Combinatorics
Calculate combinatorial quantities for integer inputs.
SciPy · Function
special.factorial
Computes the factorial of a number or array of numbers. It can use exact integer arithmetic or a faster floating-point approximation.
How it works
factorial computes the product of the positive integers through each non-negative input. With exact=False it uses the gamma-function relationship for a faster floating-point result; exact=True uses integer arithmetic and preserves exact values.
Syntax
scipy.special.factorial(n, exact=False)Parameters
| Name | Type | Description |
|---|---|---|
n | int or array_like of ints | Input value or array of values for which to compute the factorial. |
exact | bool, optional | If True, use exact long-integer arithmetic; otherwise use a floating-point approximation. |
Returns
float or int or ndarray — Factorial of n, as an integer or float depending on exact.
Key points
- The function supports scalar values as well as arrays.
- For a non-negative integer, the result multiplies every positive integer up to n.
- Set exact=True when integer precision is required.
- The calculation uses approximate mode unless exact is explicitly enabled.
- The result representation depends on the exact flag.
- Approximate mode is implemented through the gamma-function relationship.
Common mistakes
- Negative inputs produce 0 under the documented behavior.
Example: Exact and approximate factorials
import numpy as np
from scipy.special import factorial
values = np.array([3, 4, 5])
print(factorial(values, exact=True))
print(factorial(5))Computes exact factorials for an integer array and the default floating-point result for a scalar.
When to use it
Vectorized numerical computation
Apply factorial elementwise to a NumPy array.
Exact arithmetic
Choose exact integer results when rounding errors are unacceptable.
Interview questions
QWhat does scipy.special.factorial compute?
It accepts an integer or an array-like collection of integers and returns the corresponding factorial. For an array input, the result is an array with matching elementwise factorial values.
Follow-up: How can the result type change? With exact=True, results use integer arithmetic; with exact=False, results are floating-point approximations.
QWhat is the purpose of the exact argument?
exact controls the calculation method. True requests exact long-integer arithmetic, while False uses a faster floating-point approximation based on the gamma function.
Follow-up: Why might exact=False be preferable? It is faster and suitable when floating-point output and approximation are acceptable.
QWhat does factorial return for negative inputs and arrays?
The function returns a float, int, or ndarray depending on the input and exact setting. Negative n values return 0, according to the documented behavior.
Follow-up: What happens for an array containing negative values? Each negative element follows the same documented rule and contributes 0 to the output array.
Related
scipy.special.gamma