Represents a general, dense, square or rectangular Matrix.
Namespace: Extreme.Mathematics.LinearAlgebra
Assembly: Extreme.Numerics (Extreme.Numerics)
Syntax
| Visual Basic (Declaration) |
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Public Class GeneralMatrix _ Inherits Matrix _ Implements ISerializable, IDoubleStorage |
| C# |
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public class GeneralMatrix : Matrix, ISerializable, IDoubleStorage |
| C++ |
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public ref class GeneralMatrix : public Matrix, ISerializable, IDoubleStorage |
Methods
| Icon | Type | Description |
|---|---|---|
 | Add(Matrix) |
Adds a Matrix to this
GeneralMatrix.
|
| Add(Double, Matrix) |
Adds a multiple of a Matrix to this
GeneralMatrix.
|
 | Add(GeneralMatrix, GeneralMatrix) |
Adds two GeneralMatrix objects and returns the result.
|
| Add(GeneralMatrix, Double, GeneralMatrix, GeneralMatrix) |
Adds two GeneralMatrix objects and stores the
result in a third GeneralMatrix.
|
| Add(TransposeOperation, TransposeOperation, Double, Matrix) | |
| AddOuterProduct(Vector) |
Updates a matrix with the outer product of a
Vector and itself.
|
| AddOuterProduct(Double, Vector, Vector) |
Updates a matrix with the scaled outer product of two vectors.
|
| AddOuterProduct(Double, Vector) |
Updates a matrix with the scaled outer product of
a Vector and itself.
|
| AddProduct(GeneralMatrix, GeneralMatrix) |
Adds the product of two GeneralMatrix objects
to this GeneralMatrix.
|
| AddProduct(Double, GeneralMatrix, GeneralMatrix) |
Adds a multiple of the product of two GeneralMatrix object
to this GeneralMatrix.
|
| AddProductToVector(Double, Vector, TransposeOperation, Double, GeneralVector) | |
| ApplyToColumns(MultivariateRealFunction) |
Applies a function to each column in a matrix and returns the result as a vector.
|
| ApplyToRows(MultivariateRealFunction) |
Applies a function to each column in a matrix and returns the result as a vector.
|
| Clone() |
Constructs a deep copy of this Matrix.
|
| CloneData() |
Gives this instance its own copy of its elements.
|
| CloneData(MatrixElementOrder) |
Gives this instance its own copy of its elements.
|
| ComponentwiseDivide(Matrix) |
Divides the components of this instance by the corresponding
components of another matrix.
|
| ComponentwiseMultiply(Matrix) |
Multiplies the components of this instance by the corresponding
components of another matrix.
|
| CopyTo(Matrix) |
Copies the components of this Matrix
to another matrix.
|
| Equals(Object) | |
| EstimateConditionNumber() |
Calculates an estimate for the condition
number of this Matrix.
|
 | Finalize() | |
| FrobeniusNorm() |
Returns the Frobenius norm of this Matrix.
|
| GetColumn(Int32, Int32, Int32, Int32) |
Returns a column Vector for this instance
starting at the specified column and row and of the
specified length.
|
| GetColumn(Int32) |
Returns a column Vector for this instance
that points at the specified column.
|
| GetColumn(Int32, Int32, Int32) |
Returns a column Vector for this instance
starting at the specified column and row and of the
specified length.
|
| GetColumn(Int32, Range) |
Returns a column Vector 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 GeneralMatrix.
|
| GetColumnSums() |
Returns the sums of the components of each column of the matrix.
|
| GetComponents() |
Gets the components of the Vector.
|
| GetComponents(MatrixElementOrder) |
Gets the components of the Vector.
|
| GetConditionNumber() |
Calculates the condition
number of this Matrix.
|
| GetDeterminant() |
Calculates the determinant of this Matrix.
|
| GetDiagonal(Int32) |
Gets a Vector view of the specified diagonal
of this instance.
|
| GetHashCode() |
Returns the hash code for this instance.
|
| GetIdentity(Int32) |
Returns an identity matrix of the specified dimension.
|
| GetInverse() |
Calculates the inverse of this Matrix.
|
| GetObjectData(SerializationInfo, StreamingContext) |
Populates a SerializationInfo with the data
needed to serialize the target object.
|
| GetPseudoInverse() |
Calculates the Moore-Penrose pseudo-inverse of this Matrix.
|
| GetRow(Int32, Int32, Int32, Int32) |
Returns a row Vector for this instance
starting at the specified row and column and of the
specified length.
|
| GetRow(Int32) |
Returns a row Vector for this instance
that points at the specified row.
|
| GetRow(Int32, Int32, Int32) |
Returns a row Vector for this instance
over the specified range.
|
| GetRow(Int32, Range) |
Returns a row Vector for this instance
starting at the specified row and column and of the
specified length.
|
| GetRowEnumerator() |
Constructs an IEnumerator object that can be used
to enumerate the rows of this GeneralMatrix.
|
| GetRowSums() |
Returns the sums of the components of each row of the matrix.
|
| GetSingularValues() |
Gets a vector containing the singular values of the matrix.
|
| GetSubmatrix(Int32, Int32, Int32, Int32, Int32, Int32, TransposeOperation) |
Gets a GeneralMatrix that is a submatrix of
this matrix.
|
| GetSubmatrix(Range, Range, TransposeOperation) | |
| GetSubmatrix(Range, Range) | |
| GetSubmatrix(Int32, Int32, Int32, Int32) | |
| 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 Matrix.
|
| 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 this matrix is singular.
|
| MemberwiseClone() | Creates a shallow copy of the current Object. |
| Multiply(Matrix) |
Multiplies this GeneralMatrix on the right by a
Matrix.
|
| Multiply(Double) |
Multiplies this Matrix by a scalar factor.
|
| Multiply(MatrixOperationSide, TransposeOperation, TransposeOperation, Matrix) |
Multiplies this Matrix by another matrix and returns
the result.
|
| Multiply(GeneralMatrix, GeneralMatrix) |
Multiplies two Matrix objects.
|
| Multiply(GeneralMatrix, GeneralMatrix, GeneralMatrix) |
Multiplies two GeneralMatrix objects and stores
the result in a third GeneralMatrix.
|
| MultiplyByTranspose() |
Multiplies this GeneralMatrix by its
Transpose().
|
| NormInternal(Char) |
Calculates a matrix norm.
|
| OneNorm() |
Returns the 1-norm of this Matrix.
|
| PreMultiply(Matrix) |
Multiplies this GeneralMatrix on the left by a
Matrix.
|
| Rank(Double) |
Returns the numerical rank of a matrix using the specified tolerance.
|
| ScaleColumns(Vector) |
Scales the columns of the matrix by the values specified by a vector.
|
| ScaleRows(Vector) |
Scales the rows of the matrix by the values specified by a vector.
|
| SetToZero() |
Sets all elements of the matrix to zero.
|
| SetValue(Double, Int32, Int32) |
Sets the matrix component at the specified position to the specified value.
|
| ShallowCopy() |
Makes a shallow copy of this Matrix.
|
| Solve(GeneralVector, Boolean) |
Solves the system of simultaneous linear equations for the specified
right-hand side Vector.
|
| Solve(GeneralMatrix, Boolean) |
Solves the system of simultaneous linear equations for the specified
right-hand side GeneralMatrix and overwrites the
right-hand side with the solution.
|
| Solve(Vector) |
Solves the system of linear equations for the specified
right-hand side Vector.
|
| Solve(Matrix) |
Solves the system of linear equations for the specified
right-hand side Matrix.
|
| Subtract(GeneralMatrix, GeneralMatrix) |
Subtracts two GeneralMatrix objects.
|
| Subtract(GeneralMatrix, GeneralMatrix, GeneralMatrix) |
Subtracts two GeneralMatrix objects and stores the
result in a third GeneralMatrix.
|
| SubtractProduct(GeneralMatrix, GeneralMatrix) |
Subtracts the product of two GeneralMatrix object
to this GeneralMatrix.
|
| ToGeneralMatrix() |
Makes a copy of this instance and returns it as a
GeneralMatrix.
|
| ToString() | |
| ToString(String) | |
| ToString(String, IFormatProvider) | |
| Trace() |
Gets the sum of the diagonal elements of this
Matrix.
|
| Transpose() |
Returns the transpose of this instance.
|
| TwoNorm() |
Returns the two-norm of this Matrix.
|
| UnscaleColumns(Vector) |
Scales the columns of the matrix by the inverse of the values specified by a vector.
|
| UnscaleRows(Vector) |
Scales the rows of the matrix by the inverse of the values specified by a vector.
|
Constructors
| Icon | Type | Description |
|---|---|---|
| GeneralMatrixNew(Int32, Int32) |
Constructs a new GeneralMatrix with the specified
number of rows and columns
|
| GeneralMatrixNew(Int32, Int32, MatrixElementOrder) |
Constructs a new GeneralMatrix with the specified
number of rows and columns
|
| GeneralMatrixNew(Double[,,,,,](,,,,,)) |
Constructs a new GeneralMatrix from a
two-dimensional array.
|
| GeneralMatrixNew(SerializationInfo, StreamingContext) |
Constructs a new GeneralMatrix from serialization
data.
|
| GeneralMatrixNew(Int32, Int32, Double[]()) |
Constructs a new GeneralMatrix of the specified
dimensions using the specified data array.
|
| GeneralMatrixNew(Int32, Int32, Double[](), Boolean) |
Constructs a new GeneralMatrix of the specified
dimensions using the specified data array.
|
| GeneralMatrixNew(Int32, Int32, Double[](), MatrixElementOrder) |
Constructs a new GeneralMatrix of the specified
dimensions using the specified data array.
|
| GeneralMatrixNew(Int32, Int32, Double[](), MatrixElementOrder, Boolean) |
Constructs a new GeneralMatrix of the specified
dimensions using the specified data array.
|
| GeneralMatrixNew(Int32, Int32, Double) |
Constructs a new GeneralMatrix with the specified
number of rows and columns whose elements are all equal to the specified value.
|
Properties
| Icon | Type | Description |
|---|---|---|
 | ColumnCount |
Gets the number of columns in the Matrix.
|
| Columns |
Gets the ColumnCollection 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
Matrix.
|
| Item(Int32, Range) |
Gets or sets the components of a row of this Matrix.
|
| Item(Range, Range) |
Gets or sets the components of a submatrix of this Matrix.
|
| Item(Range, Int32) |
Gets or sets the components of a column of this Matrix.
|
| RowCount |
Gets the number of rows in the Matrix.
|
| Rows |
Gets the RowCollection for this instance.
|
| StorageArray |
Gets the Double array that stores
the data for the instance.
|
| StorageIncrement |
Gets the increment between successive elements of this
instance in the StorageArray.
|
| StorageOffset |
Gets the index of the first element of this instance
in the StorageArray.
|
Remarks
A matrix is a two-dimensional array of real numbers. Use the
GeneralMatrix class to represent general, dense matrices.
It is the most general implementation of the Matrix class.
No components are assumed to have a specific value, and no relationship is
assumed to exist between different components.
The components of a GeneralMatrix are stored in a one-dimensional array of Double 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 GeneralMatrix 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 GeneralMatrix can represent any matrix, it is often used as the return type of matrix operations.
Inheritance Hierarchy
System.Object
Extreme.Mathematics.LinearAlgebra.LinearTransformation
Extreme.Mathematics.LinearAlgebra.Matrix
Extreme.Mathematics.LinearAlgebra.GeneralMatrix
Extreme.Mathematics.LinearAlgebra.LinearTransformation
Extreme.Mathematics.LinearAlgebra.Matrix
Extreme.Mathematics.LinearAlgebra.GeneralMatrix
See Also
