TriangularMatrixT Class

[SerializableAttribute]
public sealed class TriangularMatrix<T> : Matrix<T>, 
	ISerializable

<SerializableAttribute>
Public NotInheritable Class TriangularMatrix(Of T)
	Inherits Matrix(Of T)
	Implements ISerializable

[SerializableAttribute]
generic<typename T>
public ref class TriangularMatrix sealed : public Matrix<T>, 
	ISerializable

[<SealedAttribute>]
[<SerializableAttribute>]
type TriangularMatrix<'T> =  
    class
        inherit Matrix<'T>
        interface ISerializable
    end

Type Parameters

T

The TriangularMatrixT type exposes the following members.

	Name	Description
	CanReshape	Gets whether the matrix can be reshaped into a vector or a matrix. (Inherited from MatrixT.)
	ColumnCount	Gets the number of columns in the matrix. (Inherited from LinearOperatorT.)
	ColumnIndex	Gets or sets the index of labels for the columns of the matrix. (Inherited from LinearOperatorT.)
	Columns	Gets the ColumnCollectionT for this instance. (Inherited from MatrixT.)
	ColumnwiseComponents	Enumerates the elements of the matrix column by column. (Inherited from MatrixT.)
	ElementOrder	Gets a value indicating the order in which the matrix elements are stored. (Overrides MatrixTElementOrder.)
	ElementType	Gets the element type of the matrix. (Inherited from LinearOperatorT.)
	IsHermitian	Gets a value that indicates if the matrix is Hermitian about the main diagonal. (Inherited from MatrixT.)
	IsImmutable	Gets whether the elements of the matrix are immutable. (Inherited from MatrixT.)
	IsLowerTriangular	Gets a value indicating whether this instance is lower triangular. (Overrides MatrixTIsLowerTriangular.)
	IsReadOnly	Gets whether the matrix can be written to. (Inherited from MatrixT.)
	IsSparse	Gets a value that indicates whether the matrix is sparse. (Overrides MatrixTIsSparse.)
	IsSymmetrical	Gets a value that indicates if the matrix is symmetrical about the main diagonal. (Inherited from MatrixT.)
	IsUnitDiagonal	Gets a value indicating whether all diagonal elements of this instance are equal to 1. (Overrides MatrixTIsUnitDiagonal.)
	IsUpperTriangular	Gets a value indicating whether this instance is upper triangular. (Overrides MatrixTIsUpperTriangular.)
	ItemFuncT, Boolean, Int32	Gets or sets the elements of a column of the matrix that meet the specified condition. (Inherited from MatrixT.)
	ItemIEnumerableInt32, Range	Gets or sets the elements of a matrix with the specified row indexes and column range. (Inherited from MatrixT.)
	ItemIEnumerableInt32, IEnumerableInt32	Gets or sets the elements of a matrix with the specified row and column indexes. (Inherited from MatrixT.)
	ItemIEnumerableInt32, Int32	Gets or sets the elements of a column with the specified indexes. (Inherited from MatrixT.)
	ItemIEnumerableInt32, Range	Gets or sets the elements of a matrix with the specified row indexes and column range. (Inherited from MatrixT.)
	ItemIndex, Index	Gets or sets the specified element in this matrix. (Inherited from MatrixT.)
	ItemIndex, Range	Gets or sets the elements of a row of this matrix. (Inherited from MatrixT.)
	ItemInt32, Range	Gets or sets the elements of a row of this matrix. (Inherited from MatrixT.)
	ItemInt32, VectorBoolean	Gets or sets the elements of a row of this matrix. (Inherited from MatrixT.)
	ItemInt32, IEnumerableInt32	Gets or sets the elements of a row with the specified indexes. (Inherited from MatrixT.)
	ItemInt32, FuncT, Boolean	Gets or sets the elements of a row of the matrix that meet the specified condition. (Inherited from MatrixT.)
	ItemInt32, Int32	Gets or sets the specified element in this matrix. (Inherited from MatrixT.)
	ItemRange, Range	Gets or sets the elements of a sub-matrix of this matrix. (Inherited from MatrixT.)
	ItemRange, IEnumerableInt32	Gets or sets the elements of a matrix with the specified row range and column indexes. (Inherited from MatrixT.)
	ItemRange, Int32	Gets or sets the elements of a column of this matrix. (Inherited from MatrixT.)
	ItemRange, IEnumerableInt32	Gets or sets the elements of a matrix with the specified row range and column indexes. (Inherited from MatrixT.)
	ItemRange, Index	Gets or sets the elements of a column of this matrix. (Inherited from MatrixT.)
	ItemRange, Range	Gets or sets the elements of a sub-matrix of this matrix. (Inherited from MatrixT.)
	ItemVectorBoolean, Int32	Gets or sets the elements of a column of this matrix. (Inherited from MatrixT.)
	MatrixDiagonal	Gets a value indicating whether all diagonal elements of this instance are structurally equal to 1. (Inherited from MatrixT.)
	MatrixTriangle	Gets a value that indicates whether a triangular matrix is upper or lower triangular. (Inherited from MatrixT.)
	NonzeroComponents	Obsolete. Gets a collection of the nonzero elements of the matrix. (Inherited from MatrixT.)
	NonzeroElements	Gets a collection of the nonzero elements of the matrix. (Inherited from MatrixT.)
	Precedence	Infrastructure. This property supports the Numerical Libraries for .NET infrastructure and is not intended to be used directly from your code. (Inherited from MatrixT.)
	RowCount	Gets the number of rows in the matrix. (Inherited from LinearOperatorT.)
	RowIndex	Gets or sets the index of labels for the rows of the matrix. (Inherited from LinearOperatorT.)
	Rows	Gets the RowCollectionT for this instance. (Inherited from MatrixT.)
	RowwiseComponents	Enumerates the elements of the matrix column by column. (Inherited from MatrixT.)
	StoredTriangle	Gets a value that indicates whether the elements of a TriangularMatrixT are stored in the upper or lower part.
	Structure	Gets a value that indicates the structure of the sparse matrix. (Inherited from MatrixT.)
	WritableComponents	Enumerates the writable elements of the matrix column by column. (Inherited from MatrixT.)

	Name	Description
	AbsInPlace	Computes the absolute value of the elements of a matrix in-place. (Inherited from MatrixT.)
	AbsoluteMax	Returns the value of the element in this matrix that has the largest absolute value. (Inherited from MatrixT.)
	AbsoluteMin	Returns the value of the element in this matrix that has the smallest absolute value. (Inherited from MatrixT.)
	AcoshInPlace	Computes the inverse hyperbolic cosine of the elements of a matrix in-place. (Inherited from MatrixT.)
	AcosInPlace	Computes the inverse cosine of the elements of a matrix in-place. (Inherited from MatrixT.)
	Add	Obsolete. Adds a constant to a matrix and returns the result. (Inherited from MatrixT.)
	AddInPlace(T)	Adds a scalar to a matrix. (Inherited from MatrixT.)
	AddInPlace(MatrixT)	Adds another matrix to this matrix in-place. (Inherited from MatrixT.)
	AddInPlace(VectorT, Dimension)	Adds a vector broadcast along the specified dimension to this matrix in-place. (Inherited from MatrixT.)
	AddProductInPlace(MatrixT, MatrixT)	Adds the product of two matrices to this matrix. (Inherited from MatrixT.)
	AddProductInPlace(MatrixT, TransposeOperation, MatrixT, TransposeOperation)	Adds the product of two matrices to this matrix. (Inherited from MatrixT.)
	AddProductToVector	Obsolete. Multiplies a VectorT by this instance and stores the result in a second vector of type DenseVectorT. (Inherited from LinearOperatorT.)
	AddScaledInPlace	Adds a scaled matrix to this matrix. (Inherited from MatrixT.)
	AddScaledProductInPlace(T, MatrixT, MatrixT)	Adds a multiple of the scaled product of two matrices to this matrix. (Inherited from MatrixT.)
	AddScaledProductInPlace(T, MatrixT, TransposeOperation, MatrixT, TransposeOperation)	Adds the scaled product of two matrices to another matrix. (Inherited from MatrixT.)
	AggregateColumnsU(AggregatorT, U)	Applies the specified aggregator to all the columns in the matrix. (Inherited from MatrixT.)
	AggregateColumnsU(AggregatorGroupU)	Applies the specified aggregator to all the columns in the matrix. (Inherited from MatrixT.)
	AggregateColumnsU(AggregatorGroupU)	Applies the specified aggregators to all the columns in the matrix. (Inherited from MatrixT.)
	AggregateColumnsU(FuncVectorT, U)	Applies the specified aggregators to all the columns in the matrix. (Inherited from MatrixT.)
	AggregateColumnsByU(IGrouping, AggregatorGroupU)	Returns a new matrix that aggregates the columns according to the specified grouping. (Inherited from MatrixT.)
	AggregateColumnsByK, U(IListK, AggregatorGroupU)	Returns a new matrix that aggregates the columns grouped by the specified vector. (Inherited from MatrixT.)
	AggregateColumnsListwiseU	Applies the specified aggregator to all the columns in the matrix, treating rows that contain any missing values as completely missing. (Inherited from MatrixT.)
	AggregateRowsU(AggregatorT, U)	Applies the specified aggregator to all the rows in the matrix. (Inherited from MatrixT.)
	AggregateRowsU(AggregatorGroupU)	Applies the specified aggregator to all the rows in the matrix. (Inherited from MatrixT.)
	AggregateRowsU(AggregatorGroupU)	Applies the specified aggregators to all the rows in the matrix. (Inherited from MatrixT.)
	AggregateRowsU(FuncVectorT, U)	Applies the specified aggregators to all the rows in the matrix. (Inherited from MatrixT.)
	AggregateRowsByU(IGrouping, AggregatorGroupU)	Returns a new matrix that aggregates the rows according to the specified grouping. (Inherited from MatrixT.)
	AggregateRowsByC, U(C, AggregatorGroupU)	Returns a new matrix that aggregates the rows grouped by the specified row. (Inherited from MatrixT.)
	AggregateRowsByK, U(IListK, AggregatorGroupU)	Returns a new matrix that aggregates the rows grouped by the specified vector. (Inherited from MatrixT.)
	AggregateRowsByR, U(R, FuncVectorT, U)	Applies the specified aggregation function to the values in each row grouped by the specified grouping row. (Inherited from MatrixT.)
	AsDenseMatrix	Returns this matrix as a dense matrix. (Inherited from MatrixT.)
	AsHermitianMatrix	Returns a matrix as a HermitianMatrixT, or if the matrix is not hermitian. (Inherited from MatrixT.)
	AsHermitianMatrix(MatrixTriangle)	Returns a HermitianMatrixT extracted from a part of the matrix. (Inherited from MatrixT.)
	AsinhInPlace	Computes the inverse hyperbolic sine of the elements of a matrix in-place. (Inherited from MatrixT.)
	AsinInPlace	Computes the inverse sine of the elements of a matrix in-place. (Inherited from MatrixT.)
	AsSymmetricMatrix	Returns a matrix as a SymmetricMatrixT, or if the matrix is not symmetrical. (Inherited from MatrixT.)
	AsSymmetricMatrix(MatrixTriangle)	Returns a SymmetricMatrixT extracted from a part of the matrix. (Inherited from MatrixT.)
	AtanhInPlace	Computes the inverse hyperbolic tangent of the elements of a matrix in-place. (Inherited from MatrixT.)
	AtanInPlace	Computes the inverse tangent of the elements of a matrix in-place. (Inherited from MatrixT.)
	CeilingInPlace	Computes the smallest integer greater than or equal to the elements of a matrix in-place. (Inherited from MatrixT.)
	Clone	Constructs a deep copy of this matrix. (Inherited from MatrixT.)
	Clone(CloningMethod)	Makes a copy of this vector using the specified method. (Inherited from MatrixT.)
	CloneData	Gives this instance its own copy of its elements. (Overrides MatrixTCloneData.)
	CloneData(MatrixElementOrder)	Gives this instance its own copy of its elements.
	CloneShape	Creates a new matrix that has the same number of rows and columns and optionally preserves the writable structure. (Inherited from MatrixT.)
	ComponentwiseDivide(MatrixT)	Obsolete. Divides the elements of this instance by the corresponding elements of another matrix. (Inherited from MatrixT.)
	ComponentwiseMultiply	Obsolete. Multiplies the elements of this instance by the corresponding elements of another matrix. (Inherited from MatrixT.)
	Conjugate	Returns the transpose of this instance. (Inherited from MatrixT.)
	ConjugateInPlace	Conjugates all elements of a matrix in-place. (Inherited from MatrixT.)
	ConjugateTranspose	Returns the transpose of this instance. (Overrides MatrixTConjugateTranspose.)
	CopyTo(MatrixT)	Copies the elements of this matrix to another matrix. (Inherited from MatrixT.)
	CopyTo(Array2DT, TransposeOperation)	Copies the elements of this matrix to another matrix. (Inherited from MatrixT.)
	CopyTo(MatrixT, TransposeOperation)	Copies the elements of this matrix to another matrix. (Overrides MatrixTCopyTo(MatrixT, TransposeOperation).)
	CopyToOrClone	Copies the elements of this vector to another matrix, if it exists; otherwise clones the matrix using the specified method. (Inherited from MatrixT.)
	CoshInPlace	Computes the hyperbolic cosine of the elements of a matrix in-place. (Inherited from MatrixT.)
	CosInPlace	Computes the cosine of the elements of a matrix in-place. (Inherited from MatrixT.)
	Dispose	Releases unmanaged resources. (Inherited from MatrixT.)
	DivideInPlace	Divides a matrix in-place by a scalar. (Inherited from MatrixT.)
	ElementwiseDivideInPlace	Divides this matrix in-place element-wise by another matrix. (Inherited from MatrixT.)
	ElementwiseMultiplyInPlace(MatrixT)	Multiplies this matrix in-place element-wise by another matrix. (Inherited from MatrixT.)
	ElementwisePowInPlace(Int32)	Raises the elements of a matrix in-place to a constant power. (Inherited from MatrixT.)
	ElementwisePowInPlace(MatrixT)	Raises this matrix in-place element-wise by another matrix. (Inherited from MatrixT.)
	ElementwisePowInPlace(VectorT, Dimension)	Raises this matrix in-place element-wise by a vector broadcast along the specified dimension. (Inherited from MatrixT.)
	EnsureWritable	Ensures that the element at the specified index in the vector can be written to. (Inherited from MatrixT.)
	EnsureWritable(Int32, Int32)	Ensures that the element at the specified index in the vector can be written to. (Inherited from MatrixT.)
	EnsureWritable(Int32, Int32, Int32, Int32)	Ensures that the element at the specified index in the vector can be written to. (Inherited from MatrixT.)
	Equals(MatrixT)	Determines whether the specified MatrixT is equal to the current MatrixT. (Inherited from MatrixT.)
	Equals(Object)	Determines whether the specified Object is equal to the current MatrixT. (Inherited from MatrixT.)
	Equals(Object, IEqualityComparer)	Returns whether an object is structurally equal to this instance. (Inherited from MatrixT.)
	EstimateConditionNumber	Calculates an estimate for the condition number of this TriangularMatrixT. (Overrides MatrixTEstimateConditionNumber.)
	ExpInPlace	Computes the exponential of the elements of a matrix in-place. (Inherited from MatrixT.)
	FillMissingValuesInPlace(T)	Replaces all missing values in a matrix with the specified value in-place. (Inherited from MatrixT.)
	FillMissingValuesInPlace(DimensionType, Direction)	Replaces all missing values in each row or column in-place with the previous or next non-missing value. (Inherited from MatrixT.)
	FillMissingValuesInPlace(VectorT, DimensionType)	Replaces all missing values in each row or column of a matrix in-place with the corresponding value from a vector. (Inherited from MatrixT.)
	FillMissingValuesInto(T, MatrixT)	Replaces all missing values in a matrix with the specified value. (Inherited from MatrixT.)
	FillMissingValuesInto(VectorT, DimensionType, MatrixT)	Replaces all missing values in each row or column with the corresponding value from a vector. (Inherited from MatrixT.)
	FillMissingValuesInto(DimensionType, Direction, MatrixT, Int32)	Replaces all missing values in each row or column with the previous or next non-missing value. (Inherited from MatrixT.)
	FloorInPlace	Computes the largest integer less than or equal to the elements of a matrix in-place. (Inherited from MatrixT.)
	FrobeniusNorm	Returns the Frobenius norm of this matrix. (Inherited from MatrixT.)
	GetR, C	Gets the value with the specified key. (Inherited from MatrixT.)
	GetCholeskyDecomposition	Returns the Cholesky decomposition of the matrix. (Inherited from MatrixT.)
	GetCholeskyDecomposition(Boolean)	Returns the Cholesky decomposition of the matrix. (Inherited from MatrixT.)
	GetColumn(Int32)	Returns a column vector for this instance that points at the specified column. (Inherited from MatrixT.)
	GetColumn(Int32, Intent)	Returns a column vector for this instance that points at the specified column. (Inherited from MatrixT.)
	GetColumn(Int32, Range)	Returns a column vector for this instance starting at the specified column and row and of the specified length. (Inherited from MatrixT.)
	GetColumn(Int32, Int32, Int32)	Returns a column vector for this instance starting at the specified column and row and of the specified length. (Inherited from MatrixT.)
	GetColumn(Int32, Int32, Int32, Int32)	Returns a column vector for this instance starting at the specified column and row and of the specified length. (Inherited from MatrixT.)
	GetColumn(Int32, Int32, Int32, Int32, Intent)	Returns a column vector for this instance starting at the specified column and row and of the specified length. (Inherited from MatrixT.)
	GetColumnEnumerator	Returns an enumerator that allows you to iterate over the columns of this instance. (Inherited from MatrixT.)
	GetColumns(IEnumerableInt32)	Returns a new matrix that contains only the columns in the specified sequence. (Inherited from MatrixT.)
	GetColumns(Int32, Int32)	Returns a matrix that contains only the specified columns of the current matrix. (Inherited from MatrixT.)
	GetColumnSums	Returns the sums of the elements of each column of the matrix. (Inherited from MatrixT.)
	GetConditionNumber	Calculates the condition number of this matrix. (Inherited from MatrixT.)
	GetDeterminant	Calculates the determinant of this TriangularMatrixT. (Overrides MatrixTGetDeterminant.)
	GetDiagonal	Gets a vector view of the diagonal elements of this instance. (Inherited from MatrixT.)
	GetDiagonal(Int32)	Gets a vector view of the specified diagonal of this instance. (Inherited from MatrixT.)
	GetDiagonal(Int32, Intent)	Gets a vector view of the specified diagonal of this instance. (Overrides MatrixTGetDiagonal(Int32, Intent).)
	GetEigenvalueDecomposition	Returns the eigenvalue decomposition for this matrix. (Inherited from MatrixT.)
	GetEigenvalueDecomposition(Boolean)	Returns the eigenvalue decomposition for this matrix. (Inherited from MatrixT.)
	GetEigenvalueDecomposition(MatrixT)	Returns the generalized eigenvalue decomposition for this matrix. (Inherited from MatrixT.)
	GetEigenvalueDecomposition(MatrixT, Boolean)	Returns the generalized eigenvalue decomposition for this matrix. (Inherited from MatrixT.)
	GetExponential	Computes the matrix exponential of a square matrix. (Inherited from MatrixT.)
	GetHashCode	Returns the hash code for this instance. (Inherited from MatrixT.)
	GetHashCode(IEqualityComparer)	Returns a hash code for this instance. (Inherited from MatrixT.)
	GetHermitianIndefiniteDecomposition	Returns the Hermitian indefinite (Bunch-Kaufman) decomposition of the matrix. (Inherited from MatrixT.)
	GetHermitianIndefiniteDecomposition(Boolean)	Returns the Hermitian indefinite (Bunch-Kaufman) decomposition of the matrix. (Inherited from MatrixT.)
	GetInverse	Calculates the inverse matrix.. (Inherited from LinearOperatorT.)
	GetInverse(Boolean)	Calculates the inverse matrix. (Overrides MatrixTGetInverse(Boolean).)
	GetLQDecomposition	Returns the LQ decomposition of the matrix. (Inherited from MatrixT.)
	GetLQDecomposition(Boolean)	Returns the LQ decomposition of the matrix. (Inherited from MatrixT.)
	GetLUDecomposition	Returns the LU decomposition of the matrix. (Inherited from MatrixT.)
	GetLUDecomposition(Boolean)	Returns the LU decomposition of the matrix. (Overrides MatrixTGetLUDecomposition(Boolean).)
	GetNearestColumnC	Gets the column nearest to the specified column key. (Inherited from MatrixT.)
	GetNearestColumnsC	Returns a new matrix that contains only the columns in the specified sequence. (Inherited from MatrixT.)
	GetNearestRowR	Gets the row nearest to the specified row key. (Inherited from MatrixT.)
	GetNearestRowsR	Returns a new matrix that contains only the rows in the specified sequence. (Inherited from MatrixT.)
	GetObjectData	Populates a SerializationInfo with the values needed to serialize the target object. (Overrides MatrixTGetObjectData(SerializationInfo, StreamingContext).)
	GetParallelColumnEnumerator	Returns a partitioner that allows you to iterate over the rows of this instance in parallel. (Inherited from MatrixT.)
	GetParallelRowEnumerator	Returns a partitioner that allows you to iterate over the rows of this instance in parallel. (Inherited from MatrixT.)
	GetPseudoInverse	Calculates the Moore-Penrose pseudo-inverse of this matrix. (Inherited from MatrixT.)
	GetQLDecomposition	Returns the QL decomposition of the matrix. (Inherited from MatrixT.)
	GetQLDecomposition(Boolean)	Returns the QL decomposition of the matrix. (Inherited from MatrixT.)
	GetQRDecomposition	Returns the QR decomposition of the matrix. (Inherited from MatrixT.)
	GetQRDecomposition(Boolean)	Returns the QR decomposition of the matrix. (Overrides MatrixTGetQRDecomposition(Boolean).)
	GetRow(Int32)	Returns a row vector for this instance that points at the specified row. (Inherited from MatrixT.)
	GetRow(Int32, Intent)	Returns a row vector for this instance that points at the specified row. (Inherited from MatrixT.)
	GetRow(Int32, Range)	Returns a row vector for this instance starting at the specified row and column and of the specified length. (Inherited from MatrixT.)
	GetRow(Int32, Int32, Int32)	Returns a row vector for this instance over the specified range. (Inherited from MatrixT.)
	GetRow(Int32, Int32, Int32, Intent)	Returns a row vector for this instance over the specified range. (Inherited from MatrixT.)
	GetRow(Int32, Int32, Int32, Int32)	Returns a row vector for this instance starting at the specified row and column and of the specified length. (Inherited from MatrixT.)
	GetRow(Int32, Int32, Int32, Int32, Intent)	Returns a row vector for this instance starting at the specified row and column and of the specified length. (Inherited from MatrixT.)
	GetRowEnumerator	Returns an enumerator that allows you to iterate over the rows of this instance. (Inherited from MatrixT.)
	GetRows(Subset)	Returns a matrix containing only the rows in the specified subset. (Inherited from MatrixT.)
	GetRows(Int32, Int32)	Returns a matrix that contains only the specified rows of the current matrix. (Inherited from MatrixT.)
	GetRowsR(IEnumerableR)	Returns a new matrix that contains only the rows in the specified sequence. (Inherited from MatrixT.)
	GetRowSums	Returns the sums of the elements of each row of the matrix. (Inherited from MatrixT.)
	GetRQDecomposition	Returns the RQ decomposition of the matrix. (Inherited from MatrixT.)
	GetRQDecomposition(Boolean)	Returns the RQ decomposition of the matrix. (Inherited from MatrixT.)
	GetSingularValueDecomposition	Returns the singular value decomposition of the matrix. (Inherited from MatrixT.)
	GetSingularValueDecomposition(MatrixT)	Returns the generalized singular value decomposition of the matrix and another matrix. (Inherited from MatrixT.)
	GetSingularValueDecomposition(SingularValueDecompositionFactors)	Returns the singular value decomposition of the matrix. (Inherited from MatrixT.)
	GetSingularValueDecomposition(MatrixT, GeneralizedSingularValueDecompositionFactors)	Returns the generalized singular value decomposition of the matrix and another matrix. (Inherited from MatrixT.)
	GetSingularValueDecomposition(SingularValueDecompositionFactors, Boolean)	Returns the singular value decomposition of the matrix. (Inherited from MatrixT.)
	GetSingularValueDecomposition(MatrixT, GeneralizedSingularValueDecompositionFactors, Boolean)	Returns the generalized singular value decomposition of the matrix and another matrix. (Inherited from MatrixT.)
	GetSingularValues	Gets a vector containing the singular values of the matrix. (Inherited from MatrixT.)
	GetSubmatrix(Range, Range)	Returns a sub-matrix of this instance. (Inherited from MatrixT.)
	GetSubmatrix(Range, Range, TransposeOperation)	Returns a sub-matrix of this instance. (Inherited from MatrixT.)
	GetSubmatrix(Int32, Int32, Int32, Int32)	Returns a sub-matrix of this instance. (Inherited from MatrixT.)
	GetSubmatrix(Int32, Int32, Int32, Int32, Int32, Int32, TransposeOperation, Intent)	Returns a sub-matrix of this instance. (Inherited from MatrixT.)
	GetSymmetricIndefiniteDecomposition	Returns the symmetric indefinite (Bunch-Kaufman) decomposition of the matrix. (Inherited from MatrixT.)
	GetSymmetricIndefiniteDecomposition(Boolean)	Returns the symmetric indefinite (Bunch-Kaufman) decomposition of the matrix. (Inherited from MatrixT.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	GetValue(Int32, Int32)	Gets the matrix component at the specified position. (Overrides MatrixTGetValue(Int32, Int32).)
	GetValue(Int32, Int32)	Gets the matrix element at the specified position. (Inherited from MatrixT.)
	GetValues	Infrastructure. (Inherited from MatrixT.)
	InfinityNorm	Returns the infinity norm of this matrix. (Inherited from MatrixT.)
	IsComponentWritable	Obsolete. Returns a value that indicates whether the value of the element at the specified row and column can be changed. (Inherited from MatrixT.)
	IsElementWritable	Returns a value that indicates whether the value of the component at the specified row and column can be changed. (Overrides MatrixTIsElementWritable(Int32, Int32).)
	IsMissing	Returns whether the value at the specified index is missing. (Inherited from MatrixT.)
	IsSingular	Gets a value indicating whether the TriangularMatrixT is singular. (Overrides MatrixTIsSingular.)
	LeastSquaresSolve(MatrixT)	Solves the system of linear equations for the specified right-hand side matrix in the least squares sense. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(DenseMatrixT, Boolean)	Solves the system of linear equations for the specified right-hand side dense matrix in the least squares sense and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	LeastSquaresSolve(DenseVectorT, Boolean)	Solves the system of linear equations for the specified right-hand side dense vector in the least squares sense and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	LeastSquaresSolveInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides in the least squares sense. (Inherited from MatrixT.)
	LeastSquaresSolveInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side in the least squares sense. (Inherited from MatrixT.)
	Log10InPlace	Computes the logarithm of the elements of a matrix in-place. (Inherited from MatrixT.)
	LogInPlace	Computes the logarithm of the elements of a matrix in-place. (Inherited from MatrixT.)
	LogInPlace(T)	Computes the logarithm of the elements of a matrix in-place. (Inherited from MatrixT.)
	MapColumnsU	Applies a vector function to each column in a matrix and returns the result as a matrix. (Inherited from MatrixT.)
	MapColumnsInPlace	Applies a function to each column in a matrix in-place. (Inherited from MatrixT.)
	MapColumnsIntoU	Applies a vector function to each column in a matrix and returns the result as a matrix. (Inherited from MatrixT.)
	MapInPlace(FuncT, T)	Applies a function in-place to the elements of a matrix. (Inherited from MatrixT.)
	MapInPlaceU(FuncT, U, T, MatrixU)	Applies a function to the elements of a matrix. (Inherited from MatrixT.)
	MapIntoU	Applies a function to the elements of a matrix. (Inherited from MatrixT.)
	MapRowsU	Applies a vector function to each row in a matrix and returns the result as a matrix. (Inherited from MatrixT.)
	MapRowsInPlace	Applies a function to each column in a matrix and returns the result as a vector. (Inherited from MatrixT.)
	MapRowsIntoU	Applies a vector function to each row in a matrix and returns the result as a matrix. (Inherited from MatrixT.)
	Max	Returns the value of the largest element in this matrix. (Inherited from MatrixT.)
	Min	Returns the value of the smallest element in this matrix. (Inherited from MatrixT.)
	Multiply(MatrixT)	Applies the linear operator to a matrix. (Inherited from LinearOperatorT.)
	Multiply(VectorT)	Applies the linear operator to a vector. (Inherited from LinearOperatorT.)
	Multiply(DenseMatrixT, TriangularMatrixT)	Multiplies a DenseMatrixT by a TriangularMatrixT.
	Multiply(TransposeOperation, MatrixT)	Obsolete. Multiplies a matrix on the left by this matrix. (Inherited from LinearOperatorT.)
	Multiply(TransposeOperation, VectorT)	Obsolete. Multiplies a vector on the left by this vector. (Inherited from LinearOperatorT.)
	Multiply(MatrixOperationSide, TransposeOperation, TransposeOperation, MatrixT)	Obsolete. Multiplies this matrix by another matrix and returns the result. (Inherited from MatrixT.)
	MultiplyInPlace	Multiplies this matrix by a scalar factor. (Overrides MatrixTMultiplyInPlace(T).)
	MultiplyTranspose(MatrixT)	Applies the transpose of the linear operator to a matrix. (Inherited from LinearOperatorT.)
	MultiplyTranspose(VectorT)	Applies the (conjugate) transpose of the linear operator to a vector. (Inherited from LinearOperatorT.)
	NegateInPlace	Negates a matrix in-place. (Inherited from MatrixT.)
	OneNorm	Returns the 1-norm of this matrix. (Inherited from MatrixT.)
	PermuteColumnsInPlace	Permutes the columns of the matrix using the specified Permutation. (Inherited from MatrixT.)
	PermuteRowsAndColumnsInPlace(Permutation)	Permutes the rows and columns of the matrix using the specified Permutation. (Inherited from MatrixT.)
	PermuteRowsAndColumnsInPlace(Permutation, Permutation)	Permutes the rows and columns of the matrix using the specified row and column Permutation. (Inherited from MatrixT.)
	PermuteRowsInPlace	Permutes the rows of the matrix using the specified Permutation. (Inherited from MatrixT.)
	Protect	Returns a read-only copy of the matrix. (Inherited from MatrixT.)
	ProtectInPlace	Protects the matrix from changes. (Inherited from MatrixT.)
	Rank	Returns the numerical rank of a matrix. (Inherited from LinearOperatorT.)
	Rank(T)	Returns the numerical rank of a matrix using the specified tolerance. (Inherited from MatrixT.)
	ReduceU	Applies a function to each row or column in a matrix and returns the result as a vector. (Inherited from MatrixT.)
	ReduceColumnsU	Applies a function to each column in a matrix and returns the result as a vector. (Inherited from MatrixT.)
	ReduceColumnsIntoU	Applies a function to each column in a matrix and returns the result as a vector. (Inherited from MatrixT.)
	ReduceRowsU	Applies a function to each row in a matrix and returns the result as a vector. (Inherited from MatrixT.)
	ReduceRowsIntoU	Applies a function to each row in a matrix and returns the result as a vector. (Inherited from MatrixT.)
	RemoveWithMissingValues	Returns a new matrix that has the rows or columns that contain missing values removed. (Inherited from MatrixT.)
	Reshape	Returns a matrix that contains the same elements listed columnwise. (Inherited from MatrixT.)
	ReshapeAsVector	Returns a vector that contains the columnwise matrix elements. (Inherited from MatrixT.)
	ScaleColumns	Obsolete. Scales the columns of the matrix by the values specified by a vector. (Inherited from MatrixT.)
	ScaleColumnsInPlace	Scales the columns of the matrix by the values specified by a vector. (Inherited from MatrixT.)
	ScaleRows	Obsolete. Scales the rows of the matrix by the values specified by a vector. (Inherited from MatrixT.)
	ScaleRowsInPlace	Scales the rows of the matrix by the values specified by a vector. (Inherited from MatrixT.)
	SetToZero	Sets all elements of the matrix to zero. (Inherited from MatrixT.)
	SetValue(T)	Sets all elements of the matrix to the specified value. (Inherited from MatrixT.)
	SetValue(T, Int32, Int32)	Sets the matrix element at the specified position to the specified value. (Inherited from MatrixT.)
	SetValue(T, Int32, Int32)	Sets the matrix component at the specified position to the specified value. (Overrides MatrixTSetValue(T, Int32, Int32).)
	ShallowCopy	Makes a shallow copy of this matrix. (Inherited from MatrixT.)
	SinhInPlace	Computes the hyperbolic sine of the elements of a matrix in-place. (Inherited from MatrixT.)
	SinInPlace	Computes the sine of the elements of a matrix in-place. (Inherited from MatrixT.)
	Solve(MatrixT)	Solves the system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperatorT.)
	Solve(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	Solve(DenseMatrixT, Boolean)	Solves the system of linear equations for the specified right-hand side dense matrix and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	Solve(DenseVectorT, Boolean)	Solves the system of linear equations for the specified right-hand side dense vector and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	SolveInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperatorT.)
	SolveInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperatorT.)
	SolveInto(TransposeOperation, MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Overrides MatrixTSolveInto(TransposeOperation, MatrixT, MatrixT).)
	SolveInto(TransposeOperation, VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Overrides MatrixTSolveInto(TransposeOperation, VectorT, VectorT).)
	SolveTranspose(MatrixT)	Solves the transposed system of linear equations for the specified right-hand side matrix. (Inherited from LinearOperatorT.)
	SolveTranspose(VectorT)	Solves the system of linear equations for the specified right-hand side vector. (Inherited from LinearOperatorT.)
	SolveTranspose(DenseMatrixT, Boolean)	Solves the transposed system of linear equations for the specified right-hand side dense matrix and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	SolveTranspose(DenseVectorT, Boolean)	Solves the transposed system of linear equations for the specified right-hand side dense vector and optionally overwrites the right-hand side with the solution. (Inherited from LinearOperatorT.)
	SolveTransposeInto(MatrixT, MatrixT)	Solves a system of equations defined by the matrix and multiple right-hand sides. (Inherited from LinearOperatorT.)
	SolveTransposeInto(VectorT, VectorT)	Solves a system of equations defined by the matrix and the specified right-hand side. (Inherited from LinearOperatorT.)
	SortColumns	Sorts each column of the matrix in ascending order. (Inherited from MatrixT.)
	SortColumns(SortOrder)	Sorts each column of the matrix in the specified order. (Inherited from MatrixT.)
	SortRows	Sorts each row of the matrix in ascending order. (Inherited from MatrixT.)
	SortRows(SortOrder)	Sorts each row of the matrix in the specified order. (Inherited from MatrixT.)
	SqrtInPlace	Computes the square root of the elements of a matrix in-place. (Inherited from MatrixT.)
	SubtractInPlace(T)	Subtracts a scalar value from the elements of this matrix in-place. (Inherited from MatrixT.)
	SubtractInPlace(MatrixT)	Subtracts another matrix from this matrix in-place. (Inherited from MatrixT.)
	SubtractInPlace(VectorT, Dimension)	Subtracts a vector broadcast along the specified dimension from this matrix in-place. (Inherited from MatrixT.)
	Sum	Returns the sum of the elements of the matrix. (Inherited from MatrixT.)
	Summarize	Returns a summary of the contents of the matrix using the default summary options. (Inherited from MatrixT.)
	Summarize(SummaryOptions)	Returns a summary of the contents of the matrix using the specified options. (Inherited from MatrixT.)
	SwapColumns	Swaps the columns with the specified indices. (Inherited from MatrixT.)
	SwapRows	Swaps the rows with the specified indices. (Inherited from MatrixT.)
	TanhInPlace	Computes the hyperbolic tangent of the elements of a matrix in-place. (Inherited from MatrixT.)
	TanInPlace	Computes the tangent of the elements of a matrix in-place. (Inherited from MatrixT.)
	ToArray	Gets the elements of the vector. (Inherited from MatrixT.)
	ToArray(MatrixElementOrder)	Gets the elements of the vector. (Inherited from MatrixT.)
	ToDataFrameR, C	Converts a matrix to a data frame with the same row and column indexes. (Inherited from MatrixT.)
	ToDataFrameR, C(IndexR, IndexC)	Converts a matrix to a data frame with the same row and column indexes. (Inherited from MatrixT.)
	ToDenseMatrix	Makes a copy of this instance and returns it as a dense matrix. (Inherited from MatrixT.)
	ToHermitianMatrix	Returns a new HermitianMatrixT extracted from a part of the matrix. (Inherited from MatrixT.)
	ToString	Returns a string that represents the current object. (Inherited from MatrixT.)
	ToString(String)	Returns a String representation of this MatrixT. (Inherited from MatrixT.)
	ToString(String, IFormatProvider)	Returns a String representation of this MatrixT. (Inherited from MatrixT.)
	ToSymmetricMatrix	Returns a new SymmetricMatrixT extracted from a part of the matrix. (Inherited from MatrixT.)
	Trace	Gets the sum of the diagonal elements of this matrix. (Inherited from MatrixT.)
	Transpose	Returns the transpose of this instance. (Overrides MatrixTTranspose.)
	TryEnsureWritable	Ensures that the element at the specified index in the vector can be written to. (Inherited from MatrixT.)
	TryEnsureWritable(Int32, Int32)	Ensures that the element at the specified index in the vector can be written to. (Inherited from MatrixT.)
	TryEnsureWritable(Int32, Int32, Int32, Int32)	Ensures that the element at the specified index in the vector can be written to. (Inherited from MatrixT.)
	TwoNorm	Returns the two-norm of this matrix. (Inherited from MatrixT.)
	UnscaleColumns	Obsolete. Unscales the columns of the matrix by the reciprocal of the values specified by a vector. (Inherited from MatrixT.)
	UnscaleColumnsInPlace	Unscales the columns of the matrix by the reciprocal of the values specified by a vector. (Inherited from MatrixT.)
	UnscaleRows	Obsolete. Unscales the rows of the matrix by the reciprocal of the values specified by a vector. (Inherited from MatrixT.)
	UnscaleRowsInPlace	Unscales the rows of the matrix by the reciprocal of the values specified by a vector. (Inherited from MatrixT.)

	Name	Description
	AbsT	Computes the absolute value of the elements of a matrix. (Defined by Matrix.)
	AcosT	Computes the inverse cosine of the elements of a matrix. (Defined by Matrix.)
	AcoshT	Computes the inverse hyperbolic cosine of the elements of a matrix. (Defined by Matrix.)
	AddScaledProductT(T, MatrixT, MatrixT)	Overloaded. Adds the scaled product of two matrices to another matrix. (Defined by Matrix.)
	AddScaledProductT(T, MatrixT, TransposeOperation, MatrixT, TransposeOperation)	Overloaded. Adds the scaled product of two matrices to another matrix. (Defined by Matrix.)
	AsinT	Computes the inverse sine of the elements of a matrix. (Defined by Matrix.)
	AsinhT	Computes the inverse hyperbolic sine of the elements of a matrix. (Defined by Matrix.)
	AtanT	Computes the inverse tangent of the elements of a matrix. (Defined by Matrix.)
	AtanhT	Computes the inverse hyperbolic tangent of the elements of a matrix. (Defined by Matrix.)
	CeilingT	Computes the smallest integer greater than or equal to the elements of a matrix. (Defined by Matrix.)
	ColumnMeansT	Returns a vector containing the means of the columns of a matrix. (Defined by Stats.)
	ConjugateT	Returns the conjugate of a matrix. (Defined by Matrix.)
	ConjugateIntoT	Conjugates the elements of a matrix. (Defined by Matrix.)
	CosT	Computes the cosine of the elements of a matrix. (Defined by Matrix.)
	CoshT	Computes the hyperbolic cosine of the elements of a matrix. (Defined by Matrix.)
	CovarianceMatrixT	Returns the covariance matrix for the columns in a matrix. (Defined by Stats.)
	ExpT	Computes the exponential of the elements of a matrix. (Defined by Matrix.)
	FloorT	Computes the largest integer less than or equal to the elements of a matrix. (Defined by Matrix.)
	LogT	Returns a matrix whose elements are the logarithms of the elements of another matrix. (Defined by Matrix.)
	Log10T	Returns a matrix whose elements are the base 10 logarithms of the elements of another matrix. (Defined by Matrix.)
	MakeDistributedT	Returns a distributed version of a matrix. (Defined by DistributedExtensions.)
	MaxT(MatrixT)	Overloaded. Returns a matrix whose elements are the maximums of the components of two vectors. (Defined by Matrix.)
	MaxT(T)	Overloaded. Returns a matrix whose elements are the maximum of the components of a matrix and a real number. (Defined by Matrix.)
	MaxIntoT(MatrixT, MatrixT)	Overloaded. Returns a matrix whose elements are the maximums of the components of two vectors. (Defined by Matrix.)
	MaxIntoT(T, MatrixT)	Overloaded. Returns a matrix whose elements are the maximum of the components of a matrix and a real number. (Defined by Matrix.)
	MinT(MatrixT)	Overloaded. Returns a matrix whose elements are the minimums of the components of two vectors. (Defined by Matrix.)
	MinT(T)	Overloaded. Returns a matrix whose elements are the minimum of the components of a matrix and a real number. (Defined by Matrix.)
	MinIntoT(MatrixT, MatrixT)	Overloaded. Returns a matrix whose elements are the minimums of the components of two vectors. (Defined by Matrix.)
	MinIntoT(T, MatrixT)	Overloaded. Returns a matrix whose elements are the minimum of the components of a matrix and a real number. (Defined by Matrix.)
	ReciprocalT	Returns a matrix whose elements are the inverses (reciprocals) of the components of another matrix. (Defined by Matrix.)
	ReciprocalIntoT	Computes the inverses (reciprocals) of the elements of a matrix. (Defined by Matrix.)
	RowMeansT	Returns a vector containing the means of the rows of a matrix. (Defined by Stats.)
	SinT	Computes the sine of the elements of a matrix. (Defined by Matrix.)
	SinhT	Computes the hyperbolic sine of the elements of a matrix. (Defined by Matrix.)
	SqrtT	Computes the square root of the elements of a matrix. (Defined by Matrix.)
	TanT	Computes the tangent of the elements of a matrix. (Defined by Matrix.)
	TanhT	Computes the hyperbolic tangent of the elements of a matrix. (Defined by Matrix.)
	ToJsonT	Returns a string containing a matrix in JSON format. (Defined by JsonFile.)

Use the TriangularMatrixT class to represent dense matrices whose elements above or below the diagonal are zero. The name is derived from the shape of the non-zero elements, which form a triangle. However, this class also represents rectangular matrices, whose non-zero elements may form a trapezoid.

A TriangularMatrixT can be either upper or lower-triangular, depending on which components are non-zero. This property is available as the StoredTriangle property. It is of type MatrixTriangle, and must be specified at construction.

Sometimes, the components on the diagonal are all equal to one. In this case, the matrix is said to be unit-diagonal, and the IsUnitDiagonal property will be . Once again, this must be specified at the time the matrix is constructed.

Only the non-zero components of a triangular matrix can be modified. The diagonal components of a unit-diagonal matrix can't be modified. An attempt to do so will result in an ComponentReadOnlyException. You can verify if a component can be modified by calling the IsElementWritable(Int32, Int32) method.

The components of a TriangularMatrixT are stored in a one-dimensional array of values. By default, components that are adjacent in a column of the matrix are adjacent in the storage array. The components are said to be stored in column major order. It is also possible to have elements stored in row major order.

Triangular matrices can be constructed from scratch, or they can be derived or extracted from a DenseMatrixT using one of the ExtractLowerTriangleT(DenseMatrixT) or ExtractUpperTriangleT(DenseMatrixT) methods.

The rows and column vectors of a triangular matrix are of type BlockVectorT.

The TriangularMatrixT class implements algorithms using the triangular matrix BLAS and LAPACK routines. These routines assume matrix components are stored in column major order. However, any necessary conversions are performed transparently. No additional work is needed. In some cases there might be a small performance penalty.

TriangularMatrixT objects are used as properties of many matrix decompositions. Both factors of the LU decomposition are triangular. So is at least one factor of the Cholesky Decomposition and the QR Decomposition.

Reference