I get the same thing. For the first expression, I get
In [69]: sz.count_ops()
Out[69]: 11378 + 9866⋅POW + 17655⋅ADD + 61510⋅MUL
So like Ondrej said, the solution here is not necessarily Cython, but to find
an algorithm for solving that Matrix equation that gives a simpler solution.
Of course, this is all assuming that the solution can be simplified. If it
really can't then there is no way around the costs of dealing with such large
expressions.
But even then, you can be smarter than what you are doing now. simplify() is a
general simplification function that can be slow. Since you know the form of
the input expression, you can get away with calling lesser simplification
functions. From what I could glean from your expression, cancel() should be
sufficient. But even then, calling cancel on just A0 causes my computer to
hang.
By the way, a more Pythonic way to write
for i in range(len(E)):
mu.append(E[i]/(2*(1+nu[i])))
is
for i, j in zip(E, nu):
mu.append(i/(2*(1 + j)))
Aaron Meurer
On Nov 18, 2010, at 12:06 AM, Ondrej Certik wrote:
> Hi Andre,
>
> On Wed, Nov 17, 2010 at 8:29 PM, freevryheid <[email protected]> wrote:
>> Hi
>>
>> I’m on a mission to code an open source elastic multi-layer analysis
>> system to calculate stress, strain and displacement response in
>> layered systems to surface loads. As proof of concept I opted to use
>> sympy and coded a simple two layer system under a single circular load
>> [1]. The vision is to eventually solve a system with many layers and/
>> or loads. Most of the solution time appears to be in simplifying the
>> functions before integration - this step is necessary to avoid
>> division by zero errors (for example). Will performance improve using
>> Cython? Any other suggestions?
>
> I tried your script and it hangs for me in the first simplify function
> print. I just tried to print the expression and it takes forever. What
> is the structure of the expressions? I tried print A0, and it's many
> pages.
>
> Can this be simplified? Can some other method be used instead of the LU solve?
>
> It seems that the expression is very big, so even things like expand()
> take forever. What kind of simplification is necessary --- maybe it's
> just expand? If so, maybe things can be expanded before they grow big
> (either use a different method than LU, or expand things before you
> pass it in).
>
> Ondrej
>
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