CODEWITHSUNDEEP
python-3.xsympy
J.Galt
J.Galt

Reputation: 533

Sympy implementation of multidimensional Rosenbrock function?

I have recently been trying to learn how to use symbolic calculus in Python. Most of the basic SymPy tutorials were easy enough, but how would I go about representing something as complex as the N-dimensional (for even N) Rosenbrock function? This function has two main complicating factors: its argument is a vector and the function accesses specific, indexed elements in this vector, and the function includes an indexed sum.

Is it possible to represent something like this in SymPy? If so, could you provide a code snippet or tips on how I could handle these two challenges?

Upvotes: 0

Views: 340

Answers (1)

Oscar Benjamin
Oscar Benjamin

Reputation: 14500

You can do this using Sum and Indexed:

https://docs.sympy.org/latest/modules/concrete.html

https://docs.sympy.org/latest/modules/tensor/indexed.html

In [34]: x = IndexedBase('x')                                                                                          

In [35]: i, n = symbols('i, n', integer=True)                                                                          

In [36]: Sn = Sum(100*(x[2*i-1]**2 - x[2*i])**2 + (x[2*i-1] - 1)**2, (i, 1, n))                                        

In [37]: Sn                                                                                                            
Out[37]: 
  n                                                    
 ____                                                  
 ╲                                                     
  ╲                                                    
   ╲  ⎛                                              2⎞
   ╱  ⎜                2       ⎛          2         ⎞ ⎟
  ╱   ⎝(x[2*i - 1] - 1)  + 100⋅⎝x[2*i - 1]  - x[2*i]⎠ ⎠
 ╱                                                     
 ‾‾‾‾                                                  
i = 1                                                  

In [38]: Sn.subs(n, 2).doit()                                                                                          
Out[38]: 
                                2                                   2
          2       ⎛    2       ⎞              2       ⎛    2       ⎞ 
(x[1] - 1)  + 100⋅⎝x[1]  - x[2]⎠  + (x[3] - 1)  + 100⋅⎝x[3]  - x[4]⎠

You can do things with Sn but there are limitations on what operations you can use without replacing n with a concrete integer.

Upvotes: 1

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