Implementation of class to represent a parametric region in space by friyaz · Pull Request #19472 · sympy/sympy

friyaz · 2020-06-01T10:28:58Z

Added an implementation of ParamRegion class.

References to other Issues or PRs

#19320

Brief description of what is fixed or changed

An object of the ParametricRegion class should represent a parametric region in space. This object can then be used to perform scalar/vector integration over parametric regions.

Other comments

Release Notes

vector
- Added class to represent a parametric region in space.

The class ParametricRegion represents a parametric region in space. Objects of this class will used to perform vector/scalar integration.

sympy-bot · 2020-06-01T10:28:59Z

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- Added class to represent a parametric region in space. (#19472 by @friyaz)

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Added an implementation of ParamRegion class.
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#19320 

#### Brief description of what is fixed or changed
An object of the ParametricRegion class should represent a parametric region in space. This object can then be used to perform scalar/vector integration over parametric regions.

#### Other comments

#### Release Notes

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* vector
  * Added class to represent a parametric region in space.
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sympy-bot · 2020-06-01T10:29:00Z

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The following commits add new files:

bbf46a6:
- sympy/vector/parametricregion.py
8d09368:
- sympy/vector/tests/test_parametricregion.py

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Upabjojr · 2020-06-01T19:53:34Z

+        >>> from sympy.vector import CoordSys3D, ParametricRegion
+        >>> r, theta = symbols("r theta")
+        >>> C = CoordSys3D('C')
+        >>> circle = ParametricRegion(C, r*cos(theta), r*sin(theta), (theta, 0, 2*pi))


Is the parametric region defined within a CoordSys3D object? Can this be made optional? It's easier to use if you don't have to define too many objects.

Yes, It will be easier if a user does not have to pass the CoordSys3D object. But we need to determine base scalars otherwise the definition of a parametric region is incomplete. A parametric representation is just defining base scalars in terms of some parameters.

We can avoid passing the CoordSys3D object if we use the base scalars of the vector/scalar field which needs to be integrated. So, if a user does not pass a CoordSys3D object, then SymPy will use the base scalars of the vector/scalar field used for integration.

C = CoordSys3D('C') R = C.locate_new('R', 3*C.i + 4*C.j + 5*C.k) p = ParametricRegion(t, t**2, (t, 0, 1)) ParametricIntegral(C.x*C.y*C.z*C.i, p) # Define p in terms of C.x, C.y and C.z ParametricIntegral(R.x*R.y, p) # Define p in terms of R.x, R.y and R.z

What about using a convention similar to Lambda?

@Upabjojr Can you please give an example.

Subclasses of basic should use __new__ instead of __init__ Also, removed check for length of defintion

Upabjojr · 2020-06-03T16:13:13Z

+    >>> r, theta = symbols("r theta")
+    >>> circle = ParametricRegion(r*cos(theta), r*sin(theta), (theta, 0, 2*pi))
+    """
+    def __new__(cls, *args, system=None):


What about defining some precise signature? *args is a bit ambiguous.

Yes, *arg is ambiguous. I used so we can define base scalars and bounds without nesting them in a tuple.

what about def __new__(cls, parameters_or_coordsys, mapping_tuple, **kwargs): ?

ParametricRegion((r, theta), (r*cos(theta), r*sin(theta)), r=(0,1), theta=(0, pi)) ParametricRegion(C, (C.y, 3, -3), C.y=(4,6))

I don't think the User should pass a tuple of parameters or CoordSys3d object.
We can easily determine the parameters using key values of the dictionary.

But we should also add an optional parameter for specifying the base scalars(see discussion above on CoordSys3D object) if a user does not want to user base scalars of the scalar/vector field. You mentioned using some lambda convention. Please explain that part.

What about this API @Upabjojr ?

def __new__(cls, system=None, mapping_tuple, **kwargs):

Example

ParametricRegion(((r*cos(theta), r*sin(theta)), r=(0,1), theta=(0, pi)) ParametricRegion(system=C, (C.y, 3, -3), C.y=(4,6))

r=(0, 1), theta=(0, pi) is not very intuitive, what about a dict of bounds?

What about this:

ParametricRegion((r, theta), (r*cos(theta), r*sin(theta)), limits={r: (0,1), theta: (0, pi)}) ParametricRegion(C, (C.y, 3, -3), limits={C.y: (4,6)})

You mentioned using some lambda convention. Please explain that part.

Define variable tuple, then mapping tuple.

I am still not sure why a user needs to pass a tuple specifying parameters. SymPy can determine them using the dict of bounds. Will it be more intuitive for users?

ParametricRegion((r*cos(theta), r*sin(theta)), limits={r: (0,1), theta: (0, pi)})

Well, a dict does not have an order, while a tuple does. Plus, it's the same definition of lambdas:

lambda r, theta: (r*cos(theta), r*sin(theta))

+1 for passing parameter_tuple then.

@Upabjojr What are your thoughts on the system parameter?
As discussed above, We have two options:

Assume that the mapping of param region is to base vectors of the scalar/vector field.

p = ParametricRegion((r, theta), (r*cos(theta), r*sin(theta)), limits={r: (0,1), theta: (0, pi)}) Integral(C.x**2*C.y, p) # C.x = r*cos(theta), C.y = r*sin(theta), C.z = C.z Integral(R.x*R.y*R.z, p) # R.x = r*cos(theta), R.y = r*sin(theta), R.z = R.z

The other option is to allow users if they wish to specify the coordinate system.

p = ParametricRegion((r, theta), (r*cos(theta), r*sin(theta)), limits={r: (0,1), theta: (0, pi)}, system = C) Integral(R.x*R.y*R.z, p) # C.x = r*cos(theta), C.y = r*sin(theta), C.z = C.z

Upabjojr · 2020-06-03T16:15:05Z

+
+def test_parametricregion():
+
+    point = ParametricRegion(3, 4)


What about ParametricRegion((), (3, 4)) to define a point? That is... first argument is the tuple of parameters (in this case an empty tuple), second one the mapping.

I think this would be more intuitive. What do you think?

@Upabjojr How will we get the definition of base scalars in terms of parameters? Also, if we fix the number of arguments to 2, we have to use nested tuples to define the bounds for more than 2 parameters

ParametricRegion((r, theta), ((r, 0, 2), (theta, 0, pi))

What about:

ParametricRegion(((r, 0, 2), (theta, 0, pi)), (r*cos(theta), r*sin(theta)))

?

I just want to have a simple API... my fear is that too many parameters will make this class difficult to use.

This one looks good to me. It is still not very simple but we have to keep some minimum parameters. They are essential for defining a parametric region.

It's the same concept for integrals:

Integral(x, x) # ==> indefinite Integral(x, (x, 0, 10)) # ==> definite

If you have a better API idea, you're welcome to suggest.

Upabjojr · 2020-06-03T16:17:01Z

+    assert point.bounds == []
+    assert point.system == None
+
+    l = ParametricRegion(C.y, (C.y, -3, 3), system=C)


Maybe we could have either ParametricRegion((y,), (y, -3, 3)) or ParametricRegion(C, (C.y, -3, 3)).

That is, if the first argument is a tuple, then it's assumed to be a list of variable-parameters. If it is a CoordSys3D object, then use its scalars as parameters.

This means that ParametricRegion would always take 2 arguments when called. What do you think of this API?

That is, if the first argument is a tuple, then it's assumed to be a list of variable-parameters. If it is a CoordSys3D object, then use its scalars as parameters.

Yes, this API looks simple and easy but

I am not able to understand what this region represents.

ParametricRegion(C, (C.y, -3, 3))

For me, ParametricRegion(C.y, (C.y, -3, 3), system=C) represents the line y=x where y varies from -3 to 3. Does this represent the same region?

For me, ParametricRegion(C.y, (C.y, -3, 3), system=C) represents the line y=x where y varies from -3 to 3. Does this represent the same region?

Oh, I see. With ParametricRegion(C, (C.y, -3, 3)) I think of the line y = -3 and z = 3, with C.y being the parameter varying along the x-axis (x-axis because it's in the first position).

line y = -3 and z = 3, with C.y being the parameter varying along the x-axis

I think we can define this region without using the coordinate scalar. How is this different from

ParametricRegion((t), (t, -3, 3))

(t) is not a tuple, (t,) is. Unfortunately Python has some strange syntax.

Okay, I somehow didn't noticed this. Then, to make it easier for users, we can put a condition like

if not isinstance(parameters, tuple): parameters = (parameters,) if not isinstance(definition, tuple): definition = (definition,)

A similar situation if a user wants to define a definition tuple of length 1.

Or maybe we can raise some value error when the user does pass a tuple.

Upabjojr · 2020-06-03T20:25:50Z

Also have a look at the image ImageSet class. It's vaguely similar to this one, maybe some of its code could be reused?

friyaz · 2020-06-04T17:08:31Z

Also have a look at the image ImageSet class. It's vaguely similar to this one, maybe some of its code could be reused?

Yes, some parts of it can be used in this class.

Upabjojr · 2020-06-08T17:11:07Z

Tests keep falling.

Upabjojr · 2020-06-08T17:12:48Z

If you fix the tests, I will merge this.

friyaz · 2020-06-08T17:13:30Z

OK, I will fix the test and improve the docstring.

…failing tests of core/test/test_args

codecov · 2020-06-08T23:50:00Z

Codecov Report

Merging #19472 into master will increase coverage by 0.020%.
The diff coverage is 100.000%.

@@              Coverage Diff              @@
##            master    #19472       +/-   ##
=============================================
+ Coverage   75.656%   75.677%   +0.020%     
=============================================
  Files          652       654        +2     
  Lines       169794    169934      +140     
  Branches     40086     40068       -18     
=============================================
+ Hits        128460    128601      +141     
  Misses       35721     35721               
+ Partials      5613      5612        -1

sylee957 · 2020-06-09T09:49:09Z

+    assert ellipse.limits == {t: (0, 8)}
+
+    cylinder = ParametricRegion((r, theta, C.z), (cos(theta), r*sin(theta), C.z), {theta: (0, 2*pi), C.z: (0, 4)})
+    assert cylinder.parameters == (r, theta, C.z)


I see you have introduced parameters_or_coordsys only because you have to deal with coordinate systems C, but as you mix coordinate scalars and ordinary symbols in this way, you can always specify the region regardless of the ambient space of the coordinate systems and it loses no generality to use ordinary symbols like x, y, z everywhere in place of coordinate systems.

And also what would be the necessary reason to pass C in place of (C.x, C.y, C.z) if they are implicitly converted any way?

And also what would be the necessary reason to pass C in place of (C.x, C.y, C.z) if they are implicitly converted any way?

Shortcut?

it loses no generality to use ordinary symbols like x, y, z everywhere in place of coordinate systems.

Yes, I agree. I think we can replace base scalars with any variable. Suppose we want to represent a rectangle:

ParametricRegion(C, (C.x, C.y), {C.x: (1, 2), C.y: (3, 5)})

We can write equiavalently write this as

ParametricRegion((x, y), (x, y), {x: (1, 2), y: (3, 5)}) # C.x = x, C.y = y, C.z = C.z

Just to make this explicit,
When we define the definition tuple ..suppose (r*cos(theta), r*(sin(theta), r*sin(phi)), this implies

C.x = r*cos(theta), C.y = r*(sin(theta), C.y = r*sin(phi)

These base scalars are assumed. They may be determined from the base scalars of the vector/scalar field for integration.
The only reason I think we may need a coordinate system variable other than for shortcut is when one needs to specify base scalars (instead of using base scalars of the vector/scalar field).

p = ParametricRegion((r, theta), (r*cos(theta), r*sin(theta)), limits={r: (0,1), theta: (0, pi)}) Integral(C.x**2*C.y, p) # C.x = r*cos(theta), C.y = r*sin(theta), C.z = C.z Integral(R.x*R.y*R.z, p) # R.x = r*cos(theta), R.y = r*sin(theta), R.z = R.z

What happens if it is Integral(R.x*C.y, p)?
Perhaps, p can have its own base scalars rather than implicitly connecting to some coordinate system scalars that are passed on?

p can have its own base scalars rather than implicitly connecting to some coordinate system scalars that are passed on?

Yes, I am in favor of this. But there should be some relationship between the coordinate system of vector/scalar field and the coordinate system of the parametric region. For calculating the integral, we need to replace base scalars in the field with parameters. This requires some connection between them.

@Upabjojr What do you think?

My original thought was just to use parameters. Mixing parameters and base scalars in the tests is a bit strange, but it's OK with me.

I think for the tests, we can leave them as it is. But for users, it should be preferred to not mix them.

What happens if it is Integral(R.x*C.y, p)?

We have to raise some kind of error if the parametric region is not associated with base scalars and depend on base scalars of the field.

friyaz · 2020-06-10T20:13:41Z

@Upabjojr I think we can merge this PR. For now, we can assume that the parametric region has the same base scalars as that of the scalar/vector field. We can raise an error if the coordinate system of the field cannot be determined.

Added a rough implementation of ParamtericRegion in sympy.vector

bbf46a6

The class ParametricRegion represents a parametric region in space. Objects of this class will used to perform vector/scalar integration.

friyaz added GSoC vector labels Jun 1, 2020

friyaz requested review from Upabjojr and divyanshu132 June 1, 2020 10:30

friyaz added 3 commits June 1, 2020 16:12

remove trailing whitespace from __init__.py

f544cf4

add pi to docstring

ff5968d

Added tests in test_args.py

4f57a74

Upabjojr reviewed Jun 1, 2020

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oscarbenjamin reviewed Jun 1, 2020

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Comment thread sympy/vector/parametricregion.py Outdated

friyaz commented Jun 2, 2020

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Comment thread sympy/vector/parametricregion.py Outdated

Use __new__ instead of __init__

7a58f05

Subclasses of basic should use __new__ instead of __init__ Also, removed check for length of defintion

friyaz requested review from Upabjojr and oscarbenjamin June 2, 2020 11:47

friyaz added 2 commits June 3, 2020 15:13

Raise ValueError when parameters specified incorrectly.

8d09368

Add test cases for ParametricRegion class

be86ee9

friyaz force-pushed the vector branch from 7758190 to be86ee9 Compare June 3, 2020 09:46

Use self.args

99ff12a

Upabjojr reviewed Jun 3, 2020

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Modified API of ParametricRegion class

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friyaz marked this pull request as draft June 5, 2020 14:40

friyaz requested a review from Upabjojr June 5, 2020 17:40

Upabjojr reviewed Jun 7, 2020

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Comment thread sympy/vector/parametricregion.py Outdated

Made limits optional

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Upabjojr reviewed Jun 8, 2020

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Comment thread sympy/core/tests/test_args.py

Modified API of ParametricRegion class, improved docstring and Fixed …

406265c

…failing tests of core/test/test_args

friyaz force-pushed the vector branch from 561d4aa to 406265c Compare June 8, 2020 21:27

friyaz marked this pull request as ready for review June 8, 2020 21:32

friyaz changed the title ~~[WIP] Implementation of class to represent a parametric region in space~~ Implementation of class to represent a parametric region in space Jun 8, 2020

friyaz requested a review from Upabjojr June 8, 2020 21:45

sylee957 reviewed Jun 9, 2020

View reviewed changes

Remove test case with mixed base scalars and parameters

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Upabjojr merged commit 5b423b2 into sympy:master Jun 10, 2020

oscarbenjamin mentioned this pull request Jun 11, 2020

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