Implemented Ellipsis in slicing Sympy Matrices.

[arihantparsoya]

This is fix for #11345. Added conditions when the argument is ellipsis.

Sample Program

>>> from sympy import *
>>> from sympy.abc import m, n
>>> X = MatrixSymbol('X', n, m)
>>> X[...]
X[:n, :m]
>>> X[2, ...]
X[2, :m]
>>> X[..., 2]
X[:n, 2]

[arihantparsoya]

@leosartaj , can your review this?

[arihantparsoya]

@asmeurer , can you review this?

[leosartaj]

This does not work.

>>> m = Matrix([[1, 2, 3], [4, 5, 6]])
>>> m[...]
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-5-0ccb1cae6e36> in <module>()
----> 1 m[...]

/home/leosartaj/anaconda/lib/python2.7/site-packages/sympy/matrices/dense.pyc in __getitem__(self, key)
     94             if isinstance(key, slice):
     95                 return self._mat[key]
---> 96             return self._mat[a2idx(key)]
     97 
     98     def __setitem__(self, key, value):

/home/leosartaj/anaconda/lib/python2.7/site-packages/sympy/matrices/matrices.pyc in a2idx(j, n)
   4412             j = j.__index__()
   4413         except AttributeError:
-> 4414             raise IndexError("Invalid index a[%r]" % (j, ))
   4415     if n is not None:
   4416         if j < 0:

IndexError: Invalid index a[Ellipsis]

[leosartaj]

This also doesn't work as expected.

>>> m = MatrixSymbol('A', 3, 4)
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-16-0ccb1cae6e36> in <module>()
----> 1 m[...]

/home/leosartaj/anaconda/lib/python2.7/site-packages/sympy/matrices/expressions/matexpr.pyc in __getitem__(self, key)
    252                 raise IndexError("Single index only supported for "
    253                                  "non-symbolic indices.")
--> 254         raise IndexError("Invalid index, wanted %s[i,j]" % self)
    255 
    256     def as_explicit(self):

IndexError: Invalid index, wanted A[i,j]

I would expect something like this

>>> m[...]
A[:3, :4]

[arihantparsoya]

@leosartaj , the following program does work in my local computer:

>>> from sympy import *
>>> m = MatrixSymbol('A', 3, 4)
>>> m[...]
A[:3, :4]

[arihantparsoya]

@leosartaj , the following program works now:

>>> from sympy import *
>>> m = Matrix([[1, 2, 3], [4, 5, 6]])
>>> m[...]
Matrix([
[1, 2, 3],
[4, 5, 6]])
>>> m[0,...]
Matrix([[1, 2, 3]])

[arihantparsoya]

@leosartaj , ping.

[arihantparsoya]

@asmeurer , ping.

[arihantparsoya]

@asmeurer , ping.

[bjodah]

this line does not have any effect.

[arihantparsoya]

Thanks for reviewing this PR. If only one among i or j is Ellipsis, then this line will have use.

Example

assert X[2, ...] == MatrixSlice(X, 2, (0, m))

[isuruf]

@bjodah is correct. the four lines below handle this.

[arihantparsoya]

Thanks, I have fixed it.

[arihantparsoya]

@leosartaj , ping.

[isuruf]

This isn't equal to m2[:] right? In other cases, ... and : are equivalent.

[arihantparsoya]

No, its not equal.

[sylee957]

Although I don't see any clear advantage of slicing with ellipsis in matrix,
I see ellipsis slicing is implemented for numpy arrays and it can follow the same convention for sympy array.
So I think that this should be implemented first to sympy NDimArray and rather backported from there for sympy matrix.