fix complex -> real error messages #1086
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This is a small PR that fixes some errors I found when updating the documentation. In two cases, there was a complex-valued array getting used as a real-valued array (and generating an error message):
In
TransferFunction._common_den
, the numerator and denominator polynomial's are computing by extracting poles and zeros and then regenerating polynomials. Because the poles and zeros can be complex, the operations generate a complex-valued array of coefficients. These should be cast back to real coefficients before assigning them back to the real-valued numerator and denominator coefficient arrays. This error showed up inexamples/cruise.ipynb
, which was also updated to remove the error message in the Output cells.In
examples/describing-function.ipynb
there was a plot of the describing function for a static nonlinearity. Because describing functions can be complex valued in general (eg, if there is hysteresis), before plotting the value of the real-valued describing function, the results needs to be explicitly cast to real (otherwise you get an error message). This was a small change in the Jupyter notebook.For the two Jupyter notebooks, all of the plots were also updated, even though they basically look the same => the changes look bigger than they are (and rendering the difference is very slow...).