Engineering Python 13C: NumPy Array Indexing and Slicing


Welcome to Engineering Python. This is a Python programming course for engineers. In this video, I’ll talk about NumPy array
indexing and slicing. We’ll start with 1D array indexing and sliding. First, we need to import numpy as np. Let’s create a 1D array a. It contains the squared values of the integer
numbers from 0 to 4. If we want to access the second number in
this array, we use a followed by a pair of brackets then a number, 2 inside the brackets. Note in Python, indexes start from 0. So, the element with an index 2 is 4. If we want to access several elements in sequence,
we can use the slicing like this, a followed by a pair of brackets and then from 2 to 5,
including 2 but not including 5. So, the result is 4, 9, and 16. In this example, because we didn’t specify
the start point, by default it starts from index 0. This 4 means we go up to index 4 but not including
4. This 2 means a step of 2, or we select every
other element. Let’s count. Select 0, skip 1, select 2, skip 3, not including
4. So the result is just the elements in locations
0 and 2. They are 0 and 4. We can also change some elements in an array. In this example, the numbers 0 and 4 will
be replaced by -100. If we want to put the array in reverse order,
we can use this expression. No start, no end, the step is -1. This is the result. This operation is not done in place. So, a does change afterwards. Now, let’s talk about 2D array indexing. We create a 2 by 3 2D array, a, using the
reshape function. This is the zeroth row, this is the first
row. To access the first row, we use a followed
by a pair of brackets, and a number 1 inside the brackets. This is the first row, which is a 1D array. To access the element at the cross of the
first row and first column, we further append another index 1 inside a pair of brackets
like this. The element at the intersection of the first
row and the first column is 4. A more common way to access a single element
is to put the row index and the column index in the same pair of brackets, separated by
a comma, like this. The result is 4. Let’s compare 2D array indexing with the indexing
of a list of lists. b is a list of two lists. b one means the first element. It is a sublist. b one one will access the first element in
this sublist. The number is 4. However, this representation, b one comma
one will not work for lists. If you run this, it will create an error. Now, let’s create another, larger 2D array
using array reshaping. It is a 5-row by 5-column array. We will use this array to demonstrate 2D array
slicing. In the following examples, we should remember
that Python indexes always start from 0. In this statement, we will access the elements
that are in the first row, and the second and third columns. In this image, these elements are marked by
red cells. They are two numbers, 7 and 8. This statement will access the elements starting
from the third row, going up to the end row, and starting from the third column, going
up to the end column. These four elements are marked by green cells. This statement will access the elements in
all the rows and the first column. These five elements are marked by purple cells. The result is a 1D row array because we already
talked about this in the previous video, NumPy does not differentiate between 1D row arrays
and 1D column arrays. In this statement, because we didn’t specify
the start and the end for rows but we did specify the step, which is 2, we will select
the zeroth row, the second row, and the fourth row. We will also select the second column, the
fourth column. The resultant cells are marked in yellow. There is another type of indexing for NumPy
arrays. They are called advanced indexing or fancy
indexing. Basically, we access the elements in one NumPy
array using another NumPy array as the index. Let’s create a 1D NumPy array, a, with 5 elements. This is the data array. Then we create another 1D array, i, with 4
elements. This is the index array. We assemble them in this format, so the data
will come from the data array, and the indexes will come from the index array. That means, we are selecting the third element,
which is 9, the first element, which is 1, the third element, which is 9 again, and the
zeroth element, which is 0. The resultant array always has the same shape
as the index array. In this case, it also has 4 elements. Fancy indexing can also be applied to 2D index
arrays. This a is still a 1D data array with 5 elements. We create an index array j, which is a 2 by
2 array. If we assemble them in this way, we are accessing
the zeroth element in a, which is 0, the third element, which is 9, the second element, which
is 4, and the first element, which is 1. Again, the elements in the resultant array
come from the data array, and the shape is determined by the index array. So, it’s a 2 by 2 2D array. For fancy indexing, both the data array and
the index arrays can be 2D arrays. Here is an example. c is a 3 by 4 2D data array. i is a 2 by 2 2D index array for the row indexes. j is a 2 by 2 2D index array for the column
indexes. If we assemble them in this way, we are selecting
the elements in the second column, the row information is determined by the index array
i. This element will be zeroth row and second
column, this will be first row and second column, this will be first row and second
column, and the last one will be the second row and second column. The result is a 2 by 2 array. Similarly, if we assemble them in this way,
the row information is determined by the index array i, and the column information is determined
by the index array j. The result is another 2 by 2 array. We can also change the values of these elements
in the data array c to -1. So, these values in the corresponding locations
are updated as a result. Boolean arrays can also be used as indexes
for fancy indexing. Let’s see some examples. We create a data array, a. It’s a 3 by 3 2D array. We create another array b, by comparing a
with 4. This is an element-wise comparison. So the result is another boolean array with
True or False values. This is our index array. We assemble them in this way. The result is a 1D array. The shape is not the same as the index array
any more. These elements are those in a and greater
than 4. We can assign a new value -1 to these locations
so the data array is changed to this. The last four numbers are replaced by -1. We further define a boolean array i. It will serve as the index array for the row
indexes. Another boolean array j. It will serve as the index array for the column
indexes. In this statement, the row information will
come from i, and we will consider all the columns. The result is the first and second rows of
the data array because only these indexes are True. In this statement, the column information
will come from j, and we will consider all the rows. The result is the zeroth and second columns
of the data array because only these indexes are True. I need to add a little bit more about fancy
indexing. Let’s create a 5 by 5 array like this one. I represent this array in this image. Suppose we want to access the elements in
the red cells in the diagonal line. We can find their indexes and put them into
two tuples. This one is 0 and 0. So, 0 and 0. This one is 2 and 2. So, 2 and 2. This one is 4 and 4. So, 4 and 4. The resultant array is just the one we wanted. If we want to access the green cells, these
two and these four, we can do it in this way. These elements are located in the first, third,
and fourth row. So, we have a list, with 1, 3, and 4. They are the row information. These elements are located in the third and
last columns. So, this starts from 3, goes to the end column. This array is what we wanted. If we want to access the purple cells, we
can use a boolean mask like this. The data type is bool. We only want the three middle elements. So, their values are ones, and the other two
on the sides are zeros. This is the boolean array we created. These elements are located on the first row,
so, this row index is 1. The column information is supplied by this
mask. This is the result array. It’s what we wanted. Lastly, if we want to access the yellow cells,
we can use a more advanced concept called the index mesh. We create an index mesh using the ix underscore
function. The first argument is the row information. Because the yellow cells are located in the
first and fourth rows. The second argument is the column information. Because the columns are not continuous, we
use the r underscore operator to stack them together in a row. This the created index mesh. We can use this mesh directly as the index
of the data array. The result is just what we wanted. At the end of this video, I’ll talk about
array stacking and splitting. We create a 2 by 2 2D array a, which contains
0 and positive numbers. We also create another 2 by 2 2D array b,
which contains 0 and negative numbers. The vstack function will merge these two arrays
vertically, a on top of b. Note that this argument is a list. A tuple also works. However, this does not work because it’s two
arguments and not a tuple. The hstack function will merge these two arrays
horizontally, a in front of b. Note that this argument is a tuple. A list also works. Array splitting is the reverse operation compare
to stacking. We create a 3 by 3 array and use it to demonstrate
the splitting. The vsplit function passes 2 arguments, the
array a, and how many parts it will be split into. In this case, it’s 3. This array will be split vertically into three
parts. The result is three rows. The hsplit function also passes 2 arguments,
the array a, and how many parts it will be split into. It’s also 3. This array will be split horizontally into
three parts. The result is three columns. Okay, that was all about NumPy array indexing
and slicing. The course materials are available on YouTube
and GitHub. You can watch the course videos in sequence. If you like this video, please subscribe and
share. I’m Yong Wang. Thanks for watching.

7 thoughts on “Engineering Python 13C: NumPy Array Indexing and Slicing

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