NMath Reference Guide

## Double |

Class for serving up generalized singular value
decompositions (GSVD) in the form of DoubleComplexGSVDecomp
instances.

Inheritance Hierarchy

Syntax

The DoubleComplexGSVDecompServer type exposes the following members.

Constructors

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

DoubleComplexGSVDecompServer | Creates a DoubleComplexGSVDecompServer for computing general singular value decomposition for matrices A and B, with all matrices of the decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) are computed. | |

DoubleComplexGSVDecompServer(Boolean, Boolean, Boolean) | Creates a DoubleComplexGSVDecompServer for computing general singular value decomposition for matrices A and B, where U, V, Q in the decomposition U'AQ = D1(0 R), V'BQ = D2(0 R) are optionally computed. |

Properties

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

ComputeQ | If true the matrix Q in the GSVD for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R) will be computed. If false it will not be computed. | |

ComputeU | If true the matrix U in the GSVD for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R) will be computed. If false it will not be computed. | |

ComputeV | If true the matrix V in the GSVD for matrices A and B - U'AQ = D1(0 R), V'BQ = D2(0 R) will be computed. If false it will not be computed. | |

InPlace | Gets and sets the in place factor option. If true the decomposition will be performed in place, overwritting the contents of the input matrices. No copies of the factored matrices are made in this case. If false the content of the input matrices will be preserved at the expense of copies being made. The default is false. |

Methods

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

Clone | Creates a deep copy of self. | |

GetDecomp | 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. |

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. DoubleComplexGSVDecompServer can be configured to optionally compute explicit representation for the matrices U, V, and Q.

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. DoubleComplexGSVDecompServer can be configured to optionally compute explicit representation for the matrices U, V, and Q.

See Also