Mixing
Exponent of a summation
Exponent of a summation
I am a very new python user.
I am trying to calculate an exponent of a summation. The array has more parameters.
import math
a = [[1, 2, 3, 4],
[5, 6, 7, 8]]
def y(i):
p = 2
total = 0
for j in range (4):
total += math.exp(a[i][j] * (p**j))
return total
Answer from this method: 7.89629603455e+13
7.89629603455e+13
The answer is way different than manual calculation below:
y = math.exp(1*(2**0) + 2*(2**1) + 3*(2**2) + 4*(2**3))
Answer: 1.9073465725e+21
1.9073465725e+21
The expected output has the sum inside the exponential, while in the loop you take the exponential first and then sum. These aren't the same.
– Jay Calamari
Jun 29 at 17:50
@RBalasubramanian, I put the correct indentation in Python. When I copy and paste, it changes.
– Duchess
Jun 29 at 17:51
I am not sure what you are trying to do but I think you have a mistake..
exp(x+y) != exp(x) + exp(y) - perhaps change to total *= ...– Daniel M
Jun 29 at 17:53
exp(x+y) != exp(x) + exp(y)
total *= ...
@MohammadAthar, I was playing around with different methods, I put the correct code. Please ignore the indentation.
– Duchess
Jun 29 at 17:54
2 Answers
2
Your mistake appears to not be a python error, but a math error in decomposing the equation. You can make one of two changes:
Solution 1: Sum all first, then take e^ of the total
import math
a = [[1, 2, 3, 4],
[5, 6, 7, 8]]
def y(i):
p = 2
total = 0
for j in range (4):
total += a[i][j] * (p**j)
return math.exp(total)
Solution 2: correctly decompose the exponent and change total += to total *=
import math
a = [[1, 2, 3, 4],
[5, 6, 7, 8]]
def y(i):
p = 2
total = 0
for j in range (4):
total *= math.exp(a[i][j] * (p**j))
return total
Solution 1 is more efficient, as it does not make duplicate calls to math.exp()
import math
a = [[1, 2, 3, 4],
[5, 6, 7, 8]]
def y(i):
p = 2
total = 1
for j in range (4):
total *= math.exp(a[i][j] * (p**j))
return total
Multiplication of exponentianals with same base is same with summing the power values.
exp(a+b)=exp(a)*exp(b)
Optimization of the code:
import math
a = [[1, 2, 3, 4],
[5, 6, 7, 8]]
def y(i):
p = 2
total = 0
for j in range (4):
total += a[i][j] * (p**j)
return math.exp(total)
Much better to simply compute the sum, then pass that as the argument to a single call to
math.exp.– chepner
Jun 29 at 18:00
math.exp
@chepner you are right but he is starter so i wrote first code because it is easier to find the false.
– MIRMIX
Jun 29 at 18:04
Note that the "optimized" code implements the mathematical formula directly.
– Code-Apprentice
Jun 29 at 18:05
@Code-Apprentice yes nice point.
– MIRMIX
Jun 29 at 18:06
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Can you post expected answer for this
– Venkata Gogu
Jun 29 at 17:47