[sympy] defining a derivative

2016-10-14 Thread Riccardo Rossi 
Dear List,

i am writing since i would like to define the output of the derivative of a 
function, and i don't have a clue of how to achieve it

to explain what i wish to do, let's consider the following script

from sympy import *

u = symbols('u')
der = symbols('der')
e = symbols('e', cls=Function)(u)
s = symbols('s', cls=Function)(e)
Derivative(e,u) = der #essentially i would like to teach to sympy to use a 
symbol for the Derivative
---> but here i get "SyntaxError: can't assign to function call"

print(diff(e,u))
print(diff(s,e))
print(diff(s,u)) #here i would like "der" to be replaced within the chain 
rule

any suggestion would be very welcome...

regards
Riccardo


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Re: [sympy] defining a derivative

2016-10-14 Thread Aaron Meurer 
If you want to define advanced things you need to subclass from
Function rather than using symbols(cls=Function). For derivatives, you
should define fdiff, which should return the derivative of the
function without consideration of the chain rule. For example, search
for "fdiff" in this file to see some examples for exp, log, and
LambertW 
https://github.com/sympy/sympy/blob/master/sympy/functions/elementary/exponential.py.

Aaron Meurer

On Fri, Oct 14, 2016 at 4:53 AM, Riccardo Rossi  wrote:
> Dear List,
>
> i am writing since i would like to define the output of the derivative of a
> function, and i don't have a clue of how to achieve it
>
> to explain what i wish to do, let's consider the following script
>
> from sympy import *
>
> u = symbols('u')
> der = symbols('der')
> e = symbols('e', cls=Function)(u)
> s = symbols('s', cls=Function)(e)
> Derivative(e,u) = der #essentially i would like to teach to sympy to use a
> symbol for the Derivative
> ---> but here i get "SyntaxError: can't assign to function call"
>
> print(diff(e,u))
> print(diff(s,e))
> print(diff(s,u)) #here i would like "der" to be replaced within the chain
> rule
>
> any suggestion would be very welcome...
>
> regards
> Riccardo
>
>
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Re: [sympy] Re: Lambdify performance with repeated subexpressions

2016-10-14 Thread Aaron Meurer 
To achieve this with lambdify you should call cse() first, then
lambdify each expression separately. We ought to build a wrapper to
make this easier (or a cse=True flag to lambdify).

Aaron Meurer

On Fri, Oct 14, 2016 at 11:06 AM, Björn Dahlgren  wrote:
>
>
> On Friday, 14 October 2016 15:09:46 UTC+2, Albert Pető wrote:
>>
>> Hi, I plan to heavily use a function generated with lambdify from a sympy
>> expression which has repeated occurences of some subexpressions.
>
>
> This functionality is available in symengine:
> https://github.com/symengine/symengine.py/blob/master/symengine/lib/symengine_wrapper.pyx#L2827
> (which you might want to consider if you are concerned about speed). If you
> want to stay pure python and only use sympy you can look at the
> source code there for how to achieve this (we are creating a closure).
>
> Best,
> Björn
>
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[sympy] Re: Lambdify performance with repeated subexpressions

2016-10-14 Thread Björn Dahlgren 


On Friday, 14 October 2016 15:09:46 UTC+2, Albert Pető wrote:
>
> Hi, I plan to heavily use a function generated with lambdify from a sympy 
> expression which has repeated occurences of some subexpressions. 
>

This functionality is available in symengine: 
https://github.com/symengine/symengine.py/blob/master/symengine/lib/symengine_wrapper.pyx#L2827
(which you might want to consider if you are concerned about speed). If you 
want to stay pure python and only use sympy you can look at the
source code there for how to achieve this (we are creating a closure).

Best,
Björn

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[sympy] Lambdify performance with repeated subexpressions

2016-10-14 Thread Albert Pető 
Hi,

I would like to evaluate certain functions created with lambdify. Those 
functions would come from rotations and would have a lot of trigonometric 
function invocations in them with the same parameters. For example, lets 
suppose that it would contain cos(a) many times. I plan to heavily use 
those generated functions, but I am concerned about the performance loss of 
evaluating cos(a) multiple times in one function invocation, when it would 
suffice to evaluate it only once.

I am not sure how lambdify treats these cases, i.e. if it would call cos(a) 
multiple times or not, or if I have to specify it explicitly. Can somebody 
tell me how it works?

Thanks for your help! :)

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[sympy] Lambdify performance with repeated subexpressions

2016-10-14 Thread Albert Pető 
Hi, I plan to heavily use a function generated with lambdify from a sympy 
expression which has repeated occurences of some subexpressions. 
Specifically it will have a lot of cosine and sine expressions with the 
same arguments. I don't know if lambdify can notice this pattern and 
evaluate that subexpression only once, or if it will call it (the numeric 
sine and cosine functions) as many times as it appears, or if I have to 
specify it somehow. I am afraid that it would mean a considerable 
performance loss if, for example, it will have to call 2-3 times as many 
trigonometric functions as a hand-written code, since I plan to use it a 
lot. Can somebody provide me some information?

Thanks in advance :)

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[sympy] Re: defining a derivative

2016-10-14 Thread Vicente Mataix Ferrándiz 
What I am using right now dear Riccardo is the following:


Suppose that my variable sigma(define as a symbol) depends of u, but at the 
same time this u is vectorial variable, which means for example in 3D the 
variable will be : u = [u_0, u_1, u_2], all the components of u are defined 
as symbols. Now I only need to do the following:

In: sigma(*u) #so sigma depends of u_0, u_1, u_2, and if we use diff:
In: print(sigma)
Out: sigma(u_0,u_1,u_2)
In: diff(sigma, u_1) 
Out: Derivative(sigma(u_0,u_1,u_2), u_1)








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