StatCovariance(Read
Definition
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.1.0+428f3840cfab98dda567bb0ed350b302533e273a
public static DoubleMatrix Covariance(
ReadOnlyDoubleMatrix data,
bool adjustForBias,
DataOperation dataOperation
)Public Shared Function Covariance (
data As ReadOnlyDoubleMatrix,
adjustForBias As Boolean,
dataOperation As DataOperation
) As DoubleMatrixpublic:
static DoubleMatrix^ Covariance(
ReadOnlyDoubleMatrix^ data,
bool adjustForBias,
DataOperation dataOperation
)static member Covariance :
data : ReadOnlyDoubleMatrix *
adjustForBias : bool *
dataOperation : DataOperation -> DoubleMatrix Parameters
- data ReadOnlyDoubleMatrix
- The data.
- adjustForBias Boolean
- If set to true signals that the covariances are adjusted for bias.
- dataOperation DataOperation
- A constant to specify if the covariances are to be computed among the rows or among the columns.
Return Value
DoubleMatrixThe covariances among the rows or the columns of the specified data, eventually adjusted for bias.
Remarks
Given a sequence of 
random
variables 
,
their covariance 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
covariance 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 covariance matrix
among the 
rows
of data.
If adjustForBias is set to false, then
is estimated through
the coefficient
where
is the sample mean of the
i-th row.
Such estimator is biased. If adjustForBias is set
to true, then
the estimator is corrected for bias
and 
is evaluated through
the coefficient
provided that 
is greater than 1;
otherwise, an exception is thrown.
Operating on columns
If dataOperation is OnColumns,
then the method returns the estimated covariance matrix among the 
columns
of data.
If adjustForBias is set to false, then
is estimated through the coefficient
where
is the sample mean of the
j-th column.
Such estimator is biased. If adjustForBias is set to true, then
the estimator is corrected for bias
and 
is evaluated through the coefficient
provided that 
is greater than 1;
otherwise, an exception is thrown.
Example
In the following example, the covariances among the rows and those among the columns of a data matrix are computed.
using System;
namespace Novacta.Analytics.CodeExamples
{
public class CovarianceExample0
{
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);
// Covariance can be adjusted for bias.
bool adjustForBias = true;
// Compute the covariances among columns.
var covarianceOnColumns = Stat.Covariance(matrix, adjustForBias, DataOperation.OnColumns);
Console.WriteLine();
Console.WriteLine("Covariances among columns:");
Console.WriteLine(covarianceOnColumns);
// Covariance is overloaded to accept data as a read-only matrix:
// compute the covariances among rows using a read-only wrapper of the data matrix.
ReadOnlyDoubleMatrix readOnlyMatrix = matrix.AsReadOnly();
var covarianceOnRows = Stat.Covariance(readOnlyMatrix, adjustForBias, DataOperation.OnRows);
Console.WriteLine();
Console.WriteLine("Covariances among rows:");
Console.WriteLine(covarianceOnRows);
}
}
}
// 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
//
//
//
// Covariances among columns:
// 10.9166667 0 5.25 -4.58333333 -15.8333333
// 0 0 0 0 0
// 5.25 0 16.9166667 -11.5833333 -1.16666667
// -4.58333333 0 -11.5833333 9.58333333 -2.5
// -15.8333333 0 -1.16666667 -2.5 41.6666667
//
//
//
// Covariances among rows:
// 12.7 -6.1 -6.1 -4.3
// -6.1 6.8 8.3 -5.85
// -6.1 8.3 18.3 -12.85
// -4.3 -5.85 -12.85 19.7
//
//Exceptions
| ArgumentNullException | data is null. |
| ArgumentException | dataOperation is not a field of
DataOperation. -or- adjustForBias is true, dataOperation is OnRows and the data number of columns is less than 2. -or- adjustForBias is true, dataOperation is OnColumns and the data number of rows is less than 2. |