Defining functions acting on matrix elements?

asked 2017-08-14 21:58:15 +0100

Asker
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Hi guys, how can I define a function able to act on the elements of a matrix, with the matrix being the input to the function? I would like the function to be a callable symbolic expression, which I hear can be differentiated and so on, whereas other entities cannot.

Here's a sample of what I mean:

f(M) = M[0,0]+M[1,1]

that is, the user will ensure that M is correctly defined as a matrix of size at least 2x2 before being passed to f(M), but at this stage the symbol M is intended just as a dummy variable, similar to z in a definition like g(z) = conjugate(z). Unfortunately, my code does not seem to work...

Thank you for your suggestions!

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Using the pure pythonical way, we can define for instance:

def tr(M):
    return M[0,0]+M[1,1]

Sample code of usage:

sage: tr( matrix( 2,2, [ 1+x, 1-x, 1-x, x^2 ] ) )
x^2 + x + 1
sage: tr( matrix( 2,2, [ 1+x, 1-x, 1-x, x^2 ] ) ).diff()
2*x + 1

Is this ok?

dan_fulea ( 2017-08-14 23:59:11 +0100 )edit

For what I need in this particular case, yes, it is fine.

Since I am new to Sage, however, I still wonder if there are cases when a callable symbolic expression acting on single elements of an input matrix is required, and how to solve the problem.

Many thanks, Dan.

Asker ( 2017-08-15 09:57:19 +0100 )edit

for "element-wise" operations, the method apply_map is useful. see for example this answer. you may post the full code that didn't work, to get more precise help.

mforets ( 2017-08-15 17:25:27 +0100 )edit

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Full MatrixSpace of 2 by 2 dense matrices over Symbolic Ring Traceback (click to the left of this block for traceback) ... AttributeError: 'sage.symbolic.expression.Expression' object has no attribute 'transpose'

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