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Imports System
Imports CenterSpace.NMath.Core
Imports CenterSpace.NMath.Matrix
Namespace CenterSpace.NMath.Core.Examples.VisualBasic
' A .NET example in Visual Basic showing how to create streams of independent random numbers.
Module IndependentStreamsExample
Sub Main()
' NMath provides classes for generating several independent streams of random
' numbers using the leapfrog and skip-ahead (blocksplitting) methods.
' IMPORTANT NOTE:
' Skip-ahead and leapfrog streams are only supported for basic random number
' generator types which provide a more efficient algorithm than generation
' of that full sequence to pick out a required subsequence. The static variable
' SkipAheadStream.SupportedGeneratorTypes contains a list of the supported
' types for SkipAheadStream.
Dim Seed As Integer = &H124
Dim GenType As RandomNumberStream.BasicRandGenType = RandomNumberStream.BasicRandGenType.MultiplicativeCongruent31
' Create a SkipAheadRandomStreams object for generating 10 independent random number streams,
' each of length 100, using the Skip Ahead method.
Dim NumberOfStreams As Integer = 5
Dim StreamLength As Integer = 1000
Dim IndStreams As New SkipAheadRandomStreams(Seed, GenType, NumberOfStreams, StreamLength)
' Create a streamLength x numberOfStreams matrix A and use the SkipAheadRandomStreams object
' created above to fill it with random numbers. Each of the numberOfStreams columns
' in the resulting matrix will contain streamLength random deviates distributed
' uniformly in the interval (0, 1). Each column of random numbers will
' be independent from the others.
Dim Dist As New DoubleRandomUniformDistribution()
Dim A As New DoubleMatrix(StreamLength, NumberOfStreams)
IndStreams.Fill(Dist, A)
Console.WriteLine()
' Print out the correlation matrix for the sample to test
' independence. Correlations should be near zero for independent
' samples.
Dim CorrelationMatrix As DoubleSymmetricMatrix = RankCorrelation(A, True)
Console.WriteLine("Spearmans Rank Correlation for independent random samples:")
Dim I, J As Integer
For I = 0 To CorrelationMatrix.Rows - 1
For J = 0 To I - 1
Console.WriteLine("Correlation between column {0} and row {1} is {2}", I, J, CorrelationMatrix(I, J).ToString("G6"))
Next
Next
' You can also generate independent streams from different probability
' distributions. Here we generate 3 streams each with a different
' distribution using the leapfrog technique.
NumberOfStreams = 3
Dim LeapfrogIndStreams As New LeapfrogRandomStreams(Seed, GenType, NumberOfStreams, StreamLength)
Dim Distributions(NumberOfStreams) As IRandomNumberDistribution(Of Double)
Distributions(0) = New DoubleRandomBetaDistribution()
Distributions(1) = New DoubleRandomExponentialDistribution()
Distributions(2) = New DoubleRandomLogNormalDistribution()
Dim C As DoubleMatrix = LeapfrogIndStreams.Next(Distributions)
' Print out the rank correlation matrix for the sample to test
' independence. Correlations should be near zero for independent
' samples.
CorrelationMatrix = RankCorrelation(C, True)
Console.WriteLine()
Console.WriteLine("Spearmans Rank Correlation for samples from different distributions:")
For I = 0 To CorrelationMatrix.Rows - 1
For J = 0 To I - 1
Console.WriteLine("Correlation between column {0} and row {1} is {2}", I, J, CorrelationMatrix(I, J).ToString("G6"))
Next
Next
' Independent streams from discrete distributions are also supported.
StreamLength = 5
GenType = RandomNumberStream.BasicRandGenType.WinchannHillCombined
LeapfrogIndStreams = New LeapfrogRandomStreams(GenType, NumberOfStreams, StreamLength)
Dim DiscreteDistributions(NumberOfStreams) As IRandomNumberDistribution(Of Integer)
DiscreteDistributions(0) = New IntRandomBernoulliDistribution(0.6)
DiscreteDistributions(1) = New IntRandomGeometricDistribution(0.2)
DiscreteDistributions(2) = New IntRandomPoissonDistribution(0.8)
Dim DiscreteRandomSamples()() As Integer = LeapfrogIndStreams.Next(Of Integer)(DiscreteDistributions)
' The ith independent stream is in the array discreteRandomSamples[i].
For I = 0 To NumberOfStreams - 1
Console.WriteLine()
Console.WriteLine("Distribution: {0}", DiscreteDistributions(I).GetType())
For J = 0 To DiscreteRandomSamples(I).Length - 1
Console.Write("{0}{1}", DiscreteRandomSamples(I)(J), If(J = DiscreteRandomSamples(I).Length, "\n", ", "))
Next
Next
Console.WriteLine()
Console.WriteLine()
Console.WriteLine("Press Enter Key")
Console.Read()
End Sub
' <summary>
' Computes the Spearman rank correlation matrix for a set of random inputs. The random
' inputs are taken to be the columns of the input matrix. The symmetric,
' positive definite matrix whose i,j entry is the Spearman correlation coefficient
' between the inputs in column i and column j is computed and returned.
' </summary>
' <param name="A">Matrix whose columns are the inputs whose Spearman rank correlation
' coefficient is computed.</param>
' <param name="useMidRankForTies">If true mid ranks are used for ranking ties.
' </param>
' <returns>The symmetric, positive definite matrix whose row i, column j
' entry is the correlation coefficient between the inputs in column i and column j
' </returns>
Function RankCorrelation(ByVal A As DoubleMatrix, ByVal useMidRankForTies As Boolean) As DoubleSymmetricMatrix
'Console.WriteLine("A.Rows " & A.Rows)
'Console.WriteLine("A.Cols " & A.Cols)
Dim N As Integer = A.Rows
'Console.WriteLine(N)
Dim SortedData(N - 1) As Double
'Console.WriteLine(SortedData.Length)
Dim Indices(N - 1) As Integer
'Console.WriteLine(Indices.Length)
Dim XRanks As New DoubleVector(N)
Dim YRanks As New DoubleVector(N)
Dim R As New DoubleSymmetricMatrix(A.Cols)
For I = 0 To A.Cols - 1
For J = 0 To A.Cols - 1
If (I = J) Then
R(I, J) = 1.0
Else
RankData(A.Col(I), SortedData, Indices, XRanks, useMidRankForTies)
RankData(A.Col(J), SortedData, Indices, YRanks, useMidRankForTies)
R(I, J) = RankCorrelationFromRanks(XRanks, YRanks)
End If
Next
Next
Return R
End Function
Sub RankData(ByVal Data As DoubleVector, ByVal SortedData() As Double, ByVal Indices() As Integer, ByVal Ranks As DoubleVector, ByVal useMidRankForTies As Boolean)
'Console.WriteLine("data: " & Data.Length & " sorted " & SortedData.Length)
If (Data.Length <> SortedData.Length) Then
Throw New InvalidArgumentException("data and sortedData arrays do not have the same length in RankData")
End If
If (Data.Length <> Indices.Length) Then
Throw New InvalidArgumentException("data and indices arrays do not have the same length in RankData")
End If
For I = 0 To Indices.Length - 1
SortedData(I) = Data(I)
Indices(I) = I
Next
Array.Sort(Of Double, Integer)(SortedData, Indices)
For I = 0 To SortedData.Length - 1
Ranks(I) = Array.IndexOf(Of Integer)(Indices, I) + 1
Next
If (useMidRankForTies) Then
ApplyMidranks(SortedData, Ranks)
End If
End Sub
Sub ApplyMidranks(ByRef Data() As Double, ByRef Ranks As DoubleVector)
For I = 1 To Data.Length - 1
If (Data(I) = Data(I - 1)) Then
Dim Start As Integer = I - 1
Dim Count As Integer = 0
Dim Ranksum As Double = 0
While (Start + Count < Data.Length & Data(Start) = Data(Start + Count))
Ranksum += Ranks(Start + Count)
Count = Count + 1
End While
Dim MidRanks As Double = Ranksum / CType(Count, Double)
For S = 0 To Count - 1
Ranks(Start + S) = MidRanks
Next
I = Start + Count
End If
Next
End Sub
Function RankCorrelationFromRanks(ByRef xRanks As DoubleVector, ByRef yRanks As DoubleVector) As Double
Dim N As Integer = xRanks.Length
If (yRanks.Length <> N) Then
Throw New InvalidArgumentException("All arrays must have same length in RankCorreleation")
End If
Dim Sum As Double = 0 ''
For I = 0 To N - 1
Dim D As Double = xRanks(I) - yRanks(I)
Sum += (D * D)
Next
Return (1.0 - ((6 * Sum) / (N * (N * N - 1))))
End Function
End Module
End Namespace
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