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5f0141ca4c
Changes made in dsp/fourier/internal/fftpack break the formatting used there, so these are reverted. There will be complaints in CI. [git-generate] gofmt -w . go generate gonum.org/v1/gonum/blas go generate gonum.org/v1/gonum/blas/gonum go generate gonum.org/v1/gonum/unit go generate gonum.org/v1/gonum/unit/constant go generate gonum.org/v1/gonum/graph/formats/dot go generate gonum.org/v1/gonum/graph/formats/rdf go generate gonum.org/v1/gonum/stat/card git checkout -- dsp/fourier/internal/fftpack
46 lines
1.1 KiB
Go
46 lines
1.1 KiB
Go
// Copyright ©2016 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package mathext
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import (
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"math"
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)
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// Digamma returns the logorithmic derivative of the gamma function at x.
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//
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// ψ(x) = d/dx (Ln (Γ(x)).
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func Digamma(x float64) float64 {
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// This is adapted from
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// http://web.science.mq.edu.au/~mjohnson/code/digamma.c
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var result float64
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switch {
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case math.IsNaN(x), math.IsInf(x, 1):
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return x
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case math.IsInf(x, -1):
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return math.NaN()
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case x == 0:
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return math.Copysign(math.Inf(1), -x)
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case x < 0:
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if x == math.Floor(x) {
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return math.NaN()
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}
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// Reflection formula, http://dlmf.nist.gov/5.5#E4
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_, r := math.Modf(x)
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result = -math.Pi / math.Tan(math.Pi*r)
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x = 1 - x
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}
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for ; x < 7; x++ {
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// Recurrence relation, http://dlmf.nist.gov/5.5#E2
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result -= 1 / x
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}
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x -= 0.5
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xx := 1 / x
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xx2 := xx * xx
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xx4 := xx2 * xx2
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// Asymptotic expansion, http://dlmf.nist.gov/5.11#E2
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result += math.Log(x) + (1.0/24.0)*xx2 - (7.0/960.0)*xx4 + (31.0/8064.0)*xx4*xx2 - (127.0/30720.0)*xx4*xx4
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return result
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}
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