SVD Class |
Namespace: Imsl.Math
The SVD type exposes the following members.
Name | Description | |
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SVD(Double) |
Construct the singular value decomposition of a rectangular matrix
with default tolerance.
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SVD(Double, Double) |
Construct the singular value decomposition of a rectangular matrix
with a given tolerance.
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Name | Description | |
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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 a hash function for a particular type. (Inherited from Object.) | |
GetS |
Returns the singular values.
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GetType | Gets the Type of the current instance. (Inherited from Object.) | |
GetU |
Returns the left singular vectors.
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GetV |
Returns the right singular vectors.
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Inverse |
Compute the Moore-Penrose generalized inverse of a real matrix.
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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 | |
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Info |
Returns the index of the first singular value for which the algorithm
converged.
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NumberOfProcessors |
Perform the parallel calculations with the maximum possible number of
processors set to NumberOfProcessors.
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Rank |
Returns the rank of the matrix used to construct this instance.
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SVD is based on the LINPACK routine SSVDC; see Dongarra et al. (1979).
Let n be the number of rows in A and let p be the number of columns in A. For any
n x p matrix A, there exists an n x n orthogonal matrix U and a p x p orthogonal matrix V such that
where , and . The scalars are called the singular values of A. The columns of U are called the left singular vectors of A. The columns of V are called the right singular vectors of A.
The estimated rank of A is the number of that is larger than a tolerance . If is the parameter tol in the program, then
The Moore-Penrose generalized inverse of the matrix is computed by partitioning the matrices U, V and as , and where the "1" matrices are k by k. The Moore-Penrose generalized inverse is .