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328 3. Reference Manual
If you set GEPSolver −> LREigenpair, note that the ProjectionVectors setting given for
ApproximateDeterminant is not passed to LREigenpair. To choose the projection vectors
for the GEP solver, change the value of GEPSolverOptions.
SingularityTest
After each approximation step, ApproximateDeterminant applies a singularity test to the matrix
A s B to ensure that removing a matrix entry has not rendered the GEP singular. The singularity
test is performed by numerical computation of the rank of A s B for some s ∈ C which is not
an eigenvalue of the GEP. However, there is no guarantee that numerical rank computation always
yields a mathematically correct result. This may cause singularity to remain undetected in some
situations, particularly when the GEP is ill-conditioned. With the option SingularityTest, you
can select the function ApproximateDeterminant uses to determine whether the GEP is singular. If
you encounter singularity problems, i.e. if detA s B ⩵ after approximating a system of circuit
equations, then you should change the value of SingularityTest and rerun the approximation.
The possible values for SingularityTest are:
SingularityTestByLU
SingularityTestByQR
Function[{M}, expr]
perform singularity tests by rank computation using
LUDecomposition
perform singularity tests by rank computation using
QRDecomposition
specify a user-defined function which returns True if the
complex-valued floating-point matrix M is singular
Values for the SingularityTest option.
TestFrequency
With the option TestFrequency, you can specify the value of the complex frequency variable s
which is used for testing whether the numerical matrix A s B is singular. For best numerical
accuracy and computing performance, it is recommended that you choose a real value of the
same order of magnitude as the modulus of the target eigenvalue. For example, if you wish to
approximate a GEP with respect to an eigenvalue s ⩵ ⨯ j ⨯ , then the option setting
TestFrequency −> 1.0*^8 constitutes an appropriate choice.
The point in the complex plane represented by the value of TestFrequency should not lie
in the neighborhood of any eigenvalue of the GEP to be approximated. An inappropriate
choice of the test frequency may result in ill-conditioned rank computation problems.