### ML_DGECON – Estimates the reciprocal of the condition number of a general real matrix

Block SymbolLicensing group: MATRIX

Function Description

The output references yA, yWORK and yIWORK are always set to the corresponding input
references uA, uWORK and uIWORK. If HLD = on then nothing is computed otherwise the
LAPACK function DGECON is called internally:

DGECON(sINORM, N, uA, LDA, anorm, rcond, uWORK, uIWORK, info);

where parameters of DGECON are set in the following way:

- If $\mathtt{\text{INORM}}=\mathtt{\text{on}}$ then the string sINORM is set to "I" else it is set to "1".
- N is number of columns of the matrix referenced by uA.
- LDA is the leading dimension of the matrix referenced by uA.
- rcond is returned reciprocal value of the condition number of the matrix referenced by uA.
- info is return code from the function DGECON.

The error flag E is set to on if:

- the reference uA or uWORK or uIWORK is not defined (i.e. input uA or uWORK or uIWORK is not connected),
- the matrix referenced by uA is not square,
- number of elements of the vector referenced by uWORK is less than $4\ast \mathtt{\text{N}}$,
- number of elements of the integer vector referenced by uIWORK is less than N,
- the call of the function DGECON 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 |

uWORK | Input reference to working vector WORK | Reference |

uIWORK | Input reference to integer working vector WORK | Reference |

INORM | Use Infinity-norm | Bool |

anorm | Norm of the original matrix A $\odot $0.0 | Double (F64) |

HLD | Hold | Bool |

Outputs

yA | Output reference to matrix A | Reference |

yWORK | Output reference to working vector WORK | Reference |

yIWORK | Output reference to integer working vector WORK | Reference |

rcond | The reciprocal of the condition number of the matrix A | Double (F64) |

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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