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DoubleComplexGSVDecomp Class

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

Namespace:  CenterSpace.NMath.Core
Assembly:  NMath (in NMath.dll) Version: 7.3
Syntax
[SerializableAttribute]
public class DoubleComplexGSVDecomp

The DoubleComplexGSVDecomp type exposes the following members.

Constructors
  NameDescription
Public methodDoubleComplexGSVDecomp(DoubleComplexMatrix, DoubleComplexMatrix)
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 methodDoubleComplexGSVDecomp(DoubleComplexMatrix, DoubleComplexMatrix, 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 conjugate 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