15.2 NumPy
3 min read•june 24, 2024
is a powerhouse for scientific computing in Python. It provides support for large, multi-dimensional arrays and matrices, enabling fast and efficient operations on datasets. This makes it essential for data science tasks and the foundation for other libraries.
NumPy offers tools for creating and manipulating arrays, from basic indexing to reshaping and joining. It also provides a wide range of mathematical and statistical functions, allowing for efficient data processing and analysis. Understanding these features is crucial for effective data manipulation in Python.
Introduction to NumPy
Purpose and features of NumPy
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- Fundamental library for scientific computing in Python
- Provides support for large, multi-dimensional arrays and matrices
- Offers a wide range of mathematical functions to efficiently operate on these arrays
- Key features enable fast and efficient operations on large datasets
- Supports allows arrays with different shapes to work together
- Provides tools for integrating C/C++ and Fortran code
- Enables the use of sophisticated mathematical and statistical functions (
,[np.sin()](https://www.fiveableKeyTerm:np.sin())
)[np.exp()](https://www.fiveableKeyTerm:np.exp())
- Essential for data science tasks
- Allows for efficient storage and manipulation of data (
,np.array()
)[np.zeros()](https://www.fiveableKeyTerm:np.zeros()) - Serves as the foundation for other data science libraries (Pandas, SciPy)
- Allows for efficient storage and manipulation of data (
Creation and manipulation of arrays
- Create arrays using
from a list or tuplenp.array()- Create arrays with specific values using functions (
,np.zeros()
,[np.ones()](https://www.fiveableKeyTerm:np.ones())
)[np.arange()](https://www.fiveableKeyTerm:np.arange()) - Specify the data type of an array using the
parameter ([dtype](https://www.fiveableKeyTerm:dtype)
)np.array([1, 2, 3], dtype=np.float64)
- Create arrays with specific values using functions (
- Array attributes provide information about the array
returns the dimensions of the array as a tuple (shape
)(3, 4)
returns the total number of elements in the array (size
)12
returns the number of dimensions (axes) of the array (ndim
)2
- Access elements using indexing and slicing
- Use square brackets
with index or slice notation ([]
,arr[0]
)arr[1:5] - Use comma-separated indices to access elements in multi-dimensional arrays (
)arr[1, 2] - Slice arrays using the
syntax (start:stop:step
)arr[0:6:2] - Use to select multiple non-contiguous elements (
)arr[[0, 2, 4]]
- Use square brackets
- Reshape arrays to change their shape without altering data
- Use
to change the shape of an array (reshape()
)arr.reshape(2, 6) - Flatten multi-dimensional arrays into 1D arrays using
or[flatten()](https://www.fiveableKeyTerm:flatten())
([ravel()](https://www.fiveableKeyTerm:ravel())
)arr.flatten()
- Use
- Join and split arrays
- Concatenate arrays using
,[np.concatenate()](https://www.fiveableKeyTerm:np.concatenate())
, and[np.vstack()](https://www.fiveableKeyTerm:np.vstack())
([np.hstack()](https://www.fiveableKeyTerm:np.hstack())
)np.concatenate((arr1, arr2)) - Split arrays into smaller arrays using
,[np.split()](https://www.fiveableKeyTerm:np.split())
, and[np.vsplit()](https://www.fiveableKeyTerm:np.vsplit())
([np.hsplit()](https://www.fiveableKeyTerm:np.hsplit())
)np.split(arr, 3)
- Concatenate arrays using
NumPy Functions and Data Processing
NumPy functions for data processing
- Perform mathematical operations on arrays
- Element-wise arithmetic operations using
,+
,-
,*
, and/
(**
)arr1 + arr2 - Apply functions like
,[np.sqrt()](https://www.fiveableKeyTerm:np.sqrt())
, andnp.exp()
for element-wise computations ([np.log()](https://www.fiveableKeyTerm:np.log())
)np.sqrt(arr) - Use trigonometric functions like
,np.sin()
, and[np.cos()](https://www.fiveableKeyTerm:np.cos())
on arrays ([np.tan()](https://www.fiveableKeyTerm:np.tan())
)np.sin(arr) - Utilize for efficient element-wise operations
- Element-wise arithmetic operations using
- Calculate statistical measures
- Summary statistics using
,[np.mean()](https://www.fiveableKeyTerm:np.mean())
,[np.median()](https://www.fiveableKeyTerm:np.median())
, and[np.std()](https://www.fiveableKeyTerm:np.std())
([np.var()](https://www.fiveableKeyTerm:np.var())
)np.mean(arr) - Find the minimum and maximum values using
and[np.min()](https://www.fiveableKeyTerm:np.min())
([np.max()](https://www.fiveableKeyTerm:np.max())
)np.max(arr) - Compute the sum and product of array elements using
and[np.sum()](https://www.fiveableKeyTerm:np.sum())
([np.prod()](https://www.fiveableKeyTerm:np.prod())
)np.sum(arr) - Specify the for operations to work along different dimensions (
)np.mean(arr, axis=0)
- Summary statistics using
- Utilize broadcasting to work with arrays of different shapes
- NumPy automatically broadcasts arrays to make their shapes compatible (
)arr1 + arr2
- NumPy automatically broadcasts arrays to make their shapes compatible (
- Mask and filter arrays
- Create boolean masks using comparison operators (
,>
,<
,==
)!= - Use boolean masks to filter arrays and select specific elements (
)arr[arr > 5] - Combine boolean masks using logical operators (
,&
,|
)~
- Create boolean masks using comparison operators (
- Generate random numbers
- Use the
module to generate random numbers (np.random
)np.random.rand(3, 4) - Create arrays with random values using functions like
and[np.random.rand()](https://www.fiveableKeyTerm:np.random.rand())
([np.random.randn()](https://www.fiveableKeyTerm:np.random.randn())
)np.random.randn(5) - Generate random integers using
([np.random.randint()](https://www.fiveableKeyTerm:np.random.randint())
)np.random.randint(0, 10, size=(2, 3))
- Use the
Advanced NumPy Concepts
- for heterogeneous data types
- Create arrays with named fields and different data types
- Access fields using dot notation or string indexing
- and performance optimization
- Understand row-major (C-style) vs. column-major (Fortran-style) order
- Use to efficiently access array elements in memory
- Array views vs. copies
- Create views of arrays without copying data
- Understand when operations create new arrays or modify existing ones
Key Terms to Review (51)
Array Indexing: Array indexing is a fundamental concept in programming that allows you to access and manipulate individual elements within an array. It provides a way to reference specific data points within a collection of related data.
Array Slicing: Array slicing is a fundamental operation in NumPy that allows you to extract a subset of elements from a NumPy array. It enables you to access and manipulate specific portions of an array based on their position or index.
Axis: In the context of NumPy, the term 'axis' refers to the dimension along which an operation is performed on a multi-dimensional array. It provides a way to specify the direction in which a function should operate, allowing for efficient and flexible data manipulation.
Broadcasting: Broadcasting is a fundamental concept in the field of NumPy, which is a powerful library for scientific computing in Python. It refers to the ability of NumPy to perform operations on arrays of different shapes, allowing them to be automatically resized or expanded to match the desired operation.
Dtype: dtype, short for 'data type', is a fundamental concept in the NumPy library that defines the type of data stored in a NumPy array. It determines the size, format, and range of values that can be represented in each element of the array.
Fancy Indexing: Fancy indexing, in the context of NumPy, refers to the advanced and flexible way of selecting and manipulating elements within a NumPy array. It allows for more complex and specific data extraction and manipulation beyond the basic indexing techniques.
Flatten(): Flatten() is a NumPy function that takes a multi-dimensional array and converts it into a one-dimensional array. It is used to simplify the structure of complex arrays and make them easier to work with.
Memory Layout: Memory layout refers to the organization and arrangement of data in a computer's memory. It describes how different types of data, such as variables, arrays, and objects, are stored and accessed within the available memory space.
Ndarray: An ndarray, or N-dimensional array, is the fundamental data structure in the NumPy library for Python. It is a multi-dimensional array that can hold elements of the same data type, allowing for efficient storage and manipulation of large datasets.
Ndarray.reshape(): The ndarray.reshape() method in NumPy is used to change the shape of an existing NumPy array without changing its data. It allows you to rearrange the elements of an array into a new shape, making it a powerful tool for data manipulation and visualization.
Ndarray.shape: The ndarray.shape attribute in NumPy provides information about the dimensions of a NumPy array. It returns a tuple that describes the size of the array along each axis.
Ndarray.size: The ndarray.size attribute in NumPy returns the total number of elements in the array. It provides information about the overall size or number of elements that make up the NumPy array object.
Np.arange(): np.arange() is a NumPy function that generates an array of evenly spaced values within a specified interval. It is a powerful tool for creating sequences of numbers, which is essential for various numerical and scientific computations in the context of the NumPy library.
Np.concatenate(): np.concatenate() is a NumPy function that joins a sequence of arrays along an existing axis to form a single array. It allows you to combine multiple arrays into one, which is a common operation in data analysis and machine learning tasks.
Np.cos(): np.cos() is a NumPy function that calculates the cosine of each element in an input array. It is a trigonometric function that returns the x-coordinate of a point on the unit circle, given the angle in radians.
Np.exp(): np.exp() is a NumPy function that calculates the exponential of each element in the input array. It is a fundamental mathematical operation that is widely used in various scientific and engineering applications, particularly in the fields of statistics, machine learning, and data analysis.
Np.hsplit(): np.hsplit() is a NumPy function that splits an array along the horizontal axis, creating a list of sub-arrays. It is a convenient way to divide a 2D array into smaller pieces for further processing or analysis.
Np.hstack(): np.hstack() is a NumPy function that horizontally stacks a sequence of arrays. It takes a sequence of arrays and concatenates them along the horizontal (column) axis, creating a single 2D array as the output.
Np.log(): np.log() is a NumPy function that calculates the natural logarithm of each element in the input array. The natural logarithm, also known as the Napier's logarithm, is a logarithm with the base e, where e is the mathematical constant approximately equal to 2.71828. This function is useful for various mathematical and scientific applications that involve exponential and logarithmic relationships.
Np.max(): np.max() is a NumPy function that returns the maximum value along a given axis of an array. It is used to find the largest element in an array or the largest element along a particular dimension of a multi-dimensional array.
Np.mean(): np.mean() is a function in the NumPy library that calculates the arithmetic mean or average of the elements in a NumPy array. It provides a simple way to determine the central tendency of a dataset, which is a crucial concept in data analysis and statistical inference.
Np.median(): np.median() is a function in the NumPy library that calculates the median value of the elements in a given array or list. The median is the middle value when the data is arranged in numerical order, and it represents the central tendency of the data set.
Np.min(): np.min() is a function in the NumPy library that returns the minimum value along a specified axis of an array. It is a powerful tool for quickly identifying the smallest element in a dataset, which can be useful for data analysis and processing tasks.
Np.ones(): np.ones() is a NumPy function that creates a new array of a specified size, filled with ones. It is a convenient way to generate arrays of a specific shape and data type, where all elements are initialized to the value of 1.
Np.prod(): np.prod() is a NumPy function that calculates the product of all the elements in a given array or along a specified axis. It is a powerful tool for performing mathematical operations on arrays in a concise and efficient manner.
Np.random.rand(): np.random.rand() is a function in the NumPy library that generates an array of random numbers with a uniform distribution between 0 and 1. It is a powerful tool for creating random data, which is essential for tasks such as statistical analysis, simulations, and machine learning.
Np.random.randint(): np.random.randint() is a function in the NumPy library that generates a random integer within a specified range. It is a powerful tool for introducing randomness and unpredictability into your Python programs, which can be useful in a variety of applications, such as simulations, games, and data analysis.
Np.random.randn(): np.random.randn() is a function in the NumPy library that generates random numbers from a normal (Gaussian) distribution with a mean of 0 and a standard deviation of 1. It is a powerful tool for generating random data that follows a bell-shaped curve, which is useful in various statistical and numerical applications.
Np.sin(): np.sin() is a NumPy function that calculates the sine of each element in an array or scalar value. It is a fundamental trigonometric function that is widely used in various scientific and mathematical applications.
Np.split(): np.split() is a NumPy function that divides a given array into multiple smaller arrays along a specified axis. It allows you to split an array into several sub-arrays without modifying the original array.
Np.sqrt(): np.sqrt() is a function in the NumPy library that calculates the square root of each element in an array or a single number. It is a powerful tool for performing mathematical operations on numerical data in a concise and efficient manner.
Np.std(): np.std() is a function in the NumPy library that calculates the standard deviation of the elements in an array or along a specified axis. The standard deviation is a measure of the spread or dispersion of a dataset, indicating how much the values vary from the mean or average value.
Np.sum(): np.sum() is a NumPy function that calculates the sum of all the elements in an array or along a specified axis. It provides a convenient way to aggregate and summarize numerical data stored in multi-dimensional arrays, which are the fundamental data structures in NumPy.
Np.tan(): np.tan() is a function in the NumPy library that calculates the tangent of an array of angles. It takes an array of angle values as input and returns an array of the corresponding tangent values.
Np.var(): np.var() is a NumPy function that calculates the variance of the elements in an array. Variance is a measure of the spread or dispersion of a dataset, indicating how far each element is from the mean value.
Np.vsplit(): np.vsplit() is a function in the NumPy library that vertically splits a given array into multiple sub-arrays. It allows you to divide a 2D array into smaller 2D arrays along the vertical axis, creating a list of these split arrays.
Np.vstack(): np.vstack() is a NumPy function that vertically stacks a sequence of arrays. It takes a sequence of arrays and concatenates them along the 'vertical' axis (row-wise) to create a single array.
Np.zeros(): np.zeros() is a function in the NumPy library that creates a new array of a specified shape, filled with zeros. It is a powerful tool for initializing arrays with a known starting point, which is essential in many numerical and scientific computing applications.
NumPy: NumPy is a powerful open-source library for numerical computing in Python, providing support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. It is a fundamental library for scientific computing in Python, and its efficient implementation and use of optimized underlying libraries make it a crucial tool for data analysis, machine learning, and a wide range of scientific and engineering applications.
Numpy.array(): numpy.array() is a fundamental function in the NumPy library that allows for the creation of multidimensional arrays, which are essential data structures for numerical computing and data analysis in Python. These arrays provide a powerful and efficient way to store and manipulate large amounts of data, enabling advanced mathematical operations and scientific computing.
Numpy.inf: In the context of the NumPy library, 'numpy.inf' is a special floating-point value that represents positive infinity. It is a constant that can be used to represent values that are larger than any finite number, indicating an unbounded or limitless quantity.
Numpy.linalg: numpy.linalg is a module within the NumPy library that provides functions and classes for performing linear algebra operations, such as matrix decomposition, solving linear systems, and calculating eigenvalues and eigenvectors. It serves as a powerful tool for working with numerical data and matrices in Python.
Numpy.pi: numpy.pi is a constant in the NumPy library that represents the mathematical constant pi, which is approximately equal to 3.14159. It is a fundamental mathematical constant that is widely used in various mathematical and scientific calculations.
Numpy.random: numpy.random is a module within the NumPy library that provides a wide range of functions for generating random numbers and random distributions. It allows for the creation of pseudo-random numbers, which can be useful in various applications such as simulations, data analysis, and machine learning.
Numpy.ufunc: A numpy.ufunc, or universal function, is a function in the NumPy library that operates on arrays element-wise, performing a specific mathematical operation. These functions are optimized for speed and can be applied to entire arrays, making them efficient for numerical computations and data analysis.
Ravel(): The ravel() function in NumPy is used to flatten a multi-dimensional array into a one-dimensional array. It takes a multi-dimensional array as input and returns a flattened one-dimensional array that contains all the elements of the original array in a sequential order.
Strides: In the context of NumPy, strides refer to the step size or the number of bytes between consecutive elements along each dimension of an array. Strides determine how the array data is interpreted and accessed, allowing for efficient memory usage and manipulation of multi-dimensional arrays.
Structured Arrays: Structured arrays, also known as record arrays or structured data types, are a feature in NumPy that allow for the storage and manipulation of data with a more complex structure than the standard numeric arrays. These arrays can contain fields or columns of different data types, similar to the structure of a database table or a spreadsheet.
Travis Oliphant: Travis Oliphant is a renowned computer scientist and mathematician who has made significant contributions to the field of scientific computing, particularly in the development of the NumPy library, a fundamental tool for numerical computing in Python.
Universal Functions (ufuncs): Universal functions, or ufuncs, are a fundamental concept in the NumPy library, which is a powerful tool for scientific computing in Python. Ufuncs are vectorized, element-wise operations that can be applied to entire arrays or individual elements, making them highly efficient and convenient for data manipulation and analysis.
Vectorization: Vectorization is the process of converting a series of scalar operations into a single vector operation, allowing for more efficient and faster computations. This concept is particularly important in the context of numerical computing and data analysis, as it enables the use of powerful mathematical libraries and hardware optimizations.