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51 lines
2.0 KiB
Go
51 lines
2.0 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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"gonum.org/v1/gonum/mathext/internal/cephes"
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)
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// GammaIncReg computes the regularized incomplete Gamma integral.
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// GammaIncReg(a,x) = (1/ Γ(a)) \int_0^x e^{-t} t^{a-1} dt
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// The input argument a must be positive and x must be non-negative or GammaIncReg
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// will panic.
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//
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// See http://mathworld.wolfram.com/IncompleteGammaFunction.html
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// or https://en.wikipedia.org/wiki/Incomplete_gamma_function for more detailed
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// information.
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func GammaIncReg(a, x float64) float64 {
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return cephes.Igam(a, x)
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}
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// GammaIncRegComp computes the complemented regularized incomplete Gamma integral.
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// GammaIncRegComp(a,x) = 1 - GammaIncReg(a,x)
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// = (1/ Γ(a)) \int_0^\infty e^{-t} t^{a-1} dt
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// The input argument a must be positive and x must be non-negative or
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// GammaIncRegComp will panic.
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func GammaIncRegComp(a, x float64) float64 {
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return cephes.IgamC(a, x)
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}
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// GammaIncRegInv computes the inverse of the regularized incomplete Gamma integral. That is,
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// it returns the x such that:
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// GammaIncReg(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 GammaIncRegInv will panic. GammaIncRegInv should return a positive
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// number, but can return NaN if there is a failure to converge.
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func GammaIncRegInv(a, y float64) float64 {
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return gammaIncRegInv(a, y)
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}
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// GammaIncRegCompInv computes the inverse of the complemented regularized incomplete Gamma
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// integral. That is, it returns the x such that:
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// GammaIncRegComp(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 GammaIncRegCompInv will panic. GammaIncRegCompInv should return a
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// positive number, but can return 0 even with non-zero y due to underflow.
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func GammaIncRegCompInv(a, y float64) float64 {
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return cephes.IgamI(a, y)
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}
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