Represents a ComplexMatrix that is symmetrical about the main diagonal.
Namespace: Extreme.Mathematics.LinearAlgebra.Complex
Assembly: Extreme.Numerics (Extreme.Numerics)
Syntax
| Visual Basic (Declaration) |
|---|
Public NotInheritable Class ComplexHermitianMatrix _ Inherits ComplexMatrix |
| C# |
|---|
public sealed class ComplexHermitianMatrix : ComplexMatrix |
| C++ |
|---|
public ref class ComplexHermitianMatrix 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.
|
| AddOuterProduct(ComplexVector) |
Updates a hermitian matrix with the outer product of
a vector and itself.
|
| AddOuterProduct(Double, ComplexVector) |
Updates a hermitian matrix with the scaled outer product
of a vector and its conjugate transpose.
|
| AddOuterProduct(ComplexMatrix) |
Updates a hermitian matrix with the product
of a matrix and its conjugate transpose.
|
| AddOuterProduct(Double, ComplexMatrix) |
Updates a hermitian matrix with the scaled outer product
of a matrix and its conjugate transpose.
|
| AddProductToVector(DoubleComplex, ComplexVector, TransposeOperation, DoubleComplex, ComplexGeneralVector) | |
| AddSymmetricOuterProduct(DoubleComplex, ComplexVector, ComplexVector) |
Updates a hermitian matrix with the scaled outer product
of a vector and a transposed vector.
|
| AddSymmetricOuterProduct(DoubleComplex, ComplexMatrix, ComplexMatrix) |
Updates a hermitian matrix with the scaled outer product
of a vector and its conjugate transpose.
|
| Clone() |
Constructs a deep copy of this ComplexMatrix.
|
| CloneData() |
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 the ComplexHermitianMatrix.
|
 | Extract(ComplexGeneralMatrix, Int32, Int32, Int32, MatrixTriangleMode, Boolean) |
Creates a ComplexHermitianMatrix from a part of a ComplexGeneralMatrix.
|
| Extract(ComplexMatrix, Int32, Int32, Int32, MatrixTriangleMode) |
Creates a ComplexHermitianMatrix from a part of a ComplexMatrix.
|
 | Finalize() | |
| FrobeniusNorm() |
Returns the Frobenius norm of this ComplexMatrix.
|
| FromOuterProduct(ComplexMatrix) |
Constructs a new ComplexHermitianMatrix
by multiplying a matrix on the left by its conjugate transpose.
|
| FromOuterProduct(ComplexMatrix, MatrixOperationSide) |
Constructs a new ComplexHermitianMatrix
by multiplying a matrix by its conjugate transpose.
|
| 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, 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 the ComplexHermitianMatrix
underlying this system of equations.
|
| 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) |
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.
|
| GetRow(Int32, Int32, Int32, Int32) |
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) |
Gets a value indicating whether the value of the component at
the specified row and column can be changed.
|
| IsSingular() |
Gets a value indicating whether the ComplexHermitianMatrix
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.
|
| 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 the system of simultaneous linear equations for the specified
right-hand side ComplexVector.
|
| Solve(ComplexGeneralMatrix, Boolean) |
Solves the system of simultaneous linear equations for the specified
right-hand side ComplexGeneralMatrix and optionally overwrites the
right-hand side with the solution.
|
| 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.
|
| SubtractOuterProduct(ComplexVector) |
Updates a hermitian matrix with the outer product of
a vector and its conjugate transpose.
|
| SubtractOuterProduct(ComplexMatrix) |
Updates a hermitian matrix by subtracting the product
of a matrix and its conjugate transpose.
|
| 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 |
|---|---|---|
| ComplexHermitianMatrixNew(Int32) |
Constructs a new ComplexHermitianMatrix
with the specified dimension.
|
| ComplexHermitianMatrixNew(Int32, DoubleComplex[](), MatrixTriangleMode) |
Constructs a new ComplexHermitianMatrix of the
specified dimension using the specified data.
|
| ComplexHermitianMatrixNew(Int32, DoubleComplex[](), MatrixTriangleMode, Boolean) |
Constructs a new ComplexHermitianMatrix of the
specified dimension using the specified data.
|
Properties
| Icon | Type | Description |
|---|---|---|
 | ColumnCount |
Gets the number of columns in the ComplexMatrix.
|
| Columns |
Gets the ComplexColumnCollection for this instance.
|
| ElementOrder |
Gets a value indicating the order in which the matrix
elements are stored.
|
| 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 the components of a
ComplexHermitianMatrix are stored in the upper or lower
triangle.
|
Remarks
Use the ComplexHermitianMatrix class to represent dense matrices whose
elements are symmetrical about the main diagonal. Symmetric matrices are
always square.
The components of a ComplexHermitianMatrix are stored in a one-dimensional array of DoubleComplex values. Thanks to the symmetry, only the upper or lower-triangular portion needs to be stored.
Symmetric matrices can be constructed from scratch, or they can be derived or extracted from the upper or lower triangular portion of a ComplexGeneralMatrix using one of the Extract(ComplexGeneralMatrix, Int32, Int32, Int32, MatrixTriangleMode, Boolean) methods.
The rows and column vectors of a hermitian matrix are of type
The ComplexHermitianMatrix class implements algorithms using the hermitian matrix BLAS and LAPACK routines. Symmetric matrices are always stored in column-major order.
ComplexRowVector and ComplexColumnVector, respectively.Inheritance Hierarchy
System.Object
Extreme.Mathematics.LinearAlgebra.Complex.ComplexLinearTransformation
Extreme.Mathematics.LinearAlgebra.Complex.ComplexMatrix
Extreme.Mathematics.LinearAlgebra.Complex.ComplexHermitianMatrix
Extreme.Mathematics.LinearAlgebra.Complex.ComplexLinearTransformation
Extreme.Mathematics.LinearAlgebra.Complex.ComplexMatrix
Extreme.Mathematics.LinearAlgebra.Complex.ComplexHermitianMatrix
See Also
