Add Bode plot

[pmli]

This PR adds the bode_plot method to InputOutputModel for drawing the Bode plot (with both magnitude and phases).

Also, an example is added to the BT tutorial. I used the constrained_layout option since the suptitle is otherwise too high, but it is an experimental feature. The documentation suggests getting axes positions and setting them explicitly for reproducibility, but I guess this would have to be done for all 12 subplots...

See #389.

Update: This PR also adds the bode method that returns magnitudes and phases used in bode_plot.

[codecov]

Codecov Report

Merging #1051 into master will decrease coverage by 0.16%.
The diff coverage is 7.69%.

Impacted Files	Coverage Δ
src/pymor/models/iosys.py	45.36% <7.69%> (-2.14%)	⬇️
src/pymor/vectorarrays/list.py	84.15% <0.00%> (-0.19%)	⬇️
src/pymor/vectorarrays/numpy.py	84.55% <0.00%> (+0.24%)	⬆️

[lbalicki]

Overall the Bode plot seems to work well. Maybe we should change the default options of the plot a little bit, such that it looks better for more examples?

With the default options of the current implementation, the example fom from the BT tutorial and w = np.logspace(10, -10, 100) in a Jupyter notebook I get the plot:

I would suggest initializing the fig, ax objects via fig, ax = plt.subplots(2 * self.output_dim, self.input_dim, sharex=True, figsize=(3 * self.input_dim, 4 * self.output_dim), constrained_layout=True), which for me results in "nice" looking graphs for a lot of different input and output dimensions. What do you think?

[lbalicki]

Change to fig, ax = plt.subplots(2 * self.output_dim, self.input_dim, sharex=True, figsize=(3 * self.input_dim, 4 * self.output_dim), constrained_layout=True)?

[pmli]

I would suggest initializing the fig, ax objects via fig, ax = plt.subplots(2 * self.output_dim, self.input_dim, sharex=True, figsize=(3 * self.input_dim, 4 * self.output_dim), constrained_layout=True), which for me results in "nice" looking graphs for a lot of different input and output dimensions. What do you think?

Sounds good. Maybe it would be good to also use plt.rcParams['figure.figsize']. I'll try and see what works.

[pmli]

Now the default Bode plot size is [self.input_dim * width, 2 * self.output_dim * height], where width, height = plt.rcParams['figure.figsize'] and constrained_layout is used. It seems that constrained_layout makes the subplots bigger, probably because it fills the margins. I'm not sure how to fix this besides just scaling the width and height.

Additionally, I found that np.unwrap can make a sequence of phases more continuous and moved the computation of magnitudes and phases to a separate bode method (similar to scipy.signal.bode).