Complex Singular Value Decomposition<T> Class
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.2
public abstract class ComplexSingularValueDecomposition<T> : Decomposition<Complex<T>>
- Inheritance
- Object → LinearOperator<Complex<T>> → Decomposition<Complex<T>> → ComplexSingularValueDecomposition<T>
Type Parameters
- T
Remarks
The singular value decomposition (SVD) of a matrix A rewrites the matrix in the form A= USVT, where U and V are orthogonal matrices, and S is a diagonal matrix whose diagonal contains the singular values of the matrix.
QRDecomposition<T> can operate in two modes. In overwrite mode, the original matrix is overwritten by the decomposition. In preserve mode, the original matrix is preserved, and a new matrix is created to hold the decomposition. You can set the mode through the Overwrite property.
SingularValueDecomposition<T> inherits from LinearOperator<T>. This means you can use it to solve systems of linear equations. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(Vector<T>) method. You can also calculate the determinant, the inverse, and an estimate for the EstimateConditionNumber().
In addition, the SingularValueDecomposition<T> class provides some unique methods. The GetPseudoInverse() method calculates the pseudo-inverse of the matrix. This is a matrix A+ such that AA+A = A.
The managed implementation of the singular value decomposition is based on the LINPACK routine DSVDC. The native version uses the LAPACK routine ?GESDD.
Constructors
Properties
Base |
Gets the underlying matrix of the decomposition.
(Inherited from Decomposition<T>) |
Column |
Gets the number of columns in the matrix.
(Inherited from LinearOperator<T>) |
Column |
Gets or sets the index of labels for the columns of the matrix.
(Inherited from LinearOperator<T>) Preliminary |
Done |
Gets or sets a value that indicates whether the decomposition
has been performed.
(Inherited from Decomposition<T>) |
Element |
Gets the element type of the matrix.
(Inherited from LinearOperator<T>) |
Factors |
Gets a collection of the matrix factors that make up the decomposition.
(Overrides Decomposition<T>.Factors) |
Left | Gets the left singular vectors of the decomposition. |
Overwrite |
Gets or sets whether the
BaseMatrix should be overwritten by
its decomposition.
(Inherited from Decomposition<T>) |
Requested | Gets or sets which factors of the singular value decomposition should be calculated. |
Right | Gets the right singular vectors of the decomposition. |
Row |
Gets the number of rows in the matrix.
(Inherited from LinearOperator<T>) |
Row |
Gets or sets the index of labels for the rows of the matrix.
(Inherited from LinearOperator<T>) Preliminary |
Singular | Gets a matrix with the singular values on the diagonal. |
Singular | Gets a vector containing the singular values. |
Methods
Decompose |
Performs the actual decomposition.
(Inherited from Decomposition<T>) |
Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
Estimate |
Calculates an estimate for the condition number of a matrix.
(Inherited from LinearOperator<T>) |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
Get |
Calculates the determinant of the decomposed
matrix.
(Overrides LinearOperator<T>.GetDeterminant()) |
Get | Serves as the default hash function. (Inherited from Object) |
Get |
Calculates the inverse matrix..
(Inherited from LinearOperator<T>) |
Get |
Calculates the inverse of the factorized
matrix.
(Overrides LinearOperator<T>.GetInverse(Boolean)) |
Get |
Populates a SerializationInfo with the data
needed to serialize the target object.
(Inherited from LinearOperator<T>) Obsolete. |
Get | Calculates the pseudo-inverse of the factorized matrix. |
Get | Calculates the pseudo-inverse of the factorized matrix. |
Get | Gets the Type of the current instance. (Inherited from Object) |
IsSingular |
Gets whether the BaseMatrix of this decomposition
is singular.
(Inherited from Decomposition<T>) |
Least |
Solves the system of linear equations for the specified
right-hand side matrix in the least squares sense.
(Inherited from LinearOperator<T>) |
Least |
Solves the system of linear equations for the specified
right-hand side vector.
(Inherited from LinearOperator<T>) |
Least |
Solves the system of linear equations for the specified
right-hand side dense matrix in the least squares sense and optionally overwrites the
right-hand side with the solution.
(Inherited from LinearOperator<T>) |
Least |
Solves the system of linear equations for the specified
right-hand side dense vector in the least squares sense and optionally
overwrites the right-hand side with the solution.
(Inherited from LinearOperator<T>) |
Least |
Solves a system of equations defined by the matrix and multiple right-hand sides in the least squares sense.
(Inherited from LinearOperator<T>) |
Least |
Solves a system of equations defined by the matrix and the specified right-hand side in the least squares sense.
(Inherited from Decomposition<T>) |
Memberwise | Creates a shallow copy of the current Object. (Inherited from Object) |
Multiply( | Applies the linear operator to a matrix. (Inherited from LinearOperator<T>) |
Multiply( | Applies the linear operator to a vector. (Inherited from LinearOperator<T>) |
Multiply |
Multiplies the matrix with a vector, adds the scaled result to another scaled
vector, and returns the result.
(Inherited from Decomposition<T>) |
Multiply |
Multiplies a matrix by the linear operator and returns the result.
(Inherited from Decomposition<T>) |
Multiply |
Multiplies a vector by the linear operator and returns the result.
(Inherited from Decomposition<T>) |
Multiply | Applies the transpose of the linear operator to a matrix. (Inherited from LinearOperator<T>) |
Multiply | Applies the (conjugate) transpose of the linear operator to a vector. (Inherited from LinearOperator<T>) |
Rank() |
Returns the numerical rank of a matrix.
(Inherited from LinearOperator<T>) |
Rank( |
Returns the numerical rank of a matrix using the specified tolerance.
(Inherited from LinearOperator<T>) |
Set |
Sets a flag that indicates the underlying matrix of this
decomposition is singular.
(Inherited from Decomposition<T>) |
Solve( |
Solves the system of linear equations for the specified
right-hand side matrix.
(Inherited from LinearOperator<T>) |
Solve( |
Solves the system of linear equations for the specified
right-hand side vector.
(Inherited from LinearOperator<T>) |
Solve( |
Solves the system of linear equations for the specified
right-hand side dense matrix and optionally overwrites the
right-hand side with the solution.
(Inherited from LinearOperator<T>) |
Solve( |
Solves the system of linear equations for the specified
right-hand side dense vector and optionally
overwrites the right-hand side with the solution.
(Inherited from LinearOperator<T>) |
Solve |
Solves a system of equations defined by the matrix and multiple right-hand sides.
(Inherited from LinearOperator<T>) |
Solve |
Solves a system of equations defined by the matrix and the specified right-hand side.
(Inherited from LinearOperator<T>) |
Solve |
Solves a system of equations defined by the matrix and multiple right-hand sides.
(Overrides LinearOperator<T>.SolveInto(TransposeOperation, Matrix<T>, Matrix<T>)) |
Solve |
Solves a system of equations defined by the matrix and the specified right-hand side.
(Overrides LinearOperator<T>.SolveInto(TransposeOperation, Vector<T>, Vector<T>)) |
Solve |
Solves the transposed system of linear equations for the specified
right-hand side matrix.
(Inherited from LinearOperator<T>) |
Solve |
Solves the system of linear equations for the specified
right-hand side vector.
(Inherited from LinearOperator<T>) |
Solve |
Solves the transposed system of linear equations for the specified
right-hand side dense matrix and optionally overwrites the
right-hand side with the solution.
(Inherited from LinearOperator<T>) |
Solve |
Solves the transposed system of linear equations for the specified
right-hand side dense vector and optionally
overwrites the right-hand side with the solution.
(Inherited from LinearOperator<T>) |
Solve |
Solves a system of equations defined by the matrix and multiple right-hand sides.
(Inherited from LinearOperator<T>) |
Solve |
Solves a system of equations defined by the matrix and the specified right-hand side.
(Inherited from LinearOperator<T>) |
ToString | Returns a string that represents the current object. (Inherited from Object) |