6.0 KiB
6.0 KiB
title | id | challengeType |
---|---|---|
Cramer's rule | 59713da0a428c1a62d7db430 | 5 |
Description
Instructions
Tests
tests:
- text: <code>cramersRule</code> is a function.
testString: assert(typeof cramersRule === 'function', '<code>cramersRule</code> is a function.');
- text: <code>cramersRule([[2, -1, 5, 1], [3, 2, 2, -6], [1, 3, 3, -1], [5, -2, -3, 3]], [-3, -32, -47, 49])</code> should return <code>[2, -12, -4, 1]</code>.
testString: assert.deepEqual(cramersRule(matrices[0], freeTerms[0]), answers[0], '<code>cramersRule([[2, -1, 5, 1], [3, 2, 2, -6], [1, 3, 3, -1], [5, -2, -3, 3]], [-3, -32, -47, 49])</code> should return <code>[2, -12, -4, 1]</code>.');
- text: <code>cramersRule([[3, 1, 1], [2, 2, 5], [1, -3, -4]], [3, -1, 2])</code> should return <code>[1, 1, -1]</code>.
testString: assert.deepEqual(cramersRule(matrices[1], freeTerms[1]), answers[1], '<code>cramersRule([[3, 1, 1], [2, 2, 5], [1, -3, -4]], [3, -1, 2])</code> should return <code>[1, 1, -1]</code>.');
Challenge Seed
function cramersRule(matrix, freeTerms) {
// Good luck!
return true;
}
After Test
const matrices = [
[
[2, -1, 5, 1],
[3, 2, 2, -6],
[1, 3, 3, -1],
[5, -2, -3, 3]
],
[
[3, 1, 1],
[2, 2, 5],
[1, -3, -4]
]
];
const freeTerms = [[-3, -32, -47, 49], [3, -1, 2]];
const answers = [[2, -12, -4, 1], [1, 1, -1]];
Solution
/**
* Compute Cramer's Rule
* @param {array} matrix x,y,z, etc. terms
* @param {array} freeTerms
* @return {array} solution for x,y,z, etc.
*/
function cramersRule(matrix, freeTerms) {
const det = detr(matrix);
const returnArray = [];
let i;
for (i = 0; i < matrix[0].length; i++) {
const tmpMatrix = insertInTerms(matrix, freeTerms, i);
returnArray.push(detr(tmpMatrix) / det);
}
return returnArray;
}
/**
* Inserts single dimensional array into
* @param {array} matrix multidimensional array to have ins inserted into
* @param {array} ins single dimensional array to be inserted vertically into matrix
* @param {array} at zero based offset for ins to be inserted into matrix
* @return {array} New multidimensional array with ins replacing the at column in matrix
*/
function insertInTerms(matrix, ins, at) {
const tmpMatrix = clone(matrix);
let i;
for (i = 0; i < matrix.length; i++) {
tmpMatrix[i][at] = ins[i];
}
return tmpMatrix;
}
/**
* Compute the determinate of a matrix. No protection, assumes square matrix
* function borrowed, and adapted from MIT Licensed numericjs library (www.numericjs.com)
* @param {array} m Input Matrix (multidimensional array)
* @return {number} result rounded to 2 decimal
*/
function detr(m) {
let ret = 1;
let j;
let k;
const A = clone(m);
const n = m[0].length;
let alpha;
for (j = 0; j < n - 1; j++) {
k = j;
for (let i = j + 1; i < n; i++) { if (Math.abs(A[i][j]) > Math.abs(A[k][j])) { k = i; } }
if (k !== j) {
const temp = A[k]; A[k] = A[j]; A[j] = temp;
ret *= -1;
}
const Aj = A[j];
for (let i = j + 1; i < n; i++) {
const Ai = A[i];
alpha = Ai[j] / Aj[j];
for (k = j + 1; k < n - 1; k += 2) {
const k1 = k + 1;
Ai[k] -= Aj[k] * alpha;
Ai[k1] -= Aj[k1] * alpha;
}
if (k !== n) { Ai[k] -= Aj[k] * alpha; }
}
if (Aj[j] === 0) { return 0; }
ret *= Aj[j];
}
return Math.round(ret * A[j][j] * 100) / 100;
}
/**
* Clone two dimensional Array using ECMAScript 5 map function and EcmaScript 3 slice
* @param {array} m Input matrix (multidimensional array) to clone
* @return {array} New matrix copy
*/
function clone(m) {
return m.map(a => a.slice());
}