Creating Arrays with NumPy

NumPy helps Python process numerical data efficiently. Python lists can hold mixed types, while a NumPy array normally stores values of one data type in a compact structure. For vectorized numerical operations over many values, this representation is often faster than an equivalent Python loop.

The core ndarray object represents an n-dimensional, fixed-size container whose elements share one data type. This design enables vectorized operations, where one expression describes work over an entire array. The official NumPy documentation provides tutorials and further examples.

Efficient numerical loops implemented in compiled native code
Vectorization allows operations on entire arrays without explicit loops
Compact storage for homogeneous numerical values
Ready-to-use mathematical operations

Vectorization means expressing an operation for an entire array instead of writing an explicit Python loop over individual elements. NumPy still performs the work element by element internally, but the loop runs in optimized compiled code.

vectorization_comparison.py

# Element multiplication using Python list (slow)
x = [1, 2, 3, 4, 5]
y = [2, 3, 4, 5, 6]
z = []
for i in range(len(x)):
  z.append(x[i] * y[i])
print("List result:", z)  # Output: List result: [2, 6, 12, 20, 30]

# Element multiplication using NumPy (fast)
import numpy as np
x_np = np.array([1, 2, 3, 4, 5])
y_np = np.array([2, 3, 4, 5, 6])
z_np = x_np * y_np
print("NumPy result:", z_np)  # Output: NumPy result: [ 2  6 12 20 30]

One-dimensional arrays are like a sequence of numbers in a single row. You can create them from Python lists using the np.array() function.

array_1d.py

import numpy as np

# Create 1D array from list
a = np.array([0, 1, 2, 3])
print("1D Array:", a)  # Output: 1D Array: [0 1 2 3]
print("Data type:", type(a))  # Output: Data type: <class 'numpy.ndarray'>
print("Shape:", a.shape)  # Output: Shape: (4,)
print("Dimensions:", a.ndim)  # Output: Dimensions: 1

array_2d.py

import numpy as np

# Create 2D array from nested list
a = np.array([[0, 1], [2, 3]])
print("2D Array:")
print(a)
# Output:
# [[0 1]
#  [2 3]]

print("Shape:", a.shape)  # Output: Shape: (2, 2)
print("Dimensions:", a.ndim)  # Output: Dimensions: 2
print("Total elements:", a.size)  # Output: Total elements: 4

A three-dimensional array can be pictured as a stack of tables. Each layer contains rows and columns, and the additional axis selects a layer.

array_3d.py

import numpy as np

# Create 3D array
a = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])
print("3D Array:")
print(a)
# Output:
# [[[ 1  2  3]
#   [ 4  5  6]]
#  [[ 7  8  9]
#   [10 11 12]]]

print("Shape:", a.shape)  # Output: Shape: (2, 2, 3)
print("Axis 0 (planes):", a.shape[0])  # Output: Axis 0 (planes): 2
print("Axis 1 (rows):", a.shape[1])  # Output: Axis 1 (rows): 2
print("Axis 2 (columns):", a.shape[2])  # Output: Axis 2 (columns): 3

Dimension	Shape	Structure	Example	Axis
One-dimensional	`(4,)`	Number sequence in single row	`[0, 1, 2, 3]`	Axis $0$ for element index
Two-dimensional	`(2, 2)`	Table with rows and columns	`[[0, 1], [2, 3]]`	Axis $0$ for rows, Axis $1$ for columns
Three-dimensional	`(2, 2, 3)`	Stack of tables (planes)	$2$ planes, each plane $2 \times 3$	Axis $0$ depth, Axis $1$ height, Axis width

The higher the array dimension, the more complex the data structure, but the basic principle remains the same. Each axis represents one dimension of data organization.

array_from_various_types.py

import numpy as np

# From list
arr_from_list = np.array([0, 1, 2, 3])
print("From list:", arr_from_list)  # Output: From list: [0 1 2 3]

# From tuple
arr_from_tuple = np.array((0, 1, 2, 3))
print("From tuple:", arr_from_tuple)  # Output: From tuple: [0 1 2 3]

# From mixture (will be converted to compatible type)
arr_mixed = np.array([0, 1, 2.5, 3])
print("From mixture:", arr_mixed)  # Output: From mixture: [0.  1.  2.5 3. ]
print("Automatic data type:", arr_mixed.dtype)  # Output: Automatic data type: float64

The np.ones() function creates an array filled with $1$ . It is useful when every element needs the same initial value.

ones_arrays.py

import numpy as np

# 1D array with value 1
a = np.ones(3)
print("1D ones:", a)  # Output: 1D ones: [1. 1. 1.]

# 2D array with value 1
a = np.ones((2, 3))
print("2D ones:")
print(a)
# Output:
# [[1. 1. 1.]
#  [1. 1. 1.]]

# 3D array with value 1
a = np.ones((2, 2, 3))
print("3D ones shape:", a.shape)  # Output: 3D ones shape: (2, 2, 3)
print("3D ones:")
print(a)
# Output:
# [[[1. 1. 1.]
#   [1. 1. 1.]]
#  [[1. 1. 1.]
#   [1. 1. 1.]]]

Besides np.ones(), there are other functions for creating arrays with special patterns:

special_arrays.py

import numpy as np

# Array with zero values
a = np.zeros((2, 3))
print("Zeros array:")
print(a)
# Output:
# [[0. 0. 0.]
#  [0. 0. 0.]]

# Identity array (diagonal 1, others 0)
a = np.eye(3, 3)
print("Identity matrix:")
print(a)
# Output:
# [[1. 0. 0.]
#  [0. 1. 0.]
#  [0. 0. 1.]]

# Diagonal array with specific values
a = np.diag((1, 2, 3))
print("Diagonal array:")
print(a)
# Output:
# [[1 0 0]
#  [0 2 0]
#  [0 0 3]]

random_arrays.py

import numpy as np

# Set seed for consistent results
np.random.seed(10)

# Array with uniform random values between 0 and 1
a = np.random.rand(2, 3)
print("Random uniform [0,1]:")
print(a)
# Output:
# [[0.77132064 0.02075195 0.63364823]
#  [0.74880388 0.49850701 0.22479665]]

# Array with normal distribution (mean=0, std=1)
a = np.random.randn(3)
print("Random normal:", a)  # Output: Random normal: [ 0.62133597 -0.72008556  0.26551159]

# Array with random integers in specific range
a = np.random.randint(1, 10, size=(2, 3))
print("Random integers [1,10):")
print(a)
# Output:
# [[7 9 2]
#  [9 5 2]]

The np.fromfunction function enables array creation based on mathematical functions. This is like having a formula to generate the value of each element based on its position.

fromfunction_array.py

import numpy as np

# Create array using function
def f(i, j):
  return i + j

# 2x3 array with values based on function f(i,j) = i + j
a = np.fromfunction(f, (2, 3))
print("Array from function f(i,j) = i + j:")
print(a)
# Output:
# [[0. 1. 2.]
#  [1. 2. 3.]]

# More complex function
def g(i, j):
  return i * j + 1

b = np.fromfunction(g, (3, 3))
print("Array from function g(i,j) = i*j + 1:")
print(b)
# Output:
# [[1. 1. 1.]
#  [1. 2. 3.]
#  [1. 3. 5.]]

The np.empty function allocates an array without initializing its element values. The existing memory contents are arbitrary, so every element must be assigned before it is read. Use it only when the array will be filled immediately.

empty_array.py

import numpy as np

# Create empty array (undefined values)
a = np.empty((3, 2))
print("Empty array (random values from memory):")
print(a)
# Output will vary because values are not initialized
# Example output:
# [[0. 0.]
#  [0. 0.]
#  [0. 0.]]

print("Shape:", a.shape)  # Output: Shape: (3, 2)
print("Dtype:", a.dtype)  # Output: Dtype: float64

The np.arange function resembles Python's range(), but returns an array and accepts floating-point arguments. For noninteger steps, floating-point rounding can make the final values less predictable, so np.linspace is often clearer when the number of points matters.

arange_arrays.py

import numpy as np

# Array from 0 to 4
a = np.arange(5)
print("arange(5):", a)  # Output: arange(5): [0 1 2 3 4]

# Array with start, stop, and step
a = np.arange(1.5, 3., 0.5)
print("arange(1.5, 3., 0.5):", a)  # Output: arange(1.5, 3., 0.5): [1.5 2.  2.5]

# Array with step that produces decimal values
a = np.arange(1.5, 4.)
print("arange(1.5, 4.):", a)  # Output: arange(1.5, 4.): [1.5 2.5 3.5]

# Parameter demonstration
print("\nParameter arange(start, end, step):")
print("- start, end, step can be float")
print("- end is excluded from result")
print("- step default is 1")
print("- start default is 0")

Unlike np.arange which uses fixed steps, np.linspace divides a range into a number of evenly spaced points.

linspace_arrays.py

import numpy as np

# Create 5 evenly spaced points between 0 and 10
a = np.linspace(0, 10, 5)
print("linspace(0, 10, 5):", a)  # Output: linspace(0, 10, 5): [ 0.   2.5  5.   7.5 10. ]

# Create 11 evenly spaced points between -1 and 1
a = np.linspace(-1, 1, 11)
print("linspace(-1, 1, 11):", a)
# Output: linspace(-1, 1, 11): [-1.  -0.8 -0.6 -0.4 -0.2  0.   0.2  0.4  0.6  0.8  1. ]

# Comparison linspace vs arange
print("\nDifference linspace vs arange:")
print("linspace: number of elements known, distance calculated")
print("arange: distance known, number of elements calculated")

Aspect	`np.arange`	`np.linspace`
Main parameters	start, stop, step	start, stop, num
Control	Distance between elements	Total number of elements
Endpoint	Excluded	Included (default)
Data type	Inferred from input	Floating point by default; configurable with `dtype`
Usage	Sequence with fixed distance	Even range division

array_info.py

import numpy as np

# Create example array
a = np.array([[1, 2, 3], [4, 5, 6]])
print("Array:")
print(a)
# Output:
# [[1 2 3]
#  [4 5 6]]

print("Shape:", a.shape)  # Output: Shape: (2, 3)
print("Size (total elements):", a.size)  # Output: Size (total elements): 6
print("Ndim (dimensions):", a.ndim)  # Output: Ndim (dimensions): 2
print("Dtype (data type):", a.dtype)  # Output: Dtype (data type): int64
print("Itemsize (bytes per element):", a.itemsize)  # Output: Itemsize (bytes per element): 8

Arrays can be reshaped using the reshape() function to rearrange dimensions without changing the data:

array_reshape.py

import numpy as np

# 1D array with 12 elements
a = np.arange(12)
print("Original array:", a)  # Output: Original array: [ 0  1  2  3  4  5  6  7  8  9 10 11]

# Reshape to 3x4
b = a.reshape(3, 4)
print("Reshape 3x4:")
print(b)
# Output:
# [[ 0  1  2  3]
#  [ 4  5  6  7]
#  [ 8  9 10 11]]

# Reshape to 2x6
c = a.reshape(2, 6)
print("Reshape 2x6:")
print(c)
# Output:
# [[ 0  1  2  3  4  5]
#  [ 6  7  8  9 10 11]]

# Reshape with -1 (automatically calculate dimension)
d = a.reshape(4, -1)
print("Reshape 4x-1 (automatic):")
print(d)
# Output:
# [[ 0  1  2]
#  [ 3  4  5]
#  [ 6  7  8]
#  [ 9 10 11]]

Creating Arrays with NumPy

NumPy Introduction

Creating Arrays with NumPy

NumPy Introduction

Manual Array Creation

Multidimensional Structure

Array Creation Functions

Constant Value Functions

Random Functions

Mathematical Functions

Arrays from Sequences

np.arange Function

np.linspace Function

Comparison arange vs linspace

Basic Operations