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| 1 | +# Universal functions (ufunc) |
| 2 | + |
| 3 | +--- |
| 4 | + |
| 5 | +A `ufunc`, short for "`universal function`," is a fundamental concept in NumPy, a powerful library for numerical computing in Python. Universal functions are highly optimized, element-wise functions designed to perform operations on data stored in NumPy arrays. |
| 6 | + |
| 7 | + |
| 8 | + |
| 9 | +## Uses of Ufuncs in NumPy |
| 10 | + |
| 11 | +Universal functions (ufuncs) in NumPy provide a wide range of functionalities for efficient and powerful numerical computations. Below is a detailed explanation of their uses: |
| 12 | + |
| 13 | +### 1. **Element-wise Operations** |
| 14 | +Ufuncs perform operations on each element of the arrays independently. |
| 15 | + |
| 16 | +```python |
| 17 | +import numpy as np |
| 18 | + |
| 19 | +A = np.array([1, 2, 3, 4]) |
| 20 | +B = np.array([5, 6, 7, 8]) |
| 21 | + |
| 22 | +# Element-wise addition |
| 23 | +np.add(A, B) # Output: array([ 6, 8, 10, 12]) |
| 24 | +``` |
| 25 | + |
| 26 | +### 2. **Broadcasting** |
| 27 | +Ufuncs support broadcasting, allowing operations on arrays with different shapes, making it possible to perform operations without explicitly reshaping arrays. |
| 28 | + |
| 29 | +```python |
| 30 | +C = np.array([1, 2, 3]) |
| 31 | +D = np.array([[1], [2], [3]]) |
| 32 | + |
| 33 | +# Broadcasting addition |
| 34 | +np.add(C, D) # Output: array([[2, 3, 4], [3, 4, 5], [4, 5, 6]]) |
| 35 | +``` |
| 36 | + |
| 37 | +### 3. **Vectorization** |
| 38 | +Ufuncs are vectorized, meaning they are implemented in low-level C code, allowing for fast execution and avoiding the overhead of Python loops. |
| 39 | + |
| 40 | +```python |
| 41 | +# Vectorized square root |
| 42 | +np.sqrt(A) # Output: array([1., 1.41421356, 1.73205081, 2.]) |
| 43 | +``` |
| 44 | + |
| 45 | +### 4. **Type Flexibility** |
| 46 | +Ufuncs handle various data types and perform automatic type casting as needed. |
| 47 | + |
| 48 | +```python |
| 49 | +E = np.array([1.0, 2.0, 3.0]) |
| 50 | +F = np.array([4, 5, 6]) |
| 51 | + |
| 52 | +# Addition with type casting |
| 53 | +np.add(E, F) # Output: array([5., 7., 9.]) |
| 54 | +``` |
| 55 | + |
| 56 | +### 5. **Reduction Operations** |
| 57 | +Ufuncs support reduction operations, such as summing all elements of an array or finding the product of all elements. |
| 58 | + |
| 59 | +```python |
| 60 | +# Summing all elements |
| 61 | +np.add.reduce(A) # Output: 10 |
| 62 | + |
| 63 | +# Product of all elements |
| 64 | +np.multiply.reduce(A) # Output: 24 |
| 65 | +``` |
| 66 | + |
| 67 | +### 6. **Accumulation Operations** |
| 68 | +Ufuncs can perform accumulation operations, which keep a running tally of the computation. |
| 69 | + |
| 70 | +```python |
| 71 | +# Cumulative sum |
| 72 | +np.add.accumulate(A) # Output: array([ 1, 3, 6, 10]) |
| 73 | +``` |
| 74 | + |
| 75 | +### 7. **Reduceat Operations** |
| 76 | +Ufuncs can perform segmented reductions using the `reduceat` method, which applies the ufunc at specified intervals. |
| 77 | + |
| 78 | +```python |
| 79 | +G = np.array([0, 1, 2, 3, 4, 5, 6, 7]) |
| 80 | +indices = [0, 2, 5] |
| 81 | +np.add.reduceat(G, indices) # Output: array([ 1, 9, 18]) |
| 82 | +``` |
| 83 | + |
| 84 | +### 8. **Outer Product** |
| 85 | +Ufuncs can compute the outer product of two arrays, producing a matrix where each element is the result of applying the ufunc to each pair of elements from the input arrays. |
| 86 | + |
| 87 | +```python |
| 88 | +# Outer product |
| 89 | +np.multiply.outer([1, 2, 3], [4, 5, 6]) |
| 90 | +# Output: array([[ 4, 5, 6], |
| 91 | +# [ 8, 10, 12], |
| 92 | +# [12, 15, 18]]) |
| 93 | +``` |
| 94 | + |
| 95 | +### 9. **Out Parameter** |
| 96 | +Ufuncs can use the `out` parameter to store results in a pre-allocated array, saving memory and improving performance. |
| 97 | + |
| 98 | +```python |
| 99 | +result = np.empty_like(A) |
| 100 | +np.multiply(A, B, out=result) # Output: array([ 5, 12, 21, 32]) |
| 101 | +``` |
| 102 | + |
| 103 | +# Create Your Own Ufunc |
| 104 | + |
| 105 | +You can create custom ufuncs for specific needs using np.frompyfunc or np.vectorize, allowing Python functions to behave like ufuncs. |
| 106 | + |
| 107 | +Here, we are using `frompyfunc()` which takes three argument: |
| 108 | + |
| 109 | +1. function - the name of the function. |
| 110 | +2. inputs - the number of input (arrays). |
| 111 | +3. outputs - the number of output arrays. |
| 112 | + |
| 113 | +```python |
| 114 | +def my_add(x, y): |
| 115 | + return x + y |
| 116 | + |
| 117 | +my_add_ufunc = np.frompyfunc(my_add, 2, 1) |
| 118 | +my_add_ufunc(A, B) # Output: array([ 6, 8, 10, 12], dtype=object) |
| 119 | +``` |
| 120 | +# Some Common Ufunc are |
| 121 | + |
| 122 | +Here are some commonly used ufuncs in NumPy: |
| 123 | + |
| 124 | +- **Arithmetic**: `np.add`, `np.subtract`, `np.multiply`, `np.divide` |
| 125 | +- **Trigonometric**: `np.sin`, `np.cos`, `np.tan` |
| 126 | +- **Exponential and Logarithmic**: `np.exp`, `np.log`, `np.log10` |
| 127 | +- **Comparison**: `np.maximum`, `np.minimum`, `np.greater`, `np.less` |
| 128 | +- **Logical**: `np.logical_and`, `np.logical_or`, `np.logical_not` |
| 129 | + |
| 130 | +For more such Ufunc, address to [Universal functions (ufunc) — NumPy](https://numpy.org/doc/stable/reference/ufuncs.html) |
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