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57 lines
1.7 KiB
Go
57 lines
1.7 KiB
Go
// Derived from SciPy's special/c_misc/gammaincinv.c
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// https://github.com/scipy/scipy/blob/master/scipy/special/c_misc/gammaincinv.c
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// Copyright ©2017 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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"gonum.org/v1/gonum/mathext/internal/cephes"
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)
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const (
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allowedATol = 1e-306
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allowedRTol = 1e-6
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)
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func gammaInc(x float64, params []float64) float64 {
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return cephes.Igam(params[0], x) - params[1]
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}
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// gammaIncInv is the inverse of the incomplete Gamma integral. That is, it
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// returns x such that:
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// Igam(a, x) = y
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// The input argument a must be positive and y must be between 0 and 1
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// inclusive or gammaIncInv will panic. gammaIncInv should return a
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// positive number, but can return NaN if there is a failure to converge.
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func gammaIncInv(a, y float64) float64 {
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// For y not small, we just use
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// IgamI(a, 1-y)
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// (inverse of the complemented incomplete Gamma integral). For y small,
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// however, 1-y is about 1, and we lose digits.
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if a <= 0 || y <= 0 || y >= 0.25 {
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return cephes.IgamI(a, 1-y)
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}
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lo := 0.0
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flo := -y
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hi := cephes.IgamI(a, 0.75)
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fhi := 0.25 - y
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params := []float64{a, y}
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// Also, after we generate a small interval by bisection above, false
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// position will do a large step from an interval of width ~1e-4 to ~1e-14
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// in one step (a=10, x=0.05, but similar for other values).
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result, bestX, _, errEst := falsePosition(lo, hi, flo, fhi, 2*machEp, 2*machEp, 1e-2*a, gammaInc, params)
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if result == fSolveMaxIterations && errEst > allowedATol+allowedRTol*math.Abs(bestX) {
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bestX = math.NaN()
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}
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return bestX
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}
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