Finally whipped up a simple Hadamard object in this branch
https://github.com/sympy/sympy/pull/1608
I don't have the .* syntax though. I haven't figured out what the ideal
Python syntax is so I've left it without an operator.
-----------------
A*(B.*C)
which should mean
\sum_j A_{ij} ( \sum_{p,q} B_{pq} * C_{pq} )_{jk}
-----------------
This can be done in this branch with the following code. There isn't any
substantial functionality here other than giving you a valid container
object. It's a simple PR. Should be in (I hope) in a couple days.
A = MatrixSymbol('A', n, m)
B = MatrixSymbol('A', m, k)
C = MatrixSymbol('A', m, k)
A*Hadamard(B, C)
On Sun, Oct 21, 2012 at 7:33 AM, Matthew Rocklin <[email protected]> wrote:
> Hi David,
>
> MatrixExprs represent matrices without explicit elements. I'm modifying
> the first half of Chris' example above
>
> >>> from sympy import MatrixSymbol
> >>> n = Symbol('n')
> >>> X = MatrixSymbol('X', n, n)
> >>> Y = MatrixSymbol('Y', n, n)
> >>> (X.T*X).I*Y
> X^-1*X'^-1*Y
>
> The result here is an expression tree from which you could generate code.
> I'm actively working on this and would be interested in hearing more about
> what you're working on.
>
> MatrixExprs don't currently contain an elementwise product but it could be
> added if there was a need. I've added an issue for this topic here
> http://code.google.com/p/sympy/issues/detail?id=3447
>
> I'm planning to take a bit of time to work on MatrixExprs this week. If
> you have some easy-to-implement feature requests this would be a good time.
> I'd be happy to see symbolic matrix expressions in wider use. I think that
> they're a good idea.
>
> Other options:
> 1. There is an old `Indexed` class in SymPy for representing and
> generating code for indexed expressions. I'm sure that this would
> support element-wise product. I hope that it would also support matrix
> multiply but I'm not sure what the state of the module is. Andy Terrel
> might have more information here.
> 2. There is the Theano project which actively thinks about code generation
> for matrix and array expressions. They tend to target people who don't do
> their own code generation but they certainly have a language that can
> represent the sorts of operations for which you're asking.
>
> Best,
> -Matthew
>
> On Sun, Oct 21, 2012 at 1:43 AM, David Ketcheson <[email protected]> wrote:
>
>> Thanks. But I don't want to specify the size of the matrices, and I
>> don't want the result to be in terms of matrix elements; I want it to still
>> appear as A*(B.*C) or something similar, as the purpose is generation of
>> MATLAB or numpy code that won't index into the matrices. I just need two
>> different kinds of multiplication operators for non-commutative symbols.
>>
>> David
>>
>>
>> On Sunday, October 21, 2012 11:31:12 AM UTC+3, smichr wrote:
>>
>>> On Sun, Oct 21, 2012 at 1:58 PM, David Ketcheson <[email protected]>
>>> wrote:
>>> > I would like to express formulas that involve both traditional
>>> matrix-matrix
>>> > multiplication and elementwise multiplication. To be clear, these are
>>> the
>>>
>>> The following is from the docs on Matrix Expressions:
>>>
>>>
>>> >>> from sympy import MatrixSymbol, Matrix
>>> >>> X = MatrixSymbol('X', 3, 3)
>>> >>> Y = MatrixSymbol('Y', 3, 3)
>>> >>> (X.T*X).I*Y
>>> X^-1*X'^-1*Y
>>>
>>> >>> Matrix(X)
>>> [X_00, X_01, X_02]
>>> [X_10, X_11, X_12]
>>> [X_20, X_21, X_22]
>>>
>>> >>> (X*Y)[1, 2]
>>> X_10*Y_02 + X_11*Y_12 + X_12*Y_22
>>>
>>> So yes, you can do abstract value-agnostic manipulations. Although
>>> there is a matrix_multiply_elementwise function that operates on
>>> regular matrices, I don't think that there is an implementation yet
>>> for MatrixExpr.
>>>
>>> Chris
>>>
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