201912G05/WebContent/echartsjs/ecStat.js

(function webpackUniversalModuleDefinition(root, factory) {
    if (typeof exports === 'object' && typeof module === 'object')
        module.exports = factory();
    else if (typeof define === 'function' && define.amd)
        define([], factory);
    else if (typeof exports === 'object')
        exports["ecStat"] = factory();
    else
        root["ecStat"] = factory();
})(this, function () {
    return /******/ (function (modules) { // webpackBootstrap
        /******/ // The module cache
        /******/
        var installedModules = {};

        /******/ // The require function
        /******/
        function __webpack_require__(moduleId) {

            /******/ // Check if module is in cache
            /******/
            if (installedModules[moduleId])
                /******/
                return installedModules[moduleId].exports;

            /******/ // Create a new module (and put it into the cache)
            /******/
            var module = installedModules[moduleId] = {
                /******/
                exports: {},
                /******/
                id: moduleId,
                /******/
                loaded: false
                /******/
            };

            /******/ // Execute the module function
            /******/
            modules[moduleId].call(module.exports, module, module.exports, __webpack_require__);

            /******/ // Flag the module as loaded
            /******/
            module.loaded = true;

            /******/ // Return the exports of the module
            /******/
            return module.exports;
            /******/
        }


        /******/ // expose the modules object (__webpack_modules__)
        /******/
        __webpack_require__.m = modules;

        /******/ // expose the module cache
        /******/
        __webpack_require__.c = installedModules;

        /******/ // __webpack_public_path__
        /******/
        __webpack_require__.p = "";

        /******/ // Load entry module and return exports
        /******/
        return __webpack_require__(0);
        /******/
    })
    /************************************************************************/
    /******/
    ([
        /* 0 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                return {

                    clustering: __webpack_require__(1),
                    regression: __webpack_require__(5),
                    statistics: __webpack_require__(6),
                    histogram: __webpack_require__(15)

                };

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 1 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var dataProcess = __webpack_require__(2);
                var dataPreprocess = dataProcess.dataPreprocess;
                var array = __webpack_require__(3);
                var arraySize = array.size;
                var sumOfColumn = array.sumOfColumn;
                var arraySum = array.sum;
                var zeros = array.zeros;
                var isArray = array.isArray;
                var mathSqrt = Math.sqrt;
                var mathPow = Math.pow;

                /**
                 * KMeans of clustering algorithm
                 * @param  {Array.<Array.<number>>} data  two-dimension array
                 * @param  {number} k   the number of clusters in a dataset
                 * @return {Object}
                 */
                function kMeans(data, k) {

                    var size = arraySize(data);
                    // create array to assign data points to centroids, also holds SE of each point
                    var clusterAssigned = zeros(size[0], 2);
                    var centroids = createRandCent(data, k);
                    var clusterChanged = true;
                    var minDist;
                    var minIndex;
                    var distIJ;
                    var ptsInClust;

                    while (clusterChanged) {
                        clusterChanged = false;
                        for (var i = 0; i < size[0]; i++) {
                            minDist = Infinity;
                            minIndex = -1;
                            for (var j = 0; j < k; j++) {
                                distIJ = distEuclid(data[i], centroids[j]);
                                if (distIJ < minDist) {
                                    minDist = distIJ;
                                    minIndex = j;
                                }
                            }
                            if (clusterAssigned[i][0] !== minIndex) {
                                clusterChanged = true;
                            }
                            clusterAssigned[i][0] = minIndex;
                            clusterAssigned[i][1] = mathPow(minDist, 2);
                        }
                        //recalculate centroids
                        for (var i = 0; i < k; i++) {
                            ptsInClust = [];
                            for (var j = 0; j < clusterAssigned.length; j++) {
                                if (clusterAssigned[j][0] === i) {
                                    ptsInClust.push(data[j]);
                                }
                            }
                            centroids[i] = meanInColumns(ptsInClust);
                        }
                    }

                    var clusterWithKmeans = {
                        centroids: centroids,
                        clusterAssigned: clusterAssigned
                    };
                    return clusterWithKmeans;
                }

                /**
                 * Calculate the average of each column in a two-dimensional array
                 *  and returns the values as an array.
                 * @param  {Array.<Array>} dataList two-dimensional array
                 * @return {Array}
                 */
                function meanInColumns(dataList) {

                    var size = arraySize(dataList);
                    var meanArray = [];
                    var sum;
                    var mean;
                    for (var j = 0; j < size[1]; j++) {
                        sum = 0;
                        for (var i = 0; i < size[0]; i++) {
                            sum += dataList[i][j];
                        }
                        mean = sum / size[0];
                        meanArray.push(mean);
                    }
                    return meanArray;
                }

                /**
                 * The combine of hierarchical clustering and k-means.
                 * @param  {Array} data   two-dimension array.
                 * @param  {[type]} k   the number of clusters in a dataset. It has to be greater than 1.
                 * @param  {boolean}  stepByStep
                 * @return {}
                 */
                function hierarchicalKMeans(data, k, stepByStep) {
                    if (k < 2) {
                        return;
                    }
                    var dataSet = dataPreprocess(data);
                    var size = arraySize(dataSet);
                    var clusterAssment = zeros(size[0], 2);
                    // initial center point
                    var centroid0 = meanInColumns(dataSet);
                    var centList = [centroid0];
                    var squareError;
                    for (var i = 0; i < size[0]; i++) {
                        squareError = distEuclid(dataSet[i], centroid0);
                        clusterAssment[i][1] = mathPow(squareError, 2);
                    }
                    var lowestSSE;
                    var ptsInClust;
                    var ptsNotClust;
                    var clusterInfo;
                    var sseSplit;
                    var sseNotSplit;
                    var index = 1;
                    var result = {
                        isEnd: false
                    };

                    function oneStep() {
                        //the existing clusters are continuously divided
                        //until the number of clusters is k
                        if (index < k) {
                            lowestSSE = Infinity;
                            var centSplit;
                            var newCentroid;
                            var newClusterAss;

                            for (var j = 0; j < centList.length; j++) {
                                ptsInClust = [];
                                ptsNotClust = [];
                                for (var i = 0; i < clusterAssment.length; i++) {
                                    if (clusterAssment[i][0] === j) {
                                        ptsInClust.push(dataSet[i]);
                                    } else {
                                        ptsNotClust.push(clusterAssment[i][1]);
                                    }
                                }
                                clusterInfo = kMeans(ptsInClust, 2);
                                sseSplit = sumOfColumn(clusterInfo.clusterAssigned, 1);
                                sseNotSplit = arraySum(ptsNotClust);
                                if (sseSplit + sseNotSplit < lowestSSE) {
                                    lowestSSE = sseNotSplit + sseSplit;
                                    centSplit = j;
                                    newCentroid = clusterInfo.centroids;
                                    newClusterAss = clusterInfo.clusterAssigned;
                                }
                            }

                            for (var i = 0; i < newClusterAss.length; i++) {
                                if (newClusterAss[i][0] === 0) {
                                    newClusterAss[i][0] = centSplit;
                                } else if (newClusterAss[i][0] === 1) {
                                    newClusterAss[i][0] = centList.length;
                                }
                            }

                            centList[centSplit] = newCentroid[0];
                            centList.push(newCentroid[1]);
                            for (i = 0, j = 0; i < clusterAssment.length && j < newClusterAss.length; i++) {
                                if (clusterAssment[i][0] === centSplit) {
                                    clusterAssment[i][0] = newClusterAss[j][0];
                                    clusterAssment[i][1] = newClusterAss[j++][1];
                                }
                            }

                            var pointInClust = [];
                            for (var i = 0; i < centList.length; i++) {
                                pointInClust[i] = [];
                                for (var j = 0; j < clusterAssment.length; j++) {
                                    if (clusterAssment[j][0] === i) {
                                        pointInClust[i].push(dataSet[j]);
                                    }
                                }
                            }

                            result.clusterAssment = clusterAssment;
                            result.centroids = centList;
                            result.pointsInCluster = pointInClust;


                            index++;
                        } else {
                            result.isEnd = true;
                        }

                        return result;
                    }

                    var step = {
                        next: oneStep
                    };

                    if (!stepByStep) {
                        var result;
                        while (!(result = step.next()).isEnd);
                        return result;
                    } else {
                        return step;
                    }

                }

                /**
                 * Create random centroid of kmeans.
                 * @param  {Array.<number>} dataSet  two-dimension array
                 * @param  {number} k   the number of centroids to be created
                 * @return {Array.<number>}   random centroids of kmeans
                 */
                function createRandCent(dataSet, k) {
                    var size = arraySize(dataSet);
                    //constructs a two-dimensional array with all values 0
                    var centroids = zeros(k, size[1]);
                    var minJ;
                    var maxJ;
                    var rangeJ;
                    //create random cluster centers, within bounds of each dimension
                    for (var j = 0; j < size[1]; j++) {
                        minJ = dataSet[0][j];
                        maxJ = dataSet[0][j];
                        for (var i = 1; i < size[0]; i++) {
                            if (dataSet[i][j] < minJ) {
                                minJ = dataSet[i][j];
                            }
                            if (dataSet[i][j] > maxJ) {
                                maxJ = dataSet[i][j];
                            }
                        }
                        rangeJ = maxJ - minJ;
                        for (var i = 0; i < k; i++) {
                            centroids[i][j] = minJ + rangeJ * Math.random();
                        }
                    }
                    return centroids;
                }

                /**
                 * Distance method for calculating similarity
                 * @param  {Array.<number>}  vec1
                 * @param  {Array.<nnumber>}  vec2
                 * @return {number}
                 */
                function distEuclid(vec1, vec2) {

                    if (!isArray(vec1) && !isArray(vec2)) {
                        return mathSqrt(mathPow(vec1 - vec2, 2));
                    }

                    var powerSum = 0;
                    //subtract the corresponding elements in the vectors
                    for (var i = 0; i < vec1.length; i++) {
                        powerSum += mathPow(vec1[i] - vec2[i], 2);
                    }

                    return mathSqrt(powerSum);
                }

                return {
                    kMeans: kMeans,
                    hierarchicalKMeans: hierarchicalKMeans
                };

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 2 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var array = __webpack_require__(3);
                var isArray = array.isArray;
                var size = array.size;
                var number = __webpack_require__(4);
                var isNumber = number.isNumber;

                /**
                 * Data preprocessing, filter the wrong data object.
                 *  for example [12,] --- missing y value
                 *              [,12] --- missing x value
                 *              [12, b] --- incorrect y value
                 *              ['a', 12] --- incorrect x value
                 * @param  {Array.<Array>} data
                 * @return {Array.<Array.<number>>}
                 */
                function dataPreprocess(data) {

                    if (!isArray(data)) {
                        throw new Error('Invalid data type, you should input an array');
                    }
                    var predata = [];
                    var arraySize = size(data);

                    if (arraySize.length === 1) {

                        for (var i = 0; i < arraySize[0]; i++) {

                            if (isNumber(data[i])) {
                                predata.push(data[i]);
                            }
                        }
                    } else if (arraySize.length === 2) {

                        for (var i = 0; i < arraySize[0]; i++) {

                            var isCorrect = true;
                            for (var j = 0; j < arraySize[1]; j++) {
                                if (!isNumber(data[i][j])) {
                                    isCorrect = false;
                                }
                            }
                            if (isCorrect) {
                                predata.push(data[i]);
                            }
                        }
                    }
                    return predata;
                }

                /**
                 * @param {string|number} val
                 * @return {number}
                 */
                function getPrecision(val) {
                    var str = val.toString();
                    // scientific notation is not considered
                    var dotIndex = str.indexOf('.');
                    return dotIndex < 0 ? 0 : str.length - 1 - dotIndex;
                }

                return {
                    dataPreprocess: dataPreprocess,
                    getPrecision: getPrecision
                };

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 3 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var objToString = Object.prototype.toString;
                var arrayProto = Array.prototype;
                var nativeMap = arrayProto.map;

                /**
                 * Get the size of a array
                 * @param  {Array} data
                 * @return {Array}
                 */
                function size(data) {
                    var s = [];
                    while (isArray(data)) {
                        s.push(data.length);
                        data = data[0];
                    }
                    return s;
                }

                /**
                 * @param {*}  value
                 * @return {boolean}
                 */
                function isArray(value) {
                    return objToString.call(value) === '[object Array]';
                }

                /**
                 * constructs a (m x n) array with all values 0
                 * @param  {number} m  the row
                 * @param  {number} n  the column
                 * @return {Array}
                 */
                function zeros(m, n) {
                    var zeroArray = [];
                    for (var i = 0; i < m; i++) {
                        zeroArray[i] = [];
                        for (var j = 0; j < n; j++) {
                            zeroArray[i][j] = 0;
                        }
                    }
                    return zeroArray;
                }

                /**
                 * Sums each element in the array.
                 * Internal use, for performance considerations, to avoid
                 * unnecessary judgments and calculations.
                 * @param  {Array} vector
                 * @return {number}
                 */
                function sum(vector) {
                    var sum = 0;
                    for (var i = 0; i < vector.length; i++) {
                        sum += vector[i];
                    }
                    return sum;
                }

                /**
                 * Computes the sum of the specified column elements in a two-dimensional array
                 * @param  {Array.<Array>} dataList  two-dimensional array
                 * @param  {number} n  the specified column, zero-based
                 * @return {number}
                 */
                function sumOfColumn(dataList, n) {
                    var sum = 0;
                    for (var i = 0; i < dataList.length; i++) {
                        sum += dataList[i][n];
                    }
                    return sum;
                }


                function ascending(a, b) {

                    return a > b ? 1 : a < b ? -1 : a === b ? 0 : NaN;

                }

                /**
                 * Binary search algorithm --- this bisector is specidfied to histogram, which every bin like that [a, b),
                 * so the return value use to add 1.
                 * @param  {Array.<number>} array
                 * @param  {number} value
                 * @param  {number} start
                 * @param  {number} end
                 * @return {number}
                 */
                function bisect(array, value, start, end) { //移出去

                    if (start == null) {
                        start = 0;
                    }
                    if (end == null) {
                        end = array.length;
                    }
                    while (start < end) {
                        var mid = Math.floor((start + end) / 2);
                        var compare = ascending(array[mid], value);
                        if (compare > 0) {
                            end = mid;
                        } else if (compare < 0) {
                            start = mid + 1;
                        } else {
                            return mid + 1;
                        }
                    }
                    return start;
                }

                /**
                 * 数组映射
                 * @memberOf module:zrender/core/util
                 * @param {Array} obj
                 * @param {Function} cb
                 * @param {*} [context]
                 * @return {Array}
                 */
                function map(obj, cb, context) {
                    if (!(obj && cb)) {
                        return;
                    }
                    if (obj.map && obj.map === nativeMap) {
                        return obj.map(cb, context);
                    } else {
                        var result = [];
                        for (var i = 0, len = obj.length; i < len; i++) {
                            result.push(cb.call(context, obj[i], i, obj));
                        }
                        return result;
                    }
                }


                return {
                    size: size,
                    isArray: isArray,
                    zeros: zeros,
                    sum: sum,
                    sumOfColumn: sumOfColumn,
                    ascending: ascending,
                    bisect: bisect,
                    map: map
                };

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 4 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                /**
                 * Test whether value is a number.
                 * @param  {*}  value
                 * @return {boolean}
                 */
                function isNumber(value) {

                    value = value === null ? NaN : +value;
                    return typeof value === 'number' && !isNaN(value);
                }

                /**
                 * Test if a number is integer.
                 * @param  {number}  value
                 * @return {boolean}
                 */
                function isInteger(value) {
                    return isFinite(value) && value === Math.round(value);
                }

                return {
                    isNumber: isNumber,
                    isInteger: isInteger
                };

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 5 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var dataProcess = __webpack_require__(2);
                var dataPreprocess = dataProcess.dataPreprocess;

                var regreMethods = {

                    /**
                     * Common linear regression algorithm
                     * @param  {Array.<Array.<number>>} data two-dimensional array
                     * @return {Object}
                     */
                    linear: function (data) {

                        var predata = dataPreprocess(data);
                        var sumX = 0;
                        var sumY = 0;
                        var sumXY = 0;
                        var sumXX = 0;
                        var len = predata.length;

                        for (var i = 0; i < len; i++) {
                            sumX += predata[i][0];
                            sumY += predata[i][1];
                            sumXY += predata[i][0] * predata[i][1];
                            sumXX += predata[i][0] * predata[i][0];
                        }

                        var gradient = ((len * sumXY) - (sumX * sumY)) / ((len * sumXX) - (sumX * sumX));
                        var intercept = (sumY / len) - ((gradient * sumX) / len);

                        var result = [];
                        for (var j = 0; j < predata.length; j++) {
                            var coordinate = [predata[j][0], gradient * predata[j][0] + intercept];
                            result.push(coordinate);
                        }

                        var string = 'y = ' + Math.round(gradient * 100) / 100 + 'x + ' + Math.round(intercept * 100) / 100;

                        return {
                            points: result,
                            parameter: {
                                gradient: gradient,
                                intercept: intercept
                            },
                            expression: string
                        };
                    },

                    /**
                     * If the raw data include [0,0] point, we should choose linearThroughOrigin
                     *   instead of linear.
                     * @param  {Array.<Array>} data  two-dimensional number array
                     * @return {Object}
                     */
                    linearThroughOrigin: function (data) {

                        var predata = dataPreprocess(data);
                        var sumXX = 0;
                        var sumXY = 0;

                        for (var i = 0; i < predata.length; i++) {
                            sumXX += predata[i][0] * predata[i][0];
                            sumXY += predata[i][0] * predata[i][1];
                        }

                        var gradient = sumXY / sumXX;
                        var result = [];

                        for (var j = 0; j < predata.length; j++) {
                            var coordinate = [predata[j][0], predata[j][0] * gradient];
                            result.push(coordinate);
                        }

                        var string = 'y = ' + Math.round(gradient * 100) / 100 + 'x';

                        return {
                            points: result,
                            parameter: {
                                gradient: gradient
                            },
                            expression: string
                        };
                    },

                    /**
                     * Exponential regression
                     * @param  {Array.<Array.<number>>} data  two-dimensional number array
                     * @return {Object}
                     */
                    exponential: function (data) {

                        var predata = dataPreprocess(data);
                        var sumX = 0;
                        var sumY = 0;
                        var sumXXY = 0;
                        var sumYlny = 0;
                        var sumXYlny = 0;
                        var sumXY = 0;

                        for (var i = 0; i < predata.length; i++) {
                            sumX += predata[i][0];
                            sumY += predata[i][1];
                            sumXY += predata[i][0] * predata[i][1];
                            sumXXY += predata[i][0] * predata[i][0] * predata[i][1];
                            sumYlny += predata[i][1] * Math.log(predata[i][1]);
                            sumXYlny += predata[i][0] * predata[i][1] * Math.log(predata[i][1]);
                        }

                        var denominator = (sumY * sumXXY) - (sumXY * sumXY);
                        var coefficient = Math.pow(Math.E, (sumXXY * sumYlny - sumXY * sumXYlny) / denominator);
                        var index = (sumY * sumXYlny - sumXY * sumYlny) / denominator;
                        var result = [];

                        for (var j = 0; j < predata.length; j++) {
                            var coordinate = [predata[j][0], coefficient * Math.pow(Math.E, index * predata[j][0])];
                            result.push(coordinate);
                        }

                        var string = 'y = ' + Math.round(coefficient * 100) / 100 + 'e^(' + Math.round(index * 100) / 100 + 'x)';

                        return {
                            points: result,
                            parameter: {
                                coefficient: coefficient,
                                index: index
                            },
                            expression: string
                        };

                    },

                    /**
                     * Logarithmic regression
                     * @param  {Array.<Array.<number>>} data  two-dimensional number array
                     * @return {Object}
                     */
                    logarithmic: function (data) {

                        var predata = dataPreprocess(data);
                        var sumlnx = 0;
                        var sumYlnx = 0;
                        var sumY = 0;
                        var sumlnxlnx = 0;

                        for (var i = 0; i < predata.length; i++) {
                            sumlnx += Math.log(predata[i][0]);
                            sumYlnx += predata[i][1] * Math.log(predata[i][0]);
                            sumY += predata[i][1];
                            sumlnxlnx += Math.pow(Math.log(predata[i][0]), 2);
                        }

                        var gradient = (i * sumYlnx - sumY * sumlnx) / (i * sumlnxlnx - sumlnx * sumlnx);
                        var intercept = (sumY - gradient * sumlnx) / i;
                        var result = [];

                        for (var j = 0; j < predata.length; j++) {
                            var coordinate = [predata[j][0], gradient * Math.log(predata[j][0]) + intercept];
                            result.push(coordinate);
                        }

                        var string =
                            'y = ' +
                            Math.round(intercept * 100) / 100 +
                            ' + ' +
                            Math.round(gradient * 100) / 100 + 'ln(x)';

                        return {
                            points: result,
                            parameter: {
                                gradient: gradient,
                                intercept: intercept
                            },
                            expression: string
                        };

                    },

                    /**
                     * Polynomial regression
                     * @param  {Array.<Array.<number>>} data  two-dimensional number array
                     * @param  {number} order  order of polynomials
                     * @return {Object}
                     */
                    polynomial: function (data, order) {

                        var predata = dataPreprocess(data);
                        if (typeof order === 'undefined') {
                            order = 2;
                        }
                        //coefficient matrix
                        var coeMatrix = [];
                        var lhs = [];
                        var k = order + 1;

                        for (var i = 0; i < k; i++) {
                            var sumA = 0;
                            for (var n = 0; n < predata.length; n++) {
                                sumA += predata[n][1] * Math.pow(predata[n][0], i);
                            }
                            lhs.push(sumA);

                            var temp = [];
                            for (var j = 0; j < k; j++) {
                                var sumB = 0;
                                for (var m = 0; m < predata.length; m++) {
                                    sumB += Math.pow(predata[m][0], i + j);
                                }
                                temp.push(sumB);
                            }
                            coeMatrix.push(temp);
                        }
                        coeMatrix.push(lhs);

                        var coeArray = gaussianElimination(coeMatrix, k);

                        var result = [];

                        for (var i = 0; i < predata.length; i++) {
                            var value = 0;
                            for (var n = 0; n < coeArray.length; n++) {
                                value += coeArray[n] * Math.pow(predata[i][0], n);
                            }
                            result.push([predata[i][0], value]);
                        }

                        var string = 'y = ';
                        for (var i = coeArray.length - 1; i >= 0; i--) {
                            if (i > 1) {
                                string += Math.round(coeArray[i] * Math.pow(10, i + 1)) / Math.pow(10, i + 1) + 'x^' + i + ' + ';
                            } else if (i === 1) {
                                string += Math.round(coeArray[i] * 100) / 100 + 'x' + ' + ';
                            } else {
                                string += Math.round(coeArray[i] * 100) / 100;
                            }
                        }

                        return {
                            points: result,
                            parameter: coeArray,
                            expression: string
                        };

                    }

                };

                /**
                 * Gaussian elimination
                 * @param  {Array.<Array.<number>>} matrix   two-dimensional number array
                 * @param  {number} number
                 * @return {Array}
                 */
                function gaussianElimination(matrix, number) {

                    for (var i = 0; i < matrix.length - 1; i++) {
                        var maxColumn = i;
                        for (var j = i + 1; j < matrix.length - 1; j++) {
                            if (Math.abs(matrix[i][j]) > Math.abs(matrix[i][maxColumn])) {
                                maxColumn = j;
                            }
                        }
                        // the matrix here is the transpose of the common Augmented matrix.
                        //  so the can perform the primary column transform, in fact, equivalent
                        //  to the primary line changes
                        for (var k = i; k < matrix.length; k++) {
                            var temp = matrix[k][i];
                            matrix[k][i] = matrix[k][maxColumn];
                            matrix[k][maxColumn] = temp;
                        }
                        for (var n = i + 1; n < matrix.length - 1; n++) {
                            for (var m = matrix.length - 1; m >= i; m--) {
                                matrix[m][n] -= matrix[m][i] / matrix[i][i] * matrix[i][n];
                            }
                        }
                    }

                    var data = new Array(number);
                    var len = matrix.length - 1;
                    for (var j = matrix.length - 2; j >= 0; j--) {
                        var temp = 0;
                        for (var i = j + 1; i < matrix.length - 1; i++) {
                            temp += matrix[i][j] * data[i];
                        }
                        data[j] = (matrix[len][j] - temp) / matrix[j][j];

                    }

                    return data;
                }

                var regression = function (regreMethod, data, order) {

                    return regreMethods[regreMethod](data, order);

                };

                return regression;

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 6 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var statistics = {};

                statistics.max = __webpack_require__(7);
                statistics.deviation = __webpack_require__(8);
                statistics.mean = __webpack_require__(10);
                statistics.median = __webpack_require__(12);
                statistics.min = __webpack_require__(14);
                statistics.quantile = __webpack_require__(13);
                statistics.sampleVariance = __webpack_require__(9);
                statistics.sum = __webpack_require__(11);

                return statistics;

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 7 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var number = __webpack_require__(4);
                var isNumber = number.isNumber;

                /**
                 * Is a method for computing the max value of a list of numbers,
                 * which will filter other data types.
                 * @param  {Array.<number>} data
                 * @return {number}
                 */
                function max(data) {

                    var maxData = -Infinity;
                    for (var i = 0; i < data.length; i++) {
                        if (isNumber(data[i]) && data[i] > maxData) {
                            maxData = data[i];
                        }
                    }
                    return maxData;
                }

                return max;

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 8 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var variance = __webpack_require__(9);

                /**
                 * Computing the deviation
                 * @param  {Array.<number>} data
                 * @return {number}
                 */
                return function (data) {

                    var squaredDeviation = variance(data);

                    return squaredDeviation ? Math.sqrt(squaredDeviation) : squaredDeviation;
                };
            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 9 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var number = __webpack_require__(4);
                var isNumber = number.isNumber;
                var mean = __webpack_require__(10);

                /**
                 * Computing the variance of list of sample
                 * @param  {Array.<number>} data
                 * @return {number}
                 */
                function sampleVariance(data) {

                    var len = data.length;
                    if (!len || len < 2) {
                        return 0;
                    }
                    if (data.length >= 2) {

                        var meanValue = mean(data);
                        var sum = 0;
                        var temple;

                        for (var i = 0; i < data.length; i++) {
                            if (isNumber(data[i])) {
                                temple = data[i] - meanValue;
                                sum += temple * temple;
                            }
                        }
                        return sum / (data.length - 1);
                    }
                }

                return sampleVariance;

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));


            /***/
        }),
        /* 10 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var sum = __webpack_require__(11);

                /**
                 * Is a method for computing the mean value of a list of numbers,
                 * which will filter other data types.
                 * @param  {Array.<number>} data
                 * @return {number}
                 */
                function mean(data) {

                    var len = data.length;

                    if (!len) {
                        return 0;
                    }

                    return sum(data) / data.length;

                }

                return mean;


            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 11 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var number = __webpack_require__(4);
                var isNumber = number.isNumber;

                /**
                 * Is a method for computing the sum of a list of numbers,
                 * which will filter other data types.
                 * @param  {Array.<number>} data
                 * @return {number}
                 */
                function sum(data) {

                    var len = data.length;

                    if (!len) {
                        return 0;
                    }
                    var sumData = 0;
                    for (var i = 0; i < len; i++) {
                        if (isNumber(data[i])) {
                            sumData += data[i];
                        }
                    }
                    return sumData;
                }

                return sum;

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 12 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var quantile = __webpack_require__(13);

                /**
                 * Is a method for computing the median value of a sorted array of numbers
                 * @param  {Array.<number>} data
                 * @return {number}
                 */
                function median(data) {

                    return quantile(data, 0.5);
                }

                return median;

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 13 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                /**
                 * Estimating quantiles from a sorted sample of numbers
                 * @see https://en.wikipedia.org/wiki/Quantile#Estimating_quantiles_from_a_sample
                 * R-7 method
                 * @param  {Array.<number>} data  sorted array
                 * @param  {number} p
                 */
                return function (data, p) {

                    var len = data.length;

                    if (!len) {
                        return 0;
                    }
                    if (p <= 0 || len < 2) {
                        return data[0];
                    }
                    if (p >= 1) {
                        return data[len - 1];
                    }
                    // in the wikipedia's R-7 method h = (N - 1)p + 1, but here array index start from 0
                    var h = (len - 1) * p;
                    var i = Math.floor(h);
                    var a = data[i];
                    var b = data[i + 1];
                    return a + (b - a) * (h - i);
                };

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 14 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var number = __webpack_require__(4);
                var isNumber = number.isNumber;

                /**
                 * Is a method for computing the min value of a list of numbers,
                 * which will filter other data types.
                 * @param  {Array.<number>} data
                 * @return {number}
                 */
                function min(data) {

                    var minData = Infinity;
                    for (var i = 0; i < data.length; i++) {
                        if (isNumber(data[i]) && data[i] < minData) {
                            minData = data[i];
                        }
                    }
                    return minData;
                }

                return min;

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 15 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var max = __webpack_require__(7);
                var min = __webpack_require__(14);
                var quantile = __webpack_require__(13);
                var deviation = __webpack_require__(8);
                var dataProcess = __webpack_require__(2);
                var dataPreprocess = dataProcess.dataPreprocess;
                var getPrecision = dataProcess.getPrecision;
                var array = __webpack_require__(3);
                var ascending = array.ascending;
                var map = array.map;
                var range = __webpack_require__(16);
                var bisect = array.bisect;
                var tickStep = __webpack_require__(17);

                /**
                 * Compute bins for histogram
                 * @param  {Array.<number>} data
                 * @param  {string} threshold
                 * @return {Object}
                 */
                function computeBins(data, threshold) {

                    if (threshold == null) {
                        threshold = thresholdMethod.squareRoot;
                    } else {
                        threshold = thresholdMethod[threshold];
                    }
                    var values = dataPreprocess(data);
                    var maxValue = max(values);
                    var minValue = min(values);
                    var binsNumber = threshold(values, minValue, maxValue);
                    var step = tickStep(minValue, maxValue, binsNumber);
                    var precision = -Math.floor(Math.log(Math.abs(maxValue - minValue) / binsNumber) / Math.LN10);

                    // return the xAxis coordinate for each bins, except the end point of the value
                    var rangeArray = range(
                        // use function toFixed() to avoid data like '0.700000001'
                        +((Math.ceil(minValue / step) * step).toFixed(precision)),
                        +((Math.floor(maxValue / step) * step).toFixed(precision)),
                        step,
                        precision
                    );

                    var len = rangeArray.length;

                    var bins = new Array(len + 1);

                    for (var i = 0; i <= len; i++) {
                        bins[i] = {};
                        bins[i].sample = [];
                        bins[i].x0 = i > 0 ?
                            rangeArray[i - 1] :
                            (rangeArray[i] - minValue) === step ?
                            minValue :
                            (rangeArray[i] - step);
                        bins[i].x1 = i < len ?
                            rangeArray[i] :
                            (maxValue - rangeArray[i - 1]) === step ?
                            maxValue :
                            rangeArray[i - 1] + step;
                    }

                    for (var i = 0; i < values.length; i++) {
                        if (minValue <= values[i] && values[i] <= maxValue) {
                            bins[bisect(rangeArray, values[i], 0, len)].sample.push(values[i]);
                        }
                    }

                    var data = map(bins, function (bin) {
                        // use function toFixed() to avoid data like '6.5666638489'
                        return [+((bin.x0 + bin.x1) / 2).toFixed(precision), bin.sample.length];
                    });

                    var customData = map(bins, function (bin) {
                        return [bin.x0, bin.x1, bin.sample.length];
                    });

                    return {
                        bins: bins,
                        data: data,
                        customData: customData
                    };
                }

                /**
                 * Four kinds of threshold methods used to
                 * compute how much bins the histogram should be divided
                 * @see  https://en.wikipedia.org/wiki/Histogram
                 * @type {Object}
                 */
                var thresholdMethod = {

                    squareRoot: function (data) {

                        var bins = Math.ceil(Math.sqrt(data.length));

                        return bins > 50 ? 50 : bins;
                    },

                    scott: function (data, min, max) {

                        return Math.ceil((max - min) / (3.5 * deviation(data) * Math.pow(data.length, -1 / 3)));
                    },

                    freedmanDiaconis: function (data, min, max) {

                        data.sort(ascending);

                        return Math.ceil(
                            (max - min) / (2 * (quantile(data, 0.75) - quantile(data, 0.25)) * Math.pow(data.length, -1 / 3))
                        );
                    },

                    sturges: function (data) {

                        return Math.ceil(Math.log(data.length) / Math.LN2) + 1;

                    }
                };

                return computeBins;

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 16 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                var dataProcess = __webpack_require__(2);
                var getPrecision = dataProcess.getPrecision;

                /**
                 * Computing range array.
                 * Adding param precision to fix range value, avoiding range[i] = 0.7000000001.
                 * @param  {number} start
                 * @param  {number} end
                 * @param  {number} step
                 * @param  {number} precision
                 * @return {Array.<number>}
                 */
                return function (start, end, step, precision) {

                    var len = arguments.length;

                    if (len < 2) {
                        end = start;
                        start = 0;
                        step = 1;
                    } else if (len < 3) {
                        step = 1;
                    } else if (len < 4) {
                        step = +step;
                        precision = getPrecision(step);
                    } else {
                        precision = +precision;
                    }

                    var n = Math.ceil(((end - start) / step).toFixed(precision));
                    var range = new Array(n + 1);
                    for (var i = 0; i < n + 1; i++) {
                        range[i] = +(start + i * step).toFixed(precision);
                    }
                    return range;
                };

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));

            /***/
        }),
        /* 17 */
        /***/
        (function (module, exports, __webpack_require__) {

            var __WEBPACK_AMD_DEFINE_RESULT__;
            !(__WEBPACK_AMD_DEFINE_RESULT__ = function (require) {

                /**
                 * Computing the length of step
                 * @see  https://github.com/d3/d3-array/blob/master/src/ticks.js
                 * @param {number} start
                 * @param {number} stop
                 * @param {number} count
                 */
                return function (start, stop, count) {

                    var step0 = Math.abs(stop - start) / count;
                    var precision = Math.floor(Math.log(step0) / Math.LN10);
                    var step1 = Math.pow(10, precision);
                    var error = step0 / step1;

                    if (error >= Math.sqrt(50)) {
                        step1 *= 10;
                    } else if (error >= Math.sqrt(10)) {
                        step1 *= 5;
                    } else if (error >= Math.sqrt(2)) {
                        step1 *= 2;
                    }
                    return +((stop >= start ? step1 : -step1).toFixed(-precision));

                };

            }.call(exports, __webpack_require__, exports, module), __WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));


            /***/
        })
        /******/
    ])
});;