Creating Arrays with NumPy

NumPy Introduction

NumPy helps Python process numerical data efficiently. While Python lists can hold mixed data types, NumPy arrays store homogeneous data in optimized structures. This design choice makes operations over many values much faster than regular Python lists.

The core ndarray object represents n-dimensional arrays with fixed sizes and identical data types throughout. This constraint lets NumPy use vectorization, which processes an entire array with one command. The numpy.org provides tutorials and examples for learning this feature in more depth.

NumPy provides several important advantages for scientific programming:

High efficiency because it's implemented in compiled C language
Vectorization allows operations on entire arrays without explicit loops
Lower memory consumption compared to Python lists
Ready-to-use mathematical operations

Vectorization is the ability to apply a single operation to an entire array at once. It's like giving commands to an entire army formation simultaneously, rather than one by one.

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]

Manual Array Creation

The most basic way to create NumPy arrays is to convert existing Python data structures into arrays.

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

Two-dimensional arrays are like tables with rows and columns. You can create them from nested lists.

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

Three-dimensional arrays can be illustrated as stacks of tables. Imagine like several sheets of paper stacked, where each sheet contains table data.

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

Multidimensional Structure

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 $2$ 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.

NumPy can create arrays from various Python data structures, including lists, tuples, and mixtures of both.

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

Array Creation Functions

NumPy provides various specialized functions for creating arrays with specific patterns or values. This is like having special molds for making cakes with consistent shapes.

Constant Value Functions

The np.ones() function creates arrays filled with the number $1$ . Useful when you need initialization with base values.

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 Functions

Random functions are useful for creating simulation data or initialization with random values.

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]]

Mathematical Functions

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 creates arrays without initializing element values. This is useful when you will fill the array with values later and want to save initialization time.

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

Arrays from Sequences

NumPy provides specialized functions for creating arrays from value sequences with specific patterns.

np.arange Function

The np.arange function is the NumPy version of Python's range(), but can generate arrays with floating-point data types and directly allocate memory for elements.

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")

np.linspace Function

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")

Comparison arange vs linspace

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	Follows input	Always float (default)
Usage	Sequence with fixed distance	Even range division

Basic Operations

After creating arrays, you can perform various operations to manipulate and analyze data.

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]]