### ML_DGEBRD – Reduces a general real matrix to bidiagonal form by an orthogonal transformation

Block SymbolLicensing group: MATRIX

Function Description

The output references yA, yD, yE, yTAUQ, yTAUP and yWORK are always set to the corresponding
input references uA, uD, uE, uTAUQ, uTAUP and uWORK. If HLD = on then nothing is computed
otherwise the LAPACK function DGEBRD is called internally:

DGEBRD(M, N, uA, LDA, uD, uE, uTAUQ, uTAUP, uWORK, info);

where parameters of DGEBRD are set in the following way:

- M is number of rows of the matrix referenced by uA.
- N is number of columns of the matrix referenced by uA.
- LDA is the leading dimension of the matrix referenced by uA.
- info is return code from the function DGEBRD.

The error flag E is set to on if:

- the reference uA or uD or uE or uTAUQ or uTAUP or uWORK is not defined (i.e. input uA or uD or uE or uTAUQ or uTAUP or uWORK is not connected),
- number of elements of any vector referenced by uD, uTAUQ and uTAUP is less than MINMN, where MINMN is minimum from M and N,
- number of elements of the vector referenced by uE is less than $\mathtt{\text{MINMN}}-1$,
- the call of the function DGEBRD returns error using the function XERBLA, see the return code info and system log.

See LAPACK documentation [7] for more details.

Inputs

uA | Input reference to matrix A | Reference |

uD | Diagonal elements of the bidiagonal matrix B | Reference |

uE | Off-diagonal elements of the bidiagonal matrix B | Reference |

uTAUQ | Reference to a vector of scalar factors of the elementary reflectors which represent the orthogonal matrix Q | Reference |

uTAUP | Reference to a vector of scalar factors of the elementary reflectors which represent the orthogonal matrix P | Reference |

uWORK | Input reference to working vector WORK | Reference |

HLD | Hold | Bool |

Outputs

yA | Output reference to matrix A | Reference |

yD | Output reference to D | Reference |

yE | Output reference to E | Reference |

yTAUQ | Output reference to TAUQ | Reference |

yTAUP | Output reference to TAUP | Reference |

yWORK | Output reference to working vector WORK | Reference |

E | Error indicator | Bool |

info | LAPACK function result info. If info = -i, the i=th argument had an illegal value | Long (I32) |

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