MatrixExponentiationRecursive(mat, m >> 1) + // return tmp * tmp = (mat ^ m/2) ^ 2 = mat ^ m + return MatMult(tmp, tmp) + } +} + +const main = () => { + const mat = [[1, 0, 2], [2, 1, 0], [0, 2, 1]] + + // mat ^ 0 = [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] + console.log(MatrixExponentiationRecursive(mat, 0)) + + // mat ^ 1 = [ [ 1, 0, 2 ], [ 2, 1, 0 ], [ 0, 2, 1 ] ] + console.log(MatrixExponentiationRecursive(mat, 1)) + + // mat ^ 2 = [ [ 1, 4, 4 ], [ 4, 1, 4 ], [ 4, 4, 1 ] ] + console.log(MatrixExponentiationRecursive(mat, 2)) + + // mat ^ 5 = [ [ 1, 4, 4 ], [ 4, 1, 4 ], [ 4, 4, 1 ] ] + console.log(MatrixExponentiationRecursive(mat, 5)) +} + +main() pFad - Phonifier reborn

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