RosettaCodeData/Task/Cramers-rule/JavaScript/cramers-rule.js

91 lines
2.3 KiB
JavaScript

var matrix = [
[2, -1, 5, 1],
[3, 2, 2, -6],
[1, 3, 3, -1],
[5, -2, -3, 3]
];
var freeTerms = [-3, -32, -47, 49];
var result = cramersRule(matrix,freeTerms);
console.log(result);
/**
* 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) {
var det = detr(matrix),
returnArray = [],
i,
tmpMatrix;
for(i=0; i < matrix[0].length; i++) {
var 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) {
var tmpMatrix = clone(matrix),
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) {
var ret = 1,
k,
A=clone(m),
n=m[0].length,
alpha;
for(var j =0; j < n-1; j++) {
k=j;
for(i=j+1;i<n;i++) { if(Math.abs(A[i][j]) > Math.abs(A[k][j])) { k = i; } }
if(k !== j) {
temp = A[k]; A[k] = A[j]; A[j] = temp;
ret *= -1;
}
Aj = A[j];
for(i=j+1;i<n;i++) {
Ai = A[i];
alpha = Ai[j]/Aj[j];
for(k=j+1;k<n-1;k+=2) {
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(function(a){return a.slice();});
}