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/* The Computer Language Shootout
http://shootout.alioth.debian.org/
contributed by Isaac Gouy
*/
object SpectralNorm {
def main(args: Array[String]) {
val n = Integer parseInt(args(0))
Console.printf("%.9f\n",
new SpectralNorm() approximate(n) )
}
}
class SpectralNorm(){
type Vector = Array[Double]
def approximate(n: Int)= {
val u = new Vector(n)
var i = 0;
while (i < n){ u(i) = 1.0; i = i+1 }
val v = new Vector(n)
i = 0
while (i < 10){
multiplyAtAv(n,u,v)
multiplyAtAv(n,v,u)
i = i+1
}
var vbv = 0.0; var vv = 0.0
i = 0
while (i < n){
vbv = vbv + u(i)*v(i)
vv = vv + v(i)*v(i)
i = i+1
}
Math sqrt(vbv/vv)
}
def a(i: Int, j: Int) = 1.0/((i+j)*(i+j+1)/2 +i+1)
def multiplyAv(n: Int, v: Vector, av: Vector) = {
var i = 0
while (i < n){
av(i) = 0.0
var j = 0
while (j < n){ av(i) = av(i) + a(i,j) * v(j); j = j+1 }
i = i+1
}
}
def multiplyAtv(n: Int, v: Vector, atv: Vector) = {
var i = 0
while (i < n){
atv(i) = 0.0
var j = 0
while (j < n){ atv(i) = atv(i) + a(j,i) * v(j); j = j+1 }
i = i+1
}
}
def multiplyAtAv(n: Int, v: Vector, atav: Vector) = {
val u = new Vector(n)
multiplyAv(n,v,u)
multiplyAtv(n,u,atav)
}
}
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