### 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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