99 lines
3 KiB
Scala
99 lines
3 KiB
Scala
import com.raquo.laminar.api.L.{*, given}
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import narr.*
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import org.scalajs.dom
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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 slash.matrix.Matrix
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import slash.matrix.decomposition.Eigen
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object CircularLawApp:
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val canvas = canvasTag(widthAttr := 600, heightAttr := 600)
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val ctx = canvas.ref.getContext("2d").asInstanceOf[dom.CanvasRenderingContext2D]
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val (eigvalSeries, runTimeReport) = randEigvalSeries[60]()
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val timeStepState = Var("0")
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def draw(timeStep: String): Unit =
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// center and normalize the coordinate system
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val width = canvas.ref.width
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val height = canvas.ref.height
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ctx.setTransform(1d, 0d, 0d, -1d, 0.5*width, 0.5*height)
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// clear the previous frame
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ctx.clearRect(-0.5*width, -0.5*width, width, height)
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// find the resolution
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val rDisp: Double = 1.5
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val res = width / (2*rDisp)
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// draw the eigenvalues
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val eigvals = eigvalSeries(timeStep.toInt)
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for n <- 0 to eigvals(0).length-1 do
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ctx.beginPath()
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ctx.arc(
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res * eigvals(0)(n),
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res * eigvals(1)(n),
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3d,
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0d, 2*math.Pi
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)
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ctx.fill()
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def complexEigenvalues[N <: Int](mat: Matrix[N, N])(using ValueOf[N]): (NArray[Double], NArray[Double]) =
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val eigen = Eigen(mat)
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(
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eigen.realEigenvalues.asInstanceOf[NArray[Double]],
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eigen.imaginaryEigenvalues.asInstanceOf[NArray[Double]]
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)
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def randEigvalSeries[N <: Int]()(using ValueOf[N]): (ArrayBuffer[(NArray[Double], NArray[Double])], String) =
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// start timing
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val startTime = System.currentTimeMillis()
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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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).times(math.sqrt(3d / dim))
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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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(eigvalSeries, runTime.toString() + " ms")
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def main(args: Array[String]): Unit =
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ctx.fillStyle = "white"
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lazy val app = div(
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idAttr := "app",
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div(runTimeReport),
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canvas,
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input(
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typ := "range",
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maxAttr := (eigvalSeries.length-1).toString,
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controlled(
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value <-- timeStepState.signal,
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onInput.mapToValue --> timeStepState.writer
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),
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timeStepState.signal --> draw
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)
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)
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renderOnDomContentLoaded(document.body, app)
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