1 What is NumPy?
NumPy (standing for Numerical Python) is a popular library in Python that can efficiently process multidimensional data arrays. It is also the foundation of other advanced Python libraries such as Pandas.
Examples of 1dimensinoal array: the elements must have the same data type
- [2, 7, 10, 6] # an array of integers, shape is (4)
- [73.5, 67.0, 87.5, 58.5, 92.0] # an array of student grades or stock prices, shape is (5)
- [Sam, John, Zoe] # an array of names, shape is (3)
Examples of 2diminsionial array: an array of array with the same shape and data type
- [ [3, 6, 4, 8],
[2, 7, 5, 9],
[4, 8, 6, 1] ] # an array with 3 elements; each element is an array with 4 integers. Shape = (3, 4)
The major features of NumPy include:
- Easily generate and store data in memory in the form of multidimensional array
- Easily load and store data on disk in binary, text, or CSV format
- Support efficient operations on data arrays, including basic arithmetic and logical operations, shape manipulation, data sorting, data slicing, linear algebra, statistical operation, discrete Fourier transform, etc.
- Vectorised computation: simple syntax for elementwise operations without using loops (e.g., a = b + c where a, b and c are three multidimensional arrays with the same shape).
In order to use NumPy, we need to import the module numpy first. A widely used convention is to use np as a short name of numpy. In this labsheet, when you see np.xxx, it is the same as numpy.xxx. Remark: the module name of NumPy library is numpy (i.e., lowercase).
import numpy as np
2 The data type of Ndimensional array: ndarray
The core of NumPy is the Ndimensional array datatype ndarray. It can store a collection of data items with the same type, i.e., the array is homogeneous. This makes it very different from list. A list is more flexible, but less efficient. ndarray can only store items with the same type, but its performance is much better than list (i.e., it takes a shorter time to process the same amount of data).
An ndarray object has the following properties:
| ndarray.ndim | The number of dimensions of the array (i.e., 1 or 2 or 3 ) |
| ndarray.shape | The dimensions of the array (i.e., number of elements in each dimension) |
| ndarray.size | The total number of elements of the array |
| ndarray.dtype | The data type of the array |
| ndarray.itemsize | The number of bytes of each data element |
| ndarray.data | The buffer that stores the data elements of the array |
NumPy supports the following popular data types:
- Integers with different sizes: int8 / int16 / int32 / int64 / uint8 / uint16 / uint32 / unit64
- Real numbers with different sizes: float16 / float32 / float64 / float128
- Complex numbers with different sizes: complex64 / complex128 / complex256
- bool
- Traditional ASCII string with constant length (one byte per character): S10 means a sting with 10 characters
- Unicode string with constant length: U10 means a string with 10 unicode characters
Example 1: Try the following statements about a two-dimensional array:
a = np.arange(20) # generate a one-dimensional array first print(a) # [ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19] a = a.reshape(4, 5) # generate a two-dimensional array from a, and assign it to a print(a) type(a) # numpy.ndarray print(a.ndim) # 2 print(a.shape) # (4, 5) print(a.dtype.name) # int32 print(a.itemsize) # 4 print(a.size) # 20
Exercise 1: Use numpy.arange() to generate a 1-dimenstional array with 100 odd numbers 1, 3, 5, , 199. Then use numpy.reshape() to generate a two-dimensional array with shape (10, 10). Print out the shape, size, and data of the two-dimensional array.
3 How to create ndarray objects?
We will study four different approaches to creating ndarray objects.
- Use the numpy.array( ) function to generate an ndarray object from any sequence-like object (e.g., list and tuple)
Example 2: Try the following statements about creating ndarrays from lists
| # import numpy as np#generate a one-dimensional array from a sequence of data data1 = [1, 2, 3, 4, 5, 6] arr1 = np.array(data1) print(arr1) print(arr1.ndim) print(arr1.shape)#generate a two-dimensional array from a sequence of sequence of datadata2 = [ [1, 2, 3, 4], [5, 6, 7, 8] ] arr2 = np.array(data2) print(arr2) print(arr2.ndim) print(arr2.shape)#generate a three-dimensional array from a sequence of sequence of sequence of datadata3 = [ [ [1, 2, 3, 4], [5, 6, 7, 8] ],[ [9, 10, 11, 12], [13, 14, 15, 16] ], [ [17, 18, 19, 20], [21, 22, 23, 24] ] ] arr3 = np.array(data3) print(arr3) print(arr3.ndim) print(arr3.shape) |
- Use the following functions to generate some special ndarray object. Use help( ) to find out the details of each function.
| Function | Example | Description |
| arange | arr = np.arange(20) | Return evenly spaced values within a given interval, simiar to the built-in range( ) function. |
| ones | arr = np.ones(10) | An array of all 1s with the given shape |
| zeros | arr = np.zeros( (2, 3) ) | An array of all 0s with the given shape |
| full | arr = np.full( (3, 4), 1.2) | An array of all specified value with the given shape |
| empty | arr = np.empty( (2, 5) ) | An array with the given shape without initial data |
eye arr = np.eye(6) A square NxN identity matrix
Example 3: Try the following statements to learn different array generating functions
arr = np.ones(10) print(arr) arr = np.zeros( (2, 3) ) print(arr) arr = np.full( (3, 4), 1.2) print(arr) arr = np.empty( (2, 5) ) print(arr) arr = np.eye(6) print(arr)
- Generate ndarray with random numbers (random sampling)
The numpy.random module provides functions to generate arrays of sample values from popular probability distributions.
Reference: https://docs.scipy.org/doc/numpy/reference/routines.random.html
Example 4: Try the following statements to generate different random arrays. Use help( ) to understand the functions random(), randint(), randn(), and uniform() in numpy.random module.
help(np.random.random) #
| arr = np.random.random((2,3)) # Return 23 random floats in half-open interval [0.0, 1.0) print(arr) arr = np.random.randint(10, 100, 10) # Return 10 random integers in half-open interval [10, 100) arr = np.random.randn(6, 3) # Draw 63 samples from standard normal distributionprint(arr) arr = np.random.uniform(-1, 1, 10) # Draw 10 samples from a uniform distribution in (-1, 1)print(arr) |
- Save ndarray to disk file, and ndarray from disk file
Example 5: Try the following statements to save ndarray as binary file and load ndarray from binary file (which was previously created by numpy.save() function).
- Binary format (which is not suitable for human to read)
arr1 = np.arange(2, 100, 2) # Return an array of [2, 4, 6, , 96, 98] with stepsize of 2 np.save(even.npy, arr1) # save ndarray to file even.npy arr2 = np.load(even.npy) # load data from even.npy and create an ndarray print(arr2)
Example 6: Try the following statements to save ndarray as txt file and load ndarray from txt file.
- Txt format (which is suitable for human to read)
arr1 = np.arange(0.0, 10.0, 0.5) np.savetxt(half.txt, arr1, fmt=%.6f) # You can use a text editor to open half.txt arr2 = np.loadtxt(half.txt) print(arr2)
Exercise 2: Create the following ndarray objects:
- Create an ndarray of shape (8, 8) and all data are 2.5
- Create an ndarray of shape (4, 4) whose values range from 0 to 15
- Create a 6 6 identity matrix
- Create a random array of size 20 with standard normal distribution and find its mean value
- Create a random array of shape (3, 6) with random integers in the range of [1, 50).
- Create a random array of shape (4, 5) with uniform distribution in the range of [0, 10). Find its maximum and minimum values and the mean value.
4 How to access and manipulate data in ndarray?
Accessing data in one-dimensional ndarray is similar to the case of list.
Array indexing: use the square brackets ([ ]) to index array values. To access a single data element in two-dimensional ndarray, you need to specify the coordinate of the element (i.e., the indices on the two axes).
If you index a multidimensional array with fewer indices than dimensions, you will get a sub-dimensional array.
Example 7: Try the following statements to access items in ndarray
arr2d = np.array([ [1,2,3], [4,5,6], [7,8,9] ]) arr1d = arr2d[2] print(arr1d) # [7, 8, 9] print(arr2d[1]) # [4, 5, 6] arr2d[1][2] = 10 # we can change the values in ndarray print(arr2d[1]) # [4, 5, 10] print(arr2d[0][2]) # 3 print(arr2d[0,2]) # 3, the same as the previous print()
Slicing: Slicing on ndarray is similar to sequence slicing, but more complicated for 2 or 3-dimensions.
arr1d = np.arange(20) print(arr1d) arr1d[:10] = 20 # change of first 10 values in arr1d to 20 print(arr1d) arr1d[10:15] = -1 # change the next 5 values to -1 print(arr1d) arr1d[-5:] = 0 # change the last 5 values in arr1d to 0 print(arr1d)
5 More data processing in ndarray
(1) Universal functions: perform elementwise operations on data in ndarrays
Mathematical functions: https://docs.scipy.org/doc/numpy/reference/routines.math.html
Example 8: Try some vectorised operations and universal functions on ndarrays:
x = np.array([1, 2, 3, 4]) y = np.array([5, 6, 6, 8]) print(x+y) # [6 8 9 12] print(x*y) # [5 12 18 32] arr = np.arange(10) print(arr) # [0 1 2 3 4 5 6 7 9 9] print(np.sqrt(arr)) # [0. 1. 1.41421356 1.73205081 2. 2.23606798 ] print(np.exp(arr))
(2) Statistics
Reference: https://docs.scipy.org/doc/numpy/reference/routines.statistics.html
Example 9: Try some statistical methods of ndarrays
arr = np.random.randn(20, 5)
print(arr) print(The mean is, arr.mean()) print(The standard deviation is, arr.std()) print(The max and min are:, arr.max(), arr.min()) print(The index of the min is {} and the index of the max is {}.format(arr.argmin(), arr.argmax()))
Additional Resources:
If you want to learn more about NumPy, please try the following series of tutorials: https://www.tutorialspoint.com/numpy/index.htm
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