Represents a ComplexMatrix whose elements above or below the main diagonal are zero.
Namespace: Extreme.Mathematics.LinearAlgebra.Complex
Assembly: Extreme.Numerics (Extreme.Numerics)
Syntax
| Visual Basic (Declaration) |
|---|
Public NotInheritable Class ComplexTriangularMatrix _ Inherits ComplexMatrix |
| C# |
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public sealed class ComplexTriangularMatrix : ComplexMatrix |
| C++ |
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public ref class ComplexTriangularMatrix sealed : public ComplexMatrix |
Methods
| Icon | Type | Description |
|---|---|---|
 | Add(TransposeOperation, TransposeOperation, DoubleComplex, ComplexMatrix) |
Adds a multiple of a ComplexMatrix to this ComplexMatrix and returns
the result.
|
| AddProductToVector(DoubleComplex, ComplexVector, TransposeOperation, DoubleComplex, ComplexGeneralVector) | |
| Clone() |
Constructs a deep copy of this ComplexMatrix.
|
| CloneData() |
Gives this instance its own copy of its elements.
|
| CloneData(MatrixElementOrder) |
Gives this instance its own copy of its elements.
|
| Conjugate() |
Returns the conjugate transpose of this instance.
|
| ConjugateTranspose() |
Returns the conjugate transpose of this instance.
|
| CopyTo(ComplexMatrix) |
Copies the components of this ComplexMatrix
to another matrix.
|
| Equals(Object) |
Determines whether the specified Object
is equal to the current ComplexMatrix.
|
| EstimateConditionNumber() |
Calculates an estimate for the condition
number of this ComplexTriangularMatrix.
|
 | ExtractLowerTriangle(ComplexGeneralMatrix, Int32, Int32, MatrixDiagonalMode) |
Constructs a ComplexTriangularMatrix whose
elements are contained in the lower triangular portion
of a ComplexGeneralMatrix.
|
| ExtractLowerTriangle(ComplexGeneralMatrix, MatrixDiagonalMode) |
Constructs a ComplexTriangularMatrix whose
elements are contained in the lower triangular portion
of a ComplexGeneralMatrix.
|
| ExtractLowerTriangle(ComplexGeneralMatrix) |
Constructs a ComplexTriangularMatrix whose
elements are contained in the lower triangular portion
of a ComplexGeneralMatrix.
|
| ExtractLowerTriangle(ComplexHermitianMatrix) |
Constructs a ComplexTriangularMatrix whose
elements are contained in the lower triangular portion
of a ComplexHermitianMatrix.
|
| ExtractLowerTriangle(ComplexHermitianMatrix, MatrixDiagonalMode) |
Constructs a ComplexTriangularMatrix whose
elements are contained in the lower triangular portion
of a ComplexHermitianMatrix.
|
| ExtractUpperTriangle(ComplexGeneralMatrix) |
Constructs a ComplexTriangularMatrix whose
elements are contained in the triangleMode triangular portion
of a ComplexGeneralMatrix.
|
| ExtractUpperTriangle(ComplexGeneralMatrix, MatrixDiagonalMode) |
Constructs a ComplexTriangularMatrix whose
elements are contained in the upper triangular portion
of a ComplexGeneralMatrix.
|
| ExtractUpperTriangle(ComplexGeneralMatrix, Int32, Int32, MatrixDiagonalMode) |
Constructs a ComplexTriangularMatrix whose
elements are contained in the upper triangular portion
of a ComplexGeneralMatrix.
|
| ExtractUpperTriangle(ComplexHermitianMatrix) |
Constructs a ComplexTriangularMatrix whose
elements are contained in the lower triangular portion
of a ComplexHermitianMatrix.
|
| ExtractUpperTriangle(ComplexHermitianMatrix, MatrixDiagonalMode) |
Constructs an upper ComplexTriangularMatrix whose
elements are contained in the upper triangular portion
of a ComplexHermitianMatrix.
|
 | Finalize() | |
| FrobeniusNorm() |
Returns the Frobenius norm of this ComplexMatrix.
|
| GetColumn(Int32, Int32, Int32, Int32) |
Returns a column ComplexVector for this instance
starting at the specified column and row and of the
specified length.
|
| GetColumn(Int32) |
Returns a column ComplexVector for this instance
that points at the specified column.
|
| GetColumn(Int32, Int32, Int32) |
Returns a column ComplexVector for this instance
starting at the specified column and row and of the
specified length.
|
| GetColumn(Int32, Range) |
Returns a column ComplexVector for this instance
starting at the specified column and row and of the
specified length.
|
| GetColumnEnumerator() |
Gets an IEnumerator than can be used to enumerate
the columns of this ComplexMatrix.
|
| GetComponents() |
Gets the components of the ComplexVector.
|
| GetComponents(MatrixElementOrder) |
Gets the components of the ComplexVector.
|
| GetDeterminant() |
Calculates the determinant of this ComplexTriangularMatrix.
|
| GetDiagonal(Int32) |
Gets a ComplexVector view of the specified diagonal
of this instance.
|
| GetHashCode() |
Returns the hash code for this instance.
|
| GetImaginaryPart() |
Returns a real matrix containing the imaginary components of the matrix.
|
| GetInverse() |
Calculates the inverse matrix.
|
| GetObjectData(SerializationInfo, StreamingContext) |
Populates a SerializationInfo with the data
needed to serialize the target object.
|
| GetRealPart() |
Returns a real matrix containing the real components of the matrix.
|
| GetRow(Int32, Int32, Int32, Int32) |
Returns a row ComplexVector for this instance
starting at the specified row and column and of the
specified length.
|
| GetRow(Int32) |
Returns a row ComplexVector for this instance
that points at the specified row.
|
| GetRow(Int32, Int32, Int32) |
Returns a row ComplexVector for this instance
over the specified range.
|
| GetRow(Int32, Range) |
Returns a row ComplexVector for this instance
starting at the specified row and column and of the
specified length.
|
| GetRowEnumerator() |
Returns an IEnumerator instance that allows you to
enumerate the rows of this ComplexMatrix.
|
| GetSubmatrix(Range, Range, TransposeOperation) |
Gets a ComplexMatrix that is a submatrix of
this ComplexMatrix.
|
| GetSubmatrix(Range, Range) |
Gets a ComplexMatrix that is a submatrix of
this ComplexMatrix.
|
| GetSubmatrix(Int32, Int32, Int32, Int32) |
Gets a ComplexMatrix that is a submatrix of
this ComplexMatrix.
|
| GetSubmatrix(Int32, Int32, Int32, Int32, Int32, Int32, TransposeOperation) |
Gets a ComplexMatrix that is a submatrix of
this ComplexMatrix.
|
| GetType() | Gets the Type of the current instance. |
| GetValue(Int32, Int32) |
Gets the matrix component at the specified position.
|
| InfinityNorm() |
Returns the infinity norm of this ComplexMatrix.
|
| IsComponentWritable(Int32, Int32) |
Returns a value that indicates whether the value of the component at
the specified row and column can be changed.
|
| IsSingular() |
Gets a value indicating whether the ComplexTriangularMatrix
is singular.
|
| MemberwiseClone() | Creates a shallow copy of the current Object. |
| Multiply(MatrixOperationSide, TransposeOperation, TransposeOperation, ComplexMatrix) |
Multiplies this ComplexMatrix by another matrix and returns
the result.
|
| Multiply(ComplexGeneralMatrix, ComplexTriangularMatrix) |
Multiplies a ComplexGeneralMatrix by a ComplexTriangularMatrix.
|
| OneNorm() |
Returns the 1-norm of this ComplexMatrix.
|
| Rank(Double) |
Returns the numerical rank of a matrix using the specified tolerance.
|
| SetValue(DoubleComplex, Int32, Int32) |
Sets the matrix component at the specified position to the specified value.
|
| ShallowCopy() |
Makes a shallow copy of this ComplexMatrix.
|
| Solve(ComplexGeneralVector, Boolean) |
Solves a triangular system of equations that this
ComplexTriangularMatrix represents.
|
| Solve(ComplexGeneralMatrix, Boolean) |
Solves a triangular system of equations that this
ComplexTriangularMatrix represents.
|
| Solve(ComplexVector) |
Solves the system of linear equations for the specified
right-hand side ComplexVector.
|
| Solve(ComplexMatrix) |
Solves the system of linear equations for the specified
right-hand side ComplexMatrix.
|
| ToGeneralMatrix() |
Makes a copy of this instance and returns it as a
ComplexGeneralMatrix.
|
| ToString() |
Returns a String representation of this
ComplexMatrix.
|
| ToString(String) |
Returns a String representation of this
ComplexMatrix.
|
| ToString(String, IFormatProvider) |
Returns a String representation of this
ComplexMatrix.
|
| Trace() |
Gets the sum of the diagonal elements of this
ComplexMatrix.
|
| Transpose() |
Returns the transpose of this instance.
|
Constructors
| Icon | Type | Description |
|---|---|---|
| ComplexTriangularMatrixNew(MatrixTriangleMode, Int32) |
Constructs a new ComplexTriangularMatrix.
|
| ComplexTriangularMatrixNew(MatrixTriangleMode, Int32, Int32) |
Constructs a new ComplexTriangularMatrix.
|
| ComplexTriangularMatrixNew(MatrixTriangleMode, Int32, Int32, MatrixDiagonalMode) |
Constructs a new ComplexTriangularMatrix.
|
| ComplexTriangularMatrixNew(MatrixTriangleMode, Int32, Int32, DoubleComplex[](), MatrixElementOrder) |
Constructs a new ComplexTriangularMatrix.
|
| ComplexTriangularMatrixNew(MatrixTriangleMode, Int32, DoubleComplex[]()) |
Constructs a new ComplexTriangularMatrix.
|
| ComplexTriangularMatrixNew(MatrixTriangleMode, Int32, Int32, DoubleComplex[](), MatrixDiagonalMode, MatrixElementOrder, Boolean) |
Constructs a new ComplexTriangularMatrix.
|
Properties
| Icon | Type | Description |
|---|---|---|
 | ColumnCount |
Gets the number of columns in the ComplexMatrix.
|
| Columns |
Gets the ComplexColumnCollection for this instance.
|
| DiagonalMode |
Gets a value that indicates whether the diagonal elements of
this ComplexTriangularMatrix are all equal to 1.
|
| ElementOrder |
Gets a value indicating the order in which the matrix
elements are stored.
|
| IsLowerTriangular |
Gets a value indicating whether this
instance is lower triangular.
|
| IsUnitDiagonal |
Gets a value indicating whether all diagonal elements
of this instance are equal to 1.
|
| IsUpperTriangular |
Gets a value indicating whether this
instance is triangleMode triangular.
|
| Item(Int32, Int32) |
Gets or sets the specified element in this
ComplexMatrix.
|
| Item(Int32, Range) |
Gets or sets the components of a row of this ComplexMatrix.
|
| Item(Range, Range) |
Gets or sets the components of a submatrix of this ComplexMatrix.
|
| Item(Range, Int32) |
Gets or sets the components of a column of this ComplexMatrix.
|
| RowCount |
Gets the number of rows in the ComplexMatrix.
|
| Rows |
Gets the ComplexRowCollection for this instance.
|
| TriangleMode |
Gets a value that indicates whether a ComplexTriangularMatrix
is upper or lower triangular.
|
Remarks
Use the ComplexTriangularMatrix 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 ComplexTriangularMatrix can be either upper or lower-triangular, depending on which components are non-zero. This property is available as the TriangleMode property. It is of type MatrixTriangleMode, 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 true. 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 IsComponentWritable(Int32, Int32) method.
The components of a ComplexTriangularMatrix are stored in a one-dimensional array of DoubleComplex 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 ComplexGeneralMatrix using one of the ExtractLowerTriangle(ComplexGeneralMatrix, Int32, Int32, MatrixDiagonalMode) or ExtractUpperTriangle(ComplexGeneralMatrix) methods.
The rows and column vectors of a triangular matrix are of type ComplexBandVector.
The ComplexTriangularMatrix 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 transparantly. No additional work is needed. In some cases there might be a small performance penalty.
ComplexTriangularMatrix objects are used as properties of many matrix decompositions. Both factors of the ComplexLUDecomposition are triangular. So is at least one factor of the ComplexCholeskyDecomposition and the ComplexQRDecomposition.
Inheritance Hierarchy
System.Object
Extreme.Mathematics.LinearAlgebra.Complex.ComplexLinearTransformation
Extreme.Mathematics.LinearAlgebra.Complex.ComplexMatrix
Extreme.Mathematics.LinearAlgebra.Complex.ComplexTriangularMatrix
Extreme.Mathematics.LinearAlgebra.Complex.ComplexLinearTransformation
Extreme.Mathematics.LinearAlgebra.Complex.ComplexMatrix
Extreme.Mathematics.LinearAlgebra.Complex.ComplexTriangularMatrix
See Also
