Added visualization/plotting of input/output data

Author: sboeschhuawei

mllib/src/main/scala/org/apache/spark/mllib/clustering/KMeans.scala

@@ -131,6 +131,7 @@ class KMeans private (
     }
 
     // Compute squared norms and cache them.
+    val collected = data.collect()
     val norms = data.map(Vectors.norm(_, 2.0))
     norms.persist()
     val zippedData = data.zip(norms).map { case (v, norm) =>

mllib/src/test/scala/org/apache/spark/mllib/clustering/PIClusteringSuite.scala

@@ -17,9 +17,9 @@
 
 package org.apache.spark.mllib.clustering
 
-import org.apache.spark.mllib.linalg.Vectors
-import org.apache.spark.{SparkConf, SparkContext}
 import org.apache.spark.graphx._
+import org.apache.spark.mllib.clustering.PICLinalg.DMatrix
+import org.apache.spark.{SparkConf, SparkContext}
 import org.scalatest.FunSuite
 
 import scala.util.Random
@@ -29,7 +29,7 @@ import scala.util.Random
  * Provides a method to run tests against a {@link SparkContext} variable that is correctly stopped
  * after each test.
  * TODO: import this from the graphx test cases package i.e. may need update to pom.xml
-*/
+ */
 trait LocalSparkContext {
   /** Runs `f` on a new SparkContext and ensures that it is stopped afterwards. */
   def withSpark[T](f: SparkContext => T) = {
@@ -50,16 +50,81 @@ trait LocalSparkContext {
  */
 class PIClusteringSuite extends FunSuite with LocalSparkContext {
 
+  import org.apache.spark.mllib.clustering.PIClusteringSuite._
+
   val PIC = PIClustering
   val LA = PICLinalg
   val RDDLA = RDDLinalg
   val A = Array
 
+  test("concentricCirclesTest") {
+    concentricCirclesTest()
+  }
+
+  def concentricCirclesTest() = {
+    val sigma = 1.0
+    val nIterations = 20
+
+    val circleSpecs = Seq(
+      // Best results for 30 points
+      CircleSpec(Point(0.0, 0.0), 0.03, .1, 3),
+      CircleSpec(Point(0.0, 0.0), 0.3, .03, 12),
+      CircleSpec(Point(0.0, 0.0), 1.0, .01, 15),
+      // Add following to get 100 points
+      CircleSpec(Point(0.0, 0.0), 1.5, .005, 30),
+      CircleSpec(Point(0.0, 0.0), 2.0, .002, 40)
+
+    )
+    val nClusters = circleSpecs.size
+    val cdata = createConcentricCirclesData(circleSpecs)
+    withSpark { sc =>
+      val vertices = new Random().shuffle(cdata.map { p =>
+        (p.label, Array(p.x, p.y))
+      })
+
+      val nVertices = vertices.length
+      val (ccenters, estCollected) = PIC.run(sc, vertices, nClusters, nIterations)
+      println(s"Cluster centers: ${ccenters.mkString(",")} " +
+        s"Estimates: ${estCollected.mkString(",")}")
+    }
+  }
+
+  test("irisData") {
+    irisData()
+  }
+
+  def irisData() = {
+    import org.apache.spark.mllib.linalg._
+    import scala.io.Source
+    val irisRaw = Source.fromFile("data/mllib/iris.data").getLines.map(_.split(","))
+    val iter: Iterator[(Array[Double], String)] = irisRaw.map { toks => (toks.slice(0, toks.length - 1).map {
+      _.toDouble
+    }, toks(toks.length - 1))
+    }
+    withSpark { sc =>
+      val irisRdd = sc.parallelize(iter.toSeq.map { case (vect, label) =>
+        (Vectors.dense(vect), label)
+      })
+      val irisVectorsRdd = irisRdd.map(_._1).cache()
+      val irisLabelsRdd = irisRdd.map(_._2)
+      val model = KMeans.train(irisVectorsRdd, 3, 10, 1)
+      val pred = model.predict(irisVectorsRdd).zip(irisLabelsRdd)
+      val predColl = pred.collect
+      irisVectorsRdd.unpersist()
+      predColl
+    }
+
+  }
+
+  def saveToMatplotLib(dmat: DMatrix, optLegend: Option[Array[String]], optLabels: Option[Array[Array[String]]]) = {
+    import breeze.plot._
+
+  }
+
   test("graphxSingleEigen") {
     graphxSingleEigen
   }
 
-  import org.apache.spark.mllib.clustering.PIClusteringSuite._
   def graphxSingleEigen() = {
 
     val (aMat, dxDat1) = createAffinityMatrix()
@@ -78,9 +143,13 @@ class PIClusteringSuite extends FunSuite with LocalSparkContext {
       val edgesRddCollected = edgesRdd.collect()
       println(s"edges=${edgesRddCollected.mkString(",")}")
       val rowSums = aMat.map { vect =>
-        vect.foldLeft(0.0){ _ + _ }
+        vect.foldLeft(0.0) {
+          _ + _
+        }
       }
-      val initialVt = PIC.createInitialVector(sc, affinityRdd.map{_._1}.collect, rowSums )
+      val initialVt = PIC.createInitialVector(sc, affinityRdd.map {
+        _._1
+      }.collect, rowSums)
       val G = PIC.createGraphFromEdges(sc, edgesRdd, nVertices, Some(initialVt))
       val printVtVectors: Boolean = true
       if (printVtVectors) {
@@ -95,7 +164,7 @@ class PIClusteringSuite extends FunSuite with LocalSparkContext {
         }.toArray
         println(s"graphInitialVt=${graphInitialVt.mkString(",")}\n"
           + s"initialVt=${initialVt.mkString(",")}")
-//        assert(LA.compareVectors(graphInitialVt, initialVtVect))
+        //        assert(LA.compareVectors(graphInitialVt, initialVtVect))
       }
       val (g2, norm, eigvect) = PIC.getPrincipalEigen(sc, G, nIterations)
       println(s"lambda=$norm eigvect=${eigvect.collect.mkString(",")}")
@@ -105,6 +174,7 @@ class PIClusteringSuite extends FunSuite with LocalSparkContext {
   test("fifteenVerticesTest") {
     fifteenVerticesTest()
   }
+
   def fifteenVerticesTest() = {
     val vertFile = "../data/graphx/new_lr_data.15.txt"
     val sigma = 1.0
@@ -115,64 +185,21 @@ class PIClusteringSuite extends FunSuite with LocalSparkContext {
       val nVertices = vertices.length
       val (ccenters, estimates) = PIC.run(sc, vertices, nClusters,
         nIterations, sigma)
-//      val collectedRdd = eigen.collect.map{_._2}
-//      println(s"DegreeMatrix:\n${LA.printMatrix(collectedRdd, nVertices, nVertices)}")
-//      println(s"Eigenvalue = $lambda EigenVectors:\n${LA.printMatrix(collectedRdd, nClusters, nVertices)}")
+      //      val collectedRdd = eigen.collect.map{_._2}
+      //      println(s"DegreeMatrix:\n${LA.printMatrix(collectedRdd, nVertices, nVertices)}")
+      //      println(s"Eigenvalue = $lambda EigenVectors:\n${LA.printMatrix(collectedRdd, nClusters, nVertices)}")
     }
   }
 
-  test("concentricCirclesTest") {
-    concentricCirclesTest()
-  }
-  def concentricCirclesTest() = {
-    val sigma = 1.0
-    val nIterations = 20
-    val circleSpecs = Seq(
-    // Best results for 30 points
-      CircleSpec(Point(0.0,0.0), 0.03, .1, 3),
-      CircleSpec(Point(0.0,0.0), 0.3, .03, 12),
-      CircleSpec(Point(0.0,0.0), 1.0, .01, 15),
-      CircleSpec(Point(0.0,0.0), 1.5, .005, 25),
-      CircleSpec(Point(0.0,0.0), 2.0, .002, 40)
-
-    // DECENT
-//      CircleSpec(Point(0.0,0.0), 0.1, .1, 5),
-//      CircleSpec(Point(0.0,0.0), 1.0, .1, 15),
-//      CircleSpec(Point(0.0,0.0), 2.5, .1, 30)
-
-    // GOOD but big (90 points)
-//      CircleSpec(Point(0.0,0.0), 0.1, .1, 5),
-//      CircleSpec(Point(0.0,0.0), 1.0, .03, 25),
-//      CircleSpec(Point(0.0,0.0), 2.5, .01, 60)
-    )
-    val nClusters = circleSpecs.size
-    val cdata = createConcentricCirclesData(circleSpecs)
-    withSpark { sc =>
-      val vertices = new Random().shuffle(cdata.map { p =>
-        (p.label, Array(p.x, p.y))
-      })
+  //  test("testLinearFnGenerator") {
+  //    val PS = PolySpec
+  //    val dr = new DRange(0.0, 5.0)
+  //    val polyInfo = A(PS(3.0, 2.0, -1.0)
+  //    val noiseRatio = 0.1
+  //    val l = List(1,2,3)
+  //    l.scanLeft(
+  //  }
 
-      val nVertices = vertices.length
-      val (ccenters, estCollected) = PIC.run(sc, vertices, nClusters, nIterations)
-      println(s"Cluster centers: ${ccenters.mkString(",")} " +
-        s"Estimates: ${estCollected.mkString(",")}")
-    }
-  }
-
-//  test("testLinearFnGenerator") {
-//    val PS = PolySpec
-//    val dr = new DRange(0.0, 5.0)
-//    val polyInfo = A(PS(3.0, 2.0, -1.0)
-//    val noiseRatio = 0.1
-//    val l = List(1,2,3)
-//    l.scanLeft(
-//  }
-
-  def printMatrix(darr: Array[Double], numRows: Int, numCols: Int): String =
-    LA.printMatrix(darr, numRows, numCols)
-
-  def printMatrix(darr: Array[Array[Double]], numRows: Int, numCols: Int): String =
-    LA.printMatrix(darr, numRows, numCols)
 }
 
 object PIClusteringSuite {
@@ -183,14 +210,17 @@ object PIClusteringSuite {
 
   case class Point(label: Long, x: Double, y: Double) {
     def this(x: Double, y: Double) = this(-1L, x, y)
+
     override def toString() = s"($label, (${pdoub(x)},${pdoub(y)}))"
   }
+
   object Point {
     def apply(x: Double, y: Double) = new Point(-1L, x, y)
   }
 
   case class CircleSpec(center: Point, radius: Double, noiseToRadiusRatio: Double,
                         nPoints: Int, uniformDistOnCircle: Boolean = true)
+
   def createConcentricCirclesData(circleSpecs: Seq[CircleSpec]) = {
     import org.apache.spark.mllib.random.StandardNormalGenerator
     val normalGen = new StandardNormalGenerator
@@ -199,9 +229,9 @@ object PIClusteringSuite {
       idStart += 1000
       val circlePoints = for (thetax <- 0 until csp.nPoints) yield {
         val theta = thetax * 2 * Math.PI / csp.nPoints
-        val (x,y) = ( csp.radius * Math.cos(theta) * (1 + normalGen.nextValue * csp.noiseToRadiusRatio),
+        val (x, y) = (csp.radius * Math.cos(theta) * (1 + normalGen.nextValue * csp.noiseToRadiusRatio),
           csp.radius * Math.sin(theta) * (1 + normalGen.nextValue * csp.noiseToRadiusRatio))
-        (Point(idStart+thetax, x,y))
+        (Point(idStart + thetax, x, y))
       }
       circlePoints
     }
@@ -211,15 +241,15 @@ object PIClusteringSuite {
   }
 
   def printPoints(points: Seq[Point]) = {
-//    val sorted = points.sortWith { case (p1, p2) =>
-//      if (LA.withinTol(p1.y-p2.y)) {
-//        p1.x <= p2.x
-//      } else {
-//        p1.y >= p2.y
-//      }
-//    }
-//    sorted.mkString("["," , ","]")
-    points.mkString("["," , ","]")
+    //    val sorted = points.sortWith { case (p1, p2) =>
+    //      if (LA.withinTol(p1.y-p2.y)) {
+    //        p1.x <= p2.x
+    //      } else {
+    //        p1.y >= p2.y
+    //      }
+    //    }
+    //    sorted.mkString("["," , ","]")
+    points.mkString("[", " , ", "]")
   }
 
   def createAffinityMatrix() = {
@@ -229,19 +259,7 @@ object PIClusteringSuite {
       A(0.8, 0.7, 0, 0.75),
       A(0.9, .5, .75, 0)
     )
-//    val asize=10
-//    val dat1 = toMat(for (ix <- 0 until asize;
-//        for cx<- 0 until asize)
-//    yield {
-//      cx match {
-//        case _ if cx < 2 => 10
-//        case _ if cx <= 7 => 0.5
-//        case _ => cx * 0.2
-//      }
-//    }, asize, asize)
-
-
-    println(s"Input mat: ${LA.printMatrix(dat1, 4,4)}")
+    println(s"Input mat: ${LA.printMatrix(dat1, 4, 4)}")
     val D = /*LA.transpose(dat1)*/ dat1.zipWithIndex.map { case (dvect, ix) =>
       val sum = dvect.foldLeft(0.0) {
         _ + _
@@ -263,8 +281,6 @@ object PIClusteringSuite {
 
   def main(args: Array[String]) {
     val pictest = new PIClusteringSuite
-//    pictest.graphxSingleEigen()
-//    pictest.fifteenVerticesTest()
     pictest.concentricCirclesTest()
   }
 }

python/pyspark/mllib/matplot.py

@@ -0,0 +1,80 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+class Plot:
+  def plotCircles(self):
+    # LABELS=self.getLabels()
+    (labels,x,y) = ([], [], [])
+    for (label, (xx,yy)) in self.getCirclePoints():
+       labels.append(int(label))
+       x.append(float(xx))
+       y.append(float(yy))
+
+    colors = ['b', 'g', 'r','y','w', 'm']
+    norm = plt.normalize()
+    norm.autoscale(x)
+    # norm.autoscale(y)
+    for (plabel, x, y) in zip(labels,x, y):
+        xcolor = colors[-1 + int(plabel / 1000)]
+        lines = plt.plot(x, y, 'x',markersize=3,color=xcolor)
+        plt.annotate(str(plabel),xy=(x,y), xytext= (-5,5),
+                     textcoords='offset points',
+                arrowprops=dict(facecolor=xcolor, shrink=0.01),
+                horizontalalignment='right', verticalalignment='bottom',
+                fontsize=6
+              )
+        # plt.plot(x, y, 'o', markersize=1,color=colors[-1 + (plabel / 1000)], label= '%s' %plabel )
+        # plt.plot(x, y)
+        # plt.plot(x, y, color='y') # , markersize=1, label= '%s' %plabel )
+
+    plt.show()
+    plt.savefig('inputs.png')
+
+  def plotOutputs(self):
+    (labels,locs,clusters) = ([], [], [])
+    (centers_sorted, out_points) = self.getOutputPoints()
+    center_index_to_magnitude_map = {cx : cm for (cx,(cm,cloc)) in centers_sorted}
+    for ((label, loc), cluster) in out_points:
+       labels.append(label)
+       locs.append(loc)
+       clusters.append(cluster)
+
+    colors = ['b', 'g', 'r','y','c', 'm']
+    markers = ['s', '+', 'x','8','D', '*']
+    norm = plt.normalize()
+    norm.autoscale(locs)
+    # norm.autoscale(y)
+    for (ix, (plabel, loc, cluster)) in enumerate(zip(labels,locs, clusters)):
+        xcolor = colors[-1 + int(plabel / 1000)]
+        clusterx = center_index_to_magnitude_map[cluster]
+        xmarker = markers[clusterx]
+        lines = plt.plot(ix, loc, xmarker,markersize=3,color=xcolor)
+        plt.yscale('linear')
+        plt.annotate(str(plabel),xy=(ix,loc), xytext= (-5,5),
+                     textcoords='offset points',
+                arrowprops=dict(facecolor=xcolor, shrink=0.01),
+                horizontalalignment='right', verticalalignment='bottom',
+                fontsize=6
+              )
+        # plt.plot(x, y, 'o', markersize=1,color=colors[-1 + (plabel / 1000)], label= '%s' %plabel )
+        # plt.plot(x, y)
+        # plt.plot(x, y, color='y') # , markersize=1, label= '%s' %plabel )
+
+    plt.show()
+    plt.savefig('outputs.png')
+
+  def getCirclePoints(self):
+    fillInLabelsHere=[(1000, (0.026055,0.000000)) , (1001, (-0.015593,0.023425)) , (1002, (-0.012923,-0.024027)) , (2000, (0.300923,0.000000)) , (2001, (0.270132,0.148135)) , (2002, (0.157354,0.261961)) , (2003, (0.000000,0.287528)) , (2004, (-0.163370,0.250285)) , (2005, (-0.257946,0.153550)) , (2006, (-0.290993,0.000000)) , (2007, (-0.241891,-0.148736)) , (2008, (-0.152099,-0.273338)) , (2009, (-0.000000,-0.313627)) , (2010, (0.140641,-0.269290)) , (2011, (0.267766,-0.145981)) , (3000, (1.000656,0.000000)) , (3001, (0.917339,0.413769)) , (3002, (0.664959,0.738677)) , (3003, (0.305250,0.931993)) , (3004, (-0.103926,0.988312)) , (3005, (-0.495637,0.866338)) , (3006, (-0.813345,0.578460)) , (3007, (-0.994044,0.205409)) , (3008, (-0.970741,-0.209993)) , (3009, (-0.812726,-0.587868)) , (3010, (-0.502153,-0.867390)) , (3011, (-0.105587,-1.000996)) , (3012, (0.309040,-0.939486)) , (3013, (0.676942,-0.740258)) , (3014, (0.922195,-0.403860)) , (4000, (1.500370,0.000000)) , (4001, (1.455509,0.372520)) , (4002, (1.313174,0.724842)) , (4003, (1.103429,1.023959)) , (4004, (0.808768,1.264479)) , (4005, (0.463024,1.435827)) , (4006, (0.093931,1.489670)) , (4007, (-0.282205,1.468860)) , (4008, (-0.641969,1.357055)) , (4009, (-0.960632,1.153854)) , (4010, (-1.208709,0.881284)) , (4011, (-1.398515,0.558539)) , (4012, (-1.480977,0.186267)) , (4013, (-1.466877,-0.188276)) , (4014, (-1.384225,-0.551507)) , (4015, (-1.210292,-0.878939)) , (4016, (-0.954331,-1.158034)) , (4017, (-0.637888,-1.365072)) , (4018, (-0.281502,-1.485258)) , (4019, (0.093529,-1.517232)) , (4020, (0.462337,-1.435428)) , (4021, (0.802200,-1.273476)) , (4022, (1.088346,-1.022671)) , (4023, (1.303522,-0.726381)) , (4024, (1.441486,-0.376954)) , (5000, (2.006090,0.000000)) , (5001, (1.975017,0.312498)) , (5002, (1.903007,0.616796)) , (5003, (1.779725,0.906926)) , (5004, (1.615806,1.176478)) , (5005, (1.418842,1.412193)) , (5006, (1.176238,1.618327)) , (5007, (0.907240,1.778774)) , (5008, (0.616737,1.907389)) , (5009, (0.312334,1.972686)) , (5010, (0.000000,2.003958)) , (5011, (-0.312175,1.978076)) , (5012, (-0.617802,1.906119)) , (5013, (-0.910539,1.783043)) , (5014, (-1.176869,1.610774)) , (5015, (-1.413218,1.413486)) , (5016, (-1.612863,1.172439)) , (5017, (-1.777011,0.909389)) , (5018, (-1.897253,0.618963)) , (5019, (-1.973228,0.312265)) , (5020, (-1.997124,0.000000)) , (5021, (-1.972173,-0.312524)) , (5022, (-1.904784,-0.617654)) , (5023, (-1.784558,-0.908745)) , (5024, (-1.618230,-1.172448)) , (5025, (-1.417072,-1.417323)) , (5026, (-1.173193,-1.611568)) , (5027, (-0.906398,-1.779951)) , (5028, (-0.619644,-1.903364)) , (5029, (-0.314077,-1.973233)) , (5030, (-0.000000,-2.001369)) , (5031, (0.312326,-1.985733)) , (5032, (0.617108,-1.897669)) , (5033, (0.905477,-1.784064)) , (5034, (1.178242,-1.623806)) , (5035, (1.410244,-1.418794)) , (5036, (1.625406,-1.176519)) , (5037, (1.774561,-0.906173)) , (5038, (1.897196,-0.618358)) , (5039, (1.969360,-0.311903))]
+    return fillInLabelsHere
+
+  def getOutputPoints(self):
+    centers = [(0,[2.9860909099353196E-4]),(1,[0.10256078249751793]),(2,[0.03543295315856783]),(3,[0.005922820396093594]),(4,[0.1126278976630788])]
+    # centers = [(0,2.9860909099353196E-4),(1,0.10256078249751793),(2,0.03543295315856783),(3,0.005922820396093594),(4,0.1126278976630788)]
+    centers_sorted = sorted(centers,key = lambda c: c[1])
+    centers_sorted_ix = list(enumerate(centers_sorted))
+    opoints = [((1000,[0.11255703573044015]),4),((1001,[0.11258575254117632]),4),((1002,[0.11257078842887869]),4),((2000,[0.10171707839616172]),1),((2001,[0.10290373550340648]),1),((2002,[0.10213543105489717]),1),((2003,[0.10392631471722016]),1),((2004,[0.10232694874744065]),1),((2005,[0.10251591585124924]),1),((2006,[0.10127088683120573]),1),((2007,[0.10253071346571023]),1),((2008,[0.1033873501355303]),1),((2009,[0.10252830585275843]),1),((2010,[0.10227294667030125]),1),((2011,[0.1025608138347488]),1),((3000,[0.035906883751883376]),2),((3001,[0.03504061712471225]),2),((3002,[0.03578644371373917]),2),((3003,[0.03652384259635414]),2),((3004,[0.03460755093576597]),2),((3005,[0.035531248714107226]),2),((3006,[0.034675624652207575]),2),((3007,[0.035952072191425356]),2),((3008,[0.03632290316860608]),2),((3009,[0.03719884210586558]),2),((3010,[0.034909360099880986]),2),((3011,[0.03451626245224591]),2),((3012,[0.036276532353686705]),2),((3013,[0.034499068006321326]),2),((3014,[0.03444715655157359]),2),((4000,[0.0063409978898199965]),0),((4001,[0.005641897862833211]),0),((4002,[0.0061989986546385325]),0),((4003,[0.005732189674461753]),0),((4004,[0.00583169713457494]),0),((4005,[0.006124006606283006]),0),((4006,[0.006096865495117659]),0),((4007,[0.005843993649928398]),0),((4008,[0.0058995813542313145]),0),((4009,[0.006066471732454353]),0),((4010,[0.00597453407106392]),0),((4011,[0.00569094398306935]),0),((4012,[0.006135281376077952]),0),((4013,[0.005764302127595832]),0),((4014,[0.006021919856338952]),0),((4015,[0.005668462670801292]),0),((4016,[0.006069813665268231]),0),((4017,[0.005834224015447166]),0),((4018,[0.005884951063841428]),0),((4019,[0.006079709703702092]),0),((4020,[0.005742608529812731]),0),((4021,[0.0059101428982749745]),0),((4022,[0.005868093983272937]),0),((4023,[0.005871154799370013]),0),((4024,[0.005934592542335712]),0),((5000,[2.812367638627021E-4]),3),((5001,[2.992710669415067E-4]),3),((5002,[3.1228235094580767E-4]),3),((5003,[2.907886025099482E-4]),3),((5004,[3.0010232120431863E-4]),3),((5005,[2.979376705248636E-4]),3),((5006,[2.9701136951793667E-4]),3),((5007,[2.9191731183498057E-4]),3),((5008,[2.9511436042104405E-4]),3),((5009,[2.999732644713502E-4]),3),((5010,[2.982000382551668E-4]),3),((5011,[2.84875034573973E-4]),3),((5012,[2.928298888404219E-4]),3),((5013,[3.067900632285769E-4]),3),((5014,[2.900538609854514E-4]),3),((5015,[2.9372966822917296E-4]),3),((5016,[3.045205684767979E-4]),3),((5017,[3.0299172395976915E-4]),3),((5018,[2.8902170153107074E-4]),3),((5019,[3.0518145810340207E-4]),3),((5020,[2.854725344557008E-4]),3),((5021,[2.9452123441530835E-4]),3),((5022,[2.989311736005669E-4]),3),((5023,[3.1641592934541227E-4]),3),((5024,[2.997541391147682E-4]),3),((5025,[2.985016516572594E-4]),3),((5026,[3.0227813918851565E-4]),3),((5027,[2.9387535815135084E-4]),3),((5028,[2.995694521972803E-4]),3),((5029,[2.9486477413906566E-4]),3),((5030,[2.938900550102159E-4]),3),((5031,[2.969700562695488E-4]),3),((5032,[3.11130411239986E-4]),3),((5033,[2.9783807673530586E-4]),3),((5034,[3.019034936161776E-4]),3),((5035,[2.8495706412754086E-4]),3),((5036,[3.081362782208011E-4]),3),((5037,[2.9365158669359705E-4]),3),((5038,[3.0311814421690064E-4]),3),((5039,[3.010157660759845E-4]),3)]
+    return (centers_sorted_ix, opoints)
+
+if __name__ == '__main__':
+    Plot().plotCircles()
+    Plot().plotOutputs()