ComplexDenseMatrix Class | Extreme Optimization Numerical Libraries for .NET Professional |

Extreme.Mathematics.LinearAlgebra.Complex

Extreme.Mathematics

Extreme.Mathematics.LinearAlgebra.Complex

**Namespace:**Extreme.Mathematics.LinearAlgebra.Complex

**Assembly:**Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 6.0.16073.0 (6.0.17114.0)

[SerializableAttribute] public sealed class ComplexDenseMatrix : ComplexMatrix, IComplexStorage, ICloneable, ISerializable

The ComplexDenseMatrix type exposes the following members.

Name | Description | |
---|---|---|

Add(ComplexMatrix) |
Adds a ComplexMatrix to this
ComplexDenseMatrix.
| |

Add(ComplexDenseMatrix, ComplexDenseMatrix) |
Adds two ComplexDenseMatrix objects and returns the result.
| |

Add(DoubleComplex, ComplexMatrix) |
Adds a multiple of a ComplexMatrix to this
ComplexDenseMatrix.
| |

Add(ComplexDenseMatrix, DoubleComplex, ComplexDenseMatrix, ComplexDenseMatrix) |
Adds two ComplexDenseMatrix objects and stores the
result in a third ComplexDenseMatrix.
| |

Add(TransposeOperation, TransposeOperation, DoubleComplex, ComplexMatrix) |
Adds a multiple of a ComplexMatrix to this ComplexMatrix and returns
the result.
(Inherited from ComplexMatrix.) | |

AddConjugateOuterProduct(ComplexVector) |
Updates a matrix with the conjugated outer product of a
complex vector and its conjugate.
| |

AddConjugateOuterProduct(DoubleComplex, ComplexVector) |
Updates a matrix with the scaled conjugated outer product of a
complex vector and its conjugate.
| |

AddConjugateOuterProduct(DoubleComplex, ComplexVector, ComplexVector) |
Updates a matrix with the scaled conjugated outer product of two vectors.
| |

AddOuterProduct(ComplexVector) |
Updates a matrix with the outer product of a
complex vector and itself.
| |

AddOuterProduct(DoubleComplex, ComplexVector) |
Updates a matrix with the scaled unconjugated outer product of
a complex vector and itself.
| |

AddOuterProduct(DoubleComplex, ComplexVector, ComplexVector) |
Updates a matrix with the scaled unconjugated outer product of two vectors.
| |

AddProduct(ComplexDenseMatrix, ComplexDenseMatrix) |
Adds the product of two ComplexDenseMatrix objects
to this ComplexDenseMatrix.
| |

AddProduct(DoubleComplex, ComplexDenseMatrix, ComplexDenseMatrix) |
Adds a multiple of the product of two ComplexDenseMatrix object
to this ComplexDenseMatrix.
| |

AddProductToVector | (Overrides ComplexMatrix | |

AsDenseMatrix |
Returns this matrix as a general matrix.
ComplexDenseMatrix.
(Inherited from ComplexMatrix.) | |

Clone |
Constructs a deep copy of this ComplexMatrix.
(Inherited from ComplexMatrix.) | |

CloneData |
Gives this instance its own copy of its elements.
(Overrides ComplexMatrix | |

CloneData(MatrixElementOrder) |
Gives this instance its own copy of its elements.
| |

ComponentwiseDivide(ComplexMatrix) | Obsolete.
Divides the components of this instance by the corresponding
components of another matrix.
(Inherited from ComplexMatrix.) | |

ComponentwiseMultiply(ComplexMatrix) | Obsolete.
Multiplies the components of this instance by the corresponding
components of another matrix.
(Inherited from ComplexMatrix.) | |

Conjugate |
Returns the conjugate transpose of this instance.
(Inherited from ComplexMatrix.) | |

ConjugateTranspose |
Returns the conjugate transpose of this instance.
(Inherited from ComplexMatrix.) | |

CopyTo |
Copies the components of this ComplexMatrix
to another matrix.
(Inherited from ComplexMatrix.) | |

ElementwiseDivideInPlace |
Divides the components of this instance by the corresponding
components of another matrix.
(Inherited from ComplexMatrix.) | |

ElementwiseMultiplyInPlace |
Multiplies the components of this instance by the corresponding
components of another matrix.
(Inherited from ComplexMatrix.) | |

Equals(Object) |
Determines whether the specified Object
is equal to the current ComplexMatrix.
(Inherited from ComplexMatrix.) | |

Equals(Object, IEqualityComparer) |
Returns whether an object is structurally equal to this instance.
(Inherited from ComplexMatrix.) | |

EstimateConditionNumber |
Calculates an estimate for the condition
number of this ComplexMatrix.
(Inherited from ComplexMatrix.) | |

FrobeniusNorm |
Returns the Frobenius norm of this ComplexMatrix.
(Inherited from ComplexMatrix.) | |

GetCholeskyDecomposition |
Returns the Cholesky decomposition of the matrix.
(Inherited from ComplexMatrix.) | |

GetCholeskyDecomposition(Boolean) |
Returns the Cholesky decomposition of the matrix.
(Overrides ComplexMatrix | |

GetColumn(Int32) |
Returns a column complex vector for this instance
that points at the specified column.
(Inherited from ComplexMatrix.) | |

GetColumn(Int32, Range) |
Returns a column complex vector for this instance
starting at the specified column and row and of the
specified length.
(Inherited from ComplexMatrix.) | |

GetColumn(Int32, Int32, Int32) |
Returns a column complex vector for this instance
starting at the specified column and row and of the
specified length.
(Inherited from ComplexMatrix.) | |

GetColumn(Int32, Int32, Int32, Int32) |
Returns a column complex vector for this instance
starting at the specified column and row and of the
specified length.
(Overrides ComplexMatrix | |

GetColumnEnumerator | Obsolete.
Gets an IEnumerator than can be used to enumerate
the columns of this ComplexDenseMatrix.
(Overrides ComplexMatrix | |

GetComponents | Obsolete.
Gets the components of the complex vector.
(Inherited from ComplexMatrix.) | |

GetComponents(MatrixElementOrder) | Obsolete.
Gets the components of the complex vector.
(Inherited from ComplexMatrix.) | |

GetConditionNumber |
Calculates the condition
number of this matrix.
(Inherited from ComplexMatrix.) | |

GetDeterminant |
Calculates the determinant of this ComplexMatrix.
(Inherited from ComplexMatrix.) | |

GetDiagonal |
Gets a complex vector view of the diagonal elements
of this instance.
(Inherited from ComplexMatrix.) | |

GetDiagonal(Int32) |
Gets a complex vector view of the specified diagonal
of this instance.
(Overrides ComplexMatrix | |

GetEigenvalueDecomposition |
Returns the eigenvalue decomposition for this matrix.
(Inherited from ComplexMatrix.) | |

GetEigenvalueDecomposition(Boolean) |
Returns the eigenvalue decomposition for this matrix.
(Overrides ComplexMatrix | |

GetHashCode |
Returns the hash code for this instance.
(Inherited from ComplexMatrix.) | |

GetHashCode(IEqualityComparer) |
Returns a hash code for this instance.
(Inherited from ComplexMatrix.) | |

GetIdentity |
Returns an identity matrix of the specified dimension.
| |

GetImaginaryPart |
Returns a real matrix containing the imaginary elements of the matrix.
(Inherited from ComplexMatrix.) | |

GetInverse |
Calculates the inverse matrix..
(Inherited from ComplexLinearOperator.) | |

GetInverse(Boolean) |
Calculates the inverse of this ComplexMatrix.
(Inherited from ComplexMatrix.) | |

GetLUDecomposition |
Returns the LU decomposition of the matrix.
(Inherited from ComplexMatrix.) | |

GetLUDecomposition(Boolean) |
Returns the LU decomposition of the matrix.
(Overrides ComplexMatrix | |

GetObjectData |
Populates a SerializationInfo with the values
needed to serialize the target object.
(Overrides ComplexMatrix | |

GetQRDecomposition |
Returns the QR decomposition of the matrix.
(Inherited from ComplexMatrix.) | |

GetQRDecomposition(Boolean) |
Returns the QR decomposition of the matrix.
(Overrides ComplexMatrix | |

GetRealPart |
Returns a real matrix containing the real elements of the matrix.
(Inherited from ComplexMatrix.) | |

GetRow(Int32) |
Returns a row complex vector for this instance
that points at the specified row.
(Inherited from ComplexMatrix.) | |

GetRow(Int32, Range) |
Returns a row complex vector for this instance
starting at the specified row and column and of the
specified length.
(Inherited from ComplexMatrix.) | |

GetRow(Int32, Int32, Int32) |
Returns a row complex vector for this instance
over the specified range.
(Inherited from ComplexMatrix.) | |

GetRow(Int32, Int32, Int32, Int32) |
Returns a row complex vector for this instance
starting at the specified row and column and of the
specified length.
(Overrides ComplexMatrix | |

GetRowEnumerator | Obsolete.
Constructs an IEnumerator object that can be used
to enumerate the rows of this ComplexDenseMatrix.
(Overrides ComplexMatrix | |

GetSingularValueDecomposition |
Returns the singular value decomposition of the matrix.
(Inherited from ComplexMatrix.) | |

GetSingularValueDecomposition(SingularValueDecompositionFactors) |
Returns the singular value decomposition of the matrix.
(Inherited from ComplexMatrix.) | |

GetSingularValueDecomposition(SingularValueDecompositionFactors, Boolean) |
Returns the singular value decomposition of the matrix.
(Overrides ComplexMatrix | |

GetSingularValues |
Gets a vector containing the singular values of the matrix.
(Inherited from ComplexMatrix.) | |

GetSubmatrix(Range, Range) |
Gets a ComplexMatrix that is a submatrix of
this ComplexMatrix.
(Inherited from ComplexMatrix.) | |

GetSubmatrix(Range, Range, TransposeOperation) |
Gets a ComplexMatrix that is a submatrix of
this ComplexMatrix.
(Inherited from ComplexMatrix.) | |

GetSubmatrix(Int32, Int32, Int32, Int32) |
Gets a ComplexMatrix that is a submatrix of
this ComplexMatrix.
(Inherited from ComplexMatrix.) | |

GetSubmatrix(Int32, Int32, Int32, Int32, Int32, Int32, TransposeOperation) |
Gets a ComplexDenseMatrix that is a submatrix of
this matrix.
(Overrides ComplexMatrix | |

GetType | Gets the Type of the current instance. (Inherited from Object.) | |

GetValue |
Gets the matrix component at the specified position.
(Overrides ComplexMatrix | |

InfinityNorm |
Returns the infinity norm of this ComplexMatrix.
(Inherited from ComplexMatrix.) | |

IsComponentWritable | Obsolete.
Returns whether the value of the component at
the specified row and column can be changed.
(Inherited from ComplexMatrix.) | |

IsElementWritable |
Gets a value indicating whether the value of the component at
the specified row and column can be changed.
(Overrides ComplexMatrix | |

IsSingular |
Gets a value indicating whether this matrix is singular.
(Inherited from ComplexMatrix.) | |

Multiply(ComplexMatrix) |
Multiplies this ComplexDenseMatrix on the right by a
ComplexMatrix.
| |

Multiply(ComplexVector) | Applies the matrix to a vector. (Inherited from ComplexMatrix.) | |

Multiply(DoubleComplex) |
Multiplies this ComplexMatrix by a scalar factor.
(Inherited from ComplexMatrix.) | |

Multiply(ComplexDenseMatrix, ComplexDenseMatrix) |
Multiplies two ComplexMatrix objects.
| |

Multiply(ComplexDenseMatrix, ComplexDenseMatrix, ComplexDenseMatrix) |
Multiplies two ComplexDenseMatrix objects and stores
the result in a third ComplexDenseMatrix.
| |

Multiply(MatrixOperationSide, TransposeOperation, TransposeOperation, ComplexMatrix) |
Multiplies this ComplexMatrix by another matrix and returns
the result.
(Overrides ComplexMatrix | |

MultiplyByConjugateTranspose |
Multiplies this ComplexDenseMatrix by its
Transpose | |

MultiplyTranspose(ComplexMatrix) | Applies the transpose of the matrix to a matrix. (Inherited from ComplexMatrix.) | |

MultiplyTranspose(ComplexVector) | Applies the transpose of the matrix to a vector. (Inherited from ComplexMatrix.) | |

OneNorm |
Returns the 1-norm of this ComplexMatrix.
(Inherited from ComplexMatrix.) | |

PermuteColumns |
Permutes the columns of the matrix using the specified Permutation.
(Inherited from ComplexMatrix.) | |

PermuteRows |
Permutes the rows of the matrix using the specified Permutation.
(Inherited from ComplexMatrix.) | |

PermuteRowsAndColumns(Permutation) |
Permutes the rows and columns of the matrix using the specified Permutation.
(Inherited from ComplexMatrix.) | |

PermuteRowsAndColumns(Permutation, Permutation) |
Permutes the rows and columns of the matrix using the specified row and column Permutation.
(Inherited from ComplexMatrix.) | |

PreMultiply |
Multiplies this ComplexDenseMatrix on the left by a
ComplexMatrix.
| |

Rank |
Returns the numerical rank of a matrix.
(Inherited from ComplexLinearOperator.) | |

Rank(Double) |
Returns the numerical rank of a matrix using the specified tolerance.
(Inherited from ComplexMatrix.) | |

ScaleColumns |
Scales the columns of the matrix by the values specified by a vector.
(Inherited from ComplexMatrix.) | |

ScaleRows |
Scales the rows of the matrix by the values specified by a vector.
(Inherited from ComplexMatrix.) | |

SetToZero |
Sets all elements of the matrix to zero.
(Inherited from ComplexMatrix.) | |

SetValue(DoubleComplex) |
Sets all elements of the matrix to the specified value.
(Inherited from ComplexMatrix.) | |

SetValue(DoubleComplex, Int32, Int32) |
Sets the matrix component at the specified position to the specified value.
(Overrides ComplexMatrix | |

ShallowCopy |
Makes a shallow copy of this ComplexMatrix.
(Inherited from ComplexMatrix.) | |

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 overwrites the
right-hand side with the solution.
(Overrides ComplexMatrix | |

Solve(ComplexDenseVector, Boolean) |
Solves the system of simultaneous linear equations for the specified
right-hand side complex vector.
(Overrides ComplexMatrix | |

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 system of simultaneous linear equations for the specified
right-hand side ComplexDenseMatrix and overwrites the
right-hand side with the solution.
(Overrides ComplexMatrix | |

SolveTranspose(ComplexDenseVector, Boolean) |
Solves the system of simultaneous linear equations for the specified
right-hand side complex vector.
(Overrides ComplexMatrix | |

Subtract(ComplexDenseMatrix, ComplexDenseMatrix) |
Subtracts two ComplexDenseMatrix objects.
| |

Subtract(ComplexDenseMatrix, ComplexDenseMatrix, ComplexDenseMatrix) |
Subtracts two ComplexDenseMatrix objects and stores the
result in a third ComplexDenseMatrix.
| |

SubtractProduct |
Subtracts the product of two ComplexDenseMatrix object
to this ComplexDenseMatrix.
| |

SwapColumns |
Swaps the columns with the specified indices.
(Inherited from ComplexMatrix.) | |

SwapRows |
Swaps the rows with the specified indices.
(Inherited from ComplexMatrix.) | |

ToArray |
Gets the components of the complex vector.
(Inherited from ComplexMatrix.) | |

ToArray(MatrixElementOrder) |
Gets the components of the complex vector.
(Inherited from ComplexMatrix.) | |

ToDenseMatrix |
Makes a copy of this instance and returns it as a
ComplexDenseMatrix.
(Inherited from ComplexMatrix.) | |

ToGeneralMatrix | Obsolete.
Makes a copy of this instance and returns it as a
ComplexDenseMatrix.
(Inherited from ComplexMatrix.) | |

ToString |
Returns a String representation of this
ComplexMatrix.
(Inherited from ComplexMatrix.) | |

ToString(String) |
Returns a String representation of this
ComplexMatrix.
(Inherited from ComplexMatrix.) | |

ToString(String, IFormatProvider) |
Returns a String representation of this
ComplexMatrix.
(Inherited from ComplexMatrix.) | |

Trace |
Gets the sum of the diagonal elements of this
ComplexMatrix.
(Inherited from ComplexMatrix.) | |

Transpose |
Returns the transpose of this instance.
(Overrides ComplexMatrix | |

UnscaleColumns |
Scales the columns of the matrix by the inverse of the values specified by a vector.
(Inherited from ComplexMatrix.) | |

UnscaleRows |
Scales the rows of the matrix by the inverse of the values specified by a vector.
(Inherited from ComplexMatrix.) |

A matrix is a two-dimensional array of real numbers. Use the
**ComplexDenseMatrix** class to represent general, dense matrices.
It is the most general implementation of the ComplexMatrix class.
No components are assumed to have a specific value, and no relationship is
assumed to exist between different components.

The components of a **ComplexDenseMatrix** 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.

The **ComplexDenseMatrix** class implements algorithms using the
general 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.

Because **ComplexDenseMatrix** can represent any matrix, it is often
used as the return type of matrix operations.

#### Numerical Libraries

Supported in: 5.x, 4.x#### Reference

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