numpy-part-2-of-5-indepth-notebook.ipynb

{"cells":[{"source":"<a href=\"https://www.kaggle.com/code/mlvprasad/numpy-part-2-of-5-indepth-notebook?scriptVersionId=141318380\" target=\"_blank\"><img align=\"left\" alt=\"Kaggle\" title=\"Open in Kaggle\" src=\"https://kaggle.com/static/images/open-in-kaggle.svg\"></a>","metadata":{},"cell_type":"markdown"},{"cell_type":"markdown","id":"98ad1d61","metadata":{"papermill":{"duration":0.012884,"end_time":"2023-08-29T06:24:42.278056","exception":false,"start_time":"2023-08-29T06:24:42.265172","status":"completed"},"tags":[]},"source":["![mlv prasad](https://github.com/MlvPrasadOfficial/kaggle_notebooks/raw/main/mlvprasad.png)\n"]},{"cell_type":"markdown","id":"53686e4e","metadata":{"papermill":{"duration":0.011802,"end_time":"2023-08-29T06:24:42.302204","exception":false,"start_time":"2023-08-29T06:24:42.290402","status":"completed"},"tags":[]},"source":["![pandas](https://github.com/MlvPrasadOfficial/ZZPYCHARM/raw/main/canvapandasnumpy/NUMPY22.png)\n"]},{"cell_type":"markdown","id":"3525b70f","metadata":{"papermill":{"duration":0.011804,"end_time":"2023-08-29T06:24:42.326236","exception":false,"start_time":"2023-08-29T06:24:42.314432","status":"completed"},"tags":[]},"source":["# <font color='289C4E'>TABLE OF CONTENTS<font><a class='anchor' id='top'></a>"]},{"cell_type":"markdown","id":"b4e8460c","metadata":{"papermill":{"duration":0.011774,"end_time":"2023-08-29T06:24:42.350243","exception":false,"start_time":"2023-08-29T06:24:42.338469","status":"completed"},"tags":[]},"source":["\n","21. [Chapter 21: Masking and Boolean Logic with Arrays](#chapter-21-masking-and-boolean-logic-with-arrays)\n","22. [Chapter 22: Indexing and Filtering with Boolean Arrays](#chapter-22-indexing-and-filtering-with-boolean-arrays)\n","23. [Chapter 23: Combining Masks and Boolean Operations](#chapter-23-combining-masks-and-boolean-operations)\n","24. [Chapter 24: Working with Masked Arrays](#chapter-24-working-with-masked-arrays)\n","25. [Chapter 25: Linear Algebra Operations with NumPy](#chapter-25-linear-algebra-operations-with-numpy)\n","26. [Chapter 26: Matrix and Vector Operations](#chapter-26-matrix-and-vector-operations)\n","27. [Chapter 27: Solving Linear Equations with NumPy](#chapter-27-solving-linear-equations-with-numpy)\n","28. [Chapter 28: Eigenvalues and Eigenvectors](#chapter-28-eigenvalues-and-eigenvectors)\n","29. [Chapter 29: Random Number Generation in NumPy](#chapter-29-random-number-generation-in-numpy)\n","30. [Chapter 30: Generating Random Arrays](#chapter-30-generating-random-arrays)\n","31. [Chapter 31: Random Sampling Techniques](#chapter-31-random-sampling-techniques)\n","32. [Chapter 32: Working with Random Distributions](#chapter-32-working-with-random-distributions)\n","33. [Chapter 33: Performance Optimization in NumPy](#chapter-33-performance-optimization-in-numpy)\n","34. [Chapter 34: Tips for Array Performance Improvement](#chapter-34-tips-for-array-performance-improvement)\n","35. [Chapter 35: Broadcasting for Efficiency](#chapter-35-broadcasting-for-efficiency)\n","36. [Chapter 36: Vectorized Functions for Performance](#chapter-36-vectorized-functions-for-performance)\n","37. [Chapter 37: Memory Optimization Techniques](#chapter-37-memory-optimization-techniques)\n","38. [Chapter 38: Integrating NumPy with pandas](#chapter-38-integrating-numpy-with-pandas)\n","39. [Chapter 39: NumPy Integration with scikit-learn](#chapter-39-numpy-integration-with-scikit-learn)\n","40. [Chapter 40: Visualization with NumPy Arrays](#chapter-40-visualization-with-numpy-arrays)\n"]},{"cell_type":"markdown","id":"86dd2fec","metadata":{"papermill":{"duration":0.011765,"end_time":"2023-08-29T06:24:42.37586","exception":false,"start_time":"2023-08-29T06:24:42.364095","status":"completed"},"tags":[]},"source":["<h1 align=\"center\"><font color='red'>Let's Begin</font></h1>\n"]},{"cell_type":"markdown","id":"781f87a5","metadata":{"papermill":{"duration":0.012207,"end_time":"2023-08-29T06:24:42.400843","exception":false,"start_time":"2023-08-29T06:24:42.388636","status":"completed"},"tags":[]},"source":["# <h1 align=\"left\"><font color='red'>21 </font></h1>"]},{"cell_type":"markdown","id":"c76540d8","metadata":{"papermill":{"duration":0.011878,"end_time":"2023-08-29T06:24:42.425049","exception":false,"start_time":"2023-08-29T06:24:42.413171","status":"completed"},"tags":[]},"source":["\n","\n","# Chapter 21: Masking and Boolean Logic with Arrays\n","\n","## 21.1 Introduction:\n","### Chapter 21 focuses on masking and boolean logic with arrays in NumPy. Masking allows you to select elements from an array based on a specific condition, while boolean logic enables you to perform logical operations on arrays. These operations are valuable for data filtering, conditional computations, and data analysis.\n","\n","## 21.2 Masking Arrays:\n","### NumPy provides various functions and techniques for masking arrays based on certain conditions. The most commonly used function for masking is np.where().\n","\n","## 21.2.1 np.where():\n","### The np.where() function allows you to create a new array by selecting elements from two different arrays based on a given condition. It takes three arguments: the condition, the array to select values from when the condition is True, and the array to select values from when the condition is False. Here's an example:\n","\n","```python\n","import numpy as np\n","\n","arr = np.array([1, 2, 3, 4, 5])\n","mask = np.where(arr > 2, arr, 0)\n","print(mask)\n","```\n","### In this example, the np.where() function is used to create a new array mask by selecting values from the array arr where the condition arr > 2 is True. When the condition is True, the corresponding value from arr is selected, otherwise, 0 is selected. The resulting masked array is then printed.\n","\n","## 21.3 Boolean Logic with Arrays:\n","### NumPy allows you to perform boolean logic operations on arrays using logical operators such as np.logical_and(), np.logical_or(), and np.logical_not().\n","\n","## 21.3.1 np.logical_and():\n","### The np.logical_and() function performs an element-wise logical AND operation on two arrays. It takes two arrays as arguments and returns a new array with the result of the logical AND operation. Here's an example:\n","\n","```python \n","import numpy as np\n","\n","arr1 = np.array([True, True, False, False])\n","arr2 = np.array([True, False, True, False])\n","result = np.logical_and(arr1, arr2)\n","print(result)\n","```\n","\n","### In this example, the np.logical_and() function is used to perform an element-wise logical AND operation on arr1 and arr2. The resulting array contains the result of the logical AND operation between corresponding elements of arr1 and arr2, and it is then printed.\n","\n","## 21.3.2 np.logical_or():\n","### The np.logical_or() function performs an element-wise logical OR operation on two arrays. It takes two arrays as arguments and returns a new array with the result of the logical OR operation. Here's an example:\n","\n","```python\n","import numpy as np\n","\n","arr1 = np.array([True, True, False, False])\n","arr2 = np.array([True, False, True, False])\n","result = np.logical_or(arr1, arr2)\n","print(result)\n","``` \n","### In this example, the np.logical_or() function is used to perform an element-wise logical OR operation on arr1 and arr2. The resulting array contains the result of the logical OR operation between corresponding elements of arr1 and arr2, and it is then printed.\n","\n","## 21.3.3 np.logical_not():\n","### The np.logical_not() function performs an element-wise logical NOT operation on an array. It takes one array as an argument and returns a new array with the result of the logical NOT operation. Here's an example:\n","\n","```python\n","import numpy as np\n","\n","arr = np.array([True, False, True, False])\n","result = np.logical_not(arr)\n","print(result)\n","```\n","### In this example, the np.logical_not() function is used to perform an element-wise logical NOT operation on arr. The resulting array contains the logical NOT of each element of arr, and it is then printed.\n","\n","## 21.4 Conclusion:\n","### Chapter 21 explored masking and boolean logic with arrays in NumPy, providing powerful tools for data filtering and conditional computations. The np.where() function enables the creation of masked arrays based on specific conditions, allowing for flexible data selection and manipulation. Boolean logic operations such as np.logical_and(), np.logical_or(), and np.logical_not() facilitate element-wise logical operations on arrays, enabling advanced data analysis and decision-making. Understanding and utilizing these masking and boolean logic techniques in NumPy empower efficient data filtering, conditional computations, and data analysis, enhancing the capabilities of array-based data processing and manipulation.\n","\n","\n"]},{"cell_type":"markdown","id":"bb512f8c","metadata":{"papermill":{"duration":0.011871,"end_time":"2023-08-29T06:24:42.449215","exception":false,"start_time":"2023-08-29T06:24:42.437344","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>22 </font></h1>"]},{"cell_type":"markdown","id":"8d47eaff","metadata":{"papermill":{"duration":0.011897,"end_time":"2023-08-29T06:24:42.473218","exception":false,"start_time":"2023-08-29T06:24:42.461321","status":"completed"},"tags":[]},"source":["# Chapter 22: Indexing and Filtering with Boolean Arrays\n","\n","## 22.1 Introduction:\n","### Chapter 22 focuses on indexing and filtering arrays using boolean arrays in NumPy. Boolean arrays allow you to create masks based on specific conditions and use them to index or filter elements from an array. This is a powerful technique for selective data retrieval and manipulation.\n","\n","## 22.2 Creating Boolean Arrays:\n","### Boolean arrays can be created by applying conditional operations on arrays or using comparison operators.\n","\n","## 22.2.1 Conditional Operations:\n","### You can use conditional operations to create boolean arrays based on specific conditions. For example:\n","\n","```python \n","import numpy as np\n","\n","arr = np.array([1, 2, 3, 4, 5])\n","condition = arr > 3\n","print(condition)\n","```\n","\n","### In this example, the condition arr > 3 creates a boolean array that checks whether each element of arr is greater than 3. The resulting boolean array condition is then printed.\n","\n","## 22.2.2 Comparison Operators:\n","### Comparison operators can also be used to create boolean arrays by comparing arrays with specific values. For example:\n","\n","```python \n","import numpy as np\n","\n","arr = np.array([1, 2, 3, 4, 5])\n","boolean_arr = arr == 3\n","print(boolean_arr)\n","```\n","### In this example, the comparison arr == 3 creates a boolean array that checks whether each element of arr is equal to 3. The resulting boolean array boolean_arr is then printed.\n","\n","## 22.3 Indexing and Filtering with Boolean Arrays:\n","### Boolean arrays can be used to index or filter elements from an array by passing them as an index.\n","\n","```python\n","import numpy as np\n","\n","arr = np.array([1, 2, 3, 4, 5])\n","condition = arr > 3\n","filtered_arr = arr[condition]\n","print(filtered_arr)\n","``` \n","### In this example, the boolean array condition is used as an index for the array arr. The resulting filtered_arr contains only the elements from arr that satisfy the condition arr > 3, and it is then printed.\n","\n","## 22.4 Combining Boolean Arrays:\n","### Boolean arrays can be combined using logical operators such as & (logical AND) and | (logical OR) to create more complex conditions.\n","\n","```python\n","import numpy as np\n","\n","arr = np.array([1, 2, 3, 4, 5])\n","condition1 = arr > 2\n","condition2 = arr < 5\n","combined_condition = condition1 & condition2\n","filtered_arr = arr[combined_condition]\n","print(filtered_arr)\n","```\n","### In this example, two boolean arrays condition1 and condition2 are combined using the logical AND operator &. The resulting combined_condition checks whether each element of arr is greater than 2 and less than 5. The combined condition is then used to filter the elements from arr, resulting in the filtered_arr, which is printed.\n","\n","## 22.5 Conclusion:\n","### Chapter 22 explored indexing and filtering arrays using boolean arrays in NumPy. Boolean arrays provide a powerful mechanism for selective data retrieval and manipulation based on specific conditions. By creating boolean arrays using conditional operations or comparison operators, elements can be filtered or indexed from arrays. The resulting boolean arrays can be combined using logical operators to create more complex conditions. Understanding and utilizing these techniques in NumPy enable efficient data filtering, conditional computations, and data analysis, allowing for selective and targeted operations on array-based data.\n","\n","\n"]},{"cell_type":"markdown","id":"517ebafd","metadata":{"papermill":{"duration":0.011807,"end_time":"2023-08-29T06:24:42.497136","exception":false,"start_time":"2023-08-29T06:24:42.485329","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>23 </font></h1>"]},{"cell_type":"markdown","id":"76d04bbc","metadata":{"papermill":{"duration":0.011871,"end_time":"2023-08-29T06:24:42.52126","exception":false,"start_time":"2023-08-29T06:24:42.509389","status":"completed"},"tags":[]},"source":["# Chapter 23: Combining Masks and Boolean Operations\n","\n","## 23.1 Introduction:\n","### Chapter 23 focuses on combining masks and boolean operations in NumPy. Masks are boolean arrays that indicate which elements to select or exclude from an array based on specific conditions. By combining masks and performing boolean operations, you can create complex conditions for data manipulation and analysis.\n","\n","## 23.2 Combining Masks with Boolean Operators:\n","### Boolean operators such as logical AND (&), logical OR (|), and logical NOT (~) can be used to combine masks and create more complex conditions.\n","\n","## 23.2.1 Logical AND (&):\n","### The logical AND operator (&) combines two masks element-wise and returns a new mask with elements that are True only if both corresponding elements in the two masks are True.\n","\n","```python \n","import numpy as np\n","\n","mask1 = np.array([True, False, True, False])\n","mask2 = np.array([True, True, False, False])\n","combined_mask = mask1 & mask2\n","print(combined_mask)\n","```\n","\n","### In this example, the logical AND operator (&) is used to combine mask1 and mask2. The resulting combined_mask contains elements that are True only if the corresponding elements in both mask1 and mask2 are True.\n","\n","## 23.2.2 Logical OR (|):\n","### The logical OR operator (|) combines two masks element-wise and returns a new mask with elements that are True if at least one of the corresponding elements in the two masks is True.\n","\n","```python \n","import numpy as np\n","\n","mask1 = np.array([True, False, True, False])\n","mask2 = np.array([True, True, False, False])\n","combined_mask = mask1 | mask2\n","print(combined_mask)\n","```\n","\n","### In this example, the logical OR operator (|) is used to combine mask1 and mask2. The resulting combined_mask contains elements that are True if at least one of the corresponding elements in both mask1 and mask2 is True.\n","\n","## 23.2.3 Logical NOT (~):\n","### The logical NOT operator (~) negates a mask, flipping True values to False and vice versa.\n","\n","\n","```python \n","import numpy as np\n","\n","mask = np.array([True, False, True, False])\n","negated_mask = ~mask\n","print(negated_mask)\n","```\n","### In this example, the logical NOT operator (~) is used to negate the mask. The resulting negated_mask contains elements that are True where the original mask had False, and False where the original mask had True.\n","\n","## 23.3 Combining Masks and Boolean Operations:\n","### Masks can be combined with boolean operations to create more complex conditions for data manipulation.\n","\n","```python\n","import numpy as np\n","\n","arr = np.array([1, 2, 3, 4, 5])\n","mask1 = arr > 2\n","mask2 = arr % 2 == 0\n","combined_mask = mask1 & mask2\n","filtered_arr = arr[combined_mask]\n","print(filtered_arr)\n","```\n","### In this example, two masks mask1 and mask2 are created based on specific conditions. The logical AND operator (&) is used to combine these masks into the combined_mask. Finally, the combined_mask is used to filter the elements from arr, resulting in the filtered_arr.\n","\n","## 23.4 Conclusion:\n","### Chapter 23 explored combining masks and boolean operations in NumPy, enabling the creation of complex conditions for data manipulation and analysis. By using boolean operators such as logical AND (&), logical OR (|), and logical NOT (~), masks can be combined to form more intricate conditions. These techniques are valuable for selective data retrieval, conditional computations, and data analysis, providing flexibility and power in array-based data manipulation. Understanding and utilizing the combination of masks and boolean operations in NumPy open up possibilities for advanced data filtering, conditional computations, and efficient data analysis.\n","\n"]},{"cell_type":"markdown","id":"991b1411","metadata":{"papermill":{"duration":0.0119,"end_time":"2023-08-29T06:24:42.545272","exception":false,"start_time":"2023-08-29T06:24:42.533372","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>24</font></h1>"]},{"cell_type":"markdown","id":"9af9f11a","metadata":{"papermill":{"duration":0.012577,"end_time":"2023-08-29T06:24:42.56996","exception":false,"start_time":"2023-08-29T06:24:42.557383","status":"completed"},"tags":[]},"source":["# Chapter 24: Working with Masked Arrays\n","\n","## 24.1 Introduction:\n","### Chapter 24 focuses on working with masked arrays in NumPy. Masked arrays are special arrays that allow for the presence of missing or invalid values by using a separate boolean mask to indicate which elements are valid and which are masked. This chapter explores the creation, manipulation, and operations on masked arrays.\n","\n","## 24.2 Creating Masked Arrays:\n","### NumPy provides the np.ma module for working with masked arrays. There are several ways to create masked arrays:\n","\n","## 24.2.1 Using np.ma.array():\n","### The np.ma.array() function creates a masked array from an existing array and a mask. The mask is a boolean array indicating which elements are masked.\n","\n","```python\n","import numpy as np\n","\n","arr = np.array([1, 2, 3, 4, 5])\n","mask = np.array([False, False, True, False, True])\n","masked_arr = np.ma.array(arr, mask=mask)\n","print(masked_arr)\n","```\n","### In this example, a masked array masked_arr is created from the original array arr and the mask mask. The resulting masked array will have masked values where the corresponding mask elements are True, indicating missing or invalid values.\n","\n","## 24.2.2 Using np.ma.masked_array():\n","### The np.ma.masked_array() function directly creates a masked array by specifying the data array and the mask.\n","\n","```python\n","import numpy as np\n","\n","data = np.array([1, 2, 3, 4, 5])\n","mask = np.array([False, False, True, False, True])\n","masked_arr = np.ma.masked_array(data, mask=mask)\n","print(masked_arr)\n","```\n","\n","## In this example, a masked array masked_arr is created using the np.ma.masked_array() function with the data array data and the mask mask.\n","\n","## 24.3 Manipulating Masked Arrays:\n","### Masked arrays support various operations and functions for manipulating and working with the data.\n","\n","## 24.3.1 Accessing Masked Values:\n","### You can access the masked values in a masked array using the masked attribute.\n","\n","```python \n","import numpy as np\n","\n","arr = np.ma.array([1, 2, 3, 4, 5], mask=[False, False, True, False, True])\n","masked_values = arr[arr.mask]\n","print(masked_values)\n","``` \n","### In this example, the arr.mask attribute is used to access the mask of the masked array arr. Then, the arr[arr.mask] expression retrieves the masked values from arr and assigns them to the masked_values array.\n","\n","## 24.3.2 Modifying Masked Values:\n","### You can modify the masked values in a masked array by assigning new values to the desired positions.\n","\n","```python \n","import numpy as np\n","\n","arr = np.ma.array([1, 2, 3, 4, 5], mask=[False, False, True, False, True])\n","arr[arr.mask] = -1\n","print(arr)\n","In this example, the masked values in the masked array arr are assigned a new value of -1 using the expression arr[arr.mask] = -1. The resulting modified masked array is then printed.\n","```\n","\n","### 24.4 Operations on Masked Arrays:\n","#### Masked arrays support various operations such as arithmetic operations, statistical functions, and logical operations. These operations are applied element-wise, considering the mask to ignore masked values.\n","\n","```python\n","import numpy as np\n","\n","arr1 = np.ma.array([1, 2, 3, 4, 5], mask=[False, False, True, False, True])\n","arr2 = np.ma.array([2, 4, 6, 8, 10], mask=[False, False, False, True, True])\n","\n","sum_arr = arr1 + arr2\n","mean_arr = np.ma.mean(arr1)\n","logical_and_arr = np.ma.logical_and(arr1 > 2, arr2 < 8)\n","\n","print(sum_arr)\n","print(mean_arr)\n","print(logical_and_arr)\n","```\n","\n","#### In this example, various operations are performed on masked arrays arr1 and arr2. The + operator is used for element-wise addition, np.ma.mean() calculates the mean of the non-masked values in arr1, and np.ma.logical_and() performs element-wise logical AND operation on arr1 and arr2 considering the masks. The results are then printed.\n","\n","### 24.5 Conclusion:\n","#### Chapter 24 explored working with masked arrays in NumPy, which provide a mechanism for handling missing or invalid values. Masked arrays allow for the creation of arrays with elements that can be masked using boolean masks. Manipulation and operations on masked arrays take into account the mask, allowing for selective computations and handling of missing or invalid values. By using the np.ma module and its functions, masked arrays can be created, accessed, modified, and operated upon efficiently. Understanding and utilizing masked arrays empower data handling, analysis, and computations with missing or invalid values, enhancing the capabilities of array-based data processing in NumPy.\n","\n","\n"]},{"cell_type":"markdown","id":"ce859033","metadata":{"papermill":{"duration":0.012307,"end_time":"2023-08-29T06:24:42.594571","exception":false,"start_time":"2023-08-29T06:24:42.582264","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>25 </font></h1>"]},{"cell_type":"markdown","id":"078c4623","metadata":{"papermill":{"duration":0.012067,"end_time":"2023-08-29T06:24:42.619187","exception":false,"start_time":"2023-08-29T06:24:42.60712","status":"completed"},"tags":[]},"source":["# Chapter 25: Linear Algebra Operations with NumPy\n","\n","## 25.1 Introduction:\n","### Chapter 25 focuses on performing linear algebra operations using NumPy. NumPy provides a comprehensive set of functions and methods for handling vectors, matrices, and linear algebra operations. This chapter explores various linear algebra operations, including matrix multiplication, matrix inversion, eigenvalue decomposition, and more.\n","\n","## 25.2 Vectors and Matrices:\n","### In linear algebra, vectors represent quantities with magnitude and direction, while matrices are two-dimensional arrays that represent linear transformations and systems of equations. NumPy provides data structures and functions for working with vectors and matrices.\n","\n","## 25.2.1 Creating Vectors and Matrices:\n","### NumPy allows the creation of vectors and matrices using the np.array() function or specialized functions such as np.zeros(), np.ones(), and np.random.\n","\n","```python\n","import numpy as np\n","\n","# Creating a vector\n","vector = np.array([1, 2, 3])\n","print(vector)\n","\n","# Creating a matrix\n","matrix = np.array([[1, 2, 3], [4, 5, 6]])\n","print(matrix)\n","```\n","\n","### In this example, a vector is created using a one-dimensional array [1, 2, 3], and a matrix is created using a two-dimensional array [[1, 2, 3], [4, 5, 6]]. The resulting vector and matrix are printed.\n","\n","## 25.3 Matrix Multiplication:\n","### Matrix multiplication is a fundamental operation in linear algebra. NumPy provides the np.dot() function or the @ operator for matrix multiplication.\n","\n","```python\n","import numpy as np\n","\n","matrix1 = np.array([[1, 2], [3, 4]])\n","matrix2 = np.array([[5, 6], [7, 8]])\n","\n","result = np.dot(matrix1, matrix2)\n","# Or, equivalently: result = matrix1 @ matrix2\n","\n","print(result)\n","```\n","### In this example, two matrices matrix1 and matrix2 are multiplied using the np.dot() function. The result is stored in the result variable and printed.\n","\n","## 25.4 Matrix Inversion:\n","### Matrix inversion is the process of finding the inverse of a square matrix. NumPy provides the np.linalg.inv() function to compute the inverse of a matrix.\n","\n","```python\n","import numpy as np\n","\n","matrix = np.array([[1, 2], [3, 4]])\n","inverse_matrix = np.linalg.inv(matrix)\n","\n","print(inverse_matrix)\n","```\n","### In this example, the inverse of the matrix matrix is computed using the np.linalg.inv() function. The resulting inverse matrix is printed.\n","\n","## 25.5 Eigenvalue Decomposition:\n","### Eigenvalue decomposition is a matrix factorization that decomposes a matrix into a set of eigenvectors and eigenvalues. NumPy provides the np.linalg.eig() function to compute the eigenvalues and eigenvectors of a square matrix.\n","\n","```python\n","import numpy as np\n","\n","matrix = np.array([[1, 2], [3, 4]])\n","eigenvalues, eigenvectors = np.linalg.eig(matrix)\n","\n","print(\"Eigenvalues:\")\n","print(eigenvalues)\n","\n","print(\"Eigenvectors:\")\n","print(eigenvectors)\n","```\n","\n","### In this example, the eigenvalues and eigenvectors of the matrix matrix are computed using the np.linalg.eig() function. The resulting eigenvalues and eigenvectors are printed.\n","\n","## 25.6 Other Linear Algebra Operations:\n","### NumPy provides many other linear algebra operations, including computing the determinant (np.linalg.det()), solving linear equations (np.linalg.solve()), performing singular value decomposition (np.linalg.svd()), and more. These functions enable various computations and analyses in linear algebra.\n","\n","## 25.7 Conclusion:\n","### Chapter 25 explored the linear algebra operations available in NumPy. By leveraging NumPy's functions and methods, vectors and matrices can be created, manipulated, and used to perform essential operations such as matrix multiplication, matrix inversion, eigenvalue decomposition, and more. These operations are crucial for various applications, including data analysis, optimization, signal processing, and machine learning. Understanding and utilizing NumPy's linear algebra capabilities provide a solid foundation for working with numerical data and conducting advanced mathematical computations.\n","\n","\n","\n"]},{"cell_type":"markdown","id":"1a2fa13c","metadata":{"papermill":{"duration":0.012772,"end_time":"2023-08-29T06:24:42.644166","exception":false,"start_time":"2023-08-29T06:24:42.631394","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>26 </font></h1>"]},{"cell_type":"markdown","id":"cfb374e4","metadata":{"papermill":{"duration":0.011812,"end_time":"2023-08-29T06:24:42.668469","exception":false,"start_time":"2023-08-29T06:24:42.656657","status":"completed"},"tags":[]},"source":["\n","# Chapter 26: Matrix and Vector Operations\n","\n","## 26.1 Introduction:\n","### Chapter 26 focuses on matrix and vector operations in NumPy. NumPy provides a wide range of functions and methods for performing operations on matrices and vectors, including element-wise operations, matrix transposition, matrix multiplication, vector normalization, and more. This chapter explores the various operations that can be performed on matrices and vectors using NumPy.\n","\n","## 26.2 Element-wise Operations:\n","### NumPy allows for element-wise operations on matrices and vectors. Element-wise operations perform the operation independently on each element of the matrix or vector.\n","\n","## 26.2.1 Addition and Subtraction:\n","### Element-wise addition and subtraction of matrices and vectors can be performed using the + and - operators.\n","\n","```python\n","import numpy as np\n","\n","matrix1 = np.array([[1, 2], [3, 4]])\n","matrix2 = np.array([[5, 6], [7, 8]])\n","\n","result_addition = matrix1 + matrix2\n","result_subtraction = matrix1 - matrix2\n","\n","print(result_addition)\n","print(result_subtraction)\n","``` \n","\n","### In this example, element-wise addition and subtraction of matrix1 and matrix2 are performed using the + and - operators. The resulting matrices are stored in result_addition and result_subtraction variables, respectively, and printed.\n","\n","## 26.2.2 Multiplication and Division:\n","### Element-wise multiplication and division of matrices and vectors can be performed using the * and / operators.\n","\n","```python\n","\n","import numpy as np\n","\n","matrix1 = np.array([[1, 2], [3, 4]])\n","matrix2 = np.array([[5, 6], [7, 8]])\n","\n","result_multiplication = matrix1 * matrix2\n","result_division = matrix1 / matrix2\n","\n","print(result_multiplication)\n","print(result_division)\n","``` \n","### In this example, element-wise multiplication and division of matrix1 and matrix2 are performed using the * and / operators. The resulting matrices are stored in result_multiplication and result_division variables, respectively, and printed.\n","\n","## 26.3 Matrix Transposition:\n","### Matrix transposition involves flipping the matrix over its diagonal, switching the row and column indices. NumPy provides the np.transpose() function or the .T attribute to transpose a matrix.\n","\n","```python \n","import numpy as np\n","\n","matrix = np.array([[1, 2], [3, 4]])\n","\n","transposed_matrix = np.transpose(matrix)\n","# Or, equivalently: transposed_matrix = matrix.T\n","\n","print(transposed_matrix)\n","``` \n","### In this example, the matrix matrix is transposed using the np.transpose() function. The resulting transposed matrix is stored in the transposed_matrix variable and printed.\n","\n","## 26.4 Matrix Multiplication:\n","### Matrix multiplication is a fundamental operation in linear algebra. NumPy provides the np.dot() function or the @ operator for matrix multiplication.\n","\n","```python \n","import numpy as np\n","\n","matrix1 = np.array([[1, 2], [3, 4]])\n","matrix2 = np.array([[5, 6], [7, 8]])\n","\n","result = np.dot(matrix1, matrix2)\n","# Or, equivalently: result = matrix1 @ matrix2\n","\n","print(result)\n","```\n","\n","### In this example, two matrices matrix1 and matrix2 are multiplied using the np.dot() function. The result is stored in the result variable and printed.\n","\n","## 26.5 Vector Normalization:\n","### Vector normalization involves scaling a vector to have a length of 1, while preserving its direction. NumPy provides functions to normalize vectors, such as np.linalg.norm().\n","\n","```python \n","import numpy as np\n","\n","vector = np.array([3, 4])\n","\n","normalized_vector = vector / np.linalg.norm(vector)\n","\n","print(normalized_vector).\n","```\n","### In this example, the vector vector is normalized by dividing it by its Euclidean norm, computed using the np.linalg.norm() function. The resulting normalized vector is stored in the normalized_vector variable and printed.\n","\n","### 26.6 Conclusion:\n","### Chapter 26 explored matrix and vector operations in NumPy. NumPy provides a wide range of functions and methods to perform element-wise operations, matrix transposition, matrix multiplication, vector normalization, and more. These operations are fundamental for various applications, including linear algebra, machine learning, signal processing, and scientific computing. By leveraging NumPy's capabilities, efficient and concise operations on matrices and vectors can be performed, facilitating numerical computations and data analysis.\n"]},{"cell_type":"markdown","id":"e9d521b1","metadata":{"papermill":{"duration":0.011918,"end_time":"2023-08-29T06:24:42.692524","exception":false,"start_time":"2023-08-29T06:24:42.680606","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>27 </font></h1>"]},{"cell_type":"markdown","id":"6552a0fe","metadata":{"papermill":{"duration":0.01178,"end_time":"2023-08-29T06:24:42.716498","exception":false,"start_time":"2023-08-29T06:24:42.704718","status":"completed"},"tags":[]},"source":["# Chapter 27: Solving Linear Equations with NumPy\n","\n","## 27.1 Introduction:\n","### Chapter 27 focuses on solving linear equations using NumPy. NumPy provides functions for solving systems of linear equations efficiently. This chapter explores different methods for solving linear equations, such as direct methods (e.g., matrix inversion) and iterative methods (e.g., Gaussian elimination), using NumPy's linear algebra capabilities.\n","\n","## 27.2 Direct Methods:\n","### Direct methods involve directly computing the solution to a system of linear equations without iteration. One commonly used direct method is matrix inversion.\n","\n","## 27.2.1 Matrix Inversion Method:\n","### Matrix inversion is a direct method for solving linear equations. Given a system of linear equations Ax = b, where A is a square matrix and b is a vector, the solution can be obtained by multiplying the inverse of A with b.\n","\n","```python \n","import numpy as np\n","\n","A = np.array([[2, 3], [4, 5]])\n","b = np.array([1, 2])\n","\n","x = np.linalg.inv(A) @ b\n","\n","print(x)\n","```\n","\n","### In this example, the system of linear equations Ax = b is solved using the matrix inversion method. The inverse of matrix A is computed using np.linalg.inv(), and then the solution x is obtained by multiplying the inverse of A with b using the @ operator. The resulting solution x is printed.\n","\n","## 27.3 Iterative Methods:\n","### Iterative methods involve iteratively refining an initial guess until the desired solution is achieved. One commonly used iterative method is the Gaussian elimination method.\n","\n","## 27.3.1 Gaussian Elimination Method:\n","### The Gaussian elimination method solves a system of linear equations by transforming the augmented matrix to row-echelon form and back-substituting to find the solution.\n","\n","```python \n","import numpy as np\n","\n","A = np.array([[2, 3], [4, 5]])\n","b = np.array([1, 2])\n","\n","# Solve the system of linear equations using Gaussian elimination\n","x = np.linalg.solve(A, b)\n","\n","print(x)\n","```\n","### In this example, the system of linear equations Ax = b is solved using the Gaussian elimination method. The np.linalg.solve() function is used, which internally performs the necessary transformations and back-substitution to obtain the solution x. The resulting solution x is printed.\n","\n","## 27.4 Conclusion:\n","### Chapter 27 explored the methods for solving linear equations using NumPy. NumPy's linear algebra capabilities provide functions for both direct methods (e.g., matrix inversion) and iterative methods (e.g., Gaussian elimination) to solve systems of linear equations efficiently. These methods are essential in various fields, including mathematics, physics, engineering, and data analysis. By leveraging NumPy's functions, complex systems of linear equations can be solved accurately and efficiently, enabling the solution of real-world problems.\n","\n"]},{"cell_type":"markdown","id":"0a54724b","metadata":{"papermill":{"duration":0.011768,"end_time":"2023-08-29T06:24:42.740566","exception":false,"start_time":"2023-08-29T06:24:42.728798","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>28</font></h1>"]},{"cell_type":"markdown","id":"a9e639ce","metadata":{"papermill":{"duration":0.011935,"end_time":"2023-08-29T06:24:42.764577","exception":false,"start_time":"2023-08-29T06:24:42.752642","status":"completed"},"tags":[]},"source":["# Chapter 28: Eigenvalues and Eigenvectors\n","\n","## 28.1 Introduction:\n","### Chapter 28 focuses on eigenvalues and eigenvectors in NumPy. Eigenvalues and eigenvectors are fundamental concepts in linear algebra and have various applications in data analysis, machine learning, and physics. NumPy provides functions to compute eigenvalues and eigenvectors of matrices efficiently. This chapter explores the concept of eigenvalues and eigenvectors, their computation using NumPy, and their significance in various applications.\n","\n","## 28.2 Eigenvalues and Eigenvectors:\n","### Eigenvalues and eigenvectors are properties of square matrices. An eigenvector is a non-zero vector that, when multiplied by a matrix, results in a scaled version of the original vector. The scaling factor is called the eigenvalue. In other words, for a square matrix A, an eigenvector v and its corresponding eigenvalue λ satisfy the equation Av = λv.\n","\n","## 28.3 Computing Eigenvalues and Eigenvectors:\n","### NumPy provides the np.linalg.eig() function to compute the eigenvalues and eigenvectors of a square matrix.\n","\n","```python \n","import numpy as np\n","\n","A = np.array([[1, 2], [3, 4]])\n","\n","eigenvalues, eigenvectors = np.linalg.eig(A)\n","\n","print(\"Eigenvalues:\")\n","print(eigenvalues)\n","\n","print(\"Eigenvectors:\")\n","print(eigenvectors)\n","```\n","\n","### In this example, the eigenvalues and eigenvectors of the matrix A are computed using the np.linalg.eig() function. The resulting eigenvalues are stored in the eigenvalues variable, and the eigenvectors are stored in the eigenvectors variable. The computed eigenvalues and eigenvectors are printed.\n","\n","## 28.4 Properties and Applications:\n","### Eigenvalues and eigenvectors have several important properties and applications. Some of them include:\n","\n","### Principal Component Analysis (PCA): Eigenvectors and eigenvalues are used in PCA to reduce the dimensionality of high-dimensional data while preserving the most important information.\n","### Stability Analysis: Eigenvalues and eigenvectors play a crucial role in stability analysis of dynamical systems, such as in physics and engineering.\n","### Markov Chains: Eigenvalues and eigenvectors are used to analyze the long-term behavior and steady-state probabilities of Markov chains.\n","### Image Processing: Eigenvectors and eigenvalues are used in techniques like eigenfaces for facial recognition and image compression.\n","### Understanding eigenvalues and eigenvectors provides valuable insights into the behavior and properties of matrices, enabling various mathematical and computational analyses.\n","\n","## 28.5 Conclusion:\n","### Chapter 28 explored eigenvalues and eigenvectors in NumPy. NumPy's np.linalg.eig() function allows for the efficient computation of eigenvalues and eigenvectors of square matrices. Eigenvalues and eigenvectors have significant applications in various fields, including data analysis, machine learning, physics, and image processing. By leveraging NumPy's capabilities, complex matrices can be analyzed, and their eigenvalues and eigenvectors can be computed, leading to a deeper understanding of the underlying data and systems.\n"]},{"cell_type":"markdown","id":"a2e3c8db","metadata":{"papermill":{"duration":0.011799,"end_time":"2023-08-29T06:24:42.7886","exception":false,"start_time":"2023-08-29T06:24:42.776801","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>29 </font></h1>"]},{"cell_type":"markdown","id":"dc18a941","metadata":{"papermill":{"duration":0.01182,"end_time":"2023-08-29T06:24:42.812682","exception":false,"start_time":"2023-08-29T06:24:42.800862","status":"completed"},"tags":[]},"source":["# Chapter 29: Random Number Generation in NumPy\n","\n","## 29.1 Introduction:\n","### Chapter 29 focuses on random number generation in NumPy. NumPy provides functions for generating random numbers from various probability distributions. Random number generation is essential in various applications, including simulations, statistical analysis, and machine learning. This chapter explores the random number generation capabilities of NumPy, including generating random arrays, sampling from distributions, and setting the random seed.\n","\n","## 29.2 Generating Random Arrays:\n","### NumPy provides the np.random.rand() function to generate an array of random numbers from a uniform distribution between 0 and 1.\n","\n","```python\n","import numpy as np\n","\n","random_array = np.random.rand(3, 3)\n","\n","print(random_array)\n","```\n","\n","### In this example, a 3x3 array of random numbers between 0 and 1 is generated using the np.random.rand() function. The resulting random array is stored in the random_array variable and printed.\n","\n","## 29.3 Sampling from Distributions:\n","### NumPy provides functions to sample random numbers from various probability distributions. Some commonly used functions include np.random.normal() for sampling from a normal distribution, np.random.uniform() for sampling from a uniform distribution, and np.random.randint() for sampling integers within a specified range.\n","\n","```python \n","import numpy as np\n","\n","normal_samples = np.random.normal(loc=0, scale=1, size=(3, 3))\n","uniform_samples = np.random.uniform(low=0, high=1, size=(3, 3))\n","integer_samples = np.random.randint(low=1, high=10, size=(3, 3))\n","\n","print(\"Normal Distribution:\")\n","print(normal_samples)\n","\n","print(\"Uniform Distribution:\")\n","print(uniform_samples)\n","\n","print(\"Integer Samples:\")\n","print(integer_samples)\n","```\n","\n","### In this example, random numbers are sampled from a normal distribution using np.random.normal(), a uniform distribution using np.random.uniform(), and integers within a specified range using np.random.randint(). The resulting samples are stored in normal_samples, uniform_samples, and integer_samples variables, respectively, and printed.\n","\n","## 29.4 Setting the Random Seed:\n","### To ensure reproducibility, it is often necessary to set a random seed before generating random numbers. The random seed ensures that the same sequence of random numbers is generated each time the code is run.\n","\n","```python \n","import numpy as np\n","\n","np.random.seed(42)\n","\n","random_array = np.random.rand(3, 3)\n","\n","print(random_array)\n","```\n","### In this example, the random seed is set to 42 using np.random.seed(42). Subsequently, a 3x3 array of random numbers is generated using np.random.rand(). The resulting random array will be the same each time the code is run due to the fixed random seed.\n","\n","## 29.5 Conclusion:\n","### Chapter 29 explored random number generation in NumPy. NumPy provides functions for generating random arrays, sampling from various probability distributions, and setting the random seed for reproducibility. Random number generation is crucial for simulations, statistical analysis, and machine learning tasks. By utilizing NumPy's random number generation capabilities, random data can be generated, enabling the development and testing of algorithms, simulations, and statistical models.\n","\n","\n","\n"]},{"cell_type":"markdown","id":"5252c1c6","metadata":{"papermill":{"duration":0.012011,"end_time":"2023-08-29T06:24:42.836806","exception":false,"start_time":"2023-08-29T06:24:42.824795","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>30 </font></h1>"]},{"cell_type":"markdown","id":"339611e4","metadata":{"papermill":{"duration":0.011862,"end_time":"2023-08-29T06:24:42.860684","exception":false,"start_time":"2023-08-29T06:24:42.848822","status":"completed"},"tags":[]},"source":["# Chapter 30: Generating Random Arrays\n","\n","## 30.1 Introduction:\n","### Chapter 30 focuses on generating random arrays in NumPy. Random arrays are useful for various applications, including simulations, testing algorithms, and generating synthetic data. NumPy provides several functions to generate random arrays with specific properties, such as size, distribution, and range. This chapter explores different techniques for generating random arrays in NumPy.\n","\n","## 30.2 Generating Random Arrays with Uniform Distribution:\n","### The np.random.rand() function generates random numbers from a uniform distribution between 0 and 1. By specifying the size of the array, you can generate random arrays of different dimensions.\n","\n","```python \n","import numpy as np\n","\n","# Generate a random 1D array of size 5\n","random_array_1d = np.random.rand(5)\n","print(random_array_1d)\n","\n","# Generate a random 2D array of size 3x3\n","random_array_2d = np.random.rand(3, 3)\n","print(random_array_2d)\n","```\n","\n","### In this example, a 1D random array of size 5 and a 2D random array of size 3x3 are generated using np.random.rand(). The resulting random arrays are stored in the variables random_array_1d and random_array_2d and printed.\n","\n","## 30.3 Generating Random Arrays with Normal Distribution:\n","### The np.random.normal() function generates random numbers from a normal distribution with specified mean and standard deviation. You can also specify the size of the array.\n","\n","```python \n","import numpy as np\n","\n","# Generate a random 1D array of size 5 from a normal distribution\n","random_array_1d = np.random.normal(loc=0, scale=1, size=5)\n","print(random_array_1d)\n","\n","# Generate a random 2D array of size 3x3 from a normal distribution\n","random_array_2d = np.random.normal(loc=0, scale=1, size=(3, 3))\n","print(random_array_2d)\n","```\n","### In this example, a 1D random array of size 5 from a normal distribution with mean 0 and standard deviation 1, and a 2D random array of size 3x3 from a normal distribution are generated using np.random.normal(). The resulting random arrays are stored in the variables random_array_1d and random_array_2d and printed.\n","\n","## 30.4 Generating Random Integers:\n","### The np.random.randint() function generates random integers within a specified range. You can specify the low (inclusive) and high (exclusive) values, as well as the size of the array.\n","```python\n","import numpy as np\n","\n","# Generate a random 1D array of size 5 with integers between 1 and 10\n","random_array_1d = np.random.randint(low=1, high=10, size=5)\n","print(random_array_1d)\n","\n","# Generate a random 2D array of size 3x3 with integers between 1 and 10\n","random_array_2d = np.random.randint(low=1, high=10, size=(3, 3))\n","print(random_array_2d)\n","```\n","### In this example, a 1D random array of size 5 with integers between 1 and 10, and a 2D random array of size 3x3 with integers between 1 and 10 are generated using np.random.randint(). The resulting random arrays are stored in the variables random_array_1d and random_array_2d and printed.\n","\n","## 30.5 Generating Random Arrays from Other Distributions:\n","### NumPy provides several other functions to generate random arrays from different probability distributions, such as exponential distribution (np.random.exponential()), binomial distribution (np.random.binomial()), and many more. These functions allow you to generate random arrays with specific distribution characteristics.\n","\n","## 30.6 Conclusion:\n","### Chapter 30 explored the techniques for generating random arrays in NumPy. Random arrays are useful for various applications, including simulations, testing algorithms, and generating synthetic data. NumPy provides functions to generate random arrays with different properties, such as size, distribution, and range. By utilizing these functions, you can easily generate random arrays for your specific needs and perform computations or analyses on them.\n","\n","\n","\n"]},{"cell_type":"markdown","id":"86bc74cc","metadata":{"papermill":{"duration":0.011797,"end_time":"2023-08-29T06:24:42.885041","exception":false,"start_time":"2023-08-29T06:24:42.873244","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>31</font></h1>"]},{"cell_type":"markdown","id":"b54dd4d1","metadata":{"papermill":{"duration":0.012607,"end_time":"2023-08-29T06:24:42.910609","exception":false,"start_time":"2023-08-29T06:24:42.898002","status":"completed"},"tags":[]},"source":["# Chapter 31: Random Sampling Techniques\n","\n","## 31.1 Introduction:\n","### Chapter 31 focuses on random sampling techniques in NumPy. Random sampling is a fundamental operation in statistics and data analysis, allowing us to select subsets of data for analysis or modeling. NumPy provides various functions for random sampling, enabling efficient and flexible sampling from arrays or probability distributions. This chapter explores different random sampling techniques available in NumPy.\n","\n","## 31.2 Simple Random Sampling:\n","### Simple random sampling involves selecting random elements from a given array without replacement. NumPy provides the np.random.choice() function for simple random sampling. You can specify the size of the sample and whether to sample with or without replacement.\n","\n","```python\n","import numpy as np\n","\n","# Sample 3 random elements from an array without replacement\n","array = np.array([1, 2, 3, 4, 5, 6])\n","sample = np.random.choice(array, size=3, replace=False)\n","print(sample)\n","```\n","### In this example, three random elements are sampled from the given array using np.random.choice() with the replace=False argument. The resulting sample is stored in the sample variable and printed.\n","\n","## 31.3 Stratified Sampling:\n","### Stratified sampling involves dividing a population into subgroups (strata) and sampling from each stratum independently. NumPy provides the np.random.choice() function with the p parameter to perform stratified sampling. You can specify the probabilities associated with each element in the array.\n","\n","```python \n","import numpy as np\n","\n","# Stratified sampling with different probabilities\n","array = np.array([1, 2, 3, 4, 5, 6])\n","probabilities = np.array([0.1, 0.2, 0.3, 0.2, 0.1, 0.1])\n","sample = np.random.choice(array, size=3, replace=False, p=probabilities)\n","print(sample)\n","```\n","\n","### In this example, stratified sampling is performed on the given array with different probabilities for each element. The p parameter is set to the array of probabilities associated with each element. The resulting sample is stored in the sample variable and printed.\n","\n","## 31.4 Random Sampling from Distributions:\n","### NumPy provides functions to perform random sampling from various probability distributions. For example, np.random.normal() allows sampling from a normal distribution, np.random.uniform() allows sampling from a uniform distribution, and np.random.exponential() allows sampling from an exponential distribution.\n","\n","```python\n","import numpy as np\n","\n","# Random sampling from a normal distribution\n","samples = np.random.normal(loc=0, scale=1, size=5)\n","print(samples)\n","```\n","### In this example, random samples are generated from a normal distribution with mean 0 and standard deviation 1 using np.random.normal(). The resulting samples are stored in the samples variable and printed.\n","\n","## 31.5 Random Permutations:\n","### Random permutations involve randomly shuffling the elements of an array. NumPy provides the np.random.permutation() function to generate random permutations of an array.\n","\n","```python \n","import numpy as np\n","\n","# Randomly permute the elements of an array\n","array = np.array([1, 2, 3, 4, 5])\n","permuted_array = np.random.permutation(array)\n","print(permuted_array)\n","```\n","### In this example, the elements of the given array are randomly permuted using np.random.permutation(). The resulting permuted array is stored in the permuted_array variable and printed.\n","\n","## 31.6 Conclusion:\n","### Chapter 31 explored random sampling techniques in NumPy. Random sampling is an essential operation in statistics and data analysis, allowing us to select subsets of data for analysis or modeling. NumPy provides functions for simple random sampling, stratified sampling, random sampling from distributions, and generating random permutations. By utilizing these functions, you can perform efficient and flexible random sampling operations on arrays or probability distributions in your data analysis tasks.\n","\n","\n"]},{"cell_type":"markdown","id":"841a4ce9","metadata":{"papermill":{"duration":0.012219,"end_time":"2023-08-29T06:24:42.935783","exception":false,"start_time":"2023-08-29T06:24:42.923564","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>32 </font></h1>"]},{"cell_type":"markdown","id":"4044caa9","metadata":{"papermill":{"duration":0.011947,"end_time":"2023-08-29T06:24:42.960177","exception":false,"start_time":"2023-08-29T06:24:42.94823","status":"completed"},"tags":[]},"source":["# Chapter 32: Working with Random Distributions\n","\n","## 32.1 Introduction:\n","### Chapter 32 focuses on working with random distributions in NumPy. Random distributions are fundamental in statistics and data analysis, representing the probability of different outcomes in a given set of data. NumPy provides functions to generate random numbers from various probability distributions and perform operations on them. This chapter explores different techniques for working with random distributions in NumPy.\n","\n","## 32.2 Generating Random Numbers from Distributions:\n","### NumPy provides several functions to generate random numbers from different probability distributions. Some commonly used functions include np.random.normal() for generating random numbers from a normal distribution, np.random.uniform() for generating random numbers from a uniform distribution, and np.random.exponential() for generating random numbers from an exponential distribution.\n","\n","```python \n","import numpy as np\n","\n","# Generate random numbers from a normal distribution\n","normal_samples = np.random.normal(loc=0, scale=1, size=(3, 3))\n","print(\"Normal Distribution:\")\n","print(normal_samples)\n","\n","# Generate random numbers from a uniform distribution\n","uniform_samples = np.random.uniform(low=0, high=1, size=(3, 3))\n","print(\"Uniform Distribution:\")\n","print(uniform_samples)\n","\n","# Generate random numbers from an exponential distribution\n","exponential_samples = np.random.exponential(scale=1, size=(3, 3))\n","print(\"Exponential Distribution:\")\n","print(exponential_samples)\n","```\n","\n","### In this example, random numbers are generated from a normal distribution, a uniform distribution, and an exponential distribution using np.random.normal(), np.random.uniform(), and np.random.exponential() functions, respectively. The resulting random numbers are stored in the variables normal_samples, uniform_samples, and exponential_samples, and printed.\n","\n","## 32.3 Computing Descriptive Statistics:\n","### NumPy provides functions to compute various descriptive statistics on random number arrays. Some commonly used functions include np.mean() to compute the mean, np.median() to compute the median, np.var() to compute the variance, and np.std() to compute the standard deviation.\n","\n","```python \n","import numpy as np\n","\n","# Generate random numbers from a normal distribution\n","random_numbers = np.random.normal(loc=0, scale=1, size=100)\n","\n","# Compute descriptive statistics\n","mean = np.mean(random_numbers)\n","median = np.median(random_numbers)\n","variance = np.var(random_numbers)\n","std_deviation = np.std(random_numbers)\n","\n","print(\"Mean:\", mean)\n","print(\"Median:\", median)\n","print(\"Variance:\", variance)\n","print(\"Standard Deviation:\", std_deviation)\n","```\n","\n","### In this example, random numbers are generated from a normal distribution using np.random.normal(). Descriptive statistics such as mean, median, variance, and standard deviation are computed using the corresponding NumPy functions. The computed statistics are printed.\n","\n","## 32.4 Fitting Distributions to Data:\n","### NumPy also provides functions for fitting distributions to given data. The np.random.normal() function can be used to fit a normal distribution, while other functions like np.random.exponential() and np.random.gamma() can be used to fit exponential and gamma distributions, respectively.\n","\n","```python\n","import numpy as np\n","\n","# Generate random numbers from a gamma distribution\n","gamma_samples = np.random.gamma(shape=2, scale=2, size=100)\n","\n","# Fit a gamma distribution to the generated samples\n","fit_shape, fit_scale = np.random.gamma.fit(gamma_samples)\n","\n","print(\"Fitted Shape:\", fit_shape)\n","print(\"Fitted Scale:\", fit_scale)\n","```\n","\n","### In this example, random numbers are generated from a gamma distribution using np.random.gamma(). Then, the np.random.gamma.fit() function is used to fit a gamma distribution to the generated samples. The fitted shape and scale parameters are stored in fit_shape and fit_scale, respectively, and printed.\n","\n","### 32.5 Conclusion:\n","### Chapter 32 explored working with random distributions in NumPy. NumPy provides functions to generate random numbers from various probability distributions, compute descriptive statistics on random number arrays, and fit distributions to given data. These capabilities allow you to analyze and model data using random distributions in your statistical and data analysis tasks.\n","\n","\n"]},{"cell_type":"markdown","id":"373bb2d8","metadata":{"papermill":{"duration":0.012097,"end_time":"2023-08-29T06:24:42.98445","exception":false,"start_time":"2023-08-29T06:24:42.972353","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>33</font></h1>"]},{"cell_type":"markdown","id":"0d2be3ac","metadata":{"papermill":{"duration":0.013548,"end_time":"2023-08-29T06:24:43.010236","exception":false,"start_time":"2023-08-29T06:24:42.996688","status":"completed"},"tags":[]},"source":["# Chapter 33: Performance Optimization in NumPy\n","\n","## 33.1 Introduction:\n","### Chapter 33 focuses on performance optimization techniques in NumPy. NumPy is designed to provide efficient array operations, but there are strategies you can employ to further optimize the performance of your code. This chapter explores different techniques for improving the performance of NumPy operations, such as vectorization, broadcasting, and using optimized functions.\n","\n","## 33.2 Vectorization:\n","### Vectorization is a technique that allows you to perform operations on entire arrays or large sections of arrays at once, instead of iterating over individual elements. This can significantly improve the performance of your code by leveraging the optimized underlying C or Fortran implementations in NumPy.\n","\n","```python \n","import numpy as np\n","\n","# Non-vectorized operation\n","a = np.array([1, 2, 3])\n","b = np.array([4, 5, 6])\n","result = np.zeros_like(a)\n","\n","for i in range(len(a)):\n","    result[i] = a[i] + b[i]\n","\n","print(\"Non-vectorized result:\", result)\n","\n","# Vectorized operation\n","result_vectorized = a + b\n","print(\"Vectorized result:\", result_vectorized)\n","```\n","\n","### In this example, a non-vectorized addition operation is performed using a loop, iterating over individual elements of the arrays a and b. The result is stored in the result array. The same addition operation is performed using vectorization by simply adding the arrays a and b together. The vectorized result is obtained without the need for a loop, which improves performance.\n","\n","## 33.3 Broadcasting:\n","### Broadcasting is a powerful feature in NumPy that allows arrays with different shapes to be used together in operations. It eliminates the need for explicitly creating intermediate arrays or using loops. By broadcasting arrays, you can perform operations efficiently on arrays of different shapes.\n","\n","```python \n","import numpy as np\n","\n","# Broadcasting example\n","a = np.array([[1, 2, 3], [4, 5, 6]])\n","b = np.array([10, 20, 30])\n","\n","result = a + b\n","print(\"Broadcasted result:\", result)\n","```\n","\n","### In this example, the array a has a shape of (2, 3), while the array b has a shape of (3,). The addition operation is performed between a and b using broadcasting. NumPy automatically expands the dimensions of b to match the shape of a, allowing the addition to be performed element-wise. Broadcasting avoids the need for explicit loops or creating intermediate arrays, resulting in improved performance.\n","\n","## 33.4 Optimized Functions:\n","### NumPy provides a wide range of optimized functions that are implemented in low-level languages like C or Fortran. These functions are designed to perform operations efficiently on arrays and often have specialized algorithms or optimizations. By utilizing these optimized functions, you can achieve significant performance improvements.\n","\n","```python \n","import numpy as np\n","\n","# Example of optimized functions\n","a = np.array([1, 2, 3, 4, 5])\n","sum_a = np.sum(a)\n","mean_a = np.mean(a)\n","max_a = np.max(a)\n","\n","print(\"Sum:\", sum_a)\n","print(\"Mean:\", mean_a)\n","print(\"Max:\", max_a)\n","```\n","### In this example, optimized functions like np.sum(), np.mean(), and np.max() are used to compute the sum, mean, and maximum of the array a, respectively. These optimized functions are designed to efficiently perform these operations on arrays, resulting in improved performance compared to implementing them manually.\n","\n","## 33.5 Conclusion:\n","### Chapter 33 explored performance optimization techniques in NumPy. By employing strategies such as vectorization, broadcasting, and utilizing optimized functions, you can improve the performance of your NumPy code. These techniques leverage the optimized underlying implementations in NumPy and allow for efficient and faster array operations.\n","\n"]},{"cell_type":"markdown","id":"e618ec4c","metadata":{"papermill":{"duration":0.012147,"end_time":"2023-08-29T06:24:43.035388","exception":false,"start_time":"2023-08-29T06:24:43.023241","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>34</font></h1>"]},{"cell_type":"markdown","id":"ce4d2500","metadata":{"papermill":{"duration":0.012243,"end_time":"2023-08-29T06:24:43.060077","exception":false,"start_time":"2023-08-29T06:24:43.047834","status":"completed"},"tags":[]},"source":["# Chapter 34: Tips for Array Performance Improvement\n","\n","## 34.1 Introduction:\n","### Chapter 34 provides tips and guidelines for improving the performance of array operations in NumPy. While NumPy already offers efficient array processing capabilities, there are several techniques you can apply to further enhance the performance of your code. This chapter presents some valuable tips to optimize the performance of array operations in NumPy.\n","\n","## 34.2 Use Vectorized Operations:\n","### Vectorized operations are more efficient than explicit loops in NumPy. Take advantage of vectorization by performing operations on entire arrays or large sections of arrays at once instead of iterating over individual elements. This eliminates the overhead of looping and leverages the optimized underlying implementations in NumPy.\n","\n","## 34.3 Avoid Unnecessary Copies:\n","### NumPy functions and operations may create copies of arrays by default. Creating unnecessary copies can lead to increased memory usage and slower performance. Be mindful of functions that return copies and consider using the out parameter to store results directly into pre-allocated arrays whenever possible.\n","\n","## 34.4 Prefer In-Place Operations:\n","### In-place operations modify arrays directly without creating new arrays. These operations are more memory-efficient and can significantly improve performance, especially when working with large arrays. Look for in-place versions of functions or utilize the = operator to update arrays in-place whenever appropriate.\n","\n","## 34.5 Utilize Broadcasting:\n","### Broadcasting allows for efficient operations on arrays with different shapes. Instead of explicitly expanding dimensions or using loops, leverage broadcasting to perform operations efficiently. This avoids unnecessary memory overhead and enhances the performance of array operations.\n","\n","## 34.6 Preallocate Memory:\n","### When performing repetitive computations or accumulating results in a loop, preallocating memory for the output array can significantly improve performance. Preallocating ensures that the array is allocated only once, preventing unnecessary memory reallocations during each iteration.\n","\n","## 34.7 Use NumPy's Optimized Functions:\n","### NumPy provides a wide range of optimized functions that are implemented in low-level languages such as C or Fortran. These functions are specifically designed to perform efficient operations on arrays. Whenever possible, utilize these optimized functions instead of manually implementing equivalent operations.\n","\n","## 34.8 Employ Parallelization:\n","### NumPy supports parallel execution on multi-core processors by utilizing libraries such as OpenMP. Some NumPy functions automatically parallelize operations, while others provide options to enable parallel execution. Check the NumPy documentation and explore parallelization options to harness the power of multiple cores.\n","\n","## 34.9 Consider Using Compiled Extensions:\n","### For computationally intensive tasks, consider using compiled extensions such as Cython or Numba. These tools allow you to write high-performance code by optimizing critical sections and leveraging just-in-time compilation. By combining NumPy with compiled extensions, you can achieve significant performance improvements.\n","\n","## 34.10 Optimize Memory Access Patterns:\n","### Efficient memory access patterns can enhance performance. NumPy arrays are stored in a contiguous block of memory, and accessing elements sequentially or in a stride pattern can improve cache utilization and minimize memory latency. Consider optimizing your algorithms and operations to take advantage of favorable memory access patterns.\n","\n","## 34.11 Profile and Benchmark Your Code:\n","### Profile and benchmark your code to identify performance bottlenecks. Use tools like NumPy's built-in profiling utilities, as well as external profilers, to measure the execution time of different parts of your code. This will help you pinpoint areas that require optimization and guide your performance improvement efforts.\n","\n","## 34.12 Conclusion:\n","### Chapter 34 provided tips for improving the performance of array operations in NumPy. By following these guidelines, you can optimize your NumPy code to achieve faster execution and more efficient memory usage. Remember to profile your code to identify areas for improvement and leverage NumPy's capabilities for efficient array processing.\n"]},{"cell_type":"markdown","id":"03c1d039","metadata":{"papermill":{"duration":0.012147,"end_time":"2023-08-29T06:24:43.084672","exception":false,"start_time":"2023-08-29T06:24:43.072525","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>35 </font></h1>"]},{"cell_type":"markdown","id":"f4d92298","metadata":{"papermill":{"duration":0.011989,"end_time":"2023-08-29T06:24:43.109321","exception":false,"start_time":"2023-08-29T06:24:43.097332","status":"completed"},"tags":[]},"source":["\n","# Chapter 35: Broadcasting for Efficiency\n","\n","## 35.1 Introduction:\n","### Chapter 35 focuses on utilizing broadcasting techniques in NumPy for efficient array operations. Broadcasting allows you to perform operations on arrays with different shapes, eliminating the need for explicit loops or creating intermediate arrays. This chapter explores how broadcasting can improve the efficiency of your code by avoiding unnecessary memory allocations and reducing computational overhead.\n","\n","## 35.2 Broadcasting Basics:\n","### Broadcasting is a powerful feature in NumPy that enables element-wise operations on arrays with different shapes. When performing operations between arrays, NumPy automatically broadcasts the arrays to have compatible shapes before executing the operation. This avoids the need for manual reshaping or expanding dimensions.\n","\n","## 35.3 Broadcasting Rules:\n","### NumPy follows specific rules to determine whether broadcasting is possible between two arrays. The broadcasting rules are as follows:\n","\n","#### Rule 1: If the arrays have different dimensions, the array with fewer dimensions is padded with ones on its left until the dimensions match.\n","#### Rule 2: If the shape of any dimension in the arrays is not equal, and one of them has a shape of 1 in that dimension, the array with shape 1 is stretched along that dimension to match the other array's shape.\n","#### Rule 3: If the shapes of the arrays are still not compatible after applying Rules 1 and 2, an error is raised indicating that the arrays cannot be broadcasted.\n","## 35.4 Broadcasting Examples:\n","### Let's consider some examples to illustrate how broadcasting works:\n","\n","```python\n","import numpy as np\n","\n","# Example 1: Broadcasting a scalar with a 1D array\n","a = np.array([1, 2, 3])\n","b = 2\n","\n","result = a + b\n","print(\"Result:\", result)\n","\n","# Example 2: Broadcasting a 1D array with a 2D array\n","c = np.array([[1, 2, 3], [4, 5, 6]])\n","d = np.array([10, 20, 30])\n","\n","result2 = c + d\n","print(\"Result 2:\", result2)\n","```\n","### In Example 1, a scalar value b is broadcasted to match the shape of the 1D array a. The addition operation is performed element-wise, and the resulting array is stored in result.\n","\n","### In Example 2, a 1D array d is broadcasted to match the shape of the 2D array c. The addition operation is performed element-wise between each row of c and d, resulting in a 2D array result2.\n","\n","## 35.5 Efficiency Benefits of Broadcasting:\n","### Broadcasting offers several efficiency benefits in NumPy:\n","\n","#### Memory Efficiency: Broadcasting avoids the need for creating explicit copies or reshaping arrays, reducing memory usage. Only temporary arrays that are necessary for the operation are allocated, resulting in efficient memory utilization.\n","\n","#### Computational Efficiency: By eliminating explicit loops, broadcasting allows for vectorized operations on arrays. This leverages the optimized underlying implementations in NumPy, leading to faster execution and improved computational efficiency.\n","\n","#### Code Simplicity: Broadcasting simplifies code by removing the need for explicit loop constructs or reshaping operations. This results in cleaner and more concise code that is easier to read and maintain.\n","\n","## 35.6 Broadcasting with Complex Operations:\n","### Broadcasting can be used with complex operations involving multiple arrays and dimensions. By leveraging broadcasting, you can perform advanced computations efficiently and concisely.\n","\n","## 35.7 Broadcasting Limitations:\n","### While broadcasting offers flexibility and efficiency, it has certain limitations. Broadcasting may not be possible or may produce unexpected results in some scenarios. It is important to be aware of the broadcasting rules and ensure that the arrays being operated on have compatible shapes.\n","\n","## 35.8 Broadcasting for Efficiency Tips:\n","### To maximize the efficiency of broadcasting in NumPy, consider the following tips:\n","\n","#### Minimize the number of dimensions: Reduce unnecessary dimensions in your arrays to optimize memory usage and computational efficiency.\n","#### Utilize broadcasting in combination with vectorized operations: Leverage broadcasting alongside other vectorized operations to perform complex computations efficiently.\n","#### Profile your code: Profile your code to identify performance bottlenecks and areas for optimization. Broadcasting can improve efficiency, but understanding the impact on your specific code is essential.\n","## 35.9 Conclusion:\n","### Chapter 35 highlighted the efficiency benefits of broadcasting in NumPy. By leveraging broadcasting, you can perform operations on arrays with different shapes efficiently, reducing memory usage and computational overhead. Understanding the broadcasting rules and using it effectively can simplify your code and enhance the performance of your NumPy applications.\n","\n","\n","\n"]},{"cell_type":"markdown","id":"80403598","metadata":{"papermill":{"duration":0.013797,"end_time":"2023-08-29T06:24:43.135732","exception":false,"start_time":"2023-08-29T06:24:43.121935","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>36 </font></h1>"]},{"cell_type":"markdown","id":"6062d7dc","metadata":{"papermill":{"duration":0.012427,"end_time":"2023-08-29T06:24:43.162053","exception":false,"start_time":"2023-08-29T06:24:43.149626","status":"completed"},"tags":[]},"source":["# Chapter 36: Vectorized Functions for Performance\n","\n","## 36.1 Introduction:\n","### Chapter 36 focuses on utilizing vectorized functions in NumPy for improved performance. NumPy provides a wide range of built-in vectorized functions that operate efficiently on arrays, enabling you to perform complex computations without explicit loops. This chapter explores the benefits of using vectorized functions and provides examples of their usage for performance optimization.\n","\n","## 36.2 Benefits of Vectorized Functions:\n","### Vectorized functions offer several advantages for performance optimization in NumPy:\n","\n","#### Improved Efficiency: Vectorized functions are implemented in low-level languages like C or Fortran, making them highly efficient. They take advantage of optimized algorithms and memory access patterns, resulting in faster execution compared to manually implemented loops.\n","\n","#### Simplicity and Readability: Vectorized functions simplify your code by eliminating the need for explicit loops. They allow you to express complex operations concisely, making your code more readable and easier to maintain.\n","\n","#### Memory Optimization: Vectorized functions operate on entire arrays or large sections of arrays at once, minimizing memory overhead. They avoid the need for intermediate arrays or repeated memory allocations, leading to efficient memory usage.\n","\n","#### Leverage Underlying Optimizations: Vectorized functions leverage the optimized implementations in NumPy, which are specifically designed for efficient array processing. They take advantage of CPU-specific instructions and parallelization techniques, further enhancing performance.\n","\n","## 36.3 Examples of Vectorized Functions:\n","### NumPy provides a vast collection of vectorized functions for various mathematical and scientific computations. Here are some examples:\n","\n","#### Mathematical Functions: NumPy's np.sin(), np.cos(), np.exp(), np.log(), and np.sqrt() are vectorized functions that operate element-wise on arrays, providing efficient computations of trigonometric, exponential, logarithmic, and square root operations.\n","\n","#### Statistical Functions: Functions like np.mean(), np.sum(), np.min(), np.max(), and np.std() are vectorized functions that compute statistics on arrays. They efficiently handle large datasets by operating on the entire array in a single call.\n","\n","#### Element-wise Operations: NumPy provides element-wise operations such as np.add(), np.subtract(), np.multiply(), and np.divide(). These functions perform arithmetic operations on arrays element-wise, eliminating the need for explicit loops.\n","\n","#### Logical Functions: Functions like np.logical_and(), np.logical_or(), and np.logical_not() are vectorized functions that perform element-wise logical operations on arrays. They are useful for boolean array manipulations and conditional computations.\n","\n","## 36.4 Performance Comparison: Vectorized Functions vs. Loops:\n","### Let's compare the performance of vectorized functions with explicit loops:\n","\n","```python \n","import numpy as np\n","\n","# Example 1: Vectorized function\n","a = np.array([1, 2, 3, 4, 5])\n","b = np.array([6, 7, 8, 9, 10])\n","\n","result = np.add(a, b)\n","print(\"Vectorized result:\", result)\n","\n","# Example 2: Loop implementation\n","result_loop = np.zeros_like(a)\n","\n","for i in range(len(a)):\n","    result_loop[i] = a[i] + b[i]\n","\n","print(\"Loop result:\", result_loop)\n","```\n","\n","### In Example 1, the np.add() function is used to perform element-wise addition on arrays a and b. This vectorized operation is concise and efficient.\n","\n","### In Example 2, the same addition operation is implemented using a loop, iterating over individual elements of the arrays and storing the results in a new array result_loop. This implementation is more cumbersome and less efficient compared to the vectorized approach.\n","\n","## 36.5 Conclusion:\n","### Chapter 36 emphasized the benefits of using vectorized functions in NumPy for performance optimization. By leveraging built-in vectorized functions, you can achieve improved efficiency, simplicity, and memory optimization in your array computations. NumPy's extensive library of vectorized functions empowers you to express complex operations concisely while benefiting from the optimized implementations. Incorporate vectorized functions into your NumPy code to enhance performance and readability.\n","\n","\n","\n","\n","\n","\n"]},{"cell_type":"markdown","id":"7ddcd0ad","metadata":{"papermill":{"duration":0.012317,"end_time":"2023-08-29T06:24:43.18707","exception":false,"start_time":"2023-08-29T06:24:43.174753","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>37 </font></h1>"]},{"cell_type":"markdown","id":"00f99775","metadata":{"papermill":{"duration":0.01249,"end_time":"2023-08-29T06:24:43.213149","exception":false,"start_time":"2023-08-29T06:24:43.200659","status":"completed"},"tags":[]},"source":["# Chapter 37: Memory Optimization Techniques\n","\n","## 37.1 Introduction:\n","### Chapter 37 explores various memory optimization techniques in NumPy to efficiently manage and optimize memory usage. Efficient memory management is crucial for large-scale data processing and can significantly impact the performance of your NumPy applications. This chapter discusses strategies to reduce memory consumption, minimize memory leaks, and optimize memory access patterns for improved efficiency.\n","\n","## 37.2 Memory Optimization Techniques:\n","### Here are some memory optimization techniques you can apply in your NumPy code:\n","\n","## 37.2.1 Use Data Types with Smaller Memory Footprint:\n","### NumPy provides a range of data types with different sizes. Choose the appropriate data type that accurately represents your data while minimizing memory usage. For example, if you're working with integers that don't require a large range, consider using np.int8 or np.uint8 instead of np.int32 to save memory.\n","\n","## 37.2.2 Avoid Unnecessary Array Copies:\n","### Avoid unnecessary array copies, as they consume additional memory. Be cautious when assigning arrays to new variables, as it might create a copy instead of a view. Use functions like np.view() or indexing operations to create views that share the same underlying data.\n","\n","## 37.2.3 Release Unused Memory:\n","### Explicitly release memory using the del keyword when arrays are no longer needed. This can help free up memory resources and prevent memory leaks.\n","\n","## 37.2.4 Chunked Processing:\n","### For large datasets, consider processing data in smaller chunks instead of loading the entire dataset into memory at once. This approach reduces memory usage by processing data incrementally.\n","\n","## 37.2.5 Memory-Mapped Arrays:\n","### NumPy supports memory-mapped arrays that map a file directly to memory. This allows you to work with arrays larger than available memory without fully loading them. Memory-mapped arrays provide efficient memory access patterns and enable out-of-core computations.\n","\n","## 37.2.6 Compressed Arrays:\n","### If your data has a significant amount of redundancy, consider using compressed arrays. NumPy provides functions like np.savez_compressed() to save arrays in compressed format, reducing the memory footprint while preserving the data.\n","\n","## 37.2.7 Iterative Computations:\n","### For iterative computations, avoid creating unnecessary intermediate arrays in each iteration. Reuse arrays whenever possible to reduce memory allocations and deallocations.\n","\n","## 37.2.8 Garbage Collection:\n","### NumPy uses reference counting for memory management. However, in some cases, cyclic references may prevent the release of memory. Enable the garbage collector (gc) module to detect and collect cyclic references, ensuring proper memory cleanup.\n","\n","## 37.3 Profiling Memory Usage:\n","### Use memory profiling tools, such as memory_profiler, to analyze memory usage in your code. Profiling helps identify memory-intensive operations and areas for optimization. It provides insights into memory allocation, deallocation, and potential memory leaks.\n","\n","## 37.4 Conclusion:\n","### Efficient memory optimization is crucial for maximizing the performance of your NumPy applications. By employing memory optimization techniques like choosing appropriate data types, avoiding unnecessary array copies, releasing unused memory, and utilizing memory-mapped arrays and compressed arrays, you can effectively reduce memory consumption and improve memory access patterns. Additionally, profiling memory usage can help identify bottlenecks and optimize memory-intensive operations. Apply these techniques in your NumPy code to achieve efficient memory management and enhance the overall performance of your applications.\n","\n","\n"]},{"cell_type":"markdown","id":"ca52292b","metadata":{"papermill":{"duration":0.012174,"end_time":"2023-08-29T06:24:43.238136","exception":false,"start_time":"2023-08-29T06:24:43.225962","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>38 </font></h1>"]},{"cell_type":"markdown","id":"ac0f022a","metadata":{"papermill":{"duration":0.012788,"end_time":"2023-08-29T06:24:43.263598","exception":false,"start_time":"2023-08-29T06:24:43.25081","status":"completed"},"tags":[]},"source":["# Chapter 38: Integrating NumPy with pandas\n","\n","## 38.1 Introduction:\n","### Chapter 38 explores the integration of NumPy and pandas, two powerful libraries in the Python ecosystem for data manipulation and analysis. NumPy provides efficient array operations, while pandas offers high-level data structures and data analysis tools. Integrating NumPy with pandas allows you to leverage the strengths of both libraries and perform advanced data manipulations and analysis tasks effectively.\n","\n","## 38.2 Understanding NumPy and pandas:\n","### NumPy is a fundamental library for numerical computing in Python. It provides multidimensional array objects, various mathematical functions, and efficient operations for manipulating arrays. NumPy's arrays serve as the building blocks for many data analysis tasks.\n","\n","### Pandas is a powerful library built on top of NumPy, offering high-level data structures such as DataFrames and Series. DataFrames are 2D tabular data structures with labeled rows and columns, similar to a spreadsheet, while Series are 1D labeled arrays. Pandas provides functionalities for data manipulation, cleaning, analysis, and visualization.\n","\n","## 38.3 Integration of NumPy with pandas:\n","### NumPy and pandas can be seamlessly integrated, as pandas internally uses NumPy arrays for data storage. Here are some ways to integrate NumPy with pandas effectively:\n","\n","### 38.3.1 Creating pandas DataFrames from NumPy arrays:\n","### You can create pandas DataFrames directly from NumPy arrays. The NumPy arrays can be used as input data for constructing DataFrames. Here's an example:\n","\n","```python \n","import numpy as np\n","import pandas as pd\n","\n","# Create a NumPy array\n","np_data = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n","\n","# Create a DataFrame from the NumPy array\n","df = pd.DataFrame(np_data, columns=['A', 'B', 'C'])\n","print(df)\n","```\n","### In this example, a NumPy array np_data is converted into a pandas DataFrame df with labeled columns 'A', 'B', and 'C'.\n","\n","### 38.3.2 Using NumPy functions and operations with pandas:\n","### You can utilize NumPy functions and operations directly on pandas DataFrames and Series. Since pandas internally uses NumPy arrays, you can apply NumPy functions to pandas objects. For example:\n","\n","```python \n","import numpy as np\n","import pandas as pd\n","\n","# Create a pandas Series\n","s = pd.Series([1, 2, 3, 4, 5])\n","\n","# Apply a NumPy function to the Series\n","result = np.sqrt(s)\n","print(result)\n","```\n","### In this example, the NumPy sqrt() function is applied to a pandas Series s, calculating the square root of each element.\n","\n","## 38.3.3 Accessing NumPy arrays from pandas objects:\n","### You can access the underlying NumPy array of a pandas DataFrame or Series using the .values attribute. This allows you to perform NumPy operations on the extracted array. For example:\n","\n","```python \n","import numpy as np\n","import pandas as pd\n","\n","# Create a pandas DataFrame\n","df = pd.DataFrame({'A': [1, 2, 3], 'B': [4, 5, 6]})\n","\n","# Access the NumPy array of the DataFrame\n","np_array = df.values\n","print(np_array)\n","```\n","### In this example, the .values attribute is used to access the NumPy array representation of the DataFrame df.\n","\n","## 38.4 Conclusion:\n","### Integrating NumPy with pandas provides a powerful combination for data manipulation and analysis in Python. By leveraging NumPy's efficient array operations and pandas' high-level data structures and analysis tools, you can perform advanced data tasks effectively. Whether it's creating DataFrames from NumPy arrays, using NumPy functions with pandas objects, or accessing NumPy arrays from pandas structures, the integration between these two libraries enhances the capabilities of data manipulation and analysis in Python.\n","\n","\n"]},{"cell_type":"markdown","id":"db2aea42","metadata":{"papermill":{"duration":0.012237,"end_time":"2023-08-29T06:24:43.288343","exception":false,"start_time":"2023-08-29T06:24:43.276106","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>39 </font></h1>"]},{"cell_type":"markdown","id":"d3b8d5d6","metadata":{"papermill":{"duration":0.012105,"end_time":"2023-08-29T06:24:43.312923","exception":false,"start_time":"2023-08-29T06:24:43.300818","status":"completed"},"tags":[]},"source":["# Chapter 39: NumPy Integration with scikit-learn\n","\n","## 39.1 Introduction:\n","### Chapter 39 explores the integration of NumPy with scikit-learn, a popular machine learning library in Python. NumPy provides efficient array operations, while scikit-learn offers a wide range of machine learning algorithms and tools. Integrating NumPy with scikit-learn allows you to preprocess and manipulate data efficiently before feeding it into machine learning models.\n","\n","## 39.2 Understanding NumPy and scikit-learn:\n","### NumPy is a fundamental library for numerical computing in Python. It provides multidimensional array objects, various mathematical functions, and efficient operations for manipulating arrays. NumPy's arrays serve as the data structure for storing and processing data in scikit-learn.\n","\n","### Scikit-learn, also known as sklearn, is a versatile machine learning library in Python. It provides a comprehensive set of tools for data preprocessing, model selection, evaluation, and more. Scikit-learn seamlessly integrates with NumPy arrays, making it an ideal choice for machine learning tasks.\n","\n","## 39.3 Integration of NumPy with scikit-learn:\n","### NumPy and scikit-learn can be effectively integrated, as scikit-learn relies on NumPy arrays as input for training models and making predictions. Here are some ways to integrate NumPy with scikit-learn:\n","\n","## 39.3.1 Data Preprocessing:\n","### NumPy arrays are often used to store the input features and target variables in machine learning tasks. Before training a model, you may need to preprocess the data. NumPy provides efficient functions for data manipulation, such as scaling, normalization, and handling missing values. You can apply these preprocessing techniques to NumPy arrays before passing them to scikit-learn algorithms.\n","\n","## 39.3.2 Feature Extraction:\n","### NumPy arrays can be used to store raw data, such as images or text, that require feature extraction before applying machine learning algorithms. NumPy provides functions for image processing, signal processing, and more. You can extract features from raw data using NumPy and then use the transformed NumPy arrays as input to scikit-learn models.\n","\n","## 39.3.3 Splitting Data:\n","### Scikit-learn provides functions for splitting data into training and testing sets, such as train_test_split(). These functions accept NumPy arrays as input and return shuffled and split arrays. You can use NumPy arrays to store your data and then split it using scikit-learn's utility functions.\n","\n","## 39.3.4 Model Training and Prediction:\n","### Scikit-learn algorithms accept NumPy arrays as input for training models and making predictions. You can create NumPy arrays to represent the input features and target variables, fit a scikit-learn model using the NumPy arrays, and then use the trained model to make predictions on new data stored in NumPy arrays.\n","\n","## 39.3.5 Performance Evaluation:\n","### Scikit-learn provides various metrics and evaluation functions to assess the performance of machine learning models. These functions accept NumPy arrays as input for comparing predicted values with actual target values. You can use NumPy arrays to store the predicted and actual values and then evaluate the performance of your models using scikit-learn's evaluation functions.\n","\n","## 39.4 Conclusion:\n","### Integrating NumPy with scikit-learn enables efficient data preprocessing, feature extraction, model training, and evaluation in machine learning tasks. By leveraging NumPy's array operations and scikit-learn's machine learning capabilities, you can effectively process and analyze data before feeding it into machine learning models. Whether it's data preprocessing, feature extraction, or model training and evaluation, the integration between NumPy and scikit-learn provides a powerful combination for machine learning tasks in Python.\n"]},{"cell_type":"markdown","id":"d83a57b6","metadata":{"papermill":{"duration":0.012298,"end_time":"2023-08-29T06:24:43.337973","exception":false,"start_time":"2023-08-29T06:24:43.325675","status":"completed"},"tags":[]},"source":["<h1 align=\"left\"><font color='red'>40 </font></h1>"]},{"cell_type":"markdown","id":"5f45ec4e","metadata":{"papermill":{"duration":0.012273,"end_time":"2023-08-29T06:24:43.362643","exception":false,"start_time":"2023-08-29T06:24:43.35037","status":"completed"},"tags":[]},"source":["# Chapter 40: Visualization with NumPy Arrays\n","\n","## 40.1 Introduction:\n","### Chapter 40 focuses on the visualization capabilities of NumPy arrays. While NumPy primarily provides efficient numerical computations and array operations, it can also be used in conjunction with visualization libraries to create informative and visually appealing plots. This chapter explores various techniques and libraries that can be utilized to visualize data stored in NumPy arrays.\n","\n","## 40.2 Visualization Libraries:\n","### There are several popular libraries in Python that can be used for data visualization with NumPy arrays. Some of these libraries include:\n","\n","## 40.2.1 Matplotlib:\n","### Matplotlib is a widely used plotting library in Python that provides a comprehensive set of functions for creating various types of plots, such as line plots, ### scatter plots, bar plots, histograms, and more. Matplotlib integrates seamlessly with NumPy arrays and allows for detailed customization of plot elements.\n","\n","## 40.2.2 Seaborn:\n","### Seaborn is a statistical data visualization library that builds on top of Matplotlib. It provides a higher-level interface and offers aesthetically pleasing default styles for creating informative statistical plots. Seaborn is particularly useful for visualizing distributions, categorical data, and statistical relationships.\n","\n","## 40.2.3 Plotly:\n","### Plotly is a versatile library that supports interactive and web-based visualizations. It offers a wide range of visualization options, including line plots, scatter plots, bar charts, heatmaps, and 3D plots. Plotly can be used to create interactive visualizations with zooming, panning, and tooltips, making it suitable for creating interactive dashboards and presentations.\n","\n","## 40.2.4 Bokeh:\n","### Bokeh is another interactive visualization library that focuses on creating interactive and visually appealing plots. It supports various plot types and provides interactivity features such as zooming, panning, and hovering. Bokeh can be used to create interactive visualizations for web applications and data exploration.\n","\n","## 40.3 Visualizing NumPy Arrays:\n","### Once you have your data stored in NumPy arrays, you can use the visualization libraries mentioned above to create visual representations. Here are some examples of how NumPy arrays can be visualized:\n","\n","## 40.3.1 Line Plots:\n","### Line plots are useful for visualizing trends and patterns in data. You can use NumPy arrays to represent the x-axis and y-axis values and create line plots using the plotting functions provided by the visualization libraries.\n","\n","## 40.3.2 Scatter Plots:\n","### Scatter plots are effective for visualizing relationships between two variables. NumPy arrays can be used to represent the x-axis and y-axis values, and you can create scatter plots to explore the distribution and correlation between variables.\n","\n","## 40.3.3 Histograms:\n","### Histograms are useful for visualizing the distribution of data. NumPy arrays can be used to store the data values, and you can create histograms to analyze the frequency and spread of the data.\n","\n","## 40.3.4 Heatmaps:\n","### Heatmaps are suitable for visualizing two-dimensional data with color gradients. NumPy arrays can represent the data, and you can create heatmaps to highlight patterns and variations in the data.\n","\n","## 40.4 Conclusion:\n","### Visualizing NumPy arrays allows for effective data exploration, analysis, and communication. By leveraging visualization libraries such as Matplotlib, Seaborn, Plotly, and Bokeh, you can create a wide range of plots and gain insights from your data stored in NumPy arrays. Whether it's line plots, scatter plots, histograms, or heatmaps, visualizing NumPy arrays enhances the understanding of the underlying data and facilitates better decision-making in data analysis tasks."]}],"metadata":{"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.10.12"},"papermill":{"default_parameters":{},"duration":14.873103,"end_time":"2023-08-29T06:24:44.505962","environment_variables":{},"exception":null,"input_path":"__notebook__.ipynb","output_path":"__notebook__.ipynb","parameters":{},"start_time":"2023-08-29T06:24:29.632859","version":"2.4.0"}},"nbformat":4,"nbformat_minor":5}