SingularValueDecompositionF Class |
Namespace: DigitalRune.Mathematics.Algebra
The SingularValueDecompositionF type exposes the following members.
Name | Description | |
---|---|---|
SingularValueDecompositionF |
Creates the singular value decomposition of the given matrix.
|
Name | Description | |
---|---|---|
Equals | (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 a hash function for a particular type. (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.) | |
ToString | Returns a string that represents the current object. (Inherited from Object.) |
Name | Description | |
---|---|---|
ConditionNumber |
Gets the condition number of A.
| |
Norm2 |
Gets the two norm of A.
| |
NumericalRank |
Gets the effective numerical rank of A.
| |
S |
Gets the diagonal matrix S with the singular values. (This property returns the internal
matrix, not a copy.)
| |
SingularValues |
Gets the vector of singular values (the diagonal of S).
| |
U |
Gets the matrix U with the left singular vectors. (This property returns the internal
matrix, not a copy.)
| |
V |
Gets the matrix V with the right singular vectors. (This property returns the internal
matrix, not a copy.)
|
For an m x n matrix A with m ≥ n, the SVD computes the matrices U, S and V so that A = U * S * VT.
U is an m x n orthogonal matrix. S is an n x n diagonal matrix. V is is a n x n orthogonal matrix.
The diagonal elements of S are the singular values. The singular values are positive or zero and ordered so that S[0, 0] ≥ S[1, 1] ≥ ...
The singular value decomposition always exists.
Applications: The matrix condition number and the effective numerical rank can be computed from this decomposition.