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 $JOBVS = on$ then the string sJOBVS is set to "V" else it is set to "N".
If $SORT = on$ 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 [8] 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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