diff --git a/packages/oncoprintjs/dist/oncoprint.bundle.js b/packages/oncoprintjs/dist/oncoprint.bundle.js
index 0b8040575e4..35982cbd95f 100644
--- a/packages/oncoprintjs/dist/oncoprint.bundle.js
+++ b/packages/oncoprintjs/dist/oncoprint.bundle.js
@@ -16184,7 +16184,7 @@ module.exports = {
/***/ (function(module, exports, __webpack_require__) {
module.exports = function() {
- return __webpack_require__(17)("/******/ (function(modules) { // webpackBootstrap\n/******/ \t// The module cache\n/******/ \tvar installedModules = {};\n/******/\n/******/ \t// The require function\n/******/ \tfunction __webpack_require__(moduleId) {\n/******/\n/******/ \t\t// Check if module is in cache\n/******/ \t\tif(installedModules[moduleId]) {\n/******/ \t\t\treturn installedModules[moduleId].exports;\n/******/ \t\t}\n/******/ \t\t// Create a new module (and put it into the cache)\n/******/ \t\tvar module = installedModules[moduleId] = {\n/******/ \t\t\ti: moduleId,\n/******/ \t\t\tl: false,\n/******/ \t\t\texports: {}\n/******/ \t\t};\n/******/\n/******/ \t\t// Execute the module function\n/******/ \t\tmodules[moduleId].call(module.exports, module, module.exports, __webpack_require__);\n/******/\n/******/ \t\t// Flag the module as loaded\n/******/ \t\tmodule.l = true;\n/******/\n/******/ \t\t// Return the exports of the module\n/******/ \t\treturn module.exports;\n/******/ \t}\n/******/\n/******/\n/******/ \t// expose the modules object (__webpack_modules__)\n/******/ \t__webpack_require__.m = modules;\n/******/\n/******/ \t// expose the module cache\n/******/ \t__webpack_require__.c = installedModules;\n/******/\n/******/ \t// define getter function for harmony exports\n/******/ \t__webpack_require__.d = function(exports, name, getter) {\n/******/ \t\tif(!__webpack_require__.o(exports, name)) {\n/******/ \t\t\tObject.defineProperty(exports, name, {\n/******/ \t\t\t\tconfigurable: false,\n/******/ \t\t\t\tenumerable: true,\n/******/ \t\t\t\tget: getter\n/******/ \t\t\t});\n/******/ \t\t}\n/******/ \t};\n/******/\n/******/ \t// getDefaultExport function for compatibility with non-harmony modules\n/******/ \t__webpack_require__.n = function(module) {\n/******/ \t\tvar getter = module && module.__esModule ?\n/******/ \t\t\tfunction getDefault() { return module['default']; } :\n/******/ \t\t\tfunction getModuleExports() { return module; };\n/******/ \t\t__webpack_require__.d(getter, 'a', getter);\n/******/ \t\treturn getter;\n/******/ \t};\n/******/\n/******/ \t// Object.prototype.hasOwnProperty.call\n/******/ \t__webpack_require__.o = function(object, property) { return Object.prototype.hasOwnProperty.call(object, property); };\n/******/\n/******/ \t// __webpack_public_path__\n/******/ \t__webpack_require__.p = \"\";\n/******/\n/******/ \t// Load entry module and return exports\n/******/ \treturn __webpack_require__(__webpack_require__.s = 2);\n/******/ })\n/************************************************************************/\n/******/ ([\n/* 0 */\n/***/ (function(module, exports) {\n\nmodule.exports = {\n euclidean: function(v1, v2) {\n var total = 0;\n for (var i = 0; i < v1.length; i++) {\n total += Math.pow(v2[i] - v1[i], 2); \n }\n return Math.sqrt(total);\n },\n manhattan: function(v1, v2) {\n var total = 0;\n for (var i = 0; i < v1.length ; i++) {\n total += Math.abs(v2[i] - v1[i]); \n }\n return total;\n },\n max: function(v1, v2) {\n var max = 0;\n for (var i = 0; i < v1.length; i++) {\n max = Math.max(max , Math.abs(v2[i] - v1[i])); \n }\n return max;\n }\n};\n\n/***/ }),\n/* 1 */\n/***/ (function(module, exports, __webpack_require__) {\n\nvar distances = __webpack_require__(0);\n\nfunction KMeans(centroids) {\n this.centroids = centroids || [];\n}\n\nKMeans.prototype.randomCentroids = function(points, k) {\n var centroids = points.slice(0); // copy\n centroids.sort(function() {\n return (Math.round(Math.random()) - 0.5);\n });\n return centroids.slice(0, k);\n}\n\nKMeans.prototype.classify = function(point, distance) {\n var min = Infinity,\n index = 0;\n\n distance = distance || \"euclidean\";\n if (typeof distance == \"string\") {\n distance = distances[distance];\n }\n\n for (var i = 0; i < this.centroids.length; i++) {\n var dist = distance(point, this.centroids[i]);\n if (dist < min) {\n min = dist;\n index = i;\n }\n }\n\n return index;\n}\n\nKMeans.prototype.cluster = function(points, k, distance, snapshotPeriod, snapshotCb) {\n k = k || Math.max(2, Math.ceil(Math.sqrt(points.length / 2)));\n\n distance = distance || \"euclidean\";\n if (typeof distance == \"string\") {\n distance = distances[distance];\n }\n\n this.centroids = this.randomCentroids(points, k);\n\n var assignment = new Array(points.length);\n var clusters = new Array(k);\n\n var iterations = 0;\n var movement = true;\n while (movement) {\n // update point-to-centroid assignments\n for (var i = 0; i < points.length; i++) {\n assignment[i] = this.classify(points[i], distance);\n }\n\n // update location of each centroid\n movement = false;\n for (var j = 0; j < k; j++) {\n var assigned = [];\n for (var i = 0; i < assignment.length; i++) {\n if (assignment[i] == j) {\n assigned.push(points[i]);\n }\n }\n\n if (!assigned.length) {\n continue;\n }\n\n var centroid = this.centroids[j];\n var newCentroid = new Array(centroid.length);\n\n for (var g = 0; g < centroid.length; g++) {\n var sum = 0;\n for (var i = 0; i < assigned.length; i++) {\n sum += assigned[i][g];\n }\n newCentroid[g] = sum / assigned.length;\n\n if (newCentroid[g] != centroid[g]) {\n movement = true;\n }\n }\n\n this.centroids[j] = newCentroid;\n clusters[j] = assigned;\n }\n\n if (snapshotCb && (iterations++ % snapshotPeriod == 0)) {\n snapshotCb(clusters);\n }\n }\n\n return clusters;\n}\n\nKMeans.prototype.toJSON = function() {\n return JSON.stringify(this.centroids);\n}\n\nKMeans.prototype.fromJSON = function(json) {\n this.centroids = JSON.parse(json);\n return this;\n}\n\nmodule.exports = KMeans;\n\nmodule.exports.kmeans = function(vectors, k) {\n return (new KMeans()).cluster(vectors, k);\n}\n\n/***/ }),\n/* 2 */\n/***/ (function(module, exports, __webpack_require__) {\n\n/*\n * Copyright (c) 2016 The Hyve B.V.\n * This code is licensed under the GNU Affero General Public License,\n * version 3, or (at your option) any later version.\n */\n\n/*\n * This file is part of cBioPortal.\n *\n * cBioPortal is free software: you can redistribute it and/or modify\n * it under the terms of the GNU Affero General Public License as\n * published by the Free Software Foundation, either version 3 of the\n * License.\n *\n * This program is distributed in the hope that it will be useful,\n * but WITHOUT ANY WARRANTY; without even the implied warranty of\n * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n * GNU Affero General Public License for more details.\n *\n * You should have received a copy of the GNU Affero General Public License\n * along with this program. If not, see .\n */\n\nvar clusterfck = __webpack_require__(3);\nvar jStat = __webpack_require__(5);\n\n/**\n * \"Routing\" logic for this worker, based on given message.\n *\n * @param m : message object with m.dimension (CASES or ENTITIES) and m.casesAndEntitites\n * which is the input for the clustering method.\n */\nonmessage = function(m) {\n console.log('Clustering worker received message');\n var result = null;\n if (m.data.dimension === \"CASES\") {\n result = hclusterCases(m.data.casesAndEntitites);\n } else if (m.data.dimension === \"ENTITIES\") {\n result = hclusterGeneticEntities(m.data.casesAndEntitites);\n } else {\n throw new Error(\"Illegal argument given to clustering-worker.js for m.data.dimension: \" + m.data.dimension);\n }\n console.log('Posting clustering result back to main script');\n postMessage(result);\n}\n\n/**\n * Returns false if any value is a valid number != 0.0,\n * and true otherwise.\n */\nvar isAllNaNs = function(values) {\n for (var i = 0; i < values.length; i++) {\n var val = values[i];\n if (!isNaN(val) && val != null && val != 0.0 ) {\n return false;\n }\n }\n return true;\n}\n\n/**\n * Distance measure using 1-spearman's correlation. This function does expect that item1 and item2\n * are an item than contains a item.preProcessedValueList attribute which is the ranked version\n * of item.orderedValueList.\n *\n */\nvar preRankedSpearmanDist = function(item1, item2) {\n //rules for NaN values:\n if (item1.isAllNaNs && item2.isAllNaNs) {\n //return distance 0\n return 0;\n }\n else if (item1.isAllNaNs || item2.isAllNaNs) {\n //return large distance:\n return 3;\n }\n //take the arrays from the preProcessedValueList:\n var ranks1 = item1.preProcessedValueList;\n var ranks2 = item2.preProcessedValueList;\n //calculate spearman's rank correlation coefficient, using pearson's distance\n //for correlation of the ranks:\n var r = jStat.corrcoeff(ranks1, ranks2);\n if (isNaN(r)) {\n //assuming the ranks1 and ranks2 lists do not contain NaN entries (and this code DOES assume all missing values have been imputed by a valid number),\n //this specific scenario should not occur, unless all values are the same (and given the same rank). In this case, there is no variation, and\n //correlation returns NaN. In theory this could happen on small number of entities being clustered. We give this a large distance:\n console.log(\"NaN in correlation calculation\");\n r = -2;\n }\n return 1 - r;\n}\n\n/**\n * Prepares the data for using spearman method in the distance function.\n * It will pre-calculate ranks and deviation and store this in inputItems[x].preProcessedValueList.\n * This pre-calculation significantly improves the performance of the clustering step itself.\n */\nvar _prepareForDistanceFunction = function(inputItems) {\n //pre-calculate ranks and configure to use last step of SPEARMAN as distance function:\n for (var i = 0; i < inputItems.length; i++) {\n var inputItem = inputItems[i];\n //check if all NaNs:\n inputItem.isAllNaNs = isAllNaNs(inputItem.orderedValueList);\n if (inputItem.isAllNaNs) {\n continue;\n }\n //rank using fractional ranking:\n var ranks = jStat.rank(inputItem.orderedValueList);\n //calculate deviation:\n inputItem.preProcessedValueList = ranks;\n }\n}\n\n/**\n * @param casesAndEntitites: Object with sample(or patient)Id and map\n * of geneticEntity/value pairs. Example:\n *\n * var a =\n * {\n * \"TCGA-AO-AA98-01\":\n * {\n * \t\"TP53\": 0.045,\n * \t\"BRA1\": -0.89\n * }\n * },\n * ...\n *\n * @return the reordered list of sample(or patient) ids, after clustering.\n */\nvar hclusterCases = function(casesAndEntitites) {\n var refEntityList = null;\n var inputItems = [];\n //add orderedValueList to all items, so the values are\n //compared in same order:\n for (var caseId in casesAndEntitites) {\n if (casesAndEntitites.hasOwnProperty(caseId)) {\n var caseObj = casesAndEntitites[caseId];\n var inputItem = new Object();\n inputItem.caseId = caseId;\n inputItem.orderedValueList = [];\n if (refEntityList == null) {\n refEntityList = getRefList(caseObj);\n }\n for (var j = 0; j < refEntityList.length; j++) {\n var entityId = refEntityList[j];\n var value = caseObj[entityId];\n inputItem.orderedValueList.push(value);\n }\n inputItems.push(inputItem);\n }\n }\n if (refEntityList.length == 1) {\n //this is a special case, where the \"clustering\" becomes a simple sorting in 1 dimension:\n //so, just sort and return inputItems:\n inputItems.sort(function (i1, i2) {\n var val1 = i1.orderedValueList[0];\n var val2 = i2.orderedValueList[0];\n //ensure NaNs are moved out (NaN or null which are seen here as equivalents to NA (not available)) to the end of the list:\n val1 = (val1 == null || isNaN(val1) ? Number.MAX_VALUE : val1);\n val2 = (val2 == null || isNaN(val2) ? Number.MAX_VALUE : val2);\n if (val1 > val2) {\n return 1;\n }\n else if (val1 < val2) {\n return -1;\n }\n return 0;\n });\n return inputItems;\n }\n //else, normal clustering:\n _prepareForDistanceFunction(inputItems);\n var clusters = clusterfck.hcluster(inputItems, preRankedSpearmanDist);\n return clusters.clusters(1)[0];\n}\n\nvar getRefList = function(caseItem) {\n var result = [];\n for (var entityId in caseItem) {\n if (caseItem.hasOwnProperty(entityId)) {\n result.push(entityId);\n }\n }\n return result;\n}\n\n/**\n * @param casesAndEntitites: same as used in hclusterCases above.\n *\n * @return the reordered list of entity ids, after clustering.\n */\nvar hclusterGeneticEntities = function(casesAndEntitites) {\n var refEntityList = null;\n var inputItems = [];\n var refCaseIdList = [];\n //add orderedValueList to all items, so the values are\n //compared in same order:\n for (var caseId in casesAndEntitites) {\n if (casesAndEntitites.hasOwnProperty(caseId)) {\n var caseObj = casesAndEntitites[caseId];\n if (refEntityList == null) {\n refEntityList = getRefList(caseObj);\n }\n //refCaseIdList:\n refCaseIdList.push(caseId);\n }\n }\n //iterate over genes, and get sample values:\n for (var i = 0; i < refEntityList.length; i++) {\n var entityId = refEntityList[i];\n var inputItem = new Object();\n inputItem.entityId = entityId;\n inputItem.orderedValueList = [];\n for (var j = 0; j < refCaseIdList.length; j++) {\n var caseId = refCaseIdList[j];\n var caseObj = casesAndEntitites[caseId];\n var value = caseObj[entityId];\n inputItem.orderedValueList.push(value);\n }\n inputItems.push(inputItem);\n }\n _prepareForDistanceFunction(inputItems);\n var clusters = clusterfck.hcluster(inputItems, preRankedSpearmanDist);\n return clusters.clusters(1)[0];\n}\n\n/***/ }),\n/* 3 */\n/***/ (function(module, exports, __webpack_require__) {\n\nmodule.exports = {\n hcluster: __webpack_require__(4),\n Kmeans: __webpack_require__(1),\n kmeans: __webpack_require__(1).kmeans\n};\n\n/***/ }),\n/* 4 */\n/***/ (function(module, exports, __webpack_require__) {\n\nvar distances = __webpack_require__(0);\n\nvar HierarchicalClustering = function(distance, linkage, threshold) {\n this.distance = distance;\n this.linkage = linkage;\n this.threshold = threshold == undefined ? Infinity : threshold;\n}\n\nHierarchicalClustering.prototype = {\n tree: function(items, snapshotPeriod, snapshotCb) {\n this.tree = [];\n this.dists = []; // distances between each pair of clusters\n this.mins = []; // closest cluster for each cluster\n this.index = []; // keep a hash of all clusters by key\n\n for (var i = 0; i < items.length; i++) {\n var cluster = {\n value: items[i],\n key: i,\n index: i,\n size: 1\n };\n this.tree[i] = cluster;\n this.index[i] = cluster;\n this.dists[i] = [];\n this.mins[i] = 0;\n }\n\n for (var i = 0; i < this.tree.length; i++) {\n for (var j = 0; j <= i; j++) {\n var dist = (i == j) ? Infinity :\n this.distance(this.tree[i].value, this.tree[j].value);\n this.dists[i][j] = dist;\n this.dists[j][i] = dist;\n\n if (dist < this.dists[i][this.mins[i]]) {\n this.mins[i] = j;\n }\n }\n }\n\n var merged = this.mergeClosest();\n var i = 0;\n while (merged) {\n if (snapshotCb && (i++ % snapshotPeriod) == 0) {\n snapshotCb(this.tree);\n }\n merged = this.mergeClosest();\n }\n\n this.tree.forEach(function(cluster) {\n // clean up metadata used for clustering\n delete cluster.key;\n delete cluster.index;\n });\n\n return this.tree;\n },\n\n mergeClosest: function() {\n // find two closest clusters from cached mins\n var minKey = 0, min = Infinity;\n for (var i = 0; i < this.tree.length; i++) {\n var key = this.tree[i].key,\n dist = this.dists[key][this.mins[key]];\n if (dist < min) {\n minKey = key;\n min = dist;\n }\n }\n if (min >= this.threshold) {\n return false;\n }\n\n var c1 = this.index[minKey],\n c2 = this.index[this.mins[minKey]];\n\n // merge two closest clusters\n var merged = {\n dist: min,\n left: c1,\n right: c2,\n key: c1.key,\n size: c1.size + c2.size\n };\n\n this.tree[c1.index] = merged;\n this.tree.splice(c2.index, 1);\n this.index[c1.key] = merged;\n\n // update distances with new merged cluster\n for (var i = 0; i < this.tree.length; i++) {\n var ci = this.tree[i];\n var dist;\n if (c1.key == ci.key) {\n dist = Infinity;\n }\n else if (this.linkage == \"single\") {\n dist = this.dists[c1.key][ci.key];\n if (this.dists[c1.key][ci.key] > this.dists[c2.key][ci.key]) {\n dist = this.dists[c2.key][ci.key];\n }\n }\n else if (this.linkage == \"complete\") {\n dist = this.dists[c1.key][ci.key];\n if (this.dists[c1.key][ci.key] < this.dists[c2.key][ci.key]) {\n dist = this.dists[c2.key][ci.key];\n }\n }\n else if (this.linkage == \"average\") {\n dist = (this.dists[c1.key][ci.key] * c1.size\n + this.dists[c2.key][ci.key] * c2.size) / (c1.size + c2.size);\n }\n else {\n dist = this.distance(ci.value, c1.value);\n }\n\n this.dists[c1.key][ci.key] = this.dists[ci.key][c1.key] = dist;\n }\n\n\n // update cached mins\n for (var i = 0; i < this.tree.length; i++) {\n var key1 = this.tree[i].key;\n if (this.mins[key1] == c1.key || this.mins[key1] == c2.key) {\n var min = key1;\n for (var j = 0; j < this.tree.length; j++) {\n var key2 = this.tree[j].key;\n if (this.dists[key1][key2] < this.dists[key1][min]) {\n min = key2;\n }\n }\n this.mins[key1] = min;\n }\n this.tree[i].index = i;\n }\n\n // clean up metadata used for clustering\n delete c1.key; delete c2.key;\n delete c1.index; delete c2.index;\n\n return true;\n },\n clusters: function(num){\n // Return all nodes if num is invalid\n if(num > this.tree.size || num < 1) num = this.tree.size\n\n var result = [],\n subtrees = [this.tree];\n\n // Get a list of root nodes for num different clusters\n while(num > 1){\n var furthest = _findNextFurthest(subtrees);\n subtrees.splice(subtrees.indexOf(furthest), 1);\n subtrees.push(furthest.left, furthest.right);\n num--;\n }\n\n // Transform the subtrees node list into a list of the subtrees leaf values\n subtrees.forEach(function(tree) {\n result.push(_getValues(tree));\n })\n\n // Split the next furthest distance root node\n function _findNextFurthest(subtrees) {\n var max = -1,\n furthest;\n subtrees.forEach(function(tree){\n if(tree.dist > max) {\n max = tree.dist;\n furthest = tree;\n }\n });\n return furthest;\n }\n\n // Traverse the tree and yield a list of the leaf node values\n function _getValues(tree) {\n if(tree.size === 1) return [tree.value];\n return _getValues(tree.left).concat(_getValues(tree.right));\n }\n\n return result;\n }\n}\n\nvar hcluster = function(items, distance, linkage, threshold, snapshot, snapshotCallback) {\n distance = distance || \"euclidean\";\n linkage = linkage || \"average\";\n\n if (typeof distance == \"string\") {\n distance = distances[distance];\n }\n var hc = new HierarchicalClustering(distance, linkage, threshold),\n tree = hc.tree(items, snapshot, snapshotCallback);\n\n return {\n tree: (threshold === undefined ? tree[0] : tree),\n clusters: hc.clusters\n };\n}\n\nmodule.exports = hcluster;\n\n\n/***/ }),\n/* 5 */\n/***/ (function(module, exports, __webpack_require__) {\n\n(function (window, factory) {\n if (true) {\n module.exports = factory();\n } else if (typeof define === 'function' && define.amd) {\n define(factory);\n } else {\n window.jStat = factory();\n }\n})(this, function () {\nvar jStat = (function(Math, undefined) {\n\n// For quick reference.\nvar concat = Array.prototype.concat;\nvar slice = Array.prototype.slice;\nvar toString = Object.prototype.toString;\n\n// Calculate correction for IEEE error\n// TODO: This calculation can be improved.\nfunction calcRdx(n, m) {\n var val = n > m ? n : m;\n return Math.pow(10,\n 17 - ~~(Math.log(((val > 0) ? val : -val)) * Math.LOG10E));\n}\n\n\nvar isArray = Array.isArray || function isArray(arg) {\n return toString.call(arg) === '[object Array]';\n};\n\n\nfunction isFunction(arg) {\n return toString.call(arg) === '[object Function]';\n}\n\n\nfunction isNumber(arg) {\n return typeof arg === 'number' && arg === arg;\n}\n\n\n// Converts the jStat matrix to vector.\nfunction toVector(arr) {\n return concat.apply([], arr);\n}\n\n\n// The one and only jStat constructor.\nfunction jStat() {\n return new jStat._init(arguments);\n}\n\n\n// TODO: Remove after all references in src files have been removed.\njStat.fn = jStat.prototype;\n\n\n// By separating the initializer from the constructor it's easier to handle\n// always returning a new instance whether \"new\" was used or not.\njStat._init = function _init(args) {\n var i;\n\n // If first argument is an array, must be vector or matrix.\n if (isArray(args[0])) {\n // Check if matrix.\n if (isArray(args[0][0])) {\n // See if a mapping function was also passed.\n if (isFunction(args[1]))\n args[0] = jStat.map(args[0], args[1]);\n // Iterate over each is faster than this.push.apply(this, args[0].\n for (var i = 0; i < args[0].length; i++)\n this[i] = args[0][i];\n this.length = args[0].length;\n\n // Otherwise must be a vector.\n } else {\n this[0] = isFunction(args[1]) ? jStat.map(args[0], args[1]) : args[0];\n this.length = 1;\n }\n\n // If first argument is number, assume creation of sequence.\n } else if (isNumber(args[0])) {\n this[0] = jStat.seq.apply(null, args);\n this.length = 1;\n\n // Handle case when jStat object is passed to jStat.\n } else if (args[0] instanceof jStat) {\n // Duplicate the object and pass it back.\n return jStat(args[0].toArray());\n\n // Unexpected argument value, return empty jStat object.\n // TODO: This is strange behavior. Shouldn't this throw or some such to let\n // the user know they had bad arguments?\n } else {\n this[0] = [];\n this.length = 1;\n }\n\n return this;\n};\njStat._init.prototype = jStat.prototype;\njStat._init.constructor = jStat;\n\n\n// Utility functions.\n// TODO: for internal use only?\njStat.utils = {\n calcRdx: calcRdx,\n isArray: isArray,\n isFunction: isFunction,\n isNumber: isNumber,\n toVector: toVector\n};\n\n\n// Easily extend the jStat object.\n// TODO: is this seriously necessary?\njStat.extend = function extend(obj) {\n var i, j;\n\n if (arguments.length === 1) {\n for (j in obj)\n jStat[j] = obj[j];\n return this;\n }\n\n for (var i = 1; i < arguments.length; i++) {\n for (j in arguments[i])\n obj[j] = arguments[i][j];\n }\n\n return obj;\n};\n\n\n// Returns the number of rows in the matrix.\njStat.rows = function rows(arr) {\n return arr.length || 1;\n};\n\n\n// Returns the number of columns in the matrix.\njStat.cols = function cols(arr) {\n return arr[0].length || 1;\n};\n\n\n// Returns the dimensions of the object { rows: i, cols: j }\njStat.dimensions = function dimensions(arr) {\n return {\n rows: jStat.rows(arr),\n cols: jStat.cols(arr)\n };\n};\n\n\n// Returns a specified row as a vector or return a sub matrix by pick some rows\njStat.row = function row(arr, index) {\n if (isArray(index)) {\n return index.map(function(i) {\n return jStat.row(arr, i);\n })\n }\n return arr[index];\n};\n\n\n// return row as array\n// rowa([[1,2],[3,4]],0) -> [1,2]\njStat.rowa = function rowa(arr, i) {\n return jStat.row(arr, i);\n};\n\n\n// Returns the specified column as a vector or return a sub matrix by pick some\n// columns\njStat.col = function col(arr, index) {\n if (isArray(index)) {\n var submat = jStat.arange(arr.length).map(function(i) {\n return new Array(index.length);\n });\n index.forEach(function(ind, i){\n jStat.arange(arr.length).forEach(function(j) {\n submat[j][i] = arr[j][ind];\n });\n });\n return submat;\n }\n var column = new Array(arr.length);\n for (var i = 0; i < arr.length; i++)\n column[i] = [arr[i][index]];\n return column;\n};\n\n\n// return column as array\n// cola([[1,2],[3,4]],0) -> [1,3]\njStat.cola = function cola(arr, i) {\n return jStat.col(arr, i).map(function(a){ return a[0] });\n};\n\n\n// Returns the diagonal of the matrix\njStat.diag = function diag(arr) {\n var nrow = jStat.rows(arr);\n var res = new Array(nrow);\n for (var row = 0; row < nrow; row++)\n res[row] = [arr[row][row]];\n return res;\n};\n\n\n// Returns the anti-diagonal of the matrix\njStat.antidiag = function antidiag(arr) {\n var nrow = jStat.rows(arr) - 1;\n var res = new Array(nrow);\n for (var i = 0; nrow >= 0; nrow--, i++)\n res[i] = [arr[i][nrow]];\n return res;\n};\n\n// Transpose a matrix or array.\njStat.transpose = function transpose(arr) {\n var obj = [];\n var objArr, rows, cols, j, i;\n\n // Make sure arr is in matrix format.\n if (!isArray(arr[0]))\n arr = [arr];\n\n rows = arr.length;\n cols = arr[0].length;\n\n for (var i = 0; i < cols; i++) {\n objArr = new Array(rows);\n for (j = 0; j < rows; j++)\n objArr[j] = arr[j][i];\n obj.push(objArr);\n }\n\n // If obj is vector, return only single array.\n return obj.length === 1 ? obj[0] : obj;\n};\n\n\n// Map a function to an array or array of arrays.\n// \"toAlter\" is an internal variable.\njStat.map = function map(arr, func, toAlter) {\n var row, nrow, ncol, res, col;\n\n if (!isArray(arr[0]))\n arr = [arr];\n\n nrow = arr.length;\n ncol = arr[0].length;\n res = toAlter ? arr : new Array(nrow);\n\n for (row = 0; row < nrow; row++) {\n // if the row doesn't exist, create it\n if (!res[row])\n res[row] = new Array(ncol);\n for (col = 0; col < ncol; col++)\n res[row][col] = func(arr[row][col], row, col);\n }\n\n return res.length === 1 ? res[0] : res;\n};\n\n\n// Cumulatively combine the elements of an array or array of arrays using a function.\njStat.cumreduce = function cumreduce(arr, func, toAlter) {\n var row, nrow, ncol, res, col;\n\n if (!isArray(arr[0]))\n arr = [arr];\n\n nrow = arr.length;\n ncol = arr[0].length;\n res = toAlter ? arr : new Array(nrow);\n\n for (row = 0; row < nrow; row++) {\n // if the row doesn't exist, create it\n if (!res[row])\n res[row] = new Array(ncol);\n if (ncol > 0)\n res[row][0] = arr[row][0];\n for (col = 1; col < ncol; col++)\n res[row][col] = func(res[row][col-1], arr[row][col]);\n }\n return res.length === 1 ? res[0] : res;\n};\n\n\n// Destructively alter an array.\njStat.alter = function alter(arr, func) {\n return jStat.map(arr, func, true);\n};\n\n\n// Generate a rows x cols matrix according to the supplied function.\njStat.create = function create(rows, cols, func) {\n var res = new Array(rows);\n var i, j;\n\n if (isFunction(cols)) {\n func = cols;\n cols = rows;\n }\n\n for (var i = 0; i < rows; i++) {\n res[i] = new Array(cols);\n for (j = 0; j < cols; j++)\n res[i][j] = func(i, j);\n }\n\n return res;\n};\n\n\nfunction retZero() { return 0; }\n\n\n// Generate a rows x cols matrix of zeros.\njStat.zeros = function zeros(rows, cols) {\n if (!isNumber(cols))\n cols = rows;\n return jStat.create(rows, cols, retZero);\n};\n\n\nfunction retOne() { return 1; }\n\n\n// Generate a rows x cols matrix of ones.\njStat.ones = function ones(rows, cols) {\n if (!isNumber(cols))\n cols = rows;\n return jStat.create(rows, cols, retOne);\n};\n\n\n// Generate a rows x cols matrix of uniformly random numbers.\njStat.rand = function rand(rows, cols) {\n if (!isNumber(cols))\n cols = rows;\n return jStat.create(rows, cols, Math.random);\n};\n\n\nfunction retIdent(i, j) { return i === j ? 1 : 0; }\n\n\n// Generate an identity matrix of size row x cols.\njStat.identity = function identity(rows, cols) {\n if (!isNumber(cols))\n cols = rows;\n return jStat.create(rows, cols, retIdent);\n};\n\n\n// Tests whether a matrix is symmetric\njStat.symmetric = function symmetric(arr) {\n var issymmetric = true;\n var size = arr.length;\n var row, col;\n\n if (arr.length !== arr[0].length)\n return false;\n\n for (row = 0; row < size; row++) {\n for (col = 0; col < size; col++)\n if (arr[col][row] !== arr[row][col])\n return false;\n }\n\n return true;\n};\n\n\n// Set all values to zero.\njStat.clear = function clear(arr) {\n return jStat.alter(arr, retZero);\n};\n\n\n// Generate sequence.\njStat.seq = function seq(min, max, length, func) {\n if (!isFunction(func))\n func = false;\n\n var arr = [];\n var hival = calcRdx(min, max);\n var step = (max * hival - min * hival) / ((length - 1) * hival);\n var current = min;\n var cnt;\n\n // Current is assigned using a technique to compensate for IEEE error.\n // TODO: Needs better implementation.\n for (cnt = 0;\n current <= max && cnt < length;\n cnt++, current = (min * hival + step * hival * cnt) / hival) {\n arr.push((func ? func(current, cnt) : current));\n }\n\n return arr;\n};\n\n\n// arange(5) -> [0,1,2,3,4]\n// arange(1,5) -> [1,2,3,4]\n// arange(5,1,-1) -> [5,4,3,2]\njStat.arange = function arange(start, end, step) {\n var rl = [];\n step = step || 1;\n if (end === undefined) {\n end = start;\n start = 0;\n }\n if (start === end || step === 0) {\n return [];\n }\n if (start < end && step < 0) {\n return [];\n }\n if (start > end && step > 0) {\n return [];\n }\n if (step > 0) {\n for (i = start; i < end; i += step) {\n rl.push(i);\n }\n } else {\n for (i = start; i > end; i += step) {\n rl.push(i);\n }\n }\n return rl;\n};\n\n\n// A=[[1,2,3],[4,5,6],[7,8,9]]\n// slice(A,{row:{end:2},col:{start:1}}) -> [[2,3],[5,6]]\n// slice(A,1,{start:1}) -> [5,6]\n// as numpy code A[:2,1:]\njStat.slice = (function(){\n function _slice(list, start, end, step) {\n // note it's not equal to range.map mode it's a bug\n var i;\n var rl = [];\n var length = list.length;\n if (start === undefined && end === undefined && step === undefined) {\n return jStat.copy(list);\n }\n\n start = start || 0;\n end = end || list.length;\n start = start >= 0 ? start : length + start;\n end = end >= 0 ? end : length + end;\n step = step || 1;\n if (start === end || step === 0) {\n return [];\n }\n if (start < end && step < 0) {\n return [];\n }\n if (start > end && step > 0) {\n return [];\n }\n if (step > 0) {\n for (i = start; i < end; i += step) {\n rl.push(list[i]);\n }\n } else {\n for (i = start; i > end;i += step) {\n rl.push(list[i]);\n }\n }\n return rl;\n }\n\n function slice(list, rcSlice) {\n rcSlice = rcSlice || {};\n if (isNumber(rcSlice.row)) {\n if (isNumber(rcSlice.col))\n return list[rcSlice.row][rcSlice.col];\n var row = jStat.rowa(list, rcSlice.row);\n var colSlice = rcSlice.col || {};\n return _slice(row, colSlice.start, colSlice.end, colSlice.step);\n }\n\n if (isNumber(rcSlice.col)) {\n var col = jStat.cola(list, rcSlice.col);\n var rowSlice = rcSlice.row || {};\n return _slice(col, rowSlice.start, rowSlice.end, rowSlice.step);\n }\n\n var rowSlice = rcSlice.row || {};\n var colSlice = rcSlice.col || {};\n var rows = _slice(list, rowSlice.start, rowSlice.end, rowSlice.step);\n return rows.map(function(row) {\n return _slice(row, colSlice.start, colSlice.end, colSlice.step);\n });\n }\n\n return slice;\n}());\n\n\n// A=[[1,2,3],[4,5,6],[7,8,9]]\n// sliceAssign(A,{row:{start:1},col:{start:1}},[[0,0],[0,0]])\n// A=[[1,2,3],[4,0,0],[7,0,0]]\njStat.sliceAssign = function sliceAssign(A, rcSlice, B) {\n if (isNumber(rcSlice.row)) {\n if (isNumber(rcSlice.col))\n return A[rcSlice.row][rcSlice.col] = B;\n rcSlice.col = rcSlice.col || {};\n rcSlice.col.start = rcSlice.col.start || 0;\n rcSlice.col.end = rcSlice.col.end || A[0].length;\n rcSlice.col.step = rcSlice.col.step || 1;\n var nl = jStat.arange(rcSlice.col.start,\n Math.min(A.length, rcSlice.col.end),\n rcSlice.col.step);\n var m = rcSlice.row;\n nl.forEach(function(n, i) {\n A[m][n] = B[i];\n });\n return A;\n }\n\n if (isNumber(rcSlice.col)) {\n rcSlice.row = rcSlice.row || {};\n rcSlice.row.start = rcSlice.row.start || 0;\n rcSlice.row.end = rcSlice.row.end || A.length;\n rcSlice.row.step = rcSlice.row.step || 1;\n var ml = jStat.arange(rcSlice.row.start,\n Math.min(A[0].length, rcSlice.row.end),\n rcSlice.row.step);\n var n = rcSlice.col;\n ml.forEach(function(m, j) {\n A[m][n] = B[j];\n });\n return A;\n }\n\n if (B[0].length === undefined) {\n B = [B];\n }\n rcSlice.row.start = rcSlice.row.start || 0;\n rcSlice.row.end = rcSlice.row.end || A.length;\n rcSlice.row.step = rcSlice.row.step || 1;\n rcSlice.col.start = rcSlice.col.start || 0;\n rcSlice.col.end = rcSlice.col.end || A[0].length;\n rcSlice.col.step = rcSlice.col.step || 1;\n var ml = jStat.arange(rcSlice.row.start,\n Math.min(A.length, rcSlice.row.end),\n rcSlice.row.step);\n var nl = jStat.arange(rcSlice.col.start,\n Math.min(A[0].length, rcSlice.col.end),\n rcSlice.col.step);\n ml.forEach(function(m, i) {\n nl.forEach(function(n, j) {\n A[m][n] = B[i][j];\n });\n });\n return A;\n};\n\n\n// [1,2,3] ->\n// [[1,0,0],[0,2,0],[0,0,3]]\njStat.diagonal = function diagonal(diagArray) {\n var mat = jStat.zeros(diagArray.length, diagArray.length);\n diagArray.forEach(function(t, i) {\n mat[i][i] = t;\n });\n return mat;\n};\n\n\n// return copy of A\njStat.copy = function copy(A) {\n return A.map(function(row) {\n if (isNumber(row))\n return row;\n return row.map(function(t) {\n return t;\n });\n });\n};\n\n\n// TODO: Go over this entire implementation. Seems a tragic waste of resources\n// doing all this work. Instead, and while ugly, use new Function() to generate\n// a custom function for each static method.\n\n// Quick reference.\nvar jProto = jStat.prototype;\n\n// Default length.\njProto.length = 0;\n\n// For internal use only.\n// TODO: Check if they're actually used, and if they are then rename them\n// to _*\njProto.push = Array.prototype.push;\njProto.sort = Array.prototype.sort;\njProto.splice = Array.prototype.splice;\njProto.slice = Array.prototype.slice;\n\n\n// Return a clean array.\njProto.toArray = function toArray() {\n return this.length > 1 ? slice.call(this) : slice.call(this)[0];\n};\n\n\n// Map a function to a matrix or vector.\njProto.map = function map(func, toAlter) {\n return jStat(jStat.map(this, func, toAlter));\n};\n\n\n// Cumulatively combine the elements of a matrix or vector using a function.\njProto.cumreduce = function cumreduce(func, toAlter) {\n return jStat(jStat.cumreduce(this, func, toAlter));\n};\n\n\n// Destructively alter an array.\njProto.alter = function alter(func) {\n jStat.alter(this, func);\n return this;\n};\n\n\n// Extend prototype with methods that have no argument.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jProto[passfunc] = function(func) {\n var self = this,\n results;\n // Check for callback.\n if (func) {\n setTimeout(function() {\n func.call(self, jProto[passfunc].call(self));\n });\n return this;\n }\n results = jStat[passfunc](this);\n return isArray(results) ? jStat(results) : results;\n };\n })(funcs[i]);\n})('transpose clear symmetric rows cols dimensions diag antidiag'.split(' '));\n\n\n// Extend prototype with methods that have one argument.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jProto[passfunc] = function(index, func) {\n var self = this;\n // check for callback\n if (func) {\n setTimeout(function() {\n func.call(self, jProto[passfunc].call(self, index));\n });\n return this;\n }\n return jStat(jStat[passfunc](this, index));\n };\n })(funcs[i]);\n})('row col'.split(' '));\n\n\n// Extend prototype with simple shortcut methods.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jProto[passfunc] = new Function(\n 'return jStat(jStat.' + passfunc + '.apply(null, arguments));');\n })(funcs[i]);\n})('create zeros ones rand identity'.split(' '));\n\n\n// Exposing jStat.\nreturn jStat;\n\n}(Math));\n(function(jStat, Math) {\n\nvar isFunction = jStat.utils.isFunction;\n\n// Ascending functions for sort\nfunction ascNum(a, b) { return a - b; }\n\nfunction clip(arg, min, max) {\n return Math.max(min, Math.min(arg, max));\n}\n\n\n// sum of an array\njStat.sum = function sum(arr) {\n var sum = 0;\n var i = arr.length;\n while (--i >= 0)\n sum += arr[i];\n return sum;\n};\n\n\n// sum squared\njStat.sumsqrd = function sumsqrd(arr) {\n var sum = 0;\n var i = arr.length;\n while (--i >= 0)\n sum += arr[i] * arr[i];\n return sum;\n};\n\n\n// sum of squared errors of prediction (SSE)\njStat.sumsqerr = function sumsqerr(arr) {\n var mean = jStat.mean(arr);\n var sum = 0;\n var i = arr.length;\n var tmp;\n while (--i >= 0) {\n tmp = arr[i] - mean;\n sum += tmp * tmp;\n }\n return sum;\n};\n\n// sum of an array in each row\njStat.sumrow = function sumrow(arr) {\n var sum = 0;\n var i = arr.length;\n while (--i >= 0)\n sum += arr[i];\n return sum;\n};\n\n// product of an array\njStat.product = function product(arr) {\n var prod = 1;\n var i = arr.length;\n while (--i >= 0)\n prod *= arr[i];\n return prod;\n};\n\n\n// minimum value of an array\njStat.min = function min(arr) {\n var low = arr[0];\n var i = 0;\n while (++i < arr.length)\n if (arr[i] < low)\n low = arr[i];\n return low;\n};\n\n\n// maximum value of an array\njStat.max = function max(arr) {\n var high = arr[0];\n var i = 0;\n while (++i < arr.length)\n if (arr[i] > high)\n high = arr[i];\n return high;\n};\n\n\n// unique values of an array\njStat.unique = function unique(arr) {\n var hash = {}, _arr = [];\n for(var i = 0; i < arr.length; i++) {\n if (!hash[arr[i]]) {\n hash[arr[i]] = true;\n _arr.push(arr[i]);\n }\n }\n return _arr;\n};\n\n\n// mean value of an array\njStat.mean = function mean(arr) {\n return jStat.sum(arr) / arr.length;\n};\n\n\n// mean squared error (MSE)\njStat.meansqerr = function meansqerr(arr) {\n return jStat.sumsqerr(arr) / arr.length;\n};\n\n\n// geometric mean of an array\njStat.geomean = function geomean(arr) {\n return Math.pow(jStat.product(arr), 1 / arr.length);\n};\n\n\n// median of an array\njStat.median = function median(arr) {\n var arrlen = arr.length;\n var _arr = arr.slice().sort(ascNum);\n // check if array is even or odd, then return the appropriate\n return !(arrlen & 1)\n ? (_arr[(arrlen / 2) - 1 ] + _arr[(arrlen / 2)]) / 2\n : _arr[(arrlen / 2) | 0 ];\n};\n\n\n// cumulative sum of an array\njStat.cumsum = function cumsum(arr) {\n return jStat.cumreduce(arr, function (a, b) { return a + b; });\n};\n\n\n// cumulative product of an array\njStat.cumprod = function cumprod(arr) {\n return jStat.cumreduce(arr, function (a, b) { return a * b; });\n};\n\n\n// successive differences of a sequence\njStat.diff = function diff(arr) {\n var diffs = [];\n var arrLen = arr.length;\n var i;\n for (var i = 1; i < arrLen; i++)\n diffs.push(arr[i] - arr[i - 1]);\n return diffs;\n};\n\n\n// ranks of an array\njStat.rank = function (arr) {\n var arrlen = arr.length;\n var sorted = arr.slice().sort(ascNum);\n var ranks = new Array(arrlen);\n for (var i = 0; i < arrlen; i++) {\n var first = sorted.indexOf(arr[i]);\n var last = sorted.lastIndexOf(arr[i]);\n if (first === last) {\n var val = first;\n } else {\n var val = (first + last) / 2;\n }\n ranks[i] = val + 1;\n }\n return ranks;\n};\n\n\n// mode of an array\n// if there are multiple modes of an array, return all of them\n// is this the appropriate way of handling it?\njStat.mode = function mode(arr) {\n var arrLen = arr.length;\n var _arr = arr.slice().sort(ascNum);\n var count = 1;\n var maxCount = 0;\n var numMaxCount = 0;\n var mode_arr = [];\n var i;\n\n for (var i = 0; i < arrLen; i++) {\n if (_arr[i] === _arr[i + 1]) {\n count++;\n } else {\n if (count > maxCount) {\n mode_arr = [_arr[i]];\n maxCount = count;\n numMaxCount = 0;\n }\n // are there multiple max counts\n else if (count === maxCount) {\n mode_arr.push(_arr[i]);\n numMaxCount++;\n }\n // resetting count for new value in array\n count = 1;\n }\n }\n\n return numMaxCount === 0 ? mode_arr[0] : mode_arr;\n};\n\n\n// range of an array\njStat.range = function range(arr) {\n return jStat.max(arr) - jStat.min(arr);\n};\n\n// variance of an array\n// flag = true indicates sample instead of population\njStat.variance = function variance(arr, flag) {\n return jStat.sumsqerr(arr) / (arr.length - (flag ? 1 : 0));\n};\n\n// pooled variance of an array of arrays\njStat.pooledvariance = function pooledvariance(arr) {\n var sumsqerr = arr.reduce(function (a, samples) {return a + jStat.sumsqerr(samples);}, 0);\n var count = arr.reduce(function (a, samples) {return a + samples.length;}, 0);\n return sumsqerr / (count - arr.length);\n};\n\n// deviation of an array\njStat.deviation = function (arr) {\n var mean = jStat.mean(arr);\n var arrlen = arr.length;\n var dev = new Array(arrlen);\n for (var i = 0; i < arrlen; i++) {\n dev[i] = arr[i] - mean;\n }\n return dev;\n};\n\n// standard deviation of an array\n// flag = true indicates sample instead of population\njStat.stdev = function stdev(arr, flag) {\n return Math.sqrt(jStat.variance(arr, flag));\n};\n\n// pooled standard deviation of an array of arrays\njStat.pooledstdev = function pooledstdev(arr) {\n return Math.sqrt(jStat.pooledvariance(arr));\n};\n\n// mean deviation (mean absolute deviation) of an array\njStat.meandev = function meandev(arr) {\n var mean = jStat.mean(arr);\n var a = [];\n for (var i = arr.length - 1; i >= 0; i--) {\n a.push(Math.abs(arr[i] - mean));\n }\n return jStat.mean(a);\n};\n\n\n// median deviation (median absolute deviation) of an array\njStat.meddev = function meddev(arr) {\n var median = jStat.median(arr);\n var a = [];\n for (var i = arr.length - 1; i >= 0; i--) {\n a.push(Math.abs(arr[i] - median));\n }\n return jStat.median(a);\n};\n\n\n// coefficient of variation\njStat.coeffvar = function coeffvar(arr) {\n return jStat.stdev(arr) / jStat.mean(arr);\n};\n\n\n// quartiles of an array\njStat.quartiles = function quartiles(arr) {\n var arrlen = arr.length;\n var _arr = arr.slice().sort(ascNum);\n return [\n _arr[ Math.round((arrlen) / 4) - 1 ],\n _arr[ Math.round((arrlen) / 2) - 1 ],\n _arr[ Math.round((arrlen) * 3 / 4) - 1 ]\n ];\n};\n\n\n// Arbitary quantiles of an array. Direct port of the scipy.stats\n// implementation by Pierre GF Gerard-Marchant.\njStat.quantiles = function quantiles(arr, quantilesArray, alphap, betap) {\n var sortedArray = arr.slice().sort(ascNum);\n var quantileVals = [quantilesArray.length];\n var n = arr.length;\n var i, p, m, aleph, k, gamma;\n\n if (typeof alphap === 'undefined')\n alphap = 3 / 8;\n if (typeof betap === 'undefined')\n betap = 3 / 8;\n\n for (var i = 0; i < quantilesArray.length; i++) {\n p = quantilesArray[i];\n m = alphap + p * (1 - alphap - betap);\n aleph = n * p + m;\n k = Math.floor(clip(aleph, 1, n - 1));\n gamma = clip(aleph - k, 0, 1);\n quantileVals[i] = (1 - gamma) * sortedArray[k - 1] + gamma * sortedArray[k];\n }\n\n return quantileVals;\n};\n\n// Returns the k-th percentile of values in a range, where k is in the\n// range 0..1, exclusive.\njStat.percentile = function percentile(arr, k) {\n var _arr = arr.slice().sort(ascNum);\n var realIndex = k * (_arr.length - 1);\n var index = parseInt(realIndex);\n var frac = realIndex - index;\n\n if (index + 1 < _arr.length) {\n return _arr[index] * (1 - frac) + _arr[index + 1] * frac;\n } else {\n return _arr[index];\n }\n}\n\n\n// The percentile rank of score in a given array. Returns the percentage\n// of all values in the input array that are less than (kind='strict') or\n// less or equal than (kind='weak') score. Default is weak.\njStat.percentileOfScore = function percentileOfScore(arr, score, kind) {\n var counter = 0;\n var len = arr.length;\n var strict = false;\n var value, i;\n\n if (kind === 'strict')\n strict = true;\n\n for (var i = 0; i < len; i++) {\n value = arr[i];\n if ((strict && value < score) ||\n (!strict && value <= score)) {\n counter++;\n }\n }\n\n return counter / len;\n};\n\n\n// Histogram (bin count) data\njStat.histogram = function histogram(arr, bins) {\n var first = jStat.min(arr);\n var binCnt = bins || 4;\n var binWidth = (jStat.max(arr) - first) / binCnt;\n var len = arr.length;\n var bins = [];\n var i;\n\n for (var i = 0; i < binCnt; i++)\n bins[i] = 0;\n for (var i = 0; i < len; i++)\n bins[Math.min(Math.floor(((arr[i] - first) / binWidth)), binCnt - 1)] += 1;\n\n return bins;\n};\n\n\n// covariance of two arrays\njStat.covariance = function covariance(arr1, arr2) {\n var u = jStat.mean(arr1);\n var v = jStat.mean(arr2);\n var arr1Len = arr1.length;\n var sq_dev = new Array(arr1Len);\n var i;\n\n for (var i = 0; i < arr1Len; i++)\n sq_dev[i] = (arr1[i] - u) * (arr2[i] - v);\n\n return jStat.sum(sq_dev) / (arr1Len - 1);\n};\n\n\n// (pearson's) population correlation coefficient, rho\njStat.corrcoeff = function corrcoeff(arr1, arr2) {\n return jStat.covariance(arr1, arr2) /\n jStat.stdev(arr1, 1) /\n jStat.stdev(arr2, 1);\n};\n\n // (spearman's) rank correlation coefficient, sp\njStat.spearmancoeff = function (arr1, arr2) {\n arr1 = jStat.rank(arr1);\n arr2 = jStat.rank(arr2);\n //return pearson's correlation of the ranks:\n return jStat.corrcoeff(arr1, arr2);\n}\n\n\n// statistical standardized moments (general form of skew/kurt)\njStat.stanMoment = function stanMoment(arr, n) {\n var mu = jStat.mean(arr);\n var sigma = jStat.stdev(arr);\n var len = arr.length;\n var skewSum = 0;\n\n for (var i = 0; i < len; i++)\n skewSum += Math.pow((arr[i] - mu) / sigma, n);\n\n return skewSum / arr.length;\n};\n\n// (pearson's) moment coefficient of skewness\njStat.skewness = function skewness(arr) {\n return jStat.stanMoment(arr, 3);\n};\n\n// (pearson's) (excess) kurtosis\njStat.kurtosis = function kurtosis(arr) {\n return jStat.stanMoment(arr, 4) - 3;\n};\n\n\nvar jProto = jStat.prototype;\n\n\n// Extend jProto with method for calculating cumulative sums and products.\n// This differs from the similar extension below as cumsum and cumprod should\n// not be run again in the case fullbool === true.\n// If a matrix is passed, automatically assume operation should be done on the\n// columns.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n // If a matrix is passed, automatically assume operation should be done on\n // the columns.\n jProto[passfunc] = function(fullbool, func) {\n var arr = [];\n var i = 0;\n var tmpthis = this;\n // Assignment reassignation depending on how parameters were passed in.\n if (isFunction(fullbool)) {\n func = fullbool;\n fullbool = false;\n }\n // Check if a callback was passed with the function.\n if (func) {\n setTimeout(function() {\n func.call(tmpthis, jProto[passfunc].call(tmpthis, fullbool));\n });\n return this;\n }\n // Check if matrix and run calculations.\n if (this.length > 1) {\n tmpthis = fullbool === true ? this : this.transpose();\n for (; i < tmpthis.length; i++)\n arr[i] = jStat[passfunc](tmpthis[i]);\n return arr;\n }\n // Pass fullbool if only vector, not a matrix. for variance and stdev.\n return jStat[passfunc](this[0], fullbool);\n };\n })(funcs[i]);\n})(('cumsum cumprod').split(' '));\n\n\n// Extend jProto with methods which don't require arguments and work on columns.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n // If a matrix is passed, automatically assume operation should be done on\n // the columns.\n jProto[passfunc] = function(fullbool, func) {\n var arr = [];\n var i = 0;\n var tmpthis = this;\n // Assignment reassignation depending on how parameters were passed in.\n if (isFunction(fullbool)) {\n func = fullbool;\n fullbool = false;\n }\n // Check if a callback was passed with the function.\n if (func) {\n setTimeout(function() {\n func.call(tmpthis, jProto[passfunc].call(tmpthis, fullbool));\n });\n return this;\n }\n // Check if matrix and run calculations.\n if (this.length > 1) {\n if (passfunc !== 'sumrow')\n tmpthis = fullbool === true ? this : this.transpose();\n for (; i < tmpthis.length; i++)\n arr[i] = jStat[passfunc](tmpthis[i]);\n return fullbool === true\n ? jStat[passfunc](jStat.utils.toVector(arr))\n : arr;\n }\n // Pass fullbool if only vector, not a matrix. for variance and stdev.\n return jStat[passfunc](this[0], fullbool);\n };\n })(funcs[i]);\n})(('sum sumsqrd sumsqerr sumrow product min max unique mean meansqerr ' +\n 'geomean median diff rank mode range variance deviation stdev meandev ' +\n 'meddev coeffvar quartiles histogram skewness kurtosis').split(' '));\n\n\n// Extend jProto with functions that take arguments. Operations on matrices are\n// done on columns.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jProto[passfunc] = function() {\n var arr = [];\n var i = 0;\n var tmpthis = this;\n var args = Array.prototype.slice.call(arguments);\n\n // If the last argument is a function, we assume it's a callback; we\n // strip the callback out and call the function again.\n if (isFunction(args[args.length - 1])) {\n var callbackFunction = args[args.length - 1];\n var argsToPass = args.slice(0, args.length - 1);\n\n setTimeout(function() {\n callbackFunction.call(tmpthis,\n jProto[passfunc].apply(tmpthis, argsToPass));\n });\n return this;\n\n // Otherwise we curry the function args and call normally.\n } else {\n var callbackFunction = undefined;\n var curriedFunction = function curriedFunction(vector) {\n return jStat[passfunc].apply(tmpthis, [vector].concat(args));\n }\n }\n\n // If this is a matrix, run column-by-column.\n if (this.length > 1) {\n tmpthis = tmpthis.transpose();\n for (; i < tmpthis.length; i++)\n arr[i] = curriedFunction(tmpthis[i]);\n return arr;\n }\n\n // Otherwise run on the vector.\n return curriedFunction(this[0]);\n };\n })(funcs[i]);\n})('quantiles percentileOfScore'.split(' '));\n\n}(jStat, Math));\n// Special functions //\n(function(jStat, Math) {\n\n// Log-gamma function\njStat.gammaln = function gammaln(x) {\n var j = 0;\n var cof = [\n 76.18009172947146, -86.50532032941677, 24.01409824083091,\n -1.231739572450155, 0.1208650973866179e-2, -0.5395239384953e-5\n ];\n var ser = 1.000000000190015;\n var xx, y, tmp;\n tmp = (y = xx = x) + 5.5;\n tmp -= (xx + 0.5) * Math.log(tmp);\n for (; j < 6; j++)\n ser += cof[j] / ++y;\n return Math.log(2.5066282746310005 * ser / xx) - tmp;\n};\n\n\n// gamma of x\njStat.gammafn = function gammafn(x) {\n var p = [-1.716185138865495, 24.76565080557592, -379.80425647094563,\n 629.3311553128184, 866.9662027904133, -31451.272968848367,\n -36144.413418691176, 66456.14382024054\n ];\n var q = [-30.8402300119739, 315.35062697960416, -1015.1563674902192,\n -3107.771671572311, 22538.118420980151, 4755.8462775278811,\n -134659.9598649693, -115132.2596755535];\n var fact = false;\n var n = 0;\n var xden = 0;\n var xnum = 0;\n var y = x;\n var i, z, yi, res, sum, ysq;\n if (y <= 0) {\n res = y % 1 + 3.6e-16;\n if (res) {\n fact = (!(y & 1) ? 1 : -1) * Math.PI / Math.sin(Math.PI * res);\n y = 1 - y;\n } else {\n return Infinity;\n }\n }\n yi = y;\n if (y < 1) {\n z = y++;\n } else {\n z = (y -= n = (y | 0) - 1) - 1;\n }\n for (var i = 0; i < 8; ++i) {\n xnum = (xnum + p[i]) * z;\n xden = xden * z + q[i];\n }\n res = xnum / xden + 1;\n if (yi < y) {\n res /= yi;\n } else if (yi > y) {\n for (var i = 0; i < n; ++i) {\n res *= y;\n y++;\n }\n }\n if (fact) {\n res = fact / res;\n }\n return res;\n};\n\n\n// lower incomplete gamma function, which is usually typeset with a\n// lower-case greek gamma as the function symbol\njStat.gammap = function gammap(a, x) {\n return jStat.lowRegGamma(a, x) * jStat.gammafn(a);\n};\n\n\n// The lower regularized incomplete gamma function, usually written P(a,x)\njStat.lowRegGamma = function lowRegGamma(a, x) {\n var aln = jStat.gammaln(a);\n var ap = a;\n var sum = 1 / a;\n var del = sum;\n var b = x + 1 - a;\n var c = 1 / 1.0e-30;\n var d = 1 / b;\n var h = d;\n var i = 1;\n // calculate maximum number of itterations required for a\n var ITMAX = -~(Math.log((a >= 1) ? a : 1 / a) * 8.5 + a * 0.4 + 17);\n var an, endval;\n\n if (x < 0 || a <= 0) {\n return NaN;\n } else if (x < a + 1) {\n for (; i <= ITMAX; i++) {\n sum += del *= x / ++ap;\n }\n return (sum * Math.exp(-x + a * Math.log(x) - (aln)));\n }\n\n for (; i <= ITMAX; i++) {\n an = -i * (i - a);\n b += 2;\n d = an * d + b;\n c = b + an / c;\n d = 1 / d;\n h *= d * c;\n }\n\n return (1 - h * Math.exp(-x + a * Math.log(x) - (aln)));\n};\n\n// natural log factorial of n\njStat.factorialln = function factorialln(n) {\n return n < 0 ? NaN : jStat.gammaln(n + 1);\n};\n\n// factorial of n\njStat.factorial = function factorial(n) {\n return n < 0 ? NaN : jStat.gammafn(n + 1);\n};\n\n// combinations of n, m\njStat.combination = function combination(n, m) {\n // make sure n or m don't exceed the upper limit of usable values\n return (n > 170 || m > 170)\n ? Math.exp(jStat.combinationln(n, m))\n : (jStat.factorial(n) / jStat.factorial(m)) / jStat.factorial(n - m);\n};\n\n\njStat.combinationln = function combinationln(n, m){\n return jStat.factorialln(n) - jStat.factorialln(m) - jStat.factorialln(n - m);\n};\n\n\n// permutations of n, m\njStat.permutation = function permutation(n, m) {\n return jStat.factorial(n) / jStat.factorial(n - m);\n};\n\n\n// beta function\njStat.betafn = function betafn(x, y) {\n // ensure arguments are positive\n if (x <= 0 || y <= 0)\n return undefined;\n // make sure x + y doesn't exceed the upper limit of usable values\n return (x + y > 170)\n ? Math.exp(jStat.betaln(x, y))\n : jStat.gammafn(x) * jStat.gammafn(y) / jStat.gammafn(x + y);\n};\n\n\n// natural logarithm of beta function\njStat.betaln = function betaln(x, y) {\n return jStat.gammaln(x) + jStat.gammaln(y) - jStat.gammaln(x + y);\n};\n\n\n// Evaluates the continued fraction for incomplete beta function by modified\n// Lentz's method.\njStat.betacf = function betacf(x, a, b) {\n var fpmin = 1e-30;\n var m = 1;\n var qab = a + b;\n var qap = a + 1;\n var qam = a - 1;\n var c = 1;\n var d = 1 - qab * x / qap;\n var m2, aa, del, h;\n\n // These q's will be used in factors that occur in the coefficients\n if (Math.abs(d) < fpmin)\n d = fpmin;\n d = 1 / d;\n h = d;\n\n for (; m <= 100; m++) {\n m2 = 2 * m;\n aa = m * (b - m) * x / ((qam + m2) * (a + m2));\n // One step (the even one) of the recurrence\n d = 1 + aa * d;\n if (Math.abs(d) < fpmin)\n d = fpmin;\n c = 1 + aa / c;\n if (Math.abs(c) < fpmin)\n c = fpmin;\n d = 1 / d;\n h *= d * c;\n aa = -(a + m) * (qab + m) * x / ((a + m2) * (qap + m2));\n // Next step of the recurrence (the odd one)\n d = 1 + aa * d;\n if (Math.abs(d) < fpmin)\n d = fpmin;\n c = 1 + aa / c;\n if (Math.abs(c) < fpmin)\n c = fpmin;\n d = 1 / d;\n del = d * c;\n h *= del;\n if (Math.abs(del - 1.0) < 3e-7)\n break;\n }\n\n return h;\n};\n\n\n// Returns the inverse of the lower regularized inomplete gamma function\njStat.gammapinv = function gammapinv(p, a) {\n var j = 0;\n var a1 = a - 1;\n var EPS = 1e-8;\n var gln = jStat.gammaln(a);\n var x, err, t, u, pp, lna1, afac;\n\n if (p >= 1)\n return Math.max(100, a + 100 * Math.sqrt(a));\n if (p <= 0)\n return 0;\n if (a > 1) {\n lna1 = Math.log(a1);\n afac = Math.exp(a1 * (lna1 - 1) - gln);\n pp = (p < 0.5) ? p : 1 - p;\n t = Math.sqrt(-2 * Math.log(pp));\n x = (2.30753 + t * 0.27061) / (1 + t * (0.99229 + t * 0.04481)) - t;\n if (p < 0.5)\n x = -x;\n x = Math.max(1e-3,\n a * Math.pow(1 - 1 / (9 * a) - x / (3 * Math.sqrt(a)), 3));\n } else {\n t = 1 - a * (0.253 + a * 0.12);\n if (p < t)\n x = Math.pow(p / t, 1 / a);\n else\n x = 1 - Math.log(1 - (p - t) / (1 - t));\n }\n\n for(; j < 12; j++) {\n if (x <= 0)\n return 0;\n err = jStat.lowRegGamma(a, x) - p;\n if (a > 1)\n t = afac * Math.exp(-(x - a1) + a1 * (Math.log(x) - lna1));\n else\n t = Math.exp(-x + a1 * Math.log(x) - gln);\n u = err / t;\n x -= (t = u / (1 - 0.5 * Math.min(1, u * ((a - 1) / x - 1))));\n if (x <= 0)\n x = 0.5 * (x + t);\n if (Math.abs(t) < EPS * x)\n break;\n }\n\n return x;\n};\n\n\n// Returns the error function erf(x)\njStat.erf = function erf(x) {\n var cof = [-1.3026537197817094, 6.4196979235649026e-1, 1.9476473204185836e-2,\n -9.561514786808631e-3, -9.46595344482036e-4, 3.66839497852761e-4,\n 4.2523324806907e-5, -2.0278578112534e-5, -1.624290004647e-6,\n 1.303655835580e-6, 1.5626441722e-8, -8.5238095915e-8,\n 6.529054439e-9, 5.059343495e-9, -9.91364156e-10,\n -2.27365122e-10, 9.6467911e-11, 2.394038e-12,\n -6.886027e-12, 8.94487e-13, 3.13092e-13,\n -1.12708e-13, 3.81e-16, 7.106e-15,\n -1.523e-15, -9.4e-17, 1.21e-16,\n -2.8e-17];\n var j = cof.length - 1;\n var isneg = false;\n var d = 0;\n var dd = 0;\n var t, ty, tmp, res;\n\n if (x < 0) {\n x = -x;\n isneg = true;\n }\n\n t = 2 / (2 + x);\n ty = 4 * t - 2;\n\n for(; j > 0; j--) {\n tmp = d;\n d = ty * d - dd + cof[j];\n dd = tmp;\n }\n\n res = t * Math.exp(-x * x + 0.5 * (cof[0] + ty * d) - dd);\n return isneg ? res - 1 : 1 - res;\n};\n\n\n// Returns the complmentary error function erfc(x)\njStat.erfc = function erfc(x) {\n return 1 - jStat.erf(x);\n};\n\n\n// Returns the inverse of the complementary error function\njStat.erfcinv = function erfcinv(p) {\n var j = 0;\n var x, err, t, pp;\n if (p >= 2)\n return -100;\n if (p <= 0)\n return 100;\n pp = (p < 1) ? p : 2 - p;\n t = Math.sqrt(-2 * Math.log(pp / 2));\n x = -0.70711 * ((2.30753 + t * 0.27061) /\n (1 + t * (0.99229 + t * 0.04481)) - t);\n for (; j < 2; j++) {\n err = jStat.erfc(x) - pp;\n x += err / (1.12837916709551257 * Math.exp(-x * x) - x * err);\n }\n return (p < 1) ? x : -x;\n};\n\n\n// Returns the inverse of the incomplete beta function\njStat.ibetainv = function ibetainv(p, a, b) {\n var EPS = 1e-8;\n var a1 = a - 1;\n var b1 = b - 1;\n var j = 0;\n var lna, lnb, pp, t, u, err, x, al, h, w, afac;\n if (p <= 0)\n return 0;\n if (p >= 1)\n return 1;\n if (a >= 1 && b >= 1) {\n pp = (p < 0.5) ? p : 1 - p;\n t = Math.sqrt(-2 * Math.log(pp));\n x = (2.30753 + t * 0.27061) / (1 + t* (0.99229 + t * 0.04481)) - t;\n if (p < 0.5)\n x = -x;\n al = (x * x - 3) / 6;\n h = 2 / (1 / (2 * a - 1) + 1 / (2 * b - 1));\n w = (x * Math.sqrt(al + h) / h) - (1 / (2 * b - 1) - 1 / (2 * a - 1)) *\n (al + 5 / 6 - 2 / (3 * h));\n x = a / (a + b * Math.exp(2 * w));\n } else {\n lna = Math.log(a / (a + b));\n lnb = Math.log(b / (a + b));\n t = Math.exp(a * lna) / a;\n u = Math.exp(b * lnb) / b;\n w = t + u;\n if (p < t / w)\n x = Math.pow(a * w * p, 1 / a);\n else\n x = 1 - Math.pow(b * w * (1 - p), 1 / b);\n }\n afac = -jStat.gammaln(a) - jStat.gammaln(b) + jStat.gammaln(a + b);\n for(; j < 10; j++) {\n if (x === 0 || x === 1)\n return x;\n err = jStat.ibeta(x, a, b) - p;\n t = Math.exp(a1 * Math.log(x) + b1 * Math.log(1 - x) + afac);\n u = err / t;\n x -= (t = u / (1 - 0.5 * Math.min(1, u * (a1 / x - b1 / (1 - x)))));\n if (x <= 0)\n x = 0.5 * (x + t);\n if (x >= 1)\n x = 0.5 * (x + t + 1);\n if (Math.abs(t) < EPS * x && j > 0)\n break;\n }\n return x;\n};\n\n\n// Returns the incomplete beta function I_x(a,b)\njStat.ibeta = function ibeta(x, a, b) {\n // Factors in front of the continued fraction.\n var bt = (x === 0 || x === 1) ? 0 :\n Math.exp(jStat.gammaln(a + b) - jStat.gammaln(a) -\n jStat.gammaln(b) + a * Math.log(x) + b *\n Math.log(1 - x));\n if (x < 0 || x > 1)\n return false;\n if (x < (a + 1) / (a + b + 2))\n // Use continued fraction directly.\n return bt * jStat.betacf(x, a, b) / a;\n // else use continued fraction after making the symmetry transformation.\n return 1 - bt * jStat.betacf(1 - x, b, a) / b;\n};\n\n\n// Returns a normal deviate (mu=0, sigma=1).\n// If n and m are specified it returns a object of normal deviates.\njStat.randn = function randn(n, m) {\n var u, v, x, y, q, mat;\n if (!m)\n m = n;\n if (n)\n return jStat.create(n, m, function() { return jStat.randn(); });\n do {\n u = Math.random();\n v = 1.7156 * (Math.random() - 0.5);\n x = u - 0.449871;\n y = Math.abs(v) + 0.386595;\n q = x * x + y * (0.19600 * y - 0.25472 * x);\n } while (q > 0.27597 && (q > 0.27846 || v * v > -4 * Math.log(u) * u * u));\n return v / u;\n};\n\n\n// Returns a gamma deviate by the method of Marsaglia and Tsang.\njStat.randg = function randg(shape, n, m) {\n var oalph = shape;\n var a1, a2, u, v, x, mat;\n if (!m)\n m = n;\n if (!shape)\n shape = 1;\n if (n) {\n mat = jStat.zeros(n,m);\n mat.alter(function() { return jStat.randg(shape); });\n return mat;\n }\n if (shape < 1)\n shape += 1;\n a1 = shape - 1 / 3;\n a2 = 1 / Math.sqrt(9 * a1);\n do {\n do {\n x = jStat.randn();\n v = 1 + a2 * x;\n } while(v <= 0);\n v = v * v * v;\n u = Math.random();\n } while(u > 1 - 0.331 * Math.pow(x, 4) &&\n Math.log(u) > 0.5 * x*x + a1 * (1 - v + Math.log(v)));\n // alpha > 1\n if (shape == oalph)\n return a1 * v;\n // alpha < 1\n do {\n u = Math.random();\n } while(u === 0);\n return Math.pow(u, 1 / oalph) * a1 * v;\n};\n\n\n// making use of static methods on the instance\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jStat.fn[passfunc] = function() {\n return jStat(\n jStat.map(this, function(value) { return jStat[passfunc](value); }));\n }\n })(funcs[i]);\n})('gammaln gammafn factorial factorialln'.split(' '));\n\n\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jStat.fn[passfunc] = function() {\n return jStat(jStat[passfunc].apply(null, arguments));\n };\n })(funcs[i]);\n})('randn'.split(' '));\n\n}(jStat, Math));\n(function(jStat, Math) {\n\n// generate all distribution instance methods\n(function(list) {\n for (var i = 0; i < list.length; i++) (function(func) {\n // distribution instance method\n jStat[func] = function(a, b, c) {\n if (!(this instanceof arguments.callee))\n return new arguments.callee(a, b, c);\n this._a = a;\n this._b = b;\n this._c = c;\n return this;\n };\n // distribution method to be used on a jStat instance\n jStat.fn[func] = function(a, b, c) {\n var newthis = jStat[func](a, b, c);\n newthis.data = this;\n return newthis;\n };\n // sample instance method\n jStat[func].prototype.sample = function(arr) {\n var a = this._a;\n var b = this._b;\n var c = this._c;\n if (arr)\n return jStat.alter(arr, function() {\n return jStat[func].sample(a, b, c);\n });\n else\n return jStat[func].sample(a, b, c);\n };\n // generate the pdf, cdf and inv instance methods\n (function(vals) {\n for (var i = 0; i < vals.length; i++) (function(fnfunc) {\n jStat[func].prototype[fnfunc] = function(x) {\n var a = this._a;\n var b = this._b;\n var c = this._c;\n if (!x && x !== 0)\n x = this.data;\n if (typeof x !== 'number') {\n return jStat.fn.map.call(x, function(x) {\n return jStat[func][fnfunc](x, a, b, c);\n });\n }\n return jStat[func][fnfunc](x, a, b, c);\n };\n })(vals[i]);\n })('pdf cdf inv'.split(' '));\n // generate the mean, median, mode and variance instance methods\n (function(vals) {\n for (var i = 0; i < vals.length; i++) (function(fnfunc) {\n jStat[func].prototype[fnfunc] = function() {\n return jStat[func][fnfunc](this._a, this._b, this._c);\n };\n })(vals[i]);\n })('mean median mode variance'.split(' '));\n })(list[i]);\n})((\n 'beta centralF cauchy chisquare exponential gamma invgamma kumaraswamy ' +\n 'laplace lognormal noncentralt normal pareto studentt weibull uniform ' +\n 'binomial negbin hypgeom poisson triangular tukey arcsine'\n).split(' '));\n\n\n\n// extend beta function with static methods\njStat.extend(jStat.beta, {\n pdf: function pdf(x, alpha, beta) {\n // PDF is zero outside the support\n if (x > 1 || x < 0)\n return 0;\n // PDF is one for the uniform case\n if (alpha == 1 && beta == 1)\n return 1;\n\n if (alpha < 512 && beta < 512) {\n return (Math.pow(x, alpha - 1) * Math.pow(1 - x, beta - 1)) /\n jStat.betafn(alpha, beta);\n } else {\n return Math.exp((alpha - 1) * Math.log(x) +\n (beta - 1) * Math.log(1 - x) -\n jStat.betaln(alpha, beta));\n }\n },\n\n cdf: function cdf(x, alpha, beta) {\n return (x > 1 || x < 0) ? (x > 1) * 1 : jStat.ibeta(x, alpha, beta);\n },\n\n inv: function inv(x, alpha, beta) {\n return jStat.ibetainv(x, alpha, beta);\n },\n\n mean: function mean(alpha, beta) {\n return alpha / (alpha + beta);\n },\n\n median: function median(alpha, beta) {\n return jStat.ibetainv(0.5, alpha, beta);\n },\n\n mode: function mode(alpha, beta) {\n return (alpha - 1 ) / ( alpha + beta - 2);\n },\n\n // return a random sample\n sample: function sample(alpha, beta) {\n var u = jStat.randg(alpha);\n return u / (u + jStat.randg(beta));\n },\n\n variance: function variance(alpha, beta) {\n return (alpha * beta) / (Math.pow(alpha + beta, 2) * (alpha + beta + 1));\n }\n});\n\n// extend F function with static methods\njStat.extend(jStat.centralF, {\n // This implementation of the pdf function avoids float overflow\n // See the way that R calculates this value:\n // https://svn.r-project.org/R/trunk/src/nmath/df.c\n pdf: function pdf(x, df1, df2) {\n var p, q, f;\n\n if (x < 0)\n return 0;\n\n if (df1 <= 2) {\n if (x === 0 && df1 < 2) {\n return Infinity;\n }\n if (x === 0 && df1 === 2) {\n return 1;\n }\n return (1 / jStat.betafn(df1 / 2, df2 / 2)) *\n Math.pow(df1 / df2, df1 / 2) *\n Math.pow(x, (df1/2) - 1) *\n Math.pow((1 + (df1 / df2) * x), -(df1 + df2) / 2);\n }\n\n p = (df1 * x) / (df2 + x * df1);\n q = df2 / (df2 + x * df1);\n f = df1 * q / 2.0;\n return f * jStat.binomial.pdf((df1 - 2) / 2, (df1 + df2 - 2) / 2, p);\n },\n\n cdf: function cdf(x, df1, df2) {\n if (x < 0)\n return 0;\n return jStat.ibeta((df1 * x) / (df1 * x + df2), df1 / 2, df2 / 2);\n },\n\n inv: function inv(x, df1, df2) {\n return df2 / (df1 * (1 / jStat.ibetainv(x, df1 / 2, df2 / 2) - 1));\n },\n\n mean: function mean(df1, df2) {\n return (df2 > 2) ? df2 / (df2 - 2) : undefined;\n },\n\n mode: function mode(df1, df2) {\n return (df1 > 2) ? (df2 * (df1 - 2)) / (df1 * (df2 + 2)) : undefined;\n },\n\n // return a random sample\n sample: function sample(df1, df2) {\n var x1 = jStat.randg(df1 / 2) * 2;\n var x2 = jStat.randg(df2 / 2) * 2;\n return (x1 / df1) / (x2 / df2);\n },\n\n variance: function variance(df1, df2) {\n if (df2 <= 4)\n return undefined;\n return 2 * df2 * df2 * (df1 + df2 - 2) /\n (df1 * (df2 - 2) * (df2 - 2) * (df2 - 4));\n }\n});\n\n\n// extend cauchy function with static methods\njStat.extend(jStat.cauchy, {\n pdf: function pdf(x, local, scale) {\n if (scale < 0) { return 0; }\n\n return (scale / (Math.pow(x - local, 2) + Math.pow(scale, 2))) / Math.PI;\n },\n\n cdf: function cdf(x, local, scale) {\n return Math.atan((x - local) / scale) / Math.PI + 0.5;\n },\n\n inv: function(p, local, scale) {\n return local + scale * Math.tan(Math.PI * (p - 0.5));\n },\n\n median: function median(local, scale) {\n return local;\n },\n\n mode: function mode(local, scale) {\n return local;\n },\n\n sample: function sample(local, scale) {\n return jStat.randn() *\n Math.sqrt(1 / (2 * jStat.randg(0.5))) * scale + local;\n }\n});\n\n\n\n// extend chisquare function with static methods\njStat.extend(jStat.chisquare, {\n pdf: function pdf(x, dof) {\n if (x < 0)\n return 0;\n return (x === 0 && dof === 2) ? 0.5 :\n Math.exp((dof / 2 - 1) * Math.log(x) - x / 2 - (dof / 2) *\n Math.log(2) - jStat.gammaln(dof / 2));\n },\n\n cdf: function cdf(x, dof) {\n if (x < 0)\n return 0;\n return jStat.lowRegGamma(dof / 2, x / 2);\n },\n\n inv: function(p, dof) {\n return 2 * jStat.gammapinv(p, 0.5 * dof);\n },\n\n mean : function(dof) {\n return dof;\n },\n\n // TODO: this is an approximation (is there a better way?)\n median: function median(dof) {\n return dof * Math.pow(1 - (2 / (9 * dof)), 3);\n },\n\n mode: function mode(dof) {\n return (dof - 2 > 0) ? dof - 2 : 0;\n },\n\n sample: function sample(dof) {\n return jStat.randg(dof / 2) * 2;\n },\n\n variance: function variance(dof) {\n return 2 * dof;\n }\n});\n\n\n\n// extend exponential function with static methods\njStat.extend(jStat.exponential, {\n pdf: function pdf(x, rate) {\n return x < 0 ? 0 : rate * Math.exp(-rate * x);\n },\n\n cdf: function cdf(x, rate) {\n return x < 0 ? 0 : 1 - Math.exp(-rate * x);\n },\n\n inv: function(p, rate) {\n return -Math.log(1 - p) / rate;\n },\n\n mean : function(rate) {\n return 1 / rate;\n },\n\n median: function (rate) {\n return (1 / rate) * Math.log(2);\n },\n\n mode: function mode(rate) {\n return 0;\n },\n\n sample: function sample(rate) {\n return -1 / rate * Math.log(Math.random());\n },\n\n variance : function(rate) {\n return Math.pow(rate, -2);\n }\n});\n\n\n\n// extend gamma function with static methods\njStat.extend(jStat.gamma, {\n pdf: function pdf(x, shape, scale) {\n if (x < 0)\n return 0;\n return (x === 0 && shape === 1) ? 1 / scale :\n Math.exp((shape - 1) * Math.log(x) - x / scale -\n jStat.gammaln(shape) - shape * Math.log(scale));\n },\n\n cdf: function cdf(x, shape, scale) {\n if (x < 0)\n return 0;\n return jStat.lowRegGamma(shape, x / scale);\n },\n\n inv: function(p, shape, scale) {\n return jStat.gammapinv(p, shape) * scale;\n },\n\n mean : function(shape, scale) {\n return shape * scale;\n },\n\n mode: function mode(shape, scale) {\n if(shape > 1) return (shape - 1) * scale;\n return undefined;\n },\n\n sample: function sample(shape, scale) {\n return jStat.randg(shape) * scale;\n },\n\n variance: function variance(shape, scale) {\n return shape * scale * scale;\n }\n});\n\n// extend inverse gamma function with static methods\njStat.extend(jStat.invgamma, {\n pdf: function pdf(x, shape, scale) {\n if (x <= 0)\n return 0;\n return Math.exp(-(shape + 1) * Math.log(x) - scale / x -\n jStat.gammaln(shape) + shape * Math.log(scale));\n },\n\n cdf: function cdf(x, shape, scale) {\n if (x <= 0)\n return 0;\n return 1 - jStat.lowRegGamma(shape, scale / x);\n },\n\n inv: function(p, shape, scale) {\n return scale / jStat.gammapinv(1 - p, shape);\n },\n\n mean : function(shape, scale) {\n return (shape > 1) ? scale / (shape - 1) : undefined;\n },\n\n mode: function mode(shape, scale) {\n return scale / (shape + 1);\n },\n\n sample: function sample(shape, scale) {\n return scale / jStat.randg(shape);\n },\n\n variance: function variance(shape, scale) {\n if (shape <= 2)\n return undefined;\n return scale * scale / ((shape - 1) * (shape - 1) * (shape - 2));\n }\n});\n\n\n// extend kumaraswamy function with static methods\njStat.extend(jStat.kumaraswamy, {\n pdf: function pdf(x, alpha, beta) {\n if (x === 0 && alpha === 1)\n return beta;\n else if (x === 1 && beta === 1)\n return alpha;\n return Math.exp(Math.log(alpha) + Math.log(beta) + (alpha - 1) *\n Math.log(x) + (beta - 1) *\n Math.log(1 - Math.pow(x, alpha)));\n },\n\n cdf: function cdf(x, alpha, beta) {\n if (x < 0)\n return 0;\n else if (x > 1)\n return 1;\n return (1 - Math.pow(1 - Math.pow(x, alpha), beta));\n },\n\n inv: function inv(p, alpha, beta) {\n return Math.pow(1 - Math.pow(1 - p, 1 / beta), 1 / alpha);\n },\n\n mean : function(alpha, beta) {\n return (beta * jStat.gammafn(1 + 1 / alpha) *\n jStat.gammafn(beta)) / (jStat.gammafn(1 + 1 / alpha + beta));\n },\n\n median: function median(alpha, beta) {\n return Math.pow(1 - Math.pow(2, -1 / beta), 1 / alpha);\n },\n\n mode: function mode(alpha, beta) {\n if (!(alpha >= 1 && beta >= 1 && (alpha !== 1 && beta !== 1)))\n return undefined;\n return Math.pow((alpha - 1) / (alpha * beta - 1), 1 / alpha);\n },\n\n variance: function variance(alpha, beta) {\n throw new Error('variance not yet implemented');\n // TODO: complete this\n }\n});\n\n\n\n// extend lognormal function with static methods\njStat.extend(jStat.lognormal, {\n pdf: function pdf(x, mu, sigma) {\n if (x <= 0)\n return 0;\n return Math.exp(-Math.log(x) - 0.5 * Math.log(2 * Math.PI) -\n Math.log(sigma) - Math.pow(Math.log(x) - mu, 2) /\n (2 * sigma * sigma));\n },\n\n cdf: function cdf(x, mu, sigma) {\n if (x < 0)\n return 0;\n return 0.5 +\n (0.5 * jStat.erf((Math.log(x) - mu) / Math.sqrt(2 * sigma * sigma)));\n },\n\n inv: function(p, mu, sigma) {\n return Math.exp(-1.41421356237309505 * sigma * jStat.erfcinv(2 * p) + mu);\n },\n\n mean: function mean(mu, sigma) {\n return Math.exp(mu + sigma * sigma / 2);\n },\n\n median: function median(mu, sigma) {\n return Math.exp(mu);\n },\n\n mode: function mode(mu, sigma) {\n return Math.exp(mu - sigma * sigma);\n },\n\n sample: function sample(mu, sigma) {\n return Math.exp(jStat.randn() * sigma + mu);\n },\n\n variance: function variance(mu, sigma) {\n return (Math.exp(sigma * sigma) - 1) * Math.exp(2 * mu + sigma * sigma);\n }\n});\n\n\n\n// extend noncentralt function with static methods\njStat.extend(jStat.noncentralt, {\n pdf: function pdf(x, dof, ncp) {\n var tol = 1e-14;\n if (Math.abs(ncp) < tol) // ncp approx 0; use student-t\n return jStat.studentt.pdf(x, dof)\n\n if (Math.abs(x) < tol) { // different formula for x == 0\n return Math.exp(jStat.gammaln((dof + 1) / 2) - ncp * ncp / 2 -\n 0.5 * Math.log(Math.PI * dof) - jStat.gammaln(dof / 2));\n }\n\n // formula for x != 0\n return dof / x *\n (jStat.noncentralt.cdf(x * Math.sqrt(1 + 2 / dof), dof+2, ncp) -\n jStat.noncentralt.cdf(x, dof, ncp));\n },\n\n cdf: function cdf(x, dof, ncp) {\n var tol = 1e-14;\n var min_iterations = 200;\n\n if (Math.abs(ncp) < tol) // ncp approx 0; use student-t\n return jStat.studentt.cdf(x, dof);\n\n // turn negative x into positive and flip result afterwards\n var flip = false;\n if (x < 0) {\n flip = true;\n ncp = -ncp;\n }\n\n var prob = jStat.normal.cdf(-ncp, 0, 1);\n var value = tol + 1;\n // use value at last two steps to determine convergence\n var lastvalue = value;\n var y = x * x / (x * x + dof);\n var j = 0;\n var p = Math.exp(-ncp * ncp / 2);\n var q = Math.exp(-ncp * ncp / 2 - 0.5 * Math.log(2) -\n jStat.gammaln(3 / 2)) * ncp;\n while (j < min_iterations || lastvalue > tol || value > tol) {\n lastvalue = value;\n if (j > 0) {\n p *= (ncp * ncp) / (2 * j);\n q *= (ncp * ncp) / (2 * (j + 1 / 2));\n }\n value = p * jStat.beta.cdf(y, j + 0.5, dof / 2) +\n q * jStat.beta.cdf(y, j+1, dof/2);\n prob += 0.5 * value;\n j++;\n }\n\n return flip ? (1 - prob) : prob;\n }\n});\n\n\n// extend normal function with static methods\njStat.extend(jStat.normal, {\n pdf: function pdf(x, mean, std) {\n return Math.exp(-0.5 * Math.log(2 * Math.PI) -\n Math.log(std) - Math.pow(x - mean, 2) / (2 * std * std));\n },\n\n cdf: function cdf(x, mean, std) {\n return 0.5 * (1 + jStat.erf((x - mean) / Math.sqrt(2 * std * std)));\n },\n\n inv: function(p, mean, std) {\n return -1.41421356237309505 * std * jStat.erfcinv(2 * p) + mean;\n },\n\n mean : function(mean, std) {\n return mean;\n },\n\n median: function median(mean, std) {\n return mean;\n },\n\n mode: function (mean, std) {\n return mean;\n },\n\n sample: function sample(mean, std) {\n return jStat.randn() * std + mean;\n },\n\n variance : function(mean, std) {\n return std * std;\n }\n});\n\n\n\n// extend pareto function with static methods\njStat.extend(jStat.pareto, {\n pdf: function pdf(x, scale, shape) {\n if (x < scale)\n return 0;\n return (shape * Math.pow(scale, shape)) / Math.pow(x, shape + 1);\n },\n\n cdf: function cdf(x, scale, shape) {\n if (x < scale)\n return 0;\n return 1 - Math.pow(scale / x, shape);\n },\n\n inv: function inv(p, scale, shape) {\n return scale / Math.pow(1 - p, 1 / shape);\n },\n\n mean: function mean(scale, shape) {\n if (shape <= 1)\n return undefined;\n return (shape * Math.pow(scale, shape)) / (shape - 1);\n },\n\n median: function median(scale, shape) {\n return scale * (shape * Math.SQRT2);\n },\n\n mode: function mode(scale, shape) {\n return scale;\n },\n\n variance : function(scale, shape) {\n if (shape <= 2)\n return undefined;\n return (scale*scale * shape) / (Math.pow(shape - 1, 2) * (shape - 2));\n }\n});\n\n\n\n// extend studentt function with static methods\njStat.extend(jStat.studentt, {\n pdf: function pdf(x, dof) {\n dof = dof > 1e100 ? 1e100 : dof;\n return (1/(Math.sqrt(dof) * jStat.betafn(0.5, dof/2))) *\n Math.pow(1 + ((x * x) / dof), -((dof + 1) / 2));\n },\n\n cdf: function cdf(x, dof) {\n var dof2 = dof / 2;\n return jStat.ibeta((x + Math.sqrt(x * x + dof)) /\n (2 * Math.sqrt(x * x + dof)), dof2, dof2);\n },\n\n inv: function(p, dof) {\n var x = jStat.ibetainv(2 * Math.min(p, 1 - p), 0.5 * dof, 0.5);\n x = Math.sqrt(dof * (1 - x) / x);\n return (p > 0.5) ? x : -x;\n },\n\n mean: function mean(dof) {\n return (dof > 1) ? 0 : undefined;\n },\n\n median: function median(dof) {\n return 0;\n },\n\n mode: function mode(dof) {\n return 0;\n },\n\n sample: function sample(dof) {\n return jStat.randn() * Math.sqrt(dof / (2 * jStat.randg(dof / 2)));\n },\n\n variance: function variance(dof) {\n return (dof > 2) ? dof / (dof - 2) : (dof > 1) ? Infinity : undefined;\n }\n});\n\n\n\n// extend weibull function with static methods\njStat.extend(jStat.weibull, {\n pdf: function pdf(x, scale, shape) {\n if (x < 0 || scale < 0 || shape < 0)\n return 0;\n return (shape / scale) * Math.pow((x / scale), (shape - 1)) *\n Math.exp(-(Math.pow((x / scale), shape)));\n },\n\n cdf: function cdf(x, scale, shape) {\n return x < 0 ? 0 : 1 - Math.exp(-Math.pow((x / scale), shape));\n },\n\n inv: function(p, scale, shape) {\n return scale * Math.pow(-Math.log(1 - p), 1 / shape);\n },\n\n mean : function(scale, shape) {\n return scale * jStat.gammafn(1 + 1 / shape);\n },\n\n median: function median(scale, shape) {\n return scale * Math.pow(Math.log(2), 1 / shape);\n },\n\n mode: function mode(scale, shape) {\n if (shape <= 1)\n return 0;\n return scale * Math.pow((shape - 1) / shape, 1 / shape);\n },\n\n sample: function sample(scale, shape) {\n return scale * Math.pow(-Math.log(Math.random()), 1 / shape);\n },\n\n variance: function variance(scale, shape) {\n return scale * scale * jStat.gammafn(1 + 2 / shape) -\n Math.pow(jStat.weibull.mean(scale, shape), 2);\n }\n});\n\n\n\n// extend uniform function with static methods\njStat.extend(jStat.uniform, {\n pdf: function pdf(x, a, b) {\n return (x < a || x > b) ? 0 : 1 / (b - a);\n },\n\n cdf: function cdf(x, a, b) {\n if (x < a)\n return 0;\n else if (x < b)\n return (x - a) / (b - a);\n return 1;\n },\n\n inv: function(p, a, b) {\n return a + (p * (b - a));\n },\n\n mean: function mean(a, b) {\n return 0.5 * (a + b);\n },\n\n median: function median(a, b) {\n return jStat.mean(a, b);\n },\n\n mode: function mode(a, b) {\n throw new Error('mode is not yet implemented');\n },\n\n sample: function sample(a, b) {\n return (a / 2 + b / 2) + (b / 2 - a / 2) * (2 * Math.random() - 1);\n },\n\n variance: function variance(a, b) {\n return Math.pow(b - a, 2) / 12;\n }\n});\n\n\n\n// extend uniform function with static methods\njStat.extend(jStat.binomial, {\n pdf: function pdf(k, n, p) {\n return (p === 0 || p === 1) ?\n ((n * p) === k ? 1 : 0) :\n jStat.combination(n, k) * Math.pow(p, k) * Math.pow(1 - p, n - k);\n },\n\n cdf: function cdf(x, n, p) {\n var binomarr = [],\n k = 0;\n if (x < 0) {\n return 0;\n }\n if (x < n) {\n for (; k <= x; k++) {\n binomarr[ k ] = jStat.binomial.pdf(k, n, p);\n }\n return jStat.sum(binomarr);\n }\n return 1;\n }\n});\n\n\n\n// extend uniform function with static methods\njStat.extend(jStat.negbin, {\n pdf: function pdf(k, r, p) {\n if (k !== k >>> 0)\n return false;\n if (k < 0)\n return 0;\n return jStat.combination(k + r - 1, r - 1) *\n Math.pow(1 - p, k) * Math.pow(p, r);\n },\n\n cdf: function cdf(x, r, p) {\n var sum = 0,\n k = 0;\n if (x < 0) return 0;\n for (; k <= x; k++) {\n sum += jStat.negbin.pdf(k, r, p);\n }\n return sum;\n }\n});\n\n\n\n// extend uniform function with static methods\njStat.extend(jStat.hypgeom, {\n pdf: function pdf(k, N, m, n) {\n // Hypergeometric PDF.\n\n // A simplification of the CDF algorithm below.\n\n // k = number of successes drawn\n // N = population size\n // m = number of successes in population\n // n = number of items drawn from population\n\n if(k !== k | 0) {\n return false;\n } else if(k < 0 || k < m - (N - n)) {\n // It's impossible to have this few successes drawn.\n return 0;\n } else if(k > n || k > m) {\n // It's impossible to have this many successes drawn.\n return 0;\n } else if (m * 2 > N) {\n // More than half the population is successes.\n\n if(n * 2 > N) {\n // More than half the population is sampled.\n\n return jStat.hypgeom.pdf(N - m - n + k, N, N - m, N - n)\n } else {\n // Half or less of the population is sampled.\n\n return jStat.hypgeom.pdf(n - k, N, N - m, n);\n }\n\n } else if(n * 2 > N) {\n // Half or less is successes.\n\n return jStat.hypgeom.pdf(m - k, N, m, N - n);\n\n } else if(m < n) {\n // We want to have the number of things sampled to be less than the\n // successes available. So swap the definitions of successful and sampled.\n return jStat.hypgeom.pdf(k, N, n, m);\n } else {\n // If we get here, half or less of the population was sampled, half or\n // less of it was successes, and we had fewer sampled things than\n // successes. Now we can do this complicated iterative algorithm in an\n // efficient way.\n\n // The basic premise of the algorithm is that we partially normalize our\n // intermediate product to keep it in a numerically good region, and then\n // finish the normalization at the end.\n\n // This variable holds the scaled probability of the current number of\n // successes.\n var scaledPDF = 1;\n\n // This keeps track of how much we have normalized.\n var samplesDone = 0;\n\n for(var i = 0; i < k; i++) {\n // For every possible number of successes up to that observed...\n\n while(scaledPDF > 1 && samplesDone < n) {\n // Intermediate result is growing too big. Apply some of the\n // normalization to shrink everything.\n\n scaledPDF *= 1 - (m / (N - samplesDone));\n\n // Say we've normalized by this sample already.\n samplesDone++;\n }\n\n // Work out the partially-normalized hypergeometric PDF for the next\n // number of successes\n scaledPDF *= (n - i) * (m - i) / ((i + 1) * (N - m - n + i + 1));\n }\n\n for(; samplesDone < n; samplesDone++) {\n // Apply all the rest of the normalization\n scaledPDF *= 1 - (m / (N - samplesDone));\n }\n\n // Bound answer sanely before returning.\n return Math.min(1, Math.max(0, scaledPDF));\n }\n },\n\n cdf: function cdf(x, N, m, n) {\n // Hypergeometric CDF.\n\n // This algorithm is due to Prof. Thomas S. Ferguson, ,\n // and comes from his hypergeometric test calculator at\n // .\n\n // x = number of successes drawn\n // N = population size\n // m = number of successes in population\n // n = number of items drawn from population\n\n if(x < 0 || x < m - (N - n)) {\n // It's impossible to have this few successes drawn or fewer.\n return 0;\n } else if(x >= n || x >= m) {\n // We will always have this many successes or fewer.\n return 1;\n } else if (m * 2 > N) {\n // More than half the population is successes.\n\n if(n * 2 > N) {\n // More than half the population is sampled.\n\n return jStat.hypgeom.cdf(N - m - n + x, N, N - m, N - n)\n } else {\n // Half or less of the population is sampled.\n\n return 1 - jStat.hypgeom.cdf(n - x - 1, N, N - m, n);\n }\n\n } else if(n * 2 > N) {\n // Half or less is successes.\n\n return 1 - jStat.hypgeom.cdf(m - x - 1, N, m, N - n);\n\n } else if(m < n) {\n // We want to have the number of things sampled to be less than the\n // successes available. So swap the definitions of successful and sampled.\n return jStat.hypgeom.cdf(x, N, n, m);\n } else {\n // If we get here, half or less of the population was sampled, half or\n // less of it was successes, and we had fewer sampled things than\n // successes. Now we can do this complicated iterative algorithm in an\n // efficient way.\n\n // The basic premise of the algorithm is that we partially normalize our\n // intermediate sum to keep it in a numerically good region, and then\n // finish the normalization at the end.\n\n // Holds the intermediate, scaled total CDF.\n var scaledCDF = 1;\n\n // This variable holds the scaled probability of the current number of\n // successes.\n var scaledPDF = 1;\n\n // This keeps track of how much we have normalized.\n var samplesDone = 0;\n\n for(var i = 0; i < x; i++) {\n // For every possible number of successes up to that observed...\n\n while(scaledCDF > 1 && samplesDone < n) {\n // Intermediate result is growing too big. Apply some of the\n // normalization to shrink everything.\n\n var factor = 1 - (m / (N - samplesDone));\n\n scaledPDF *= factor;\n scaledCDF *= factor;\n\n // Say we've normalized by this sample already.\n samplesDone++;\n }\n\n // Work out the partially-normalized hypergeometric PDF for the next\n // number of successes\n scaledPDF *= (n - i) * (m - i) / ((i + 1) * (N - m - n + i + 1));\n\n // Add to the CDF answer.\n scaledCDF += scaledPDF;\n }\n\n for(; samplesDone < n; samplesDone++) {\n // Apply all the rest of the normalization\n scaledCDF *= 1 - (m / (N - samplesDone));\n }\n\n // Bound answer sanely before returning.\n return Math.min(1, Math.max(0, scaledCDF));\n }\n }\n});\n\n\n\n// extend uniform function with static methods\njStat.extend(jStat.poisson, {\n pdf: function pdf(k, l) {\n if (l < 0 || (k % 1) !== 0 || k < 0) {\n return 0;\n }\n\n return Math.pow(l, k) * Math.exp(-l) / jStat.factorial(k);\n },\n\n cdf: function cdf(x, l) {\n var sumarr = [],\n k = 0;\n if (x < 0) return 0;\n for (; k <= x; k++) {\n sumarr.push(jStat.poisson.pdf(k, l));\n }\n return jStat.sum(sumarr);\n },\n\n mean : function(l) {\n return l;\n },\n\n variance : function(l) {\n return l;\n },\n\n sample: function sample(l) {\n var p = 1, k = 0, L = Math.exp(-l);\n do {\n k++;\n p *= Math.random();\n } while (p > L);\n return k - 1;\n }\n});\n\n// extend triangular function with static methods\njStat.extend(jStat.triangular, {\n pdf: function pdf(x, a, b, c) {\n if (b <= a || c < a || c > b) {\n return NaN;\n } else {\n if (x < a || x > b) {\n return 0;\n } else if (x < c) {\n return (2 * (x - a)) / ((b - a) * (c - a));\n } else if (x === c) {\n return (2 / (b - a));\n } else { // x > c\n return (2 * (b - x)) / ((b - a) * (b - c));\n }\n }\n },\n\n cdf: function cdf(x, a, b, c) {\n if (b <= a || c < a || c > b)\n return NaN;\n if (x <= a)\n return 0;\n else if (x >= b)\n return 1;\n if (x <= c)\n return Math.pow(x - a, 2) / ((b - a) * (c - a));\n else // x > c\n return 1 - Math.pow(b - x, 2) / ((b - a) * (b - c));\n },\n\n inv: function inv(p, a, b, c) {\n if (b <= a || c < a || c > b) {\n return NaN;\n } else {\n if (p <= ((c - a) / (b - a))) {\n return a + (b - a) * Math.sqrt(p * ((c - a) / (b - a)));\n } else { // p > ((c - a) / (b - a))\n return a + (b - a) * (1 - Math.sqrt((1 - p) * (1 - ((c - a) / (b - a)))));\n }\n }\n },\n\n mean: function mean(a, b, c) {\n return (a + b + c) / 3;\n },\n\n median: function median(a, b, c) {\n if (c <= (a + b) / 2) {\n return b - Math.sqrt((b - a) * (b - c)) / Math.sqrt(2);\n } else if (c > (a + b) / 2) {\n return a + Math.sqrt((b - a) * (c - a)) / Math.sqrt(2);\n }\n },\n\n mode: function mode(a, b, c) {\n return c;\n },\n\n sample: function sample(a, b, c) {\n var u = Math.random();\n if (u < ((c - a) / (b - a)))\n return a + Math.sqrt(u * (b - a) * (c - a))\n return b - Math.sqrt((1 - u) * (b - a) * (b - c));\n },\n\n variance: function variance(a, b, c) {\n return (a * a + b * b + c * c - a * b - a * c - b * c) / 18;\n }\n});\n\n\n// extend arcsine function with static methods\njStat.extend(jStat.arcsine, {\n pdf: function pdf(x, a, b) {\n if (b <= a) return NaN;\n\n return (x <= a || x >= b) ? 0 :\n (2 / Math.PI) *\n Math.pow(Math.pow(b - a, 2) -\n Math.pow(2 * x - a - b, 2), -0.5);\n },\n\n cdf: function cdf(x, a, b) {\n if (x < a)\n return 0;\n else if (x < b)\n return (2 / Math.PI) * Math.asin(Math.sqrt((x - a)/(b - a)));\n return 1;\n },\n\n inv: function(p, a, b) {\n return a + (0.5 - 0.5 * Math.cos(Math.PI * p)) * (b - a);\n },\n\n mean: function mean(a, b) {\n if (b <= a) return NaN;\n return (a + b) / 2;\n },\n\n median: function median(a, b) {\n if (b <= a) return NaN;\n return (a + b) / 2;\n },\n\n mode: function mode(a, b) {\n throw new Error('mode is not yet implemented');\n },\n\n sample: function sample(a, b) {\n return ((a + b) / 2) + ((b - a) / 2) *\n Math.sin(2 * Math.PI * jStat.uniform.sample(0, 1));\n },\n\n variance: function variance(a, b) {\n if (b <= a) return NaN;\n return Math.pow(b - a, 2) / 8;\n }\n});\n\n\nfunction laplaceSign(x) { return x / Math.abs(x); }\n\njStat.extend(jStat.laplace, {\n pdf: function pdf(x, mu, b) {\n return (b <= 0) ? 0 : (Math.exp(-Math.abs(x - mu) / b)) / (2 * b);\n },\n\n cdf: function cdf(x, mu, b) {\n if (b <= 0) { return 0; }\n\n if(x < mu) {\n return 0.5 * Math.exp((x - mu) / b);\n } else {\n return 1 - 0.5 * Math.exp(- (x - mu) / b);\n }\n },\n\n mean: function(mu, b) {\n return mu;\n },\n\n median: function(mu, b) {\n return mu;\n },\n\n mode: function(mu, b) {\n return mu;\n },\n\n variance: function(mu, b) {\n return 2 * b * b;\n },\n\n sample: function sample(mu, b) {\n var u = Math.random() - 0.5;\n\n return mu - (b * laplaceSign(u) * Math.log(1 - (2 * Math.abs(u))));\n }\n});\n\nfunction tukeyWprob(w, rr, cc) {\n var nleg = 12;\n var ihalf = 6;\n\n var C1 = -30;\n var C2 = -50;\n var C3 = 60;\n var bb = 8;\n var wlar = 3;\n var wincr1 = 2;\n var wincr2 = 3;\n var xleg = [\n 0.981560634246719250690549090149,\n 0.904117256370474856678465866119,\n 0.769902674194304687036893833213,\n 0.587317954286617447296702418941,\n 0.367831498998180193752691536644,\n 0.125233408511468915472441369464\n ];\n var aleg = [\n 0.047175336386511827194615961485,\n 0.106939325995318430960254718194,\n 0.160078328543346226334652529543,\n 0.203167426723065921749064455810,\n 0.233492536538354808760849898925,\n 0.249147045813402785000562436043\n ];\n\n var qsqz = w * 0.5;\n\n // if w >= 16 then the integral lower bound (occurs for c=20)\n // is 0.99999999999995 so return a value of 1.\n\n if (qsqz >= bb)\n return 1.0;\n\n // find (f(w/2) - 1) ^ cc\n // (first term in integral of hartley's form).\n\n var pr_w = 2 * jStat.normal.cdf(qsqz, 0, 1, 1, 0) - 1; // erf(qsqz / M_SQRT2)\n // if pr_w ^ cc < 2e-22 then set pr_w = 0\n if (pr_w >= Math.exp(C2 / cc))\n pr_w = Math.pow(pr_w, cc);\n else\n pr_w = 0.0;\n\n // if w is large then the second component of the\n // integral is small, so fewer intervals are needed.\n\n var wincr;\n if (w > wlar)\n wincr = wincr1;\n else\n wincr = wincr2;\n\n // find the integral of second term of hartley's form\n // for the integral of the range for equal-length\n // intervals using legendre quadrature. limits of\n // integration are from (w/2, 8). two or three\n // equal-length intervals are used.\n\n // blb and bub are lower and upper limits of integration.\n\n var blb = qsqz;\n var binc = (bb - qsqz) / wincr;\n var bub = blb + binc;\n var einsum = 0.0;\n\n // integrate over each interval\n\n var cc1 = cc - 1.0;\n for (var wi = 1; wi <= wincr; wi++) {\n var elsum = 0.0;\n var a = 0.5 * (bub + blb);\n\n // legendre quadrature with order = nleg\n\n var b = 0.5 * (bub - blb);\n\n for (var jj = 1; jj <= nleg; jj++) {\n var j, xx;\n if (ihalf < jj) {\n j = (nleg - jj) + 1;\n xx = xleg[j-1];\n } else {\n j = jj;\n xx = -xleg[j-1];\n }\n var c = b * xx;\n var ac = a + c;\n\n // if exp(-qexpo/2) < 9e-14,\n // then doesn't contribute to integral\n\n var qexpo = ac * ac;\n if (qexpo > C3)\n break;\n\n var pplus = 2 * jStat.normal.cdf(ac, 0, 1, 1, 0);\n var pminus= 2 * jStat.normal.cdf(ac, w, 1, 1, 0);\n\n // if rinsum ^ (cc-1) < 9e-14,\n // then doesn't contribute to integral\n\n var rinsum = (pplus * 0.5) - (pminus * 0.5);\n if (rinsum >= Math.exp(C1 / cc1)) {\n rinsum = (aleg[j-1] * Math.exp(-(0.5 * qexpo))) * Math.pow(rinsum, cc1);\n elsum += rinsum;\n }\n }\n elsum *= (((2.0 * b) * cc) / Math.sqrt(2 * Math.PI));\n einsum += elsum;\n blb = bub;\n bub += binc;\n }\n\n // if pr_w ^ rr < 9e-14, then return 0\n pr_w += einsum;\n if (pr_w <= Math.exp(C1 / rr))\n return 0;\n\n pr_w = Math.pow(pr_w, rr);\n if (pr_w >= 1) // 1 was iMax was eps\n return 1;\n return pr_w;\n}\n\nfunction tukeyQinv(p, c, v) {\n var p0 = 0.322232421088;\n var q0 = 0.993484626060e-01;\n var p1 = -1.0;\n var q1 = 0.588581570495;\n var p2 = -0.342242088547;\n var q2 = 0.531103462366;\n var p3 = -0.204231210125;\n var q3 = 0.103537752850;\n var p4 = -0.453642210148e-04;\n var q4 = 0.38560700634e-02;\n var c1 = 0.8832;\n var c2 = 0.2368;\n var c3 = 1.214;\n var c4 = 1.208;\n var c5 = 1.4142;\n var vmax = 120.0;\n\n var ps = 0.5 - 0.5 * p;\n var yi = Math.sqrt(Math.log(1.0 / (ps * ps)));\n var t = yi + (((( yi * p4 + p3) * yi + p2) * yi + p1) * yi + p0)\n / (((( yi * q4 + q3) * yi + q2) * yi + q1) * yi + q0);\n if (v < vmax) t += (t * t * t + t) / v / 4.0;\n var q = c1 - c2 * t;\n if (v < vmax) q += -c3 / v + c4 * t / v;\n return t * (q * Math.log(c - 1.0) + c5);\n}\n\njStat.extend(jStat.tukey, {\n cdf: function cdf(q, nmeans, df) {\n // Identical implementation as the R ptukey() function as of commit 68947\n var rr = 1;\n var cc = nmeans;\n\n var nlegq = 16;\n var ihalfq = 8;\n\n var eps1 = -30.0;\n var eps2 = 1.0e-14;\n var dhaf = 100.0;\n var dquar = 800.0;\n var deigh = 5000.0;\n var dlarg = 25000.0;\n var ulen1 = 1.0;\n var ulen2 = 0.5;\n var ulen3 = 0.25;\n var ulen4 = 0.125;\n var xlegq = [\n 0.989400934991649932596154173450,\n 0.944575023073232576077988415535,\n 0.865631202387831743880467897712,\n 0.755404408355003033895101194847,\n 0.617876244402643748446671764049,\n 0.458016777657227386342419442984,\n 0.281603550779258913230460501460,\n 0.950125098376374401853193354250e-1\n ];\n var alegq = [\n 0.271524594117540948517805724560e-1,\n 0.622535239386478928628438369944e-1,\n 0.951585116824927848099251076022e-1,\n 0.124628971255533872052476282192,\n 0.149595988816576732081501730547,\n 0.169156519395002538189312079030,\n 0.182603415044923588866763667969,\n 0.189450610455068496285396723208\n ];\n\n if (q <= 0)\n return 0;\n\n // df must be > 1\n // there must be at least two values\n\n if (df < 2 || rr < 1 || cc < 2) return NaN;\n\n if (!Number.isFinite(q))\n return 1;\n\n if (df > dlarg)\n return tukeyWprob(q, rr, cc);\n\n // calculate leading constant\n\n var f2 = df * 0.5;\n var f2lf = ((f2 * Math.log(df)) - (df * Math.log(2))) - jStat.gammaln(f2);\n var f21 = f2 - 1.0;\n\n // integral is divided into unit, half-unit, quarter-unit, or\n // eighth-unit length intervals depending on the value of the\n // degrees of freedom.\n\n var ff4 = df * 0.25;\n var ulen;\n if (df <= dhaf) ulen = ulen1;\n else if (df <= dquar) ulen = ulen2;\n else if (df <= deigh) ulen = ulen3;\n else ulen = ulen4;\n\n f2lf += Math.log(ulen);\n\n // integrate over each subinterval\n\n var ans = 0.0;\n\n for (var i = 1; i <= 50; i++) {\n var otsum = 0.0;\n\n // legendre quadrature with order = nlegq\n // nodes (stored in xlegq) are symmetric around zero.\n\n var twa1 = (2 * i - 1) * ulen;\n\n for (var jj = 1; jj <= nlegq; jj++) {\n var j, t1;\n if (ihalfq < jj) {\n j = jj - ihalfq - 1;\n t1 = (f2lf + (f21 * Math.log(twa1 + (xlegq[j] * ulen))))\n - (((xlegq[j] * ulen) + twa1) * ff4);\n } else {\n j = jj - 1;\n t1 = (f2lf + (f21 * Math.log(twa1 - (xlegq[j] * ulen))))\n + (((xlegq[j] * ulen) - twa1) * ff4);\n }\n\n // if exp(t1) < 9e-14, then doesn't contribute to integral\n var qsqz;\n if (t1 >= eps1) {\n if (ihalfq < jj) {\n qsqz = q * Math.sqrt(((xlegq[j] * ulen) + twa1) * 0.5);\n } else {\n qsqz = q * Math.sqrt(((-(xlegq[j] * ulen)) + twa1) * 0.5);\n }\n\n // call wprob to find integral of range portion\n\n var wprb = tukeyWprob(qsqz, rr, cc);\n var rotsum = (wprb * alegq[j]) * Math.exp(t1);\n otsum += rotsum;\n }\n // end legendre integral for interval i\n // L200:\n }\n\n // if integral for interval i < 1e-14, then stop.\n // However, in order to avoid small area under left tail,\n // at least 1 / ulen intervals are calculated.\n if (i * ulen >= 1.0 && otsum <= eps2)\n break;\n\n // end of interval i\n // L330:\n\n ans += otsum;\n }\n\n if (otsum > eps2) { // not converged\n throw new Error('tukey.cdf failed to converge');\n }\n if (ans > 1)\n ans = 1;\n return ans;\n },\n\n inv: function(p, nmeans, df) {\n // Identical implementation as the R qtukey() function as of commit 68947\n var rr = 1;\n var cc = nmeans;\n\n var eps = 0.0001;\n var maxiter = 50;\n\n // df must be > 1 ; there must be at least two values\n if (df < 2 || rr < 1 || cc < 2) return NaN;\n\n if (p < 0 || p > 1) return NaN;\n if (p === 0) return 0;\n if (p === 1) return Infinity;\n\n // Initial value\n\n var x0 = tukeyQinv(p, cc, df);\n\n // Find prob(value < x0)\n\n var valx0 = jStat.tukey.cdf(x0, nmeans, df) - p;\n\n // Find the second iterate and prob(value < x1).\n // If the first iterate has probability value\n // exceeding p then second iterate is 1 less than\n // first iterate; otherwise it is 1 greater.\n\n var x1;\n if (valx0 > 0.0)\n x1 = Math.max(0.0, x0 - 1.0);\n else\n x1 = x0 + 1.0;\n var valx1 = jStat.tukey.cdf(x1, nmeans, df) - p;\n\n // Find new iterate\n\n var ans;\n for(var iter = 1; iter < maxiter; iter++) {\n ans = x1 - ((valx1 * (x1 - x0)) / (valx1 - valx0));\n valx0 = valx1;\n\n // New iterate must be >= 0\n\n x0 = x1;\n if (ans < 0.0) {\n ans = 0.0;\n valx1 = -p;\n }\n // Find prob(value < new iterate)\n\n valx1 = jStat.tukey.cdf(ans, nmeans, df) - p;\n x1 = ans;\n\n // If the difference between two successive\n // iterates is less than eps, stop\n\n var xabs = Math.abs(x1 - x0);\n if (xabs < eps)\n return ans;\n }\n\n throw new Error('tukey.inv failed to converge');\n }\n});\n\n}(jStat, Math));\n/* Provides functions for the solution of linear system of equations, integration, extrapolation,\n * interpolation, eigenvalue problems, differential equations and PCA analysis. */\n\n(function(jStat, Math) {\n\nvar push = Array.prototype.push;\nvar isArray = jStat.utils.isArray;\n\nfunction isUsable(arg) {\n return isArray(arg) || arg instanceof jStat;\n}\n\njStat.extend({\n\n // add a vector/matrix to a vector/matrix or scalar\n add: function add(arr, arg) {\n // check if arg is a vector or scalar\n if (isUsable(arg)) {\n if (!isUsable(arg[0])) arg = [ arg ];\n return jStat.map(arr, function(value, row, col) {\n return value + arg[row][col];\n });\n }\n return jStat.map(arr, function(value) { return value + arg; });\n },\n\n // subtract a vector or scalar from the vector\n subtract: function subtract(arr, arg) {\n // check if arg is a vector or scalar\n if (isUsable(arg)) {\n if (!isUsable(arg[0])) arg = [ arg ];\n return jStat.map(arr, function(value, row, col) {\n return value - arg[row][col] || 0;\n });\n }\n return jStat.map(arr, function(value) { return value - arg; });\n },\n\n // matrix division\n divide: function divide(arr, arg) {\n if (isUsable(arg)) {\n if (!isUsable(arg[0])) arg = [ arg ];\n return jStat.multiply(arr, jStat.inv(arg));\n }\n return jStat.map(arr, function(value) { return value / arg; });\n },\n\n // matrix multiplication\n multiply: function multiply(arr, arg) {\n var row, col, nrescols, sum, nrow, ncol, res, rescols;\n // eg: arr = 2 arg = 3 -> 6 for res[0][0] statement closure\n if (arr.length === undefined && arg.length === undefined) {\n return arr * arg;\n }\n nrow = arr.length,\n ncol = arr[0].length,\n res = jStat.zeros(nrow, nrescols = (isUsable(arg)) ? arg[0].length : ncol),\n rescols = 0;\n if (isUsable(arg)) {\n for (; rescols < nrescols; rescols++) {\n for (row = 0; row < nrow; row++) {\n sum = 0;\n for (col = 0; col < ncol; col++)\n sum += arr[row][col] * arg[col][rescols];\n res[row][rescols] = sum;\n }\n }\n return (nrow === 1 && rescols === 1) ? res[0][0] : res;\n }\n return jStat.map(arr, function(value) { return value * arg; });\n },\n\n // outer([1,2,3],[4,5,6])\n // ===\n // [[1],[2],[3]] times [[4,5,6]]\n // ->\n // [[4,5,6],[8,10,12],[12,15,18]]\n outer:function outer(A, B) {\n return jStat.multiply(A.map(function(t){ return [t] }), [B]);\n },\n\n\n // Returns the dot product of two matricies\n dot: function dot(arr, arg) {\n if (!isUsable(arr[0])) arr = [ arr ];\n if (!isUsable(arg[0])) arg = [ arg ];\n // convert column to row vector\n var left = (arr[0].length === 1 && arr.length !== 1) ? jStat.transpose(arr) : arr,\n right = (arg[0].length === 1 && arg.length !== 1) ? jStat.transpose(arg) : arg,\n res = [],\n row = 0,\n nrow = left.length,\n ncol = left[0].length,\n sum, col;\n for (; row < nrow; row++) {\n res[row] = [];\n sum = 0;\n for (col = 0; col < ncol; col++)\n sum += left[row][col] * right[row][col];\n res[row] = sum;\n }\n return (res.length === 1) ? res[0] : res;\n },\n\n // raise every element by a scalar\n pow: function pow(arr, arg) {\n return jStat.map(arr, function(value) { return Math.pow(value, arg); });\n },\n\n // exponentiate every element\n exp: function exp(arr) {\n return jStat.map(arr, function(value) { return Math.exp(value); });\n },\n\n // generate the natural log of every element\n log: function exp(arr) {\n return jStat.map(arr, function(value) { return Math.log(value); });\n },\n\n // generate the absolute values of the vector\n abs: function abs(arr) {\n return jStat.map(arr, function(value) { return Math.abs(value); });\n },\n\n // computes the p-norm of the vector\n // In the case that a matrix is passed, uses the first row as the vector\n norm: function norm(arr, p) {\n var nnorm = 0,\n i = 0;\n // check the p-value of the norm, and set for most common case\n if (isNaN(p)) p = 2;\n // check if multi-dimensional array, and make vector correction\n if (isUsable(arr[0])) arr = arr[0];\n // vector norm\n for (; i < arr.length; i++) {\n nnorm += Math.pow(Math.abs(arr[i]), p);\n }\n return Math.pow(nnorm, 1 / p);\n },\n\n // computes the angle between two vectors in rads\n // In case a matrix is passed, this uses the first row as the vector\n angle: function angle(arr, arg) {\n return Math.acos(jStat.dot(arr, arg) / (jStat.norm(arr) * jStat.norm(arg)));\n },\n\n // augment one matrix by another\n // Note: this function returns a matrix, not a jStat object\n aug: function aug(a, b) {\n var newarr = [];\n for (var i = 0; i < a.length; i++) {\n newarr.push(a[i].slice());\n }\n for (var i = 0; i < newarr.length; i++) {\n push.apply(newarr[i], b[i]);\n }\n return newarr;\n },\n\n // The inv() function calculates the inverse of a matrix\n // Create the inverse by augmenting the matrix by the identity matrix of the\n // appropriate size, and then use G-J elimination on the augmented matrix.\n inv: function inv(a) {\n var rows = a.length;\n var cols = a[0].length;\n var b = jStat.identity(rows, cols);\n var c = jStat.gauss_jordan(a, b);\n var result = [];\n var i = 0;\n var j;\n\n //We need to copy the inverse portion to a new matrix to rid G-J artifacts\n for (; i < rows; i++) {\n result[i] = [];\n for (j = cols; j < c[0].length; j++)\n result[i][j - cols] = c[i][j];\n }\n return result;\n },\n\n // calculate the determinant of a matrix\n det: function det(a) {\n var alen = a.length,\n alend = alen * 2,\n vals = new Array(alend),\n rowshift = alen - 1,\n colshift = alend - 1,\n mrow = rowshift - alen + 1,\n mcol = colshift,\n i = 0,\n result = 0,\n j;\n // check for special 2x2 case\n if (alen === 2) {\n return a[0][0] * a[1][1] - a[0][1] * a[1][0];\n }\n for (; i < alend; i++) {\n vals[i] = 1;\n }\n for (var i = 0; i < alen; i++) {\n for (j = 0; j < alen; j++) {\n vals[(mrow < 0) ? mrow + alen : mrow ] *= a[i][j];\n vals[(mcol < alen) ? mcol + alen : mcol ] *= a[i][j];\n mrow++;\n mcol--;\n }\n mrow = --rowshift - alen + 1;\n mcol = --colshift;\n }\n for (var i = 0; i < alen; i++) {\n result += vals[i];\n }\n for (; i < alend; i++) {\n result -= vals[i];\n }\n return result;\n },\n\n gauss_elimination: function gauss_elimination(a, b) {\n var i = 0,\n j = 0,\n n = a.length,\n m = a[0].length,\n factor = 1,\n sum = 0,\n x = [],\n maug, pivot, temp, k;\n a = jStat.aug(a, b);\n maug = a[0].length;\n for(var i = 0; i < n; i++) {\n pivot = a[i][i];\n j = i;\n for (k = i + 1; k < m; k++) {\n if (pivot < Math.abs(a[k][i])) {\n pivot = a[k][i];\n j = k;\n }\n }\n if (j != i) {\n for(k = 0; k < maug; k++) {\n temp = a[i][k];\n a[i][k] = a[j][k];\n a[j][k] = temp;\n }\n }\n for (j = i + 1; j < n; j++) {\n factor = a[j][i] / a[i][i];\n for(k = i; k < maug; k++) {\n a[j][k] = a[j][k] - factor * a[i][k];\n }\n }\n }\n for (var i = n - 1; i >= 0; i--) {\n sum = 0;\n for (j = i + 1; j<= n - 1; j++) {\n sum = sum + x[j] * a[i][j];\n }\n x[i] =(a[i][maug - 1] - sum) / a[i][i];\n }\n return x;\n },\n\n gauss_jordan: function gauss_jordan(a, b) {\n var m = jStat.aug(a, b),\n h = m.length,\n w = m[0].length;\n var c = 0;\n // find max pivot\n for (var y = 0; y < h; y++) {\n var maxrow = y;\n for (var y2 = y+1; y2 < h; y2++) {\n if (Math.abs(m[y2][y]) > Math.abs(m[maxrow][y]))\n maxrow = y2;\n }\n var tmp = m[y];\n m[y] = m[maxrow];\n m[maxrow] = tmp\n for (var y2 = y+1; y2 < h; y2++) {\n c = m[y2][y] / m[y][y];\n for (var x = y; x < w; x++) {\n m[y2][x] -= m[y][x] * c;\n }\n }\n }\n // backsubstitute\n for (var y = h-1; y >= 0; y--) {\n c = m[y][y];\n for (var y2 = 0; y2 < y; y2++) {\n for (var x = w-1; x > y-1; x--) {\n m[y2][x] -= m[y][x] * m[y2][y] / c;\n }\n }\n m[y][y] /= c;\n for (var x = h; x < w; x++) {\n m[y][x] /= c;\n }\n }\n return m;\n },\n\n // solve equation\n // Ax=b\n // A is upper triangular matrix\n // A=[[1,2,3],[0,4,5],[0,6,7]]\n // b=[1,2,3]\n // triaUpSolve(A,b) // -> [2.666,0.1666,1.666]\n // if you use matrix style\n // A=[[1,2,3],[0,4,5],[0,6,7]]\n // b=[[1],[2],[3]]\n // will return [[2.666],[0.1666],[1.666]]\n triaUpSolve: function triaUpSolve(A, b) {\n var size = A[0].length;\n var x = jStat.zeros(1, size)[0];\n var parts;\n var matrix_mode = false;\n\n if (b[0].length != undefined) {\n b = b.map(function(i){ return i[0] });\n matrix_mode = true;\n }\n\n jStat.arange(size - 1, -1, -1).forEach(function(i) {\n parts = jStat.arange(i + 1, size).map(function(j) {\n return x[j] * A[i][j];\n });\n x[i] = (b[i] - jStat.sum(parts)) / A[i][i];\n });\n\n if (matrix_mode)\n return x.map(function(i){ return [i] });\n return x;\n },\n\n triaLowSolve: function triaLowSolve(A, b) {\n // like to triaUpSolve but A is lower triangular matrix\n var size = A[0].length;\n var x = jStat.zeros(1, size)[0];\n var parts;\n\n var matrix_mode=false;\n if (b[0].length != undefined) {\n b = b.map(function(i){ return i[0] });\n matrix_mode = true;\n }\n\n jStat.arange(size).forEach(function(i) {\n parts = jStat.arange(i).map(function(j) {\n return A[i][j] * x[j];\n });\n x[i] = (b[i] - jStat.sum(parts)) / A[i][i];\n })\n\n if (matrix_mode)\n return x.map(function(i){ return [i] });\n return x;\n },\n\n\n // A -> [L,U]\n // A=LU\n // L is lower triangular matrix\n // U is upper triangular matrix\n lu: function lu(A) {\n var size = A.length;\n //var L=jStat.diagonal(jStat.ones(1,size)[0]);\n var L = jStat.identity(size);\n var R = jStat.zeros(A.length, A[0].length);\n var parts;\n jStat.arange(size).forEach(function(t) {\n R[0][t] = A[0][t];\n });\n jStat.arange(1, size).forEach(function(l) {\n jStat.arange(l).forEach(function(i) {\n parts = jStat.arange(i).map(function(jj) {\n return L[l][jj] * R[jj][i];\n });\n L[l][i] = (A[l][i] - jStat.sum(parts)) / R[i][i];\n });\n jStat.arange(l, size).forEach(function(j) {\n parts = jStat.arange(l).map(function(jj) {\n return L[l][jj] * R[jj][j];\n });\n R[l][j] = A[i][j] - jStat.sum(parts);\n });\n });\n return [L, R];\n },\n\n // A -> T\n // A=TT'\n // T is lower triangular matrix\n cholesky: function cholesky(A) {\n var size = A.length;\n var T = jStat.zeros(A.length, A[0].length);\n var parts;\n jStat.arange(size).forEach(function(i) {\n parts = jStat.arange(i).map(function(t) {\n return Math.pow(T[i][t],2);\n });\n T[i][i] = Math.sqrt(A[i][i] - jStat.sum(parts));\n jStat.arange(i + 1, size).forEach(function(j) {\n parts = jStat.arange(i).map(function(t) {\n return T[i][t] * T[j][t];\n });\n T[j][i] = (A[i][j] - jStat.sum(parts)) / T[i][i];\n });\n });\n return T;\n },\n\n\n gauss_jacobi: function gauss_jacobi(a, b, x, r) {\n var i = 0;\n var j = 0;\n var n = a.length;\n var l = [];\n var u = [];\n var d = [];\n var xv, c, h, xk;\n for (; i < n; i++) {\n l[i] = [];\n u[i] = [];\n d[i] = [];\n for (j = 0; j < n; j++) {\n if (i > j) {\n l[i][j] = a[i][j];\n u[i][j] = d[i][j] = 0;\n } else if (i < j) {\n u[i][j] = a[i][j];\n l[i][j] = d[i][j] = 0;\n } else {\n d[i][j] = a[i][j];\n l[i][j] = u[i][j] = 0;\n }\n }\n }\n h = jStat.multiply(jStat.multiply(jStat.inv(d), jStat.add(l, u)), -1);\n c = jStat.multiply(jStat.inv(d), b);\n xv = x;\n xk = jStat.add(jStat.multiply(h, x), c);\n i = 2;\n while (Math.abs(jStat.norm(jStat.subtract(xk,xv))) > r) {\n xv = xk;\n xk = jStat.add(jStat.multiply(h, xv), c);\n i++;\n }\n return xk;\n },\n\n gauss_seidel: function gauss_seidel(a, b, x, r) {\n var i = 0;\n var n = a.length;\n var l = [];\n var u = [];\n var d = [];\n var j, xv, c, h, xk;\n for (; i < n; i++) {\n l[i] = [];\n u[i] = [];\n d[i] = [];\n for (j = 0; j < n; j++) {\n if (i > j) {\n l[i][j] = a[i][j];\n u[i][j] = d[i][j] = 0;\n } else if (i < j) {\n u[i][j] = a[i][j];\n l[i][j] = d[i][j] = 0;\n } else {\n d[i][j] = a[i][j];\n l[i][j] = u[i][j] = 0;\n }\n }\n }\n h = jStat.multiply(jStat.multiply(jStat.inv(jStat.add(d, l)), u), -1);\n c = jStat.multiply(jStat.inv(jStat.add(d, l)), b);\n xv = x;\n xk = jStat.add(jStat.multiply(h, x), c);\n i = 2;\n while (Math.abs(jStat.norm(jStat.subtract(xk, xv))) > r) {\n xv = xk;\n xk = jStat.add(jStat.multiply(h, xv), c);\n i = i + 1;\n }\n return xk;\n },\n\n SOR: function SOR(a, b, x, r, w) {\n var i = 0;\n var n = a.length;\n var l = [];\n var u = [];\n var d = [];\n var j, xv, c, h, xk;\n for (; i < n; i++) {\n l[i] = [];\n u[i] = [];\n d[i] = [];\n for (j = 0; j < n; j++) {\n if (i > j) {\n l[i][j] = a[i][j];\n u[i][j] = d[i][j] = 0;\n } else if (i < j) {\n u[i][j] = a[i][j];\n l[i][j] = d[i][j] = 0;\n } else {\n d[i][j] = a[i][j];\n l[i][j] = u[i][j] = 0;\n }\n }\n }\n h = jStat.multiply(jStat.inv(jStat.add(d, jStat.multiply(l, w))),\n jStat.subtract(jStat.multiply(d, 1 - w),\n jStat.multiply(u, w)));\n c = jStat.multiply(jStat.multiply(jStat.inv(jStat.add(d,\n jStat.multiply(l, w))), b), w);\n xv = x;\n xk = jStat.add(jStat.multiply(h, x), c);\n i = 2;\n while (Math.abs(jStat.norm(jStat.subtract(xk, xv))) > r) {\n xv = xk;\n xk = jStat.add(jStat.multiply(h, xv), c);\n i++;\n }\n return xk;\n },\n\n householder: function householder(a) {\n var m = a.length;\n var n = a[0].length;\n var i = 0;\n var w = [];\n var p = [];\n var alpha, r, k, j, factor;\n for (; i < m - 1; i++) {\n alpha = 0;\n for (j = i + 1; j < n; j++)\n alpha += (a[j][i] * a[j][i]);\n factor = (a[i + 1][i] > 0) ? -1 : 1;\n alpha = factor * Math.sqrt(alpha);\n r = Math.sqrt((((alpha * alpha) - a[i + 1][i] * alpha) / 2));\n w = jStat.zeros(m, 1);\n w[i + 1][0] = (a[i + 1][i] - alpha) / (2 * r);\n for (k = i + 2; k < m; k++) w[k][0] = a[k][i] / (2 * r);\n p = jStat.subtract(jStat.identity(m, n),\n jStat.multiply(jStat.multiply(w, jStat.transpose(w)), 2));\n a = jStat.multiply(p, jStat.multiply(a, p));\n }\n return a;\n },\n\n // A -> [Q,R]\n // Q is orthogonal matrix\n // R is upper triangular\n QR: (function() {\n // x -> Q\n // find a orthogonal matrix Q st.\n // Qx=y\n // y is [||x||,0,0,...]\n\n // quick ref\n var sum = jStat.sum;\n var range = jStat.arange;\n\n function get_Q1(x) {\n var size = x.length;\n var norm_x = jStat.norm(x, 2);\n var e1 = jStat.zeros(1, size)[0];\n e1[0] = 1;\n var u = jStat.add(jStat.multiply(jStat.multiply(e1, norm_x), -1), x);\n var norm_u = jStat.norm(u, 2);\n var v = jStat.divide(u, norm_u);\n var Q = jStat.subtract(jStat.identity(size),\n jStat.multiply(jStat.outer(v, v), 2));\n return Q;\n }\n\n function qr(A) {\n var size = A[0].length;\n var QList = [];\n jStat.arange(size).forEach(function(i) {\n var x = jStat.slice(A, { row: { start: i }, col: i });\n var Q = get_Q1(x);\n var Qn = jStat.identity(A.length);\n Qn = jStat.sliceAssign(Qn, { row: { start: i }, col: { start: i }}, Q);\n A = jStat.multiply(Qn, A);\n QList.push(Qn);\n });\n var Q = QList.reduce(function(x, y){ return jStat.multiply(x,y) });\n var R = A;\n return [Q, R];\n }\n\n function qr2(x) {\n // quick impletation\n // https://www.stat.wisc.edu/~larget/math496/qr.html\n\n var n = x.length;\n var p = x[0].length;\n\n x = jStat.copy(x);\n r = jStat.zeros(p, p);\n\n var i,j,k;\n for(j = 0; j < p; j++){\n r[j][j] = Math.sqrt(sum(range(n).map(function(i){\n return x[i][j] * x[i][j];\n })));\n for(i = 0; i < n; i++){\n x[i][j] = x[i][j] / r[j][j];\n }\n for(k = j+1; k < p; k++){\n r[j][k] = sum(range(n).map(function(i){\n return x[i][j] * x[i][k];\n }));\n for(i = 0; i < n; i++){\n x[i][k] = x[i][k] - x[i][j]*r[j][k];\n }\n }\n }\n return [x, r];\n }\n\n return qr2;\n }()),\n\n lstsq: (function(A, b) {\n // solve least squard problem for Ax=b as QR decomposition way if b is\n // [[b1],[b2],[b3]] form will return [[x1],[x2],[x3]] array form solution\n // else b is [b1,b2,b3] form will return [x1,x2,x3] array form solution\n function R_I(A) {\n A = jStat.copy(A);\n var size = A.length;\n var I = jStat.identity(size);\n jStat.arange(size - 1, -1, -1).forEach(function(i) {\n jStat.sliceAssign(\n I, { row: i }, jStat.divide(jStat.slice(I, { row: i }), A[i][i]));\n jStat.sliceAssign(\n A, { row: i }, jStat.divide(jStat.slice(A, { row: i }), A[i][i]));\n jStat.arange(i).forEach(function(j) {\n var c = jStat.multiply(A[j][i], -1);\n var Aj = jStat.slice(A, { row: j });\n var cAi = jStat.multiply(jStat.slice(A, { row: i }), c);\n jStat.sliceAssign(A, { row: j }, jStat.add(Aj, cAi));\n var Ij = jStat.slice(I, { row: j });\n var cIi = jStat.multiply(jStat.slice(I, { row: i }), c);\n jStat.sliceAssign(I, { row: j }, jStat.add(Ij, cIi));\n })\n });\n return I;\n }\n\n function qr_solve(A, b){\n var array_mode = false;\n if (b[0].length === undefined) {\n // [c1,c2,c3] mode\n b = b.map(function(x){ return [x] });\n array_mode = true;\n }\n var QR = jStat.QR(A);\n var Q = QR[0];\n var R = QR[1];\n var attrs = A[0].length;\n var Q1 = jStat.slice(Q,{col:{end:attrs}});\n var R1 = jStat.slice(R,{row:{end:attrs}});\n var RI = R_I(R1);\n\t var Q2 = jStat.transpose(Q1);\n\n\t if(Q2[0].length === undefined){\n\t\t Q2 = [Q2]; // The confusing jStat.multifly implementation threat nature process again.\n\t }\n\n var x = jStat.multiply(jStat.multiply(RI, Q2), b);\n\n\t if(x.length === undefined){\n\t\t x = [[x]]; // The confusing jStat.multifly implementation threat nature process again.\n\t }\n\n\n if (array_mode)\n return x.map(function(i){ return i[0] });\n return x;\n }\n\n return qr_solve;\n }()),\n\n jacobi: function jacobi(a) {\n var condition = 1;\n var count = 0;\n var n = a.length;\n var e = jStat.identity(n, n);\n var ev = [];\n var b, i, j, p, q, maxim, theta, s;\n // condition === 1 only if tolerance is not reached\n while (condition === 1) {\n count++;\n maxim = a[0][1];\n p = 0;\n q = 1;\n for (var i = 0; i < n; i++) {\n for (j = 0; j < n; j++) {\n if (i != j) {\n if (maxim < Math.abs(a[i][j])) {\n maxim = Math.abs(a[i][j]);\n p = i;\n q = j;\n }\n }\n }\n }\n if (a[p][p] === a[q][q])\n theta = (a[p][q] > 0) ? Math.PI / 4 : -Math.PI / 4;\n else\n theta = Math.atan(2 * a[p][q] / (a[p][p] - a[q][q])) / 2;\n s = jStat.identity(n, n);\n s[p][p] = Math.cos(theta);\n s[p][q] = -Math.sin(theta);\n s[q][p] = Math.sin(theta);\n s[q][q] = Math.cos(theta);\n // eigen vector matrix\n e = jStat.multiply(e, s);\n b = jStat.multiply(jStat.multiply(jStat.inv(s), a), s);\n a = b;\n condition = 0;\n for (var i = 1; i < n; i++) {\n for (j = 1; j < n; j++) {\n if (i != j && Math.abs(a[i][j]) > 0.001) {\n condition = 1;\n }\n }\n }\n }\n for (var i = 0; i < n; i++) ev.push(a[i][i]);\n //returns both the eigenvalue and eigenmatrix\n return [e, ev];\n },\n\n rungekutta: function rungekutta(f, h, p, t_j, u_j, order) {\n var k1, k2, u_j1, k3, k4;\n if (order === 2) {\n while (t_j <= p) {\n k1 = h * f(t_j, u_j);\n k2 = h * f(t_j + h, u_j + k1);\n u_j1 = u_j + (k1 + k2) / 2;\n u_j = u_j1;\n t_j = t_j + h;\n }\n }\n if (order === 4) {\n while (t_j <= p) {\n k1 = h * f(t_j, u_j);\n k2 = h * f(t_j + h / 2, u_j + k1 / 2);\n k3 = h * f(t_j + h / 2, u_j + k2 / 2);\n k4 = h * f(t_j +h, u_j + k3);\n u_j1 = u_j + (k1 + 2 * k2 + 2 * k3 + k4) / 6;\n u_j = u_j1;\n t_j = t_j + h;\n }\n }\n return u_j;\n },\n\n romberg: function romberg(f, a, b, order) {\n var i = 0;\n var h = (b - a) / 2;\n var x = [];\n var h1 = [];\n var g = [];\n var m, a1, j, k, I, d;\n while (i < order / 2) {\n I = f(a);\n for (j = a, k = 0; j <= b; j = j + h, k++) x[k] = j;\n m = x.length;\n for (j = 1; j < m - 1; j++) {\n I += (((j % 2) !== 0) ? 4 : 2) * f(x[j]);\n }\n I = (h / 3) * (I + f(b));\n g[i] = I;\n h /= 2;\n i++;\n }\n a1 = g.length;\n m = 1;\n while (a1 !== 1) {\n for (j = 0; j < a1 - 1; j++)\n h1[j] = ((Math.pow(4, m)) * g[j + 1] - g[j]) / (Math.pow(4, m) - 1);\n a1 = h1.length;\n g = h1;\n h1 = [];\n m++;\n }\n return g;\n },\n\n richardson: function richardson(X, f, x, h) {\n function pos(X, x) {\n var i = 0;\n var n = X.length;\n var p;\n for (; i < n; i++)\n if (X[i] === x) p = i;\n return p;\n }\n var n = X.length,\n h_min = Math.abs(x - X[pos(X, x) + 1]),\n i = 0,\n g = [],\n h1 = [],\n y1, y2, m, a, j;\n while (h >= h_min) {\n y1 = pos(X, x + h);\n y2 = pos(X, x);\n g[i] = (f[y1] - 2 * f[y2] + f[2 * y2 - y1]) / (h * h);\n h /= 2;\n i++;\n }\n a = g.length;\n m = 1;\n while (a != 1) {\n for (j = 0; j < a - 1; j++)\n h1[j] = ((Math.pow(4, m)) * g[j + 1] - g[j]) / (Math.pow(4, m) - 1);\n a = h1.length;\n g = h1;\n h1 = [];\n m++;\n }\n return g;\n },\n\n simpson: function simpson(f, a, b, n) {\n var h = (b - a) / n;\n var I = f(a);\n var x = [];\n var j = a;\n var k = 0;\n var i = 1;\n var m;\n for (; j <= b; j = j + h, k++)\n x[k] = j;\n m = x.length;\n for (; i < m - 1; i++) {\n I += ((i % 2 !== 0) ? 4 : 2) * f(x[i]);\n }\n return (h / 3) * (I + f(b));\n },\n\n hermite: function hermite(X, F, dF, value) {\n var n = X.length;\n var p = 0;\n var i = 0;\n var l = [];\n var dl = [];\n var A = [];\n var B = [];\n var j;\n for (; i < n; i++) {\n l[i] = 1;\n for (j = 0; j < n; j++) {\n if (i != j) l[i] *= (value - X[j]) / (X[i] - X[j]);\n }\n dl[i] = 0;\n for (j = 0; j < n; j++) {\n if (i != j) dl[i] += 1 / (X [i] - X[j]);\n }\n A[i] = (1 - 2 * (value - X[i]) * dl[i]) * (l[i] * l[i]);\n B[i] = (value - X[i]) * (l[i] * l[i]);\n p += (A[i] * F[i] + B[i] * dF[i]);\n }\n return p;\n },\n\n lagrange: function lagrange(X, F, value) {\n var p = 0;\n var i = 0;\n var j, l;\n var n = X.length;\n for (; i < n; i++) {\n l = F[i];\n for (j = 0; j < n; j++) {\n // calculating the lagrange polynomial L_i\n if (i != j) l *= (value - X[j]) / (X[i] - X[j]);\n }\n // adding the lagrange polynomials found above\n p += l;\n }\n return p;\n },\n\n cubic_spline: function cubic_spline(X, F, value) {\n var n = X.length;\n var i = 0, j;\n var A = [];\n var B = [];\n var alpha = [];\n var c = [];\n var h = [];\n var b = [];\n var d = [];\n for (; i < n - 1; i++)\n h[i] = X[i + 1] - X[i];\n alpha[0] = 0;\n for (var i = 1; i < n - 1; i++) {\n alpha[i] = (3 / h[i]) * (F[i + 1] - F[i]) -\n (3 / h[i-1]) * (F[i] - F[i-1]);\n }\n for (var i = 1; i < n - 1; i++) {\n A[i] = [];\n B[i] = [];\n A[i][i-1] = h[i-1];\n A[i][i] = 2 * (h[i - 1] + h[i]);\n A[i][i+1] = h[i];\n B[i][0] = alpha[i];\n }\n c = jStat.multiply(jStat.inv(A), B);\n for (j = 0; j < n - 1; j++) {\n b[j] = (F[j + 1] - F[j]) / h[j] - h[j] * (c[j + 1][0] + 2 * c[j][0]) / 3;\n d[j] = (c[j + 1][0] - c[j][0]) / (3 * h[j]);\n }\n for (j = 0; j < n; j++) {\n if (X[j] > value) break;\n }\n j -= 1;\n return F[j] + (value - X[j]) * b[j] + jStat.sq(value-X[j]) *\n c[j] + (value - X[j]) * jStat.sq(value - X[j]) * d[j];\n },\n\n gauss_quadrature: function gauss_quadrature() {\n throw new Error('gauss_quadrature not yet implemented');\n },\n\n PCA: function PCA(X) {\n var m = X.length;\n var n = X[0].length;\n var flag = false;\n var i = 0;\n var j, temp1;\n var u = [];\n var D = [];\n var result = [];\n var temp2 = [];\n var Y = [];\n var Bt = [];\n var B = [];\n var C = [];\n var V = [];\n var Vt = [];\n for (var i = 0; i < m; i++) {\n u[i] = jStat.sum(X[i]) / n;\n }\n for (var i = 0; i < n; i++) {\n B[i] = [];\n for(j = 0; j < m; j++) {\n B[i][j] = X[j][i] - u[j];\n }\n }\n B = jStat.transpose(B);\n for (var i = 0; i < m; i++) {\n C[i] = [];\n for (j = 0; j < m; j++) {\n C[i][j] = (jStat.dot([B[i]], [B[j]])) / (n - 1);\n }\n }\n result = jStat.jacobi(C);\n V = result[0];\n D = result[1];\n Vt = jStat.transpose(V);\n for (var i = 0; i < D.length; i++) {\n for (j = i; j < D.length; j++) {\n if(D[i] < D[j]) {\n temp1 = D[i];\n D[i] = D[j];\n D[j] = temp1;\n temp2 = Vt[i];\n Vt[i] = Vt[j];\n Vt[j] = temp2;\n }\n }\n }\n Bt = jStat.transpose(B);\n for (var i = 0; i < m; i++) {\n Y[i] = [];\n for (j = 0; j < Bt.length; j++) {\n Y[i][j] = jStat.dot([Vt[i]], [Bt[j]]);\n }\n }\n return [X, D, Vt, Y];\n }\n});\n\n// extend jStat.fn with methods that require one argument\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jStat.fn[passfunc] = function(arg, func) {\n var tmpthis = this;\n // check for callback\n if (func) {\n setTimeout(function() {\n func.call(tmpthis, jStat.fn[passfunc].call(tmpthis, arg));\n }, 15);\n return this;\n }\n if (typeof jStat[passfunc](this, arg) === 'number')\n return jStat[passfunc](this, arg);\n else\n return jStat(jStat[passfunc](this, arg));\n };\n }(funcs[i]));\n}('add divide multiply subtract dot pow exp log abs norm angle'.split(' ')));\n\n}(jStat, Math));\n(function(jStat, Math) {\n\nvar slice = [].slice;\nvar isNumber = jStat.utils.isNumber;\nvar isArray = jStat.utils.isArray;\n\n// flag==true denotes use of sample standard deviation\n// Z Statistics\njStat.extend({\n // 2 different parameter lists:\n // (value, mean, sd)\n // (value, array, flag)\n zscore: function zscore() {\n var args = slice.call(arguments);\n if (isNumber(args[1])) {\n return (args[0] - args[1]) / args[2];\n }\n return (args[0] - jStat.mean(args[1])) / jStat.stdev(args[1], args[2]);\n },\n\n // 3 different paramter lists:\n // (value, mean, sd, sides)\n // (zscore, sides)\n // (value, array, sides, flag)\n ztest: function ztest() {\n var args = slice.call(arguments);\n var z;\n if (isArray(args[1])) {\n // (value, array, sides, flag)\n z = jStat.zscore(args[0],args[1],args[3]);\n return (args[2] === 1) ?\n (jStat.normal.cdf(-Math.abs(z), 0, 1)) :\n (jStat.normal.cdf(-Math.abs(z), 0, 1)*2);\n } else {\n if (args.length > 2) {\n // (value, mean, sd, sides)\n z = jStat.zscore(args[0],args[1],args[2]);\n return (args[3] === 1) ?\n (jStat.normal.cdf(-Math.abs(z),0,1)) :\n (jStat.normal.cdf(-Math.abs(z),0,1)* 2);\n } else {\n // (zscore, sides)\n z = args[0];\n return (args[1] === 1) ?\n (jStat.normal.cdf(-Math.abs(z),0,1)) :\n (jStat.normal.cdf(-Math.abs(z),0,1)*2);\n }\n }\n }\n});\n\njStat.extend(jStat.fn, {\n zscore: function zscore(value, flag) {\n return (value - this.mean()) / this.stdev(flag);\n },\n\n ztest: function ztest(value, sides, flag) {\n var zscore = Math.abs(this.zscore(value, flag));\n return (sides === 1) ?\n (jStat.normal.cdf(-zscore, 0, 1)) :\n (jStat.normal.cdf(-zscore, 0, 1) * 2);\n }\n});\n\n// T Statistics\njStat.extend({\n // 2 parameter lists\n // (value, mean, sd, n)\n // (value, array)\n tscore: function tscore() {\n var args = slice.call(arguments);\n return (args.length === 4) ?\n ((args[0] - args[1]) / (args[2] / Math.sqrt(args[3]))) :\n ((args[0] - jStat.mean(args[1])) /\n (jStat.stdev(args[1], true) / Math.sqrt(args[1].length)));\n },\n\n // 3 different paramter lists:\n // (value, mean, sd, n, sides)\n // (tscore, n, sides)\n // (value, array, sides)\n ttest: function ttest() {\n var args = slice.call(arguments);\n var tscore;\n if (args.length === 5) {\n tscore = Math.abs(jStat.tscore(args[0], args[1], args[2], args[3]));\n return (args[4] === 1) ?\n (jStat.studentt.cdf(-tscore, args[3]-1)) :\n (jStat.studentt.cdf(-tscore, args[3]-1)*2);\n }\n if (isNumber(args[1])) {\n tscore = Math.abs(args[0])\n return (args[2] == 1) ?\n (jStat.studentt.cdf(-tscore, args[1]-1)) :\n (jStat.studentt.cdf(-tscore, args[1]-1) * 2);\n }\n tscore = Math.abs(jStat.tscore(args[0], args[1]))\n return (args[2] == 1) ?\n (jStat.studentt.cdf(-tscore, args[1].length-1)) :\n (jStat.studentt.cdf(-tscore, args[1].length-1) * 2);\n }\n});\n\njStat.extend(jStat.fn, {\n tscore: function tscore(value) {\n return (value - this.mean()) / (this.stdev(true) / Math.sqrt(this.cols()));\n },\n\n ttest: function ttest(value, sides) {\n return (sides === 1) ?\n (1 - jStat.studentt.cdf(Math.abs(this.tscore(value)), this.cols()-1)) :\n (jStat.studentt.cdf(-Math.abs(this.tscore(value)), this.cols()-1)*2);\n }\n});\n\n// F Statistics\njStat.extend({\n // Paramter list is as follows:\n // (array1, array2, array3, ...)\n // or it is an array of arrays\n // array of arrays conversion\n anovafscore: function anovafscore() {\n var args = slice.call(arguments),\n expVar, sample, sampMean, sampSampMean, tmpargs, unexpVar, i, j;\n if (args.length === 1) {\n tmpargs = new Array(args[0].length);\n for (var i = 0; i < args[0].length; i++) {\n tmpargs[i] = args[0][i];\n }\n args = tmpargs;\n }\n // 2 sample case\n if (args.length === 2) {\n return jStat.variance(args[0]) / jStat.variance(args[1]);\n }\n // Builds sample array\n sample = new Array();\n for (var i = 0; i < args.length; i++) {\n sample = sample.concat(args[i]);\n }\n sampMean = jStat.mean(sample);\n // Computes the explained variance\n expVar = 0;\n for (var i = 0; i < args.length; i++) {\n expVar = expVar + args[i].length * Math.pow(jStat.mean(args[i]) - sampMean, 2);\n }\n expVar /= (args.length - 1);\n // Computes unexplained variance\n unexpVar = 0;\n for (var i = 0; i < args.length; i++) {\n sampSampMean = jStat.mean(args[i]);\n for (j = 0; j < args[i].length; j++) {\n unexpVar += Math.pow(args[i][j] - sampSampMean, 2);\n }\n }\n unexpVar /= (sample.length - args.length);\n return expVar / unexpVar;\n },\n\n // 2 different paramter setups\n // (array1, array2, array3, ...)\n // (anovafscore, df1, df2)\n anovaftest: function anovaftest() {\n var args = slice.call(arguments),\n df1, df2, n, i;\n if (isNumber(args[0])) {\n return 1 - jStat.centralF.cdf(args[0], args[1], args[2]);\n }\n anovafscore = jStat.anovafscore(args);\n df1 = args.length - 1;\n n = 0;\n for (var i = 0; i < args.length; i++) {\n n = n + args[i].length;\n }\n df2 = n - df1 - 1;\n return 1 - jStat.centralF.cdf(anovafscore, df1, df2);\n },\n\n ftest: function ftest(fscore, df1, df2) {\n return 1 - jStat.centralF.cdf(fscore, df1, df2);\n }\n});\n\njStat.extend(jStat.fn, {\n anovafscore: function anovafscore() {\n return jStat.anovafscore(this.toArray());\n },\n\n anovaftes: function anovaftes() {\n var n = 0;\n var i;\n for (var i = 0; i < this.length; i++) {\n n = n + this[i].length;\n }\n return jStat.ftest(this.anovafscore(), this.length - 1, n - this.length);\n }\n});\n\n// Tukey's range test\njStat.extend({\n // 2 parameter lists\n // (mean1, mean2, n1, n2, sd)\n // (array1, array2, sd)\n qscore: function qscore() {\n var args = slice.call(arguments);\n var mean1, mean2, n1, n2, sd;\n if (isNumber(args[0])) {\n mean1 = args[0];\n mean2 = args[1];\n n1 = args[2];\n n2 = args[3];\n sd = args[4];\n } else {\n mean1 = jStat.mean(args[0]);\n mean2 = jStat.mean(args[1]);\n n1 = args[0].length;\n n2 = args[1].length;\n sd = args[2];\n }\n return Math.abs(mean1 - mean2) / (sd * Math.sqrt((1 / n1 + 1 / n2) / 2));\n },\n\n // 3 different parameter lists:\n // (qscore, n, k)\n // (mean1, mean2, n1, n2, sd, n, k)\n // (array1, array2, sd, n, k)\n qtest: function qtest() {\n var args = slice.call(arguments);\n\n var qscore;\n if (args.length === 3) {\n qscore = args[0];\n args = args.slice(1);\n } else if (args.length === 7) {\n qscore = jStat.qscore(args[0], args[1], args[2], args[3], args[4]);\n args = args.slice(5);\n } else {\n qscore = jStat.qscore(args[0], args[1], args[2]);\n args = args.slice(3);\n }\n\n var n = args[0];\n var k = args[1];\n\n return 1 - jStat.tukey.cdf(qscore, k, n - k);\n },\n\n tukeyhsd: function tukeyhsd(arrays) {\n var sd = jStat.pooledstdev(arrays);\n var means = arrays.map(function (arr) {return jStat.mean(arr);});\n var n = arrays.reduce(function (n, arr) {return n + arr.length;}, 0);\n\n var results = [];\n for (var i = 0; i < arrays.length; ++i) {\n for (var j = i + 1; j < arrays.length; ++j) {\n var p = jStat.qtest(means[i], means[j], arrays[i].length, arrays[j].length, sd, n, arrays.length);\n results.push([[i, j], p]);\n }\n }\n\n return results;\n }\n});\n\n// Error Bounds\njStat.extend({\n // 2 different parameter setups\n // (value, alpha, sd, n)\n // (value, alpha, array)\n normalci: function normalci() {\n var args = slice.call(arguments),\n ans = new Array(2),\n change;\n if (args.length === 4) {\n change = Math.abs(jStat.normal.inv(args[1] / 2, 0, 1) *\n args[2] / Math.sqrt(args[3]));\n } else {\n change = Math.abs(jStat.normal.inv(args[1] / 2, 0, 1) *\n jStat.stdev(args[2]) / Math.sqrt(args[2].length));\n }\n ans[0] = args[0] - change;\n ans[1] = args[0] + change;\n return ans;\n },\n\n // 2 different parameter setups\n // (value, alpha, sd, n)\n // (value, alpha, array)\n tci: function tci() {\n var args = slice.call(arguments),\n ans = new Array(2),\n change;\n if (args.length === 4) {\n change = Math.abs(jStat.studentt.inv(args[1] / 2, args[3] - 1) *\n args[2] / Math.sqrt(args[3]));\n } else {\n change = Math.abs(jStat.studentt.inv(args[1] / 2, args[2].length - 1) *\n jStat.stdev(args[2], true) / Math.sqrt(args[2].length));\n }\n ans[0] = args[0] - change;\n ans[1] = args[0] + change;\n return ans;\n },\n\n significant: function significant(pvalue, alpha) {\n return pvalue < alpha;\n }\n});\n\njStat.extend(jStat.fn, {\n normalci: function normalci(value, alpha) {\n return jStat.normalci(value, alpha, this.toArray());\n },\n\n tci: function tci(value, alpha) {\n return jStat.tci(value, alpha, this.toArray());\n }\n});\n\n// internal method for calculating the z-score for a difference of proportions test\nfunction differenceOfProportions(p1, n1, p2, n2) {\n if (p1 > 1 || p2 > 1 || p1 <= 0 || p2 <= 0) {\n throw new Error(\"Proportions should be greater than 0 and less than 1\")\n }\n var pooled = (p1 * n1 + p2 * n2) / (n1 + n2);\n var se = Math.sqrt(pooled * (1 - pooled) * ((1/n1) + (1/n2)));\n return (p1 - p2) / se;\n}\n\n// Difference of Proportions\njStat.extend(jStat.fn, {\n oneSidedDifferenceOfProportions: function oneSidedDifferenceOfProportions(p1, n1, p2, n2) {\n var z = differenceOfProportions(p1, n1, p2, n2);\n return jStat.ztest(z, 1);\n },\n\n twoSidedDifferenceOfProportions: function twoSidedDifferenceOfProportions(p1, n1, p2, n2) {\n var z = differenceOfProportions(p1, n1, p2, n2);\n return jStat.ztest(z, 2);\n }\n});\n\n}(jStat, Math));\njStat.models = (function(){\n\n function sub_regress(endog, exog) {\n return ols(endog, exog);\n }\n\n function sub_regress(exog) {\n var var_count = exog[0].length;\n var modelList = jStat.arange(var_count).map(function(endog_index) {\n var exog_index =\n jStat.arange(var_count).filter(function(i){return i!==endog_index});\n return ols(jStat.col(exog, endog_index).map(function(x){ return x[0] }),\n jStat.col(exog, exog_index))\n });\n return modelList;\n }\n\n // do OLS model regress\n // exog have include const columns ,it will not generate it .In fact, exog is\n // \"design matrix\" look at\n //https://en.wikipedia.org/wiki/Design_matrix\n function ols(endog, exog) {\n var nobs = endog.length;\n var df_model = exog[0].length - 1;\n var df_resid = nobs-df_model - 1;\n var coef = jStat.lstsq(exog, endog);\n var predict =\n jStat.multiply(exog, coef.map(function(x) { return [x] }))\n .map(function(p) { return p[0] });\n var resid = jStat.subtract(endog, predict);\n var ybar = jStat.mean(endog);\n // constant cause problem\n // var SST = jStat.sum(endog.map(function(y) {\n // return Math.pow(y-ybar,2);\n // }));\n var SSE = jStat.sum(predict.map(function(f) {\n return Math.pow(f - ybar, 2);\n }));\n var SSR = jStat.sum(endog.map(function(y, i) {\n return Math.pow(y - predict[i], 2);\n }));\n var SST = SSE + SSR;\n var R2 = (SSE / SST);\n return {\n exog:exog,\n endog:endog,\n nobs:nobs,\n df_model:df_model,\n df_resid:df_resid,\n coef:coef,\n predict:predict,\n resid:resid,\n ybar:ybar,\n SST:SST,\n SSE:SSE,\n SSR:SSR,\n R2:R2\n };\n }\n\n // H0: b_I=0\n // H1: b_I!=0\n function t_test(model) {\n var subModelList = sub_regress(model.exog);\n //var sigmaHat=jStat.stdev(model.resid);\n var sigmaHat = Math.sqrt(model.SSR / (model.df_resid));\n var seBetaHat = subModelList.map(function(mod) {\n var SST = mod.SST;\n var R2 = mod.R2;\n return sigmaHat / Math.sqrt(SST * (1 - R2));\n });\n var tStatistic = model.coef.map(function(coef, i) {\n return (coef - 0) / seBetaHat[i];\n });\n var pValue = tStatistic.map(function(t) {\n var leftppf = jStat.studentt.cdf(t, model.df_resid);\n return (leftppf > 0.5 ? 1 - leftppf : leftppf) * 2;\n });\n var c = jStat.studentt.inv(0.975, model.df_resid);\n var interval95 = model.coef.map(function(coef, i) {\n var d = c * seBetaHat[i];\n return [coef - d, coef + d];\n })\n return {\n se: seBetaHat,\n t: tStatistic,\n p: pValue,\n sigmaHat: sigmaHat,\n interval95: interval95\n };\n }\n\n function F_test(model) {\n var F_statistic =\n (model.R2 / model.df_model) / ((1 - model.R2) / model.df_resid);\n var fcdf = function(x, n1, n2) {\n return jStat.beta.cdf(x / (n2 / n1 + x), n1 / 2, n2 / 2)\n }\n var pvalue = 1 - fcdf(F_statistic, model.df_model, model.df_resid);\n return { F_statistic: F_statistic, pvalue: pvalue };\n }\n\n function ols_wrap(endog, exog) {\n var model = ols(endog,exog);\n var ttest = t_test(model);\n var ftest = F_test(model);\n // Provide the Wherry / Ezekiel / McNemar / Cohen Adjusted R^2\n // Which matches the 'adjusted R^2' provided by R's lm package\n var adjust_R2 =\n 1 - (1 - model.R2) * ((model.nobs - 1) / (model.df_resid));\n model.t = ttest;\n model.f = ftest;\n model.adjust_R2 = adjust_R2;\n return model;\n }\n\n return { ols: ols_wrap };\n})();\n // Make it compatible with previous version.\n jStat.jStat = jStat;\n\n return jStat;\n});\n\n\n/***/ })\n/******/ ]);", null);
+ return __webpack_require__(17)("/******/ (function(modules) { // webpackBootstrap\n/******/ \t// The module cache\n/******/ \tvar installedModules = {};\n/******/\n/******/ \t// The require function\n/******/ \tfunction __webpack_require__(moduleId) {\n/******/\n/******/ \t\t// Check if module is in cache\n/******/ \t\tif(installedModules[moduleId]) {\n/******/ \t\t\treturn installedModules[moduleId].exports;\n/******/ \t\t}\n/******/ \t\t// Create a new module (and put it into the cache)\n/******/ \t\tvar module = installedModules[moduleId] = {\n/******/ \t\t\ti: moduleId,\n/******/ \t\t\tl: false,\n/******/ \t\t\texports: {}\n/******/ \t\t};\n/******/\n/******/ \t\t// Execute the module function\n/******/ \t\tmodules[moduleId].call(module.exports, module, module.exports, __webpack_require__);\n/******/\n/******/ \t\t// Flag the module as loaded\n/******/ \t\tmodule.l = true;\n/******/\n/******/ \t\t// Return the exports of the module\n/******/ \t\treturn module.exports;\n/******/ \t}\n/******/\n/******/\n/******/ \t// expose the modules object (__webpack_modules__)\n/******/ \t__webpack_require__.m = modules;\n/******/\n/******/ \t// expose the module cache\n/******/ \t__webpack_require__.c = installedModules;\n/******/\n/******/ \t// define getter function for harmony exports\n/******/ \t__webpack_require__.d = function(exports, name, getter) {\n/******/ \t\tif(!__webpack_require__.o(exports, name)) {\n/******/ \t\t\tObject.defineProperty(exports, name, {\n/******/ \t\t\t\tconfigurable: false,\n/******/ \t\t\t\tenumerable: true,\n/******/ \t\t\t\tget: getter\n/******/ \t\t\t});\n/******/ \t\t}\n/******/ \t};\n/******/\n/******/ \t// getDefaultExport function for compatibility with non-harmony modules\n/******/ \t__webpack_require__.n = function(module) {\n/******/ \t\tvar getter = module && module.__esModule ?\n/******/ \t\t\tfunction getDefault() { return module['default']; } :\n/******/ \t\t\tfunction getModuleExports() { return module; };\n/******/ \t\t__webpack_require__.d(getter, 'a', getter);\n/******/ \t\treturn getter;\n/******/ \t};\n/******/\n/******/ \t// Object.prototype.hasOwnProperty.call\n/******/ \t__webpack_require__.o = function(object, property) { return Object.prototype.hasOwnProperty.call(object, property); };\n/******/\n/******/ \t// __webpack_public_path__\n/******/ \t__webpack_require__.p = \"\";\n/******/\n/******/ \t// Load entry module and return exports\n/******/ \treturn __webpack_require__(__webpack_require__.s = 2);\n/******/ })\n/************************************************************************/\n/******/ ([\n/* 0 */\n/***/ (function(module, exports) {\n\nmodule.exports = {\n euclidean: function(v1, v2) {\n var total = 0;\n for (var i = 0; i < v1.length; i++) {\n total += Math.pow(v2[i] - v1[i], 2); \n }\n return Math.sqrt(total);\n },\n manhattan: function(v1, v2) {\n var total = 0;\n for (var i = 0; i < v1.length ; i++) {\n total += Math.abs(v2[i] - v1[i]); \n }\n return total;\n },\n max: function(v1, v2) {\n var max = 0;\n for (var i = 0; i < v1.length; i++) {\n max = Math.max(max , Math.abs(v2[i] - v1[i])); \n }\n return max;\n }\n};\n\n/***/ }),\n/* 1 */\n/***/ (function(module, exports, __webpack_require__) {\n\nvar distances = __webpack_require__(0);\n\nfunction KMeans(centroids) {\n this.centroids = centroids || [];\n}\n\nKMeans.prototype.randomCentroids = function(points, k) {\n var centroids = points.slice(0); // copy\n centroids.sort(function() {\n return (Math.round(Math.random()) - 0.5);\n });\n return centroids.slice(0, k);\n}\n\nKMeans.prototype.classify = function(point, distance) {\n var min = Infinity,\n index = 0;\n\n distance = distance || \"euclidean\";\n if (typeof distance == \"string\") {\n distance = distances[distance];\n }\n\n for (var i = 0; i < this.centroids.length; i++) {\n var dist = distance(point, this.centroids[i]);\n if (dist < min) {\n min = dist;\n index = i;\n }\n }\n\n return index;\n}\n\nKMeans.prototype.cluster = function(points, k, distance, snapshotPeriod, snapshotCb) {\n k = k || Math.max(2, Math.ceil(Math.sqrt(points.length / 2)));\n\n distance = distance || \"euclidean\";\n if (typeof distance == \"string\") {\n distance = distances[distance];\n }\n\n this.centroids = this.randomCentroids(points, k);\n\n var assignment = new Array(points.length);\n var clusters = new Array(k);\n\n var iterations = 0;\n var movement = true;\n while (movement) {\n // update point-to-centroid assignments\n for (var i = 0; i < points.length; i++) {\n assignment[i] = this.classify(points[i], distance);\n }\n\n // update location of each centroid\n movement = false;\n for (var j = 0; j < k; j++) {\n var assigned = [];\n for (var i = 0; i < assignment.length; i++) {\n if (assignment[i] == j) {\n assigned.push(points[i]);\n }\n }\n\n if (!assigned.length) {\n continue;\n }\n\n var centroid = this.centroids[j];\n var newCentroid = new Array(centroid.length);\n\n for (var g = 0; g < centroid.length; g++) {\n var sum = 0;\n for (var i = 0; i < assigned.length; i++) {\n sum += assigned[i][g];\n }\n newCentroid[g] = sum / assigned.length;\n\n if (newCentroid[g] != centroid[g]) {\n movement = true;\n }\n }\n\n this.centroids[j] = newCentroid;\n clusters[j] = assigned;\n }\n\n if (snapshotCb && (iterations++ % snapshotPeriod == 0)) {\n snapshotCb(clusters);\n }\n }\n\n return clusters;\n}\n\nKMeans.prototype.toJSON = function() {\n return JSON.stringify(this.centroids);\n}\n\nKMeans.prototype.fromJSON = function(json) {\n this.centroids = JSON.parse(json);\n return this;\n}\n\nmodule.exports = KMeans;\n\nmodule.exports.kmeans = function(vectors, k) {\n return (new KMeans()).cluster(vectors, k);\n}\n\n/***/ }),\n/* 2 */\n/***/ (function(module, exports, __webpack_require__) {\n\n/*\n * Copyright (c) 2016 The Hyve B.V.\n * This code is licensed under the GNU Affero General Public License,\n * version 3, or (at your option) any later version.\n */\n\n/*\n * This file is part of cBioPortal.\n *\n * cBioPortal is free software: you can redistribute it and/or modify\n * it under the terms of the GNU Affero General Public License as\n * published by the Free Software Foundation, either version 3 of the\n * License.\n *\n * This program is distributed in the hope that it will be useful,\n * but WITHOUT ANY WARRANTY; without even the implied warranty of\n * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n * GNU Affero General Public License for more details.\n *\n * You should have received a copy of the GNU Affero General Public License\n * along with this program. If not, see .\n */\n\nvar clusterfck = __webpack_require__(3);\nvar jStat = __webpack_require__(5);\n\n/**\n * \"Routing\" logic for this worker, based on given message.\n *\n * @param m : message object with m.dimension (CASES or ENTITIES) and m.casesAndEntitites\n * which is the input for the clustering method.\n */\nonmessage = function(m) {\n console.log('Clustering worker received message');\n var result = null;\n if (m.data.dimension === \"CASES\") {\n result = hclusterCases(m.data.casesAndEntitites);\n } else if (m.data.dimension === \"ENTITIES\") {\n result = hclusterGeneticEntities(m.data.casesAndEntitites);\n } else {\n throw new Error(\"Illegal argument given to clustering-worker.js for m.data.dimension: \" + m.data.dimension);\n }\n console.log('Posting clustering result back to main script');\n postMessage(result);\n}\n\n/**\n * Returns false if any value is a valid number != 0.0,\n * and true otherwise.\n */\nvar isAllNaNs = function(values) {\n for (var i = 0; i < values.length; i++) {\n var val = values[i];\n if (!isNaN(val) && val != null && val != 0.0 ) {\n return false;\n }\n }\n return true;\n}\n\n/**\n * Distance measure using 1-spearman's correlation. This function does expect that item1 and item2\n * are an item than contains a item.preProcessedValueList attribute which is the ranked version\n * of item.orderedValueList.\n *\n */\nvar preRankedSpearmanDist = function(item1, item2) {\n //rules for NaN values:\n if (item1.isAllNaNs && item2.isAllNaNs) {\n //return distance 0\n return 0;\n }\n else if (item1.isAllNaNs || item2.isAllNaNs) {\n //return large distance:\n return 3;\n }\n //take the arrays from the preProcessedValueList:\n var ranks1 = item1.preProcessedValueList;\n var ranks2 = item2.preProcessedValueList;\n //calculate spearman's rank correlation coefficient, using pearson's distance\n //for correlation of the ranks:\n var r = jStat.corrcoeff(ranks1, ranks2);\n if (isNaN(r)) {\n //assuming the ranks1 and ranks2 lists do not contain NaN entries (and this code DOES assume all missing values have been imputed by a valid number),\n //this specific scenario should not occur, unless all values are the same (and given the same rank). In this case, there is no variation, and\n //correlation returns NaN. In theory this could happen on small number of entities being clustered. We give this a large distance:\n console.log(\"NaN in correlation calculation\");\n r = -2;\n }\n return 1 - r;\n}\n\n/**\n * Prepares the data for using spearman method in the distance function.\n * It will pre-calculate ranks and deviation and store this in inputItems[x].preProcessedValueList.\n * This pre-calculation significantly improves the performance of the clustering step itself.\n */\nvar _prepareForDistanceFunction = function(inputItems) {\n //pre-calculate ranks and configure to use last step of SPEARMAN as distance function:\n // and put all NaNs items at the end\n var allNaN = [];\n var notAllNaN = [];\n for (var i = 0; i < inputItems.length; i++) {\n var inputItem = inputItems[i];\n //check if all NaNs:\n inputItem.isAllNaNs = isAllNaNs(inputItem.orderedValueList);\n if (inputItem.isAllNaNs) {\n allNaN.push(inputItem);\n continue;\n } else {\n notAllNaN.push(inputItem);\n }\n //rank using fractional ranking:\n var ranks = jStat.rank(inputItem.orderedValueList);\n //calculate deviation:\n inputItem.preProcessedValueList = ranks;\n }\n return notAllNaN.concat(allNaN);\n}\n\n/**\n * @param casesAndEntitites: Object with sample(or patient)Id and map\n * of geneticEntity/value pairs. Example:\n *\n * var a =\n * {\n * \"TCGA-AO-AA98-01\":\n * {\n * \t\"TP53\": 0.045,\n * \t\"BRA1\": -0.89\n * }\n * },\n * ...\n *\n * @return the reordered list of sample(or patient) ids, after clustering.\n */\nvar hclusterCases = function(casesAndEntitites) {\n var refEntityList = null;\n var inputItems = [];\n //add orderedValueList to all items, so the values are\n //compared in same order:\n for (var caseId in casesAndEntitites) {\n if (casesAndEntitites.hasOwnProperty(caseId)) {\n var caseObj = casesAndEntitites[caseId];\n var inputItem = new Object();\n inputItem.caseId = caseId;\n inputItem.orderedValueList = [];\n if (refEntityList == null) {\n refEntityList = getRefList(caseObj);\n }\n for (var j = 0; j < refEntityList.length; j++) {\n var entityId = refEntityList[j];\n var value = caseObj[entityId];\n inputItem.orderedValueList.push(value);\n }\n inputItems.push(inputItem);\n }\n }\n if (refEntityList.length == 1) {\n //this is a special case, where the \"clustering\" becomes a simple sorting in 1 dimension:\n //so, just sort and return inputItems:\n inputItems.sort(function (i1, i2) {\n var val1 = i1.orderedValueList[0];\n var val2 = i2.orderedValueList[0];\n //ensure NaNs are moved out (NaN or null which are seen here as equivalents to NA (not available)) to the end of the list:\n val1 = (val1 == null || isNaN(val1) ? Number.MAX_VALUE : val1);\n val2 = (val2 == null || isNaN(val2) ? Number.MAX_VALUE : val2);\n if (val1 > val2) {\n return 1;\n }\n else if (val1 < val2) {\n return -1;\n }\n return 0;\n });\n return inputItems;\n }\n //else, normal clustering:\n inputItems = _prepareForDistanceFunction(inputItems);\n var clusters = clusterfck.hcluster(inputItems, preRankedSpearmanDist);\n return clusters.clusters(1)[0];\n}\n\nvar getRefList = function(caseItem) {\n var result = [];\n for (var entityId in caseItem) {\n if (caseItem.hasOwnProperty(entityId)) {\n result.push(entityId);\n }\n }\n return result;\n}\n\n/**\n * @param casesAndEntitites: same as used in hclusterCases above.\n *\n * @return the reordered list of entity ids, after clustering.\n */\nvar hclusterGeneticEntities = function(casesAndEntitites) {\n var refEntityList = null;\n var inputItems = [];\n var refCaseIdList = [];\n //add orderedValueList to all items, so the values are\n //compared in same order:\n for (var caseId in casesAndEntitites) {\n if (casesAndEntitites.hasOwnProperty(caseId)) {\n var caseObj = casesAndEntitites[caseId];\n if (refEntityList == null) {\n refEntityList = getRefList(caseObj);\n }\n //refCaseIdList:\n refCaseIdList.push(caseId);\n }\n }\n //iterate over genes, and get sample values:\n for (var i = 0; i < refEntityList.length; i++) {\n var entityId = refEntityList[i];\n var inputItem = new Object();\n inputItem.entityId = entityId;\n inputItem.orderedValueList = [];\n for (var j = 0; j < refCaseIdList.length; j++) {\n var caseId = refCaseIdList[j];\n var caseObj = casesAndEntitites[caseId];\n var value = caseObj[entityId];\n inputItem.orderedValueList.push(value);\n }\n inputItems.push(inputItem);\n }\n _prepareForDistanceFunction(inputItems);\n var clusters = clusterfck.hcluster(inputItems, preRankedSpearmanDist);\n return clusters.clusters(1)[0];\n}\n\n/***/ }),\n/* 3 */\n/***/ (function(module, exports, __webpack_require__) {\n\nmodule.exports = {\n hcluster: __webpack_require__(4),\n Kmeans: __webpack_require__(1),\n kmeans: __webpack_require__(1).kmeans\n};\n\n/***/ }),\n/* 4 */\n/***/ (function(module, exports, __webpack_require__) {\n\nvar distances = __webpack_require__(0);\n\nvar HierarchicalClustering = function(distance, linkage, threshold) {\n this.distance = distance;\n this.linkage = linkage;\n this.threshold = threshold == undefined ? Infinity : threshold;\n}\n\nHierarchicalClustering.prototype = {\n tree: function(items, snapshotPeriod, snapshotCb) {\n this.tree = [];\n this.dists = []; // distances between each pair of clusters\n this.mins = []; // closest cluster for each cluster\n this.index = []; // keep a hash of all clusters by key\n\n for (var i = 0; i < items.length; i++) {\n var cluster = {\n value: items[i],\n key: i,\n index: i,\n size: 1\n };\n this.tree[i] = cluster;\n this.index[i] = cluster;\n this.dists[i] = [];\n this.mins[i] = 0;\n }\n\n for (var i = 0; i < this.tree.length; i++) {\n for (var j = 0; j <= i; j++) {\n var dist = (i == j) ? Infinity :\n this.distance(this.tree[i].value, this.tree[j].value);\n this.dists[i][j] = dist;\n this.dists[j][i] = dist;\n\n if (dist < this.dists[i][this.mins[i]]) {\n this.mins[i] = j;\n }\n }\n }\n\n var merged = this.mergeClosest();\n var i = 0;\n while (merged) {\n if (snapshotCb && (i++ % snapshotPeriod) == 0) {\n snapshotCb(this.tree);\n }\n merged = this.mergeClosest();\n }\n\n this.tree.forEach(function(cluster) {\n // clean up metadata used for clustering\n delete cluster.key;\n delete cluster.index;\n });\n\n return this.tree;\n },\n\n mergeClosest: function() {\n // find two closest clusters from cached mins\n var minKey = 0, min = Infinity;\n for (var i = 0; i < this.tree.length; i++) {\n var key = this.tree[i].key,\n dist = this.dists[key][this.mins[key]];\n if (dist < min) {\n minKey = key;\n min = dist;\n }\n }\n if (min >= this.threshold) {\n return false;\n }\n\n var c1 = this.index[minKey],\n c2 = this.index[this.mins[minKey]];\n\n // merge two closest clusters\n var merged = {\n dist: min,\n left: c1,\n right: c2,\n key: c1.key,\n size: c1.size + c2.size\n };\n\n this.tree[c1.index] = merged;\n this.tree.splice(c2.index, 1);\n this.index[c1.key] = merged;\n\n // update distances with new merged cluster\n for (var i = 0; i < this.tree.length; i++) {\n var ci = this.tree[i];\n var dist;\n if (c1.key == ci.key) {\n dist = Infinity;\n }\n else if (this.linkage == \"single\") {\n dist = this.dists[c1.key][ci.key];\n if (this.dists[c1.key][ci.key] > this.dists[c2.key][ci.key]) {\n dist = this.dists[c2.key][ci.key];\n }\n }\n else if (this.linkage == \"complete\") {\n dist = this.dists[c1.key][ci.key];\n if (this.dists[c1.key][ci.key] < this.dists[c2.key][ci.key]) {\n dist = this.dists[c2.key][ci.key];\n }\n }\n else if (this.linkage == \"average\") {\n dist = (this.dists[c1.key][ci.key] * c1.size\n + this.dists[c2.key][ci.key] * c2.size) / (c1.size + c2.size);\n }\n else {\n dist = this.distance(ci.value, c1.value);\n }\n\n this.dists[c1.key][ci.key] = this.dists[ci.key][c1.key] = dist;\n }\n\n\n // update cached mins\n for (var i = 0; i < this.tree.length; i++) {\n var key1 = this.tree[i].key;\n if (this.mins[key1] == c1.key || this.mins[key1] == c2.key) {\n var min = key1;\n for (var j = 0; j < this.tree.length; j++) {\n var key2 = this.tree[j].key;\n if (this.dists[key1][key2] < this.dists[key1][min]) {\n min = key2;\n }\n }\n this.mins[key1] = min;\n }\n this.tree[i].index = i;\n }\n\n // clean up metadata used for clustering\n delete c1.key; delete c2.key;\n delete c1.index; delete c2.index;\n\n return true;\n },\n clusters: function(num){\n // Return all nodes if num is invalid\n if(num > this.tree.size || num < 1) num = this.tree.size\n\n var result = [],\n subtrees = [this.tree];\n\n // Get a list of root nodes for num different clusters\n while(num > 1){\n var furthest = _findNextFurthest(subtrees);\n subtrees.splice(subtrees.indexOf(furthest), 1);\n subtrees.push(furthest.left, furthest.right);\n num--;\n }\n\n // Transform the subtrees node list into a list of the subtrees leaf values\n subtrees.forEach(function(tree) {\n result.push(_getValues(tree));\n })\n\n // Split the next furthest distance root node\n function _findNextFurthest(subtrees) {\n var max = -1,\n furthest;\n subtrees.forEach(function(tree){\n if(tree.dist > max) {\n max = tree.dist;\n furthest = tree;\n }\n });\n return furthest;\n }\n\n // Traverse the tree and yield a list of the leaf node values\n function _getValues(tree) {\n if(tree.size === 1) return [tree.value];\n return _getValues(tree.left).concat(_getValues(tree.right));\n }\n\n return result;\n }\n}\n\nvar hcluster = function(items, distance, linkage, threshold, snapshot, snapshotCallback) {\n distance = distance || \"euclidean\";\n linkage = linkage || \"average\";\n\n if (typeof distance == \"string\") {\n distance = distances[distance];\n }\n var hc = new HierarchicalClustering(distance, linkage, threshold),\n tree = hc.tree(items, snapshot, snapshotCallback);\n\n return {\n tree: (threshold === undefined ? tree[0] : tree),\n clusters: hc.clusters\n };\n}\n\nmodule.exports = hcluster;\n\n\n/***/ }),\n/* 5 */\n/***/ (function(module, exports, __webpack_require__) {\n\n(function (window, factory) {\n if (true) {\n module.exports = factory();\n } else if (typeof define === 'function' && define.amd) {\n define(factory);\n } else {\n window.jStat = factory();\n }\n})(this, function () {\nvar jStat = (function(Math, undefined) {\n\n// For quick reference.\nvar concat = Array.prototype.concat;\nvar slice = Array.prototype.slice;\nvar toString = Object.prototype.toString;\n\n// Calculate correction for IEEE error\n// TODO: This calculation can be improved.\nfunction calcRdx(n, m) {\n var val = n > m ? n : m;\n return Math.pow(10,\n 17 - ~~(Math.log(((val > 0) ? val : -val)) * Math.LOG10E));\n}\n\n\nvar isArray = Array.isArray || function isArray(arg) {\n return toString.call(arg) === '[object Array]';\n};\n\n\nfunction isFunction(arg) {\n return toString.call(arg) === '[object Function]';\n}\n\n\nfunction isNumber(arg) {\n return typeof arg === 'number' && arg === arg;\n}\n\n\n// Converts the jStat matrix to vector.\nfunction toVector(arr) {\n return concat.apply([], arr);\n}\n\n\n// The one and only jStat constructor.\nfunction jStat() {\n return new jStat._init(arguments);\n}\n\n\n// TODO: Remove after all references in src files have been removed.\njStat.fn = jStat.prototype;\n\n\n// By separating the initializer from the constructor it's easier to handle\n// always returning a new instance whether \"new\" was used or not.\njStat._init = function _init(args) {\n var i;\n\n // If first argument is an array, must be vector or matrix.\n if (isArray(args[0])) {\n // Check if matrix.\n if (isArray(args[0][0])) {\n // See if a mapping function was also passed.\n if (isFunction(args[1]))\n args[0] = jStat.map(args[0], args[1]);\n // Iterate over each is faster than this.push.apply(this, args[0].\n for (var i = 0; i < args[0].length; i++)\n this[i] = args[0][i];\n this.length = args[0].length;\n\n // Otherwise must be a vector.\n } else {\n this[0] = isFunction(args[1]) ? jStat.map(args[0], args[1]) : args[0];\n this.length = 1;\n }\n\n // If first argument is number, assume creation of sequence.\n } else if (isNumber(args[0])) {\n this[0] = jStat.seq.apply(null, args);\n this.length = 1;\n\n // Handle case when jStat object is passed to jStat.\n } else if (args[0] instanceof jStat) {\n // Duplicate the object and pass it back.\n return jStat(args[0].toArray());\n\n // Unexpected argument value, return empty jStat object.\n // TODO: This is strange behavior. Shouldn't this throw or some such to let\n // the user know they had bad arguments?\n } else {\n this[0] = [];\n this.length = 1;\n }\n\n return this;\n};\njStat._init.prototype = jStat.prototype;\njStat._init.constructor = jStat;\n\n\n// Utility functions.\n// TODO: for internal use only?\njStat.utils = {\n calcRdx: calcRdx,\n isArray: isArray,\n isFunction: isFunction,\n isNumber: isNumber,\n toVector: toVector\n};\n\n\n// Easily extend the jStat object.\n// TODO: is this seriously necessary?\njStat.extend = function extend(obj) {\n var i, j;\n\n if (arguments.length === 1) {\n for (j in obj)\n jStat[j] = obj[j];\n return this;\n }\n\n for (var i = 1; i < arguments.length; i++) {\n for (j in arguments[i])\n obj[j] = arguments[i][j];\n }\n\n return obj;\n};\n\n\n// Returns the number of rows in the matrix.\njStat.rows = function rows(arr) {\n return arr.length || 1;\n};\n\n\n// Returns the number of columns in the matrix.\njStat.cols = function cols(arr) {\n return arr[0].length || 1;\n};\n\n\n// Returns the dimensions of the object { rows: i, cols: j }\njStat.dimensions = function dimensions(arr) {\n return {\n rows: jStat.rows(arr),\n cols: jStat.cols(arr)\n };\n};\n\n\n// Returns a specified row as a vector or return a sub matrix by pick some rows\njStat.row = function row(arr, index) {\n if (isArray(index)) {\n return index.map(function(i) {\n return jStat.row(arr, i);\n })\n }\n return arr[index];\n};\n\n\n// return row as array\n// rowa([[1,2],[3,4]],0) -> [1,2]\njStat.rowa = function rowa(arr, i) {\n return jStat.row(arr, i);\n};\n\n\n// Returns the specified column as a vector or return a sub matrix by pick some\n// columns\njStat.col = function col(arr, index) {\n if (isArray(index)) {\n var submat = jStat.arange(arr.length).map(function(i) {\n return new Array(index.length);\n });\n index.forEach(function(ind, i){\n jStat.arange(arr.length).forEach(function(j) {\n submat[j][i] = arr[j][ind];\n });\n });\n return submat;\n }\n var column = new Array(arr.length);\n for (var i = 0; i < arr.length; i++)\n column[i] = [arr[i][index]];\n return column;\n};\n\n\n// return column as array\n// cola([[1,2],[3,4]],0) -> [1,3]\njStat.cola = function cola(arr, i) {\n return jStat.col(arr, i).map(function(a){ return a[0] });\n};\n\n\n// Returns the diagonal of the matrix\njStat.diag = function diag(arr) {\n var nrow = jStat.rows(arr);\n var res = new Array(nrow);\n for (var row = 0; row < nrow; row++)\n res[row] = [arr[row][row]];\n return res;\n};\n\n\n// Returns the anti-diagonal of the matrix\njStat.antidiag = function antidiag(arr) {\n var nrow = jStat.rows(arr) - 1;\n var res = new Array(nrow);\n for (var i = 0; nrow >= 0; nrow--, i++)\n res[i] = [arr[i][nrow]];\n return res;\n};\n\n// Transpose a matrix or array.\njStat.transpose = function transpose(arr) {\n var obj = [];\n var objArr, rows, cols, j, i;\n\n // Make sure arr is in matrix format.\n if (!isArray(arr[0]))\n arr = [arr];\n\n rows = arr.length;\n cols = arr[0].length;\n\n for (var i = 0; i < cols; i++) {\n objArr = new Array(rows);\n for (j = 0; j < rows; j++)\n objArr[j] = arr[j][i];\n obj.push(objArr);\n }\n\n // If obj is vector, return only single array.\n return obj.length === 1 ? obj[0] : obj;\n};\n\n\n// Map a function to an array or array of arrays.\n// \"toAlter\" is an internal variable.\njStat.map = function map(arr, func, toAlter) {\n var row, nrow, ncol, res, col;\n\n if (!isArray(arr[0]))\n arr = [arr];\n\n nrow = arr.length;\n ncol = arr[0].length;\n res = toAlter ? arr : new Array(nrow);\n\n for (row = 0; row < nrow; row++) {\n // if the row doesn't exist, create it\n if (!res[row])\n res[row] = new Array(ncol);\n for (col = 0; col < ncol; col++)\n res[row][col] = func(arr[row][col], row, col);\n }\n\n return res.length === 1 ? res[0] : res;\n};\n\n\n// Cumulatively combine the elements of an array or array of arrays using a function.\njStat.cumreduce = function cumreduce(arr, func, toAlter) {\n var row, nrow, ncol, res, col;\n\n if (!isArray(arr[0]))\n arr = [arr];\n\n nrow = arr.length;\n ncol = arr[0].length;\n res = toAlter ? arr : new Array(nrow);\n\n for (row = 0; row < nrow; row++) {\n // if the row doesn't exist, create it\n if (!res[row])\n res[row] = new Array(ncol);\n if (ncol > 0)\n res[row][0] = arr[row][0];\n for (col = 1; col < ncol; col++)\n res[row][col] = func(res[row][col-1], arr[row][col]);\n }\n return res.length === 1 ? res[0] : res;\n};\n\n\n// Destructively alter an array.\njStat.alter = function alter(arr, func) {\n return jStat.map(arr, func, true);\n};\n\n\n// Generate a rows x cols matrix according to the supplied function.\njStat.create = function create(rows, cols, func) {\n var res = new Array(rows);\n var i, j;\n\n if (isFunction(cols)) {\n func = cols;\n cols = rows;\n }\n\n for (var i = 0; i < rows; i++) {\n res[i] = new Array(cols);\n for (j = 0; j < cols; j++)\n res[i][j] = func(i, j);\n }\n\n return res;\n};\n\n\nfunction retZero() { return 0; }\n\n\n// Generate a rows x cols matrix of zeros.\njStat.zeros = function zeros(rows, cols) {\n if (!isNumber(cols))\n cols = rows;\n return jStat.create(rows, cols, retZero);\n};\n\n\nfunction retOne() { return 1; }\n\n\n// Generate a rows x cols matrix of ones.\njStat.ones = function ones(rows, cols) {\n if (!isNumber(cols))\n cols = rows;\n return jStat.create(rows, cols, retOne);\n};\n\n\n// Generate a rows x cols matrix of uniformly random numbers.\njStat.rand = function rand(rows, cols) {\n if (!isNumber(cols))\n cols = rows;\n return jStat.create(rows, cols, Math.random);\n};\n\n\nfunction retIdent(i, j) { return i === j ? 1 : 0; }\n\n\n// Generate an identity matrix of size row x cols.\njStat.identity = function identity(rows, cols) {\n if (!isNumber(cols))\n cols = rows;\n return jStat.create(rows, cols, retIdent);\n};\n\n\n// Tests whether a matrix is symmetric\njStat.symmetric = function symmetric(arr) {\n var issymmetric = true;\n var size = arr.length;\n var row, col;\n\n if (arr.length !== arr[0].length)\n return false;\n\n for (row = 0; row < size; row++) {\n for (col = 0; col < size; col++)\n if (arr[col][row] !== arr[row][col])\n return false;\n }\n\n return true;\n};\n\n\n// Set all values to zero.\njStat.clear = function clear(arr) {\n return jStat.alter(arr, retZero);\n};\n\n\n// Generate sequence.\njStat.seq = function seq(min, max, length, func) {\n if (!isFunction(func))\n func = false;\n\n var arr = [];\n var hival = calcRdx(min, max);\n var step = (max * hival - min * hival) / ((length - 1) * hival);\n var current = min;\n var cnt;\n\n // Current is assigned using a technique to compensate for IEEE error.\n // TODO: Needs better implementation.\n for (cnt = 0;\n current <= max && cnt < length;\n cnt++, current = (min * hival + step * hival * cnt) / hival) {\n arr.push((func ? func(current, cnt) : current));\n }\n\n return arr;\n};\n\n\n// arange(5) -> [0,1,2,3,4]\n// arange(1,5) -> [1,2,3,4]\n// arange(5,1,-1) -> [5,4,3,2]\njStat.arange = function arange(start, end, step) {\n var rl = [];\n step = step || 1;\n if (end === undefined) {\n end = start;\n start = 0;\n }\n if (start === end || step === 0) {\n return [];\n }\n if (start < end && step < 0) {\n return [];\n }\n if (start > end && step > 0) {\n return [];\n }\n if (step > 0) {\n for (i = start; i < end; i += step) {\n rl.push(i);\n }\n } else {\n for (i = start; i > end; i += step) {\n rl.push(i);\n }\n }\n return rl;\n};\n\n\n// A=[[1,2,3],[4,5,6],[7,8,9]]\n// slice(A,{row:{end:2},col:{start:1}}) -> [[2,3],[5,6]]\n// slice(A,1,{start:1}) -> [5,6]\n// as numpy code A[:2,1:]\njStat.slice = (function(){\n function _slice(list, start, end, step) {\n // note it's not equal to range.map mode it's a bug\n var i;\n var rl = [];\n var length = list.length;\n if (start === undefined && end === undefined && step === undefined) {\n return jStat.copy(list);\n }\n\n start = start || 0;\n end = end || list.length;\n start = start >= 0 ? start : length + start;\n end = end >= 0 ? end : length + end;\n step = step || 1;\n if (start === end || step === 0) {\n return [];\n }\n if (start < end && step < 0) {\n return [];\n }\n if (start > end && step > 0) {\n return [];\n }\n if (step > 0) {\n for (i = start; i < end; i += step) {\n rl.push(list[i]);\n }\n } else {\n for (i = start; i > end;i += step) {\n rl.push(list[i]);\n }\n }\n return rl;\n }\n\n function slice(list, rcSlice) {\n rcSlice = rcSlice || {};\n if (isNumber(rcSlice.row)) {\n if (isNumber(rcSlice.col))\n return list[rcSlice.row][rcSlice.col];\n var row = jStat.rowa(list, rcSlice.row);\n var colSlice = rcSlice.col || {};\n return _slice(row, colSlice.start, colSlice.end, colSlice.step);\n }\n\n if (isNumber(rcSlice.col)) {\n var col = jStat.cola(list, rcSlice.col);\n var rowSlice = rcSlice.row || {};\n return _slice(col, rowSlice.start, rowSlice.end, rowSlice.step);\n }\n\n var rowSlice = rcSlice.row || {};\n var colSlice = rcSlice.col || {};\n var rows = _slice(list, rowSlice.start, rowSlice.end, rowSlice.step);\n return rows.map(function(row) {\n return _slice(row, colSlice.start, colSlice.end, colSlice.step);\n });\n }\n\n return slice;\n}());\n\n\n// A=[[1,2,3],[4,5,6],[7,8,9]]\n// sliceAssign(A,{row:{start:1},col:{start:1}},[[0,0],[0,0]])\n// A=[[1,2,3],[4,0,0],[7,0,0]]\njStat.sliceAssign = function sliceAssign(A, rcSlice, B) {\n if (isNumber(rcSlice.row)) {\n if (isNumber(rcSlice.col))\n return A[rcSlice.row][rcSlice.col] = B;\n rcSlice.col = rcSlice.col || {};\n rcSlice.col.start = rcSlice.col.start || 0;\n rcSlice.col.end = rcSlice.col.end || A[0].length;\n rcSlice.col.step = rcSlice.col.step || 1;\n var nl = jStat.arange(rcSlice.col.start,\n Math.min(A.length, rcSlice.col.end),\n rcSlice.col.step);\n var m = rcSlice.row;\n nl.forEach(function(n, i) {\n A[m][n] = B[i];\n });\n return A;\n }\n\n if (isNumber(rcSlice.col)) {\n rcSlice.row = rcSlice.row || {};\n rcSlice.row.start = rcSlice.row.start || 0;\n rcSlice.row.end = rcSlice.row.end || A.length;\n rcSlice.row.step = rcSlice.row.step || 1;\n var ml = jStat.arange(rcSlice.row.start,\n Math.min(A[0].length, rcSlice.row.end),\n rcSlice.row.step);\n var n = rcSlice.col;\n ml.forEach(function(m, j) {\n A[m][n] = B[j];\n });\n return A;\n }\n\n if (B[0].length === undefined) {\n B = [B];\n }\n rcSlice.row.start = rcSlice.row.start || 0;\n rcSlice.row.end = rcSlice.row.end || A.length;\n rcSlice.row.step = rcSlice.row.step || 1;\n rcSlice.col.start = rcSlice.col.start || 0;\n rcSlice.col.end = rcSlice.col.end || A[0].length;\n rcSlice.col.step = rcSlice.col.step || 1;\n var ml = jStat.arange(rcSlice.row.start,\n Math.min(A.length, rcSlice.row.end),\n rcSlice.row.step);\n var nl = jStat.arange(rcSlice.col.start,\n Math.min(A[0].length, rcSlice.col.end),\n rcSlice.col.step);\n ml.forEach(function(m, i) {\n nl.forEach(function(n, j) {\n A[m][n] = B[i][j];\n });\n });\n return A;\n};\n\n\n// [1,2,3] ->\n// [[1,0,0],[0,2,0],[0,0,3]]\njStat.diagonal = function diagonal(diagArray) {\n var mat = jStat.zeros(diagArray.length, diagArray.length);\n diagArray.forEach(function(t, i) {\n mat[i][i] = t;\n });\n return mat;\n};\n\n\n// return copy of A\njStat.copy = function copy(A) {\n return A.map(function(row) {\n if (isNumber(row))\n return row;\n return row.map(function(t) {\n return t;\n });\n });\n};\n\n\n// TODO: Go over this entire implementation. Seems a tragic waste of resources\n// doing all this work. Instead, and while ugly, use new Function() to generate\n// a custom function for each static method.\n\n// Quick reference.\nvar jProto = jStat.prototype;\n\n// Default length.\njProto.length = 0;\n\n// For internal use only.\n// TODO: Check if they're actually used, and if they are then rename them\n// to _*\njProto.push = Array.prototype.push;\njProto.sort = Array.prototype.sort;\njProto.splice = Array.prototype.splice;\njProto.slice = Array.prototype.slice;\n\n\n// Return a clean array.\njProto.toArray = function toArray() {\n return this.length > 1 ? slice.call(this) : slice.call(this)[0];\n};\n\n\n// Map a function to a matrix or vector.\njProto.map = function map(func, toAlter) {\n return jStat(jStat.map(this, func, toAlter));\n};\n\n\n// Cumulatively combine the elements of a matrix or vector using a function.\njProto.cumreduce = function cumreduce(func, toAlter) {\n return jStat(jStat.cumreduce(this, func, toAlter));\n};\n\n\n// Destructively alter an array.\njProto.alter = function alter(func) {\n jStat.alter(this, func);\n return this;\n};\n\n\n// Extend prototype with methods that have no argument.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jProto[passfunc] = function(func) {\n var self = this,\n results;\n // Check for callback.\n if (func) {\n setTimeout(function() {\n func.call(self, jProto[passfunc].call(self));\n });\n return this;\n }\n results = jStat[passfunc](this);\n return isArray(results) ? jStat(results) : results;\n };\n })(funcs[i]);\n})('transpose clear symmetric rows cols dimensions diag antidiag'.split(' '));\n\n\n// Extend prototype with methods that have one argument.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jProto[passfunc] = function(index, func) {\n var self = this;\n // check for callback\n if (func) {\n setTimeout(function() {\n func.call(self, jProto[passfunc].call(self, index));\n });\n return this;\n }\n return jStat(jStat[passfunc](this, index));\n };\n })(funcs[i]);\n})('row col'.split(' '));\n\n\n// Extend prototype with simple shortcut methods.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jProto[passfunc] = new Function(\n 'return jStat(jStat.' + passfunc + '.apply(null, arguments));');\n })(funcs[i]);\n})('create zeros ones rand identity'.split(' '));\n\n\n// Exposing jStat.\nreturn jStat;\n\n}(Math));\n(function(jStat, Math) {\n\nvar isFunction = jStat.utils.isFunction;\n\n// Ascending functions for sort\nfunction ascNum(a, b) { return a - b; }\n\nfunction clip(arg, min, max) {\n return Math.max(min, Math.min(arg, max));\n}\n\n\n// sum of an array\njStat.sum = function sum(arr) {\n var sum = 0;\n var i = arr.length;\n while (--i >= 0)\n sum += arr[i];\n return sum;\n};\n\n\n// sum squared\njStat.sumsqrd = function sumsqrd(arr) {\n var sum = 0;\n var i = arr.length;\n while (--i >= 0)\n sum += arr[i] * arr[i];\n return sum;\n};\n\n\n// sum of squared errors of prediction (SSE)\njStat.sumsqerr = function sumsqerr(arr) {\n var mean = jStat.mean(arr);\n var sum = 0;\n var i = arr.length;\n var tmp;\n while (--i >= 0) {\n tmp = arr[i] - mean;\n sum += tmp * tmp;\n }\n return sum;\n};\n\n// sum of an array in each row\njStat.sumrow = function sumrow(arr) {\n var sum = 0;\n var i = arr.length;\n while (--i >= 0)\n sum += arr[i];\n return sum;\n};\n\n// product of an array\njStat.product = function product(arr) {\n var prod = 1;\n var i = arr.length;\n while (--i >= 0)\n prod *= arr[i];\n return prod;\n};\n\n\n// minimum value of an array\njStat.min = function min(arr) {\n var low = arr[0];\n var i = 0;\n while (++i < arr.length)\n if (arr[i] < low)\n low = arr[i];\n return low;\n};\n\n\n// maximum value of an array\njStat.max = function max(arr) {\n var high = arr[0];\n var i = 0;\n while (++i < arr.length)\n if (arr[i] > high)\n high = arr[i];\n return high;\n};\n\n\n// unique values of an array\njStat.unique = function unique(arr) {\n var hash = {}, _arr = [];\n for(var i = 0; i < arr.length; i++) {\n if (!hash[arr[i]]) {\n hash[arr[i]] = true;\n _arr.push(arr[i]);\n }\n }\n return _arr;\n};\n\n\n// mean value of an array\njStat.mean = function mean(arr) {\n return jStat.sum(arr) / arr.length;\n};\n\n\n// mean squared error (MSE)\njStat.meansqerr = function meansqerr(arr) {\n return jStat.sumsqerr(arr) / arr.length;\n};\n\n\n// geometric mean of an array\njStat.geomean = function geomean(arr) {\n return Math.pow(jStat.product(arr), 1 / arr.length);\n};\n\n\n// median of an array\njStat.median = function median(arr) {\n var arrlen = arr.length;\n var _arr = arr.slice().sort(ascNum);\n // check if array is even or odd, then return the appropriate\n return !(arrlen & 1)\n ? (_arr[(arrlen / 2) - 1 ] + _arr[(arrlen / 2)]) / 2\n : _arr[(arrlen / 2) | 0 ];\n};\n\n\n// cumulative sum of an array\njStat.cumsum = function cumsum(arr) {\n return jStat.cumreduce(arr, function (a, b) { return a + b; });\n};\n\n\n// cumulative product of an array\njStat.cumprod = function cumprod(arr) {\n return jStat.cumreduce(arr, function (a, b) { return a * b; });\n};\n\n\n// successive differences of a sequence\njStat.diff = function diff(arr) {\n var diffs = [];\n var arrLen = arr.length;\n var i;\n for (var i = 1; i < arrLen; i++)\n diffs.push(arr[i] - arr[i - 1]);\n return diffs;\n};\n\n\n// ranks of an array\njStat.rank = function (arr) {\n var arrlen = arr.length;\n var sorted = arr.slice().sort(ascNum);\n var ranks = new Array(arrlen);\n for (var i = 0; i < arrlen; i++) {\n var first = sorted.indexOf(arr[i]);\n var last = sorted.lastIndexOf(arr[i]);\n if (first === last) {\n var val = first;\n } else {\n var val = (first + last) / 2;\n }\n ranks[i] = val + 1;\n }\n return ranks;\n};\n\n\n// mode of an array\n// if there are multiple modes of an array, return all of them\n// is this the appropriate way of handling it?\njStat.mode = function mode(arr) {\n var arrLen = arr.length;\n var _arr = arr.slice().sort(ascNum);\n var count = 1;\n var maxCount = 0;\n var numMaxCount = 0;\n var mode_arr = [];\n var i;\n\n for (var i = 0; i < arrLen; i++) {\n if (_arr[i] === _arr[i + 1]) {\n count++;\n } else {\n if (count > maxCount) {\n mode_arr = [_arr[i]];\n maxCount = count;\n numMaxCount = 0;\n }\n // are there multiple max counts\n else if (count === maxCount) {\n mode_arr.push(_arr[i]);\n numMaxCount++;\n }\n // resetting count for new value in array\n count = 1;\n }\n }\n\n return numMaxCount === 0 ? mode_arr[0] : mode_arr;\n};\n\n\n// range of an array\njStat.range = function range(arr) {\n return jStat.max(arr) - jStat.min(arr);\n};\n\n// variance of an array\n// flag = true indicates sample instead of population\njStat.variance = function variance(arr, flag) {\n return jStat.sumsqerr(arr) / (arr.length - (flag ? 1 : 0));\n};\n\n// pooled variance of an array of arrays\njStat.pooledvariance = function pooledvariance(arr) {\n var sumsqerr = arr.reduce(function (a, samples) {return a + jStat.sumsqerr(samples);}, 0);\n var count = arr.reduce(function (a, samples) {return a + samples.length;}, 0);\n return sumsqerr / (count - arr.length);\n};\n\n// deviation of an array\njStat.deviation = function (arr) {\n var mean = jStat.mean(arr);\n var arrlen = arr.length;\n var dev = new Array(arrlen);\n for (var i = 0; i < arrlen; i++) {\n dev[i] = arr[i] - mean;\n }\n return dev;\n};\n\n// standard deviation of an array\n// flag = true indicates sample instead of population\njStat.stdev = function stdev(arr, flag) {\n return Math.sqrt(jStat.variance(arr, flag));\n};\n\n// pooled standard deviation of an array of arrays\njStat.pooledstdev = function pooledstdev(arr) {\n return Math.sqrt(jStat.pooledvariance(arr));\n};\n\n// mean deviation (mean absolute deviation) of an array\njStat.meandev = function meandev(arr) {\n var mean = jStat.mean(arr);\n var a = [];\n for (var i = arr.length - 1; i >= 0; i--) {\n a.push(Math.abs(arr[i] - mean));\n }\n return jStat.mean(a);\n};\n\n\n// median deviation (median absolute deviation) of an array\njStat.meddev = function meddev(arr) {\n var median = jStat.median(arr);\n var a = [];\n for (var i = arr.length - 1; i >= 0; i--) {\n a.push(Math.abs(arr[i] - median));\n }\n return jStat.median(a);\n};\n\n\n// coefficient of variation\njStat.coeffvar = function coeffvar(arr) {\n return jStat.stdev(arr) / jStat.mean(arr);\n};\n\n\n// quartiles of an array\njStat.quartiles = function quartiles(arr) {\n var arrlen = arr.length;\n var _arr = arr.slice().sort(ascNum);\n return [\n _arr[ Math.round((arrlen) / 4) - 1 ],\n _arr[ Math.round((arrlen) / 2) - 1 ],\n _arr[ Math.round((arrlen) * 3 / 4) - 1 ]\n ];\n};\n\n\n// Arbitary quantiles of an array. Direct port of the scipy.stats\n// implementation by Pierre GF Gerard-Marchant.\njStat.quantiles = function quantiles(arr, quantilesArray, alphap, betap) {\n var sortedArray = arr.slice().sort(ascNum);\n var quantileVals = [quantilesArray.length];\n var n = arr.length;\n var i, p, m, aleph, k, gamma;\n\n if (typeof alphap === 'undefined')\n alphap = 3 / 8;\n if (typeof betap === 'undefined')\n betap = 3 / 8;\n\n for (var i = 0; i < quantilesArray.length; i++) {\n p = quantilesArray[i];\n m = alphap + p * (1 - alphap - betap);\n aleph = n * p + m;\n k = Math.floor(clip(aleph, 1, n - 1));\n gamma = clip(aleph - k, 0, 1);\n quantileVals[i] = (1 - gamma) * sortedArray[k - 1] + gamma * sortedArray[k];\n }\n\n return quantileVals;\n};\n\n// Returns the k-th percentile of values in a range, where k is in the\n// range 0..1, exclusive.\njStat.percentile = function percentile(arr, k) {\n var _arr = arr.slice().sort(ascNum);\n var realIndex = k * (_arr.length - 1);\n var index = parseInt(realIndex);\n var frac = realIndex - index;\n\n if (index + 1 < _arr.length) {\n return _arr[index] * (1 - frac) + _arr[index + 1] * frac;\n } else {\n return _arr[index];\n }\n}\n\n\n// The percentile rank of score in a given array. Returns the percentage\n// of all values in the input array that are less than (kind='strict') or\n// less or equal than (kind='weak') score. Default is weak.\njStat.percentileOfScore = function percentileOfScore(arr, score, kind) {\n var counter = 0;\n var len = arr.length;\n var strict = false;\n var value, i;\n\n if (kind === 'strict')\n strict = true;\n\n for (var i = 0; i < len; i++) {\n value = arr[i];\n if ((strict && value < score) ||\n (!strict && value <= score)) {\n counter++;\n }\n }\n\n return counter / len;\n};\n\n\n// Histogram (bin count) data\njStat.histogram = function histogram(arr, bins) {\n var first = jStat.min(arr);\n var binCnt = bins || 4;\n var binWidth = (jStat.max(arr) - first) / binCnt;\n var len = arr.length;\n var bins = [];\n var i;\n\n for (var i = 0; i < binCnt; i++)\n bins[i] = 0;\n for (var i = 0; i < len; i++)\n bins[Math.min(Math.floor(((arr[i] - first) / binWidth)), binCnt - 1)] += 1;\n\n return bins;\n};\n\n\n// covariance of two arrays\njStat.covariance = function covariance(arr1, arr2) {\n var u = jStat.mean(arr1);\n var v = jStat.mean(arr2);\n var arr1Len = arr1.length;\n var sq_dev = new Array(arr1Len);\n var i;\n\n for (var i = 0; i < arr1Len; i++)\n sq_dev[i] = (arr1[i] - u) * (arr2[i] - v);\n\n return jStat.sum(sq_dev) / (arr1Len - 1);\n};\n\n\n// (pearson's) population correlation coefficient, rho\njStat.corrcoeff = function corrcoeff(arr1, arr2) {\n return jStat.covariance(arr1, arr2) /\n jStat.stdev(arr1, 1) /\n jStat.stdev(arr2, 1);\n};\n\n // (spearman's) rank correlation coefficient, sp\njStat.spearmancoeff = function (arr1, arr2) {\n arr1 = jStat.rank(arr1);\n arr2 = jStat.rank(arr2);\n //return pearson's correlation of the ranks:\n return jStat.corrcoeff(arr1, arr2);\n}\n\n\n// statistical standardized moments (general form of skew/kurt)\njStat.stanMoment = function stanMoment(arr, n) {\n var mu = jStat.mean(arr);\n var sigma = jStat.stdev(arr);\n var len = arr.length;\n var skewSum = 0;\n\n for (var i = 0; i < len; i++)\n skewSum += Math.pow((arr[i] - mu) / sigma, n);\n\n return skewSum / arr.length;\n};\n\n// (pearson's) moment coefficient of skewness\njStat.skewness = function skewness(arr) {\n return jStat.stanMoment(arr, 3);\n};\n\n// (pearson's) (excess) kurtosis\njStat.kurtosis = function kurtosis(arr) {\n return jStat.stanMoment(arr, 4) - 3;\n};\n\n\nvar jProto = jStat.prototype;\n\n\n// Extend jProto with method for calculating cumulative sums and products.\n// This differs from the similar extension below as cumsum and cumprod should\n// not be run again in the case fullbool === true.\n// If a matrix is passed, automatically assume operation should be done on the\n// columns.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n // If a matrix is passed, automatically assume operation should be done on\n // the columns.\n jProto[passfunc] = function(fullbool, func) {\n var arr = [];\n var i = 0;\n var tmpthis = this;\n // Assignment reassignation depending on how parameters were passed in.\n if (isFunction(fullbool)) {\n func = fullbool;\n fullbool = false;\n }\n // Check if a callback was passed with the function.\n if (func) {\n setTimeout(function() {\n func.call(tmpthis, jProto[passfunc].call(tmpthis, fullbool));\n });\n return this;\n }\n // Check if matrix and run calculations.\n if (this.length > 1) {\n tmpthis = fullbool === true ? this : this.transpose();\n for (; i < tmpthis.length; i++)\n arr[i] = jStat[passfunc](tmpthis[i]);\n return arr;\n }\n // Pass fullbool if only vector, not a matrix. for variance and stdev.\n return jStat[passfunc](this[0], fullbool);\n };\n })(funcs[i]);\n})(('cumsum cumprod').split(' '));\n\n\n// Extend jProto with methods which don't require arguments and work on columns.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n // If a matrix is passed, automatically assume operation should be done on\n // the columns.\n jProto[passfunc] = function(fullbool, func) {\n var arr = [];\n var i = 0;\n var tmpthis = this;\n // Assignment reassignation depending on how parameters were passed in.\n if (isFunction(fullbool)) {\n func = fullbool;\n fullbool = false;\n }\n // Check if a callback was passed with the function.\n if (func) {\n setTimeout(function() {\n func.call(tmpthis, jProto[passfunc].call(tmpthis, fullbool));\n });\n return this;\n }\n // Check if matrix and run calculations.\n if (this.length > 1) {\n if (passfunc !== 'sumrow')\n tmpthis = fullbool === true ? this : this.transpose();\n for (; i < tmpthis.length; i++)\n arr[i] = jStat[passfunc](tmpthis[i]);\n return fullbool === true\n ? jStat[passfunc](jStat.utils.toVector(arr))\n : arr;\n }\n // Pass fullbool if only vector, not a matrix. for variance and stdev.\n return jStat[passfunc](this[0], fullbool);\n };\n })(funcs[i]);\n})(('sum sumsqrd sumsqerr sumrow product min max unique mean meansqerr ' +\n 'geomean median diff rank mode range variance deviation stdev meandev ' +\n 'meddev coeffvar quartiles histogram skewness kurtosis').split(' '));\n\n\n// Extend jProto with functions that take arguments. Operations on matrices are\n// done on columns.\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jProto[passfunc] = function() {\n var arr = [];\n var i = 0;\n var tmpthis = this;\n var args = Array.prototype.slice.call(arguments);\n\n // If the last argument is a function, we assume it's a callback; we\n // strip the callback out and call the function again.\n if (isFunction(args[args.length - 1])) {\n var callbackFunction = args[args.length - 1];\n var argsToPass = args.slice(0, args.length - 1);\n\n setTimeout(function() {\n callbackFunction.call(tmpthis,\n jProto[passfunc].apply(tmpthis, argsToPass));\n });\n return this;\n\n // Otherwise we curry the function args and call normally.\n } else {\n var callbackFunction = undefined;\n var curriedFunction = function curriedFunction(vector) {\n return jStat[passfunc].apply(tmpthis, [vector].concat(args));\n }\n }\n\n // If this is a matrix, run column-by-column.\n if (this.length > 1) {\n tmpthis = tmpthis.transpose();\n for (; i < tmpthis.length; i++)\n arr[i] = curriedFunction(tmpthis[i]);\n return arr;\n }\n\n // Otherwise run on the vector.\n return curriedFunction(this[0]);\n };\n })(funcs[i]);\n})('quantiles percentileOfScore'.split(' '));\n\n}(jStat, Math));\n// Special functions //\n(function(jStat, Math) {\n\n// Log-gamma function\njStat.gammaln = function gammaln(x) {\n var j = 0;\n var cof = [\n 76.18009172947146, -86.50532032941677, 24.01409824083091,\n -1.231739572450155, 0.1208650973866179e-2, -0.5395239384953e-5\n ];\n var ser = 1.000000000190015;\n var xx, y, tmp;\n tmp = (y = xx = x) + 5.5;\n tmp -= (xx + 0.5) * Math.log(tmp);\n for (; j < 6; j++)\n ser += cof[j] / ++y;\n return Math.log(2.5066282746310005 * ser / xx) - tmp;\n};\n\n\n// gamma of x\njStat.gammafn = function gammafn(x) {\n var p = [-1.716185138865495, 24.76565080557592, -379.80425647094563,\n 629.3311553128184, 866.9662027904133, -31451.272968848367,\n -36144.413418691176, 66456.14382024054\n ];\n var q = [-30.8402300119739, 315.35062697960416, -1015.1563674902192,\n -3107.771671572311, 22538.118420980151, 4755.8462775278811,\n -134659.9598649693, -115132.2596755535];\n var fact = false;\n var n = 0;\n var xden = 0;\n var xnum = 0;\n var y = x;\n var i, z, yi, res, sum, ysq;\n if (y <= 0) {\n res = y % 1 + 3.6e-16;\n if (res) {\n fact = (!(y & 1) ? 1 : -1) * Math.PI / Math.sin(Math.PI * res);\n y = 1 - y;\n } else {\n return Infinity;\n }\n }\n yi = y;\n if (y < 1) {\n z = y++;\n } else {\n z = (y -= n = (y | 0) - 1) - 1;\n }\n for (var i = 0; i < 8; ++i) {\n xnum = (xnum + p[i]) * z;\n xden = xden * z + q[i];\n }\n res = xnum / xden + 1;\n if (yi < y) {\n res /= yi;\n } else if (yi > y) {\n for (var i = 0; i < n; ++i) {\n res *= y;\n y++;\n }\n }\n if (fact) {\n res = fact / res;\n }\n return res;\n};\n\n\n// lower incomplete gamma function, which is usually typeset with a\n// lower-case greek gamma as the function symbol\njStat.gammap = function gammap(a, x) {\n return jStat.lowRegGamma(a, x) * jStat.gammafn(a);\n};\n\n\n// The lower regularized incomplete gamma function, usually written P(a,x)\njStat.lowRegGamma = function lowRegGamma(a, x) {\n var aln = jStat.gammaln(a);\n var ap = a;\n var sum = 1 / a;\n var del = sum;\n var b = x + 1 - a;\n var c = 1 / 1.0e-30;\n var d = 1 / b;\n var h = d;\n var i = 1;\n // calculate maximum number of itterations required for a\n var ITMAX = -~(Math.log((a >= 1) ? a : 1 / a) * 8.5 + a * 0.4 + 17);\n var an, endval;\n\n if (x < 0 || a <= 0) {\n return NaN;\n } else if (x < a + 1) {\n for (; i <= ITMAX; i++) {\n sum += del *= x / ++ap;\n }\n return (sum * Math.exp(-x + a * Math.log(x) - (aln)));\n }\n\n for (; i <= ITMAX; i++) {\n an = -i * (i - a);\n b += 2;\n d = an * d + b;\n c = b + an / c;\n d = 1 / d;\n h *= d * c;\n }\n\n return (1 - h * Math.exp(-x + a * Math.log(x) - (aln)));\n};\n\n// natural log factorial of n\njStat.factorialln = function factorialln(n) {\n return n < 0 ? NaN : jStat.gammaln(n + 1);\n};\n\n// factorial of n\njStat.factorial = function factorial(n) {\n return n < 0 ? NaN : jStat.gammafn(n + 1);\n};\n\n// combinations of n, m\njStat.combination = function combination(n, m) {\n // make sure n or m don't exceed the upper limit of usable values\n return (n > 170 || m > 170)\n ? Math.exp(jStat.combinationln(n, m))\n : (jStat.factorial(n) / jStat.factorial(m)) / jStat.factorial(n - m);\n};\n\n\njStat.combinationln = function combinationln(n, m){\n return jStat.factorialln(n) - jStat.factorialln(m) - jStat.factorialln(n - m);\n};\n\n\n// permutations of n, m\njStat.permutation = function permutation(n, m) {\n return jStat.factorial(n) / jStat.factorial(n - m);\n};\n\n\n// beta function\njStat.betafn = function betafn(x, y) {\n // ensure arguments are positive\n if (x <= 0 || y <= 0)\n return undefined;\n // make sure x + y doesn't exceed the upper limit of usable values\n return (x + y > 170)\n ? Math.exp(jStat.betaln(x, y))\n : jStat.gammafn(x) * jStat.gammafn(y) / jStat.gammafn(x + y);\n};\n\n\n// natural logarithm of beta function\njStat.betaln = function betaln(x, y) {\n return jStat.gammaln(x) + jStat.gammaln(y) - jStat.gammaln(x + y);\n};\n\n\n// Evaluates the continued fraction for incomplete beta function by modified\n// Lentz's method.\njStat.betacf = function betacf(x, a, b) {\n var fpmin = 1e-30;\n var m = 1;\n var qab = a + b;\n var qap = a + 1;\n var qam = a - 1;\n var c = 1;\n var d = 1 - qab * x / qap;\n var m2, aa, del, h;\n\n // These q's will be used in factors that occur in the coefficients\n if (Math.abs(d) < fpmin)\n d = fpmin;\n d = 1 / d;\n h = d;\n\n for (; m <= 100; m++) {\n m2 = 2 * m;\n aa = m * (b - m) * x / ((qam + m2) * (a + m2));\n // One step (the even one) of the recurrence\n d = 1 + aa * d;\n if (Math.abs(d) < fpmin)\n d = fpmin;\n c = 1 + aa / c;\n if (Math.abs(c) < fpmin)\n c = fpmin;\n d = 1 / d;\n h *= d * c;\n aa = -(a + m) * (qab + m) * x / ((a + m2) * (qap + m2));\n // Next step of the recurrence (the odd one)\n d = 1 + aa * d;\n if (Math.abs(d) < fpmin)\n d = fpmin;\n c = 1 + aa / c;\n if (Math.abs(c) < fpmin)\n c = fpmin;\n d = 1 / d;\n del = d * c;\n h *= del;\n if (Math.abs(del - 1.0) < 3e-7)\n break;\n }\n\n return h;\n};\n\n\n// Returns the inverse of the lower regularized inomplete gamma function\njStat.gammapinv = function gammapinv(p, a) {\n var j = 0;\n var a1 = a - 1;\n var EPS = 1e-8;\n var gln = jStat.gammaln(a);\n var x, err, t, u, pp, lna1, afac;\n\n if (p >= 1)\n return Math.max(100, a + 100 * Math.sqrt(a));\n if (p <= 0)\n return 0;\n if (a > 1) {\n lna1 = Math.log(a1);\n afac = Math.exp(a1 * (lna1 - 1) - gln);\n pp = (p < 0.5) ? p : 1 - p;\n t = Math.sqrt(-2 * Math.log(pp));\n x = (2.30753 + t * 0.27061) / (1 + t * (0.99229 + t * 0.04481)) - t;\n if (p < 0.5)\n x = -x;\n x = Math.max(1e-3,\n a * Math.pow(1 - 1 / (9 * a) - x / (3 * Math.sqrt(a)), 3));\n } else {\n t = 1 - a * (0.253 + a * 0.12);\n if (p < t)\n x = Math.pow(p / t, 1 / a);\n else\n x = 1 - Math.log(1 - (p - t) / (1 - t));\n }\n\n for(; j < 12; j++) {\n if (x <= 0)\n return 0;\n err = jStat.lowRegGamma(a, x) - p;\n if (a > 1)\n t = afac * Math.exp(-(x - a1) + a1 * (Math.log(x) - lna1));\n else\n t = Math.exp(-x + a1 * Math.log(x) - gln);\n u = err / t;\n x -= (t = u / (1 - 0.5 * Math.min(1, u * ((a - 1) / x - 1))));\n if (x <= 0)\n x = 0.5 * (x + t);\n if (Math.abs(t) < EPS * x)\n break;\n }\n\n return x;\n};\n\n\n// Returns the error function erf(x)\njStat.erf = function erf(x) {\n var cof = [-1.3026537197817094, 6.4196979235649026e-1, 1.9476473204185836e-2,\n -9.561514786808631e-3, -9.46595344482036e-4, 3.66839497852761e-4,\n 4.2523324806907e-5, -2.0278578112534e-5, -1.624290004647e-6,\n 1.303655835580e-6, 1.5626441722e-8, -8.5238095915e-8,\n 6.529054439e-9, 5.059343495e-9, -9.91364156e-10,\n -2.27365122e-10, 9.6467911e-11, 2.394038e-12,\n -6.886027e-12, 8.94487e-13, 3.13092e-13,\n -1.12708e-13, 3.81e-16, 7.106e-15,\n -1.523e-15, -9.4e-17, 1.21e-16,\n -2.8e-17];\n var j = cof.length - 1;\n var isneg = false;\n var d = 0;\n var dd = 0;\n var t, ty, tmp, res;\n\n if (x < 0) {\n x = -x;\n isneg = true;\n }\n\n t = 2 / (2 + x);\n ty = 4 * t - 2;\n\n for(; j > 0; j--) {\n tmp = d;\n d = ty * d - dd + cof[j];\n dd = tmp;\n }\n\n res = t * Math.exp(-x * x + 0.5 * (cof[0] + ty * d) - dd);\n return isneg ? res - 1 : 1 - res;\n};\n\n\n// Returns the complmentary error function erfc(x)\njStat.erfc = function erfc(x) {\n return 1 - jStat.erf(x);\n};\n\n\n// Returns the inverse of the complementary error function\njStat.erfcinv = function erfcinv(p) {\n var j = 0;\n var x, err, t, pp;\n if (p >= 2)\n return -100;\n if (p <= 0)\n return 100;\n pp = (p < 1) ? p : 2 - p;\n t = Math.sqrt(-2 * Math.log(pp / 2));\n x = -0.70711 * ((2.30753 + t * 0.27061) /\n (1 + t * (0.99229 + t * 0.04481)) - t);\n for (; j < 2; j++) {\n err = jStat.erfc(x) - pp;\n x += err / (1.12837916709551257 * Math.exp(-x * x) - x * err);\n }\n return (p < 1) ? x : -x;\n};\n\n\n// Returns the inverse of the incomplete beta function\njStat.ibetainv = function ibetainv(p, a, b) {\n var EPS = 1e-8;\n var a1 = a - 1;\n var b1 = b - 1;\n var j = 0;\n var lna, lnb, pp, t, u, err, x, al, h, w, afac;\n if (p <= 0)\n return 0;\n if (p >= 1)\n return 1;\n if (a >= 1 && b >= 1) {\n pp = (p < 0.5) ? p : 1 - p;\n t = Math.sqrt(-2 * Math.log(pp));\n x = (2.30753 + t * 0.27061) / (1 + t* (0.99229 + t * 0.04481)) - t;\n if (p < 0.5)\n x = -x;\n al = (x * x - 3) / 6;\n h = 2 / (1 / (2 * a - 1) + 1 / (2 * b - 1));\n w = (x * Math.sqrt(al + h) / h) - (1 / (2 * b - 1) - 1 / (2 * a - 1)) *\n (al + 5 / 6 - 2 / (3 * h));\n x = a / (a + b * Math.exp(2 * w));\n } else {\n lna = Math.log(a / (a + b));\n lnb = Math.log(b / (a + b));\n t = Math.exp(a * lna) / a;\n u = Math.exp(b * lnb) / b;\n w = t + u;\n if (p < t / w)\n x = Math.pow(a * w * p, 1 / a);\n else\n x = 1 - Math.pow(b * w * (1 - p), 1 / b);\n }\n afac = -jStat.gammaln(a) - jStat.gammaln(b) + jStat.gammaln(a + b);\n for(; j < 10; j++) {\n if (x === 0 || x === 1)\n return x;\n err = jStat.ibeta(x, a, b) - p;\n t = Math.exp(a1 * Math.log(x) + b1 * Math.log(1 - x) + afac);\n u = err / t;\n x -= (t = u / (1 - 0.5 * Math.min(1, u * (a1 / x - b1 / (1 - x)))));\n if (x <= 0)\n x = 0.5 * (x + t);\n if (x >= 1)\n x = 0.5 * (x + t + 1);\n if (Math.abs(t) < EPS * x && j > 0)\n break;\n }\n return x;\n};\n\n\n// Returns the incomplete beta function I_x(a,b)\njStat.ibeta = function ibeta(x, a, b) {\n // Factors in front of the continued fraction.\n var bt = (x === 0 || x === 1) ? 0 :\n Math.exp(jStat.gammaln(a + b) - jStat.gammaln(a) -\n jStat.gammaln(b) + a * Math.log(x) + b *\n Math.log(1 - x));\n if (x < 0 || x > 1)\n return false;\n if (x < (a + 1) / (a + b + 2))\n // Use continued fraction directly.\n return bt * jStat.betacf(x, a, b) / a;\n // else use continued fraction after making the symmetry transformation.\n return 1 - bt * jStat.betacf(1 - x, b, a) / b;\n};\n\n\n// Returns a normal deviate (mu=0, sigma=1).\n// If n and m are specified it returns a object of normal deviates.\njStat.randn = function randn(n, m) {\n var u, v, x, y, q, mat;\n if (!m)\n m = n;\n if (n)\n return jStat.create(n, m, function() { return jStat.randn(); });\n do {\n u = Math.random();\n v = 1.7156 * (Math.random() - 0.5);\n x = u - 0.449871;\n y = Math.abs(v) + 0.386595;\n q = x * x + y * (0.19600 * y - 0.25472 * x);\n } while (q > 0.27597 && (q > 0.27846 || v * v > -4 * Math.log(u) * u * u));\n return v / u;\n};\n\n\n// Returns a gamma deviate by the method of Marsaglia and Tsang.\njStat.randg = function randg(shape, n, m) {\n var oalph = shape;\n var a1, a2, u, v, x, mat;\n if (!m)\n m = n;\n if (!shape)\n shape = 1;\n if (n) {\n mat = jStat.zeros(n,m);\n mat.alter(function() { return jStat.randg(shape); });\n return mat;\n }\n if (shape < 1)\n shape += 1;\n a1 = shape - 1 / 3;\n a2 = 1 / Math.sqrt(9 * a1);\n do {\n do {\n x = jStat.randn();\n v = 1 + a2 * x;\n } while(v <= 0);\n v = v * v * v;\n u = Math.random();\n } while(u > 1 - 0.331 * Math.pow(x, 4) &&\n Math.log(u) > 0.5 * x*x + a1 * (1 - v + Math.log(v)));\n // alpha > 1\n if (shape == oalph)\n return a1 * v;\n // alpha < 1\n do {\n u = Math.random();\n } while(u === 0);\n return Math.pow(u, 1 / oalph) * a1 * v;\n};\n\n\n// making use of static methods on the instance\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jStat.fn[passfunc] = function() {\n return jStat(\n jStat.map(this, function(value) { return jStat[passfunc](value); }));\n }\n })(funcs[i]);\n})('gammaln gammafn factorial factorialln'.split(' '));\n\n\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jStat.fn[passfunc] = function() {\n return jStat(jStat[passfunc].apply(null, arguments));\n };\n })(funcs[i]);\n})('randn'.split(' '));\n\n}(jStat, Math));\n(function(jStat, Math) {\n\n// generate all distribution instance methods\n(function(list) {\n for (var i = 0; i < list.length; i++) (function(func) {\n // distribution instance method\n jStat[func] = function(a, b, c) {\n if (!(this instanceof arguments.callee))\n return new arguments.callee(a, b, c);\n this._a = a;\n this._b = b;\n this._c = c;\n return this;\n };\n // distribution method to be used on a jStat instance\n jStat.fn[func] = function(a, b, c) {\n var newthis = jStat[func](a, b, c);\n newthis.data = this;\n return newthis;\n };\n // sample instance method\n jStat[func].prototype.sample = function(arr) {\n var a = this._a;\n var b = this._b;\n var c = this._c;\n if (arr)\n return jStat.alter(arr, function() {\n return jStat[func].sample(a, b, c);\n });\n else\n return jStat[func].sample(a, b, c);\n };\n // generate the pdf, cdf and inv instance methods\n (function(vals) {\n for (var i = 0; i < vals.length; i++) (function(fnfunc) {\n jStat[func].prototype[fnfunc] = function(x) {\n var a = this._a;\n var b = this._b;\n var c = this._c;\n if (!x && x !== 0)\n x = this.data;\n if (typeof x !== 'number') {\n return jStat.fn.map.call(x, function(x) {\n return jStat[func][fnfunc](x, a, b, c);\n });\n }\n return jStat[func][fnfunc](x, a, b, c);\n };\n })(vals[i]);\n })('pdf cdf inv'.split(' '));\n // generate the mean, median, mode and variance instance methods\n (function(vals) {\n for (var i = 0; i < vals.length; i++) (function(fnfunc) {\n jStat[func].prototype[fnfunc] = function() {\n return jStat[func][fnfunc](this._a, this._b, this._c);\n };\n })(vals[i]);\n })('mean median mode variance'.split(' '));\n })(list[i]);\n})((\n 'beta centralF cauchy chisquare exponential gamma invgamma kumaraswamy ' +\n 'laplace lognormal noncentralt normal pareto studentt weibull uniform ' +\n 'binomial negbin hypgeom poisson triangular tukey arcsine'\n).split(' '));\n\n\n\n// extend beta function with static methods\njStat.extend(jStat.beta, {\n pdf: function pdf(x, alpha, beta) {\n // PDF is zero outside the support\n if (x > 1 || x < 0)\n return 0;\n // PDF is one for the uniform case\n if (alpha == 1 && beta == 1)\n return 1;\n\n if (alpha < 512 && beta < 512) {\n return (Math.pow(x, alpha - 1) * Math.pow(1 - x, beta - 1)) /\n jStat.betafn(alpha, beta);\n } else {\n return Math.exp((alpha - 1) * Math.log(x) +\n (beta - 1) * Math.log(1 - x) -\n jStat.betaln(alpha, beta));\n }\n },\n\n cdf: function cdf(x, alpha, beta) {\n return (x > 1 || x < 0) ? (x > 1) * 1 : jStat.ibeta(x, alpha, beta);\n },\n\n inv: function inv(x, alpha, beta) {\n return jStat.ibetainv(x, alpha, beta);\n },\n\n mean: function mean(alpha, beta) {\n return alpha / (alpha + beta);\n },\n\n median: function median(alpha, beta) {\n return jStat.ibetainv(0.5, alpha, beta);\n },\n\n mode: function mode(alpha, beta) {\n return (alpha - 1 ) / ( alpha + beta - 2);\n },\n\n // return a random sample\n sample: function sample(alpha, beta) {\n var u = jStat.randg(alpha);\n return u / (u + jStat.randg(beta));\n },\n\n variance: function variance(alpha, beta) {\n return (alpha * beta) / (Math.pow(alpha + beta, 2) * (alpha + beta + 1));\n }\n});\n\n// extend F function with static methods\njStat.extend(jStat.centralF, {\n // This implementation of the pdf function avoids float overflow\n // See the way that R calculates this value:\n // https://svn.r-project.org/R/trunk/src/nmath/df.c\n pdf: function pdf(x, df1, df2) {\n var p, q, f;\n\n if (x < 0)\n return 0;\n\n if (df1 <= 2) {\n if (x === 0 && df1 < 2) {\n return Infinity;\n }\n if (x === 0 && df1 === 2) {\n return 1;\n }\n return (1 / jStat.betafn(df1 / 2, df2 / 2)) *\n Math.pow(df1 / df2, df1 / 2) *\n Math.pow(x, (df1/2) - 1) *\n Math.pow((1 + (df1 / df2) * x), -(df1 + df2) / 2);\n }\n\n p = (df1 * x) / (df2 + x * df1);\n q = df2 / (df2 + x * df1);\n f = df1 * q / 2.0;\n return f * jStat.binomial.pdf((df1 - 2) / 2, (df1 + df2 - 2) / 2, p);\n },\n\n cdf: function cdf(x, df1, df2) {\n if (x < 0)\n return 0;\n return jStat.ibeta((df1 * x) / (df1 * x + df2), df1 / 2, df2 / 2);\n },\n\n inv: function inv(x, df1, df2) {\n return df2 / (df1 * (1 / jStat.ibetainv(x, df1 / 2, df2 / 2) - 1));\n },\n\n mean: function mean(df1, df2) {\n return (df2 > 2) ? df2 / (df2 - 2) : undefined;\n },\n\n mode: function mode(df1, df2) {\n return (df1 > 2) ? (df2 * (df1 - 2)) / (df1 * (df2 + 2)) : undefined;\n },\n\n // return a random sample\n sample: function sample(df1, df2) {\n var x1 = jStat.randg(df1 / 2) * 2;\n var x2 = jStat.randg(df2 / 2) * 2;\n return (x1 / df1) / (x2 / df2);\n },\n\n variance: function variance(df1, df2) {\n if (df2 <= 4)\n return undefined;\n return 2 * df2 * df2 * (df1 + df2 - 2) /\n (df1 * (df2 - 2) * (df2 - 2) * (df2 - 4));\n }\n});\n\n\n// extend cauchy function with static methods\njStat.extend(jStat.cauchy, {\n pdf: function pdf(x, local, scale) {\n if (scale < 0) { return 0; }\n\n return (scale / (Math.pow(x - local, 2) + Math.pow(scale, 2))) / Math.PI;\n },\n\n cdf: function cdf(x, local, scale) {\n return Math.atan((x - local) / scale) / Math.PI + 0.5;\n },\n\n inv: function(p, local, scale) {\n return local + scale * Math.tan(Math.PI * (p - 0.5));\n },\n\n median: function median(local, scale) {\n return local;\n },\n\n mode: function mode(local, scale) {\n return local;\n },\n\n sample: function sample(local, scale) {\n return jStat.randn() *\n Math.sqrt(1 / (2 * jStat.randg(0.5))) * scale + local;\n }\n});\n\n\n\n// extend chisquare function with static methods\njStat.extend(jStat.chisquare, {\n pdf: function pdf(x, dof) {\n if (x < 0)\n return 0;\n return (x === 0 && dof === 2) ? 0.5 :\n Math.exp((dof / 2 - 1) * Math.log(x) - x / 2 - (dof / 2) *\n Math.log(2) - jStat.gammaln(dof / 2));\n },\n\n cdf: function cdf(x, dof) {\n if (x < 0)\n return 0;\n return jStat.lowRegGamma(dof / 2, x / 2);\n },\n\n inv: function(p, dof) {\n return 2 * jStat.gammapinv(p, 0.5 * dof);\n },\n\n mean : function(dof) {\n return dof;\n },\n\n // TODO: this is an approximation (is there a better way?)\n median: function median(dof) {\n return dof * Math.pow(1 - (2 / (9 * dof)), 3);\n },\n\n mode: function mode(dof) {\n return (dof - 2 > 0) ? dof - 2 : 0;\n },\n\n sample: function sample(dof) {\n return jStat.randg(dof / 2) * 2;\n },\n\n variance: function variance(dof) {\n return 2 * dof;\n }\n});\n\n\n\n// extend exponential function with static methods\njStat.extend(jStat.exponential, {\n pdf: function pdf(x, rate) {\n return x < 0 ? 0 : rate * Math.exp(-rate * x);\n },\n\n cdf: function cdf(x, rate) {\n return x < 0 ? 0 : 1 - Math.exp(-rate * x);\n },\n\n inv: function(p, rate) {\n return -Math.log(1 - p) / rate;\n },\n\n mean : function(rate) {\n return 1 / rate;\n },\n\n median: function (rate) {\n return (1 / rate) * Math.log(2);\n },\n\n mode: function mode(rate) {\n return 0;\n },\n\n sample: function sample(rate) {\n return -1 / rate * Math.log(Math.random());\n },\n\n variance : function(rate) {\n return Math.pow(rate, -2);\n }\n});\n\n\n\n// extend gamma function with static methods\njStat.extend(jStat.gamma, {\n pdf: function pdf(x, shape, scale) {\n if (x < 0)\n return 0;\n return (x === 0 && shape === 1) ? 1 / scale :\n Math.exp((shape - 1) * Math.log(x) - x / scale -\n jStat.gammaln(shape) - shape * Math.log(scale));\n },\n\n cdf: function cdf(x, shape, scale) {\n if (x < 0)\n return 0;\n return jStat.lowRegGamma(shape, x / scale);\n },\n\n inv: function(p, shape, scale) {\n return jStat.gammapinv(p, shape) * scale;\n },\n\n mean : function(shape, scale) {\n return shape * scale;\n },\n\n mode: function mode(shape, scale) {\n if(shape > 1) return (shape - 1) * scale;\n return undefined;\n },\n\n sample: function sample(shape, scale) {\n return jStat.randg(shape) * scale;\n },\n\n variance: function variance(shape, scale) {\n return shape * scale * scale;\n }\n});\n\n// extend inverse gamma function with static methods\njStat.extend(jStat.invgamma, {\n pdf: function pdf(x, shape, scale) {\n if (x <= 0)\n return 0;\n return Math.exp(-(shape + 1) * Math.log(x) - scale / x -\n jStat.gammaln(shape) + shape * Math.log(scale));\n },\n\n cdf: function cdf(x, shape, scale) {\n if (x <= 0)\n return 0;\n return 1 - jStat.lowRegGamma(shape, scale / x);\n },\n\n inv: function(p, shape, scale) {\n return scale / jStat.gammapinv(1 - p, shape);\n },\n\n mean : function(shape, scale) {\n return (shape > 1) ? scale / (shape - 1) : undefined;\n },\n\n mode: function mode(shape, scale) {\n return scale / (shape + 1);\n },\n\n sample: function sample(shape, scale) {\n return scale / jStat.randg(shape);\n },\n\n variance: function variance(shape, scale) {\n if (shape <= 2)\n return undefined;\n return scale * scale / ((shape - 1) * (shape - 1) * (shape - 2));\n }\n});\n\n\n// extend kumaraswamy function with static methods\njStat.extend(jStat.kumaraswamy, {\n pdf: function pdf(x, alpha, beta) {\n if (x === 0 && alpha === 1)\n return beta;\n else if (x === 1 && beta === 1)\n return alpha;\n return Math.exp(Math.log(alpha) + Math.log(beta) + (alpha - 1) *\n Math.log(x) + (beta - 1) *\n Math.log(1 - Math.pow(x, alpha)));\n },\n\n cdf: function cdf(x, alpha, beta) {\n if (x < 0)\n return 0;\n else if (x > 1)\n return 1;\n return (1 - Math.pow(1 - Math.pow(x, alpha), beta));\n },\n\n inv: function inv(p, alpha, beta) {\n return Math.pow(1 - Math.pow(1 - p, 1 / beta), 1 / alpha);\n },\n\n mean : function(alpha, beta) {\n return (beta * jStat.gammafn(1 + 1 / alpha) *\n jStat.gammafn(beta)) / (jStat.gammafn(1 + 1 / alpha + beta));\n },\n\n median: function median(alpha, beta) {\n return Math.pow(1 - Math.pow(2, -1 / beta), 1 / alpha);\n },\n\n mode: function mode(alpha, beta) {\n if (!(alpha >= 1 && beta >= 1 && (alpha !== 1 && beta !== 1)))\n return undefined;\n return Math.pow((alpha - 1) / (alpha * beta - 1), 1 / alpha);\n },\n\n variance: function variance(alpha, beta) {\n throw new Error('variance not yet implemented');\n // TODO: complete this\n }\n});\n\n\n\n// extend lognormal function with static methods\njStat.extend(jStat.lognormal, {\n pdf: function pdf(x, mu, sigma) {\n if (x <= 0)\n return 0;\n return Math.exp(-Math.log(x) - 0.5 * Math.log(2 * Math.PI) -\n Math.log(sigma) - Math.pow(Math.log(x) - mu, 2) /\n (2 * sigma * sigma));\n },\n\n cdf: function cdf(x, mu, sigma) {\n if (x < 0)\n return 0;\n return 0.5 +\n (0.5 * jStat.erf((Math.log(x) - mu) / Math.sqrt(2 * sigma * sigma)));\n },\n\n inv: function(p, mu, sigma) {\n return Math.exp(-1.41421356237309505 * sigma * jStat.erfcinv(2 * p) + mu);\n },\n\n mean: function mean(mu, sigma) {\n return Math.exp(mu + sigma * sigma / 2);\n },\n\n median: function median(mu, sigma) {\n return Math.exp(mu);\n },\n\n mode: function mode(mu, sigma) {\n return Math.exp(mu - sigma * sigma);\n },\n\n sample: function sample(mu, sigma) {\n return Math.exp(jStat.randn() * sigma + mu);\n },\n\n variance: function variance(mu, sigma) {\n return (Math.exp(sigma * sigma) - 1) * Math.exp(2 * mu + sigma * sigma);\n }\n});\n\n\n\n// extend noncentralt function with static methods\njStat.extend(jStat.noncentralt, {\n pdf: function pdf(x, dof, ncp) {\n var tol = 1e-14;\n if (Math.abs(ncp) < tol) // ncp approx 0; use student-t\n return jStat.studentt.pdf(x, dof)\n\n if (Math.abs(x) < tol) { // different formula for x == 0\n return Math.exp(jStat.gammaln((dof + 1) / 2) - ncp * ncp / 2 -\n 0.5 * Math.log(Math.PI * dof) - jStat.gammaln(dof / 2));\n }\n\n // formula for x != 0\n return dof / x *\n (jStat.noncentralt.cdf(x * Math.sqrt(1 + 2 / dof), dof+2, ncp) -\n jStat.noncentralt.cdf(x, dof, ncp));\n },\n\n cdf: function cdf(x, dof, ncp) {\n var tol = 1e-14;\n var min_iterations = 200;\n\n if (Math.abs(ncp) < tol) // ncp approx 0; use student-t\n return jStat.studentt.cdf(x, dof);\n\n // turn negative x into positive and flip result afterwards\n var flip = false;\n if (x < 0) {\n flip = true;\n ncp = -ncp;\n }\n\n var prob = jStat.normal.cdf(-ncp, 0, 1);\n var value = tol + 1;\n // use value at last two steps to determine convergence\n var lastvalue = value;\n var y = x * x / (x * x + dof);\n var j = 0;\n var p = Math.exp(-ncp * ncp / 2);\n var q = Math.exp(-ncp * ncp / 2 - 0.5 * Math.log(2) -\n jStat.gammaln(3 / 2)) * ncp;\n while (j < min_iterations || lastvalue > tol || value > tol) {\n lastvalue = value;\n if (j > 0) {\n p *= (ncp * ncp) / (2 * j);\n q *= (ncp * ncp) / (2 * (j + 1 / 2));\n }\n value = p * jStat.beta.cdf(y, j + 0.5, dof / 2) +\n q * jStat.beta.cdf(y, j+1, dof/2);\n prob += 0.5 * value;\n j++;\n }\n\n return flip ? (1 - prob) : prob;\n }\n});\n\n\n// extend normal function with static methods\njStat.extend(jStat.normal, {\n pdf: function pdf(x, mean, std) {\n return Math.exp(-0.5 * Math.log(2 * Math.PI) -\n Math.log(std) - Math.pow(x - mean, 2) / (2 * std * std));\n },\n\n cdf: function cdf(x, mean, std) {\n return 0.5 * (1 + jStat.erf((x - mean) / Math.sqrt(2 * std * std)));\n },\n\n inv: function(p, mean, std) {\n return -1.41421356237309505 * std * jStat.erfcinv(2 * p) + mean;\n },\n\n mean : function(mean, std) {\n return mean;\n },\n\n median: function median(mean, std) {\n return mean;\n },\n\n mode: function (mean, std) {\n return mean;\n },\n\n sample: function sample(mean, std) {\n return jStat.randn() * std + mean;\n },\n\n variance : function(mean, std) {\n return std * std;\n }\n});\n\n\n\n// extend pareto function with static methods\njStat.extend(jStat.pareto, {\n pdf: function pdf(x, scale, shape) {\n if (x < scale)\n return 0;\n return (shape * Math.pow(scale, shape)) / Math.pow(x, shape + 1);\n },\n\n cdf: function cdf(x, scale, shape) {\n if (x < scale)\n return 0;\n return 1 - Math.pow(scale / x, shape);\n },\n\n inv: function inv(p, scale, shape) {\n return scale / Math.pow(1 - p, 1 / shape);\n },\n\n mean: function mean(scale, shape) {\n if (shape <= 1)\n return undefined;\n return (shape * Math.pow(scale, shape)) / (shape - 1);\n },\n\n median: function median(scale, shape) {\n return scale * (shape * Math.SQRT2);\n },\n\n mode: function mode(scale, shape) {\n return scale;\n },\n\n variance : function(scale, shape) {\n if (shape <= 2)\n return undefined;\n return (scale*scale * shape) / (Math.pow(shape - 1, 2) * (shape - 2));\n }\n});\n\n\n\n// extend studentt function with static methods\njStat.extend(jStat.studentt, {\n pdf: function pdf(x, dof) {\n dof = dof > 1e100 ? 1e100 : dof;\n return (1/(Math.sqrt(dof) * jStat.betafn(0.5, dof/2))) *\n Math.pow(1 + ((x * x) / dof), -((dof + 1) / 2));\n },\n\n cdf: function cdf(x, dof) {\n var dof2 = dof / 2;\n return jStat.ibeta((x + Math.sqrt(x * x + dof)) /\n (2 * Math.sqrt(x * x + dof)), dof2, dof2);\n },\n\n inv: function(p, dof) {\n var x = jStat.ibetainv(2 * Math.min(p, 1 - p), 0.5 * dof, 0.5);\n x = Math.sqrt(dof * (1 - x) / x);\n return (p > 0.5) ? x : -x;\n },\n\n mean: function mean(dof) {\n return (dof > 1) ? 0 : undefined;\n },\n\n median: function median(dof) {\n return 0;\n },\n\n mode: function mode(dof) {\n return 0;\n },\n\n sample: function sample(dof) {\n return jStat.randn() * Math.sqrt(dof / (2 * jStat.randg(dof / 2)));\n },\n\n variance: function variance(dof) {\n return (dof > 2) ? dof / (dof - 2) : (dof > 1) ? Infinity : undefined;\n }\n});\n\n\n\n// extend weibull function with static methods\njStat.extend(jStat.weibull, {\n pdf: function pdf(x, scale, shape) {\n if (x < 0 || scale < 0 || shape < 0)\n return 0;\n return (shape / scale) * Math.pow((x / scale), (shape - 1)) *\n Math.exp(-(Math.pow((x / scale), shape)));\n },\n\n cdf: function cdf(x, scale, shape) {\n return x < 0 ? 0 : 1 - Math.exp(-Math.pow((x / scale), shape));\n },\n\n inv: function(p, scale, shape) {\n return scale * Math.pow(-Math.log(1 - p), 1 / shape);\n },\n\n mean : function(scale, shape) {\n return scale * jStat.gammafn(1 + 1 / shape);\n },\n\n median: function median(scale, shape) {\n return scale * Math.pow(Math.log(2), 1 / shape);\n },\n\n mode: function mode(scale, shape) {\n if (shape <= 1)\n return 0;\n return scale * Math.pow((shape - 1) / shape, 1 / shape);\n },\n\n sample: function sample(scale, shape) {\n return scale * Math.pow(-Math.log(Math.random()), 1 / shape);\n },\n\n variance: function variance(scale, shape) {\n return scale * scale * jStat.gammafn(1 + 2 / shape) -\n Math.pow(jStat.weibull.mean(scale, shape), 2);\n }\n});\n\n\n\n// extend uniform function with static methods\njStat.extend(jStat.uniform, {\n pdf: function pdf(x, a, b) {\n return (x < a || x > b) ? 0 : 1 / (b - a);\n },\n\n cdf: function cdf(x, a, b) {\n if (x < a)\n return 0;\n else if (x < b)\n return (x - a) / (b - a);\n return 1;\n },\n\n inv: function(p, a, b) {\n return a + (p * (b - a));\n },\n\n mean: function mean(a, b) {\n return 0.5 * (a + b);\n },\n\n median: function median(a, b) {\n return jStat.mean(a, b);\n },\n\n mode: function mode(a, b) {\n throw new Error('mode is not yet implemented');\n },\n\n sample: function sample(a, b) {\n return (a / 2 + b / 2) + (b / 2 - a / 2) * (2 * Math.random() - 1);\n },\n\n variance: function variance(a, b) {\n return Math.pow(b - a, 2) / 12;\n }\n});\n\n\n\n// extend uniform function with static methods\njStat.extend(jStat.binomial, {\n pdf: function pdf(k, n, p) {\n return (p === 0 || p === 1) ?\n ((n * p) === k ? 1 : 0) :\n jStat.combination(n, k) * Math.pow(p, k) * Math.pow(1 - p, n - k);\n },\n\n cdf: function cdf(x, n, p) {\n var binomarr = [],\n k = 0;\n if (x < 0) {\n return 0;\n }\n if (x < n) {\n for (; k <= x; k++) {\n binomarr[ k ] = jStat.binomial.pdf(k, n, p);\n }\n return jStat.sum(binomarr);\n }\n return 1;\n }\n});\n\n\n\n// extend uniform function with static methods\njStat.extend(jStat.negbin, {\n pdf: function pdf(k, r, p) {\n if (k !== k >>> 0)\n return false;\n if (k < 0)\n return 0;\n return jStat.combination(k + r - 1, r - 1) *\n Math.pow(1 - p, k) * Math.pow(p, r);\n },\n\n cdf: function cdf(x, r, p) {\n var sum = 0,\n k = 0;\n if (x < 0) return 0;\n for (; k <= x; k++) {\n sum += jStat.negbin.pdf(k, r, p);\n }\n return sum;\n }\n});\n\n\n\n// extend uniform function with static methods\njStat.extend(jStat.hypgeom, {\n pdf: function pdf(k, N, m, n) {\n // Hypergeometric PDF.\n\n // A simplification of the CDF algorithm below.\n\n // k = number of successes drawn\n // N = population size\n // m = number of successes in population\n // n = number of items drawn from population\n\n if(k !== k | 0) {\n return false;\n } else if(k < 0 || k < m - (N - n)) {\n // It's impossible to have this few successes drawn.\n return 0;\n } else if(k > n || k > m) {\n // It's impossible to have this many successes drawn.\n return 0;\n } else if (m * 2 > N) {\n // More than half the population is successes.\n\n if(n * 2 > N) {\n // More than half the population is sampled.\n\n return jStat.hypgeom.pdf(N - m - n + k, N, N - m, N - n)\n } else {\n // Half or less of the population is sampled.\n\n return jStat.hypgeom.pdf(n - k, N, N - m, n);\n }\n\n } else if(n * 2 > N) {\n // Half or less is successes.\n\n return jStat.hypgeom.pdf(m - k, N, m, N - n);\n\n } else if(m < n) {\n // We want to have the number of things sampled to be less than the\n // successes available. So swap the definitions of successful and sampled.\n return jStat.hypgeom.pdf(k, N, n, m);\n } else {\n // If we get here, half or less of the population was sampled, half or\n // less of it was successes, and we had fewer sampled things than\n // successes. Now we can do this complicated iterative algorithm in an\n // efficient way.\n\n // The basic premise of the algorithm is that we partially normalize our\n // intermediate product to keep it in a numerically good region, and then\n // finish the normalization at the end.\n\n // This variable holds the scaled probability of the current number of\n // successes.\n var scaledPDF = 1;\n\n // This keeps track of how much we have normalized.\n var samplesDone = 0;\n\n for(var i = 0; i < k; i++) {\n // For every possible number of successes up to that observed...\n\n while(scaledPDF > 1 && samplesDone < n) {\n // Intermediate result is growing too big. Apply some of the\n // normalization to shrink everything.\n\n scaledPDF *= 1 - (m / (N - samplesDone));\n\n // Say we've normalized by this sample already.\n samplesDone++;\n }\n\n // Work out the partially-normalized hypergeometric PDF for the next\n // number of successes\n scaledPDF *= (n - i) * (m - i) / ((i + 1) * (N - m - n + i + 1));\n }\n\n for(; samplesDone < n; samplesDone++) {\n // Apply all the rest of the normalization\n scaledPDF *= 1 - (m / (N - samplesDone));\n }\n\n // Bound answer sanely before returning.\n return Math.min(1, Math.max(0, scaledPDF));\n }\n },\n\n cdf: function cdf(x, N, m, n) {\n // Hypergeometric CDF.\n\n // This algorithm is due to Prof. Thomas S. Ferguson, ,\n // and comes from his hypergeometric test calculator at\n // .\n\n // x = number of successes drawn\n // N = population size\n // m = number of successes in population\n // n = number of items drawn from population\n\n if(x < 0 || x < m - (N - n)) {\n // It's impossible to have this few successes drawn or fewer.\n return 0;\n } else if(x >= n || x >= m) {\n // We will always have this many successes or fewer.\n return 1;\n } else if (m * 2 > N) {\n // More than half the population is successes.\n\n if(n * 2 > N) {\n // More than half the population is sampled.\n\n return jStat.hypgeom.cdf(N - m - n + x, N, N - m, N - n)\n } else {\n // Half or less of the population is sampled.\n\n return 1 - jStat.hypgeom.cdf(n - x - 1, N, N - m, n);\n }\n\n } else if(n * 2 > N) {\n // Half or less is successes.\n\n return 1 - jStat.hypgeom.cdf(m - x - 1, N, m, N - n);\n\n } else if(m < n) {\n // We want to have the number of things sampled to be less than the\n // successes available. So swap the definitions of successful and sampled.\n return jStat.hypgeom.cdf(x, N, n, m);\n } else {\n // If we get here, half or less of the population was sampled, half or\n // less of it was successes, and we had fewer sampled things than\n // successes. Now we can do this complicated iterative algorithm in an\n // efficient way.\n\n // The basic premise of the algorithm is that we partially normalize our\n // intermediate sum to keep it in a numerically good region, and then\n // finish the normalization at the end.\n\n // Holds the intermediate, scaled total CDF.\n var scaledCDF = 1;\n\n // This variable holds the scaled probability of the current number of\n // successes.\n var scaledPDF = 1;\n\n // This keeps track of how much we have normalized.\n var samplesDone = 0;\n\n for(var i = 0; i < x; i++) {\n // For every possible number of successes up to that observed...\n\n while(scaledCDF > 1 && samplesDone < n) {\n // Intermediate result is growing too big. Apply some of the\n // normalization to shrink everything.\n\n var factor = 1 - (m / (N - samplesDone));\n\n scaledPDF *= factor;\n scaledCDF *= factor;\n\n // Say we've normalized by this sample already.\n samplesDone++;\n }\n\n // Work out the partially-normalized hypergeometric PDF for the next\n // number of successes\n scaledPDF *= (n - i) * (m - i) / ((i + 1) * (N - m - n + i + 1));\n\n // Add to the CDF answer.\n scaledCDF += scaledPDF;\n }\n\n for(; samplesDone < n; samplesDone++) {\n // Apply all the rest of the normalization\n scaledCDF *= 1 - (m / (N - samplesDone));\n }\n\n // Bound answer sanely before returning.\n return Math.min(1, Math.max(0, scaledCDF));\n }\n }\n});\n\n\n\n// extend uniform function with static methods\njStat.extend(jStat.poisson, {\n pdf: function pdf(k, l) {\n if (l < 0 || (k % 1) !== 0 || k < 0) {\n return 0;\n }\n\n return Math.pow(l, k) * Math.exp(-l) / jStat.factorial(k);\n },\n\n cdf: function cdf(x, l) {\n var sumarr = [],\n k = 0;\n if (x < 0) return 0;\n for (; k <= x; k++) {\n sumarr.push(jStat.poisson.pdf(k, l));\n }\n return jStat.sum(sumarr);\n },\n\n mean : function(l) {\n return l;\n },\n\n variance : function(l) {\n return l;\n },\n\n sample: function sample(l) {\n var p = 1, k = 0, L = Math.exp(-l);\n do {\n k++;\n p *= Math.random();\n } while (p > L);\n return k - 1;\n }\n});\n\n// extend triangular function with static methods\njStat.extend(jStat.triangular, {\n pdf: function pdf(x, a, b, c) {\n if (b <= a || c < a || c > b) {\n return NaN;\n } else {\n if (x < a || x > b) {\n return 0;\n } else if (x < c) {\n return (2 * (x - a)) / ((b - a) * (c - a));\n } else if (x === c) {\n return (2 / (b - a));\n } else { // x > c\n return (2 * (b - x)) / ((b - a) * (b - c));\n }\n }\n },\n\n cdf: function cdf(x, a, b, c) {\n if (b <= a || c < a || c > b)\n return NaN;\n if (x <= a)\n return 0;\n else if (x >= b)\n return 1;\n if (x <= c)\n return Math.pow(x - a, 2) / ((b - a) * (c - a));\n else // x > c\n return 1 - Math.pow(b - x, 2) / ((b - a) * (b - c));\n },\n\n inv: function inv(p, a, b, c) {\n if (b <= a || c < a || c > b) {\n return NaN;\n } else {\n if (p <= ((c - a) / (b - a))) {\n return a + (b - a) * Math.sqrt(p * ((c - a) / (b - a)));\n } else { // p > ((c - a) / (b - a))\n return a + (b - a) * (1 - Math.sqrt((1 - p) * (1 - ((c - a) / (b - a)))));\n }\n }\n },\n\n mean: function mean(a, b, c) {\n return (a + b + c) / 3;\n },\n\n median: function median(a, b, c) {\n if (c <= (a + b) / 2) {\n return b - Math.sqrt((b - a) * (b - c)) / Math.sqrt(2);\n } else if (c > (a + b) / 2) {\n return a + Math.sqrt((b - a) * (c - a)) / Math.sqrt(2);\n }\n },\n\n mode: function mode(a, b, c) {\n return c;\n },\n\n sample: function sample(a, b, c) {\n var u = Math.random();\n if (u < ((c - a) / (b - a)))\n return a + Math.sqrt(u * (b - a) * (c - a))\n return b - Math.sqrt((1 - u) * (b - a) * (b - c));\n },\n\n variance: function variance(a, b, c) {\n return (a * a + b * b + c * c - a * b - a * c - b * c) / 18;\n }\n});\n\n\n// extend arcsine function with static methods\njStat.extend(jStat.arcsine, {\n pdf: function pdf(x, a, b) {\n if (b <= a) return NaN;\n\n return (x <= a || x >= b) ? 0 :\n (2 / Math.PI) *\n Math.pow(Math.pow(b - a, 2) -\n Math.pow(2 * x - a - b, 2), -0.5);\n },\n\n cdf: function cdf(x, a, b) {\n if (x < a)\n return 0;\n else if (x < b)\n return (2 / Math.PI) * Math.asin(Math.sqrt((x - a)/(b - a)));\n return 1;\n },\n\n inv: function(p, a, b) {\n return a + (0.5 - 0.5 * Math.cos(Math.PI * p)) * (b - a);\n },\n\n mean: function mean(a, b) {\n if (b <= a) return NaN;\n return (a + b) / 2;\n },\n\n median: function median(a, b) {\n if (b <= a) return NaN;\n return (a + b) / 2;\n },\n\n mode: function mode(a, b) {\n throw new Error('mode is not yet implemented');\n },\n\n sample: function sample(a, b) {\n return ((a + b) / 2) + ((b - a) / 2) *\n Math.sin(2 * Math.PI * jStat.uniform.sample(0, 1));\n },\n\n variance: function variance(a, b) {\n if (b <= a) return NaN;\n return Math.pow(b - a, 2) / 8;\n }\n});\n\n\nfunction laplaceSign(x) { return x / Math.abs(x); }\n\njStat.extend(jStat.laplace, {\n pdf: function pdf(x, mu, b) {\n return (b <= 0) ? 0 : (Math.exp(-Math.abs(x - mu) / b)) / (2 * b);\n },\n\n cdf: function cdf(x, mu, b) {\n if (b <= 0) { return 0; }\n\n if(x < mu) {\n return 0.5 * Math.exp((x - mu) / b);\n } else {\n return 1 - 0.5 * Math.exp(- (x - mu) / b);\n }\n },\n\n mean: function(mu, b) {\n return mu;\n },\n\n median: function(mu, b) {\n return mu;\n },\n\n mode: function(mu, b) {\n return mu;\n },\n\n variance: function(mu, b) {\n return 2 * b * b;\n },\n\n sample: function sample(mu, b) {\n var u = Math.random() - 0.5;\n\n return mu - (b * laplaceSign(u) * Math.log(1 - (2 * Math.abs(u))));\n }\n});\n\nfunction tukeyWprob(w, rr, cc) {\n var nleg = 12;\n var ihalf = 6;\n\n var C1 = -30;\n var C2 = -50;\n var C3 = 60;\n var bb = 8;\n var wlar = 3;\n var wincr1 = 2;\n var wincr2 = 3;\n var xleg = [\n 0.981560634246719250690549090149,\n 0.904117256370474856678465866119,\n 0.769902674194304687036893833213,\n 0.587317954286617447296702418941,\n 0.367831498998180193752691536644,\n 0.125233408511468915472441369464\n ];\n var aleg = [\n 0.047175336386511827194615961485,\n 0.106939325995318430960254718194,\n 0.160078328543346226334652529543,\n 0.203167426723065921749064455810,\n 0.233492536538354808760849898925,\n 0.249147045813402785000562436043\n ];\n\n var qsqz = w * 0.5;\n\n // if w >= 16 then the integral lower bound (occurs for c=20)\n // is 0.99999999999995 so return a value of 1.\n\n if (qsqz >= bb)\n return 1.0;\n\n // find (f(w/2) - 1) ^ cc\n // (first term in integral of hartley's form).\n\n var pr_w = 2 * jStat.normal.cdf(qsqz, 0, 1, 1, 0) - 1; // erf(qsqz / M_SQRT2)\n // if pr_w ^ cc < 2e-22 then set pr_w = 0\n if (pr_w >= Math.exp(C2 / cc))\n pr_w = Math.pow(pr_w, cc);\n else\n pr_w = 0.0;\n\n // if w is large then the second component of the\n // integral is small, so fewer intervals are needed.\n\n var wincr;\n if (w > wlar)\n wincr = wincr1;\n else\n wincr = wincr2;\n\n // find the integral of second term of hartley's form\n // for the integral of the range for equal-length\n // intervals using legendre quadrature. limits of\n // integration are from (w/2, 8). two or three\n // equal-length intervals are used.\n\n // blb and bub are lower and upper limits of integration.\n\n var blb = qsqz;\n var binc = (bb - qsqz) / wincr;\n var bub = blb + binc;\n var einsum = 0.0;\n\n // integrate over each interval\n\n var cc1 = cc - 1.0;\n for (var wi = 1; wi <= wincr; wi++) {\n var elsum = 0.0;\n var a = 0.5 * (bub + blb);\n\n // legendre quadrature with order = nleg\n\n var b = 0.5 * (bub - blb);\n\n for (var jj = 1; jj <= nleg; jj++) {\n var j, xx;\n if (ihalf < jj) {\n j = (nleg - jj) + 1;\n xx = xleg[j-1];\n } else {\n j = jj;\n xx = -xleg[j-1];\n }\n var c = b * xx;\n var ac = a + c;\n\n // if exp(-qexpo/2) < 9e-14,\n // then doesn't contribute to integral\n\n var qexpo = ac * ac;\n if (qexpo > C3)\n break;\n\n var pplus = 2 * jStat.normal.cdf(ac, 0, 1, 1, 0);\n var pminus= 2 * jStat.normal.cdf(ac, w, 1, 1, 0);\n\n // if rinsum ^ (cc-1) < 9e-14,\n // then doesn't contribute to integral\n\n var rinsum = (pplus * 0.5) - (pminus * 0.5);\n if (rinsum >= Math.exp(C1 / cc1)) {\n rinsum = (aleg[j-1] * Math.exp(-(0.5 * qexpo))) * Math.pow(rinsum, cc1);\n elsum += rinsum;\n }\n }\n elsum *= (((2.0 * b) * cc) / Math.sqrt(2 * Math.PI));\n einsum += elsum;\n blb = bub;\n bub += binc;\n }\n\n // if pr_w ^ rr < 9e-14, then return 0\n pr_w += einsum;\n if (pr_w <= Math.exp(C1 / rr))\n return 0;\n\n pr_w = Math.pow(pr_w, rr);\n if (pr_w >= 1) // 1 was iMax was eps\n return 1;\n return pr_w;\n}\n\nfunction tukeyQinv(p, c, v) {\n var p0 = 0.322232421088;\n var q0 = 0.993484626060e-01;\n var p1 = -1.0;\n var q1 = 0.588581570495;\n var p2 = -0.342242088547;\n var q2 = 0.531103462366;\n var p3 = -0.204231210125;\n var q3 = 0.103537752850;\n var p4 = -0.453642210148e-04;\n var q4 = 0.38560700634e-02;\n var c1 = 0.8832;\n var c2 = 0.2368;\n var c3 = 1.214;\n var c4 = 1.208;\n var c5 = 1.4142;\n var vmax = 120.0;\n\n var ps = 0.5 - 0.5 * p;\n var yi = Math.sqrt(Math.log(1.0 / (ps * ps)));\n var t = yi + (((( yi * p4 + p3) * yi + p2) * yi + p1) * yi + p0)\n / (((( yi * q4 + q3) * yi + q2) * yi + q1) * yi + q0);\n if (v < vmax) t += (t * t * t + t) / v / 4.0;\n var q = c1 - c2 * t;\n if (v < vmax) q += -c3 / v + c4 * t / v;\n return t * (q * Math.log(c - 1.0) + c5);\n}\n\njStat.extend(jStat.tukey, {\n cdf: function cdf(q, nmeans, df) {\n // Identical implementation as the R ptukey() function as of commit 68947\n var rr = 1;\n var cc = nmeans;\n\n var nlegq = 16;\n var ihalfq = 8;\n\n var eps1 = -30.0;\n var eps2 = 1.0e-14;\n var dhaf = 100.0;\n var dquar = 800.0;\n var deigh = 5000.0;\n var dlarg = 25000.0;\n var ulen1 = 1.0;\n var ulen2 = 0.5;\n var ulen3 = 0.25;\n var ulen4 = 0.125;\n var xlegq = [\n 0.989400934991649932596154173450,\n 0.944575023073232576077988415535,\n 0.865631202387831743880467897712,\n 0.755404408355003033895101194847,\n 0.617876244402643748446671764049,\n 0.458016777657227386342419442984,\n 0.281603550779258913230460501460,\n 0.950125098376374401853193354250e-1\n ];\n var alegq = [\n 0.271524594117540948517805724560e-1,\n 0.622535239386478928628438369944e-1,\n 0.951585116824927848099251076022e-1,\n 0.124628971255533872052476282192,\n 0.149595988816576732081501730547,\n 0.169156519395002538189312079030,\n 0.182603415044923588866763667969,\n 0.189450610455068496285396723208\n ];\n\n if (q <= 0)\n return 0;\n\n // df must be > 1\n // there must be at least two values\n\n if (df < 2 || rr < 1 || cc < 2) return NaN;\n\n if (!Number.isFinite(q))\n return 1;\n\n if (df > dlarg)\n return tukeyWprob(q, rr, cc);\n\n // calculate leading constant\n\n var f2 = df * 0.5;\n var f2lf = ((f2 * Math.log(df)) - (df * Math.log(2))) - jStat.gammaln(f2);\n var f21 = f2 - 1.0;\n\n // integral is divided into unit, half-unit, quarter-unit, or\n // eighth-unit length intervals depending on the value of the\n // degrees of freedom.\n\n var ff4 = df * 0.25;\n var ulen;\n if (df <= dhaf) ulen = ulen1;\n else if (df <= dquar) ulen = ulen2;\n else if (df <= deigh) ulen = ulen3;\n else ulen = ulen4;\n\n f2lf += Math.log(ulen);\n\n // integrate over each subinterval\n\n var ans = 0.0;\n\n for (var i = 1; i <= 50; i++) {\n var otsum = 0.0;\n\n // legendre quadrature with order = nlegq\n // nodes (stored in xlegq) are symmetric around zero.\n\n var twa1 = (2 * i - 1) * ulen;\n\n for (var jj = 1; jj <= nlegq; jj++) {\n var j, t1;\n if (ihalfq < jj) {\n j = jj - ihalfq - 1;\n t1 = (f2lf + (f21 * Math.log(twa1 + (xlegq[j] * ulen))))\n - (((xlegq[j] * ulen) + twa1) * ff4);\n } else {\n j = jj - 1;\n t1 = (f2lf + (f21 * Math.log(twa1 - (xlegq[j] * ulen))))\n + (((xlegq[j] * ulen) - twa1) * ff4);\n }\n\n // if exp(t1) < 9e-14, then doesn't contribute to integral\n var qsqz;\n if (t1 >= eps1) {\n if (ihalfq < jj) {\n qsqz = q * Math.sqrt(((xlegq[j] * ulen) + twa1) * 0.5);\n } else {\n qsqz = q * Math.sqrt(((-(xlegq[j] * ulen)) + twa1) * 0.5);\n }\n\n // call wprob to find integral of range portion\n\n var wprb = tukeyWprob(qsqz, rr, cc);\n var rotsum = (wprb * alegq[j]) * Math.exp(t1);\n otsum += rotsum;\n }\n // end legendre integral for interval i\n // L200:\n }\n\n // if integral for interval i < 1e-14, then stop.\n // However, in order to avoid small area under left tail,\n // at least 1 / ulen intervals are calculated.\n if (i * ulen >= 1.0 && otsum <= eps2)\n break;\n\n // end of interval i\n // L330:\n\n ans += otsum;\n }\n\n if (otsum > eps2) { // not converged\n throw new Error('tukey.cdf failed to converge');\n }\n if (ans > 1)\n ans = 1;\n return ans;\n },\n\n inv: function(p, nmeans, df) {\n // Identical implementation as the R qtukey() function as of commit 68947\n var rr = 1;\n var cc = nmeans;\n\n var eps = 0.0001;\n var maxiter = 50;\n\n // df must be > 1 ; there must be at least two values\n if (df < 2 || rr < 1 || cc < 2) return NaN;\n\n if (p < 0 || p > 1) return NaN;\n if (p === 0) return 0;\n if (p === 1) return Infinity;\n\n // Initial value\n\n var x0 = tukeyQinv(p, cc, df);\n\n // Find prob(value < x0)\n\n var valx0 = jStat.tukey.cdf(x0, nmeans, df) - p;\n\n // Find the second iterate and prob(value < x1).\n // If the first iterate has probability value\n // exceeding p then second iterate is 1 less than\n // first iterate; otherwise it is 1 greater.\n\n var x1;\n if (valx0 > 0.0)\n x1 = Math.max(0.0, x0 - 1.0);\n else\n x1 = x0 + 1.0;\n var valx1 = jStat.tukey.cdf(x1, nmeans, df) - p;\n\n // Find new iterate\n\n var ans;\n for(var iter = 1; iter < maxiter; iter++) {\n ans = x1 - ((valx1 * (x1 - x0)) / (valx1 - valx0));\n valx0 = valx1;\n\n // New iterate must be >= 0\n\n x0 = x1;\n if (ans < 0.0) {\n ans = 0.0;\n valx1 = -p;\n }\n // Find prob(value < new iterate)\n\n valx1 = jStat.tukey.cdf(ans, nmeans, df) - p;\n x1 = ans;\n\n // If the difference between two successive\n // iterates is less than eps, stop\n\n var xabs = Math.abs(x1 - x0);\n if (xabs < eps)\n return ans;\n }\n\n throw new Error('tukey.inv failed to converge');\n }\n});\n\n}(jStat, Math));\n/* Provides functions for the solution of linear system of equations, integration, extrapolation,\n * interpolation, eigenvalue problems, differential equations and PCA analysis. */\n\n(function(jStat, Math) {\n\nvar push = Array.prototype.push;\nvar isArray = jStat.utils.isArray;\n\nfunction isUsable(arg) {\n return isArray(arg) || arg instanceof jStat;\n}\n\njStat.extend({\n\n // add a vector/matrix to a vector/matrix or scalar\n add: function add(arr, arg) {\n // check if arg is a vector or scalar\n if (isUsable(arg)) {\n if (!isUsable(arg[0])) arg = [ arg ];\n return jStat.map(arr, function(value, row, col) {\n return value + arg[row][col];\n });\n }\n return jStat.map(arr, function(value) { return value + arg; });\n },\n\n // subtract a vector or scalar from the vector\n subtract: function subtract(arr, arg) {\n // check if arg is a vector or scalar\n if (isUsable(arg)) {\n if (!isUsable(arg[0])) arg = [ arg ];\n return jStat.map(arr, function(value, row, col) {\n return value - arg[row][col] || 0;\n });\n }\n return jStat.map(arr, function(value) { return value - arg; });\n },\n\n // matrix division\n divide: function divide(arr, arg) {\n if (isUsable(arg)) {\n if (!isUsable(arg[0])) arg = [ arg ];\n return jStat.multiply(arr, jStat.inv(arg));\n }\n return jStat.map(arr, function(value) { return value / arg; });\n },\n\n // matrix multiplication\n multiply: function multiply(arr, arg) {\n var row, col, nrescols, sum, nrow, ncol, res, rescols;\n // eg: arr = 2 arg = 3 -> 6 for res[0][0] statement closure\n if (arr.length === undefined && arg.length === undefined) {\n return arr * arg;\n }\n nrow = arr.length,\n ncol = arr[0].length,\n res = jStat.zeros(nrow, nrescols = (isUsable(arg)) ? arg[0].length : ncol),\n rescols = 0;\n if (isUsable(arg)) {\n for (; rescols < nrescols; rescols++) {\n for (row = 0; row < nrow; row++) {\n sum = 0;\n for (col = 0; col < ncol; col++)\n sum += arr[row][col] * arg[col][rescols];\n res[row][rescols] = sum;\n }\n }\n return (nrow === 1 && rescols === 1) ? res[0][0] : res;\n }\n return jStat.map(arr, function(value) { return value * arg; });\n },\n\n // outer([1,2,3],[4,5,6])\n // ===\n // [[1],[2],[3]] times [[4,5,6]]\n // ->\n // [[4,5,6],[8,10,12],[12,15,18]]\n outer:function outer(A, B) {\n return jStat.multiply(A.map(function(t){ return [t] }), [B]);\n },\n\n\n // Returns the dot product of two matricies\n dot: function dot(arr, arg) {\n if (!isUsable(arr[0])) arr = [ arr ];\n if (!isUsable(arg[0])) arg = [ arg ];\n // convert column to row vector\n var left = (arr[0].length === 1 && arr.length !== 1) ? jStat.transpose(arr) : arr,\n right = (arg[0].length === 1 && arg.length !== 1) ? jStat.transpose(arg) : arg,\n res = [],\n row = 0,\n nrow = left.length,\n ncol = left[0].length,\n sum, col;\n for (; row < nrow; row++) {\n res[row] = [];\n sum = 0;\n for (col = 0; col < ncol; col++)\n sum += left[row][col] * right[row][col];\n res[row] = sum;\n }\n return (res.length === 1) ? res[0] : res;\n },\n\n // raise every element by a scalar\n pow: function pow(arr, arg) {\n return jStat.map(arr, function(value) { return Math.pow(value, arg); });\n },\n\n // exponentiate every element\n exp: function exp(arr) {\n return jStat.map(arr, function(value) { return Math.exp(value); });\n },\n\n // generate the natural log of every element\n log: function exp(arr) {\n return jStat.map(arr, function(value) { return Math.log(value); });\n },\n\n // generate the absolute values of the vector\n abs: function abs(arr) {\n return jStat.map(arr, function(value) { return Math.abs(value); });\n },\n\n // computes the p-norm of the vector\n // In the case that a matrix is passed, uses the first row as the vector\n norm: function norm(arr, p) {\n var nnorm = 0,\n i = 0;\n // check the p-value of the norm, and set for most common case\n if (isNaN(p)) p = 2;\n // check if multi-dimensional array, and make vector correction\n if (isUsable(arr[0])) arr = arr[0];\n // vector norm\n for (; i < arr.length; i++) {\n nnorm += Math.pow(Math.abs(arr[i]), p);\n }\n return Math.pow(nnorm, 1 / p);\n },\n\n // computes the angle between two vectors in rads\n // In case a matrix is passed, this uses the first row as the vector\n angle: function angle(arr, arg) {\n return Math.acos(jStat.dot(arr, arg) / (jStat.norm(arr) * jStat.norm(arg)));\n },\n\n // augment one matrix by another\n // Note: this function returns a matrix, not a jStat object\n aug: function aug(a, b) {\n var newarr = [];\n for (var i = 0; i < a.length; i++) {\n newarr.push(a[i].slice());\n }\n for (var i = 0; i < newarr.length; i++) {\n push.apply(newarr[i], b[i]);\n }\n return newarr;\n },\n\n // The inv() function calculates the inverse of a matrix\n // Create the inverse by augmenting the matrix by the identity matrix of the\n // appropriate size, and then use G-J elimination on the augmented matrix.\n inv: function inv(a) {\n var rows = a.length;\n var cols = a[0].length;\n var b = jStat.identity(rows, cols);\n var c = jStat.gauss_jordan(a, b);\n var result = [];\n var i = 0;\n var j;\n\n //We need to copy the inverse portion to a new matrix to rid G-J artifacts\n for (; i < rows; i++) {\n result[i] = [];\n for (j = cols; j < c[0].length; j++)\n result[i][j - cols] = c[i][j];\n }\n return result;\n },\n\n // calculate the determinant of a matrix\n det: function det(a) {\n var alen = a.length,\n alend = alen * 2,\n vals = new Array(alend),\n rowshift = alen - 1,\n colshift = alend - 1,\n mrow = rowshift - alen + 1,\n mcol = colshift,\n i = 0,\n result = 0,\n j;\n // check for special 2x2 case\n if (alen === 2) {\n return a[0][0] * a[1][1] - a[0][1] * a[1][0];\n }\n for (; i < alend; i++) {\n vals[i] = 1;\n }\n for (var i = 0; i < alen; i++) {\n for (j = 0; j < alen; j++) {\n vals[(mrow < 0) ? mrow + alen : mrow ] *= a[i][j];\n vals[(mcol < alen) ? mcol + alen : mcol ] *= a[i][j];\n mrow++;\n mcol--;\n }\n mrow = --rowshift - alen + 1;\n mcol = --colshift;\n }\n for (var i = 0; i < alen; i++) {\n result += vals[i];\n }\n for (; i < alend; i++) {\n result -= vals[i];\n }\n return result;\n },\n\n gauss_elimination: function gauss_elimination(a, b) {\n var i = 0,\n j = 0,\n n = a.length,\n m = a[0].length,\n factor = 1,\n sum = 0,\n x = [],\n maug, pivot, temp, k;\n a = jStat.aug(a, b);\n maug = a[0].length;\n for(var i = 0; i < n; i++) {\n pivot = a[i][i];\n j = i;\n for (k = i + 1; k < m; k++) {\n if (pivot < Math.abs(a[k][i])) {\n pivot = a[k][i];\n j = k;\n }\n }\n if (j != i) {\n for(k = 0; k < maug; k++) {\n temp = a[i][k];\n a[i][k] = a[j][k];\n a[j][k] = temp;\n }\n }\n for (j = i + 1; j < n; j++) {\n factor = a[j][i] / a[i][i];\n for(k = i; k < maug; k++) {\n a[j][k] = a[j][k] - factor * a[i][k];\n }\n }\n }\n for (var i = n - 1; i >= 0; i--) {\n sum = 0;\n for (j = i + 1; j<= n - 1; j++) {\n sum = sum + x[j] * a[i][j];\n }\n x[i] =(a[i][maug - 1] - sum) / a[i][i];\n }\n return x;\n },\n\n gauss_jordan: function gauss_jordan(a, b) {\n var m = jStat.aug(a, b),\n h = m.length,\n w = m[0].length;\n var c = 0;\n // find max pivot\n for (var y = 0; y < h; y++) {\n var maxrow = y;\n for (var y2 = y+1; y2 < h; y2++) {\n if (Math.abs(m[y2][y]) > Math.abs(m[maxrow][y]))\n maxrow = y2;\n }\n var tmp = m[y];\n m[y] = m[maxrow];\n m[maxrow] = tmp\n for (var y2 = y+1; y2 < h; y2++) {\n c = m[y2][y] / m[y][y];\n for (var x = y; x < w; x++) {\n m[y2][x] -= m[y][x] * c;\n }\n }\n }\n // backsubstitute\n for (var y = h-1; y >= 0; y--) {\n c = m[y][y];\n for (var y2 = 0; y2 < y; y2++) {\n for (var x = w-1; x > y-1; x--) {\n m[y2][x] -= m[y][x] * m[y2][y] / c;\n }\n }\n m[y][y] /= c;\n for (var x = h; x < w; x++) {\n m[y][x] /= c;\n }\n }\n return m;\n },\n\n // solve equation\n // Ax=b\n // A is upper triangular matrix\n // A=[[1,2,3],[0,4,5],[0,6,7]]\n // b=[1,2,3]\n // triaUpSolve(A,b) // -> [2.666,0.1666,1.666]\n // if you use matrix style\n // A=[[1,2,3],[0,4,5],[0,6,7]]\n // b=[[1],[2],[3]]\n // will return [[2.666],[0.1666],[1.666]]\n triaUpSolve: function triaUpSolve(A, b) {\n var size = A[0].length;\n var x = jStat.zeros(1, size)[0];\n var parts;\n var matrix_mode = false;\n\n if (b[0].length != undefined) {\n b = b.map(function(i){ return i[0] });\n matrix_mode = true;\n }\n\n jStat.arange(size - 1, -1, -1).forEach(function(i) {\n parts = jStat.arange(i + 1, size).map(function(j) {\n return x[j] * A[i][j];\n });\n x[i] = (b[i] - jStat.sum(parts)) / A[i][i];\n });\n\n if (matrix_mode)\n return x.map(function(i){ return [i] });\n return x;\n },\n\n triaLowSolve: function triaLowSolve(A, b) {\n // like to triaUpSolve but A is lower triangular matrix\n var size = A[0].length;\n var x = jStat.zeros(1, size)[0];\n var parts;\n\n var matrix_mode=false;\n if (b[0].length != undefined) {\n b = b.map(function(i){ return i[0] });\n matrix_mode = true;\n }\n\n jStat.arange(size).forEach(function(i) {\n parts = jStat.arange(i).map(function(j) {\n return A[i][j] * x[j];\n });\n x[i] = (b[i] - jStat.sum(parts)) / A[i][i];\n })\n\n if (matrix_mode)\n return x.map(function(i){ return [i] });\n return x;\n },\n\n\n // A -> [L,U]\n // A=LU\n // L is lower triangular matrix\n // U is upper triangular matrix\n lu: function lu(A) {\n var size = A.length;\n //var L=jStat.diagonal(jStat.ones(1,size)[0]);\n var L = jStat.identity(size);\n var R = jStat.zeros(A.length, A[0].length);\n var parts;\n jStat.arange(size).forEach(function(t) {\n R[0][t] = A[0][t];\n });\n jStat.arange(1, size).forEach(function(l) {\n jStat.arange(l).forEach(function(i) {\n parts = jStat.arange(i).map(function(jj) {\n return L[l][jj] * R[jj][i];\n });\n L[l][i] = (A[l][i] - jStat.sum(parts)) / R[i][i];\n });\n jStat.arange(l, size).forEach(function(j) {\n parts = jStat.arange(l).map(function(jj) {\n return L[l][jj] * R[jj][j];\n });\n R[l][j] = A[i][j] - jStat.sum(parts);\n });\n });\n return [L, R];\n },\n\n // A -> T\n // A=TT'\n // T is lower triangular matrix\n cholesky: function cholesky(A) {\n var size = A.length;\n var T = jStat.zeros(A.length, A[0].length);\n var parts;\n jStat.arange(size).forEach(function(i) {\n parts = jStat.arange(i).map(function(t) {\n return Math.pow(T[i][t],2);\n });\n T[i][i] = Math.sqrt(A[i][i] - jStat.sum(parts));\n jStat.arange(i + 1, size).forEach(function(j) {\n parts = jStat.arange(i).map(function(t) {\n return T[i][t] * T[j][t];\n });\n T[j][i] = (A[i][j] - jStat.sum(parts)) / T[i][i];\n });\n });\n return T;\n },\n\n\n gauss_jacobi: function gauss_jacobi(a, b, x, r) {\n var i = 0;\n var j = 0;\n var n = a.length;\n var l = [];\n var u = [];\n var d = [];\n var xv, c, h, xk;\n for (; i < n; i++) {\n l[i] = [];\n u[i] = [];\n d[i] = [];\n for (j = 0; j < n; j++) {\n if (i > j) {\n l[i][j] = a[i][j];\n u[i][j] = d[i][j] = 0;\n } else if (i < j) {\n u[i][j] = a[i][j];\n l[i][j] = d[i][j] = 0;\n } else {\n d[i][j] = a[i][j];\n l[i][j] = u[i][j] = 0;\n }\n }\n }\n h = jStat.multiply(jStat.multiply(jStat.inv(d), jStat.add(l, u)), -1);\n c = jStat.multiply(jStat.inv(d), b);\n xv = x;\n xk = jStat.add(jStat.multiply(h, x), c);\n i = 2;\n while (Math.abs(jStat.norm(jStat.subtract(xk,xv))) > r) {\n xv = xk;\n xk = jStat.add(jStat.multiply(h, xv), c);\n i++;\n }\n return xk;\n },\n\n gauss_seidel: function gauss_seidel(a, b, x, r) {\n var i = 0;\n var n = a.length;\n var l = [];\n var u = [];\n var d = [];\n var j, xv, c, h, xk;\n for (; i < n; i++) {\n l[i] = [];\n u[i] = [];\n d[i] = [];\n for (j = 0; j < n; j++) {\n if (i > j) {\n l[i][j] = a[i][j];\n u[i][j] = d[i][j] = 0;\n } else if (i < j) {\n u[i][j] = a[i][j];\n l[i][j] = d[i][j] = 0;\n } else {\n d[i][j] = a[i][j];\n l[i][j] = u[i][j] = 0;\n }\n }\n }\n h = jStat.multiply(jStat.multiply(jStat.inv(jStat.add(d, l)), u), -1);\n c = jStat.multiply(jStat.inv(jStat.add(d, l)), b);\n xv = x;\n xk = jStat.add(jStat.multiply(h, x), c);\n i = 2;\n while (Math.abs(jStat.norm(jStat.subtract(xk, xv))) > r) {\n xv = xk;\n xk = jStat.add(jStat.multiply(h, xv), c);\n i = i + 1;\n }\n return xk;\n },\n\n SOR: function SOR(a, b, x, r, w) {\n var i = 0;\n var n = a.length;\n var l = [];\n var u = [];\n var d = [];\n var j, xv, c, h, xk;\n for (; i < n; i++) {\n l[i] = [];\n u[i] = [];\n d[i] = [];\n for (j = 0; j < n; j++) {\n if (i > j) {\n l[i][j] = a[i][j];\n u[i][j] = d[i][j] = 0;\n } else if (i < j) {\n u[i][j] = a[i][j];\n l[i][j] = d[i][j] = 0;\n } else {\n d[i][j] = a[i][j];\n l[i][j] = u[i][j] = 0;\n }\n }\n }\n h = jStat.multiply(jStat.inv(jStat.add(d, jStat.multiply(l, w))),\n jStat.subtract(jStat.multiply(d, 1 - w),\n jStat.multiply(u, w)));\n c = jStat.multiply(jStat.multiply(jStat.inv(jStat.add(d,\n jStat.multiply(l, w))), b), w);\n xv = x;\n xk = jStat.add(jStat.multiply(h, x), c);\n i = 2;\n while (Math.abs(jStat.norm(jStat.subtract(xk, xv))) > r) {\n xv = xk;\n xk = jStat.add(jStat.multiply(h, xv), c);\n i++;\n }\n return xk;\n },\n\n householder: function householder(a) {\n var m = a.length;\n var n = a[0].length;\n var i = 0;\n var w = [];\n var p = [];\n var alpha, r, k, j, factor;\n for (; i < m - 1; i++) {\n alpha = 0;\n for (j = i + 1; j < n; j++)\n alpha += (a[j][i] * a[j][i]);\n factor = (a[i + 1][i] > 0) ? -1 : 1;\n alpha = factor * Math.sqrt(alpha);\n r = Math.sqrt((((alpha * alpha) - a[i + 1][i] * alpha) / 2));\n w = jStat.zeros(m, 1);\n w[i + 1][0] = (a[i + 1][i] - alpha) / (2 * r);\n for (k = i + 2; k < m; k++) w[k][0] = a[k][i] / (2 * r);\n p = jStat.subtract(jStat.identity(m, n),\n jStat.multiply(jStat.multiply(w, jStat.transpose(w)), 2));\n a = jStat.multiply(p, jStat.multiply(a, p));\n }\n return a;\n },\n\n // A -> [Q,R]\n // Q is orthogonal matrix\n // R is upper triangular\n QR: (function() {\n // x -> Q\n // find a orthogonal matrix Q st.\n // Qx=y\n // y is [||x||,0,0,...]\n\n // quick ref\n var sum = jStat.sum;\n var range = jStat.arange;\n\n function get_Q1(x) {\n var size = x.length;\n var norm_x = jStat.norm(x, 2);\n var e1 = jStat.zeros(1, size)[0];\n e1[0] = 1;\n var u = jStat.add(jStat.multiply(jStat.multiply(e1, norm_x), -1), x);\n var norm_u = jStat.norm(u, 2);\n var v = jStat.divide(u, norm_u);\n var Q = jStat.subtract(jStat.identity(size),\n jStat.multiply(jStat.outer(v, v), 2));\n return Q;\n }\n\n function qr(A) {\n var size = A[0].length;\n var QList = [];\n jStat.arange(size).forEach(function(i) {\n var x = jStat.slice(A, { row: { start: i }, col: i });\n var Q = get_Q1(x);\n var Qn = jStat.identity(A.length);\n Qn = jStat.sliceAssign(Qn, { row: { start: i }, col: { start: i }}, Q);\n A = jStat.multiply(Qn, A);\n QList.push(Qn);\n });\n var Q = QList.reduce(function(x, y){ return jStat.multiply(x,y) });\n var R = A;\n return [Q, R];\n }\n\n function qr2(x) {\n // quick impletation\n // https://www.stat.wisc.edu/~larget/math496/qr.html\n\n var n = x.length;\n var p = x[0].length;\n\n x = jStat.copy(x);\n r = jStat.zeros(p, p);\n\n var i,j,k;\n for(j = 0; j < p; j++){\n r[j][j] = Math.sqrt(sum(range(n).map(function(i){\n return x[i][j] * x[i][j];\n })));\n for(i = 0; i < n; i++){\n x[i][j] = x[i][j] / r[j][j];\n }\n for(k = j+1; k < p; k++){\n r[j][k] = sum(range(n).map(function(i){\n return x[i][j] * x[i][k];\n }));\n for(i = 0; i < n; i++){\n x[i][k] = x[i][k] - x[i][j]*r[j][k];\n }\n }\n }\n return [x, r];\n }\n\n return qr2;\n }()),\n\n lstsq: (function(A, b) {\n // solve least squard problem for Ax=b as QR decomposition way if b is\n // [[b1],[b2],[b3]] form will return [[x1],[x2],[x3]] array form solution\n // else b is [b1,b2,b3] form will return [x1,x2,x3] array form solution\n function R_I(A) {\n A = jStat.copy(A);\n var size = A.length;\n var I = jStat.identity(size);\n jStat.arange(size - 1, -1, -1).forEach(function(i) {\n jStat.sliceAssign(\n I, { row: i }, jStat.divide(jStat.slice(I, { row: i }), A[i][i]));\n jStat.sliceAssign(\n A, { row: i }, jStat.divide(jStat.slice(A, { row: i }), A[i][i]));\n jStat.arange(i).forEach(function(j) {\n var c = jStat.multiply(A[j][i], -1);\n var Aj = jStat.slice(A, { row: j });\n var cAi = jStat.multiply(jStat.slice(A, { row: i }), c);\n jStat.sliceAssign(A, { row: j }, jStat.add(Aj, cAi));\n var Ij = jStat.slice(I, { row: j });\n var cIi = jStat.multiply(jStat.slice(I, { row: i }), c);\n jStat.sliceAssign(I, { row: j }, jStat.add(Ij, cIi));\n })\n });\n return I;\n }\n\n function qr_solve(A, b){\n var array_mode = false;\n if (b[0].length === undefined) {\n // [c1,c2,c3] mode\n b = b.map(function(x){ return [x] });\n array_mode = true;\n }\n var QR = jStat.QR(A);\n var Q = QR[0];\n var R = QR[1];\n var attrs = A[0].length;\n var Q1 = jStat.slice(Q,{col:{end:attrs}});\n var R1 = jStat.slice(R,{row:{end:attrs}});\n var RI = R_I(R1);\n\t var Q2 = jStat.transpose(Q1);\n\n\t if(Q2[0].length === undefined){\n\t\t Q2 = [Q2]; // The confusing jStat.multifly implementation threat nature process again.\n\t }\n\n var x = jStat.multiply(jStat.multiply(RI, Q2), b);\n\n\t if(x.length === undefined){\n\t\t x = [[x]]; // The confusing jStat.multifly implementation threat nature process again.\n\t }\n\n\n if (array_mode)\n return x.map(function(i){ return i[0] });\n return x;\n }\n\n return qr_solve;\n }()),\n\n jacobi: function jacobi(a) {\n var condition = 1;\n var count = 0;\n var n = a.length;\n var e = jStat.identity(n, n);\n var ev = [];\n var b, i, j, p, q, maxim, theta, s;\n // condition === 1 only if tolerance is not reached\n while (condition === 1) {\n count++;\n maxim = a[0][1];\n p = 0;\n q = 1;\n for (var i = 0; i < n; i++) {\n for (j = 0; j < n; j++) {\n if (i != j) {\n if (maxim < Math.abs(a[i][j])) {\n maxim = Math.abs(a[i][j]);\n p = i;\n q = j;\n }\n }\n }\n }\n if (a[p][p] === a[q][q])\n theta = (a[p][q] > 0) ? Math.PI / 4 : -Math.PI / 4;\n else\n theta = Math.atan(2 * a[p][q] / (a[p][p] - a[q][q])) / 2;\n s = jStat.identity(n, n);\n s[p][p] = Math.cos(theta);\n s[p][q] = -Math.sin(theta);\n s[q][p] = Math.sin(theta);\n s[q][q] = Math.cos(theta);\n // eigen vector matrix\n e = jStat.multiply(e, s);\n b = jStat.multiply(jStat.multiply(jStat.inv(s), a), s);\n a = b;\n condition = 0;\n for (var i = 1; i < n; i++) {\n for (j = 1; j < n; j++) {\n if (i != j && Math.abs(a[i][j]) > 0.001) {\n condition = 1;\n }\n }\n }\n }\n for (var i = 0; i < n; i++) ev.push(a[i][i]);\n //returns both the eigenvalue and eigenmatrix\n return [e, ev];\n },\n\n rungekutta: function rungekutta(f, h, p, t_j, u_j, order) {\n var k1, k2, u_j1, k3, k4;\n if (order === 2) {\n while (t_j <= p) {\n k1 = h * f(t_j, u_j);\n k2 = h * f(t_j + h, u_j + k1);\n u_j1 = u_j + (k1 + k2) / 2;\n u_j = u_j1;\n t_j = t_j + h;\n }\n }\n if (order === 4) {\n while (t_j <= p) {\n k1 = h * f(t_j, u_j);\n k2 = h * f(t_j + h / 2, u_j + k1 / 2);\n k3 = h * f(t_j + h / 2, u_j + k2 / 2);\n k4 = h * f(t_j +h, u_j + k3);\n u_j1 = u_j + (k1 + 2 * k2 + 2 * k3 + k4) / 6;\n u_j = u_j1;\n t_j = t_j + h;\n }\n }\n return u_j;\n },\n\n romberg: function romberg(f, a, b, order) {\n var i = 0;\n var h = (b - a) / 2;\n var x = [];\n var h1 = [];\n var g = [];\n var m, a1, j, k, I, d;\n while (i < order / 2) {\n I = f(a);\n for (j = a, k = 0; j <= b; j = j + h, k++) x[k] = j;\n m = x.length;\n for (j = 1; j < m - 1; j++) {\n I += (((j % 2) !== 0) ? 4 : 2) * f(x[j]);\n }\n I = (h / 3) * (I + f(b));\n g[i] = I;\n h /= 2;\n i++;\n }\n a1 = g.length;\n m = 1;\n while (a1 !== 1) {\n for (j = 0; j < a1 - 1; j++)\n h1[j] = ((Math.pow(4, m)) * g[j + 1] - g[j]) / (Math.pow(4, m) - 1);\n a1 = h1.length;\n g = h1;\n h1 = [];\n m++;\n }\n return g;\n },\n\n richardson: function richardson(X, f, x, h) {\n function pos(X, x) {\n var i = 0;\n var n = X.length;\n var p;\n for (; i < n; i++)\n if (X[i] === x) p = i;\n return p;\n }\n var n = X.length,\n h_min = Math.abs(x - X[pos(X, x) + 1]),\n i = 0,\n g = [],\n h1 = [],\n y1, y2, m, a, j;\n while (h >= h_min) {\n y1 = pos(X, x + h);\n y2 = pos(X, x);\n g[i] = (f[y1] - 2 * f[y2] + f[2 * y2 - y1]) / (h * h);\n h /= 2;\n i++;\n }\n a = g.length;\n m = 1;\n while (a != 1) {\n for (j = 0; j < a - 1; j++)\n h1[j] = ((Math.pow(4, m)) * g[j + 1] - g[j]) / (Math.pow(4, m) - 1);\n a = h1.length;\n g = h1;\n h1 = [];\n m++;\n }\n return g;\n },\n\n simpson: function simpson(f, a, b, n) {\n var h = (b - a) / n;\n var I = f(a);\n var x = [];\n var j = a;\n var k = 0;\n var i = 1;\n var m;\n for (; j <= b; j = j + h, k++)\n x[k] = j;\n m = x.length;\n for (; i < m - 1; i++) {\n I += ((i % 2 !== 0) ? 4 : 2) * f(x[i]);\n }\n return (h / 3) * (I + f(b));\n },\n\n hermite: function hermite(X, F, dF, value) {\n var n = X.length;\n var p = 0;\n var i = 0;\n var l = [];\n var dl = [];\n var A = [];\n var B = [];\n var j;\n for (; i < n; i++) {\n l[i] = 1;\n for (j = 0; j < n; j++) {\n if (i != j) l[i] *= (value - X[j]) / (X[i] - X[j]);\n }\n dl[i] = 0;\n for (j = 0; j < n; j++) {\n if (i != j) dl[i] += 1 / (X [i] - X[j]);\n }\n A[i] = (1 - 2 * (value - X[i]) * dl[i]) * (l[i] * l[i]);\n B[i] = (value - X[i]) * (l[i] * l[i]);\n p += (A[i] * F[i] + B[i] * dF[i]);\n }\n return p;\n },\n\n lagrange: function lagrange(X, F, value) {\n var p = 0;\n var i = 0;\n var j, l;\n var n = X.length;\n for (; i < n; i++) {\n l = F[i];\n for (j = 0; j < n; j++) {\n // calculating the lagrange polynomial L_i\n if (i != j) l *= (value - X[j]) / (X[i] - X[j]);\n }\n // adding the lagrange polynomials found above\n p += l;\n }\n return p;\n },\n\n cubic_spline: function cubic_spline(X, F, value) {\n var n = X.length;\n var i = 0, j;\n var A = [];\n var B = [];\n var alpha = [];\n var c = [];\n var h = [];\n var b = [];\n var d = [];\n for (; i < n - 1; i++)\n h[i] = X[i + 1] - X[i];\n alpha[0] = 0;\n for (var i = 1; i < n - 1; i++) {\n alpha[i] = (3 / h[i]) * (F[i + 1] - F[i]) -\n (3 / h[i-1]) * (F[i] - F[i-1]);\n }\n for (var i = 1; i < n - 1; i++) {\n A[i] = [];\n B[i] = [];\n A[i][i-1] = h[i-1];\n A[i][i] = 2 * (h[i - 1] + h[i]);\n A[i][i+1] = h[i];\n B[i][0] = alpha[i];\n }\n c = jStat.multiply(jStat.inv(A), B);\n for (j = 0; j < n - 1; j++) {\n b[j] = (F[j + 1] - F[j]) / h[j] - h[j] * (c[j + 1][0] + 2 * c[j][0]) / 3;\n d[j] = (c[j + 1][0] - c[j][0]) / (3 * h[j]);\n }\n for (j = 0; j < n; j++) {\n if (X[j] > value) break;\n }\n j -= 1;\n return F[j] + (value - X[j]) * b[j] + jStat.sq(value-X[j]) *\n c[j] + (value - X[j]) * jStat.sq(value - X[j]) * d[j];\n },\n\n gauss_quadrature: function gauss_quadrature() {\n throw new Error('gauss_quadrature not yet implemented');\n },\n\n PCA: function PCA(X) {\n var m = X.length;\n var n = X[0].length;\n var flag = false;\n var i = 0;\n var j, temp1;\n var u = [];\n var D = [];\n var result = [];\n var temp2 = [];\n var Y = [];\n var Bt = [];\n var B = [];\n var C = [];\n var V = [];\n var Vt = [];\n for (var i = 0; i < m; i++) {\n u[i] = jStat.sum(X[i]) / n;\n }\n for (var i = 0; i < n; i++) {\n B[i] = [];\n for(j = 0; j < m; j++) {\n B[i][j] = X[j][i] - u[j];\n }\n }\n B = jStat.transpose(B);\n for (var i = 0; i < m; i++) {\n C[i] = [];\n for (j = 0; j < m; j++) {\n C[i][j] = (jStat.dot([B[i]], [B[j]])) / (n - 1);\n }\n }\n result = jStat.jacobi(C);\n V = result[0];\n D = result[1];\n Vt = jStat.transpose(V);\n for (var i = 0; i < D.length; i++) {\n for (j = i; j < D.length; j++) {\n if(D[i] < D[j]) {\n temp1 = D[i];\n D[i] = D[j];\n D[j] = temp1;\n temp2 = Vt[i];\n Vt[i] = Vt[j];\n Vt[j] = temp2;\n }\n }\n }\n Bt = jStat.transpose(B);\n for (var i = 0; i < m; i++) {\n Y[i] = [];\n for (j = 0; j < Bt.length; j++) {\n Y[i][j] = jStat.dot([Vt[i]], [Bt[j]]);\n }\n }\n return [X, D, Vt, Y];\n }\n});\n\n// extend jStat.fn with methods that require one argument\n(function(funcs) {\n for (var i = 0; i < funcs.length; i++) (function(passfunc) {\n jStat.fn[passfunc] = function(arg, func) {\n var tmpthis = this;\n // check for callback\n if (func) {\n setTimeout(function() {\n func.call(tmpthis, jStat.fn[passfunc].call(tmpthis, arg));\n }, 15);\n return this;\n }\n if (typeof jStat[passfunc](this, arg) === 'number')\n return jStat[passfunc](this, arg);\n else\n return jStat(jStat[passfunc](this, arg));\n };\n }(funcs[i]));\n}('add divide multiply subtract dot pow exp log abs norm angle'.split(' ')));\n\n}(jStat, Math));\n(function(jStat, Math) {\n\nvar slice = [].slice;\nvar isNumber = jStat.utils.isNumber;\nvar isArray = jStat.utils.isArray;\n\n// flag==true denotes use of sample standard deviation\n// Z Statistics\njStat.extend({\n // 2 different parameter lists:\n // (value, mean, sd)\n // (value, array, flag)\n zscore: function zscore() {\n var args = slice.call(arguments);\n if (isNumber(args[1])) {\n return (args[0] - args[1]) / args[2];\n }\n return (args[0] - jStat.mean(args[1])) / jStat.stdev(args[1], args[2]);\n },\n\n // 3 different paramter lists:\n // (value, mean, sd, sides)\n // (zscore, sides)\n // (value, array, sides, flag)\n ztest: function ztest() {\n var args = slice.call(arguments);\n var z;\n if (isArray(args[1])) {\n // (value, array, sides, flag)\n z = jStat.zscore(args[0],args[1],args[3]);\n return (args[2] === 1) ?\n (jStat.normal.cdf(-Math.abs(z), 0, 1)) :\n (jStat.normal.cdf(-Math.abs(z), 0, 1)*2);\n } else {\n if (args.length > 2) {\n // (value, mean, sd, sides)\n z = jStat.zscore(args[0],args[1],args[2]);\n return (args[3] === 1) ?\n (jStat.normal.cdf(-Math.abs(z),0,1)) :\n (jStat.normal.cdf(-Math.abs(z),0,1)* 2);\n } else {\n // (zscore, sides)\n z = args[0];\n return (args[1] === 1) ?\n (jStat.normal.cdf(-Math.abs(z),0,1)) :\n (jStat.normal.cdf(-Math.abs(z),0,1)*2);\n }\n }\n }\n});\n\njStat.extend(jStat.fn, {\n zscore: function zscore(value, flag) {\n return (value - this.mean()) / this.stdev(flag);\n },\n\n ztest: function ztest(value, sides, flag) {\n var zscore = Math.abs(this.zscore(value, flag));\n return (sides === 1) ?\n (jStat.normal.cdf(-zscore, 0, 1)) :\n (jStat.normal.cdf(-zscore, 0, 1) * 2);\n }\n});\n\n// T Statistics\njStat.extend({\n // 2 parameter lists\n // (value, mean, sd, n)\n // (value, array)\n tscore: function tscore() {\n var args = slice.call(arguments);\n return (args.length === 4) ?\n ((args[0] - args[1]) / (args[2] / Math.sqrt(args[3]))) :\n ((args[0] - jStat.mean(args[1])) /\n (jStat.stdev(args[1], true) / Math.sqrt(args[1].length)));\n },\n\n // 3 different paramter lists:\n // (value, mean, sd, n, sides)\n // (tscore, n, sides)\n // (value, array, sides)\n ttest: function ttest() {\n var args = slice.call(arguments);\n var tscore;\n if (args.length === 5) {\n tscore = Math.abs(jStat.tscore(args[0], args[1], args[2], args[3]));\n return (args[4] === 1) ?\n (jStat.studentt.cdf(-tscore, args[3]-1)) :\n (jStat.studentt.cdf(-tscore, args[3]-1)*2);\n }\n if (isNumber(args[1])) {\n tscore = Math.abs(args[0])\n return (args[2] == 1) ?\n (jStat.studentt.cdf(-tscore, args[1]-1)) :\n (jStat.studentt.cdf(-tscore, args[1]-1) * 2);\n }\n tscore = Math.abs(jStat.tscore(args[0], args[1]))\n return (args[2] == 1) ?\n (jStat.studentt.cdf(-tscore, args[1].length-1)) :\n (jStat.studentt.cdf(-tscore, args[1].length-1) * 2);\n }\n});\n\njStat.extend(jStat.fn, {\n tscore: function tscore(value) {\n return (value - this.mean()) / (this.stdev(true) / Math.sqrt(this.cols()));\n },\n\n ttest: function ttest(value, sides) {\n return (sides === 1) ?\n (1 - jStat.studentt.cdf(Math.abs(this.tscore(value)), this.cols()-1)) :\n (jStat.studentt.cdf(-Math.abs(this.tscore(value)), this.cols()-1)*2);\n }\n});\n\n// F Statistics\njStat.extend({\n // Paramter list is as follows:\n // (array1, array2, array3, ...)\n // or it is an array of arrays\n // array of arrays conversion\n anovafscore: function anovafscore() {\n var args = slice.call(arguments),\n expVar, sample, sampMean, sampSampMean, tmpargs, unexpVar, i, j;\n if (args.length === 1) {\n tmpargs = new Array(args[0].length);\n for (var i = 0; i < args[0].length; i++) {\n tmpargs[i] = args[0][i];\n }\n args = tmpargs;\n }\n // 2 sample case\n if (args.length === 2) {\n return jStat.variance(args[0]) / jStat.variance(args[1]);\n }\n // Builds sample array\n sample = new Array();\n for (var i = 0; i < args.length; i++) {\n sample = sample.concat(args[i]);\n }\n sampMean = jStat.mean(sample);\n // Computes the explained variance\n expVar = 0;\n for (var i = 0; i < args.length; i++) {\n expVar = expVar + args[i].length * Math.pow(jStat.mean(args[i]) - sampMean, 2);\n }\n expVar /= (args.length - 1);\n // Computes unexplained variance\n unexpVar = 0;\n for (var i = 0; i < args.length; i++) {\n sampSampMean = jStat.mean(args[i]);\n for (j = 0; j < args[i].length; j++) {\n unexpVar += Math.pow(args[i][j] - sampSampMean, 2);\n }\n }\n unexpVar /= (sample.length - args.length);\n return expVar / unexpVar;\n },\n\n // 2 different paramter setups\n // (array1, array2, array3, ...)\n // (anovafscore, df1, df2)\n anovaftest: function anovaftest() {\n var args = slice.call(arguments),\n df1, df2, n, i;\n if (isNumber(args[0])) {\n return 1 - jStat.centralF.cdf(args[0], args[1], args[2]);\n }\n anovafscore = jStat.anovafscore(args);\n df1 = args.length - 1;\n n = 0;\n for (var i = 0; i < args.length; i++) {\n n = n + args[i].length;\n }\n df2 = n - df1 - 1;\n return 1 - jStat.centralF.cdf(anovafscore, df1, df2);\n },\n\n ftest: function ftest(fscore, df1, df2) {\n return 1 - jStat.centralF.cdf(fscore, df1, df2);\n }\n});\n\njStat.extend(jStat.fn, {\n anovafscore: function anovafscore() {\n return jStat.anovafscore(this.toArray());\n },\n\n anovaftes: function anovaftes() {\n var n = 0;\n var i;\n for (var i = 0; i < this.length; i++) {\n n = n + this[i].length;\n }\n return jStat.ftest(this.anovafscore(), this.length - 1, n - this.length);\n }\n});\n\n// Tukey's range test\njStat.extend({\n // 2 parameter lists\n // (mean1, mean2, n1, n2, sd)\n // (array1, array2, sd)\n qscore: function qscore() {\n var args = slice.call(arguments);\n var mean1, mean2, n1, n2, sd;\n if (isNumber(args[0])) {\n mean1 = args[0];\n mean2 = args[1];\n n1 = args[2];\n n2 = args[3];\n sd = args[4];\n } else {\n mean1 = jStat.mean(args[0]);\n mean2 = jStat.mean(args[1]);\n n1 = args[0].length;\n n2 = args[1].length;\n sd = args[2];\n }\n return Math.abs(mean1 - mean2) / (sd * Math.sqrt((1 / n1 + 1 / n2) / 2));\n },\n\n // 3 different parameter lists:\n // (qscore, n, k)\n // (mean1, mean2, n1, n2, sd, n, k)\n // (array1, array2, sd, n, k)\n qtest: function qtest() {\n var args = slice.call(arguments);\n\n var qscore;\n if (args.length === 3) {\n qscore = args[0];\n args = args.slice(1);\n } else if (args.length === 7) {\n qscore = jStat.qscore(args[0], args[1], args[2], args[3], args[4]);\n args = args.slice(5);\n } else {\n qscore = jStat.qscore(args[0], args[1], args[2]);\n args = args.slice(3);\n }\n\n var n = args[0];\n var k = args[1];\n\n return 1 - jStat.tukey.cdf(qscore, k, n - k);\n },\n\n tukeyhsd: function tukeyhsd(arrays) {\n var sd = jStat.pooledstdev(arrays);\n var means = arrays.map(function (arr) {return jStat.mean(arr);});\n var n = arrays.reduce(function (n, arr) {return n + arr.length;}, 0);\n\n var results = [];\n for (var i = 0; i < arrays.length; ++i) {\n for (var j = i + 1; j < arrays.length; ++j) {\n var p = jStat.qtest(means[i], means[j], arrays[i].length, arrays[j].length, sd, n, arrays.length);\n results.push([[i, j], p]);\n }\n }\n\n return results;\n }\n});\n\n// Error Bounds\njStat.extend({\n // 2 different parameter setups\n // (value, alpha, sd, n)\n // (value, alpha, array)\n normalci: function normalci() {\n var args = slice.call(arguments),\n ans = new Array(2),\n change;\n if (args.length === 4) {\n change = Math.abs(jStat.normal.inv(args[1] / 2, 0, 1) *\n args[2] / Math.sqrt(args[3]));\n } else {\n change = Math.abs(jStat.normal.inv(args[1] / 2, 0, 1) *\n jStat.stdev(args[2]) / Math.sqrt(args[2].length));\n }\n ans[0] = args[0] - change;\n ans[1] = args[0] + change;\n return ans;\n },\n\n // 2 different parameter setups\n // (value, alpha, sd, n)\n // (value, alpha, array)\n tci: function tci() {\n var args = slice.call(arguments),\n ans = new Array(2),\n change;\n if (args.length === 4) {\n change = Math.abs(jStat.studentt.inv(args[1] / 2, args[3] - 1) *\n args[2] / Math.sqrt(args[3]));\n } else {\n change = Math.abs(jStat.studentt.inv(args[1] / 2, args[2].length - 1) *\n jStat.stdev(args[2], true) / Math.sqrt(args[2].length));\n }\n ans[0] = args[0] - change;\n ans[1] = args[0] + change;\n return ans;\n },\n\n significant: function significant(pvalue, alpha) {\n return pvalue < alpha;\n }\n});\n\njStat.extend(jStat.fn, {\n normalci: function normalci(value, alpha) {\n return jStat.normalci(value, alpha, this.toArray());\n },\n\n tci: function tci(value, alpha) {\n return jStat.tci(value, alpha, this.toArray());\n }\n});\n\n// internal method for calculating the z-score for a difference of proportions test\nfunction differenceOfProportions(p1, n1, p2, n2) {\n if (p1 > 1 || p2 > 1 || p1 <= 0 || p2 <= 0) {\n throw new Error(\"Proportions should be greater than 0 and less than 1\")\n }\n var pooled = (p1 * n1 + p2 * n2) / (n1 + n2);\n var se = Math.sqrt(pooled * (1 - pooled) * ((1/n1) + (1/n2)));\n return (p1 - p2) / se;\n}\n\n// Difference of Proportions\njStat.extend(jStat.fn, {\n oneSidedDifferenceOfProportions: function oneSidedDifferenceOfProportions(p1, n1, p2, n2) {\n var z = differenceOfProportions(p1, n1, p2, n2);\n return jStat.ztest(z, 1);\n },\n\n twoSidedDifferenceOfProportions: function twoSidedDifferenceOfProportions(p1, n1, p2, n2) {\n var z = differenceOfProportions(p1, n1, p2, n2);\n return jStat.ztest(z, 2);\n }\n});\n\n}(jStat, Math));\njStat.models = (function(){\n\n function sub_regress(endog, exog) {\n return ols(endog, exog);\n }\n\n function sub_regress(exog) {\n var var_count = exog[0].length;\n var modelList = jStat.arange(var_count).map(function(endog_index) {\n var exog_index =\n jStat.arange(var_count).filter(function(i){return i!==endog_index});\n return ols(jStat.col(exog, endog_index).map(function(x){ return x[0] }),\n jStat.col(exog, exog_index))\n });\n return modelList;\n }\n\n // do OLS model regress\n // exog have include const columns ,it will not generate it .In fact, exog is\n // \"design matrix\" look at\n //https://en.wikipedia.org/wiki/Design_matrix\n function ols(endog, exog) {\n var nobs = endog.length;\n var df_model = exog[0].length - 1;\n var df_resid = nobs-df_model - 1;\n var coef = jStat.lstsq(exog, endog);\n var predict =\n jStat.multiply(exog, coef.map(function(x) { return [x] }))\n .map(function(p) { return p[0] });\n var resid = jStat.subtract(endog, predict);\n var ybar = jStat.mean(endog);\n // constant cause problem\n // var SST = jStat.sum(endog.map(function(y) {\n // return Math.pow(y-ybar,2);\n // }));\n var SSE = jStat.sum(predict.map(function(f) {\n return Math.pow(f - ybar, 2);\n }));\n var SSR = jStat.sum(endog.map(function(y, i) {\n return Math.pow(y - predict[i], 2);\n }));\n var SST = SSE + SSR;\n var R2 = (SSE / SST);\n return {\n exog:exog,\n endog:endog,\n nobs:nobs,\n df_model:df_model,\n df_resid:df_resid,\n coef:coef,\n predict:predict,\n resid:resid,\n ybar:ybar,\n SST:SST,\n SSE:SSE,\n SSR:SSR,\n R2:R2\n };\n }\n\n // H0: b_I=0\n // H1: b_I!=0\n function t_test(model) {\n var subModelList = sub_regress(model.exog);\n //var sigmaHat=jStat.stdev(model.resid);\n var sigmaHat = Math.sqrt(model.SSR / (model.df_resid));\n var seBetaHat = subModelList.map(function(mod) {\n var SST = mod.SST;\n var R2 = mod.R2;\n return sigmaHat / Math.sqrt(SST * (1 - R2));\n });\n var tStatistic = model.coef.map(function(coef, i) {\n return (coef - 0) / seBetaHat[i];\n });\n var pValue = tStatistic.map(function(t) {\n var leftppf = jStat.studentt.cdf(t, model.df_resid);\n return (leftppf > 0.5 ? 1 - leftppf : leftppf) * 2;\n });\n var c = jStat.studentt.inv(0.975, model.df_resid);\n var interval95 = model.coef.map(function(coef, i) {\n var d = c * seBetaHat[i];\n return [coef - d, coef + d];\n })\n return {\n se: seBetaHat,\n t: tStatistic,\n p: pValue,\n sigmaHat: sigmaHat,\n interval95: interval95\n };\n }\n\n function F_test(model) {\n var F_statistic =\n (model.R2 / model.df_model) / ((1 - model.R2) / model.df_resid);\n var fcdf = function(x, n1, n2) {\n return jStat.beta.cdf(x / (n2 / n1 + x), n1 / 2, n2 / 2)\n }\n var pvalue = 1 - fcdf(F_statistic, model.df_model, model.df_resid);\n return { F_statistic: F_statistic, pvalue: pvalue };\n }\n\n function ols_wrap(endog, exog) {\n var model = ols(endog,exog);\n var ttest = t_test(model);\n var ftest = F_test(model);\n // Provide the Wherry / Ezekiel / McNemar / Cohen Adjusted R^2\n // Which matches the 'adjusted R^2' provided by R's lm package\n var adjust_R2 =\n 1 - (1 - model.R2) * ((model.nobs - 1) / (model.df_resid));\n model.t = ttest;\n model.f = ftest;\n model.adjust_R2 = adjust_R2;\n return model;\n }\n\n return { ols: ols_wrap };\n})();\n // Make it compatible with previous version.\n jStat.jStat = jStat;\n\n return jStat;\n});\n\n\n/***/ })\n/******/ ]);", null);
};
/***/ }),
diff --git a/packages/oncoprintjs/src/js/workers/clustering-worker.js b/packages/oncoprintjs/src/js/workers/clustering-worker.js
index 351f007588e..d08d0f12c30 100644
--- a/packages/oncoprintjs/src/js/workers/clustering-worker.js
+++ b/packages/oncoprintjs/src/js/workers/clustering-worker.js
@@ -97,18 +97,25 @@ var preRankedSpearmanDist = function(item1, item2) {
*/
var _prepareForDistanceFunction = function(inputItems) {
//pre-calculate ranks and configure to use last step of SPEARMAN as distance function:
+ // and put all NaNs items at the end
+ var allNaN = [];
+ var notAllNaN = [];
for (var i = 0; i < inputItems.length; i++) {
var inputItem = inputItems[i];
//check if all NaNs:
inputItem.isAllNaNs = isAllNaNs(inputItem.orderedValueList);
if (inputItem.isAllNaNs) {
+ allNaN.push(inputItem);
continue;
+ } else {
+ notAllNaN.push(inputItem);
}
//rank using fractional ranking:
var ranks = jStat.rank(inputItem.orderedValueList);
//calculate deviation:
inputItem.preProcessedValueList = ranks;
}
+ return notAllNaN.concat(allNaN);
}
/**
@@ -169,7 +176,7 @@ var hclusterCases = function(casesAndEntitites) {
return inputItems;
}
//else, normal clustering:
- _prepareForDistanceFunction(inputItems);
+ inputItems = _prepareForDistanceFunction(inputItems);
var clusters = clusterfck.hcluster(inputItems, preRankedSpearmanDist);
return clusters.clusters(1)[0];
}