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Merge pull request #48 from flatironinstitute/ess-stats
frontend: effective sample size and related stats
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| /* eslint-disable @typescript-eslint/no-inferrable-types */ | ||
| /* eslint-disable @typescript-eslint/no-unused-vars */ | ||
| /* eslint-disable prefer-const */ | ||
| /* | ||
| * Free FFT and convolution (TypeScript) | ||
| * | ||
| * Copyright (c) 2022 Project Nayuki. (MIT License) | ||
| * https://www.nayuki.io/page/free-small-fft-in-multiple-languages | ||
| * | ||
| * Permission is hereby granted, free of charge, to any person obtaining a copy of | ||
| * this software and associated documentation files (the "Software"), to deal in | ||
| * the Software without restriction, including without limitation the rights to | ||
| * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of | ||
| * the Software, and to permit persons to whom the Software is furnished to do so, | ||
| * subject to the following conditions: | ||
| * - The above copyright notice and this permission notice shall be included in | ||
| * all copies or substantial portions of the Software. | ||
| * - The Software is provided "as is", without warranty of any kind, express or | ||
| * implied, including but not limited to the warranties of merchantability, | ||
| * fitness for a particular purpose and noninfringement. In no event shall the | ||
| * authors or copyright holders be liable for any claim, damages or other | ||
| * liability, whether in an action of contract, tort or otherwise, arising from, | ||
| * out of or in connection with the Software or the use or other dealings in the | ||
| * Software. | ||
| */ | ||
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| /* | ||
| * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector. | ||
| * The vector can have any length. This is a wrapper function. | ||
| */ | ||
| export function transform(real: Array<number>|Float64Array, imag: Array<number>|Float64Array): void { | ||
| const n: number = real.length; | ||
| if (n != imag.length) | ||
| throw new RangeError("Mismatched lengths"); | ||
| if (n == 0) | ||
| return; | ||
| else if ((n & (n - 1)) == 0) // Is power of 2 | ||
| transformRadix2(real, imag); | ||
| else // More complicated algorithm for arbitrary sizes | ||
| transformBluestein(real, imag); | ||
| } | ||
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| /* | ||
| * Computes the inverse discrete Fourier transform (IDFT) of the given complex vector, storing the result back into the vector. | ||
| * The vector can have any length. This is a wrapper function. This transform does not perform scaling, so the inverse is not a true inverse. | ||
| */ | ||
| export function inverseTransform(real: Array<number>|Float64Array, imag: Array<number>|Float64Array): void { | ||
| transform(imag, real); | ||
| } | ||
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| /* | ||
| * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector. | ||
| * The vector's length must be a power of 2. Uses the Cooley-Tukey decimation-in-time radix-2 algorithm. | ||
| */ | ||
| function transformRadix2(real: Array<number>|Float64Array, imag: Array<number>|Float64Array): void { | ||
| // Length variables | ||
| const n: number = real.length; | ||
| if (n != imag.length) | ||
| throw new RangeError("Mismatched lengths"); | ||
| if (n == 1) // Trivial transform | ||
| return; | ||
| let levels: number = -1; | ||
| for (let i = 0; i < 32; i++) { | ||
| if (1 << i == n) | ||
| levels = i; // Equal to log2(n) | ||
| } | ||
| if (levels == -1) | ||
| throw new RangeError("Length is not a power of 2"); | ||
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| // Trigonometric tables | ||
| let cosTable = new Array<number>(n / 2); | ||
| let sinTable = new Array<number>(n / 2); | ||
| for (let i = 0; i < n / 2; i++) { | ||
| cosTable[i] = Math.cos(2 * Math.PI * i / n); | ||
| sinTable[i] = Math.sin(2 * Math.PI * i / n); | ||
| } | ||
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| // Bit-reversed addressing permutation | ||
| for (let i = 0; i < n; i++) { | ||
| const j: number = reverseBits(i, levels); | ||
| if (j > i) { | ||
| let temp: number = real[i]; | ||
| real[i] = real[j]; | ||
| real[j] = temp; | ||
| temp = imag[i]; | ||
| imag[i] = imag[j]; | ||
| imag[j] = temp; | ||
| } | ||
| } | ||
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| // Cooley-Tukey decimation-in-time radix-2 FFT | ||
| for (let size = 2; size <= n; size *= 2) { | ||
| const halfsize: number = size / 2; | ||
| const tablestep: number = n / size; | ||
| for (let i = 0; i < n; i += size) { | ||
| for (let j = i, k = 0; j < i + halfsize; j++, k += tablestep) { | ||
| const l: number = j + halfsize; | ||
| const tpre: number = real[l] * cosTable[k] + imag[l] * sinTable[k]; | ||
| const tpim: number = -real[l] * sinTable[k] + imag[l] * cosTable[k]; | ||
| real[l] = real[j] - tpre; | ||
| imag[l] = imag[j] - tpim; | ||
| real[j] += tpre; | ||
| imag[j] += tpim; | ||
| } | ||
| } | ||
| } | ||
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| // Returns the integer whose value is the reverse of the lowest 'width' bits of the integer 'val'. | ||
| function reverseBits(val: number, width: number): number { | ||
| let result: number = 0; | ||
| for (let i = 0; i < width; i++) { | ||
| result = (result << 1) | (val & 1); | ||
| val >>>= 1; | ||
| } | ||
| return result; | ||
| } | ||
| } | ||
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| /* | ||
| * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector. | ||
| * The vector can have any length. This requires the convolution function, which in turn requires the radix-2 FFT function. | ||
| * Uses Bluestein's chirp z-transform algorithm. | ||
| */ | ||
| function transformBluestein(real: Array<number>|Float64Array, imag: Array<number>|Float64Array): void { | ||
| // Find a power-of-2 convolution length m such that m >= n * 2 + 1 | ||
| const n: number = real.length; | ||
| if (n != imag.length) | ||
| throw new RangeError("Mismatched lengths"); | ||
| let m: number = 1; | ||
| while (m < n * 2 + 1) | ||
| m *= 2; | ||
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| // Trigonometric tables | ||
| let cosTable = new Array<number>(n); | ||
| let sinTable = new Array<number>(n); | ||
| for (let i = 0; i < n; i++) { | ||
| const j: number = i * i % (n * 2); // This is more accurate than j = i * i | ||
| cosTable[i] = Math.cos(Math.PI * j / n); | ||
| sinTable[i] = Math.sin(Math.PI * j / n); | ||
| } | ||
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| // Temporary vectors and preprocessing | ||
| let areal: Array<number> = newArrayOfZeros(m); | ||
| let aimag: Array<number> = newArrayOfZeros(m); | ||
| for (let i = 0; i < n; i++) { | ||
| areal[i] = real[i] * cosTable[i] + imag[i] * sinTable[i]; | ||
| aimag[i] = -real[i] * sinTable[i] + imag[i] * cosTable[i]; | ||
| } | ||
| let breal: Array<number> = newArrayOfZeros(m); | ||
| let bimag: Array<number> = newArrayOfZeros(m); | ||
| breal[0] = cosTable[0]; | ||
| bimag[0] = sinTable[0]; | ||
| for (let i = 1; i < n; i++) { | ||
| breal[i] = breal[m - i] = cosTable[i]; | ||
| bimag[i] = bimag[m - i] = sinTable[i]; | ||
| } | ||
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| // Convolution | ||
| let creal = new Array<number>(m); | ||
| let cimag = new Array<number>(m); | ||
| convolveComplex(areal, aimag, breal, bimag, creal, cimag); | ||
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| // Postprocessing | ||
| for (let i = 0; i < n; i++) { | ||
| real[i] = creal[i] * cosTable[i] + cimag[i] * sinTable[i]; | ||
| imag[i] = -creal[i] * sinTable[i] + cimag[i] * cosTable[i]; | ||
| } | ||
| } | ||
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| /* | ||
| * Computes the circular convolution of the given real vectors. Each vector's length must be the same. | ||
| */ | ||
| // function convolveReal(xvec: Array<number>|Float64Array, yvec: Array<number>|Float64Array, outvec: Array<number>|Float64Array): void { | ||
| // const n: number = xvec.length; | ||
| // if (n != yvec.length || n != outvec.length) | ||
| // throw new RangeError("Mismatched lengths"); | ||
| // convolveComplex(xvec, newArrayOfZeros(n), yvec, newArrayOfZeros(n), outvec, newArrayOfZeros(n)); | ||
| // } | ||
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| /* | ||
| * Computes the circular convolution of the given complex vectors. Each vector's length must be the same. | ||
| */ | ||
| function convolveComplex( | ||
| xreal: Array<number>|Float64Array, ximag: Array<number>|Float64Array, | ||
| yreal: Array<number>|Float64Array, yimag: Array<number>|Float64Array, | ||
| outreal: Array<number>|Float64Array, outimag: Array<number>|Float64Array): void { | ||
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| const n: number = xreal.length; | ||
| if (n != ximag.length || n != yreal.length || n != yimag.length | ||
| || n != outreal.length || n != outimag.length) | ||
| throw new RangeError("Mismatched lengths"); | ||
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| xreal = xreal.slice(); | ||
| ximag = ximag.slice(); | ||
| yreal = yreal.slice(); | ||
| yimag = yimag.slice(); | ||
| transform(xreal, ximag); | ||
| transform(yreal, yimag); | ||
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| for (let i = 0; i < n; i++) { | ||
| const temp: number = xreal[i] * yreal[i] - ximag[i] * yimag[i]; | ||
| ximag[i] = ximag[i] * yreal[i] + xreal[i] * yimag[i]; | ||
| xreal[i] = temp; | ||
| } | ||
| inverseTransform(xreal, ximag); | ||
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| for (let i = 0; i < n; i++) { // Scaling (because this FFT implementation omits it) | ||
| outreal[i] = xreal[i] / n; | ||
| outimag[i] = ximag[i] / n; | ||
| } | ||
| } | ||
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| function newArrayOfZeros(n: number): Array<number> { | ||
| let result: Array<number> = []; | ||
| for (let i = 0; i < n; i++) | ||
| result.push(0); | ||
| return result; | ||
| } |
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