Useful NumPy Functions

Useful NumPy Functions#

You now know how to create arrays and do math on them. This page covers additional functions you’ll reach for regularly: checking array properties, reshaping, generating random numbers, sorting, and more.

Think of this as a reference you’ll come back to when you need something specific.

Checking Array Properties#

When debugging or setting up a problem, you often need to know what you’re working with:

import numpy as np

T = np.array([[100, 80, 60],
              [50, 40, 30]])

print(T.shape)    # (2, 3) - 2 rows, 3 columns
print(T.size)     # 6 - total number of elements
print(T.ndim)     # 2 - number of dimensions
print(len(T))     # 2 - length of first dimension (number of rows)

The shape is especially important. When your code crashes with a “shape mismatch” error, this is how you figure out what went wrong.

Reshaping Arrays#

Sometimes you need to change the shape of an array without changing its data. This comes up when:

  • Converting a 1D solution back to a 2D grid

  • Preparing data for matrix operations

  • Flattening a 2D array to 1D for easier processing

import numpy as np

# Start with a 1D array
a = np.array([1, 2, 3, 4, 5, 6])

# Reshape to 2x3
b = a.reshape((2, 3))
print(b)

Output:

[[1 2 3]
 [4 5 6]]

You can also go the other way, flattening a 2D array to 1D:

c = b.flatten()
print(c)  # [1 2 3 4 5 6]

Warning

The total number of elements must stay the same. You can’t reshape 6 elements into a 2×4 array.

Random Numbers#

Random numbers are essential for:

  • Testing your code with different inputs

  • Monte Carlo simulations

  • Adding noise to signals

  • Initializing iterative methods with random guesses

Uniform Random Numbers (0 to 1)#

import numpy as np

# 5 random numbers between 0 and 1
r = np.random.rand(5)
print(r)

Output (yours will differ):

[0.417 0.720 0.000 0.302 0.147]

Random Integers#

# 10 random integers from 0 to 99
r = np.random.randint(0, 100, size=10)
print(r)

Normal (Gaussian) Distribution#

For simulating measurement noise or natural variation:

# Mean = 0, Standard deviation = 1, 5 samples
r = np.random.randn(5)
print(r)

# Mean = 50, Standard deviation = 10, 100 samples
measurements = 50 + 10 * np.random.randn(100)

Reproducible Random Numbers#

For debugging, you want the same “random” numbers each time:

np.random.seed(42)  # Any integer works
r = np.random.rand(5)
# Now r will be the same every time you run this

Sorting#

Sorting is useful for finding medians, percentiles, or organizing results:

import numpy as np

data = np.array([3.2, 1.5, 4.8, 2.1, 3.9])

sorted_data = np.sort(data)
print(sorted_data)  # [1.5 2.1 3.2 3.9 4.8]

If you need the indices that would sort the array (useful for sorting one array based on another):

indices = np.argsort(data)
print(indices)  # [1 3 0 4 2] - element 1 is smallest, then 3, etc.

Finding Values#

Where Is a Condition True?#

Find indices where a condition is met:

import numpy as np

T = np.array([100, 80, 60, 40, 20])

# Where is T less than 50?
indices = np.where(T < 50)
print(indices)  # (array([3, 4]),) - indices 3 and 4

# Get the actual values
print(T[T < 50])  # [40 20]

This is useful for finding points where a solution exceeds a threshold or changes sign.

Maximum and Minimum Locations#

data = np.array([3.2, 1.5, 4.8, 2.1])

print(np.argmax(data))  # 2 - index of maximum (4.8)
print(np.argmin(data))  # 1 - index of minimum (1.5)

Combining Arrays#

Stacking Vertically or Horizontally#

import numpy as np

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])

# Stack vertically (as rows)
v = np.vstack([a, b])
print(v)

Output:

[[1 2 3]
 [4 5 6]]

# Stack horizontally (side by side)
h = np.hstack([a, b])
print(h)  # [1 2 3 4 5 6]

Concatenating Along an Axis#

For more control:

c = np.concatenate([a, b])  # Same as hstack for 1D
print(c)  # [1 2 3 4 5 6]

Copying Arrays#

This is a common source of bugs. Watch carefully:

import numpy as np

a = np.array([1, 2, 3])
b = a        # b is NOT a copy! It's the same array.
b[0] = 99
print(a)     # [99 2 3] - a changed too!

To make an independent copy:

a = np.array([1, 2, 3])
b = a.copy()  # Now b is independent
b[0] = 99
print(a)      # [1 2 3] - a is unchanged

Always use .copy() when you want to modify an array without affecting the original.

Iterating Over Arrays#

Usually you should avoid loops with NumPy (use vectorization instead). But sometimes you need to iterate:

import numpy as np

x = np.array([10, 20, 30])

# Simple iteration
for val in x:
    print(val)

# With index
for i, val in enumerate(x):
    print(f"x[{i}] = {val}")

For 2D arrays:

T = np.array([[1, 2], [3, 4]])

# Iterate over rows
for row in T:
    print(row)

# Iterate over all elements
for val in T.flat:
    print(val)

But remember: if you can express it without a loop, do that instead. It’s faster and cleaner.

Quick Reference#

What you need

Code

Shape of array

a.shape

Number of elements

a.size

Number of dimensions

a.ndim

Reshape

a.reshape((m, n))

Flatten to 1D

a.flatten()

Random 0-1

np.random.rand(n)

Random integers

np.random.randint(low, high, size=n)

Normal distribution

np.random.randn(n)

Set random seed

np.random.seed(42)

Sort

np.sort(a)

Indices that sort

np.argsort(a)

Where condition is true

np.where(a > 0)

Index of max/min

np.argmax(a), np.argmin(a)

Stack vertically

np.vstack([a, b])

Stack horizontally

np.hstack([a, b])

Make a copy

a.copy()

What’s Next?#

You now have a solid foundation in NumPy. As you work through the course, you’ll use these tools constantly:

  • shape to debug dimension mismatches

  • reshape to convert between 1D and 2D representations

  • Random numbers for testing and Monte Carlo methods

  • where to find points meeting specific conditions

When you encounter a new NumPy function in lecture code, you can look it up in the NumPy documentation.

Contents