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

Block SymbolLicensing group: MATRIX
PIC

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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