Represents a matrix, a two-dimensional array of real numbers.
Namespace: Extreme.Mathematics.LinearAlgebra.Complex
Assembly: Extreme.Numerics (Extreme.Numerics)
Syntax
| Visual Basic (Declaration) |
|---|
Public MustInherit Class ComplexMatrix _ Inherits ComplexLinearTransformation _ Implements IFormattable |
| C# |
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public abstract class ComplexMatrix : ComplexLinearTransformation, IFormattable |
| C++ |
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public ref class ComplexMatrix abstract : public ComplexLinearTransformation, IFormattable |
Methods
| Icon | Type | Description |
|---|---|---|
  | Add(ComplexMatrix, ComplexMatrix) |
Adds two ComplexMatrix objects.
|
| Add(TransposeOperation, TransposeOperation, DoubleComplex, ComplexMatrix) |
Adds a multiple of a ComplexMatrix to this ComplexMatrix and returns
the result.
|
| Addition(ComplexMatrix, ComplexMatrix) |
Adds two ComplexMatrix objects.
|
| AddProductToVector(DoubleComplex, ComplexVector, TransposeOperation, DoubleComplex, ComplexGeneralVector) |
Multiplies a ComplexVector by this ComplexMatrix
and stores the result in a second vector of type ComplexGeneralVector.
|
| 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.
|
| Equality(ComplexMatrix, ComplexMatrix) |
Returns a value indicating whether two instances
of ComplexMatrix are equal.
|
| Equals(Object) |
Determines whether the specified Object
is equal to the current ComplexMatrix.
|
| EstimateConditionNumber() |
Calculates an estimate for the condition
number of this ComplexMatrix.
|
 | Finalize() | |
| FrobeniusNorm() |
Returns the Frobenius norm of this ComplexMatrix.
|
| 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 this ComplexMatrix.
|
| GetDiagonal() |
Gets a ComplexVector view of the diagonal elements
of this instance.
|
| 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 of this ComplexMatrix.
|
| 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.
|
| Inequality(ComplexMatrix, ComplexMatrix) |
Returns a value indicating whether two instances
of ComplexMatrix are not equal.
|
| 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 this matrix 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(ComplexMatrix, ComplexMatrix) |
Multiplies two ComplexMatrix objects.
|
| Multiply(ComplexMatrix, ComplexVector) |
Multiplies a ComplexVector by a
ComplexMatrix.
|
| Multiply(ComplexVector, ComplexMatrix) |
Multiplies a ComplexVector by a
ComplexMatrix.
|
| Multiply(ComplexVector, ComplexMatrix) |
Multiplies a ComplexVector by a
ComplexMatrix.
|
| Multiply(ComplexMatrix, ComplexMatrix) |
Multiplies two ComplexMatrix objects.
|
| Multiply(ComplexMatrix, ComplexVector) |
Multiplies a ComplexVector by a
ComplexMatrix.
|
| 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 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.
|
| Subtract(ComplexMatrix, ComplexMatrix) |
Subtracts two ComplexMatrix objects.
|
| Subtraction(ComplexMatrix, ComplexMatrix) |
Subtracts two ComplexMatrix objects.
|
| 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 |
|---|---|---|
| ComplexMatrixNew(Int32, Int32) |
Constructs a new ComplexMatrix of the specified
dimensions using the specified data array.
|
| ComplexMatrixNew(SerializationInfo, StreamingContext) |
Constructs a new ComplexMatrix from serialization
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.
|
Remarks
ComplexMatrix is the abstract base class for representing real matrices,
two-dimensional arrays of double-precision floating-point numbers. An application
can perform operations on matrices using instances of the ComplexMatrix class,
while descendant classes implement specialized algorithms for specific types of matrices.
The ComplexMatrix class provides methods and properties for all the common operations on matrices, including arithmetic operations, calculating norms and solving systems of simultaneous linear equations. Various methods allow you to access individual components as well as rows and columns and submatrices.
Since ComplexMatrix is an abstract base class and cannot be instantiated directly. Instead, use one of its derived classes. These are:
| Class | Description |
|---|---|
| ComplexGeneralMatrix | Represents a general, dense, square or rectangular matrix. |
| ComplexTriangularMatrix | Represents an upper or lower-triangular matrix, a matrix whose elements below or above the main diagonal are zero. |
| ComplexHermitianMatrix | Represents a square matrix whose elements are symmetrical around the main diagonal. |
Note that the specialized classes exploit certain structural properties to perform many calculations more quickly than the general algorithms implemented by ComplexMatrix.
ComplexMatrix provides an indexer property. For convenient access to the rows or columns of a ComplexMatrix or parts thereof, use the GetRow(Int32) and GetColumn(Int32) methods.
Overloaded versions of the major arithmetic operators are provided for languages that support them. For languages that don't support operator overloading, equivalent staticSharedstatic methods are supplied.
Many matrix decompositions exist, serving a variety of purposes. Each of them has its own class. In this release the ComplexLUDecomposition and the ComplexQRDecomposition are supported. For positive-definite ComplexHermitianMatrix, the ComplexCholeskyDecomposition is available.
Inheritance Hierarchy
System.Object
Extreme.Mathematics.LinearAlgebra.Complex.ComplexLinearTransformation
Extreme.Mathematics.LinearAlgebra.Complex.ComplexMatrix
Extreme.Mathematics.LinearAlgebra.Complex.ComplexLinearTransformation
Extreme.Mathematics.LinearAlgebra.Complex.ComplexMatrix
See Also
