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| 1 | +/** |
| 2 | +* @license |
| 3 | +* |
| 4 | +* Regression.JS - Regression functions for javascript |
| 5 | +* http://tom-alexander.github.com/regression-js/ |
| 6 | +* |
| 7 | +* copyright(c) 2013 Tom Alexander |
| 8 | +* Licensed under the MIT license. |
| 9 | +* |
| 10 | +**/ |
| 11 | + |
| 12 | +;(function() { |
| 13 | + 'use strict'; |
| 14 | + |
| 15 | + var gaussianElimination = function(a, o) { |
| 16 | + var i = 0, j = 0, k = 0, maxrow = 0, tmp = 0, n = a.length - 1, x = new Array(o); |
| 17 | + for (i = 0; i < n; i++) { |
| 18 | + maxrow = i; |
| 19 | + for (j = i + 1; j < n; j++) { |
| 20 | + if (Math.abs(a[i][j]) > Math.abs(a[i][maxrow])) |
| 21 | + maxrow = j; |
| 22 | + } |
| 23 | + for (k = i; k < n + 1; k++) { |
| 24 | + tmp = a[k][i]; |
| 25 | + a[k][i] = a[k][maxrow]; |
| 26 | + a[k][maxrow] = tmp; |
| 27 | + } |
| 28 | + for (j = i + 1; j < n; j++) { |
| 29 | + for (k = n; k >= i; k--) { |
| 30 | + a[k][j] -= a[k][i] * a[i][j] / a[i][i]; |
| 31 | + } |
| 32 | + } |
| 33 | + } |
| 34 | + for (j = n - 1; j >= 0; j--) { |
| 35 | + tmp = 0; |
| 36 | + for (k = j + 1; k < n; k++) |
| 37 | + tmp += a[k][j] * x[k]; |
| 38 | + x[j] = (a[n][j] - tmp) / a[j][j]; |
| 39 | + } |
| 40 | + return (x); |
| 41 | + }; |
| 42 | + |
| 43 | + var methods = { |
| 44 | + linear: function(data) { |
| 45 | + var sum = [0, 0, 0, 0, 0], n = 0, results = []; |
| 46 | + |
| 47 | + for (; n < data.length; n++) { |
| 48 | + if (data[n][1]) { |
| 49 | + sum[0] += data[n][0]; |
| 50 | + sum[1] += data[n][1]; |
| 51 | + sum[2] += data[n][0] * data[n][0]; |
| 52 | + sum[3] += data[n][0] * data[n][1]; |
| 53 | + sum[4] += data[n][1] * data[n][1]; |
| 54 | + } |
| 55 | + } |
| 56 | + |
| 57 | + var gradient = (n * sum[3] - sum[0] * sum[1]) / (n * sum[2] - sum[0] * sum[0]); |
| 58 | + var intercept = (sum[1] / n) - (gradient * sum[0]) / n; |
| 59 | + // var correlation = (n * sum[3] - sum[0] * sum[1]) / Math.sqrt((n * sum[2] - sum[0] * sum[0]) * (n * sum[4] - sum[1] * sum[1])); |
| 60 | + |
| 61 | + for (var i = 0, len = data.length; i < len; i++) { |
| 62 | + var coordinate = [data[i][0], data[i][0] * gradient + intercept]; |
| 63 | + results.push(coordinate); |
| 64 | + } |
| 65 | + |
| 66 | + var string = 'y = ' + Math.round(gradient*100) / 100 + 'x + ' + Math.round(intercept*100) / 100; |
| 67 | + |
| 68 | + return {equation: [gradient, intercept], points: results, string: string}; |
| 69 | + }, |
| 70 | + |
| 71 | + exponential: function(data) { |
| 72 | + var sum = [0, 0, 0, 0, 0, 0], n = 0, results = []; |
| 73 | + |
| 74 | + for (len = data.length; n < len; n++) { |
| 75 | + if (data[n][1]) { |
| 76 | + sum[0] += data[n][0]; |
| 77 | + sum[1] += data[n][1]; |
| 78 | + sum[2] += data[n][0] * data[n][0] * data[n][1]; |
| 79 | + sum[3] += data[n][1] * Math.log(data[n][1]); |
| 80 | + sum[4] += data[n][0] * data[n][1] * Math.log(data[n][1]); |
| 81 | + sum[5] += data[n][0] * data[n][1]; |
| 82 | + } |
| 83 | + } |
| 84 | + |
| 85 | + var denominator = (sum[1] * sum[2] - sum[5] * sum[5]); |
| 86 | + var A = Math.pow(Math.E, (sum[2] * sum[3] - sum[5] * sum[4]) / denominator); |
| 87 | + var B = (sum[1] * sum[4] - sum[5] * sum[3]) / denominator; |
| 88 | + |
| 89 | + for (var i = 0, len = data.length; i < len; i++) { |
| 90 | + var coordinate = [data[i][0], A * Math.pow(Math.E, B * data[i][0])]; |
| 91 | + results.push(coordinate); |
| 92 | + } |
| 93 | + |
| 94 | + var string = 'y = ' + Math.round(A*100) / 100 + 'e^(' + Math.round(B*100) / 100 + 'x)'; |
| 95 | + |
| 96 | + return {equation: [A, B], points: results, string: string}; |
| 97 | + }, |
| 98 | + |
| 99 | + logarithmic: function(data) { |
| 100 | + var sum = [0, 0, 0, 0], n = 0, results = []; |
| 101 | + |
| 102 | + for (len = data.length; n < len; n++) { |
| 103 | + if (data[n][1]) { |
| 104 | + sum[0] += Math.log(data[n][0]); |
| 105 | + sum[1] += data[n][1] * Math.log(data[n][0]); |
| 106 | + sum[2] += data[n][1]; |
| 107 | + sum[3] += Math.pow(Math.log(data[n][0]), 2); |
| 108 | + } |
| 109 | + } |
| 110 | + |
| 111 | + var B = (n * sum[1] - sum[2] * sum[0]) / (n * sum[3] - sum[0] * sum[0]); |
| 112 | + var A = (sum[2] - B * sum[0]) / n; |
| 113 | + |
| 114 | + for (var i = 0, len = data.length; i < len; i++) { |
| 115 | + var coordinate = [data[i][0], A + B * Math.log(data[i][0])]; |
| 116 | + results.push(coordinate); |
| 117 | + } |
| 118 | + |
| 119 | + var string = 'y = ' + Math.round(A*100) / 100 + ' + ' + Math.round(B*100) / 100 + ' ln(x)'; |
| 120 | + |
| 121 | + return {equation: [A, B], points: results, string: string}; |
| 122 | + }, |
| 123 | + |
| 124 | + power: function(data) { |
| 125 | + var sum = [0, 0, 0, 0], n = 0, results = []; |
| 126 | + |
| 127 | + for (len = data.length; n < len; n++) { |
| 128 | + if (data[n][1]) { |
| 129 | + sum[0] += Math.log(data[n][0]); |
| 130 | + sum[1] += Math.log(data[n][1]) * Math.log(data[n][0]); |
| 131 | + sum[2] += Math.log(data[n][1]); |
| 132 | + sum[3] += Math.pow(Math.log(data[n][0]), 2); |
| 133 | + } |
| 134 | + } |
| 135 | + |
| 136 | + var B = (n * sum[1] - sum[2] * sum[0]) / (n * sum[3] - sum[0] * sum[0]); |
| 137 | + var A = Math.pow(Math.E, (sum[2] - B * sum[0]) / n); |
| 138 | + |
| 139 | + for (var i = 0, len = data.length; i < len; i++) { |
| 140 | + var coordinate = [data[i][0], A * Math.pow(data[i][0] , B)]; |
| 141 | + results.push(coordinate); |
| 142 | + } |
| 143 | + |
| 144 | + var string = 'y = ' + Math.round(A*100) / 100 + 'x^' + Math.round(B*100) / 100; |
| 145 | + |
| 146 | + return {equation: [A, B], points: results, string: string}; |
| 147 | + }, |
| 148 | + |
| 149 | + polynomial: function(data, order) { |
| 150 | + if(typeof order == 'undefined'){ |
| 151 | + order = 2; |
| 152 | + } |
| 153 | + var lhs = [], rhs = [], results = [], a = 0, b = 0, i = 0, k = order + 1; |
| 154 | + |
| 155 | + for (; i < k; i++) { |
| 156 | + for (var l = 0, len = data.length; l < len; l++) { |
| 157 | + if (data[l][1]) { |
| 158 | + a += Math.pow(data[l][0], i) * data[l][1]; |
| 159 | + } |
| 160 | + } |
| 161 | + lhs.push(a), a = 0; |
| 162 | + var c = []; |
| 163 | + for (var j = 0; j < k; j++) { |
| 164 | + for (var l = 0, len = data.length; l < len; l++) { |
| 165 | + if (data[l][1]) { |
| 166 | + b += Math.pow(data[l][0], i + j); |
| 167 | + } |
| 168 | + } |
| 169 | + c.push(b), b = 0; |
| 170 | + } |
| 171 | + rhs.push(c); |
| 172 | + } |
| 173 | + rhs.push(lhs); |
| 174 | + |
| 175 | + var equation = gaussianElimination(rhs, k); |
| 176 | + |
| 177 | + for (var i = 0, len = data.length; i < len; i++) { |
| 178 | + var answer = 0; |
| 179 | + for (var w = 0; w < equation.length; w++) { |
| 180 | + answer += equation[w] * Math.pow(data[i][0], w); |
| 181 | + } |
| 182 | + results.push([data[i][0], answer]); |
| 183 | + } |
| 184 | + |
| 185 | + var string = 'y = '; |
| 186 | + |
| 187 | + for(var i = equation.length-1; i >= 0; i--){ |
| 188 | + if(i > 1) string += Math.round(equation[i]*100) / 100 + 'x^' + i + ' + '; |
| 189 | + else if (i == 1) string += Math.round(equation[i]*100) / 100 + 'x' + ' + '; |
| 190 | + else string += Math.round(equation[i]*100) / 100; |
| 191 | + } |
| 192 | + |
| 193 | + return {equation: equation, points: results, string: string}; |
| 194 | + } |
| 195 | + }; |
| 196 | + |
| 197 | +var regression = (function(method, data, order) { |
| 198 | + |
| 199 | + if (typeof method == 'string') { |
| 200 | + return methods[method](data, order); |
| 201 | + } |
| 202 | + }); |
| 203 | + |
| 204 | +if (typeof exports !== 'undefined') { |
| 205 | + module.exports = regression; |
| 206 | +} else { |
| 207 | + window.regression = regression; |
| 208 | +} |
| 209 | + |
| 210 | +}()); |
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