IGLib
1.7.2
The IGLib base library EXTENDED - with other lilbraries and applications.
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Represents the Cholesky Decomposition of a symmetric, positive definite matrix. More...
Public Member Functions | |
SquareMatrix | SquareRootMatrix () |
Returns the Cholesky square root matrix. More... | |
ColumnVector | Solve (IList< double > rhs) |
Computes the solution vector that, when multiplied by the original matrix, produces the given left-hand side vector. More... | |
SymmetricMatrix | Inverse () |
Computes the inverse of the original matrix. More... | |
double | Determinant () |
Computes the determinant of the original matrix. More... | |
Properties | |
int | Dimension [get] |
Gets the dimension of the system. More... | |
Represents the Cholesky Decomposition of a symmetric, positive definite matrix.
A Cholesky decomposition represents a matrix as the product of a lower-left triangular matrix and its transpose. For example:
The Choleksy decomposition of a symmetric, positive definite matrix can be obtained using the SymmetricMatrix.CholeskyDecomposition method of the SymmetricMatrix class.
Here is an example that uses a Cholesky decomposition to solve a linear algebra problem.
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Returns the Cholesky square root matrix.
Referenced by Test.MultivariateSampleTest.CreateMultivariateNormalSample().
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Computes the solution vector that, when multiplied by the original matrix, produces the given left-hand side vector.
rhs | The right-hand-side vector. |
Referenced by Meta.Numerics.Statistics.MultivariateSample.LinearRegression_Internal().
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Computes the inverse of the original matrix.
Referenced by Meta.Numerics.Statistics.UncertainMeasurementSample< T >.FitToFunction(), Meta.Numerics.Statistics.Distributions.WeibullDistribution.FitToSample(), Meta.Numerics.Statistics.Distributions.BetaDistribution.FitToSample(), Meta.Numerics.Statistics.Distributions.GammaDistribution.FitToSample(), Meta.Numerics.Statistics.MultivariateSample.LinearRegression_Internal(), Meta.Numerics.Statistics.Sample.MaximumLikelihoodFit(), and Test.SymmetricMatrixTest.SymmetricMatrixDecomposition().
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Computes the determinant of the original matrix.
Referenced by Test.SymmetricMatrixTest.CatalanHankelMatrixDeterminant(), and Test.MultiIntegrateTest.GaussianIntegrals().
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Gets the dimension of the system.
Referenced by Test.SymmetricMatrixTest.SymmetricMatrixDecomposition().