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Data manipulation in Python is nearly synonymous with NumPy array manipulation: even newer tools like Pandas (Chapter 3) are built around the NumPy array. This section will present several examples of using NumPy array manipulation to access data and subarrays, and to split, reshape, and join the arrays. While the types of operations shown here may seem a bit dry and pedantic, they comprise the building blocks of many other examples used throughout the book. Get to know them well!
We'll cover a few categories of basic array manipulations here:
First let's discuss some useful array attributes. We'll start by defining three random arrays, a one-dimensional, two-dimensional, and three-dimensional array. We'll use NumPy's random number generator, which we will seed with a set value in order to ensure that the same random arrays are generated each time this code is run:
In [1]:
import numpy as np
np.random.seed(0) # seed for reproducibility
x1 = np.random.randint(10, size=6) # One-dimensional array
x2 = np.random.randint(10, size=(3, 4)) # Two-dimensional array
x3 = np.random.randint(10, size=(3, 4, 5)) # Three-dimensional array
Each array has attributes ndim (the number of dimensions), shape (the size of each dimension), and size (the total size of the array):
In [2]:
print("x3 ndim: ", x3.ndim)
print("x3 shape:", x3.shape)
print("x3 size: ", x3.size)
Another useful attribute is the dtype, the data type of the array (which we discussed previously in Understanding Data Types in Python):
In [3]:
print("dtype:", x3.dtype)
Other attributes include itemsize, which lists the size (in bytes) of each array element, and nbytes, which lists the total size (in bytes) of the array:
In [4]:
print("itemsize:", x3.itemsize, "bytes")
print("nbytes:", x3.nbytes, "bytes")
In general, we expect that nbytes is equal to itemsize times size.
If you are familiar with Python's standard list indexing, indexing in NumPy will feel quite familiar. In a one-dimensional array, the $i^{th}$ value (counting from zero) can be accessed by specifying the desired index in square brackets, just as with Python lists:
In [5]:
x1
Out[5]:
In [6]:
x1[0]
Out[6]:
In [7]:
x1[4]
Out[7]:
To index from the end of the array, you can use negative indices:
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x1[-1]
Out[8]:
In [9]:
x1[-2]
Out[9]:
In a multi-dimensional array, items can be accessed using a comma-separated tuple of indices:
In [10]:
x2
Out[10]:
In [11]:
x2[0, 0]
Out[11]:
In [12]:
x2[2, 0]
Out[12]:
In [13]:
x2[2, -1]
Out[13]:
Values can also be modified using any of the above index notation:
In [14]:
x2[0, 0] = 12
x2
Out[14]:
Keep in mind that, unlike Python lists, NumPy arrays have a fixed type. This means, for example, that if you attempt to insert a floating-point value to an integer array, the value will be silently truncated. Don't be caught unaware by this behavior!
In [15]:
x1[0] = 3.14159 # this will be truncated!
x1
Out[15]:
Just as we can use square brackets to access individual array elements, we can also use them to access subarrays with the slice notation, marked by the colon (:) character.
The NumPy slicing syntax follows that of the standard Python list; to access a slice of an array x, use this:
x[start:stop:step]
If any of these are unspecified, they default to the values start=0, stop=size of dimension, step=1.
We'll take a look at accessing sub-arrays in one dimension and in multiple dimensions.
In [16]:
x = np.arange(10)
x
Out[16]:
In [17]:
x[:5] # first five elements
Out[17]:
In [18]:
x[5:] # elements after index 5
Out[18]:
In [19]:
x[4:7] # middle sub-array
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In [20]:
x[::2] # every other element
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In [21]:
x[1::2] # every other element, starting at index 1
Out[21]:
A potentially confusing case is when the step value is negative.
In this case, the defaults for start and stop are swapped.
This becomes a convenient way to reverse an array:
In [22]:
x[::-1] # all elements, reversed
Out[22]:
In [23]:
x[5::-2] # reversed every other from index 5
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In [24]:
x2
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In [25]:
x2[:2, :3] # two rows, three columns
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In [26]:
x2[:3, ::2] # all rows, every other column
Out[26]:
Finally, subarray dimensions can even be reversed together:
In [27]:
x2[::-1, ::-1]
Out[27]:
In [28]:
print(x2[:, 0]) # first column of x2
In [29]:
print(x2[0, :]) # first row of x2
In the case of row access, the empty slice can be omitted for a more compact syntax:
In [30]:
print(x2[0]) # equivalent to x2[0, :]
One important–and extremely useful–thing to know about array slices is that they return views rather than copies of the array data. This is one area in which NumPy array slicing differs from Python list slicing: in lists, slices will be copies. Consider our two-dimensional array from before:
In [31]:
print(x2)
Let's extract a $2 \times 2$ subarray from this:
In [32]:
x2_sub = x2[:2, :2]
print(x2_sub)
Now if we modify this subarray, we'll see that the original array is changed! Observe:
In [33]:
x2_sub[0, 0] = 99
print(x2_sub)
In [34]:
print(x2)
This default behavior is actually quite useful: it means that when we work with large datasets, we can access and process pieces of these datasets without the need to copy the underlying data buffer.
In [35]:
x2_sub_copy = x2[:2, :2].copy()
print(x2_sub_copy)
If we now modify this subarray, the original array is not touched:
In [36]:
x2_sub_copy[0, 0] = 42
print(x2_sub_copy)
In [37]:
print(x2)
In [38]:
grid = np.arange(1, 10).reshape((3, 3))
print(grid)
Note that for this to work, the size of the initial array must match the size of the reshaped array.
Where possible, the reshape method will use a no-copy view of the initial array, but with non-contiguous memory buffers this is not always the case.
Another common reshaping pattern is the conversion of a one-dimensional array into a two-dimensional row or column matrix.
This can be done with the reshape method, or more easily done by making use of the newaxis keyword within a slice operation:
In [39]:
x = np.array([1, 2, 3])
# row vector via reshape
x.reshape((1, 3))
Out[39]:
In [40]:
# row vector via newaxis
x[np.newaxis, :]
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In [41]:
# column vector via reshape
x.reshape((3, 1))
Out[41]:
In [42]:
# column vector via newaxis
x[:, np.newaxis]
Out[42]:
We will see this type of transformation often throughout the remainder of the book.
In [43]:
x = np.array([1, 2, 3])
y = np.array([3, 2, 1])
np.concatenate([x, y])
Out[43]:
You can also concatenate more than two arrays at once:
In [44]:
z = [99, 99, 99]
print(np.concatenate([x, y, z]))
It can also be used for two-dimensional arrays:
In [45]:
grid = np.array([[1, 2, 3],
[4, 5, 6]])
In [46]:
# concatenate along the first axis
np.concatenate([grid, grid])
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In [47]:
# concatenate along the second axis (zero-indexed)
np.concatenate([grid, grid], axis=1)
Out[47]:
For working with arrays of mixed dimensions, it can be clearer to use the np.vstack (vertical stack) and np.hstack (horizontal stack) functions:
In [48]:
x = np.array([1, 2, 3])
grid = np.array([[9, 8, 7],
[6, 5, 4]])
# vertically stack the arrays
np.vstack([x, grid])
Out[48]:
In [49]:
# horizontally stack the arrays
y = np.array([[99],
[99]])
np.hstack([grid, y])
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Similary, np.dstack will stack arrays along the third axis.
In [50]:
x = [1, 2, 3, 99, 99, 3, 2, 1]
x1, x2, x3 = np.split(x, [3, 5])
print(x1, x2, x3)
Notice that N split-points, leads to N + 1 subarrays.
The related functions np.hsplit and np.vsplit are similar:
In [51]:
grid = np.arange(16).reshape((4, 4))
grid
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In [52]:
upper, lower = np.vsplit(grid, [2])
print(upper)
print(lower)
In [53]:
left, right = np.hsplit(grid, [2])
print(left)
print(right)
Similarly, np.dsplit will split arrays along the third axis.