StatCorrelation(Double
Definition
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.1.0+428f3840cfab98dda567bb0ed350b302533e273a
public static DoubleMatrix Correlation(
DoubleMatrix data,
DataOperation dataOperation
)Public Shared Function Correlation (
data As DoubleMatrix,
dataOperation As DataOperation
) As DoubleMatrixpublic:
static DoubleMatrix^ Correlation(
DoubleMatrix^ data,
DataOperation dataOperation
)static member Correlation :
data : DoubleMatrix *
dataOperation : DataOperation -> DoubleMatrix Parameters
- data DoubleMatrix
- The data.
- dataOperation DataOperation
- A constant to specify if the correlations are to be computed among the rows or among the columns.
Return Value
DoubleMatrixThe correlations among the rows or the columns of the specified data.
Remarks
Given a sequence of 
random variables 
,
their correlation matrix can be defined as that having generic entry:
By interpreting the rows or the columns of data as samples drawn from
random variables, this method returns estimates of the correlation matrix of such variables.
Let 
and
be the data
number of rows and columns, respectively, and define
Operating on rows
If dataOperation is OnRows,
then the method returns the estimated correlation matrix,
say 
,
among the 
rows
of data.
For 
entry
is NaN if
at least one among the l-th and k-th rows has zero variance.
Otherwise, 
is estimated through the coefficient
where
is the sample mean of the
i-th row.
Operating on columns
If dataOperation is OnColumns,
then the method returns the estimated correlation matrix
among the 
columns
of data.
For 
entry
is NaN if
at least one among the l-th and k-th columns has zero variance.
Otherwise, 
is estimated
through the coefficient
where
is the sample mean of the
j-th column.
Example
In the following example, the correlations among the rows and those among the columns of a data matrix are computed.
using System;
namespace Novacta.Analytics.CodeExamples
{
public class CorrelationExample0
{
public void Main()
{
// Create a matrix.
var data = new double[20] {
1, 2, -3, 6, -2,
2, 2, 2, 0, 7,
-3, 2, 3, 2, 9,
5, 2, 7, -1, -4
};
var matrix = DoubleMatrix.Dense(4, 5, data, StorageOrder.RowMajor);
Console.WriteLine("The data matrix:");
Console.WriteLine(matrix);
// Compute the correlations among columns.
var correlationOnColumns = Stat.Correlation(matrix, DataOperation.OnColumns);
Console.WriteLine();
Console.WriteLine("Correlations among columns:");
Console.WriteLine(correlationOnColumns);
// Correlation is overloaded to accept data as a read-only matrix:
// compute the correlations among rows using a read-only wrapper of the data matrix.
ReadOnlyDoubleMatrix readOnlyMatrix = matrix.AsReadOnly();
var correlationOnRows = Stat.Correlation(readOnlyMatrix, DataOperation.OnRows);
Console.WriteLine();
Console.WriteLine("Correlations among rows:");
Console.WriteLine(correlationOnRows);
}
}
}
// Executing method Main() produces the following output:
//
// The data matrix:
// 1 2 -3 6 -2
// 2 2 2 0 7
// -3 2 3 2 9
// 5 2 7 -1 -4
//
//
//
// Correlations among columns:
// 1 NaN 0.38632862 -0.448103279 -0.742391432
// NaN NaN NaN NaN NaN
// 0.38632862 NaN 1 -0.909741195 -0.0439435374
// -0.448103279 NaN -0.909741195 1 -0.125108648
// -0.742391432 NaN -0.0439435374 -0.125108648 1
//
//
//
// Correlations among rows:
// 1 -0.656407475 -0.400131212 -0.271852594
// -0.656407475 1 0.744043096 -0.505438473
// -0.400131212 0.744043096 1 -0.676775253
// -0.271852594 -0.505438473 -0.676775253 1
//
//Exceptions
| ArgumentNullException | data is null. |
| ArgumentException | dataOperation is not a field of DataOperation. |