Created
December 4, 2011 01:09
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An example of automatic differentiation in Scala. It is straightforward porting of http://www.kmonos.net/wlog/123.html#_2257111201
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| object AutomaticDifferentiation { | |
| case class Dual[X](x: X, dx: X) | |
| def dual(x: Double) = Dual(x, 1.0) | |
| implicit val dualDoubleIsFractional: Fractional[Dual[Double]] = new Fractional[Dual[Double]] { | |
| override def plus(x: Dual[Double], r: Dual[Double]) = Dual(x.x + r.x, x.dx * 1 + r.dx * 1) | |
| override def minus(x: Dual[Double], r: Dual[Double]) = Dual(x.x - r.x, x.dx * 1 + r.dx * -1) | |
| override def times(x: Dual[Double], r: Dual[Double]) = Dual(x.x * r.x, x.dx * r.x + r.dx * x.x) | |
| override def div(x: Dual[Double], r: Dual[Double]) = Dual(x.x / r.x, x.dx * (1 / r.x) + r.dx * (- x.x / r.x / r.x)) | |
| override def fromInt(x: Int): Dual[Double] = Dual(x, 0.0) | |
| override def negate(x: Dual[Double]): Dual[Double] = sys.error("not implemented") | |
| override def toDouble(x: Dual[Double]): Double = sys.error("not implemented") | |
| override def toFloat(x: Dual[Double]): Float = sys.error("not implemented") | |
| override def toInt(x: Dual[Double]): Int = sys.error("not implemented") | |
| override def toLong(x: Dual[Double]): Long = sys.error("not implemented") | |
| override def compare(x: Dual[Double], y: Dual[Double]): Int = sys.error("not implemented") | |
| } | |
| //static dual var( double x ) { return dual(x, 1.0); } | |
| def mySqrt[Real:Fractional](x: Real): Real = { | |
| val N = implicitly[Fractional[Real]] | |
| import N._ | |
| var y = one | |
| val two = plus(one, one) | |
| for(i <- 0 to 100) { | |
| y = div(plus(y, div(x, y)), two) | |
| } | |
| y | |
| } | |
| def main(args: Array[String]) { | |
| printf("%g%n", mySqrt(2.0)); | |
| printf("%g%n", mySqrt(3.0)); | |
| printf("%g%n", mySqrt(5.0)); | |
| printf("%g%n", mySqrt(0.25)); | |
| // --------------------------- // | |
| printf("%s%n", mySqrt(dual(2.0))); | |
| printf("%s%n", mySqrt(dual(3.0))); | |
| printf("%s%n", mySqrt(dual(5.0))); | |
| printf("%s%n", mySqrt(dual(0.25))); | |
| } | |
| } |
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| $ scalac AutomaticDifferentiation.scala | |
| $ scala AutomaticDifferentiation | |
| 1.41421 | |
| 1.73205 | |
| 2.23607 | |
| 0.500000 | |
| Dual(1.414213562373095,0.35355339059327373) | |
| Dual(1.7320508075688772,0.28867513459481287) | |
| Dual(2.23606797749979,0.22360679774997896) | |
| Dual(0.5,1.0) |
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