NMath Reference Guide

## Double |

Class DoubleComplexSVDecomp represents the singular value decomposition (SVD)
of a matrix.

Inheritance Hierarchy

Syntax

The DoubleComplexSVDecomp type exposes the following members.

Constructors

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

DoubleComplexSVDecomp | Constructs an empty singular value decomposition instance. | |

DoubleComplexSVDecomp(DoubleComplexMatrix) | Constructs a singular value decomposition of a given matrix. |

Properties

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

Cols | Gets the number of columns in the matrix that the decomposition represents. | |

Fail | Gets the status of the decomposition. | |

LeftVectors | Gets the matrix whose columns are the left singular vectors of this decomposition. | |

NumberLeftVectors | Gets the number of left singular vectors in the decomposition. | |

NumberRightVectors | Gets the number of right singular vectors in the decomposition. | |

Rank | Gets the rank of the matrix which this decomposition represents. | |

RightVectors | Gets the matrix whose columns are the right singular vectors of this decomposition. | |

Rows | Gets the number of rows in the matrix that this decomposition represents. | |

SingularValues | Gets the singular values of this decomposition. The values are non-negative and arranged in decreasing order. |

Methods

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

Clone | Creates a deep copy of this decomposition. | |

Factor | Builds a decomposition for the matrix A. | |

LeftVector | Returns the specified left singular vector. | |

RightVector | Returns the specified right singular vector. | |

SingularValue | Returns the specified singular value. | |

Truncate | Truncates all singular values that are less than a given tolerance by setting them to zero. |

Remarks

The singular value decomposition is a representation of a matrix
A of the form:
where U and V are orthogonal, S is diagonal, and
V' denotes the transpose of the matrix V.
The entries along the diagonal of S are the singular values.
The columns of U are the left singular vectors, and the columns
of V are the right singular vectors. By default, the reduced
singular value decomposition and all singular vectors are computed.
If you want the full singular value decomposition, or just the singular
values computed, use class DoubleSVDecompServer.

C#

A = USV'

See Also