# 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.