NMath Reference Guide

## Double |

Class DoubleComplexGSVDecomp computes the generalized singular value
decomposition (GSVD) of a pair of general rectangular matrices.

Inheritance Hierarchy

Syntax

The DoubleComplexGSVDecomp type exposes the following members.

Constructors

Name | Description | |
---|---|---|

DoubleComplexGSVDecomp(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. | |

DoubleComplexGSVDecomp(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. |

Properties

Name | Description | |
---|---|---|

ComputeQ | Returns true if the matrix Q in the decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) was computed. | |

ComputeU | Returns true if the matrix U in the decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) was computed. | |

ComputeV | Returns true if the matrix V in the decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) was computed. | |

D1 | 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) | |

D2 | 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) | |

IsGood | Returns true if the decomposition was successfully computed. Returns false if the procedure failed to converge. | |

Q | 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) | |

R | 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) | |

RankOfATranspose_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. | |

U | 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) | |

V | 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) | |

Zero_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. |

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.

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