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package breeze.numerics

/*
Copyright 2012 David Hall

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.
*/


/**
 * Implementations of the Bessel functions, based on Numerical Recipes
 *
 * @author dlwh
 */
object Bessel {
  private val i0p = Array(9.999999999999997e-1, 2.466405579426905e-1, 1.478980363444585e-2,
    3.826993559940360e-4, 5.395676869878828e-6, 4.700912200921704e-8,
    2.733894920915608e-10, 1.115830108455192e-12, 3.301093025084127e-15,
    7.209167098020555e-18, 1.166898488777214e-20, 1.378948246502109e-23,
    1.124884061857506e-26, 5.498556929587117e-30)
  private val i0q = Array(4.463598170691436e-1, 1.702205745042606e-3, 2.792125684538934e-6,
    2.369902034785866e-9, 8.965900179621208e-13)
  private val i0pp = Array(1.192273748120670e-1, 1.947452015979746e-1, 7.629241821600588e-2,
    8.474903580801549e-3, 2.023821945835647e-4)
  private val i0qq = Array(2.962898424533095e-1, 4.866115913196384e-1, 1.938352806477617e-1,
    2.261671093400046e-2, 6.450448095075585e-4, 1.529835782400450e-6)

  def i0(x: Double) = {
    val ax = x.abs
    if (ax < 15.0) {
      val y = x * x
      polyval(i0p, y) / polyval(i0q, 225.0 - y)
    } else {
      val z = 1.0 - 15.0 / ax
      exp(ax) * polyval(i0pp, z) / (polyval(i0qq, z) * sqrt(ax))
    }
  }


  private val A_i1 = Array(
    2.77791411276104639959E-18,
    -2.11142121435816608115E-17,
    1.55363195773620046921E-16,
    -1.10559694773538630805E-15,
    7.60068429473540693410E-15,
    -5.04218550472791168711E-14,
    3.22379336594557470981E-13,
    -1.98397439776494371520E-12,
    1.17361862988909016308E-11,
    -6.66348972350202774223E-11,
    3.62559028155211703701E-10,
    -1.88724975172282928790E-9,
    9.38153738649577178388E-9,
    -4.44505912879632808065E-8,
    2.00329475355213526229E-7,
    -8.56872026469545474066E-7,
    3.47025130813767847674E-6,
    -1.32731636560394358279E-5,
    4.78156510755005422638E-5,
    -1.61760815825896745588E-4,
    5.12285956168575772895E-4,
    -1.51357245063125314899E-3,
    4.15642294431288815669E-3,
    -1.05640848946261981558E-2,
    2.47264490306265168283E-2,
    -5.29459812080949914269E-2,
    1.02643658689847095384E-1,
    -1.76416518357834055153E-1,
    2.52587186443633654823E-1
  )

  private val B_i1 = Array(
    7.51729631084210481353E-18,
    4.41434832307170791151E-18,
    -4.65030536848935832153E-17,
    -3.20952592199342395980E-17,
    2.96262899764595013876E-16,
    3.30820231092092828324E-16,
    -1.88035477551078244854E-15,
    -3.81440307243700780478E-15,
    1.04202769841288027642E-14,
    4.27244001671195135429E-14,
    -2.10154184277266431302E-14,
    -4.08355111109219731823E-13,
    -7.19855177624590851209E-13,
    2.03562854414708950722E-12,
    1.41258074366137813316E-11,
    3.25260358301548823856E-11,
    -1.89749581235054123450E-11,
    -5.58974346219658380687E-10,
    -3.83538038596423702205E-9,
    -2.63146884688951950684E-8,
    -2.51223623787020892529E-7,
    -3.88256480887769039346E-6,
    -1.10588938762623716291E-4,
    -9.76109749136146840777E-3,
    7.78576235018280120474E-1
  )

  // Taken from colt
  def i1(x: Double) = {
    var y: Double = Double.NaN
    var z = x.abs

    if (z <= 8.0) {
      y = (z / 2.0) - 2.0
      z = chbevl(y, A_i1, 29) * z * math.exp(z)
    }
    else {
      z = math.exp(z) * chbevl(32.0 / z - 2.0, B_i1, 25) / math.sqrt(z)
    }
    if (x < 0.0)
      z = -z
    (z)
  }

  private def chbevl(x: Double, coef: Array[Double], N: Int) = {
    var b0 = 0.0
    var b1 = 0.0
    var b2 = 0.0

    var p = 0
    var i = N - 1

    b0 = coef(p)
    p += 1
    b1 = 0.0
    i = N - 1

    do {
      b2 = b1
      b1 = b0
      b0 = x * b1 - b2 + coef(p)
      p += 1
      i -= 1
    } while (i > 0)

    (0.5 * (b0 - b2))
  }
}