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DoubleGSVDecomp Class

Class DoubleGSVDecomp computes the generalized singular value decomposition (GSVD) of a pair of general rectangular matrices.
Inheritance Hierarchy
SystemObject
  CenterSpace.NMath.CoreDoubleGSVDecomp

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4
Syntax
[SerializableAttribute]
public class DoubleGSVDecomp

The DoubleGSVDecomp type exposes the following members.

Constructors
 NameDescription
Public methodDoubleGSVDecomp(DoubleMatrix, DoubleMatrix) Computes the general singular value decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) for two matrices A and B. U, V, and Q are computed. A and B must have the same number of columns.
Public methodDoubleGSVDecomp(DoubleMatrix, DoubleMatrix, Boolean, Boolean, Boolean) Computes the general singular value decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) for two matrices A and B, optionally computing U, V, and Q. A and B must have the same number of columns.
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Properties
 NameDescription
Public propertyComputeQ Returns true if the matrix Q in the decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) was computed.
Public propertyComputeU Returns true if the matrix U in the decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) was computed.
Public propertyComputeV Returns true if the matrix V in the decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) was computed.
Public propertyD1 Gets the matrix D1 in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R)
Public propertyD2 Gets the matrix D2 in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R)
Public propertyIsGood Returns true if the decomposition was successfully computed. Returns false if the procedure failed to converge.
Public propertyQ Gets the matrix Q in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R)
Public propertyR Gets the matrix R in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R)
Public propertyRankOfATranspose_BTranspose Gets the effective numerical rank of (A' B'), where Z' denotes the transpose of the matrix Z and A and B are the decomposed matrices.
Public propertyU Gets the matrix U in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R)
Public propertyV Gets the matrix V in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R)
Public propertyZero_R Gets the matrix (0 R) in the general singular value decomposition for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R) (0 R) is the matrix obtained by prepending columns of all zeros to the upper triangular matrix R.
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Remarks
The GSVD computed for an m x n matrix A and a p x n matrix B has the form
U'AQ = D1(0 R), V'BQ = D2(0 R)
where U, V, and Q are orthogonal matrices, R is a nonsigular upper triangular matrix, D1 and D2 are diagonal matrices, and Z' denotes the transpose of the matrix Z. (0 R) is the matrix obtained by prepending columns of all zeros to the upper triangular matrix R.
See Also