### ML_DGEES – Computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors

Block SymbolLicensing group: MATRIX

Function Description

The output references yA, yWR, yWI, yVS, yWORK and yBWORK are always set to the
corresponding input references uA, uWR, uWI, uVS, uWORK and uBWORK. If HLD = on then nothing
is computed otherwise the LAPACK function DGEES is called internally:

DGEES(sJOBVS, sSORT, SELECT, N, uA, LDA, sdim, uWR, uWI, uVS, LDVS,uWORK,

LWORK, uBWORK, info);

where parameters of DGEES are set in the following way:

- If $\mathtt{\text{JOBVS}}=\mathtt{\text{on}}$ then the string sJOBVS is set to "V" else it is set to "N".
- If $\mathtt{\text{SORT}}=\mathtt{\text{on}}$ then the string sSORT is set to "S" else it is set to "N".
- SELECT is the reference to Boolean eigenvalues sorting function which in this function block returns always true (i.e. on).
- N is number of columns of the matrix referenced by uA.
- LDA is the leading dimension of the matrix referenced by uA.
- sdim is returned number of eigenvalues for which the function SELECT is true.
- LDVS is the leading dimension of the matrix referenced by uVS.
- LWORK is number of elements in the vector referenced by uWORK.
- info is return code from the function DGEES.

The error flag E is set to on if:

- the reference uA or uWR or uWI or uVS or uWORK or uBWORK is not defined (i.e. input uA or uWR or uWI or uVS or uWORK or uBWORK is not connected),
- the matrix referenced by uA is not square,
- number of elements of any vector referenced by uWR, uWI and uBWORK is less than N,
- number of columns of the matrix referenced by uVS is not equal to N,
- the call of the function DGEES 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 |

uWR | Input reference to vector of real parts of eigenvalues | Reference |

uWI | Input reference to vector of imaginary parts of eigenvalues | Reference |

uVS | Input reference to orthogonal matrix of Schur vectors | Reference |

uWORK | Input reference to working vector WORK | Reference |

uBWORK | Input reference to Boolean working vector WORK | Reference |

JOBVS | If true then Schur vectors are computed | Bool |

SORT | If true then eigenvalues are sorted | Bool |

HLD | Hold | Bool |

Outputs

yA | Output reference to matrix A | Reference |

yWR | Output reference to vector of real parts of eigenvalues | Reference |

yWI | Output reference to vector of imaginary parts of eigenvalues | Reference |

yVS | Output reference to VS | Reference |

yWORK | Output reference to working vector WORK | Reference |

yBWORK | Output reference to Boolean working vector WORK | Reference |

sdim | If SORT then number of eigenvalues for which SELECT is true else 0 | Long (I32) |

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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