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dirichlet.scala
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dirichlet.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
package stats
import algebra.instances.all.*
import algebra.ring.AdditiveMonoid
import cats.Applicative
import cats.NonEmptyParallel
import cats.NonEmptyTraverse
import cats.syntax.all.*
import schrodinger.kernel
import schrodinger.kernel.Dirichlet
import schrodinger.math.LogDouble
import schrodinger.math.special.gamma
object dirichlet:
given [F[_]: Applicative, G[_]: NonEmptyTraverse: NonEmptyParallel]
: Dirichlet[Density[F, LogDouble, _], G[Double]] with
def dirichlet(concentration: G[Double]) =
val normalizingConstant =
gamma(AdditiveMonoid[Double].sum(concentration.toIterable))
/ concentration.reduceMap(gamma)(_ * _)
Density { x =>
val density =
(concentration, x).parMapN((alpha, x) => LogDouble(x) ** (alpha - 1)).reduce(_ * _)
(normalizingConstant * density).pure
}