## How can I make a combined power function faster?

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I made this function pretty quickly to find the combined powers of everything in a list, but I'm pretty sure there is a way to make it faster. It returns a 2 item list, with the combined powers and the list formatted for export.

```#The input for this function is a list of numbers (but string data type)
def find(x):
total = int(x[0])
for i in range (1,len(x)):
total = total ** int(x[i])
value = [total,'^'.join(x)]
return value
```

This will calculate the values faster than what you currently have:

```import functools
import operator

l = [2, 3, 4]

functools.reduce(operator.pow, l)
## 4096
```

If you want to show the chain of values in the list too, as in the original post, you can define a function e.g. like this one:

```def func(vals):
vals_string = '^'.join(str(val) for val in vals)
total = functools.reduce(operator.pow, vals)
return [total, vals_string]
```

Usage example:

```l = [2, 3, 4, 5]
result = func(l)
print(result)
## [1152921504606846976, '2^3^4^5']
```

Raise numbers to a power: here's how to exponentiate , Example: do exponentiation in Python with ** Calculate Python exponents with the pow() function A quick example of math.pow() is:. The only way to get data into PBI is through power Query. PBI has power query and power pivot as modelling tools. Unlike excel version, you cannot bring data directly in Power Pivot, so you have a query from a website. (google sheets in your case). If the refresh time is slow, then the query is slow.

You want to avoid doing a stack of exponentiations, as those are expensive. Multiplication is cheaper, so you can save computing power by multiplying all the values to the right of the first one, and then raising the first to that power.

```from functools import reduce
from operator import mul
from typing import List

def find(x: List[int]) -> int:
return x[0]**reduce(mul, x[1:], 1)
```

You could also do

```def find(i: int, *updog: int) -> int:
return i ** reduce(mul, updog, 1)
```

and call it like `find(*[2,1,2,3,4])` or `find(2, 1, 2, 3)`.

Either way, this uses the function signature to provide a stricter guarantee that the initial value is set, rather than having undefined behavior if the list is empty.

Wow, a big C/C++ code speedup!!!, I'm not sure about you all, but I use the function "pow( double, Its entirly possible that that compilier can make the function as fast as to write an implementation which combined the performance benefits from both of them. A combined-cycle power plant uses both a gas and a steam turbine together to produce up to 50 percent more electricity from the same fuel than a traditional simple-cycle plant. The waste heat from the gas turbine is routed to the nearby steam turbine, which generates extra power. Improve Performance with Digital

You can use NumPy's `power.accumulate()` to have cumulative exponents. However, you will soon run into large numbers for a large input list. The `[-1]` here gives you the cumulative of all the elements

```import numpy as np

def find(x):
total = np.power.accumulate(x)[-1]
value = [total,'^'.join(map(str, inp))]
return value

x = np.array([2,3,4,5])

print (find(x))
# [1152921504606846976, '2^3^4^5']
```

Modular Exponentiation in Python, Pow function calculates in O(log n) time in python but it takes a lot of time when the value of xy and then mod it with p to get (xy) % p evaluated. the (%) operator takes a lot of time, so a Fast Modular Exponentiation is used. of Non- Zero elements in Python list � Python | Merge Python key values to list� Power query will then show all the items available to the workbook. This will include all the power query functions! If you click on any of the functions listed, you’ll be taken to a mini help guide for that function. The function name is shown. There is a brief description of what the function does. You can test out the function on your data.

You can use `functools.reduce()`:

```from functools import reduce
import operator

reduce(operator.pow, list)
```

What `reduce()` does is it applies the first parameter to every element in the second.

Powers, exponentials, and logs, Do you still believe the statement? Make the x scale big and the y scale huge! The function e-x decreases faster at infinity than any negative power. Plot y = e-x � Here’s the deal: You can use POWER QUERY to match two column and get values (By using Merge Option). Yes, you heard it right, you can do VLOOKUP in Power Query. As you know: “VLOOKUP matches values from a column and then return the values from the same row of the different column or from the same column.”

3.4: Power Functions and Polynomial Functions, Both of these are examples of power functions because they consist of a The behavior of the graph of a function as the input values get very We want to write a formula for the area covered by the oil slick by combining two functions. that term will grow significantly faster than the other terms as x gets� The quotient rule is D (f/g) = [gD (f) - fD (g)]/ g^2. You take the function on the bottom and multiply it by the derivative of the function on the top. Then you subtract the function of the top multiplied by the derivative of the bottom function. Then you divide all of that by the function on the bottom squared.

This popular technique has been made more convenient and more expansive. To start the process of combining files from the same folder, select Get Data, choose File > Folder, and then select Connect. Enter the folder path, select OK, and then select Transform Data to see the folder's files in Power Query Editor.

We vary f and g indepdendently and combine the results, and ignore results from them moving together. The Chain Rule: It's Not So Bad. Let's say g depends on f, which depends on x: The chain rule lets us "zoom into" a function and see how an initial change (x) can effect the final result down the line (g). Interpretation 1: Convert the rates

• line 5 raises: `TypeError: sequence item 0: expected str instance, int found` when I use input `[1,2,3,4]`
• This appears to be written to take a list of string representations of integers, not a list of integers. Also, it's backwards from the usual convention for powers - `2^3^4` usually means `2^(3^4)`, but you're computing `(2^3)^4`.
• I think you forgot to handle the case where `len(x) == 1`. Other than that, this is a valid simplification.
• Adding the extra argument for `reduce` is definitely good. I'm not so sure about the empty-`x` handling - I would be more inclined to raise an exception. I don't see a strong argument for `find([]) == 1` making sense.
• @user2357112 I have supplied an alternative approach that separates out the first value. I think I prefer it because it makes it really stinking obvious and strict that that first value has to exist for the thing to make sense. Sure, we could raise an `IndexError`, but a `TypeError: find() missing 1 required positional argument` is much clearer IMO.
• First, NumPy ufuncs have a `reduce` method that's more appropriate than `accumulate`. Second, the results quickly overflow the largest data type NumPy offers.
• the description of `reduce()` is how i'd describe what `map()` does... note that `reduce()` works on binary functions, whereas map doesn't have to. from the official docs for functools.reduce(): "Apply function of two arguments cumulatively to the items of sequence, from left to right, so as to reduce the sequence to a single value."