[WIP] Reconstruction constructor in CoordSys3D #13056

szymag · 2017-07-27T19:30:13Z

This PR introduces to constructor transformation equation.
These equations will be obtain from rotation_matrix, location (for translations), and for changing type of coordinate system. After obtaining these equations, method for transformation composition will be used.

We need to deal with two situation. When we want to connect our coordinate system (parent coordinate system) and when we want to just set transformation equations.

Add rotation_equations.

Set rotation_equations to None for parent None and rotation_matrix None

Upabjojr · 2017-07-27T20:07:40Z

sympy/vector/coordsysrect.py

-        trans_eq3 = matrix[6]*self.x + matrix[7]*self.y + matrix[8]*self.z
+        trans_eq1 = matrix[0]*variables[0] + matrix[1]*variables[1] + matrix[2]*variables[2]
+        trans_eq2 = matrix[3]*variables[0] + matrix[4]*variables[1] + matrix[5]*variables[2]
+        trans_eq3 = matrix[6]*variables[0] + matrix[7]*variables[1] + matrix[8]*variables[2]

        return trans_eq1, trans_eq2, trans_eq3


if we operate with lambda, it would be easier.

Upabjojr · 2017-07-27T20:09:30Z

sympy/vector/coordsysrect.py

@@ -98,6 +98,33 @@ def __new__(cls, name, location=None, rotation_matrix=None,
            location = Vector.zero
            origin = Point(name + '.origin')



What to do here:

check that if ŧransformation is None.

if it is None, computer transformation from the rotation and traslation. Make identity if they are also None.

if it is not None, check that rotation and translation are None

transform transformation to a Lambda.

I'm not sure why do that.
You assume that we have to use transformation or (rotation and translation), so transformation should have information about every three transformations.
I think that it could be easier sometimes to split transformation into steps. For example for transformation set cylindrical and for location set some vector.

We do it the general way, no need to complicate the code with special cases. Translations are subsets of transformations. In the special cases of rotation and translations, we could store some markers to remind of the special case (and remember the steps).

Upabjojr · 2017-07-27T20:11:24Z

I suggest to return lambda objects from the methods, so you can compose the transformations by simply calculating f(*g(x)).

szymag · 2017-07-29T17:38:43Z

I suggest to return lambda objects from the methods, so you can compose the transformations by simply calculating f(*g(x)).

I used your idea in constructor, when rotation_equations and translation_equations are obtained.

Upabjojr · 2017-07-31T16:11:29Z

sympy/vector/coordsysrect.py

@@ -109,12 +156,11 @@ def __new__(cls, name, location=None, rotation_matrix=None,
        # they may actually be 'coincident' wrt the root system.
        if parent is not None:
            obj = super(CoordSys3D, cls).__new__(
-                cls, Symbol(name), location, parent_orient, parent)
+                cls, Symbol(name), transformation, parent)


transformation need to be defined.

transformation has to be a SymPy type, if we are going to use a lambda, we need to use SymPy's Lambda (with capital L).

Upabjojr · 2017-07-31T16:12:02Z

sympy/vector/coordsysrect.py

+            if parent is None:
+                transformation_equations = None
+            else:
+                transformation_equations = None


The aim is to define transformation, we may not need transformation_equations.

Upabjojr · 2017-07-31T16:13:53Z

sympy/vector/coordsysrect.py

+                raise ValueError
+
+            if parent is None:
+                transformation_equations = None


Why None? We have transformation != None in this case. We should just check that transformation is correct (and transform it to a SymPy type).

I didn't implement this part yet.
I just put None to create some structure for case when transformation is not None.

I think that we need to think first, how transformation should look like. Should we just use _connect_to_standard_cartesian?

That code can be OK. I would prefer that transformation be finally transformed into a Lambda object, it makes more sense with the hashing.

Upabjojr · 2017-07-31T16:14:26Z

sympy/vector/coordsysrect.py

@@ -174,7 +220,7 @@ def __new__(cls, name, location=None, rotation_matrix=None,

        obj._parent_rotation_matrix = parent_orient
        obj._origin = origin
-
+        obj.transformation_equations = transformation_equations


Store transformation, not transformation_equations (they are the same thing in the end).

Upabjojr · 2017-07-31T16:18:24Z

sympy/vector/coordsysrect.py

+                    raise ValueError("The transformation equation does not "
+                                     "create orthogonal coordinate system")
+        else:
+            if not (location and rotation_matrix) is None:


This condition is wrong. Both have to be None otherwise raise an exception

Upabjojr · 2017-08-01T19:51:00Z

sympy/vector/coordsysrect.py

+                lame_coefficients = connect_to[1]
+                inverse_transformation = connect_to[2]
+            else:
+                transformation = None


This is definitely wrong.

I didn't cover this scenario. When you accept the case when parent is None I will update this part.
I wrote about it on gitter

Let's remove the parent case. Sorry, didn't read gitter.

Upabjojr · 2017-08-01T19:56:43Z

sympy/vector/coordsysrect.py

+                # See lines 80:99. Location is somehow treated only when parent is put.
+                # We are not able to create independent vector, so we can't assign
+                # anything to location.
+                translation_equations = lambda x, y, z: (x, y, z)


I believe we should treat the parent as being a default standard coordinate system if it is not specified. Otherwise what sense does it make to specify the transformation?

Upabjojr · 2017-08-01T19:59:25Z

sympy/vector/coordsysrect.py

+                x, y, z = symbols('x y z')
+                transformation = rotation_equations(*translation_equations(x, y, z))
+                lame_coefficients = _set_lame_coefficient_mapping('cartesian', (x, y, z))
+                inverse_transformation = None


Well, this could be specified. You just have to immagine that there is some default coordinate system used as a reference if parent == None.

Upabjojr · 2017-08-01T19:59:50Z

sympy/vector/coordsysrect.py

+                lame_coefficients = _set_lame_coefficient_mapping('cartesian', (x, y, z))
+                inverse_transformation = None
+
+                if not CoordSys3D._check_orthogonality(transformation, (x, y, z)):


If there are only rotations and translations, we don't need this check.

Upabjojr · 2017-08-01T20:00:58Z

sympy/vector/coordsysrect.py

@@ -98,6 +213,65 @@ def __new__(cls, name, location=None, rotation_matrix=None,
            location = Vector.zero
            origin = Point(name + '.origin')

+        if transformation is None:
+            if parent is None:


This if loop is not very useful. The case where parent == None and parent != None could be handled by the same code.

It could be, but the one difference between these two cases is with variables. When we have parent we can construct transformation equations using base scalars from parent system. Otherwise we can't.

We are using lambdas in order to avoid this problem.

OK, I see. I will simplify this

Another thing is translation. Without parent it doesn't have sense, so we need to distinguish two cases. But I think we can still simplify the code a bit.

Why doesn't it make sense? Anyway, the code in the master supports location even without parent, so we need to keep the compatibility.

Upabjojr · 2017-08-01T20:01:32Z

sympy/vector/coordsysrect.py

+                lame_coefficients = _set_lame_coefficient_mapping('cartesian', parent.base_scalars())
+                inverse_transformation = _set_inv_trans_equations('cartesian', parent.base_scalars())
+
+                if not CoordSys3D._check_orthogonality(transformation, parent.base_scalars()):


useless check, it will always pass (for rotations and translations).

Upabjojr · 2017-08-01T20:02:26Z

sympy/vector/coordsysrect.py

+            if location is not None and rotation_matrix is not None:
+                raise ValueError
+
+            if parent is None:


I would remove this if.

Upabjojr · 2017-08-02T01:19:39Z

sympy/vector/coordsysrect.py

+            else:
+                inverse_transformation_equations = None
+
+        elif isinstance(curv_coord_type, (tuple, list, Tuple, collections.Callable)):


Callable should be a separate case.

Almost finished constructor. Lame_coefficinets, transformation, inverse_transfromation are Lambda, so they can easily depend on desired variables. Creating base scalars with custom str has the same form as base scalars created in standard name: class_name + '.' + variable_names.

Upabjojr · 2017-08-02T20:48:52Z

sympy/vector/coordsysrect.py

-                    rotation_lambda = lambda x, y, z: (x, y, z)
+            if rotation_matrix is not None:
+                rotation_lambda = \
+                    lambda x, y, z: parent._rotation_trans_equations(parent_orient, (x, y, z))


with lambda no need for parent here.

Upabjojr · 2017-08-02T20:51:11Z

sympy/vector/coordsysrect.py

-        obj._inverse_transformation = inverse_transformation
+        obj._h1, obj._h2, obj._h3 = lame_coefficients(obj._x, obj._y, obj._z)
+        if parent is not None:
+            obj._transformation = transformation(parent._x, parent._y, parent._z)


I think transformation should remain a Lambda.

Upabjojr · 2017-08-02T20:53:42Z

sympy/vector/coordsysrect.py

+            obj._transformation = transformation(parent._x, parent._y, parent._z)
+        else:
+            obj._transformation = transformation(obj._x, obj._y, obj._z)
+        obj._inverse_transformation = inverse_transformation(obj._x, obj._y, obj._z)


also this one, I think it's easier if it remains in the lambda form.

Upabjojr · 2017-08-02T20:55:51Z

sympy/vector/coordsysrect.py


        """

        x1, x2, x3 = symbols("x1, x2, x3", cls=Dummy)

        if isinstance(curv_coord_type, string_types):
-            if variables is None:
-                variables = _default_variables(curv_coord_type)
-
            transformation_equations = _set_transformation_equations_mapping(curv_coord_type)


transformation_equations is a lambda, we need a SymPy Lambda (capital L) for hashing and internal stuff of SymPy.

Upabjojr · 2017-08-02T20:57:30Z

sympy/vector/coordsysrect.py

+                raise ValueError("The transformation equation does not "
+                                 "create orthogonal coordinate system")
+
+            lame_coefficients = cls._calculate_lame_coefficients(transformation_equations(*variables), variables)


do we really need to pass variables here? I believe a single lambda is enough.

It was the most difficult part for me and I didn't find clear solution with lambda but I can try once again.

in _calculate_lame_coefficients you can use some Dummy variables.

OK, I will try.

Remove parameter variables from _calculate_lame_coefficinets, _calculate_inv_trans_equations, _check_orthogonality All transformation in constructor are Lambda object.

Inverse transformation is calculated only when user needs it. when transformation is choosen from pre-defined ones, inverse is also set.

Remove dependency of parameter variables from every method. Change form of setting transformation. Variable names should be put together with equations. Remove simplify in _calculate_lame_coefficients for a while. Useage of simplify produce errors which isn't resolve yet.

szymag · 2017-08-07T14:53:59Z

sympy/vector/coordsysrect.py

+        if transformation is None:
+            transformation = Tuple(rotation_matrix, location)
+
+        if isinstance(transformation, Tuple):


Why that?
In this case, we are not able to set transformation as equations with variables. Previously, we could do that. For example:

a = CoordSys3D('a', transformation=Tuple(((x*cos(y), x*sin(y), z)), (x, y, z)))

But now you assumed that in following manner we're providing rotation and translation transformations.
Look at the code in _connect_to_cartesian method, lines 363:367

I thought a bit over the weekend, if we pass a rotation and/or translation, it needs to be stored in transformation and passed to the superclass (SymPy's hashing requirements). If we transform the rotation and/or translation into a Lambda, the code will slow down a lot, because when the class is reconstructed all orthogonality checks and computations are performed (at least, I think that's the problem).

We can still pass the transformation equations by wrapping them in a Lambda.

The main problem is that when calling the superclass in the constructor, we need a fixed argument order. The same argument order must return the same object if called on the constructor. This requirement is pretty restrictive on the way we may write the constructor, so we need to choose a precise way to pack the information without losing speed.

Simplification in constructor. Remove unnescessary if condition. Fix tests, doctests.

Upabjojr · 2017-08-09T19:32:06Z

sympy/vector/tests/test_coordsysrect.py

-    raises(ValueError, lambda: a._connect_to_standard_cartesian((x, y, z)))
-
-
-def test_check_orthogonality():


why has this test disappeared?

I must did it earlier, but I shouldn't. I will do it

Upabjojr · 2017-08-09T19:32:49Z

sympy/vector/tests/test_coordsysrect.py

    assert simplify(a.lame_coefficients()) == (1, sqrt(a.x**2), 1)

-    raises(ValueError, lambda: a._connect_to_standard_cartesian((x, y, z)))


we can test invalid parameters to the constructor

Upabjojr · 2017-08-09T19:34:41Z

sympy/vector/tests/test_printing.py

-v.append(a*N.i - b*N.j)
-v.append((a**2 + N.x)*N.i + N.k)
-v.append((a**2 + b)*N.i + 3*(C.y - c)*N.k)
+v.append(a * N.i)


These changes should be reverted.

I don't know why, but some expression change their order like was c - C.y and know C.y - c

Upabjojr · 2017-08-09T19:35:18Z

sympy/vector/tests/test_printing.py

 ⎛ 2    ⎞ N_i + ⎛⌠        ⎞ N_k\n\
 ⎝a  + b⎠       ⎜⎮ f(b) db⎟    \n\
               ⎝⌡        ⎠    \
 """)
 pretty_v_11 = u(
-"""\
+    """\


I didn't notice that. I will revert

Upabjojr · 2017-08-09T19:35:39Z

sympy/vector/tests/test_printing.py

@@ -68,26 +70,26 @@ def upretty(expr):

 for x in v:
    d.append(x | N.k)
-s = 3*N.x**2*C.y
+s = 3 * N.x ** 2 * C.y


did you use some auto-formatter?

I think so, by mistake

Upabjojr · 2017-08-09T20:41:51Z

sympy/vector/tests/test_coordsysrect.py

-    assert a._check_orthogonality() is True
+    x, y, z = symbols('x y z')
+    u,v = symbols('u, v')
+    a = CoordSys3D('a', transformation=((x*sin(y)*cos(z), x*sin(y)*sin(z), x*cos(y)), (x, y, z)))


shouldn't the tuple (x, y, z) come before the expression?

That's why I suggest to simply use: lambda x, y, z: (x*sin(y)*cos(z), x*sin(y)*sin(z), x*cos(y))

I will add also support for lambda.

Upabjojr · 2017-08-09T20:42:43Z

sympy/vector/tests/test_coordsysrect.py

    assert simplify(a.lame_coefficients()) == (1, sqrt(a.x**2), 1)
-    a._connect_to_standard_cartesian(((x, y, z), (x * sin(y) * cos(z), x * sin(y) * sin(z), x * cos(y))), inverse=False)


why is the block from here on still missing?

We do not support now these type of transformation.
Here we mainly tested _connect_to_standard_cartesian which now is removed

Just pass a lambda to CoordSys3D constructor. You added support for this tuples.

…g/sympy into reconstruction_constructor

Upabjojr · 2017-08-10T13:37:57Z

sympy/vector/coordsysrect.py

                raise TypeError("rotation_matrix should be an Immutable" +
                                "Matrix instance")
-            parent_orient = rotation_matrix
+                rotation_matrix = rotation_matrix.as_immutable()


This should be de-indented

Variables now are first in tuple. Add support for python's lambda. Add test for wrong transformation argument in constructor. Fix indent inconstructor.

szymag and others added 4 commits July 27, 2017 17:59

Add structure for transformation equations in constructor.

1cf0d8e

Add rotation_equations.

Merge branch 'master' into reconstruction_constructor

bc16490

Add transformation equations.

6cb3a2e

Set rotation_equations to None for parent None and rotation_matrix None

Update coordsysrect.py

bc6d63d

Upabjojr reviewed Jul 27, 2017

View reviewed changes

szymag added 2 commits July 29, 2017 19:35

Update _rotation_trans_equations, _translation_trans_equations.

b227693

Update constructor.

165b98c

Check orthogonality in constructor.

d08dc10

Upabjojr reviewed Jul 31, 2017

View reviewed changes

Update code appling Upabjojr suggestion.

6925316

Upabjojr reviewed Aug 1, 2017

View reviewed changes

Adapt methods for transformation.

181c2a5

szymag force-pushed the reconstruction_constructor branch from 5ef983a to 181c2a5 Compare August 1, 2017 20:18

Upabjojr reviewed Aug 2, 2017

View reviewed changes

Upabjojr and others added 3 commits August 1, 2017 21:24

Update coordsysrect.py

705fd5c

Update coordsysrect.py

e4a29c7

Upabjojr reviewed Aug 2, 2017

View reviewed changes

szymag added 2 commits August 3, 2017 21:50

Apply comments.

74a491c

Remove parameter variables from _calculate_lame_coefficinets, _calculate_inv_trans_equations, _check_orthogonality All transformation in constructor are Lambda object.

Pass tests from test_coordsysret.py.

ad3b703

Inverse transformation is calculated only when user needs it. when transformation is choosen from pre-defined ones, inverse is also set.

szymag force-pushed the reconstruction_constructor branch from ed4caf2 to ad3b703 Compare August 4, 2017 15:51

szymag and others added 2 commits August 5, 2017 22:00

Huge refactory to CoordSys3D constructor

2fe8fc7

szymag commented Aug 7, 2017

View reviewed changes

Support for custom transformation equations.

30fdac9

szymag and others added 3 commits August 9, 2017 20:11

Fix base vectors, base scalars name printing.

198501b

Simplification in constructor. Remove unnescessary if condition. Fix tests, doctests.

Fixes to gradient/divergence/curl

ef8537b

inverse transformation for rotation/translation

42783d4

Upabjojr reviewed Aug 9, 2017

View reviewed changes

Revert unwanted changes

8a517c3

Upabjojr reviewed Aug 9, 2017

View reviewed changes

szymag added 5 commits August 10, 2017 10:18

Revert unwanted changes

0219eab

Merge branch 'reconstruction_constructor' of https://github.com/szyma…

ee3226e

…g/sympy into reconstruction_constructor

Merge branch 'master' into reconstruction_constructor

8aef7e4

Merge branch 'master' into reconstruction_constructor

78e9bd4

Merge branch 'reconstruction_constructor' of https://github.com/szyma…

bebff57

…g/sympy into reconstruction_constructor

szymag force-pushed the reconstruction_constructor branch from f7acc15 to bebd39f Compare August 10, 2017 12:05

Upabjojr reviewed Aug 10, 2017

View reviewed changes

Revert order in transformation.

a6fc5bd

Variables now are first in tuple. Add support for python's lambda. Add test for wrong transformation argument in constructor. Fix indent inconstructor.

szymag force-pushed the reconstruction_constructor branch from bebd39f to a6fc5bd Compare August 10, 2017 13:47

Upabjojr and others added 2 commits August 10, 2017 13:09

fixes to directional_derivative, tests restored

c242261

Fix printing error.

063ab1b

szymag force-pushed the reconstruction_constructor branch from 870a844 to 063ab1b Compare August 11, 2017 15:47

Upabjojr merged commit c08f558 into sympy:master Aug 12, 2017

szymag deleted the reconstruction_constructor branch August 23, 2017 08:01

		@@ -98,6 +98,33 @@ def __new__(cls, name, location=None, rotation_matrix=None,
		location = Vector.zero
		origin = Point(name + '.origin')

		raises(ValueError, lambda: a._connect_to_standard_cartesian((x, y, z)))


		def test_check_orthogonality():

		assert simplify(a.lame_coefficients()) == (1, sqrt(a.x**2), 1)

		raises(ValueError, lambda: a._connect_to_standard_cartesian((x, y, z)))

		assert simplify(a.lame_coefficients()) == (1, sqrt(a.x**2), 1)
		a._connect_to_standard_cartesian(((x, y, z), (x * sin(y) * cos(z), x * sin(y) * sin(z), x * cos(y))), inverse=False)

[WIP] Reconstruction constructor in CoordSys3D #13056

[WIP] Reconstruction constructor in CoordSys3D #13056

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szymag commented Jul 27, 2017

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Upabjojr commented Jul 27, 2017

szymag commented Jul 29, 2017

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Upabjojr Jul 31, 2017 • edited Loading

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Upabjojr Jul 31, 2017 •

edited

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