526 lines
15 KiB
JavaScript
526 lines
15 KiB
JavaScript
'use strict';
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const rational = require('./rational');
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const merge = require('./merge');
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const generate = require('./generate');
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/**
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* Pass a 2-dimensional array that will return a function accepting indices to access the matrix
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*
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* @param mat array that initializes the matrix
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* @returns function with the array initialized and access to method that perform operations on the matrix
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*/
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function matrix(mat) {
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if (!Array.isArray(mat)) {
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throw new Error('Input should be of type array');
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}
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let _matrix = function() {
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let args = (arguments.length === 1 ? [arguments[0]] : Array.apply(null, arguments));
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return read(mat, args);
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}
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return Object.assign(_matrix, _mat(mat));
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}
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matrix.gen = generate;
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/**
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* Private function that returns an object containing methods
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* that perform operations on the matrix
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*
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* @param mat array that initializes the matrix
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* @returns object of methods performing matrix operations
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*/
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function _mat(mat) {
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return {
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size: () => size(mat),
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add: (operand) => operate(mat, operand, addition),
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sub: (operand) => operate(mat, operand, subtraction),
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mul: (operand) => operate(mat, operand, multiplication),
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div: (operand) => operate(mat, operand, division),
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prod: (operand) => prod(mat, operand),
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trans: () => trans(mat),
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set: function() {
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let args = (arguments.length === 1 ? [arguments[0]] : Array.apply(null, arguments));
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return {
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to: (val) => replace(mat, val, args)
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}
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},
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det: () => determinant(mat),
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inv: () => invert(mat),
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merge: merge(mat),
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map: (func) => map(mat, func),
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equals: (operand) => equals(mat, operand),
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};
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}
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module.exports = matrix;
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/**
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* Calculates the size of the array across each dimension
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*
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* @param mat input matrix that initialized the function
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* @returns size of the matrix as an array
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*/
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function size(mat) {
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let s = [];
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while (Array.isArray(mat)) {
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s.push(mat.length);
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mat = mat[0];
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}
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return s;
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}
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/**
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* Private function to calculate the dimensions of the matrix
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*
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* @param mat input matrix that initializes the function
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* @returns integer indicating the number of dimensions
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*/
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function dimensions(mat) {
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return size(mat).length;
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}
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/**
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* Outputs the original matrix or a particular element or a matrix that is part of the original
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*
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* @param mat input matrix that initializes the function
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* @param args indices to access one or more array elements
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* @returns array or single element
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*/
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function read(mat, args) {
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if (args.length === 0) {
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return mat;
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} else {
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return extract(mat, args);
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}
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}
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/**
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* Private function to extract a single element or a matrix that is part of the original
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*
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* @param mat input matrix that initializes the function
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* @param args indices to access one or more array elements
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* @returns array or single element
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*/
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function extract(mat, args) {
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let dim = dimensions(mat);
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for (let i = 0; i < dim; i++) {
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let d = args[i];
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if (d === undefined) {
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break;
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}
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if (Array.isArray(d)) {
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// if an element of args is an array, more extraction is needed
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mat = extractRange(mat, d, i);
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} else if (Number.isInteger(d)) {
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if (dimensions(mat) > 1 && i > 0) {
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mat = mat.map(function(elem) {
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return [elem[d]];
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});
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} else {
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mat = mat[d];
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}
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}
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}
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return mat;
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}
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/**
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* Private function to extract a portion of the array based on the specified range
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*
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* @param mat input matrix that initialized the function
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* @param arg single argument containing the range specified as an array
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* @param ind the current index of the arguments while extracting the matrix
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* @returns array from the specified range
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*/
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function extractRange(mat, arg, ind) {
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if (!arg.length) {
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return mat;
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} else if (arg.length === 2) {
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let reverse = arg[0] > arg[1];
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let first = (!reverse) ? arg[0] : arg[1];
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let last = (!reverse) ? arg[1]: arg[0];
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if (dimensions(mat) > 1 && ind > 0) {
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return mat.map(function(elem) {
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if (reverse) {
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return elem.slice(first, last+1).reverse();
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}
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return elem.slice(first, last+1);
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})
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} else {
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mat = mat.slice(first, last+1);
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return (reverse && mat.reverse()) || mat;
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}
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}
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}
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/**
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* Replaces the specified index in the matrix with the specified value
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*
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* @param mat input matrix that initialized the function
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* @param value specified value that replace current value at index or indices
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* @param args index or indices passed in arguments to initialized function
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* @returns replaced matrix
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*/
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function replace(mat, value, args) { //TODO: Clean this function up
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let result = clone(mat);
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let prev = args[0];
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let start = prev[0] || 0;
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let end = prev[1] && prev[1] + 1 || mat.length;
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if (!Array.isArray(prev) && args.length === 1) {
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result[prev].fill(value);
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} else if (args.length === 1) {
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for (let ind = start; ind < end; ind++) {
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result[ind].fill(value);
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}
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}
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for (let i = 1; i < args.length; i++) {
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let first = Array.isArray(args[i]) ? args[i][0] || 0 : args[i];
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let last = Array.isArray(args[i]) ? args[i][1] && args[i][1] + 1 || mat[0].length : args[i] + 1;
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if (!Array.isArray(prev)) {
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result[prev].fill(value, first, last);
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} else {
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for (let ind = start; ind < end; ind++) {
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result[ind].fill(value, first, last);
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}
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}
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}
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return result;
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}
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/**
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* Operates on two matrices of the same size
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*
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* @param mat input matrix that initialized the function
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* @param operand second matrix with which operation is performed
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* @param operation function performing the desired operation
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* @returns result of the operation
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*/
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function operate(mat, operand, operation) {
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let result = [];
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let op = operand();
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for (let i = 0; i < mat.length; i++) {
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let op1 = mat[i];
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let op2 = op[i];
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result.push(op1.map(function(elem, ind) {
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return operation(elem, op2[ind]);
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}));
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}
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return result;
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}
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/**
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* Finds the product of two matrices
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*
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* @param mat input matrix that initialized the function
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* @param operand second matrix with which operation is performed
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* @returns the product of the two matrices
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*/
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function prod(mat, operand) {
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let op1 = mat;
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let op2 = operand();
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let size1 = size(op1);
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let size2 = size(op2);
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let result = [];
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if (size1[1] === size2[0]) {
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for (let i = 0; i < size1[0]; i++) {
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result[i] = [];
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for (let j = 0; j < size2[1]; j++) {
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for (let k = 0; k < size1[1]; k++) {
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if (result[i][j] === undefined) {
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result[i][j] = 0;
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}
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result[i][j] += multiplication(op1[i][k], op2[k][j]);
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}
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}
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}
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}
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return result;
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}
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/**
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* Returns the transpose of a matrix, swaps rows with columns
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*
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* @param mat input matrix that initialized the function
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* @returns a matrix with rows and columns swapped from the original matrix
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*/
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function trans(mat) {
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let input = mat;
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let s = size(mat);
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let output = [];
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for (let i = 0; i < s[0]; i++) {
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for (let j = 0; j < s[1]; j++) {
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if (Array.isArray(output[j])) {
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output[j].push(input[i][j]);
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} else {
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output[j] = [input[i][j]];
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}
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}
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}
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return output;
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}
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/**
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* Private method to clone the matrix
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*
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* @param mat input matrix that initialized the function
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* @returns cloned matrix
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*/
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function clone(mat) {
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let result = [];
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for (let i = 0; i < mat.length; i++) {
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result.push(mat[i].slice(0));
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}
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return result;
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}
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/**
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* Performs addition
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*
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* @param op1 first operand
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* @param op2 second operand
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* @returns result
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*/
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function addition(op1, op2) {
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return op1 + op2;
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}
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/**
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* Performs subtraction
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*
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* @param op1 first operand
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* @param op2 second operand
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* @returns result
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*/
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function subtraction(op1, op2) {
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return op1 - op2;
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}
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/**
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* Performs multiplication
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*
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* @param op1 first operand
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* @param op2 second operand
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* @returns result
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*/
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function multiplication(op1, op2) {
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return op1 * op2;
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}
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/**
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* Performs division
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*
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* @param op1 first operand
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* @param op2 second operand
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* @returns result
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*/
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function division(op1, op2) {
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return op1/op2;
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}
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/**
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* Computes the determinant using row reduced echelon form
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* Works best if the elements are integers or rational numbers
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* The matrix must be a square
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*
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* @param mat input matrix that initialized the function
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* @returns determinant value as a number
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*/
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function determinant(mat) {
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let rationalized = rationalize(mat);
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let siz = size(mat);
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let det = rational(1);
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let sign = 1;
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for (let i = 0; i < siz[0] - 1; i++) {
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for (let j = i + 1; j < siz[0]; j++) {
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if (rationalized[j][i].num === 0) {
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continue;
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}
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if (rationalized[i][i].num === 0) {
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interchange(rationalized, i, j);
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sign = -sign;
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continue;
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}
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let temp = rationalized[j][i].div(rationalized[i][i]);
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temp = rational(Math.abs(temp.num), temp.den);
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if (Math.sign(rationalized[j][i].num) === Math.sign(rationalized[i][i].num)) {
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temp = rational(-temp.num, temp.den);
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}
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for (let k = 0; k < siz[1]; k++) {
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rationalized[j][k] = temp.mul(rationalized[i][k]).add(rationalized[j][k]);
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}
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}
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}
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det = rationalized.reduce((prev, curr, index) => prev.mul(curr[index]), rational(1));
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return sign * det.num/det.den;
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}
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/**
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* Interchanges one row index with another on passed matrix
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*
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* @param mat input matrix
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* @param ind1 one of the row indices to exchange
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* @param ind2 one of the row indices to exchange
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*/
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function interchange(mat, ind1, ind2) {
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let temp = mat[ind1];
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mat[ind1] = mat[ind2];
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mat[ind2] = temp;
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}
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/**
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* Inverts the input square matrix using row reduction technique
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* Works best if the elements are integers or rational numbers
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* The matrix has to be a square and non-singular
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*
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* @param mat input matrix
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* @returns inverse of the input matrix
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*/
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function invert(mat) {
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let rationalized = rationalize(mat);
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let siz = size(mat);
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let result = rationalize(generate(1).diag(siz[0]));
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// row reduction
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let i = 0;
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let j = 0;
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while (j < siz[0]) {
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if (rationalized[i][j].num === 0) {
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for (let k = i + 1; k < siz[0]; k++) {
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if (rationalized[k][j].num !== 0) {
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interchange(rationalized, i, k);
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interchange(result, i, k);
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}
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}
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}
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if (rationalized[i][j].num !== 0) {
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if (rationalized[i][j].num !== 1 || rationalized[i][j].den !== 1) {
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let factor = rational(rationalized[i][j].num, rationalized[i][j].den);
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for (let col = 0; col < siz[1]; col++) {
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rationalized[i][col] = rationalized[i][col].div(factor);
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result[i][col] = result[i][col].div(factor);
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}
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}
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for (let k = i + 1; k < siz[0]; k++) {
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let temp = rationalized[k][j];
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for (let col = 0; col < siz[1]; col++) {
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rationalized[k][col] = rationalized[k][col].sub(temp.mul(rationalized[i][col]));
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result[k][col] = result[k][col].sub(temp.mul(result[i][col]));
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}
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}
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}
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i += 1;
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j += 1;
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}
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// Further reduction to convert rationalized to identity
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let last = siz[0] - 1;
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if (rationalized[last][last].num !== 1 || rationalized[last][last].den !== 1) {
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let factor = rational(rationalized[last][last].num, rationalized[last][last].den);
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for (let col = 0; col < siz[1]; col++) {
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rationalized[last][col] = rationalized[last][col].div(factor);
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result[last][col] = result[last][col].div(factor);
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}
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}
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for (let i = siz[0] - 1; i > 0; i--) {
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for (let j = i - 1; j >= 0; j--) {
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let temp = rational(-rationalized[j][i].num, rationalized[j][i].den);
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for (let k = 0; k < siz[1]; k++) {
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rationalized[j][k] = temp.mul(rationalized[i][k]).add(rationalized[j][k]);
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result[j][k] = temp.mul(result[i][k]).add(result[j][k]);
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}
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}
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}
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return derationalize(result);
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}
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/**
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* Applies a given function over the matrix, elementwise. Similar to Array.map()
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* The supplied function is provided 4 arguments:
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* the current element,
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* the row index,
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* the col index,
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* the matrix.
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*
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* @param mat input matrix
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* @returns matrix of same dimensions with values altered by the function.
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*/
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function map(mat, func) {
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const s = size(mat);
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const result = [];
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for (let i = 0; i < s[0]; i++) {
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if(Array.isArray(mat[i])) {
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result[i] = [];
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for (let j = 0; j < s[1]; j++) {
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result[i][j] = func(mat[i][j], [i, j], mat);
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}
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} else {
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result[i] = func(mat[i], [i, 0], mat);
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}
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}
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return result;
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}
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/**
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* Converts a matrix of numbers to all rational type objects
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*
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* @param mat input matrix
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* @returns matrix with elements of type rational
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*/
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function rationalize(mat) {
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let rationalized = [];
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mat.forEach((row, ind) => {
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rationalized.push(row.map((ele) => rational(ele)));
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});
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return rationalized;
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}
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/**
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* Converts a rationalized matrix to all numerical values
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*
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* @param mat input matrix
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* @returns matrix with numerical values
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*/
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function derationalize(mat) {
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let derationalized = [];
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mat.forEach((row, ind) => {
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derationalized.push(row.map((ele) => ele.num/ele.den));
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});
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return derationalized;
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}
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/**
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* Checks the equality of two matrices
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* @param mat input matrix
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* @param operand second matrix
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*/
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function equals(mat, operand) {
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let op1 = mat;
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let op2 = operand();
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let size1 = size(op1);
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let size2 = size(op2);
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if (!size1.every((val, ind) => val === size2[ind])) {
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return false;
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}
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return op1.every((val, ind1) => val.every((ele, ind2) => Math.abs(ele - op2[ind1][ind2]) < 1e-10));
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}
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