NumPy Scientific Computing Cheat Sheet

Updated 2026-05-15

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NumPy is the foundational library for numerical computing in Python, providing efficient multi-dimensional array objects (ndarray) and a vast collection of mathematical functions that operate on arrays. Built on optimized C and Fortran libraries (BLAS/LAPACK), NumPy enables vectorized operations that eliminate Python loops and execute at near-native speed. Understanding broadcasting rules, memory layout, and array views versus copies is essential — these concepts allow you to write code that is not only fast but also memory-efficient, forming the backbone of scientific Python workflows from data analysis to deep learning.

What This Cheat Sheet Covers

This topic spans 23 focused tables and 219 indexed concepts, 129 flashcards. Below is a complete table-by-table outline of this topic, spanning foundational concepts through advanced details.

Table 1: Array Creation — Initialization and ConstructionTable 2: Data Types (dtype) — Type System and CastingTable 3: Array Attributes — Inspection and MetadataTable 4: Basic Indexing and Slicing — Element AccessTable 5: Advanced Indexing — Boolean and Fancy IndexingTable 6: Broadcasting — Shape Compatibility for OperationsTable 7: Universal Functions (ufuncs) — Vectorized Element-wise OperationsTable 8: Array Manipulation — Shape TransformationTable 9: Array Joining and Splitting — Combining and Dividing ArraysTable 10: Statistical Operations — Aggregations and Descriptive StatisticsTable 11: Linear Algebra — Matrix Operations and DecompositionsTable 12: Random Number Generation — Sampling and DistributionsTable 13: Sorting and Searching — Ordering and LocationTable 14: Set Operations — Unique Values and Set MathTable 15: Logical Operations — Element-wise Boolean LogicTable 16: NaN Handling — Operations Ignoring Missing ValuesTable 17: Masked Arrays — Handling Invalid or Missing DataTable 18: Array Input/Output — Saving and LoadingTable 19: FFT — Frequency Domain AnalysisTable 20: Polynomial Operations — Curve Fitting and EvaluationTable 21: Advanced Operations — Specialized TechniquesTable 22: Memory and Performance — Optimization TechniquesTable 23: Integration and Interoperability — Working with Other Libraries

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Table 1: Array Creation — Initialization and Construction

Every NumPy workflow starts by getting data into an array, and there are many doors in. Use np.array() when you already have the values, zeros, ones, or empty to pre-allocate a buffer you'll fill later, and arange or linspace to generate evenly spaced sequences. The specialized constructors—eye, diag, fromfunction—save you from building common matrix patterns by hand.

Method	Example	Description
np.array()	`arr = np.array([1, 2, 3])`	• Create array from Python list or tuple • most common creation method for known data
np.zeros()	`np.zeros((3, 4))`	• Initialize array filled with zeros • specify shape as tuple
np.ones()	`np.ones((2, 3), dtype=int)`	• Create array filled with ones • optional dtype specification
np.empty()	`np.empty((2, 2))`	• Allocate uninitialized array • fastest creation but contains arbitrary values
np.full()	`np.full((3, 3), 7)`	Fill array with specified constant value.
np.arange()	`np.arange(0, 10, 2)`	• Generate evenly spaced values within interval • works like Python `range()` but returns ndarray
np.linspace()	`np.linspace(0, 1, 50)`	Create array of specified number of evenly spaced points including endpoints.
np.logspace()	`np.logspace(0, 3, 4)`	• Generate logarithmically spaced values • useful for exponential scales.
np.eye()	`np.eye(3)`	Create identity matrix with ones on diagonal and zeros elsewhere.
np.identity()	`np.identity(4)`	• Square identity matrix • equivalent to `np.eye(n)` for square matrices
np.diag()	`np.diag([1, 2, 3])`	Extract diagonal or construct diagonal matrix from 1D array.
np.fromfunction()	`np.fromfunction(lambda i,j: i+j, (3,3))`	• Construct array by executing function over each coordinate • indices passed as arguments

Table 2: Data Types (dtype) — Type System and Casting

Unlike a Python list, every NumPy array has a single fixed dtype, and that choice drives both memory use and speed. Picking int32 over int64 or float32 over float64 can halve your memory footprint, while falling back to the object dtype quietly disables vectorization and tanks performance. These rows cover the numeric, boolean, string, and structured types plus how to cast between them with astype().

Type	Example	Description
int8, int16, int32, int64	`np.array([1, 2], dtype=np.int32)`	• Signed integers with 8, 16, 32, or 64 bits • controls memory and range

The rest of this section is part of the full cheat sheet

Table 3: Array Attributes — Inspection and Metadata

When something goes wrong with array math, the first thing you check is the array's own metadata. shape, ndim, and size answer "what does this thing look like," while dtype and itemsize describe what's inside each cell. The deeper attributes—strides and flags—expose how the data is actually laid out in memory, which is where view-versus-copy bugs and performance surprises tend to hide.

Attribute	Example	Description
shape	`arr.shape`	• Tuple of array dimensions • most frequently used inspection property

The rest of this section is part of the full cheat sheet

Table 4: Basic Indexing and Slicing — Element Access

This is the bread-and-butter syntax for reaching into an array. Single indices, negative indices, and start:stop:step slices work much like Python lists, but NumPy extends them across multiple axes with comma-separated indexing. The crucial thing to remember is that basic slices return views—they share memory with the original, so writing to a slice changes the parent array.

Technique	Example	Description
single element	`arr[2]`	• Access element by index • 0-based indexing like Python lists

The rest of this section is part of the full cheat sheet

Table 1: Array Creation — Initialization and Construction

Method	Example	Description
np.array()	`arr = np.array([1, 2, 3])`	• Create array from Python list or tuple • most common creation method for known data
np.zeros()	`np.zeros((3, 4))`	• Initialize array filled with zeros • specify shape as tuple
np.ones()	`np.ones((2, 3), dtype=int)`	• Create array filled with ones • optional dtype specification
np.empty()	`np.empty((2, 2))`	• Allocate uninitialized array • fastest creation but contains arbitrary values
np.full()	`np.full((3, 3), 7)`	Fill array with specified constant value.
np.arange()	`np.arange(0, 10, 2)`	• Generate evenly spaced values within interval • works like Python `range()` but returns ndarray
np.linspace()	`np.linspace(0, 1, 50)`	Create array of specified number of evenly spaced points including endpoints.
np.logspace()	`np.logspace(0, 3, 4)`	• Generate logarithmically spaced values • useful for exponential scales.
np.eye()	`np.eye(3)`	Create identity matrix with ones on diagonal and zeros elsewhere.
np.identity()	`np.identity(4)`	• Square identity matrix • equivalent to `np.eye(n)` for square matrices
np.diag()	`np.diag([1, 2, 3])`	Extract diagonal or construct diagonal matrix from 1D array.
np.fromfunction()	`np.fromfunction(lambda i,j: i+j, (3,3))`	• Construct array by executing function over each coordinate • indices passed as arguments

Table 2: Data Types (dtype) — Type System and Casting

Type	Example	Description
int8, int16, int32, int64	`np.array([1, 2], dtype=np.int32)`	• Signed integers with 8, 16, 32, or 64 bits • controls memory and range

Table 3: Array Attributes — Inspection and Metadata

Attribute	Example	Description
shape	`arr.shape`	• Tuple of array dimensions • most frequently used inspection property

Table 4: Basic Indexing and Slicing — Element Access

Technique	Example	Description
single element	`arr[2]`	• Access element by index • 0-based indexing like Python lists