Opened 10 years ago
Last modified 5 years ago
#12075 needs_work enhancement
Create callable matrices in function notation
Reported by: | kcrisman | Owned by: | burcin |
---|---|---|---|
Priority: | major | Milestone: | sage-6.4 |
Component: | symbolics | Keywords: | sd35.5 |
Cc: | jason | Merged in: | |
Authors: | Geoffrey Ehrman | Reviewers: | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
In this sage-support post, the poster wants the following notation to work.
R_theta(theta)=matrix(SR,[[cos(theta),sin(theta),0],[-sin(theta),cos(theta),0],[0,0,1]])
This is sort of #1722 on steroids.
In the thread above, there are a number of good ideas. The final one is
I think this would be a good project for a person wanting to learn more about how to do Sage development. The modifications to symbolic_expression should be easy (check for a nested list/tuple structure). Then you would need to make a new function() method, in $SAGE_ROOT/devel/sage/sage/matrix/matrix2.pyx probably, that would create a corresponding matrix over the CallableSymbolicRing. You can see an example for vectors in $SAGE_ROOT/devel/sage/sage/modules/free_module.pyx (look for "def function" in that file). Then if you are ambitious, create a new matrix subclass for callable symbolic expressions that mirrors what $SAGE_ROOT/devel/sage/sage/modules/vector_callable_symbolic_dense.py does for vectors (i.e., changes the printing). }}}[[Image()]]
Attachments (3)
Change History (22)
comment:1 Changed 10 years ago by
comment:2 Changed 10 years ago by
Really? Without the word matrix
? I guess that the preparser would in theory catch this as an error, but it seems a little bit of an overreach to me.
Could one then make a matrix M
by doing one of
M() = [[1,2],[2,3]] M(1) = [[1,2],[2,3]] M(x) = [[1,2],[2,3]]
and are any of those suspicious?
comment:3 Changed 10 years ago by
Right now, these work to create vectors:
M(x)=[1,2,x]
so I see the nested list as a natural extension of the syntax to matrices.
comment:4 Changed 10 years ago by
Nice, and then you are right that this is natural.
You mean
V(x) = [1,2,x]
of course.
comment:5 Changed 10 years ago by
Little note: the definition of function() for vectors is located in modules/free_module_element.pyx rather than modules/free_module.pyx.
comment:6 Changed 10 years ago by
- Keywords sd35.5 added
comment:7 Changed 10 years ago by
- Description modified (diff)
Progress thus far:
- calculus/all.py is modified so that sage recognizes the creation of callable symbolic matrices via function notation. In particular:
sage: m(X) = [[cos(X), -sin(X)],[sin(X), cos(X)]]
and is now valid syntax.
- Things that work correctly:
sage: m(pi/2) [ 0 -1] [ 1 0] sage: m.trace() X |--> 2*cos(X) sage: m(3).eigenvalues() [-I*sin(3) + cos(3), I*sin(3) + cos(3)] sage: m.derivative() [X |--> -sin(X) X |--> -cos(X)] [ X |--> cos(X) X |--> -sin(X)] sage: m.kernel() Vector space of degree 2 and dimension 0 over Callable function ring with arguments (X,) Basis matrix: [] sage: m.image() Vector space of degree 2 and dimension 2 over Callable function ring with arguments (X,) Basis matrix: [X |--> 1 X |--> 0] [X |--> 0 X |--> 1]
Things that don't work (and should?):
sage: m.eigenvalues() NotImplementedError ...
Things that I'm not sure about/work incorrectly(?):
sage: m.charpoly() (X |--> 1)*x^2 + (X |--> -2*cos(X))*x + X |--> sin(X)^2 + cos(X)^2 sage: m.echelon_form() [X |--> 1 X |--> 0] [X |--> 0 X |--> 1]
What remains to do:
- Matrix.function() is defined in sage/matrix/matrix2.pyx. It might be better placed in sage/matrix/matrix_generic_dense.pyx as the method for function() is defined only for FreeModuleElement_generic_dense. (Minor)
- Matrix.function() is written as an exact analog to FreeModuleElement_generic_dense.function(). This is the cause of the problem I mentioned in (2). I think the root of the problem is that the vector case is being coerced to the correct class via the category framework and the matrix class is currently lacks the code needed to coerce correctly. It's also quite possible there's a better way to write this method. I've looked through some of the matrix and module code however, and I don't yet have any sensible ideas.
- Generalizing from (2) I've tried to make function notation for matrices as similar to function notation for vectors as similar as possible. Is this sensible, or are there enough salient differences that this is unreasonable?
- The file sage/matrix/matrix_callable_symbolic_dense.py purposely produces several doctest failures due again to the type issue in (2). Any other failures should be considered bugs.
Changed 10 years ago by
comment:8 Changed 10 years ago by
- Status changed from new to needs_info
comment:9 Changed 10 years ago by
- Status changed from needs_info to needs_review
comment:10 Changed 10 years ago by
- Status changed from needs_review to needs_work
comment:11 Changed 10 years ago by
The typing issue was minor - it's handled by _get_matrix_class() in matrix_space.py. However, matrix_callable_symbolic_dense.py is may currently be unusable as written.
Changed 10 years ago by
Same content as trac_12298-v2.patch, just named correctly. Apply instead of trac_12075.patch
comment:12 Changed 10 years ago by
The current version is working correctly and is probably usable in most applications. That said, I'm leaving the status as needs works as there are a few more (mostly minor, I think) remaining things to do:
Remaining issues:
- Fix the doctests in matrix2.pyx and matrix_callable_symbolic_dense.pyx. I know v2 is has these two files failing doctests; it may be that other files are also failing as I have not yet run sage --testall.
- Partial evaluation does not return a callable matrix. See #12302 for more details, as this is the exact same issue and the fix should be (basically) the same - a modification to _ _call_ _() so the function recognizes partial evaluation.
Comments:
- I'm leaving the definition of function() in matrix2.pyx unless someone with more experience withh the matrix module chimes in and says differently.
- While working with this bug I unearthed bug #12302. In addition to the fixes probably being nearly identical, 12302 may have implications for this patch since
sage: m(x) = [[x,x],[0,x]] sage: type(m) <type 'sage.matrix.matrix_callable_symbolic_dense.Matrix_callable_symbolic_dense'> sage: type(m[0]) <class 'sage.modules.vector_callable_symbolic_dense.Vector_callable_symbolic_dense'>
comment:13 Changed 9 years ago by
Just pinging myself and others. This came up in http://ask.sagemath.org/question/2744/symbolic-function-from-rm-to-rn
comment:14 Changed 8 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:15 Changed 8 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:16 Changed 8 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:17 Changed 7 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:18 Changed 5 years ago by
As of v7.6, the requirement in Description works:
sage: R_theta(theta) = matrix(SR,[[cos(theta),sin(theta),0],[-sin(theta),cos(theta),0],[0,0,1]]) sage: R_theta theta |--> [ cos(theta) sin(theta) 0] [-sin(theta) cos(theta) 0] [ 0 0 1]
is this ticket obsolete or not?
However, there is a closely related use case which does fail:
sage: theta = var('theta') sage: R_theta(theta) = vector([cos(theta),sin(theta),0]) ... TypeError: unable to convert (cos(theta), sin(theta), 0) to a symbolic expression
This was asked in when i must use lambda.
I guess this is #11507.
comment:19 Changed 5 years ago by
if you happen to read this, note that as of v7.6 evaluation of a callable matrix in function notation does not work as expected:
sage: var('x y') (x, y) sage: f(x) = sin(x) sage: f(x+y) # ok sin(x + y) sage: f(x) = matrix([[sin(x)],[cos(x)]]) sage: f(x+y) # not ok [sin(x)] [cos(x)]
This was asked in functions of variables with matrices.
.. but i couldn't find (yet) an open ticket about this.
I think I would like this syntax instead:
That's what the above development hint is geared towards.