public class ComplexLUDecomposition : ComplexDecomposition

Public Class ComplexLUDecomposition
	Inherits ComplexDecomposition

public ref class ComplexLUDecomposition : public ComplexDecomposition

type ComplexLUDecomposition =  
    class
        inherit ComplexDecomposition
    end

The ComplexLUDecomposition type exposes the following members.

	Name	Description
	ComplexLUDecomposition	Constructs a new ComplexLUDecomposition object.

	Name	Description
	BaseMatrix	Gets the underlying matrix of the decomposition. (Inherited from ComplexDecomposition.)
	ColumnPermutation	Gets the permutation that generated by the pivoting procedure.
	Done	Gets or sets whether the decomposition has been performed. (Inherited from ComplexDecomposition.)
	Factors	Gets a collection of the matrix factors that make up the decomposition. (Overrides ComplexDecompositionFactors.)
	LowerTriangularFactor	Returns the lower triangular component of this ComplexLUDecomposition.
	Overwrite	Gets or sets a value indicating whether the BaseMatrix should be overwritten by its decomposition. (Inherited from ComplexDecomposition.)
	RowPermutation	Gets the permutation that generated by the pivoting procedure.
	UpperTriangularFactor	Gets the upper triangular component of this ComplexLUDecomposition.

	Name	Description
	ApplyP(ComplexMatrix)	Obsolete. Applies the permutation P of the decomposition PA= LU to a ComplexMatrix and returns the result as a ComplexDenseMatrix.
	ApplyP(ComplexVector)	Obsolete. Applies the permutation P of the decomposition PA= LU to a ComplexVector.
	ApplyP(ComplexDenseMatrix, Boolean)	Obsolete. Applies the permutation P of the decomposition PA= LU to a ComplexDenseMatrix.
	ApplyP(ComplexVector, Boolean)	Obsolete. Applies the permutation P of the decomposition PA= LU to a ComplexVector.
	Decompose	Performs the actual decomposition. (Overrides ComplexDecompositionDecompose.)
	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 ComplexLinearOperatorEstimateConditionNumber.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetDeterminant	Calculates the determinant of the decomposed ComplexMatrix. (Overrides ComplexLinearOperatorGetDeterminant.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetInverse	Calculates the inverse matrix.. (Inherited from ComplexLinearOperator.)
	GetInverse(Boolean)	Calculates the inverse of the factorized ComplexMatrix. (Overrides ComplexLinearOperatorGetInverse(Boolean).)
	GetObjectData	Populates a SerializationInfo with the data needed to serialize the target object. (Inherited from ComplexLinearOperator.)
	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 ComplexDecomposition.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Multiply(ComplexMatrix)	Multiplies the decomposition to a matrix. (Inherited from ComplexDecomposition.)
	Multiply(ComplexVector)	Applies the base matrix of the decomposition to a vector. (Inherited from ComplexDecomposition.)
	MultiplyTranspose(ComplexMatrix)	Multiplies the transpose of the decomposition to a matrix. (Inherited from ComplexDecomposition.)
	MultiplyTranspose(ComplexVector)	Multiplies the transpose of the decomposition to a vector. (Inherited from ComplexDecomposition.)
	Rank	Returns the numerical rank of a matrix. (Inherited from ComplexLinearOperator.)
	Rank(Double)	Returns the numerical rank of a matrix using the specified tolerance. (Overrides ComplexLinearOperatorRank(Double).)
	SetSingular	Sets a flag that indicates the underlying matrix of this decomposition is singular. (Inherited from ComplexDecomposition.)
	Solve(ComplexMatrix)	Solves the system of linear equations for the specified right-hand side ComplexMatrix. (Inherited from ComplexLinearOperator.)
	Solve(ComplexVector)	Solves the system of linear equations for the specified right-hand side complex vector. (Inherited from ComplexLinearOperator.)
	Solve(ComplexDenseMatrix, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side ComplexDenseMatrix and optionally overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolve(ComplexDenseMatrix, Boolean).)
	Solve(ComplexDenseVector, Boolean)	Solves the system of simultaneous linear equations for the specified right-hand side complex vector. (Overrides ComplexLinearOperatorSolve(ComplexDenseVector, Boolean).)
	SolveTranspose(ComplexMatrix)	Solves the transposed system of linear equations for the specified right-hand side ComplexMatrix. (Inherited from ComplexLinearOperator.)
	SolveTranspose(ComplexVector)	Solves the system of linear equations for the specified right-hand side complex vector. (Inherited from ComplexLinearOperator.)
	SolveTranspose(ComplexDenseMatrix, Boolean)	Solves the transposed system of linear equations for the specified right-hand side ComplexDenseMatrix and optionally overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolveTranspose(ComplexDenseMatrix, Boolean).)
	SolveTranspose(ComplexDenseVector, Boolean)	Solves the transposed system of linear equations for the specified right-hand side ComplexDenseVector and optionally overwrites the right-hand side with the solution. (Overrides ComplexLinearOperatorSolveTranspose(ComplexDenseVector, Boolean).)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

The LU decomposition of a matrix A rewrites the matrix in the form PAQ = LU, where P and P are permutation matrices, L is a unit lower-triangular matrix, and U is an upper-triangular matrix.

ComplexLUDecomposition 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.

ComplexLUDecomposition inherits from LinearOperator. 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(ComplexDenseVector, Boolean) method. You can also calculate the determinant, the inverse, and an estimate for the EstimateConditionNumber.

Numerical Libraries

Reference