Improving the Plotting module

[Shivam Vats]

Hi

I'm Shivam Vats, a second year undergraduate Maths and Computing student at IIT, Kharagpur, India. I'll be applying for Gsoc 

2015 with Sympy. I've got a few patches merged and have been exploring Sympy for over a few months. Though I've not decided 

on my proposal, recently while looking into the plotting module I realised that there is a lot of work to do in it. The rationale for this

post is to clear my doubts and get everyone's views regarding the issues in the plotting module. I'd appreciate any help.

ISSUES/BUGS

1) Sympy can't interpret the assumptions about the variables in the equations. eg:

   

                     x = Symbol('x', positive=True)

                     plot(x)

It plots on the default [-10,10] interval, where it clearly shouldn't. My  PR 8701 is a start, but it solves the problem only for 

positive and negative variables. However the basic question is whether we should check the range given by the user and 

whether we want to have a smarter default range than the present [-10, 10].

In my opinion, a function that finds the domain of the function, taking into account the assumptions about the variables in it

should work.

2) Currently if the ylim is not specified, plot adjusts the scale to show the whole graph. In many cases it may not be desired 

 (Try plotting 1/x with default values) Instead of this default behaviour, one which limits the ylim to say a factor(just an example) 

  of the max(x) should give better results, something like:                                          

                                   if parent.ylim:  

                                       self.ax.set_ylim(parent.ylim)

                                   else:

                                   starts = [s.start for s in parent._series]

                                   ends = [s.end for s in parent._series]
                                   self.ax.set_ylim(10*min(starts), 10*max(ends))

TODOs

1) ContourSeries class in plot.py is currently not used anywhere:- I found this piece of code lying unused. Do we want to create a plot_contour

   function on the lines of plot?

2) A more general way to calculate aesthetics:- I found this in the code. Could someone please elaborate on what features we might want 

   to add? Currently it can handle a function.

3) Adaptive sampling for 3D plot as Stefan mentions here https://groups.google.com/forum/#!topic/sympy/xHnYUtJVnx0

   using triangular meshes: I don't  understand the method right now, but would be more than happy to work on it if someone could give me 

  some  pointers on how to start.

Cheers!

[Aaron Meurer]

On Fri, Jan 2, 2015 at 9:32 AM, Shivam Vats <shiv...@gmail.com> wrote:

Hi

I'm Shivam Vats, a second year undergraduate Maths and Computing student at IIT, Kharagpur, India. I'll be applying for Gsoc 

2015 with Sympy. I've got a few patches merged and have been exploring Sympy for over a few months. Though I've not decided 

on my proposal, recently while looking into the plotting module I realised that there is a lot of work to do in it. The rationale for this

post is to clear my doubts and get everyone's views regarding the issues in the plotting module. I'd appreciate any help.

ISSUES/BUGS

1) Sympy can't interpret the assumptions about the variables in the equations. eg:

   

                     x = Symbol('x', positive=True)

                     plot(x)

It plots on the default [-10,10] interval, where it clearly shouldn't. My  PR 8701 is a start, but it solves the problem only for 

positive and negative variables. However the basic question is whether we should check the range given by the user and 

whether we want to have a smarter default range than the present [-10, 10].

I think you're confusing the viewing range and the function range. The viewing range can be anything. If the function has no values for some points in the viewing range, it should not plot them. So for instance, you can plot sqrt(x) or log(x) in [-10, 10], and it will simply have no plotted points in the negative region. We shouldn't disallow showing the negative axis for them or anything like that.

 

In my opinion, a function that finds the domain of the function, taking into account the assumptions about the variables in it

should work. 

2) Currently if the ylim is not specified, plot adjusts the scale to show the whole graph. In many cases it may not be desired 

 (Try plotting 1/x with default values) Instead of this default behaviour, one which limits the ylim to say a factor(just an example) 

  of the max(x) should give better results, something like:                                          

                                   if parent.ylim:  

                                       self.ax.set_ylim(parent.ylim)

                                   else:

                                   starts = [s.start for s in parent._series]

                                   ends = [s.end for s in parent._series]
                                   self.ax.set_ylim(10*min(starts), 10*max(ends))

TODOs

1) ContourSeries class in plot.py is currently not used anywhere:- I found this piece of code lying unused. Do we want to create a plot_contour

   function on the lines of plot?

2) A more general way to calculate aesthetics:- I found this in the code. Could someone please elaborate on what features we might want 

   to add? Currently it can handle a function.

3) Adaptive sampling for 3D plot as Stefan mentions here https://groups.google.com/forum/#!topic/sympy/xHnYUtJVnx0

   using triangular meshes: I don't  understand the method right now, but would be more than happy to work on it if someone could give me 

  some  pointers on how to start.

These all sound like important fixes, though for a GSoC project, you might want to have something more substantial (of course, small fixes like this are also great to do during the summer, but typically GSoC projects have some larger goal). Unless one of these really is more work than I thought it was, in which case please correct me.

Aaron Meurer

Cheers!

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[Shivam Vats]

@Aaron Sorry for the late reply. 

I agree with you. What I'd suggested was just a hack and it occurred to mainly because it was giving a visual output equivalent 

to a function not having values in certain intervals. That is why I talked about (in my pr) creating a methid that calculates

the domain of the function, taking into account the assumptions about the variables in the function. That should be the 

full solution.

As for the GSoc project, you are absolutely right. These are only some of the issues I could see with Sympy's plotting. I was 

hoping to start a discussion and then get suggestions as to what more the community wants the plotting module to do. Given 

that Sympy's plotting isn't very sophisticated, I think it's important to know what sort of capabilities are desired.