PolynomialRegression.js

/*
MIT License

Copyright (c) 2017 mljs

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/

class Matrix {

    /**
     * performs backward substitution on a matrix
     * @param anyMatrix - a matrix that has already undergone forward substitution
     * @param arr - an array that will ultimately be the final output for A0 - Ak
     * @param row - last row index
     * @param col - column index
     * @returns {*}
     */
    backwardSubstitution (anyMatrix, arr, row, col) {
        if (row < 0 || col < 0) {
            return arr;
        } 
        else {
            const rows  = anyMatrix.length;
            const cols  = anyMatrix[0].length - 1;
            let current = 0;
            let counter = 0;

            for (let i = cols - 1; i >= col; i--) {

                if (i === col) {
                    current = anyMatrix[row][cols] / anyMatrix[row][i];


                } else {
                    anyMatrix[row][cols] -= anyMatrix[row][i] * arr[rows - 1 - counter];
                    counter++;
                }
            }

            arr[row] = current;
            return this.backwardSubstitution(anyMatrix, arr, row - 1, col - 1);
        }
    }


    /**
     * Combines a square matrix with a matrix with K rows and only 1 column for GJ Elimination
     * @param left
     * @param right
     * @returns {*[]}
     */
    combineMatrices (left, right){

        const rows         = right.length;
        const cols         = left[0].length;
        const returnMatrix = [];

        for (let i = 0; i < rows; i++) {
            returnMatrix.push([]);

            for (let j = 0; j <= cols; j++) {

                if (j === cols) {

                    returnMatrix[i][j] = right[i];

                } else {

                    returnMatrix[i][j] = left[i][j];
                }
            }
        }

        return returnMatrix;
    };

    /**
     * Performs forward elimination for GJ elimination to form an upper right triangle matrix
     * @param anyMatrix
     * @returns {*[]}
     */
    forwardElimination(anyMatrix){

        const rows    = anyMatrix.length;
        const cols    = anyMatrix[0].length;
        const matrix  = [];
        //returnMatrix = anyMatrix;
        for (let i = 0; i < rows; i++) {

            matrix.push([]);

            for (let j = 0; j < cols; j++) {
                matrix[i][j] = anyMatrix[i][j];
            }
        }

        for (let x = 0; x < rows - 1; x++) {

            for (let z = x; z < rows - 1; z++) {

                const numerator   = matrix[z + 1][x];
                const denominator = matrix[x][x];
                const result      = numerator / denominator;


                for (let i = 0; i < cols; i++) {

                    matrix[z + 1][i] = matrix[z + 1][i] - (result * matrix[x][i]);
                }
            }
        }
        return matrix;
    };

    /**
     * THIS METHOD ACTS LIKE A CONTROLLER AND PERFORMS ALL THE NECESSARY STEPS OF GJ ELIMINATION TO PRODUCE
     * THE TERMS NECESSARY FOR POLYNOMIAL REGRESSION USING THE LEAST SQUARES METHOD WHERE SUM(RESIDUALS) = 0
     * @param leftMatrix
     * @param rightMatrix
     * @returns {*}
     */
    gaussianJordanElimination(leftMatrix, rightMatrix) {

        const combined       = this.combineMatrices(leftMatrix, rightMatrix);
        const fwdIntegration = this.forwardElimination(combined);
        //NOW, FINAL STEP IS BACKWARD SUBSTITUTION WHICH RETURNS THE TERMS NECESSARY FOR POLYNOMIAL REGRESSION
        return this.backwardSubstitution(fwdIntegration, [], fwdIntegration.length - 1, fwdIntegration[0].length - 2);
    }

    /**
     * returns the identity matrix for a matrix such that anyMatrix * identitymatrix = anyMatrix
     * This is useful for inverting a matrix
     * @param anyMatrix
     * @returns {*[]}
     */
    identityMatrix (anyMatrix){

        const rows           = anyMatrix.length;
        const cols           = anyMatrix[0].length;
        const identityMatrix = [[]];

        for (let i = 0; i < rows; i++) {
            for (let j = 0; j < cols; j++) {
                if (j == i) {
                    identityMatrix[i][j] = 1;
                } else {
                    identityMatrix[i][j] = 0;
                }
            }
        }
        return identityMatrix;
    }


    /**
     * calculates the product of 2 matrices
     * @param matrix1
     * @param matrix2
     * @returns {*}
     */
    matrixProduct (matrix1, matrix2) {
        const numCols1 = matrix1[0].length;
        const numRows2 = matrix2.length;

        if (numCols1 != numRows2) {
            return false;
        }

        const product = [[]];

        for (let rows = 0; rows < numRows2; rows++) {
            for (let cols = 0; cols < numCols1; cols++) {
                product[rows][cols] = this.doMultiplication(matrix1, matrix2, rows,
                    cols, numCols1);
            }
        }
        return product;
    };

    /**
     * performs multiplication for an individual matrix cell
     * @param matrix1
     * @param matrix2
     * @param row
     * @param col
     * @param numCol
     * @returns {number}
     */
    doMultiplication (matrix1, matrix2, row, col, numCol) {
        let counter = 0;
        let result  = 0;
        while (counter < numCol) {
            result += matrix1[row][counter] * matrix2[counter][col];
            counter++;
        }
        return result;
    }


    /**
     * Multiplies a row of a matrix - 1 of the fundamental matrix operations
     * @param anyMatrix
     * @param rowNum
     * @param multiplier
     * @returns {*[]}
     */
    multiplyRow (anyMatrix, rowNum, multiplier){
        const rows    = anyMatrix.length;
        const cols    = anyMatrix[0].length;
        const mMatrix = [[]];

        for (let i = 0; i < rows; i++) {
            for (let j = 0; j < cols; j++) {
                if (i == rowNum) {
                    mMatrix[i][j] = anyMatrix[i][j] * multiplier;
                } else {
                    mMatrix[i][j] = anyMatrix[i][j];
                }
            }
        }

        return mMatrix;
    }
}

/**
 * Simple data point object for use as a consistent data storage mechanism
 * @param x
 * @param y
 * @constructor
 */
class DataPoint {
    constructor(x,y){
        this.x = x;
        this.y = y;
    }
}

/**
 * The constructor for a PolynomialRegression object an example of it's usage is below
 *
 *
 * var someData = [];
 * someData.push(new DataPoint(0.0, 1.0));
 * someData.push(new DataPoint(1.0, 3.0));
 * someData.push(new DataPoint(2.0, 6.0));
 * someData.push(new DataPoint(3.0, 9.0));
 * someData.push(new DataPoint(4.0, 12.0));
 * someData.push(new DataPoint(5.0, 15.0));
 * someData.push(new DataPoint(6.0, 18.0));
 *
 * var poly = new PolynomialRegression(someData, 3);
 * var terms = poly.getTerms();
 *
 * for(var i = 0; i < terms.length; i++){
 *    console.log("term " + i, terms[i]);
 * }
 * console.log(poly.predictY(terms, 5.0));
 *
 *
 *
 * @param theData
 * @param degrees
 * @constructor
 */
class PolynomialRegression {

    /**
     *
     * @param {Array} list
     * @param {Number} degrees
     * @returns {PolynomialRegression}
     */
    static read(list, degrees){
        const data_points = list.map(item => {
            return new DataPoint(item.x, item.y);
        });

        return new PolynomialRegression(data_points, degrees);
    }
    
    constructor(data_points, degrees) {
        //private object variables
        this.data        = data_points;
        this.degree      = degrees;
        this.matrix      = new Matrix();
        this.leftMatrix  = [];
        this.rightMatrix = [];
    
        this.generateLeftMatrix();
        this.generateRightMatrix();
    }
    
    /**
     * Sums up all x coordinates raised to a power
     * @param anyData
     * @param power
     * @returns {number}
     */
    sumX (anyData, power) {
        let sum = 0;
        for (let i = 0; i < anyData.length; i++) {
            sum += Math.pow(anyData[i].x, power);
        }
        return sum;
    }
    
    
    /**
     * sums up all x * y where x is raised to a power
     * @param anyData
     * @param power
     * @returns {number}
     */
    sumXTimesY(anyData, power){
        let sum = 0;
        for (let i = 0; i < anyData.length; i++) {
            sum += Math.pow(anyData[i].x, power) * anyData[i].y;
        }
        return sum;
    }
    
    
    /**
     * Sums up all Y's raised to a power
     * @param anyData
     * @param power
     * @returns {number}
     */
    sumY (anyData, power){
        let sum = 0;
        for (let i = 0; i < anyData.length; i++) {
            sum += Math.pow(anyData[i].y, power);
        }
        return sum;
    }
    
    /**
     * generate the left matrix
     */
    generateLeftMatrix(){
        for (let i = 0; i <= this.degree; i++) {
            this.leftMatrix.push([]);
            for (let j = 0; j <= this.degree; j++) {
                if (i === 0 && j === 0) {
                    this.leftMatrix[i][j] = this.data.length;
                } else {
                    this.leftMatrix[i][j] = this.sumX(this.data, (i + j));
                }
            }
        }
    }
    
    /**
     * generates the right hand matrix
     */
    generateRightMatrix(){
        for (let i = 0; i <= this.degree; i++) {
            if (i === 0) {
                this.rightMatrix[i] = this.sumY(this.data, 1);
            } else {
                this.rightMatrix[i] = this.sumXTimesY(this.data, i);
            }
        }
    }
    
    
    /**
     * gets the terms for a polynomial
     * @returns {*}
     */
    getTerms(){
        return this.matrix.gaussianJordanElimination(this.leftMatrix, this.rightMatrix);
    }
    
    /**
     * Predicts the Y value of a data set based on polynomial coefficients and the value of an independent variable
     * @param terms
     * @param x
     * @returns {number}
     */
    predictY(terms, x){
    
        let result = 0;
        for (let i = terms.length - 1; i >= 0; i--) {
            if (i === 0) {
                result += terms[i];
            } else {
                result += terms[i] * Math.pow(x, i);
            }
        }
        return result;
    }
}