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29 lines
768 B
Go
29 lines
768 B
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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// ψ(x) = d/dx (Ln (Γ(x)).
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// Note that if x is a negative integer in [-7, 0] this function will return
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// negative Inf.
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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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for ; x < 7.0; x++ {
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result -= 1 / x
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}
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x -= 1.0 / 2.0
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xx := 1.0 / x
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xx2 := xx * xx
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xx4 := xx2 * xx2
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result += math.Log(x) + (1./24.)*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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