Merge pull request #1093 from Yogeshkarma/main

Added the Universal Functions file under NumPy directory

contrib/numpy/index.md

@@ -11,3 +11,4 @@
 - [Sorting NumPy Arrays](sorting-array.md)
 - [NumPy Array Iteration](array-iteration.md)
 - [Concatenation of Arrays](concatenation-of-arrays.md)
+- [Universal Functions (Ufunc)](universal-functions.md)

contrib/numpy/universal-functions.md

@@ -0,0 +1,130 @@
+# Universal functions (ufunc)
+
+---
+
+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. 
+
+
+
+## Uses of Ufuncs in NumPy
+
+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:
+
+### 1. **Element-wise Operations**
+Ufuncs perform operations on each element of the arrays independently.
+
+```python
+import numpy as np
+
+A = np.array([1, 2, 3, 4])
+B = np.array([5, 6, 7, 8])
+
+# Element-wise addition
+np.add(A, B)  # Output: array([ 6,  8, 10, 12])
+```
+
+### 2. **Broadcasting**
+Ufuncs support broadcasting, allowing operations on arrays with different shapes, making it possible to perform operations without explicitly reshaping arrays.
+
+```python
+C = np.array([1, 2, 3])
+D = np.array([[1], [2], [3]])
+
+# Broadcasting addition
+np.add(C, D)  # Output: array([[2, 3, 4], [3, 4, 5], [4, 5, 6]])
+```
+
+### 3. **Vectorization**
+Ufuncs are vectorized, meaning they are implemented in low-level C code, allowing for fast execution and avoiding the overhead of Python loops.
+
+```python
+# Vectorized square root
+np.sqrt(A)  # Output: array([1., 1.41421356, 1.73205081, 2.])
+```
+
+### 4. **Type Flexibility**
+Ufuncs handle various data types and perform automatic type casting as needed.
+
+```python
+E = np.array([1.0, 2.0, 3.0])
+F = np.array([4, 5, 6])
+
+# Addition with type casting
+np.add(E, F)  # Output: array([5., 7., 9.])
+```
+
+### 5. **Reduction Operations**
+Ufuncs support reduction operations, such as summing all elements of an array or finding the product of all elements.
+
+```python
+# Summing all elements
+np.add.reduce(A)  # Output: 10
+
+# Product of all elements
+np.multiply.reduce(A)  # Output: 24
+```
+
+### 6. **Accumulation Operations**
+Ufuncs can perform accumulation operations, which keep a running tally of the computation.
+
+```python
+# Cumulative sum
+np.add.accumulate(A)  # Output: array([ 1,  3,  6, 10])
+```
+
+### 7. **Reduceat Operations**
+Ufuncs can perform segmented reductions using the `reduceat` method, which applies the ufunc at specified intervals.
+
+```python
+G = np.array([0, 1, 2, 3, 4, 5, 6, 7])
+indices = [0, 2, 5]
+np.add.reduceat(G, indices)  # Output: array([ 1,  9, 18])
+```
+
+### 8. **Outer Product**
+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.
+
+```python
+# Outer product
+np.multiply.outer([1, 2, 3], [4, 5, 6])  
+# Output: array([[ 4,  5,  6],
+#                [ 8, 10, 12],
+#                [12, 15, 18]])
+```
+
+### 9. **Out Parameter**
+Ufuncs can use the `out` parameter to store results in a pre-allocated array, saving memory and improving performance.
+
+```python
+result = np.empty_like(A)
+np.multiply(A, B, out=result)  # Output: array([ 5, 12, 21, 32])
+```
+
+# Create Your Own Ufunc
+
+You can create custom ufuncs for specific needs using np.frompyfunc or np.vectorize, allowing Python functions to behave like ufuncs.
+
+Here, we are using `frompyfunc()` which takes three argument:
+
+1. function - the name of the function.
+2. inputs - the number of input  (arrays).
+3. outputs - the number of output arrays.
+
+```python
+def my_add(x, y):
+    return x + y
+
+my_add_ufunc = np.frompyfunc(my_add, 2, 1)
+my_add_ufunc(A, B)  # Output: array([ 6,  8, 10, 12], dtype=object)
+```
+# Some Common Ufunc are
+
+Here are some commonly used ufuncs in NumPy:
+
+- **Arithmetic**: `np.add`, `np.subtract`, `np.multiply`, `np.divide`
+- **Trigonometric**: `np.sin`, `np.cos`, `np.tan`
+- **Exponential and Logarithmic**: `np.exp`, `np.log`, `np.log10`
+- **Comparison**: `np.maximum`, `np.minimum`, `np.greater`, `np.less`
+- **Logical**: `np.logical_and`, `np.logical_or`, `np.logical_not`
+
+For more such Ufunc, address to  [Universal functions (ufunc) — NumPy](https://numpy.org/doc/stable/reference/ufuncs.html)