MATLAB^®

Function Reference

Desktop Tools and Development Environment

Startup and Shutdown	Startup and shutdown options, preferences
Command Window and History	Control Command Window and History, enter statements and run functions
Help for Using MATLAB	Command line help, online documentation in the Help browser, demos
Workspace, Search Path, and File Operations	Work with files, MATLAB search path, manage variables
Programming Tools	Edit and debug M-files, improve performance, source control, publish results
System	Identify current computer, license, product version, and more

Startup and Shutdown

exit	Terminate MATLAB program (same as `quit`)
finish	Termination M-file for MATLAB program
matlab (UNIX)	Start MATLAB program (UNIX platforms)
matlab (Windows)	Start MATLAB program (Windows platforms)
matlabrc	Startup M-file for MATLAB program
prefdir	Directory containing preferences, history, and layout files
preferences	Open Preferences dialog box
quit	Terminate MATLAB program
startup	Startup M-file for user-defined options
userpath	View or change user portion of search path

Command Window and History

clc	Clear Command Window
commandhistory	Open Command History window, or select it if already open
commandwindow	Open Command Window, or select it if already open
diary	Save session to file
dos	Execute DOS command and return result
format	Set display format for output
home	Move cursor to upper-left corner of Command Window
matlabcolon (matlab:)	Run specified function via hyperlink
more	Control paged output for Command Window
perl	Call Perl script using appropriate operating system executable
system	Execute operating system command and return result
unix	Execute UNIX command and return result

Help for Using MATLAB

builddocsearchdb	Build searchable documentation database
demo	Access product demos via Help browser
doc	Reference page in Help browser
docopt	Web browser for UNIX platforms
docsearch	Open Help browser and search for specified term
echodemo	Run M-file demo step-by-step in Command Window
help	Help for functions in Command Window
helpbrowser	Open Help browser to access all online documentation and demos
helpwin	Provide access to M-file help for all functions
info	Information about contacting The MathWorks
lookfor	Search for keyword in all help entries
playshow	Run M-file demo (deprecated; use `echodemo` instead)
support	Open MathWorks Technical Support Web page
web	Open Web site or file in Web browser or Help browser
whatsnew	Release Notes for MathWorks products

Workspace, Search Path, and File Operations

Workspace	Manage variables
Search Path	View and change MATLAB search path
File Operations	View and change files and directories

Workspace

assignin	Assign value to variable in specified workspace
clear	Remove items from workspace, freeing up system memory
evalin	Execute MATLAB expression in specified workspace
exist	Check existence of variable, function, directory, or Java programming language class
openvar	Open workspace variable in Variable Editor or other tool for graphical editing
pack	Consolidate workspace memory
uiimport	Open Import Wizard to import data
which	Locate functions and files
who, whos	List variables in workspace
workspace	Open Workspace browser to manage workspace

Search Path

addpath	Add directories to search path
genpath	Generate path string
partialpath	Partial pathname description
path	View or change search path
path2rc	Save current search path to `pathdef.m` file
pathsep	Path separator for current platform
pathtool	Open Set Path dialog box to view and change search path
restoredefaultpath	Restore default search path
rmpath	Remove directories from search path
savepath	Save current search path
userpath	View or change user portion of search path

File Operations

Programming Tools

M-File Editing and Debugging	Edit and debug M-files
M-File Performance	Improve performance and find potential problems in M-files
Source Control	Interface MATLAB with source control system
Publishing	Publish M-file code and results

M-File Editing and Debugging

clipboard	Copy and paste strings to and from system clipboard
datatipinfo	Produce short description of input variable
dbclear	Clear breakpoints
dbcont	Resume execution
dbdown	Change local workspace context when in debug mode
dbquit	Quit debug mode
dbstack	Function call stack
dbstatus	List all breakpoints
dbstep	Execute one or more lines from current breakpoint
dbstop	Set breakpoints
dbtype	List M-file with line numbers
dbup	Change local workspace context
debug	List M-file debugging functions
edit	Edit or create M-file
keyboard	Input from keyboard

M-File Performance

bench	MATLAB Benchmark
mlint	Check M-files for possible problems
mlintrpt	Run `mlint` for file or directory, reporting results in browser
pack	Consolidate workspace memory
profile	Profile execution time for function
profsave	Save profile report in HTML format
rehash	Refresh function and file system path caches
sparse	Create sparse matrix
zeros	Create array of all zeros

Source Control

checkin	Check files into a source control system (UNIX platforms)
checkout	Check files out of a source control system (UNIX platforms)
cmopts	Name of source control system
customverctrl	Allow custom source control system (UNIX platforms)
undocheckout	Undo previous checkout from source control system (UNIX platforms)
verctrl	Source control actions (Windows platforms)

Publishing

grabcode	MATLAB code from M-files published to HTML
notebook	Open M-book in Microsoft Word software (on Microsoft Windows platforms)
publish	Publish M-file containing cells, saving output to a file of specified type
snapnow	Force snapshot of image for inclusion in published document

System

Operating System Interface	Exchange operating system information and commands with MATLAB
MATLAB Version and License	Information about MATLAB version and license

Operating System Interface

clipboard	Copy and paste strings to and from system clipboard
computer	Information about computer on which MATLAB software is running
dos	Execute DOS command and return result
getenv	Environment variable
hostid	Server host identification number
maxNumCompThreads	Controls maximum number of computational threads
perl	Call Perl script using appropriate operating system executable
setenv	Set environment variable
system	Execute operating system command and return result
unix	Execute UNIX command and return result
winqueryreg	Item from Windows registry

MATLAB Version and License

ismac	Determine if version is for Mac OS X platform
ispc	Determine if version is for Windows (PC) platform
isstudent	Determine if version is Student Version
isunix	Determine if version is for UNIX platform.
javachk	Generate error message based on Sun Java feature support
license	Return license number or perform licensing task
prefdir	Directory containing preferences, history, and layout files
usejava	Determine whether Sun Java feature is supported in MATLAB software
ver	Version information for MathWorks products
verLessThan	Compare toolbox version to specified version string
version	Version number for the MATLAB software

Mathematics

Arrays and Matrices	Basic array operators and operations, creation of elementary and specialized arrays and matrices
Linear Algebra	Matrix analysis, linear equations, eigenvalues, singular values, logarithms, exponentials, factorization
Elementary Math	Trigonometry, exponentials and logarithms, complex values, rounding, remainders, discrete math
Polynomials	Multiplication, division, evaluation, roots, derivatives, integration, eigenvalue problem, curve fitting, partial fraction expansion
Interpolation and Computational Geometry	Interpolation, Delaunay triangulation and tessellation, convex hulls, Voronoi diagrams, domain generation
Cartesian Coordinate System Conversion	Conversions between Cartesian and polar or spherical coordinates
Nonlinear Numerical Methods	Differential equations, optimization, integration
Specialized Math	Airy, Bessel, Jacobi, Legendre, beta, elliptic, error, exponential integral, gamma functions
Sparse Matrices	Elementary sparse matrices, operations, reordering algorithms, linear algebra, iterative methods, tree operations
Math Constants	Pi, imaginary unit, infinity, Not-a-Number, largest and smallest positive floating point numbers, floating point relative accuracy

Arrays and Matrices

Basic Information	Display array contents, get array information, determine array type
Operators	Arithmetic operators
Elementary Matrices and Arrays	Create elementary arrays of different types, generate arrays for plotting, array indexing, etc.
Array Operations	Operate on array content, apply function to each array element, find cumulative product or sum, etc.
Array Manipulation	Create, sort, rotate, permute, reshape, and shift array contents
Specialized Matrices	Create Hadamard, Companion, Hankel, Vandermonde, Pascal matrices, etc.

Basic Information

disp	Display text or array
display	Display text or array (overloaded method)
isempty	Determine whether array is empty
isequal	Test arrays for equality
isequalwithequalnans	Test arrays for equality, treating NaNs as equal
isfinite	Array elements that are finite
isfloat	Determine whether input is floating-point array
isinf	Array elements that are infinite
isinteger	Determine whether input is integer array
islogical	Determine whether input is logical array
isnan	Array elements that are NaN
isnumeric	Determine whether input is numeric array
isscalar	Determine whether input is scalar
issparse	Determine whether input is sparse
isvector	Determine whether input is vector
length	Length of vector
max	Largest elements in array
min	Smallest elements in array
ndims	Number of array dimensions
numel	Number of elements in array or subscripted array expression
size	Array dimensions

Operators

+	Addition
+	Unary plus
-	Subtraction
-	Unary minus
*	Matrix multiplication
^	Matrix power
\	Backslash or left matrix divide
/	Slash or right matrix divide
'	Transpose
.'	Nonconjugated transpose
.*	Array multiplication (element-wise)
.^	Array power (element-wise)
.\	Left array divide (element-wise)
./	Right array divide (element-wise)

Elementary Matrices and Arrays

blkdiag	Construct block diagonal matrix from input arguments
create (RandStream)	Create random number streams
diag	Diagonal matrices and diagonals of matrix
eye	Identity matrix
freqspace	Frequency spacing for frequency response
get (RandStream)	Random stream properties
getDefaultStream (RandStream)	Default random number stream
ind2sub	Subscripts from linear index
linspace	Generate linearly spaced vectors
list (RandStream)	Random number generator algorithms
logspace	Generate logarithmically spaced vectors
meshgrid	Generate `X` and `Y` arrays for 3-D plots
ndgrid	Generate arrays for N-D functions and interpolation
ones	Create array of all ones
rand	Uniformly distributed pseudorandom numbers
rand (RandStream)	Uniformly distributed random numbers
randi	Uniformly distributed pseudorandom integers
randi (RandStream)	Uniformly distributed pseudorandom integers
randn	Normally distributed pseudorandom numbers
randn (RandStream)	Normally distributed pseudorandom numbers
randperm (RandStream)
RandStream	Random number stream
RandStream (RandStream)	Random number stream
set (RandStream)	Set a random stream property
setDefaultStream (RandStream)	Set the default random number stream
sub2ind	Single index from subscripts
zeros	Create array of all zeros

Array Operations

See Linear Algebra and Elementary Math for other array operations.

accumarray	Construct array with accumulation
arrayfun	Apply function to each element of array
bsxfun	Apply element-by-element binary operation to two arrays with singleton expansion enabled
cast	Cast variable to different data type
cross	Vector cross product
cumprod	Cumulative product
cumsum	Cumulative sum
dot	Vector dot product
idivide	Integer division with rounding option
kron	Kronecker tensor product
prod	Product of array elements
sum	Sum of array elements
tril	Lower triangular part of matrix
triu	Upper triangular part of matrix

Array Manipulation

blkdiag	Construct block diagonal matrix from input arguments
cat	Concatenate arrays along specified dimension
circshift	Shift array circularly
diag	Diagonal matrices and diagonals of matrix
end	Terminate block of code, or indicate last array index
flipdim	Flip array along specified dimension
fliplr	Flip matrix left to right
flipud	Flip matrix up to down
horzcat	Concatenate arrays horizontally
inline	Construct inline object
ipermute	Inverse permute dimensions of N-D array
permute	Rearrange dimensions of N-D array
repmat	Replicate and tile array
reshape	Reshape array
rot90	Rotate matrix 90 degrees
shiftdim	Shift dimensions
sort	Sort array elements in ascending or descending order
sortrows	Sort rows in ascending order
squeeze	Remove singleton dimensions
vectorize	Vectorize expression
vertcat	Concatenate arrays vertically

Specialized Matrices

compan	Companion matrix
gallery	Test matrices
hadamard	Hadamard matrix
hankel	Hankel matrix
hilb	Hilbert matrix
invhilb	Inverse of Hilbert matrix
magic	Magic square
pascal	Pascal matrix
rosser	Classic symmetric eigenvalue test problem
toeplitz	Toeplitz matrix
vander	Vandermonde matrix
wilkinson	Wilkinson's eigenvalue test matrix

Linear Algebra

Matrix Analysis	Compute norm, rank, determinant, condition number, etc.
Linear Equations	Solve linear systems, least squares, LU factorization, Cholesky factorization, etc.
Eigenvalues and Singular Values	Eigenvalues, eigenvectors, Schur decomposition, Hessenburg matrices, etc.
Matrix Logarithms and Exponentials	Matrix logarithms, exponentials, square root
Factorization	Cholesky, LU, and QR factorizations, diagonal forms, singular value decomposition

Matrix Analysis

cond	Condition number with respect to inversion
condeig	Condition number with respect to eigenvalues
det	Matrix determinant
norm	Vector and matrix norms
normest	2-norm estimate
null	Null space
orth	Range space of matrix
rank	Rank of matrix
rcond	Matrix reciprocal condition number estimate
rref	Reduced row echelon form
subspace	Angle between two subspaces
trace	Sum of diagonal elements

Linear Equations

chol	Cholesky factorization
cholinc	Sparse incomplete Cholesky and Cholesky-Infinity factorizations
cond	Condition number with respect to inversion
condest	1-norm condition number estimate
funm	Evaluate general matrix function
ilu	Sparse incomplete LU factorization
inv	Matrix inverse
linsolve	Solve linear system of equations
lscov	Least-squares solution in presence of known covariance
lsqnonneg	Solve nonnegative least-squares constraints problem
lu	LU matrix factorization
luinc	Sparse incomplete LU factorization
pinv	Moore-Penrose pseudoinverse of matrix
qr	Orthogonal-triangular decomposition
rcond	Matrix reciprocal condition number estimate

Eigenvalues and Singular Values

balance	Diagonal scaling to improve eigenvalue accuracy
cdf2rdf	Convert complex diagonal form to real block diagonal form
condeig	Condition number with respect to eigenvalues
eig	Eigenvalues and eigenvectors
eigs	Largest eigenvalues and eigenvectors of a matrix
gsvd	Generalized singular value decomposition
hess	Hessenberg form of matrix
ordeig	Eigenvalues of quasitriangular matrices
ordqz	Reorder eigenvalues in QZ factorization
ordschur	Reorder eigenvalues in Schur factorization
poly	Polynomial with specified roots
polyeig	Polynomial eigenvalue problem
rsf2csf	Convert real Schur form to complex Schur form
schur	Schur decomposition
sqrtm	Matrix square root
ss2tf	Convert state-space filter parameters to transfer function form
svd	Singular value decomposition
svds	Find singular values and vectors

Matrix Logarithms and Exponentials

expm	Matrix exponential
logm	Matrix logarithm
sqrtm	Matrix square root

Factorization

balance	Diagonal scaling to improve eigenvalue accuracy
cdf2rdf	Convert complex diagonal form to real block diagonal form
chol	Cholesky factorization
cholinc	Sparse incomplete Cholesky and Cholesky-Infinity factorizations
cholupdate	Rank 1 update to Cholesky factorization
gsvd	Generalized singular value decomposition
ilu	Sparse incomplete LU factorization
lu	LU matrix factorization
luinc	Sparse incomplete LU factorization
planerot	Givens plane rotation
qr	Orthogonal-triangular decomposition
qrdelete	Remove column or row from QR factorization
qrinsert	Insert column or row into QR factorization
qrupdate
qz	QZ factorization for generalized eigenvalues
rsf2csf	Convert real Schur form to complex Schur form
svd	Singular value decomposition

Elementary Math

Trigonometric	Trigonometric functions with results in radians or degrees
Exponential	Exponential, logarithm, power, and root functions
Complex	Numbers with real and imaginary components, phase angles
Rounding and Remainder	Rounding, modulus, and remainder
Discrete Math	Prime factors, factorials, permutations, rational fractions, least common multiple, greatest common divisor

Trigonometric

acos	Inverse cosine; result in radians
acosd	Inverse cosine; result in degrees
acosh	Inverse hyperbolic cosine
acot	Inverse cotangent; result in radians
acotd	Inverse cotangent; result in degrees
acoth	Inverse hyperbolic cotangent
acsc	Inverse cosecant; result in radians
acscd	Inverse cosecant; result in degrees
acsch	Inverse hyperbolic cosecant
asec	Inverse secant; result in radians
asecd	Inverse secant; result in degrees
asech	Inverse hyperbolic secant
asin	Inverse sine; result in radians
asind	Inverse sine; result in degrees
asinh	Inverse hyperbolic sine
atan	Inverse tangent; result in radians
atan2	Four-quadrant inverse tangent
atand	Inverse tangent; result in degrees
atanh	Inverse hyperbolic tangent
cos	Cosine of argument in radians
cosd	Cosine of argument in degrees
cosh	Hyperbolic cosine
cot	Cotangent of argument in radians
cotd	Cotangent of argument in degrees
coth	Hyperbolic cotangent
csc	Cosecant of argument in radians
cscd	Cosecant of argument in degrees
csch	Hyperbolic cosecant
hypot	Square root of sum of squares
sec	Secant of argument in radians
secd	Secant of argument in degrees
sech	Hyperbolic secant
sin	Sine of argument in radians
sind	Sine of argument in degrees
sinh	Hyperbolic sine of argument in radians
tan	Tangent of argument in radians
tand	Tangent of argument in degrees
tanh	Hyperbolic tangent

Exponential

exp	Exponential
expm1	Compute `exp(x)-1` accurately for small values of `x`
log	Natural logarithm
log10	Common (base 10) logarithm
log1p	Compute `log(1+x)` accurately for small values of `x`
log2	Base 2 logarithm and dissect floating-point numbers into exponent and mantissa
nextpow2	Next higher power of 2
nthroot	Real `n`th root of real numbers
pow2	Base 2 power and scale floating-point numbers
reallog	Natural logarithm for nonnegative real arrays
realpow	Array power for real-only output
realsqrt	Square root for nonnegative real arrays
sqrt	Square root

Complex

abs	Absolute value and complex magnitude
angle	Phase angle
complex	Construct complex data from real and imaginary components
conj	Complex conjugate
cplxpair	Sort complex numbers into complex conjugate pairs
i	Imaginary unit
imag	Imaginary part of complex number
isreal	Check if input is real array
j	Imaginary unit
real	Real part of complex number
sign	Signum function
unwrap	Correct phase angles to produce smoother phase plots

Rounding and Remainder

ceil	Round toward positive infinity
fix	Round toward zero
floor	Round toward negative infinity
idivide	Integer division with rounding option
mod	Modulus after division
rem	Remainder after division
round	Round to nearest integer

Discrete Math

factor	Prime factors
factorial	Factorial function
gcd	Greatest common divisor
isprime	Array elements that are prime numbers
lcm	Least common multiple
nchoosek	Binomial coefficient or all combinations
perms	All possible permutations
primes	Generate list of prime numbers
rat, rats	Rational fraction approximation

Polynomials

conv	Convolution and polynomial multiplication
deconv	Deconvolution and polynomial division
poly	Polynomial with specified roots
polyder	Polynomial derivative
polyeig	Polynomial eigenvalue problem
polyfit	Polynomial curve fitting
polyint	Integrate polynomial analytically
polyval	Polynomial evaluation
polyvalm	Matrix polynomial evaluation
residue	Convert between partial fraction expansion and polynomial coefficients
roots	Polynomial roots

Interpolation and Computational Geometry

Interpolation	Data interpolation, data gridding, polynomial evaluation, nearest point search
Delaunay Triangulation and Tessellation	Delaunay triangulation and tessellation, triangular surface and mesh plots
Convex Hull	Plot convex hull, plotting functions
Voronoi Diagrams	Plot Voronoi diagram, patch graphics object, plotting functions
Domain Generation	Generate arrays for 3-D plots, or for N-D functions and interpolation

Interpolation

dsearch	Search Delaunay triangulation for nearest point
dsearchn	N-D nearest point search
griddata	Data gridding
griddata3	Data gridding and hypersurface fitting for 3-D data
griddatan	Data gridding and hypersurface fitting (dimension >= 2)
interp1	1-D data interpolation (table lookup)
interp1q	Quick 1-D linear interpolation
interp2	2-D data interpolation (table lookup)
interp3	3-D data interpolation (table lookup)
interpft	1-D interpolation using FFT method
interpn	N-D data interpolation (table lookup)
meshgrid	Generate `X` and `Y` arrays for 3-D plots
mkpp	Make piecewise polynomial
ndgrid	Generate arrays for N-D functions and interpolation
padecoef	Padé approximation of time delays
pchip	Piecewise Cubic Hermite Interpolating Polynomial (PCHIP)
ppval	Evaluate piecewise polynomial
spline	Cubic spline data interpolation
tsearchn	N-D closest simplex search
unmkpp	Piecewise polynomial details

Delaunay Triangulation and Tessellation

delaunay	Delaunay triangulation
delaunay3	3-D Delaunay tessellation
delaunayn	N-D Delaunay tessellation
dsearch	Search Delaunay triangulation for nearest point
dsearchn	N-D nearest point search
tetramesh	Tetrahedron mesh plot
trimesh	Triangular mesh plot
triplot	2-D triangular plot
trisurf	Triangular surface plot
tsearch	Search for enclosing Delaunay triangle
tsearchn	N-D closest simplex search

Convex Hull

convhull	Convex hull
convhulln	N-D convex hull
patch	Create patch graphics object
plot	2-D line plot
trisurf	Triangular surface plot

Voronoi Diagrams

dsearch	Search Delaunay triangulation for nearest point
patch	Create patch graphics object
plot	2-D line plot
voronoi	Voronoi diagram
voronoin	N-D Voronoi diagram

Domain Generation

meshgrid	Generate `X` and `Y` arrays for 3-D plots
ndgrid	Generate arrays for N-D functions and interpolation

Cartesian Coordinate System Conversion

cart2pol	Transform Cartesian coordinates to polar or cylindrical
cart2sph	Transform Cartesian coordinates to spherical
pol2cart	Transform polar or cylindrical coordinates to Cartesian
sph2cart	Transform spherical coordinates to Cartesian

Nonlinear Numerical Methods

Ordinary Differential Equations	Solve stiff and nonstiff differential equations, define the problem, set solver options, evaluate solution
Delay Differential Equations	Solve delay differential equations with constant and general delays, set solver options, evaluate solution
Boundary Value Problems	Solve boundary value problems for ordinary differential equations, set solver options, evaluate solution
Partial Differential Equations	Solve initial-boundary value problems for parabolic-elliptic PDEs, evaluate solution
Optimization	Find minimum of single and multivariable functions, solve nonnegative least-squares constraint problem
Numerical Integration (Quadrature)	Evaluate Simpson, Lobatto, and vectorized quadratures, evaluate double and triple integrals

Ordinary Differential Equations

decic	Compute consistent initial conditions for `ode15i`
deval	Evaluate solution of differential equation problem
ode15i	Solve fully implicit differential equations, variable order method
ode23, ode45, ode113, ode15s, ode23s, ode23t, ode23tb	Solve initial value problems for ordinary differential equations
odefile	Define differential equation problem for ordinary differential equation solvers
odeget	Ordinary differential equation options parameters
odeset	Create or alter options structure for ordinary differential equation solvers
odextend	Extend solution of initial value problem for ordinary differential equation

Delay Differential Equations

dde23	Solve delay differential equations (DDEs) with constant delays
ddeget	Extract properties from delay differential equations options structure
ddesd	Solve delay differential equations (DDEs) with general delays
ddeset	Create or alter delay differential equations options structure
deval	Evaluate solution of differential equation problem

Boundary Value Problems

bvp4c	Solve boundary value problems for ordinary differential equations
bvp5c	Solve boundary value problems for ordinary differential equations
bvpget	Extract properties from options structure created with `bvpset`
bvpinit	Form initial guess for `bvp4c`
bvpset	Create or alter options structure of boundary value problem
bvpxtend	Form guess structure for extending boundary value solutions
deval	Evaluate solution of differential equation problem

Partial Differential Equations

pdepe	Solve initial-boundary value problems for parabolic-elliptic PDEs in 1-D
pdeval	Evaluate numerical solution of PDE using output of `pdepe`

Optimization

fminbnd	Find minimum of single-variable function on fixed interval
fminsearch	Find minimum of unconstrained multivariable function using derivative-free method
fzero	Find root of continuous function of one variable
lsqnonneg	Solve nonnegative least-squares constraints problem
optimget	Optimization options values
optimset	Create or edit optimization options structure

Numerical Integration (Quadrature)

dblquad	Numerically evaluate double integral
quad	Numerically evaluate integral, adaptive Simpson quadrature
quadgk	Numerically evaluate integral, adaptive Gauss-Kronrod quadrature
quadl	Numerically evaluate integral, adaptive Lobatto quadrature
quadv	Vectorized quadrature
triplequad	Numerically evaluate triple integral

Specialized Math

airy	Airy functions
besselh	Bessel function of third kind (Hankel function)
besseli	Modified Bessel function of first kind
besselj	Bessel function of first kind
besselk	Modified Bessel function of second kind
bessely	Bessel function of second kind
beta	Beta function
betainc	Incomplete beta function
betaln	Logarithm of beta function
ellipj	Jacobi elliptic functions
ellipke	Complete elliptic integrals of first and second kind
erf, erfc, erfcx, erfinv, erfcinv	Error functions
expint	Exponential integral
gamma, gammainc, gammaln	Gamma functions
legendre	Associated Legendre functions
psi	Psi (polygamma) function

Sparse Matrices

Elementary Sparse Matrices	Create random and nonrandom sparse matrices
Full to Sparse Conversion	Convert full matrix to sparse, sparse matrix to full
Sparse Matrix Manipulation	Test matrix for sparseness, get information on sparse matrix, allocate sparse matrix, apply function to nonzero elements, visualize sparsity pattern
Reordering Algorithms	Random, column, minimum degree, Dulmage-Mendelsohn, and reverse Cuthill-McKee permutations
Linear Algebra	Compute norms, eigenvalues, factorizations, least squares, structural rank
Linear Equations (Iterative Methods)	Methods for conjugate and biconjugate gradients, residuals, lower quartile
Tree Operations	Elimination trees, tree plotting, factorization analysis

Elementary Sparse Matrices

spdiags	Extract and create sparse band and diagonal matrices
speye	Sparse identity matrix
sprand	Sparse uniformly distributed random matrix
sprandn	Sparse normally distributed random matrix
sprandsym	Sparse symmetric random matrix

Full to Sparse Conversion

find	Find indices and values of nonzero elements
full	Convert sparse matrix to full matrix
sparse	Create sparse matrix
spconvert	Import matrix from sparse matrix external format

Sparse Matrix Manipulation

issparse	Determine whether input is sparse
nnz	Number of nonzero matrix elements
nonzeros	Nonzero matrix elements
nzmax	Amount of storage allocated for nonzero matrix elements
spalloc	Allocate space for sparse matrix
spfun	Apply function to nonzero sparse matrix elements
spones	Replace nonzero sparse matrix elements with ones
spparms	Set parameters for sparse matrix routines
spy	Visualize sparsity pattern

Reordering Algorithms

amd	Approximate minimum degree permutation
colamd	Column approximate minimum degree permutation
colperm	Sparse column permutation based on nonzero count
dmperm	Dulmage-Mendelsohn decomposition
ldl	Block LDL' factorization for Hermitian indefinite matrices
randperm	Random permutation
symamd	Symmetric approximate minimum degree permutation
symrcm	Sparse reverse Cuthill-McKee ordering

Linear Algebra

cholinc	Sparse incomplete Cholesky and Cholesky-Infinity factorizations
condest	1-norm condition number estimate
eigs	Largest eigenvalues and eigenvectors of a matrix
ilu	Sparse incomplete LU factorization
luinc	Sparse incomplete LU factorization
normest	2-norm estimate
spaugment	Form least squares augmented system
sprank	Structural rank
svds	Find singular values and vectors

Linear Equations (Iterative Methods)

bicg	Biconjugate gradients method
bicgstab	Biconjugate gradients stabilized method
cgs	Conjugate gradients squared method
gmres	Generalized minimum residual method (with restarts)
lsqr	LSQR method
minres	Minimum residual method
pcg	Preconditioned conjugate gradients method
qmr	Quasi-minimal residual method
symmlq	Symmetric LQ method

Tree Operations

etree	Elimination tree
etreeplot	Plot elimination tree
gplot	Plot nodes and links representing adjacency matrix
symbfact	Symbolic factorization analysis
treelayout	Lay out tree or forest
treeplot	Plot picture of tree

Math Constants

eps	Floating-point relative accuracy
i	Imaginary unit
Inf	Infinity
intmax	Largest value of specified integer type
intmin	Smallest value of specified integer type
j	Imaginary unit
NaN	Not-a-Number
pi	Ratio of circle's circumference to its diameter, π
realmax	Largest positive floating-point number
realmin	Smallest positive normalized floating-point number

Data Analysis

Basic Operations	Sums, products, sorting
Descriptive Statistics	Statistical summaries of data
Filtering and Convolution	Data preprocessing
Interpolation and Regression	Data fitting
Fourier Transforms	Frequency content of data
Derivatives and Integrals	Data rates and accumulations
Time Series Objects	Methods for `timeseries` objects
Time Series Collections	Methods for `tscollection` objects

Basic Operations

brush	Interactively mark, delete, modify, and save observations in graphs
cumprod	Cumulative product
cumsum	Cumulative sum
linkdata	Automatically update graphs when variables change
prod	Product of array elements
sort	Sort array elements in ascending or descending order
sortrows	Sort rows in ascending order
sum	Sum of array elements

Descriptive Statistics

corrcoef	Correlation coefficients
cov	Covariance matrix
max	Largest elements in array
mean	Average or mean value of array
median	Median value of array
min	Smallest elements in array
mode	Most frequent values in array
std	Standard deviation
var	Variance

Filtering and Convolution

conv	Convolution and polynomial multiplication
conv2	2-D convolution
convn	N-D convolution
deconv	Deconvolution and polynomial division
detrend	Remove linear trends
filter	1-D digital filter
filter2	2-D digital filter

Interpolation and Regression

interp1	1-D data interpolation (table lookup)
interp2	2-D data interpolation (table lookup)
interp3	3-D data interpolation (table lookup)
interpn	N-D data interpolation (table lookup)
mldivide \, mrdivide /	Left or right matrix division
polyfit	Polynomial curve fitting
polyval	Polynomial evaluation

Fourier Transforms

abs	Absolute value and complex magnitude
angle	Phase angle
cplxpair	Sort complex numbers into complex conjugate pairs
fft	Discrete Fourier transform
fft2	2-D discrete Fourier transform
fftn	N-D discrete Fourier transform
fftshift	Shift zero-frequency component to center of spectrum
fftw	Interface to FFTW library run-time algorithm tuning control
ifft	Inverse discrete Fourier transform
ifft2	2-D inverse discrete Fourier transform
ifftn	N-D inverse discrete Fourier transform
ifftshift	Inverse FFT shift
nextpow2	Next higher power of 2
unwrap	Correct phase angles to produce smoother phase plots

Derivatives and Integrals

cumtrapz	Cumulative trapezoidal numerical integration
del2	Discrete Laplacian
diff	Differences and approximate derivatives
gradient	Numerical gradient
polyder	Polynomial derivative
polyint	Integrate polynomial analytically
trapz	Trapezoidal numerical integration

Time Series Objects

Utilities	Combine `timeseries` objects, query and set `timeseries` object properties, plot `timeseries` objects
Data Manipulation	Add or delete data, manipulate `timeseries` objects
Event Data	Add or delete events, create new `timeseries` objects based on event data
Descriptive Statistics	Descriptive statistics for `timeseries` objects

Utilities

get (timeseries)	Query `timeseries` object property values
getdatasamplesize	Size of data sample in `timeseries` object
getqualitydesc	Data quality descriptions
isempty (timeseries)	Determine whether `timeseries` object is empty
length (timeseries)	Length of time vector
plot (timeseries)	Plot time series
set (timeseries)	Set properties of `timeseries` object
size (timeseries)	Size of `timeseries` object
timeseries	Create `timeseries` object
tsdata.event	Construct event object for `timeseries` object
tsprops	Help on `timeseries` object properties
tstool	Open Time Series Tools GUI

Data Manipulation

addsample	Add data sample to `timeseries` object
ctranspose (timeseries)	Transpose `timeseries` object
delsample	Remove sample from `timeseries` object
detrend (timeseries)	Subtract mean or best-fit line and all `NaN`s from time series
filter (timeseries)	Shape frequency content of time series
getabstime (timeseries)	Extract date-string time vector into cell array
getinterpmethod	Interpolation method for `timeseries` object
getsampleusingtime (timeseries)	Extract data samples into new `timeseries` object
idealfilter (timeseries)	Apply ideal (noncausal) filter to `timeseries` object
resample (timeseries)	Select or interpolate `timeseries` data using new time vector
setabstime (timeseries)	Set times of `timeseries` object as date strings
setinterpmethod	Set default interpolation method for `timeseries` object
synchronize	Synchronize and resample two `timeseries` objects using common time vector
transpose (timeseries)	Transpose `timeseries` object
vertcat (timeseries)	Vertical concatenation of `timeseries` objects

Event Data

addevent	Add event to `timeseries` object
delevent	Remove `tsdata.event` objects from `timeseries` object
gettsafteratevent	New `timeseries` object with samples occurring at or after event
gettsafterevent	New `timeseries` object with samples occurring after event
gettsatevent	New `timeseries` object with samples occurring at event
gettsbeforeatevent	New `timeseries` object with samples occurring before or at event
gettsbeforeevent	New `timeseries` object with samples occurring before event
gettsbetweenevents	New `timeseries` object with samples occurring between events

Descriptive Statistics

iqr (timeseries)	Interquartile range of `timeseries` data
max (timeseries)	Maximum value of `timeseries` data
mean (timeseries)	Mean value of `timeseries` data
median (timeseries)	Median value of `timeseries` data
min (timeseries)	Minimum value of `timeseries` data
std (timeseries)	Standard deviation of `timeseries` data
sum (timeseries)	Sum of `timeseries` data
var (timeseries)	Variance of `timeseries` data

Time Series Collections

Utilities	Query and set `tscollection` object properties, plot `tscollection` objects
Data Manipulation	Add or delete data, manipulate `tscollection` objects

Utilities

get (tscollection)	Query `tscollection` object property values
isempty (tscollection)	Determine whether `tscollection` object is empty
length (tscollection)	Length of time vector
plot (timeseries)	Plot time series
set (tscollection)	Set properties of `tscollection` object
size (tscollection)	Size of `tscollection` object
tscollection	Create `tscollection` object
tstool	Open Time Series Tools GUI

Data Manipulation

addsampletocollection	Add sample to `tscollection` object
addts	Add `timeseries` object to `tscollection` object
delsamplefromcollection	Remove sample from `tscollection` object
getabstime (tscollection)	Extract date-string time vector into cell array
getsampleusingtime (tscollection)	Extract data samples into new `tscollection` object
gettimeseriesnames	Cell array of names of `timeseries` objects in `tscollection` object
horzcat (tscollection)	Horizontal concatenation for `tscollection` objects
removets	Remove `timeseries` objects from `tscollection` object
resample (tscollection)	Select or interpolate data in `tscollection` using new time vector
setabstime (tscollection)	Set times of `tscollection` object as date strings
settimeseriesnames	Change name of `timeseries` object in `tscollection`
vertcat (tscollection)	Vertical concatenation for `tscollection` objects

Programming and Data Types

Data Types	Numeric, character, structures, cell arrays, and data type conversion
Data Type Conversion	Convert one numeric type to another, numeric to string, string to numeric, structure to cell array, etc.
Operators and Special Characters	Arithmetic, relational, and logical operators, and special characters
Strings	Create, identify, manipulate, parse, evaluate, and compare strings
Bit-Wise Operations	Perform set, shift, and, or, compare, etc. on specific bit fields
Logical Operations	Evaluate conditions, testing for true or false
Relational Operations	Compare values for equality, greater than, less than, etc.
Set Operations	Find set members, unions, intersections, etc.
Date and Time Operations	Obtain information about dates and times
Programming in MATLAB	M-files, function/expression evaluation, program control, function handles, object oriented programming, error handling

Data Types

Numeric Types	Integer and floating-point data
Characters and Strings	Characters and arrays of characters
Structures	Data of varying types and sizes stored in fields of a structure
Cell Arrays	Data of varying types and sizes stored in cells of array
Function Handles	Invoke a function indirectly via handle
Java Classes and Objects	Access Java classes through MATLAB interface
Data Type Identification	Determine data type of a variable

Numeric Types

arrayfun	Apply function to each element of array
cast	Cast variable to different data type
cat	Concatenate arrays along specified dimension
class	Create object or return class of object
find	Find indices and values of nonzero elements
intmax	Largest value of specified integer type
intmin	Smallest value of specified integer type
intwarning	Control state of integer warnings
ipermute	Inverse permute dimensions of N-D array
isa	Determine whether input is object of given class
isequal	Test arrays for equality
isequalwithequalnans	Test arrays for equality, treating NaNs as equal
isfinite	Array elements that are finite
isinf	Array elements that are infinite
isnan	Array elements that are NaN
isnumeric	Determine whether input is numeric array
isreal	Check if input is real array
isscalar	Determine whether input is scalar
isvector	Determine whether input is vector
permute	Rearrange dimensions of N-D array
realmax	Largest positive floating-point number
realmin	Smallest positive normalized floating-point number
reshape	Reshape array
squeeze	Remove singleton dimensions
zeros	Create array of all zeros

Characters and Strings

See Strings for all string-related functions.

cellstr	Create cell array of strings from character array
char	Convert to character array (string)
eval	Execute string containing MATLAB expression
findstr	Find string within another, longer string
isstr	Determine whether input is character array
regexp, regexpi	Match regular expression
sprintf	Write formatted data to string
sscanf	Read formatted data from string
strcat	Concatenate strings horizontally
strcmp, strcmpi	Compare strings
strings	String handling
strjust	Justify character array
strmatch	Find possible matches for string
strread	Read formatted data from string
strrep	Find and replace substring
strtrim	Remove leading and trailing white space from string
strvcat	Concatenate strings vertically

Structures

arrayfun	Apply function to each element of array
cell2struct	Convert cell array to structure array
class	Create object or return class of object
deal	Distribute inputs to outputs
fieldnames	Field names of structure, or public fields of object
getfield	Field of structure array
isa	Determine whether input is object of given class
isequal	Test arrays for equality
isfield	Determine whether input is structure array field
isscalar	Determine whether input is scalar
isstruct	Determine whether input is structure array
isvector	Determine whether input is vector
orderfields	Order fields of structure array
rmfield	Remove fields from structure

cd	Change working directory
copyfile	Copy file or directory
delete	Remove files or graphics objects
dir	Directory listing
exist	Check existence of variable, function, directory, or Java programming language class
fileattrib	Set or get attributes of file or directory
filebrowser	Current Directory browser
isdir	Determine whether input is a directory
lookfor	Search for keyword in all help entries
ls	Directory contents
matlabroot	Root directory
mkdir	Make new directory
movefile	Move file or directory
pwd	Identify current directory
recycle	Set option to move deleted files to recycle folder
rehash	Refresh function and file system path caches
rmdir	Remove directory
toolboxdir	Root directory for specified toolbox
type	Display contents of file
visdiff	Compare two text files, MAT-Files, or binary files
what	List MATLAB files in current directory
which	Locate functions and files