[GSOC 1.4.1] Refactor Pole Zero Plot to use Algebraic methods

[faze-geek]

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[github-actions[bot]]

Benchmark results from GitHub Actions

Lower numbers are good, higher numbers are bad. A ratio less than 1 means a speed up and greater than 1 means a slowdown. Green lines beginning with + are slowdowns (the PR is slower then master or master is slower than the previous release). Red lines beginning with - are speedups.

Significantly changed benchmark results (PR vs master)

Significantly changed benchmark results (master vs previous release)

       before           after         ratio
     [8059df73]       [3236f743]
     <sympy-1.12^0>                 
-       102±0.7ms       67.1±0.4ms     0.66  integrate.TimeIntegrationRisch02.time_doit(10)
-        2.46±0ms          787±3μs     0.32  polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'sparse')
-     12.0±0.06ms      2.35±0.01ms     0.20  polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'sparse')
-       439±0.8μs       97.1±0.4μs     0.22  polys.TimePREM_QuadraticNonMonicGCD.time_op(1, 'sparse')
-     5.54±0.01ms        433±0.8μs     0.08  polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'sparse')
-     12.1±0.06ms      1.30±0.01ms     0.11  polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'sparse')
-      7.86±0.7ms      4.74±0.03ms     0.60  polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(2, 'sparse')
-      31.9±0.1ms       14.3±0.1ms     0.45  polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'sparse')
-     8.34±0.02ms         1.39±0ms     0.17  polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(1, 'sparse')
-      19.1±0.1ms      11.0±0.05ms     0.58  polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(2, 'sparse')
-       244±0.6ms       84.4±0.2ms     0.35  polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'sparse')
-     7.40±0.06ms          640±2μs     0.09  polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'sparse')
-        31.7±1ms         1.02±0ms     0.03  polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'sparse')
-         720±4μs          233±6μs     0.32  polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(1, 'sparse')
-     7.46±0.04ms          236±2μs     0.03  polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'sparse')
-        19.5±1ms          244±1μs     0.01  polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'sparse')
-         196±5μs          110±5μs     0.56  solve.TimeMatrixOperations.time_rref(3, 0)
-       369±0.5μs        129±0.8μs     0.35  solve.TimeMatrixOperations.time_rref(4, 0)
-      38.6±0.9ms       16.6±0.3ms     0.43  solve.TimeSolveLinSys189x49.time_solve_lin_sys

Full benchmark results can be found as artifacts in GitHub Actions (click on checks at the top of the PR).

[faze-geek]

Hi @moorepants All methods for roots now use Sympy. But as discussed about the lack of implementations in another pr, to eliminate Matplotlib we would need support for Sympy scatter plot. An issue is raised since quite sometime. Should we go ahead an merge this? Refactoring other plots will then follow. Since we are not sure when the implementation will be made, I suggest we continue refactoring and eliminating the numerical methods as much as possible. If and when we have a scatter plot, replacing them in the current code would not be difficult.

[moorepants]

The general procedure for adding new plotting methods/functions should be:

1. Utilize sympy plot commands to make the plot.
2. If there are missing sympy plot features, then add them.

If the features aren't present in sympy.plot and you don't want to add them, then you should postpone adding a new plot.

When working with existing plot functions/methods in sympy...control, try to move them to using sympy.plot features.

We should "eat our own dog food" anytime we need plots in SymPy.

[faze-geek]

Thanks !

The general procedure for adding new plotting methods/functions should be:

1. Utilize sympy plot commands to make the plot.
2. If there are missing sympy plot features, then add them.

If the features aren't present in sympy.plot and you don't want to add them, then you should postpone adding a new plot.

Okay sure. All 6 plots in control module use numpy for sampling and matplotlib for plotting as of now. Maybe this was not followed in last GSOC for the control package. I intend to stick to the control module for the time being of the project. As and when, the plot features are added I will update the prs 👍

When working with existing plot functions/methods in sympy...control, try to move them to using sympy.plot features.

I will investigate where this replacement is feasible.