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320 3. Reference Manual
Find the pole of the buffer
circuit near
theta ⩵ ⨯ i and the
corresponding left and
right eigenvectors.
In[13]:= lreigenpairs = LREigenpair[mnabuffersym, 3.0*^6 I]
Out[13]=
279586. 2.89305 10 6 ,
1.70056 10 18 2.18582 10 18 , 0.101704 0.218124 ,
0.0281952 0.414952 , 0.175266 0.0104981 ,
1.70111 10 18 2.18582 10 18 , 0.177763 0.0195432 ,
0.000145936 0.000121065 , 0.177854 0.0196025 ,
0.175419 0.0103065 , 0.175107 0.0106381 ,
0.0284306 0.414988 , 0.0281891 0.414953 ,
0.175267 0.0105033 , 0.0281827 0.414949 ,
0.175266 0.0104982 , 0.177756 0.019539 ,
0.0000145936 0.0000121065 , 0.0000145936 0.0000121065 ,
9.51282 10 19 4.50211 10 19 , 0.055128 0.256781 ,
0.108991 0.0369544 , 0.0952012 0.0116717 ,
9.51537 10 19 4.50194 10 19 , 0.109187 0.515199 ,
0.000239817 0.0000548798 , 0.108876 0.515278 ,
0.0952466 0.0115085 , 0.0952183 0.0115916 ,
0.10892 0.0367968 , 0.108987 0.0369774 ,
0.0952038 0.0116972 , 0.109 0.0369492 ,
0.0951948 0.011671 , 0.109209 0.515193 ,
0.0000239817 5.48798 10 6 , 0.0000239817 5.48798 10 6 ,
3.6194 10 13 , 6.0309 10 12 , 4
Show the eigenvalue. In[14]:= lreigenpairs[[1, 1]]
Out[14]= 279586. 2.89305 10 6
Compare the eigenvalue
with the result of the QZ
algorithm.
In[15]:= Cases[PolesByQZ[mnabuffersym], _Complex]
Out[15]=
279586. 2.89305 10 6 , 279586. 2.89305 10 6
3.8.8 ApproximateDeterminant
ApproximateDeterminant[dae, lambda, error]
approximates the equations dae with respect to the pole
closest to the initial guess lambda where dae has to be an
AC DAEObject and error has to be a positive real value
ApproximateDeterminant[dae, zvar, lambda, error]
approximates the equations dae with respect to the zero of
the transfer function from the input signal to the output
zvar
Command structure of ApproximateDeterminant.
With ApproximateDeterminant you can approximate a linear symbolic matrix equation Ts x ⩵ b
directly with respect to a particular eigenvalue Λ (a pole or a zero). By discarding all terms which
have little or no influence on Λ, ApproximateDeterminant reduces both the complexity and the
degree of the characteristic polynomial Ps ⩵ det Ts. Provided that the eigenvalue of interest is
located sufficiently far apart from other eigenvalues, the polynomial degree can be reduced to if Λ