# Functions for Creating NumPy Arrays¶

This section presents standard methods for creating NumPy arrays of varying shapes and contents. NumPy provides a laundry list of functions for creating arrays:

>>> import numpy as np

# creating an array from a Python sequence
>>> np.array([i**2 for i in range(5)])
array([ 0,  1,  4,  9, 16])

# creating an array filled with ones
>>> np.ones((2, 4))
array([[ 1.,  1.,  1.,  1.],
[ 1.,  1.,  1.,  1.]])

# creating an array of evenly-spaced points
>>> np.linspace(0, 10, 5)
array([  0. ,   2.5,   5. ,   7.5,  10. ])

# creating an array by sampling 10 numbers
# randomly from a mean-1, std-dev-5 normal
# distribution
>>> np.random.normal(1, 5, 10)
array([ 2.549537  ,  2.75144951,  0.60031823,  3.75185732,  4.65543858,
0.55779525,  1.15574987, -1.98461337,  5.39771083, -7.81395192])

# creating an array of a specified datatype
>>> np.array([1.5, 3.20, 5.78], dtype=int)
array([1, 3, 5])


## Creating Arrays from Python Sequences¶

You can create an array from a Python list or tuple by using NumPy’s array function. NumPy will interpret the structure of the data it receives to determine the dimensionality and shape of the array. For example, a single list of numbers will be used to create a 1-dimensional array:

# a list of numbers will become a 1D-array
>>> np.array([1., 2., 3.])  # shape: (3,)
array([ 1.,  2.,  3.])


Nested lists/tuples will be used to construct multidimensional arrays. For example, a “list of equal-length lists of numbers” will lead to a 2-dimensional array; each of the inner-lists comprises a row of the array. Thus a list of two, length-three lists will produce a (2,3)-shaped array:

# a list of lists of numbers will produce a 2D-array
>>> np.array([[1., 2., 3.], [4., 5., 6.]])  # shape: (2, 3)
array([[ 1.,  2.,  3.],
[ 4.,  5.,  6.]])


A “list of equal-length lists, of equal-length lists of numbers” creates a 3D-array, and so on. Recall that using repeated concatenation, [0]*3 will produce [0, 0, 0]. Using this, let’s create two lists, each containing three lists, each containing four zeros; feeding this to np.array thus produces a 2x3x4 array of zeros:

# A list of lists of lists of zeros creates a 3D-array
>>> np.array([[[0]*4]*3]*2)
array([[[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]],

[[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]])


You will seldom use lists to form high-dimensional arrays like this. Instead, there are other array-creation functions that are more amendable to generating high-dimensional data, which we will introduce next. For example, we will see that the np.zeros function is a much more civilized way to create a high-dimensional array of zeros.

Warning!

You actually can create an array from lists of unequal lengths. The resulting array is not an ND-array as it has no well-defined dimensionality. Instead, something called an object-array is produced, which does not benefit from the majority of NumPy’s features. This is a relatively obscure feature of the NumPy library, and should be avoided unless you really know what you’re doing!

## Creating Constant Arrays: zeros and ones¶

NumPy provides the functions zeros and ones, which will fill an array of user-specified shape with 0s and 1s, respectively:

# create a 3x4 array of zeros
>>> np.zeros((3, 4))
array([[ 0.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.],
[ 0.,  0.,  0.,  0.]])

# create a shape-(4,) array of ones
>>> np.ones((4,))
array([ 1.,  1.,  1.,  1.])


NumPy provides additional functions for creating constant-valued arrays. Please refer to the official documentation for a complete listing.

## Creating Sequential Arrays: arange and linspace¶

The arange function allows you to initialize a sequence of integers based on a starting point (inclusive), stopping point (exclusive), and step size. This is very similar to the range function; however arange immediately creates this sequence as an array, whereas range produces a generator.

>>> np.arange(0, 10, 1)  # start (included): 0, stop (excluded): 10, step:1
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

# supplying one value to arange amounts to specifying the stop value
# start=0 and step=1 are then used as defaults
>>> np.arange(10)  # equivalent to: start: 0, stop: 10, step:1
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

>>> np.arange(-5, 6, 2) # start (included): -5, stop (excluded): 6, step:2
array([-5, -3, -1,  1,  3,  5])


The linspace function allows you to generate $$N$$ evenly-spaced points within a user-specified interval $$[i, j]$$ ($$i$$ and $$j$$ are included in the interval). This is often used to generate a domain of values on which to evaluate a mathematical function (e.g. if you want to the sine function from $$-\pi$$ to $$\pi$$ on a finely-divided grid).

# generate five evenly-spaced points on the interval [-1, 1]
>>> np.linspace(-1, 1, 5)
array([-1. , -0.5,  0. ,  0.5,  1. ])

# generate two evenly-spaced points on the interval [3, 4]
>>> np.linspace(3, 4, 2)
array([ 3.,  4.])

# generate 100 evenly-spaced points on the interval [-pi, pi]
>>> np.linspace(-np.pi, np.pi, 100)
array([-3.14159265, ..., 3.14159265])


Numpy has other functions for creating sequential arrays, such as producing an array spaced evenly on a log-scaled interval. See the official documentation for a complete listing.

## Creating Arrays Using Random Sampling¶

Several functions can be accessed from np.random, which populate arrays of a user-specified shape by drawing randomly from a specified statistical distribution:

# create a shape-(3,3) array by drawing its entries randomly
# from the uniform distribution [0, 1)
>>> np.random.rand(3,3)
array([[ 0.09542611,  0.13183498,  0.39836068],
[ 0.7358235 ,  0.77640024,  0.74913595],
[ 0.37702688,  0.86617624,  0.39846429]])

# create a shape-(5,) array by drawing its entries randomly
# from a mean-0, variance-1 normal (a.k.a. Gaussian) distribution
>>> np.random.randn(5)
array([-1.11262121, -0.35392007,  0.4245215 , -0.81995588,  0.65412323])


There are many more functions to read about that allow you to draw from a wide variety of statistical distributions. This only scratches the surface of random number generation in NumPy.

## Creating an Array with a Specified Data Type¶

Each of the preceding functions used to create an array can be passed a so-called ‘keyword’ argument, dtype, which instructs NumPy to use a specified data type when producing the contents of the array.

# populate an array using 32-bit floating point numbers
>>> np.array([1, 2, 3], dtype="float32")
array([ 1.,  2.,  3.], dtype=float32)

# default data type produced by arange is 32-bit integers
>>> np.arange(0, 4).dtype
dtype('int32')

# the data type produced by arange can be specified otherwise
>>> np.arange(0, 4, dtype="float16")
array([ 0.,  1.,  2.,  3.], dtype=float16)

# generate shape-(4,4) array of 64-bit complex-valued 0s
>>> np.zeros((4, 4), dtype="complex64")
array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],
[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]], dtype=complex64)


Refer to the official NumPy documentation for the complete list of available array datatypes.

## Joining Arrays Together¶

Similar to Python lists and tuples, NumPy arrays can be concatenated together. However, because NumPy’s arrays can be multi-dimensional, we can choose the dimension along which arrays are joined.

# demonstrating methods for joining arrays
>>> x = np.array([1, 2, 3])
>>> y = np.array([-1, -2, -3])

# stack x and y "vertically"
>>> np.vstack([x, y])
array([[ 1,  2,  3],
[-1, -2, -3]])

# stack x and y "horizontally"
>>> np.hstack([x, y])
array([ 1,  2,  3, -1, -2, -3])


A complete listing of functions for joining arrays can be found in the official NumPy documentation. There are also corresponding functions for splitting an array into independent arrays.