SystemObject Extreme.Mathematics.LinearAlgebraSingleLinearTransformation Extreme.Mathematics.LinearAlgebraSingleDecomposition Extreme.Mathematics.LinearAlgebraSingleSparseLUDecomposition
Namespace: Extreme.Mathematics.LinearAlgebraAssembly: Extreme.Numerics.Version4x.Net40 (in Extreme.Numerics.Version4x.Net40.dll) Version: 4.2.11333.0 (5.0.12317.0)
public sealed class SingleSparseLUDecomposition : SingleDecomposition
Public NotInheritable Class SingleSparseLUDecomposition
Inherits SingleDecomposition
public ref class SingleSparseLUDecomposition sealed : public SingleDecomposition
[<SealedAttribute>]
type SingleSparseLUDecomposition =
class
inherit SingleDecomposition
end
The SingleSparseLUDecomposition type exposes the following members.
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| Name | Description |
---|
 | ApplyP(SingleMatrix) | |
 | ApplyP(SingleVector) |
Applies the permutation P of the decomposition
PA= LU to a vector.
|
 | ApplyP(SingleMatrix, Boolean) | |
 | ApplyP(SingleVector, Boolean) |
Applies the permutation P of the decomposition
PA= LU to a vector.
|
 | ApplyP(SingleMatrix, TransposeOperation, Boolean) | |
 | ApplyP(SingleVector, TransposeOperation, Boolean) |
Applies the permutation P of the decomposition
PA= LU to a vector.
|
 | Decompose |
Performs the actual LU decomposition.
(Overrides SingleDecompositionDecompose.) |
 | Equals | Determines whether the specified Object is equal to the current Object. (Inherited from Object.) |
 | EstimateConditionNumber |
Calculates an estimate for the condition
number of the matrix underlying this
system of equations.
(Overrides SingleLinearTransformationEstimateConditionNumber.) |
 | GetDeterminant | (Overrides SingleLinearTransformationGetDeterminant.) |
 | GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) |
 | GetInverse | (Overrides SingleLinearTransformationGetInverse.) |
 | GetObjectData | (Inherited from SingleLinearTransformation.) |
 | GetType | Gets the Type of the current instance. (Inherited from Object.) |
 | IsSingular |
Gets a value indicating whether the BaseMatrix of this decomposition
is singular.
(Inherited from SingleDecomposition.) |
 | Rank |
Returns the numerical rank of a matrix.
(Inherited from SingleLinearTransformation.) |
 | Rank(Single) |
Returns the numerical rank of a matrix using the specified tolerance.
(Overrides SingleLinearTransformationRank(Single).) |
 | Solve(SingleMatrix) |
Solves the system of linear equations for the specified
right-hand side SingleMatrix.
(Inherited from SingleLinearTransformation.) |
 | Solve(SingleVector) |
Solves the system of linear equations for the specified
right-hand side SingleVector.
(Inherited from SingleLinearTransformation.) |
 | Solve(SingleDenseMatrix, Boolean) |
Solves the system of simultaneous linear equations for the specified
right-hand side SingleDenseMatrix and optionally
overwrites the right-hand side with the solution.
(Overrides SingleLinearTransformationSolve(SingleDenseMatrix, Boolean).) |
 | Solve(SingleDenseVector, Boolean) |
Solves the system of simultaneous linear equations for the specified
right-hand side SingleVector.
(Overrides SingleLinearTransformationSolve(SingleDenseVector, Boolean).) |
 | SolveTranspose(SingleMatrix) |
Solves the transposed system of linear equations for the specified
right-hand side SingleMatrix.
(Inherited from SingleLinearTransformation.) |
 | SolveTranspose(SingleVector) |
Solves the system of linear equations for the specified
right-hand side SingleVector.
(Inherited from SingleLinearTransformation.) |
 | SolveTranspose(SingleDenseMatrix, Boolean) |
Solves the transposed system of linear equations for the specified
right-hand side SingleDenseMatrix and optionally overwrites the
right-hand side with the solution.
(Overrides SingleLinearTransformationSolveTranspose(SingleDenseMatrix, Boolean).) |
 | SolveTranspose(SingleDenseVector, Boolean) |
Solves the transposed system of linear equations for the specified
right-hand side DenseVector and optionally
overwrites the right-hand side with the solution.
(Overrides SingleLinearTransformationSolveTranspose(SingleDenseVector, Boolean).) |
 | ToString | Returns a string that represents the current object. (Inherited from Object.) |
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The LU decomposition of a matrix
A rewrites the
matrix in the form
A=
PLU, where
P is a permutation matrix,
L is a
unit
lower-triangular
matrix, and
U is an
upper-triangular matrix.
SingleSparseLUDecomposition can operate in two modes.
In overwrite mode, the original matrix is overwritten
by the decomposition. In preserve mode, the original matrix
is preserved, and a new matrix is created to hold the
decomposition. You can set the mode through the
Overwrite property.
SingleSparseLUDecomposition inherits from
SingleLinearTransformation. This means you can
use it to solve systems of linear equations. You can
solve for a single right-hand side, or for multiple
right-hand sides using the Solve(SingleDenseVector, Boolean) method.
You can also calculate the determinant,
the inverse, and an estimate for the
EstimateConditionNumber.
Numerical Libraries
Supported in: 5.x, 4.x
Reference