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* @license\n * Copyright 2018 Google LLC. All Rights Reserved.\n * Licensed under the Apache License, Version 2.0 (the \"License\");\n * you may not use this file except in compliance with the License.\n * You may obtain a copy of the License at\n *\n * http://www.apache.org/licenses/LICENSE-2.0\n *\n * Unless required by applicable law or agreed to in writing, software\n * distributed under the License is distributed on an \"AS IS\" BASIS,\n * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n * See the License for the specific language governing permissions and\n * limitations under the License.\n * =============================================================================\n */\n\nimport * as seedrandom from 'seedrandom';\n\nimport {expectNumbersClose, testEpsilon} from '../test_util';\nimport {TypedArray} from '../types';\n\nexport interface RandomBase {\n nextValue(): number;\n}\n\nexport interface RandomGamma {\n nextValue(): number;\n}\n\nexport interface RandNormalDataTypes {\n float32: Float32Array;\n int32: Int32Array;\n}\n\nexport interface RandGammaDataTypes {\n float32: Float32Array;\n int32: Int32Array;\n}\n\n// https://en.wikipedia.org/wiki/Marsaglia_polar_method\nexport class MPRandGauss implements RandomBase {\n private mean: number;\n private stdDev: number;\n private nextVal: number;\n private dtype?: keyof RandNormalDataTypes;\n private truncated?: boolean;\n private upper?: number;\n private lower?: number;\n private random: seedrandom.prng;\n\n constructor(\n mean: number, stdDeviation: number, dtype?: keyof RandNormalDataTypes,\n truncated?: boolean, seed?: number) {\n this.mean = mean;\n this.stdDev = stdDeviation;\n this.dtype = dtype;\n this.nextVal = NaN;\n this.truncated = truncated;\n if (this.truncated) {\n this.upper = this.mean + this.stdDev * 2;\n this.lower = this.mean - this.stdDev * 2;\n }\n const seedValue = seed ? seed : Math.random();\n this.random = seedrandom.alea(seedValue.toString());\n }\n\n /** Returns next sample from a Gaussian distribution. */\n public nextValue(): number {\n if (!isNaN(this.nextVal)) {\n const value = this.nextVal;\n this.nextVal = NaN;\n return value;\n }\n\n let resultX: number, resultY: number;\n let isValid = false;\n while (!isValid) {\n let v1: number, v2: number, s: number;\n do {\n v1 = 2 * this.random() - 1;\n v2 = 2 * this.random() - 1;\n s = v1 * v1 + v2 * v2;\n } while (s >= 1 || s === 0);\n\n const mul = Math.sqrt(-2.0 * Math.log(s) / s);\n resultX = this.mean + this.stdDev * v1 * mul;\n resultY = this.mean + this.stdDev * v2 * mul;\n\n if (!this.truncated || this.isValidTruncated(resultX)) {\n isValid = true;\n }\n }\n\n if (!this.truncated || this.isValidTruncated(resultY)) {\n this.nextVal = this.convertValue(resultY);\n }\n return this.convertValue(resultX);\n }\n\n /** Handles proper rounding for non-floating-point numbers. */\n private convertValue(value: number): number {\n if (this.dtype == null || this.dtype === 'float32') {\n return value;\n }\n return Math.round(value);\n }\n\n /** Returns true if less than 2-standard-deviations from the mean. */\n private isValidTruncated(value: number): boolean {\n return value <= this.upper && value >= this.lower;\n }\n}\n\n// Marsaglia, George, and Wai Wan Tsang. 2000. \"A Simple Method for Generating\n// Gamma Variables.\"\nexport class RandGamma implements RandomGamma {\n private alpha: number;\n private beta: number;\n private d: number;\n private c: number;\n private dtype?: keyof RandGammaDataTypes;\n private randu: seedrandom.prng;\n private randn: MPRandGauss;\n\n constructor(\n alpha: number, beta: number, dtype: keyof RandGammaDataTypes,\n seed?: number) {\n this.alpha = alpha;\n this.beta = 1 / beta; // convert rate to scale parameter\n this.dtype = dtype;\n\n const seedValue = seed ? seed : Math.random();\n this.randu = seedrandom.alea(seedValue.toString());\n this.randn = new MPRandGauss(0, 1, dtype, false, this.randu());\n\n if (alpha < 1) {\n this.d = alpha + (2 / 3);\n } else {\n this.d = alpha - (1 / 3);\n }\n this.c = 1 / Math.sqrt(9 * this.d);\n }\n\n /** Returns next sample from a gamma distribution. */\n public nextValue(): number {\n let x2: number, v0: number, v1: number, x: number, u: number, v: number;\n while (true) {\n do {\n x = this.randn.nextValue();\n v = 1 + (this.c * x);\n } while (v <= 0);\n v *= v * v;\n x2 = x * x;\n v0 = 1 - (0.331 * x2 * x2);\n v1 = (0.5 * x2) + (this.d * (1 - v + Math.log(v)));\n u = this.randu();\n if (u < v0 || Math.log(u) < v1) {\n break;\n }\n }\n v = (1 / this.beta) * this.d * v;\n if (this.alpha < 1) {\n v *= Math.pow(this.randu(), 1 / this.alpha);\n }\n return this.convertValue(v);\n }\n /** Handles proper rounding for non-floating-point numbers. */\n private convertValue(value: number): number {\n if (this.dtype === 'float32') {\n return value;\n }\n return Math.round(value);\n }\n}\n\nexport class UniformRandom implements RandomBase {\n private min: number;\n private range: number;\n private random: seedrandom.prng;\n private dtype?: keyof RandNormalDataTypes;\n\n constructor(\n min = 0, max = 1, dtype?: keyof RandNormalDataTypes,\n seed?: string|number) {\n this.min = min;\n this.range = max - min;\n this.dtype = dtype;\n if (seed == null) {\n seed = Math.random();\n }\n if (typeof seed === 'number') {\n seed = seed.toString();\n }\n\n if (!this.canReturnFloat() && this.range <= 1) {\n throw new Error(\n `The difference between ${min} - ${max} <= 1 and dtype is not float`);\n }\n this.random = seedrandom.alea(seed);\n }\n\n /** Handles proper rounding for non floating point numbers. */\n private canReturnFloat = () =>\n (this.dtype == null || this.dtype === 'float32');\n\n private convertValue(value: number): number {\n if (this.canReturnFloat()) {\n return value;\n }\n return Math.round(value);\n }\n\n nextValue() {\n return this.convertValue(this.min + this.range * this.random());\n }\n}\n\nexport function jarqueBeraNormalityTest(values: TypedArray|number[]) {\n // https://en.wikipedia.org/wiki/Jarque%E2%80%93Bera_test\n const n = values.length;\n const s = skewness(values);\n const k = kurtosis(values);\n const jb = n / 6 * (Math.pow(s, 2) + 0.25 * Math.pow(k - 3, 2));\n // JB test requires 2-degress of freedom from Chi-Square @ 0.95:\n // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm\n const CHI_SQUARE_2DEG = 5.991;\n if (jb > CHI_SQUARE_2DEG) {\n throw new Error(`Invalid p-value for JB: ${jb}`);\n }\n}\n\nexport function expectArrayInMeanStdRange(\n actual: TypedArray|number[], expectedMean: number, expectedStdDev: number,\n epsilon?: number) {\n if (epsilon == null) {\n epsilon = testEpsilon();\n }\n const actualMean = mean(actual);\n expectNumbersClose(actualMean, expectedMean, epsilon);\n expectNumbersClose(\n standardDeviation(actual, actualMean), expectedStdDev, epsilon);\n}\n\nfunction mean(values: TypedArray|number[]) {\n let sum = 0;\n for (let i = 0; i < values.length; i++) {\n sum += values[i];\n }\n return sum / values.length;\n}\n\nfunction standardDeviation(values: TypedArray|number[], mean: number) {\n let squareDiffSum = 0;\n for (let i = 0; i < values.length; i++) {\n const diff = values[i] - mean;\n squareDiffSum += diff * diff;\n }\n return Math.sqrt(squareDiffSum / values.length);\n}\n\nfunction kurtosis(values: TypedArray|number[]) {\n // https://en.wikipedia.org/wiki/Kurtosis\n const valuesMean = mean(values);\n const n = values.length;\n let sum2 = 0;\n let sum4 = 0;\n for (let i = 0; i < n; i++) {\n const v = values[i] - valuesMean;\n sum2 += Math.pow(v, 2);\n sum4 += Math.pow(v, 4);\n }\n return (1 / n) * sum4 / Math.pow((1 / n) * sum2, 2);\n}\n\nfunction skewness(values: TypedArray|number[]) {\n // https://en.wikipedia.org/wiki/Skewness\n const valuesMean = mean(values);\n const n = values.length;\n let sum2 = 0;\n let sum3 = 0;\n for (let i = 0; i < n; i++) {\n const v = values[i] - valuesMean;\n sum2 += Math.pow(v, 2);\n sum3 += Math.pow(v, 3);\n }\n return (1 / n) * sum3 / Math.pow((1 / (n - 1)) * sum2, 3 / 2);\n}\n"]} |