NumPy Cheat Sheet — Comprehensive Edition

01Setup & Constantscreate · inspect

import numpy as np★
Universal alias — always np.
np.__version__ np.show_config()
Version / BLAS-LAPACK backend in use.
np.pi np.e np.euler_gamma
Math constants.
np.inf np.nan np.newaxis★
Infinity / not-a-number / axis-insertion token.
np.iinfo(np.int32) np.finfo(np.float64)
Integer / float type limits & precision.

02Array Creationcreate

np.array([1,2,3], dtype=np.float64)★
Build from a list; set dtype explicitly.
np.zeros((3,4)) np.ones((2,3)) np.full((2,2),7)★
Filled arrays of a given shape.
np.arange(0,10,2) np.linspace(0,1,5)★
Ranges: fixed step / fixed count.
np.eye(4) np.identity(3) np.diag(v)
Identity / diagonal matrices.
np.zeros_like(a) np.empty((2,2))
Match another's shape / uninitialized (fast).
np.fromfunction(f, (3,3)) np.meshgrid(x, y)★
Build from a function / coordinate grids.

03Attributes & Inspectioninspect

a.shape a.ndim a.size★
Axis sizes / number of axes / total elements.
a.dtype a.itemsize a.nbytes★
Element type / bytes per item / total bytes.
a.astype(np.float32)★
Cast to a new dtype — returns a copy.
a.T a.flags a.strides
Transpose / memory layout / byte strides.
a.tolist() a.item(0)
Back to Python list / scalar.

04Indexing & Slicingindex & search

a[2] a[1, 3] a[1:4]★
Element / 2D element / slice (0-indexed).
a[:, 1] a[::-1]★
Whole column / reverse an axis.
a[start:stop:step]
Full slice syntax, on any axis.
a[..., 0]
... (Ellipsis) fills in remaining axes.
basic slices → viewsview
No copy — the data is shared.

05Boolean & Fancy Indexingindex & search

a[a > 5]★
Elements matching a boolean condition.
a[(a>2) & (a<9)]
Combine masks with & | ~ (not and/or).
a[[0,2,4]] a[rows[:,None], cols]★
Fancy indexing — pick by index arrays.
np.where(cond, x, y)★
Vectorized if/else, elementwise.
np.take(a, idx) np.put(a, idx, vals)
Gather / scatter by flat index.
boolean / fancy → copycopy
Always returns new, independent memory.

06Index Generation & Selectionindex & search

np.nonzero(a) np.argwhere(a)★
Indices of non-zero / True elements.
np.select([c1,c2], [v1,v2], default=0)★
Multi-condition vectorized choice.
np.take_along_axis(a, idx, axis=1)
Gather using argsort/argmax indices.
np.ix_(rows, cols) np.indices((3,3))
Open mesh for cross-indexing / index grids.
np.diag_indices(3) np.tril / np.triu
Diagonal / lower-upper triangle indices.
np.fill_diagonal(a, 0)
Write the diagonal in place.

07Reshaping & Axis Movesshape & combine

a.reshape(3, 4) a.reshape(-1)★
New shape (-1 infers a dimension).
a.T a.mT np.transpose(a, axes)★
Transpose; .mT = matrix transpose (2.0+).
a.ravel()view
Flatten to 1D, sharing memory if possible.
a.flatten()copy
Flatten to 1D — always a new array.
np.moveaxis(a,0,-1) np.swapaxes(a,0,1)
Reorder axes.
a[:,None] np.expand_dims / np.squeeze★
Add / drop length-1 axes.

08Combining & Splittingshape & combine

np.concatenate([a,b], axis=0)★
Join along an existing axis.
np.vstack np.hstack np.column_stack★
Row / column stacking shortcuts.
np.stack([a,b], axis=0)★
Join along a brand-new axis.
np.split(a, 3) np.hsplit / np.vsplit
Split into equal sub-arrays.
np.block([[a, b], [c, d]])
Assemble a grid of blocks.

09Tiling & Rearrangingshape & combine

np.tile(a, (2,3)) np.repeat(a, 3)★
Tile the whole array / repeat each element.
np.roll(a, 2) np.flip(a, axis=0)★
Circular shift / reverse along an axis.
np.rot90(a) np.fliplr / np.flipud
Rotate / mirror a 2D array.
np.pad(a, 1, mode='constant')★
Pad edges (constant, edge, reflect…).
np.insert / np.append / np.deletecopy
Add/remove elements — each rebuilds the array.

10Copies vs. Viewsinspect

a.copy()★
Independent deep copy — safe to mutate.
a.view() a.view(np.int32)
New array object, same memory / reinterpret dtype.
b = a[1:3]alias
A slice is a view — editing b edits a.
np.shares_memory(a, b)
Check whether two arrays alias.
np.ascontiguousarray(a) a.base
Force C-contiguous / find the owning array.

11Arithmetic & Universal Functionsmath & ufuncs

a + b a - b a * b a / b a ** 2★
Elementwise — no explicit loops.
np.sqrt np.exp np.log np.log10★
Elementwise math — all ufuncs.
np.abs np.sign np.round np.floor np.ceil
Magnitude / sign / rounding.
np.mod(a,b) np.clip(a, 0, 1)
Modulo / clamp into a range.
a @ b np.matmul(a, b)★
Matrix multiply — not elementwise.
np.maximum(a,b) np.minimum(a,b)
Elementwise pairwise max / min.

12Trig & Special Mathmath & ufuncs

np.sin np.cos np.tan★
Trig functions (radians).
np.arctan2(y, x) np.hypot(x, y)
Quadrant-aware angle / Euclidean length.
np.deg2rad np.rad2deg
Angle unit conversion.
np.sinh np.cosh np.tanh
Hyperbolic functions.
np.gradient(a) np.diff(a) np.cumprod(a)★
Numerical gradient / differences / running product.
np.interp(x, xp, fp) np.convolve(a, v)
1D interpolation / convolution.

13Broadcastingmath & ufuncs

compare shapes right-to-left★
Trailing dims must match, or one must be 1.
(3,4) + (4,) → (3,4)
A row vector broadcasts across every row.
(3,1) + (1,4) → (3,4)
Column & row combine into a grid.
a - a.mean(axis=0)★
Common pattern: centering columns.
np.broadcast_to(a, (3,4)) np.broadcast_shapes(...)
Explicit broadcast / predict result shape.
(3,4) + (2,4) → errorValueError
Mismatched non-1 dims don't align.

14Ufunc Methods & Controlmath & ufuncs

np.add.reduce(a) np.add.accumulate(a)★
Fold / cumulative-fold with any ufunc.
np.add.outer(a, b)
All-pairs application → outer table.
np.add.at(a, idx, vals)★
Unbuffered in-place add — handles repeated indices.
np.add.reduceat(a, indices)
Segmented reductions.
out=... where=... keepdims=True
Common ufunc kwargs (write-target, mask, keep rank).

15Aggregations & Statisticsaggregate / stats

a.sum(axis=0) a.prod() a.cumsum()★
Total / product / running total.
a.mean() a.std() a.var() np.median(a)★
Central tendency & spread.
a.min() a.max() a.ptp()
Extremes / peak-to-peak range.
np.percentile(a, [25,75]) np.quantile(a, .9)★
Percentiles / quantiles.
np.average(a, weights=w)
Weighted mean.
np.corrcoef(a) np.cov(a)
Correlation / covariance matrix.

16NaN-Aware Stats & Histogramsaggregate / stats

np.nanmean np.nansum np.nanstd★
Aggregates that skip NaN.
np.nanmax np.nanargmax np.nanmedian
NaN-safe extremes & median.
np.histogram(a, bins=10)★
Counts per bin (also histogram2d, histogramdd).
np.bincount(a) np.digitize(a, bins)★
Integer counts / assign values to bins.

17Sorting, Searching & Countingindex & search

np.sort(a) a.sort()★
Sorted copy / in-place sort.
np.argsort(a) np.argmin / np.argmax★
Indices that sort / of the min/max.
np.searchsorted(a, x) np.partition(a, k)
Insertion point / k-th element pivot.
np.count_nonzero(a) np.unique(a, return_counts=True)★
Count truthy / distinct values + counts.
np.unique_values np.unique_counts
Array-API split variants (2.0+).

18Logic, Comparison & Set Opsmath & ufuncs

np.any(a) np.all(a)★
At least one / every element truthy.
np.isnan np.isinf np.isfinite★
Special-value masks (never == np.nan).
np.array_equal(a,b) np.allclose(a,b)★
Exact / tolerant equality.
np.logical_and / or / not / xor
Elementwise boolean logic.
np.intersect1d np.union1d np.setdiff1d★
Set operations on 1D arrays.
np.isin(a, b)
Membership mask.

19Linear Algebramodule · np.linalg

a @ b np.dot np.linalg.multi_dot([...])★
Matrix / chained products.
np.linalg.solve(A, b)★
Solve Ax=b — faster & stabler than inv.
np.linalg.inv(A) np.linalg.pinv(A)
Inverse / Moore-Penrose pseudo-inverse.
np.linalg.det np.linalg.matrix_rank np.trace
Determinant / rank / trace.
np.linalg.eig np.linalg.svd np.linalg.qr★
Eigen / singular-value / QR decomposition.
np.linalg.cholesky np.linalg.lstsq(A, b)
Cholesky / least-squares solve.
np.linalg.norm np.einsum('ij,jk->ik', a, b)★
Norm / Einstein-summation (very general).

20Fourier Transformsmodule · np.fft

np.fft.fft(a) np.fft.ifft(A)★
1D discrete FFT / inverse.
np.fft.rfft(a) np.fft.irfft(A)★
Real-input FFT — half the output, no waste.
np.fft.fft2 np.fft.fftn
2D / N-dimensional transforms.
np.fft.fftfreq(n, d) np.fft.rfftfreq(n)★
Frequency bins for the output.
np.fft.fftshift(A) np.fft.ifftshift(A)
Center the zero-frequency component.

21Random Numbersmodule · Generator API

rng = np.random.default_rng(seed)★
Modern, recommended entry point.
rng.random((2,3)) rng.integers(0,10,size=5)★
Uniform floats / random ints.
rng.normal(0,1,100) rng.uniform rng.poisson★
Draw from named distributions.
rng.choice(a, size=3, replace=False)
Random sample (with/without replacement).
rng.shuffle(a) rng.permutation(a)
Shuffle in place / return a shuffled copy.
prefer default_rng over np.random.seed
Legacy global functions still work but aren't advised.

22Polynomialsmodule · np.polynomial

from numpy.polynomial import Polynomial as P★
Modern polynomial class (replaces np.poly1d).
p = P([1, -2, 3]) p(x)
Build 1 - 2x + 3x² and evaluate it.
P.fit(x, y, deg=2)★
Least-squares polynomial fit.
p.roots() p.deriv() p.integ()
Roots / derivative / integral.
Chebyshev Legendre Hermite
Other orthogonal-basis classes.

23Masked Arraysmodule · np.ma

m = np.ma.masked_array(a, mask=[0,1,0])★
Array with per-element validity flags.
np.ma.masked_where(a < 0, a)★
Mask by condition.
np.ma.masked_invalid(a)
Mask NaN / inf automatically.
m.mean() m.sum()
Aggregations skip masked entries.
m.filled(0) m.compressed()
Replace masks / drop them to a 1D array.

24String Operationsmodule · np.strings

np.strings.upper(a) np.strings.lower(a)★
Vectorized case ops (2.0+, ufunc-backed).
np.strings.add(a, b) np.strings.multiply(a, 3)
Elementwise concat / repeat.
np.strings.contains np.strings.startswith★
Boolean text tests.
np.strings.strip np.strings.replace
Trim / find-and-replace.
np.strings replaces np.char
Prefer np.strings; np.char is legacy.

25Structured & Record Arrayscompound dtypes · np.rec

dt = np.dtype([('name','U10'), ('age','i4')])★
Compound dtype — named, typed fields.
a = np.array([('Ann', 30)], dtype=dt)
Table-like array of records.
a['name'] a['age']★
Access a whole field like a column.
r = a.view(np.recarray) r.name
Record array — attribute-style field access.
for tabular data, pandas is usually better
Structured arrays suit fixed C-struct interop.

26Datetimes & Timedeltasdatetime64

np.datetime64('2024-07-01') np.datetime64('now')★
Typed calendar timestamp.
np.arange('2024-01','2024-06', dtype='datetime64[M]')★
Range over months (or D/h/m/s).
d2 - d1 np.timedelta64(1, 'D')
Date arithmetic yields timedeltas.
np.busday_count(start, end)
Count business days between dates.
arr.astype('datetime64[D]')
Change datetime resolution.

27Stride Tricks & Iterationmodule · lib.stride_tricks

np.lib.stride_tricks.sliding_window_view(a, 3)★
Rolling windows — zero-copy view.
np.lib.stride_tricks.as_strided(a, shape, strides)unsafe
Raw stride hack — can read out of bounds.
np.vectorize(pyfunc)
Wrap a scalar function (convenience, not speed).
np.frompyfunc(f, nin, nout)
Turn a Python function into a ufunc-like object.
np.apply_along_axis(f, axis, a)
Apply a 1D function along one axis.

28Save, Load & I/Oinspect

np.save('f.npy', a) np.load('f.npy')★
Binary single-array round-trip.
np.savez('f.npz', a=x, b=y)
Save several named arrays (compressed: savez_compressed).
np.savetxt('f.csv', a, delimiter=',')
Write a plain-text / CSV file.
np.loadtxt('f.csv', delimiter=',')★
Read a simple, fully-regular text file.
np.genfromtxt('f.csv', delimiter=',', names=True)★
Read text with gaps / headers gracefully.
np.frombuffer np.memmap('f', mode='r')
Zero-copy from bytes / on-disk big arrays.

29Performance & Gotchashandle with care

vectorize, don't loop
Python element loops are slow — use ufuncs.
a += 1truncates
In-place on an int array silently truncates floats.
np.append in a loopslow
Reallocates each call — build a list, convert once.
a @ b beats a big einsum for simple products
Use the specific op; reserve einsum for complex contractions.
views alias memory
Copy before mutating a slice you intend to keep.

★Common dtypesanywhere you see dtype=

int8/16/32/64 uint8/16/32/64
Signed / unsigned integers.
float16/32/64★
Half / single / double (default float64).
complex64/128
Complex numbers.
bool_ object_
Boolean / arbitrary Python objects (slow).
datetime64[D] timedelta64[s]★
Typed dates / durations.
'U10' 'S5' StringDType()
Fixed Unicode/bytes / variable strings (2.0+).
np.int / np.float removed
NEP 52 dropped these aliases — use int/np.int64.

★Axis Quick-Readanywhere you see axis=

axis=0★
Collapse rows — operate down each column.
axis=1★
Collapse columns — operate across each row.
axis=None (default)
Flatten first, then aggregate the whole array.
axis=-1
Always "the last axis", for any ndim.
keepdims=True
Keep the reduced axis as size 1 (for broadcasting).

★Testing & Type Toolsnp.testing

np.testing.assert_allclose(a, b)★
Tolerant array equality for tests.
np.testing.assert_array_equal(a, b)
Exact array equality.
np.can_cast(a.dtype, np.int32) np.result_type(a, b)
Cast-safety check / promotion rules.
np.typing.NDArray[np.float64]
Type hints for array-typed signatures.

numpy cheat sheet v2 · all modules

I · Core: Create, Inspect & Index the ndarray — everyday array work

II · Shape, Combine & Views reshape · stack · split · copies vs views

III · Math, Ufuncs & Broadcasting elementwise ops · trig · reductions

IV · Aggregate, Sort, Search & Logic reductions · NaN-aware · histograms

V · Specialized Submodules linalg · fft · random · polynomial

VI · Masked, Strings, Structured, Dates & Performance ma · strings · rec · datetime64 · stride tricks

Axis reductions, broadcasting & strides

axis=0 vs axis=1 ★

Broadcasting: (3,1) + (1,4) ★

Strides: one buffer, many shapes ★

Views vs. copies ★

Worth memorizing