NumPy Universal Functions with Examples
Python’s NumPy library is essential for performing numerical calculations. Among its many capabilities, NumPy offers a potent utility known as “Universal Functions,” or “ufuncs.” NumPy is a flexible and high-performance library thanks to Ufuncs, which are essential for effectively carrying out element-wise operations on arrays.
We’ll discuss what ufuncs are, what they perform, and their parameters in this blog post. We’ll also include a table of frequently used ufuncs, along with in-depth descriptions, sample code, and expected outcomes.
What Are Ufuncs in NumPy?
A fundamental component of NumPy that enables element-wise operations on arrays is known as ufuncs. These operations are performed on array items by using a vectorized form of the stated operation. This results in efficient and clear code because the identical operation is carried out on every element of the array without the need for explicit loops.
What Do Ufuncs (Universal Functions) Do?
Numerous mathematical, logical, and bitwise operations are carried out on NumPy arrays by Ufuncs. Because they use highly optimised C and Fortran implementations to power calculations, they are very helpful when working with enormous datasets.
Ufunc Parameters: Ufuncs typically take one or more NumPy arrays as input and return a new array as output. The common parameters for ufuncs include:
x and y (optional): Input arrays.
out (optional): Specifies where to store the result. It allows for in-place operations.
where (optional): A boolean condition that controls which elements are operated on.
Ufunc’s other optional keywords:
‘casting’ (new in v1.6): Determines the casting policy (‘no’, ‘equiv’, ‘safe’, ‘same_kind’, or ‘unsafe’).
‘order’ (new in v1.6): Specifies the memory layout of the output (‘C’, ‘F’, ‘A’, or ‘K’).
‘dtype’ (new in v1.6): Overrides the data type of calculation and output arrays.
‘subok’ (new in v1.6): If false, ensure the output is a strict array, not a subtype.
‘signature’: Provides a specific data type signature for ufunc input and output types.
‘extobj’: Specifies ufunc buffer size, error mode integer, and error callback function. Useful for optimization in certain cases.
Various types of Ufuncs:
NumPy’s Universal Functions (ufuncs) cover a wide range of operations, making them a versatile tool for performing element-wise operations on arrays. These ufuncs can be categorized into several types based on their primary functionality:
Arithmetic Ufuncs:
1. np.add: Element-wise addition.
2. np.subtract: Element-wise subtraction.
3. np.multiply: Element-wise multiplication.
4. np.divide: Element-wise division.
5. np.floor_divide: Element-wise floor division.
6. np.power: Element-wise exponentiation.
7. np.mod: Element-wise modulo operation.
8. np.abs: Element-wise absolute value.
9. np.negative: Element-wise negation.
Mathematical Ufuncs:
1. np.sqrt: Square root of each element.
2. np.exp: Exponential function (e^x) for each element.
3. np.log, np.log10, np.log2: Natural logarithm, base-10 logarithm, and base-2 logarithm, respectively.
4. np.sin, np.cos, np.tan: Trigonometric functions.
5. np.arcsin, np.arccos, np.arctan: Inverse trigonometric functions.
6. np.sinh, np.cosh, np.tanh: Hyperbolic trigonometric functions.
7. np.arcsinh, np.arccosh, np.arctanh: Inverse hyperbolic trigonometric functions.
Comparative Ufuncs:
1. np.greater, np.greater_equal: Element-wise comparison for greater than and greater than or equal to.
2. np.less, np.less_equal: Element-wise comparison for less than and less than or equal to.
3. np.equal, np.not_equal: Element-wise comparison for equality and inequality.
Logical Ufuncs:
1. np.logical_and, np.logical_or, np.logical_xor: Element-wise logical operations.
2. np.logical_not: Element-wise logical NOT operation.
Bitwise Ufuncs:
1. np.bitwise_and, np.bitwise_or, np.bitwise_xor: Element-wise bitwise operations.
2. np.invert: Element-wise bitwise NOT operation (bitwise inversion).
Rounding and Truncation Ufuncs:
1. np.round: Round elements to the nearest integer or specified number of decimals.
2. np.floor: Round elements down to the nearest integer.
3. np.ceil: Round elements up to the nearest integer.
4. np.trunc: Truncate decimal values, keeping only the integer part.
Statistical Ufuncs:
1. np.mean, np.median: Compute the mean and median of array elements.
2. np.min, np.max: Finds the minimum and maximum values present in an array.
3. np.std, np.var: Calculate the standard deviation and variance of elements.
Special Ufuncs:
1. np.isnan: Check for NaN (Not-a-Number) values in an array.
2. np.isinf: Check for infinity values in an array.
3. np.isfinite: Check for finite values in an array.
4. np.unique: Find unique elements in an array.
Trigonometric and Hyperbolic Ufuncs:
1. np.deg2rad, np.rad2deg: Convert between degrees and radians.
2. np.hypot: Calculate the hypotenuse of right triangles.
Common Ufuncs
Here’s a table of some frequently used ufuncs along with their descriptions:
| Ufunc Name | Description | Example Code | Expected Output |
| np.add | Element-wise addition of two arrays. | np.add([1, 2, 3], [4, 5, 6]) | [5, 7, 9] |
| np.subtract | Element-wise subtraction of two arrays. | np.subtract([4, 5, 6], [1, 2, 3]) | [3, 3, 3] |
| np.multiply | Element-wise multiplication of two arrays. | np.multiply([1, 2, 3], [4, 5, 6]) | [4, 10, 18] |
| np.divide | Element-wise division of two arrays. | np.divide([4, 5, 6], [1, 2, 3]) | [4.0, 2.5, 2.0] |
| np.sqrt | Provides the square root of each element in an array. | np.sqrt([4, 9, 16]) | [2.0, 3.0, 4.0] |
| np.exp | Exponential function (e^x) for each element. | np.exp([1, 2, 3]) | [2.71828183, 7.3890561, 20.08553692] |
| np.sin | Sine of each element in an array. | np.sin([0, np.pi/2, np.pi]) | [0.0, 1.0, 0.0] |
| np.cos | Cosine of each element in an array. | np.cos([0, np.pi/2, np.pi]) | [1.0, 0.0, -1.0] |
| np.logical_and | Element-wise logical AND between two arrays. | np.logical_and([True, True, False], [True, False, False]) | [True, False, False] |
Example Code and Outputs
import numpy as np
# Example arrays
arr1 = np.array([1, 2, 3])
arr2 = np.array([4, 5, 6])
# Element-wise addition
result_add = np.add(arr1, arr2)
print("Element-wise addition:", result_add)
# Element-wise multiplication
result_multiply = np.multiply(arr1, arr2)
print("Element-wise multiplication:", result_multiply)
# Square root
result_sqrt = np.sqrt(arr1)
print("Square root:", result_sqrt)
# Element-wise logical AND
result_logical_and = np.logical_and([True, True, False], [True, False, False])
print("Element-wise logical AND:", result_logical_and)
Expected Outputs:
Element-wise addition: [5 7 9]
Element-wise multiplication: [ 4 10 18]
Square root: [1. 1.41421356 1.73205081]
Element-wise logical AND: [ True False False]
Conclusion:
These are only a few of the NumPy ufuncs that are often used. The efficient design of Ufuncs makes it possible to execute vectorized operations on arrays, substantially simplifying your code and enhancing speed when handling huge datasets. Effective data manipulation and scientific computing in Python require an understanding of the various ufuncs and how to apply them.
Hope this guide gives you an insight on how to use them in your code. Happy Coding!