### ML_DGEEV – Computes the eigenvalues and, optionally, the left and/or right eigenvectors

Block SymbolLicensing group: MATRIX

Function Description

The output references yA, yWR, yWI, yVL, yVR and yWORK are always set to the corresponding
input references uA, uWR, uWI, uVL, uVR and uWORK. If HLD = on then nothing is computed
otherwise the LAPACK function DGEEV is called internally:

DGEEV(sJOBVL, sJOBVR, N, uA, LDA, uWR, uWI, uVL, LDVL, uVR, LDVR,

uWORK, LWORK, info);

where parameters of DGEEV are set in the following way:

- If $\mathtt{\text{JOBVL}}=\mathtt{\text{on}}$ then the string sJOBVL is set to "V" else it is set to "N".
- If $\mathtt{\text{JOBVR}}=\mathtt{\text{on}}$ then the string sJOBVR is set to "V" else it is set to "N".
- N is number of columns of the matrix referenced by uA.
- LDA, LDVL and LDVR are leading dimensions of the matrices referenced by uA, uVL and uVR.
- LWORK is number of elements of the vector referenced by uWORK.
- info is return code from the function DGEEV.

The error flag E is set to on if:

- the reference uA or uWR or uWI or uVL or uVR or uWORK is not defined (i.e. input uA or uWR or uWI or uVL or uVR or uWORK is not connected),
- the matrix referenced by uA is not square,
- number of elements of vectors referenced by uWR or uWI is less than N,
- number of columns of matrices referenced by uVL or uVR is not equal to N,
- the call of the function DGEEV 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 |

uVL | Input reference to matrix of left eigenvectors | Reference |

uVR | Input reference to matrix of right eigenvectors | Reference |

uWORK | Input reference to working vector WORK | Reference |

JOBVL | If true then left eigenvectors are computed | Bool |

JOBVR | If true then right eigenvectors are computed | 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 |

yVL | Output reference to VL | Reference |

yVR | Output reference to VR | 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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