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144bfb8faf
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144bfb8faf | ||
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27ada6566b |
@ -3,7 +3,7 @@
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<head>
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<head>
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<meta charset="UTF-8">
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<meta charset="UTF-8">
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<title>The circular law</title>
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<title>The circular law</title>
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<script type="text/javascript" src="./target/scala-3.4.2/circular-law-fastopt/main.js"></script>
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<script type="text/javascript" src="./target/scala-3.4.2/circular-law-opt/main.js"></script>
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<link rel="stylesheet" href="main.css"/>
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<link rel="stylesheet" href="main.css"/>
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</head>
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</head>
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<body></body>
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<body></body>
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@ -2,6 +2,7 @@ import com.raquo.laminar.api.L.{*, given}
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import narr.*
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import narr.*
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import org.scalajs.dom
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import org.scalajs.dom
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import org.scalajs.dom.document
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import org.scalajs.dom.document
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import scala.collection.mutable.ArrayBuffer
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import scala.math.{cos, sin}
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import scala.math.{cos, sin}
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import slash.matrix.Matrix
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import slash.matrix.Matrix
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import slash.matrix.decomposition.Eigen
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import slash.matrix.decomposition.Eigen
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@ -38,36 +39,45 @@ object CircularLawApp:
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)
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)
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ctx.fill()
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ctx.fill()
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def eigvalsRotated[N <: Int](A: Matrix[N, N], time: Double)(using ValueOf[N]): (NArray[Double], NArray[Double]) =
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def complexEigenvalues[N <: Int](mat: Matrix[N, N])(using ValueOf[N]): (NArray[Double], NArray[Double]) =
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// create transformation
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val eigen = Eigen(mat)
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val maxFreq = 4
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val T = Matrix.identity[N, N]
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val dim: Int = valueOf[N]
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for n <- 0 to dim by 2 do
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val a = cos(math.Pi * time * (n % maxFreq))
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val b = sin(math.Pi * time * (n % maxFreq))
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T(n, n) = a
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T(n+1, n) = b
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T(n, n+1) = -b
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T(n+1, n+1) = a
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// find eigenvalues
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val eigen = Eigen(T*A)
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(
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(
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eigen.realEigenvalues.asInstanceOf[NArray[Double]],
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eigen.realEigenvalues.asInstanceOf[NArray[Double]],
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eigen.imaginaryEigenvalues.asInstanceOf[NArray[Double]]
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eigen.imaginaryEigenvalues.asInstanceOf[NArray[Double]]
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)
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)
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def randEigvalSeries[N <: Int]()(using ValueOf[N]): (List[(NArray[Double], NArray[Double])], String) =
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def randEigvalSeries[N <: Int]()(using ValueOf[N]): (ArrayBuffer[(NArray[Double], NArray[Double])], String) =
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val timeRes = 100
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// start timing
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val dim: Int = valueOf[N]
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val startTime = System.currentTimeMillis()
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val startTime = System.currentTimeMillis()
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val A = new Matrix[N, N](
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// initialize the random matrix step
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val dim: Int = valueOf[N]
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var randMat = new Matrix[N, N](
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NArray.tabulate(dim*dim)(k => (math.E*k*k) % 2 - 1)
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NArray.tabulate(dim*dim)(k => (math.E*k*k) % 2 - 1)
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).times(math.sqrt(3d / dim))
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).times(math.sqrt(3d / dim))
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val series = List.tabulate(timeRes)(t => eigvalsRotated(A, t.toDouble / timeRes))
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// initialize the rotation step
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val timeRes = 100
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val maxFreq = 4
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val rotStep = Matrix.identity[N, N]
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for n <- 0 to dim by 2 do
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val ang = math.Pi * (n % maxFreq) / timeRes
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val cos_ang = cos(ang)
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val sin_ang = sin(ang)
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rotStep(n, n) = cos_ang
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rotStep(n+1, n) = sin_ang
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rotStep(n, n+1) = -sin_ang
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rotStep(n+1, n+1) = cos_ang
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// find the eigenvalues
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val eigvalSeries = ArrayBuffer(complexEigenvalues(randMat))
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for _ <- 1 to timeRes-1 do
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randMat = rotStep * randMat
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eigvalSeries += complexEigenvalues(randMat)
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// finish timing
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val runTime = System.currentTimeMillis() - startTime
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val runTime = System.currentTimeMillis() - startTime
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(series, runTime.toString() + " ms")
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(eigvalSeries, runTime.toString() + " ms")
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def main(args: Array[String]): Unit =
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def main(args: Array[String]): Unit =
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ctx.fillStyle = "white"
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ctx.fillStyle = "white"
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