Bug fixes on matrix derivatives

[Upabjojr]

References to other Issues or PRs

Brief description of what is fixed or changed

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Release Notes

• matrices
  • more fixes to matrix derivatives and related modules.

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• matrices
  • more fixes to matrix derivatives and related modules. (#17583 by @Upabjojr)

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* matrices
  * more fixes to matrix derivatives and related modules.
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Update

The release notes on the wiki have been updated.

[codecov]

Codecov Report

Merging #17583 into master will decrease coverage by 4.029%.
The diff coverage is 85.714%.

@@             Coverage Diff              @@
##            master    #17583      +/-   ##
============================================
- Coverage   74.802%   70.772%   -4.03%     
============================================
  Files          633       633              
  Lines       164836    164869      +33     
  Branches     38750     38766      +16     
============================================
- Hits        123301    116682    -6619     
- Misses       36127     42691    +6564     
- Partials      5408      5496      +88

[oscarbenjamin]

Lambda has .is_identity for this. Returning function(expr) will check that the signature of the function is actually compatible though e.g.:

In [1]: function = Lambda((x, y), x+y)                                                                                            

In [2]: expr = 2                                                                                                                  

In [3]: function(2)                                                                                                               
---------------------------------------------------------------------------
BadArgumentsError

[oscarbenjamin]

I guess a better example would be:

In [7]: function = Lambda((x, y), (x, y))                                                                                         

In [8]: function.is_identity                                                                                                      
Out[8]: True

[oscarbenjamin]

I know this isn't being added in this PR but this construction seems like a bad idea. The function should be part of the args rather than messing with func like this.

[Upabjojr]

Well, this way you keep the same parameters as in the function definition. Methods applying to functions should also apply here.

[oscarbenjamin]

Can you give an example of why this is needed? Why can't the class be (basically):

class ElementWiseApplyFunction(MatrixExpr):
    def __new__(cls, function, expr):
        # Pass function as part of args
        obj = MatrixExpr.__new__(cls, function, expr)

A similar construction using classes created on the fly is used for UndefinedFunction but I think that should be changed as well.

[Upabjojr]

A generic Python function may not be sympifiable. That's why the argument is hidden.

[oscarbenjamin]

A generic Python function is turned into a Lambda:

sympy/sympy/matrices/expressions/applyfunc.py

Lines 46 to 51 in fcf84d9

	def __new__(cls, function, expr):
	obj = MatrixExpr.__new__(cls, expr)
	if not isinstance(function, FunctionClass):
	d = Dummy("d")
	function = Lambda(d, function(d))
	obj._function = function