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Gamma.scala
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Gamma.scala
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/*
* Copyright 2021 Arman Bilge
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package schrodinger.kernel
import algebra.ring.MultiplicativeMonoid
import cats.Monad
import cats.syntax.all.*
trait Gamma[F[_], A]:
def gamma(shape: A, rate: A): F[A]
object Gamma:
inline def apply[F[_], A](shape: A, rate: A)(using g: Gamma[F, A]): F[A] =
g.gamma(shape, rate)
given [F[_]: Monad](using Uniform[F, Double], Gaussian[F, Double]): Gamma[F, Double] with
def gamma(shape: Double, rate: Double) =
val U = Uniform.standard
val G = Gaussian.standard
val scale = 1 / rate
val none = Option.empty[Double].pure
def ahrensDieter: F[Double] =
val oneOverAlpha = 1 / shape
val bGSOptim = 1 + shape / Math.E
val go: F[Option[Double]] = U.flatMap { u =>
val p = bGSOptim * u
if p <= 1 then
val x = Math.pow(p, oneOverAlpha)
U.flatMap { u2 =>
if u2 > Math.exp(-x) then none
else (scale * x).some.pure
}
else
val x = -Math.log((bGSOptim - p) * oneOverAlpha)
U.flatMap { u2 =>
if u2 <= Math.pow(x, shape - 1) then (scale * x).some.pure
else none
}
}
go.untilDefinedM
def marsagliaTsang: F[Double] =
val dOptim = shape - 1 / 3.0
val cOptim = (1 / 3.0) / Math.sqrt(dOptim)
val go: F[Option[Double]] = G.flatMap { x =>
val oPcTx = 1 + cOptim * x
val v = oPcTx * oPcTx * oPcTx
if v <= 0 then none
else
val x2 = x * x
U.flatMap { u =>
if u < 1 - 0.0331 * x2 * x2 then Some(scale * dOptim * v).pure
else if Math.log(u) < 0.5 * x2 + dOptim * (1 - v + Math.log(v)) then
Some(scale * dOptim * v).pure
else none
}
}
go.untilDefinedM
if shape < 1 then ahrensDieter else marsagliaTsang