NumPy Indexing & Reshaping

Q: How do I swap rows and columns?

matrix.T or np.transpose(matrix) for 2-D. np.swapaxes(a, 0, 1) when rank > 2.

Q: Can reshape change total elements?

No - total size must match: np.prod(shape) == a.size. Use np.resize only when you intentionally want repetition or truncation.

Q: How do I index a 3-D volume?

vol[z, y, x] - slowest axis first in C order. Document axis meaning in function docstrings.

Q: Why does flat indexing differ from 2-D?

a[5] on 2-D uses C-order ravel index. Prefer a[row, col] or np.unravel_index for clarity.

Q: How do I filter and keep 2-D shape?

Boolean mask on rows: a[mask, :] keeps columns intact. a[mask] alone always flattens selected elements to 1-D.

Q: What does ellipsis ... do?

a[..., 0] selects index 0 on the last axis, all prior axes full. Useful for N-D arrays without listing every colon.

Q: How do I stack vs concatenate?

np.stack adds a new axis; np.concatenate joins along an existing axis. np.vstack / hstack are convenience wrappers.

Q: Is x[i, j] the same as x[(i, j)]?

Yes for ndarray - tuple index lists dimensions. x[i][j] indexes twice and can break on non-square structures.

Indexing selects and rearranges ndarray data along axes; reshaping changes shape without changing values when the total size stays constant.

Recipe

Quick-reference recipe card - copy-paste ready.

import numpy as np
 
matrix = np.arange(12).reshape(3, 4)
rows = matrix[1:3, ::2]          # slice rows 1-2, every other column
cols = matrix[:, [0, 3]]         # fancy index columns 0 and 3
flat = matrix.reshape(-1)        # 1-D view when possible

When to reach for this:

Extracting submatrices for batch processing
Reordering dimensions before passing data to ML models
Building masks for conditional updates
Aligning shapes for broadcasting across axes

Working Example

import numpy as np
 
# 4 regions x 6 months
sales = np.array(
    [[10, 12, 11, 13, 14, 15],
     [8, 9, 10, 9, 11, 12],
     [20, 18, 19, 21, 22, 23],
     [5, 6, 5, 7, 6, 8]],
    dtype=np.int32,
)
 
# Q1 only: months 0-2, all regions
q1 = sales[:, 0:3]
 
# Top two regions by total sales
totals = sales.sum(axis=1)
top_idx = np.argsort(totals)[-2:]
top_regions = sales[top_idx]
 
# Stack region vectors as columns for correlation
wide = sales.T  # shape (6, 4) - months as rows
 
# Flag months where any region beat 20
hot_months = np.where(sales.max(axis=0) >= 20)[0]
 
print("q1 shape:", q1.shape)
print("top regions:", top_idx)
print("hot months:", hot_months)

What this demonstrates:

Column slicing with start:stop on axis=1
Reduction along axis=1 then argsort for row selection
.T transpose as a reshape shortcut
np.where on max(axis=0) to index columns by condition

Deep Dive

How It Works

Basic slicing (start:stop:step) uses strides to produce a view sharing memory.
Integer array indexing gathers elements in arbitrary order and usually copies.
Boolean masks must match broadcastable shape; arr[mask] returns a 1-D selection.
reshape returns a view when strides allow; otherwise it copies.

Indexing Modes

Style	Example	Copy?
Slice	`a[2:5]`	Usually view
Integer list	`a[[1, 3]]`	Copy
Boolean mask	`a[a > 0]`	Copy
`np.take`	`np.take(a, idx, axis=0)`	Configurable

Axis Conventions

`axis`	2-D meaning
`0`	Down rows (aggregate columns)
`1`	Across columns (aggregate rows)
`-1`	Last dimension

Python Notes

import numpy as np
 
# Insert axis for broadcasting
row = np.array([1, 2, 3])
col = row[:, np.newaxis]  # shape (3, 1)
 
# ravel vs flatten: flatten always copies
a = np.arange(6).reshape(2, 3)
flat_view = a.ravel()
flat_copy = a.flatten()

Gotchas

Assigning through fancy index - a[[0, 1]] = 5 may not behave like repeated slice assignment. Fix: assign to .copy() or use np.put.
Negative strides views - reversing with a[::-1] can make some reshapes copy unexpectedly. Fix: call .copy() before downstream C extensions.
Boolean mask shape - a[mask] on 2-D needs mask shape (rows, cols) or broadcastable. Fix: mask = mask & (a > 0) with aligned shapes.
Off-by-one slices - a[1:3] excludes index 3; unlike range. Fix: remember stop is exclusive.
reshape size mismatch - reshape(3, 5) on 12 elements raises. Fix: use -1 for one inferred dimension: reshape(3, -1).

Alternatives

Alternative	Use When	Don't Use When
`np.einsum`	Explicit tensor contractions	Simple row/column picks
pandas `.loc`	Labeled rows/columns	Pure numeric ndarray kernels
`np.take_along_axis`	Sorting values per row	Whole-matrix slices suffice
`np.moveaxis`	Reordering 3-D+ tensors	Simple `.T` on 2-D

FAQs

What is the difference between view and copy?

Views share data buffer; copies are independent.
Mutating a view affects the parent unless you copied first.

How do I select every other row?

import numpy as np
a = np.arange(10)
every_other = a[::2]

How do I swap rows and columns?

matrix.T or np.transpose(matrix) for 2-D.
np.swapaxes(a, 0, 1) when rank > 2.

Can reshape change total elements?

No - total size must match: np.prod(shape) == a.size.
Use np.resize only when you intentionally want repetition or truncation.

How do I index a 3-D volume?

vol[z, y, x] - slowest axis first in C order.
Document axis meaning in function docstrings.

Why does flat indexing differ from 2-D?

a[5] on 2-D uses C-order ravel index.
Prefer a[row, col] or np.unravel_index for clarity.

How do I filter and keep 2-D shape?

Boolean mask on rows: a[mask, :] keeps columns intact.
a[mask] alone always flattens selected elements to 1-D.

What does ellipsis `...` do?

a[..., 0] selects index 0 on the last axis, all prior axes full.
Useful for N-D arrays without listing every colon.

How do I stack vs concatenate?

np.stack adds a new axis; np.concatenate joins along an existing axis.
np.vstack / hstack are convenience wrappers.

Is x[i, j] the same as x[(i, j)]?

Yes for ndarray - tuple index lists dimensions.
x[i][j] indexes twice and can break on non-square structures.

NumPy Arrays - creation, dtypes, broadcasting
pandas Series & DataFrames - .loc / .iloc analogs
Performance & Memory - views vs copies at scale
Data Analysis Basics - intro examples

Stack versions: This page was written for Python 3.14.0 (stable 3.14, maintenance 3.13), FastAPI 0.115+, Django 5.2, Flask 3.1, Pydantic 2, PyTorch 2.6+, pandas 2.2+, Polars 1.x, ruff 0.9+, and uv 0.6+.

Recipe

Quick-reference recipe card - copy-paste ready.

import numpy as np
 
matrix = np.arange(12).reshape(3, 4)
rows = matrix[1:3, ::2]          # slice rows 1-2, every other column
cols = matrix[:, [0, 3]]         # fancy index columns 0 and 3
flat = matrix.reshape(-1)        # 1-D view when possible

When to reach for this:

Extracting submatrices for batch processing
Reordering dimensions before passing data to ML models
Building masks for conditional updates
Aligning shapes for broadcasting across axes

Working Example

import numpy as np
 
# 4 regions x 6 months
sales = np.array(
    [[10, 12, 11, 13, 14, 15],
     [8, 9, 10, 9, 11, 12],
     [20, 18, 19, 21, 22, 23],
     [5, 6, 5, 7, 6, 8]],
    dtype=np.int32,
)
 
# Q1 only: months 0-2, all regions
q1 = sales[:, 0:3]
 
# Top two regions by total sales
totals = sales.sum(axis=1)
top_idx = np.argsort(totals)[-2:]
top_regions = sales[top_idx]
 
# Stack region vectors as columns for correlation
wide = sales.T  # shape (6, 4) - months as rows
 
# Flag months where any region beat 20
hot_months = np.where(sales.max(axis=0) >= 20)[0]
 
print("q1 shape:", q1.shape)
print("top regions:", top_idx)
print("hot months:", hot_months)

What this demonstrates:

Column slicing with start:stop on axis=1
Reduction along axis=1 then argsort for row selection
.T transpose as a reshape shortcut
np.where on max(axis=0) to index columns by condition

Deep Dive

How It Works

Basic slicing (start:stop:step) uses strides to produce a view sharing memory.
Integer array indexing gathers elements in arbitrary order and usually copies.
Boolean masks must match broadcastable shape; arr[mask] returns a 1-D selection.
reshape returns a view when strides allow; otherwise it copies.

Indexing Modes

Style	Example	Copy?
Slice	`a[2:5]`	Usually view
Integer list	`a[[1, 3]]`	Copy
Boolean mask	`a[a > 0]`	Copy
`np.take`	`np.take(a, idx, axis=0)`	Configurable

Axis Conventions

`axis`	2-D meaning
`0`	Down rows (aggregate columns)
`1`	Across columns (aggregate rows)
`-1`	Last dimension

Python Notes

import numpy as np
 
# Insert axis for broadcasting
row = np.array([1, 2, 3])
col = row[:, np.newaxis]  # shape (3, 1)
 
# ravel vs flatten: flatten always copies
a = np.arange(6).reshape(2, 3)
flat_view = a.ravel()
flat_copy = a.flatten()

Gotchas

Assigning through fancy index - a[[0, 1]] = 5 may not behave like repeated slice assignment. Fix: assign to .copy() or use np.put.
Negative strides views - reversing with a[::-1] can make some reshapes copy unexpectedly. Fix: call .copy() before downstream C extensions.
Boolean mask shape - a[mask] on 2-D needs mask shape (rows, cols) or broadcastable. Fix: mask = mask & (a > 0) with aligned shapes.
Off-by-one slices - a[1:3] excludes index 3; unlike range. Fix: remember stop is exclusive.
reshape size mismatch - reshape(3, 5) on 12 elements raises. Fix: use -1 for one inferred dimension: reshape(3, -1).

Alternatives

Alternative	Use When	Don't Use When
`np.einsum`	Explicit tensor contractions	Simple row/column picks
pandas `.loc`	Labeled rows/columns	Pure numeric ndarray kernels
`np.take_along_axis`	Sorting values per row	Whole-matrix slices suffice
`np.moveaxis`	Reordering 3-D+ tensors	Simple `.T` on 2-D

FAQs

What is the difference between view and copy?

Views share data buffer; copies are independent.
Mutating a view affects the parent unless you copied first.

How do I select every other row?

import numpy as np
a = np.arange(10)
every_other = a[::2]

How do I swap rows and columns?

matrix.T or np.transpose(matrix) for 2-D.
np.swapaxes(a, 0, 1) when rank > 2.

Can reshape change total elements?

No - total size must match: np.prod(shape) == a.size.
Use np.resize only when you intentionally want repetition or truncation.

How do I index a 3-D volume?

vol[z, y, x] - slowest axis first in C order.
Document axis meaning in function docstrings.

Why does flat indexing differ from 2-D?

a[5] on 2-D uses C-order ravel index.
Prefer a[row, col] or np.unravel_index for clarity.

How do I filter and keep 2-D shape?

Boolean mask on rows: a[mask, :] keeps columns intact.
a[mask] alone always flattens selected elements to 1-D.

What does ellipsis `...` do?

a[..., 0] selects index 0 on the last axis, all prior axes full.
Useful for N-D arrays without listing every colon.

How do I stack vs concatenate?

np.stack adds a new axis; np.concatenate joins along an existing axis.
np.vstack / hstack are convenience wrappers.

Is x[i, j] the same as x[(i, j)]?

Yes for ndarray - tuple index lists dimensions.
x[i][j] indexes twice and can break on non-square structures.

NumPy Arrays - creation, dtypes, broadcasting
pandas Series & DataFrames - .loc / .iloc analogs
Performance & Memory - views vs copies at scale
Data Analysis Basics - intro examples

Stack versions: This page was written for Python 3.14.0 (stable 3.14, maintenance 3.13), FastAPI 0.115+, Django 5.2, Flask 3.1, Pydantic 2, PyTorch 2.6+, pandas 2.2+, Polars 1.x, ruff 0.9+, and uv 0.6+.

NumPy Indexing & Reshaping

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NumPy Indexing & Reshaping