Functions and IdentityMultiple

[ChristopherChudzicki]

The Issue

In MatrixGrader problems, if IdentityMultiple instances are passed to functions, students currently receive unhelpful generic error messages:

from mitxgraders import FormulaGrader

grader = MatrixGrader(answers='1')
grader(None, 'sin(I)'
# raises:
# StudentFacingError: Invalid Input: Could not check input 'sin(I)'

This is bad.

(The actual cause of this error is an isinf check in calc.py's eval_function parse action. However: I suggest that this issue should be for discussing the intended behavior, not the source of the bug.)

Original motivation of IdentityMultiple

My thinking with IdentityMultiple originally was:

• in MatrixGrader problems, 'I' for identity should always be available, so authors should not need to declare it as a specified constant.
• The dimension of the identity operator is usually irrelevant:
  • True for binary operations add/subtract and multiple/divide
  • True (but not implemented) for functions determinant, transpose, conjugation
  • False for tensor product; False for functions trace, norm
• In specific problems where identity's dimension does matter, the author should declare auser_constant with identity of relevant size. (Either overriding 'I', or declaring 'I_2', 'I_3', etc.)

Resolutions

Shape is a bit more important for the identity matrix than I originally realized. In particular, I see no way to handle trace and norm for generic-dimensional identity operators.

I'm not sure what the best approach to resolve this is. Two ideas:

• Idea A: Implement functions like det, trans, etc, and provide special error messages fortrace andnorm.

  • Pros: Automatically declared I of generic dimension that works in almost all situations.
  • Cons: Hard to maintain lots of special cases. Also, authors need to understand how IdentityMultiple works in order to implement their own matrix functions.

• Idea B: Abandon IdentityMultiple all together. Provide a helper function Identity(n) for authors to declare identity matrix of specific size through user_constants.

  • Pros: More explicit; fewer special cases; automatically resolves #101; identities declared this way would work automatically with tensor products and any numpy matrix function.
  • Cons: Requires extra declaration by author. Requires author to think about dimensionality in problems where it might be irrelevant.

I am personally rather fond of IdentityMultiple, but I am actually leaning toward Idea B.

[jolyonb]

Note that det is also dependent on the dimensionality.

I too am quite fond of IdentityMultiple, but I think you're right that Idea B is probably the better way to go. Being explicit about what something is will ultimately lead to less confusion than having a clever but ill-defined construct.

I propose that in addition to exposing a helper function Identity(n), we have an additional key like identity_dim (default None) that will populate I with the identity of the appropriate dimension. This reduces the author load just that little bit.

[jolyonb]

Resolved by #105.