CODEWITHSUNDEEP
sympy
gmas80
gmas80

Reputation: 1268

Calculation of a formula with summation term

I am a newbie with the sympy library, and I am having trouble to calculate the mean after have defined the formula:

import sympy as sp
import numpy as np
sp.init_printing()

mu, N, i, x_i = sp.symbols( 'mu N i x_i' )
mu_form = sp.Eq( mu , (1/N) * sp.Sum( x_i, (i, 1, N) ) )

Now I want to define a list of values for x_i to actually calculate the mean.. I have attempted in such a way, but it does not seem to work properly:

x_i_val = (1, 1, 3, 3, 2, 2, 2, 2)
mu_val = mu_form.subs( [(x_i, x_i_val), (N, 8)] )

I am not interested in the mean in particular, I want to understand the way to calculate the result of such a formula, with a summation inside.

I did not have luck in finding a minimal example in the available tutorials and Googling.

Upvotes: 1

Views: 746

Answers (1)

asmeurer
asmeurer

Reputation: 91480

The symbol x_i is not related to the symbol i. It prints with a subscript, but that is just a printing convention.

A better choice is IndexedBase. There's a fix from https://github.com/sympy/sympy/pull/8065 that makes this easier, but for now, you can do something like this:

In [13]: x = IndexedBase('x')

In [14]: mu_form = sp.Eq( mu , (1/N) * sp.Sum( x[i], (i, 1, N) ) )

In [15]: mu_form = mu_form.subs(N, 8).doit()

This expands the sum, so that you can substitute the terms:

In [16]: mu_form
Out[16]:
    x[1]   x[2]   x[3]   x[4]   x[5]   x[6]   x[7]   x[8]
μ = ──── + ──── + ──── + ──── + ──── + ──── + ──── + ────
     8      8      8      8      8      8      8      8

In [20]: mu_form = mu_form.subs({x[i]: x_i_val[i - 1] for i in range(1, 9)})

In [21]: mu_form
Out[21]: μ = 2

By the way, it's a lot easier to deal with things if you start your indices at 0 instead of 1, since that's what Python does.

Upvotes: 2

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