| // Copyright ©2016 The gonum Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style |
| // license that can be found in the LICENSE file. |
| |
| package mathext |
| |
| import ( |
| "gonum.org/v1/gonum/mathext/internal/cephes" |
| ) |
| |
| // GammaInc computes the incomplete Gamma integral. |
| // GammaInc(a,x) = (1/ Γ(a)) \int_0^x e^{-t} t^{a-1} dt |
| // The input argument a must be positive and x must be non-negative or GammaInc |
| // will panic. |
| // |
| // See http://mathworld.wolfram.com/IncompleteGammaFunction.html |
| // or https://en.wikipedia.org/wiki/Incomplete_gamma_function for more detailed |
| // information. |
| func GammaInc(a, x float64) float64 { |
| return cephes.Igam(a, x) |
| } |
| |
| // GammaIncComp computes the complemented incomplete Gamma integral. |
| // GammaIncComp(a,x) = 1 - GammaInc(a,x) |
| // = (1/ Γ(a)) \int_0^\infty e^{-t} t^{a-1} dt |
| // The input argument a must be positive and x must be non-negative or |
| // GammaIncComp will panic. |
| func GammaIncComp(a, x float64) float64 { |
| return cephes.IgamC(a, x) |
| } |
| |
| // GammaIncInv computes the inverse of the incomplete Gamma integral. That is, |
| // it returns the x such that: |
| // GammaInc(a, x) = y |
| // The input argument a must be positive and y must be between 0 and 1 |
| // inclusive or GammaIncInv will panic. GammaIncInv should return a positive |
| // number, but can return NaN if there is a failure to converge. |
| func GammaIncInv(a, y float64) float64 { |
| return gammaIncInv(a, y) |
| } |
| |
| // GammaIncCompInv computes the inverse of the complemented incomplete Gamma |
| // integral. That is, it returns the x such that: |
| // GammaIncComp(a, x) = y |
| // The input argument a must be positive and y must be between 0 and 1 |
| // inclusive or GammaIncCompInv will panic. GammaIncCompInv should return a |
| // positive number, but can return 0 even with non-zero y due to underflow. |
| func GammaIncCompInv(a, y float64) float64 { |
| return cephes.IgamI(a, y) |
| } |