MATLAB § stdlib

Standard library

MATLAB’s standard library is, by the standards of general-purpose languages, enormous. The base product ships with several thousand functions covering numerical linear algebra, signal processing, statistics, numerical integration, optimisation, graphics, and file I/O; the toolboxes add many thousands more in specialised domains. This page is a guided tour of the base library — the functions a working MATLAB programmer reaches for without needing to install anything additional. Toolbox-specific functions are noted where they fill an important gap.

Elementary math

The element-wise math functions accept arrays and return arrays of the same shape:

Family	Functions
Trigonometry	`sin`, `cos`, `tan`, `asin`, `acos`, `atan`, `atan2`, `sind`, `cosd`, `tand` (degree versions)
Hyperbolic	`sinh`, `cosh`, `tanh`, `asinh`, `acosh`, `atanh`
Exponential / log	`exp`, `log`, `log2`, `log10`, `expm1`, `log1p`
Powers / roots	`sqrt`, `cbrt`, `nthroot`, `hypot`
Rounding	`round`, `floor`, `ceil`, `fix`, `mod`, `rem`, `sign`
Special	`gamma`, `gammaln`, `factorial`, `beta`, `erf`, `erfc`, `besselj`, `bessely`, `airy`
Complex	`real`, `imag`, `conj`, `abs`, `angle`

The sind/cosd/tand family takes degrees rather than radians — a small but practical convenience for engineering work.

Linear algebra

The base library exposes most of LAPACK and ARPACK through high-level functions:

A = rand(5);
b = rand(5, 1);

x = A \ b;                  % solve A*x = b
[L, U, P] = lu(A);          % LU with pivoting
[Q, R] = qr(A);             % QR
[U, S, V] = svd(A);         % SVD
[V, D] = eig(A);            % eigendecomposition
R = chol(A' * A);           % Cholesky (requires positive definite)

inv(A)                       % inverse — rarely the right choice; A\eye is similar
pinv(A)                      % Moore-Penrose pseudo-inverse
det(A)                       % determinant
trace(A)                     % trace
rank(A)                      % numerical rank
cond(A)                      % condition number
norm(A)                      % 2-norm (largest singular value)
null(A)                      % null-space basis
orth(A)                      % column-space basis

The matrix-function family — expm, logm, sqrtm, funm — computes matrix functions (not element-wise). The convention is that f(A) is element-wise; fm(A) (with the trailing m) is the matrix function. The pair sqrt(A) and sqrtm(A) are the most-cited example of the distinction.

Reduction and statistics

Function	Returns
`sum`, `prod`	Sum / product along a dimension
`mean`, `median`, `mode`	Central tendency
`min`, `max`	Extreme values (and their indices)
`std`, `var`	Standard deviation, variance
`cumsum`, `cumprod`, `cummax`, `cummin`	Cumulative
`diff`	First-order difference
`any`, `all`	Logical reductions
`nnz`	Count of non-zero entries
`unique`	Unique values, sorted
`histcounts`, `histogram`	Histogram
`corrcoef`, `cov`	Correlation, covariance
`quantile`, `prctile`	Quantiles

Most reductions accept a dim argument to specify the dimension along which to reduce; without it, they collapse along the first non-singleton dimension. The 'all' keyword reduces over every dimension to a scalar. The 'omitnan' option skips NaN values.

A = magic(4);
sum(A)                       % 1×4: column sums
sum(A, 2)                    % 4×1: row sums
sum(A, 'all')                % scalar: total
mean(A, 'omitnan')           % skip NaN

Sorting and searching

sort(x)                              % ascending
sort(x, 'descend')                   % descending
[sorted, idx] = sort(x);             % with permutation
sortrows(A)                          % lexicographic on rows
unique(x)                            % unique values
find(x > 5)                          % indices of non-zero entries
ismember(x, [1 2 3])                 % membership test
intersect(a, b)                      % set intersection
union(a, b)                          % set union
setdiff(a, b)                        % set difference

The find function is essential MATLAB idiom: applied to a logical array, it returns the linear indices of the true entries.

Random numbers

rand(3, 3)                   % uniform [0, 1)
randn(3, 3)                  % standard normal
randi(10, 3, 3)              % integer in 1..10
randperm(10)                 % random permutation of 1..10
randsample(1:100, 10)        % sample without replacement
rng(42)                      % seed the generator
s = rng;                     % save state
rng(s)                       % restore

The Statistics Toolbox extends the library with random('Normal', mu, sigma, m, n) and many specific distributions; the base library covers uniform, normal, and integer sampling.

Numerical algorithms

Family	Functions	Notes
Root-finding	`fzero`, `roots`	Scalar root and polynomial roots
Optimisation (unconstrained scalar)	`fminbnd`, `fminsearch`	Derivative-free
Numerical integration	`integral`, `integral2`, `integral3`, `trapz`, `quad2d`	Adaptive and trapezoidal
ODEs	`ode45`, `ode23`, `ode113`, `ode15s`, `ode23s`	Runge-Kutta and stiff solvers
Interpolation	`interp1`, `interp2`, `interp3`, `interpn`, `griddedInterpolant`, `scatteredInterpolant`	1-d through N-d
FFT	`fft`, `ifft`, `fft2`, `fftn`, `fftshift`	Fast Fourier transforms
Polynomials	`polyval`, `polyfit`, `roots`, `poly`, `conv`, `deconv`	Evaluation, fitting, roots
Curve fitting	`polyfit`, `lsqnonlin`, `lsqcurvefit`	The latter two require Optimization Toolbox

% Quick example: solve y' = -2y, y(0) = 1
[t, y] = ode45(@(t, y) -2*y, [0 5], 1);
plot(t, y)

File I/O

The principal entry points:

Function	Reads / writes
`readtable`, `writetable`	Tables from/to CSV, Excel, text
`readmatrix`, `writematrix`	Numeric matrices from/to text
`readmatrix`, `csvread`	Numeric CSV (older API)
`load`, `save`	MAT-files (the native MATLAB binary format)
`fopen`, `fclose`, `fread`, `fwrite`, `fprintf`, `fscanf`	Low-level file I/O (C-style)
`readtimetable`, `writetimetable`	Time-series tables
`parquetread`, `parquetwrite`	Apache Parquet
`h5read`, `h5write`, `h5create`	HDF5
`ncread`, `ncwrite`	NetCDF
`xmlread`, `xmlwrite`, `readstruct`, `writestruct`	XML / JSON / structured formats
`imread`, `imwrite`	Images (most formats)
`audioread`, `audiowrite`	Audio (WAV, MP3, FLAC)
`videoReader`, `videoWriter`	Video

File I/O is covered at greater length in File I/O and MEX.

Strings and regular expressions

Function	Action
`sprintf`, `compose`	Build a string (returns char / string)
`fprintf`	Print to file or console
`disp`, `display`	Display a value
`strcmp`, `strcmpi`, `strncmp`	String comparison
`strfind`	First index of substring
`strrep`, `replace`	Substring replacement
`strsplit`, `split`, `join`	Tokenise and join
`regexp`, `regexprep`, `regexpi`	Regular expressions
`upper`, `lower`, `strtrim`, `strip`, `pad`	Case and trimming
`contains`, `startsWith`, `endsWith`	Predicates on strings

The string class methods (covered in Strings and char arrays) overlap with these and are usually the cleaner choice in new code.

Date and time

Class	Construction
`datetime`	`datetime('today')`, `datetime(2024, 1, 15)`
`duration`	`hours(5)`, `minutes(30)`, `seconds(1.5)`
`calendarDuration`	`calmonths(3)`, `calyears(1)`

now = datetime("now");
yesterday = now - days(1);
weeksAhead = now + calweeks(4);
elapsed = duration(0, 30, 0);    % 30 minutes

The classes integrate with table and timetable; the older datenum / datevec functions remain available but are discouraged in new code.

Graphics

The 2-d plotting workhorses:

Function	Plots
`plot(x, y)`	Line plot
`scatter(x, y)`	Scatter
`bar(x, y)`, `barh`	Bar chart
`histogram(x)`	Histogram
`boxplot(x)`	Box plot
`errorbar(x, y, err)`	Error bars
`stairs(x, y)`, `stem(x, y)`	Step / stem
`imagesc(A)`, `imshow(A)`	Image / matrix display
`contour(X, Y, Z)`, `contourf`	Contours
`quiver(X, Y, U, V)`	Vector field

For 3-d: plot3, surf, mesh, surfc, scatter3, streamline. The figure, axes, title, xlabel, ylabel, legend, colorbar, xlim, ylim, grid, hold family configures the surrounding plot. Modern code uses tiledlayout and nexttile (R2019b+) to compose multi-panel figures; older code used subplot.

figure
tiledlayout(2, 2)
nexttile; plot(1:10);  title("Linear")
nexttile; semilogy(1:10);  title("Log y")
nexttile; histogram(randn(1000, 1));  title("Histogram")
nexttile; imagesc(magic(10)); title("Imagesc")

Where the standard library ends

The base library covers an enormous surface; the toolboxes extend it further. The most-commonly-installed toolboxes are:

Statistics and Machine Learning — distributions, hypothesis tests, classification, regression, clustering, machine-learning algorithms.
Signal Processing — filter design, spectral estimation, filter banks.
Image Processing — morphology, registration, segmentation, region properties.
Control System — LTI models, root locus, PID tuning.
Optimization and Global Optimization — linear, quadratic, nonlinear, integer programming, and global solvers.
Symbolic Math — computer-algebra system.
Curve Fitting — interactive curve and surface fitting.
Deep Learning — training and inference of neural networks.

Each toolbox is a separately licensed addition; check ver to see which are installed on the current MATLAB. The official function reference at mathworks.com/help/matlab is the authoritative index and is the right place to look up details on individual functions.