[polymer] Merge of master into polymer10-migration

tracing/third_party/mannwhitneyu/mannwhitneyu.js

+'use strict';
+
+(function(exports) {
+
+    var rank = {
+        /*
+         * Standart ranking
+         *
+         * The MIT License, Copyright (c) 2014 Ben Magyar
+         */
+        standard: function(array, key) {
+            // sort the array
+            array = array.sort(function(a, b) {
+                var x = a[key];
+                var y = b[key];
+                return ((x < y) ? -1 : ((x > y) ? 1 : 0));
+            });
+            // assign a naive ranking
+            for (var i = 1; i < array.length + 1; i++) {
+                array[i - 1]['rank'] = i;
+            }
+            return array;
+        },
+        /*
+         * Fractional ranking
+         *
+         * The MIT License, Copyright (c) 2014 Ben Magyar
+         */
+        fractional: function(array, key) {
+            array = this.standard(array, key);
+            // now apply fractional
+            var pos = 0;
+            while (pos < array.length) {
+                var sum = 0;
+                var i = 0;
+                for (i = 0; array[pos + i + 1] && (array[pos + i][key] === array[pos + i + 1][key]); i++) {
+                    sum += array[pos + i]['rank'];
+                }
+                sum += array[pos + i]['rank'];
+                var endPos = pos + i + 1;
+                for (pos; pos < endPos; pos++) {
+                    array[pos]['rank'] = sum / (i + 1);
+                }
+                pos = endPos;
+            }
+            return array;
+        },
+        rank: function(x, y) {
+            var nx = x.length,
+                ny = y.length,
+                combined = [],
+                ranked;
+            while (nx--) {
+                combined.push({
+                    set: 'x',
+                    val: x[nx]
+                });
+            }
+            while (ny--) {
+                combined.push({
+                    set: 'y',
+                    val: y[ny]
+                });
+            }
+            ranked = this.fractional(combined, 'val');
+            return ranked
+        }
+    };
+
+    /*
+    * Error function
+    *
+    * The MIT License, Copyright (c) 2013 jStat
+    */
+    var erf = function erf(x) {
+        var cof = [-1.3026537197817094, 6.4196979235649026e-1, 1.9476473204185836e-2, -9.561514786808631e-3, -9.46595344482036e-4, 3.66839497852761e-4,
+            4.2523324806907e-5, -2.0278578112534e-5, -1.624290004647e-6,
+            1.303655835580e-6, 1.5626441722e-8, -8.5238095915e-8,
+            6.529054439e-9, 5.059343495e-9, -9.91364156e-10, -2.27365122e-10, 9.6467911e-11, 2.394038e-12, -6.886027e-12, 8.94487e-13, 3.13092e-13, -1.12708e-13, 3.81e-16, 7.106e-15, -1.523e-15, -9.4e-17, 1.21e-16, -2.8e-17
+        ];
+        var j = cof.length - 1;
+        var isneg = false;
+        var d = 0;
+        var dd = 0;
+        var t, ty, tmp, res;
+
+        if (x < 0) {
+            x = -x;
+            isneg = true;
+        }
+
+        t = 2 / (2 + x);
+        ty = 4 * t - 2;
+
+        for (; j > 0; j--) {
+            tmp = d;
+            d = ty * d - dd + cof[j];
+            dd = tmp;
+        }
+
+        res = t * Math.exp(-x * x + 0.5 * (cof[0] + ty * d) - dd);
+        return isneg ? res - 1 : 1 - res;
+    };
+
+    /*
+    * Normal distribution CDF
+    *
+    * The MIT License, Copyright (c) 2013 jStat
+    */
+    var dnorm = function(x, mean, std) {
+        return 0.5 * (1 + erf((x - mean) / Math.sqrt(2 * std * std)));
+    }
+
+    var statistic = function(x, y) {
+        var ranked = rank.rank(x, y),
+            nr = ranked.length,
+            nx = x.length,
+            ny = y.length,
+            ranksums = {
+                x: 0,
+                y: 0
+            },
+            i = 0, t = 0, nt = 1, tcf, ux, uy;
+
+        while (i < nr) {
+            if (i > 0) {
+                if (ranked[i].val == ranked[i-1].val) {
+                    nt++;
+                } else {
+                    if (nt > 1) {
+                        t += Math.pow(nt, 3) - nt
+                        nt = 1;
+                    }
+                }
+            }
+            ranksums[ranked[i].set] += ranked[i].rank
+            i++;
+        }
+        tcf = 1 - (t / (Math.pow(nr, 3) - nr))
+        ux = nx*ny + (nx*(nx+1)/2) - ranksums.x;
+        uy = nx*ny - ux;
+
+        return {
+            tcf: tcf,
+            ux: ux,
+            uy: uy,
+            big: Math.max(ux, uy),
+            small: Math.min(ux, uy)
+        }
+    }
+
+    exports.test = function(x, y, alt, corr) {
+        // set default value for alternative
+        alt = typeof alt !== 'undefined' ? alt : 'two-sided';
+        // set default value for continuity
+        corr = typeof corr !== 'undefined' ? corr : true;
+        var nx = x.length, // x's size
+            ny = y.length, // y's size
+            f = 1,
+            u, mu, std, z, p;
+
+        // test statistic
+        u = statistic(x, y);
+
+        // mean compute and correct if given
+        if (corr) {
+            mu = (nx * ny / 2) + 0.5;
+        } else {
+            mu = nx * ny / 2;
+        }
+
+        // compute standard deviation using tie correction factor
+        std = Math.sqrt(u.tcf * nx * ny * (nx + ny + 1) / 12);
+
+        // compute z according to given alternative
+        if (alt == 'less') {
+            z = (u.ux - mu) / std;
+        } else if (alt == 'greater') {
+            z = (u.uy - mu) / std;
+        } else if (alt == 'two-sided') {
+            z = Math.abs((u.big - mu) / std);
+        } else {
+            console.log('Unknown alternative argument');
+        }
+
+        // factor to correct two sided p-value
+        if (alt == 'two-sided') {
+            f = 2;
+        }
+
+        // compute p-value using CDF of standard normal
+        p = dnorm(-z, 0, 1) * f;
+
+        return {U: u.small, p: p};
+    }
+
+})(typeof exports === 'undefined' ? this['mannwhitneyu'] = {} : exports);