SvdT Class |
A class which encapsulates the functionality of the singular value decomposition (SVD).
Suppose M is an m-by-n matrix whose entries are real numbers. Then there exists a factorization of the form M = UΣVT where: - U is an m-by-m unitary matrix; - Σ is m-by-n diagonal matrix with nonnegative real numbers on the diagonal; - VT denotes transpose of V, an n-by-n unitary matrix; Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined by M (though the matrices U and V are not). The diagonal entries of Σ are known as the singular values of M.
Inheritance HierarchyNamespace: Altaxo.Calc.LinearAlgebra.Factorization
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntaxpublic abstract class Svd<T> : ISolver<T> where T : struct, new(), IEquatable<T>, IFormattable
Type Parameters
- T
- Supported data types are double, single, Altaxo.Calc.LinearAlgebra.Complex, and Altaxo.Calc.LinearAlgebra.Complex32.
The SvdT type exposes the following members.
ConstructorsProperties| Name | Description | |
|---|---|---|
 | ConditionNumber | Gets the condition number max(S) / min(S) |
| Determinant | Gets the determinant of the square matrix for which the SVD was computed. |
| L2Norm | Gets the two norm of the MatrixT. |
| Rank | Gets the effective numerical matrix rank. |
| S | Gets the singular values (Σ) of matrix in ascending value. |
| U | Gets the left singular vectors (U - m-by-m unitary matrix) |
| VT | Gets the transpose right singular vectors (transpose of V, an n-by-n unitary matrix) |
| W | Returns the singular values as a diagonal MatrixT. |
Methods| Name | Description | |
|---|---|---|
 | Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| Solve(MatrixT) | Solves a system of linear equations, AX = B, with A SVD factorized. |
| Solve(VectorT) | Solves a system of linear equations, Ax = b, with A SVD factorized. |
| Solve(MatrixT, MatrixT) | Solves a system of linear equations, AX = B, with A SVD factorized. |
| Solve(VectorT, VectorT) | Solves a system of linear equations, Ax = b, with A SVD factorized. |
| ToString | Returns a string that represents the current object. (Inherited from Object) |
Fields| Name | Description | |
|---|---|---|
 | VectorsComputed | Indicating whether U and VT matrices have been computed during SVD factorization. |
RemarksSee Also