Mathematics

Most of the below functionality described in the core MATLAB Mathematics documentation has equivalent, often identical, functionality (more often that not with the same syntax) described in the Base.Mathematics section of the Julia manual. Specific equivalents are identified below; often these have the same names as in Matlab, otherwise the Julia equivalent name is noted.

Elementary Math

Arithmetic

See Arithmetic Operators in the Julia manual. Note that in Julia the operators are themselves methods and can be used anywhere a method can. See e.g. the example in the documentation for Base.map.

`plus` Addition

`uplus` Unary plus

`minus` Subtraction

`uminus` Unary minus

`times` Element-wise multiplication

`rdivide` Right array division

`ldivide` Left array division

`power` Element-wise power

`mtimes` Matrix Multiplication

`mrdivide` Solve systems of linear equations $xA=B$ for $x$

`mldivide` Solve systems of linear equations $Ax=B$ for $x$

`mpower` Matrix power

`cumprod` Cumulative product

`cumsum` Cumulative sum

`diff` Differences and Approximate Derivatives

`movsum` Moving sum

`prod` Product of array elements

`sum` Sum of array elements

`ceil` Round toward positive infinity

`fix` Round toward zero

`floor` Round toward negative infinity

`idivide` Integer division with rounding option

`mod` Remainder after division (modulo operation)

`rem` Remainder after division

`round` Round to nearest decimal or integer

`bsxfun` Apply element-wise operation to two arrays with implicit expansion enabled

Trigonometry

See Trigonometric and Hyperbolic functions in the Julia manual.

`sin` Sine of argument in radians

`sind` Sine of argument in degrees

`asin` Inverse sine in radians

`asind` Inverse sine in degrees

`sinh` Hyperbolic sine of argument in radians

`asinh` Inverse hyperbolic sine

`cos` Cosine of argument in radians

`cosd` Cosine of argument in degrees

`acos` Inverse cosine in radians

`acosd` Inverse cosine in degrees

`cosh` Hyperbolic cosine

`acosh` Inverse hyperbolic cosine

`tan` Tangent of argument in radians

`tand` Tangent of argument in degrees

`atan` Inverse tangent in radians

`atand` Inverse tangent in degrees

`atan2` Four-quadrant inverse tangent

`atan2d` Four-quadrant inverse tangent in degrees

`tanh` Hyperbolic tangent

`atanh` Inverse hyperbolic tangent

`csc` Cosecant of input angle in radians

`cscd` Cosecant of argument in degrees

`acsc` Inverse cosecant in radians

`acscd` Inverse cosecant in degrees

`csch` Hyperbolic cosecant

`acsch` Inverse hyperbolic cosecant

`sec` Secant of angle in radians

`secd` Secant of argument in degrees

`asec` Inverse secant in radians

`asecd` Inverse secant in degrees

`sech` Hyperbolic secant

`asech` Inverse hyperbolic secant

`cot` Cotangent of angle in radians

`cotd` Cotangent of argument in degrees

`acot` Inverse cotangent in radians

`acotd` Inverse cotangent in degrees

`coth` Hyperbolic cotangent

`acoth` Inverse hyperbolic cotangent

`hypot` Square root of sum of squares (hypotenuse)

`deg2rad` Convert angle from degrees to radians

`rad2deg` Convert angle from radians to degrees

Exponents and Logarithms

See Powers, logs and roots in the Julia manual.

`exp` Exponential

`expm1` Compute $e^{x}-1$ accurately for small values of x

`log` Natural logarithm

`log10` Common logarithm (base 10)

`log1p` Compute log(1+x) accurately for small values of x

`log2` Base 2 logarithm and floating-point number dissection

`nextpow2` Exponent of next higher power of 2

`nthroot` Real nth 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 Numbers

See Complex Numbers in the Julia manual.

`abs` Absolute value and complex magnitude

`angle` Phase angle

`complex` Create complex array

`conj` Complex conjugate

`cplxpair` Sort complex numbers into complex conjugate pairs

`i` Imaginary unit

`imag` Imaginary part of complex number

`isreal` Determine whether array is real

`j` Imaginary unit

`real` Real part of complex number

`sign` Sign function (signum function)

`unwrap` Correct phase angles to produce smoother phase plots

Discrete Math

Equivalents available in Julia Base

`factorial` Factorial of input

`gcd` Greatest common divisor

`lcm` Least common multiple

Equivalents available in JuliaMath/Primes.jl

`factor` Prime factors

`primes` Prime numbers less than or equal to input value

`isprime` Determine which array elements are prime

`nchoosek` Binomial coefficient or all combinations (Julia: `binomial`)

Others

`perms` All possible permutations

The Julia Permutations.permutations(a) function ( Permutations.jl package) returns an iterator object (because the number of permutations can be very large), and in lexicographic order rather than reverse lexicographic. Therefore a drop-in equivalent could be constructed as follows:

julia> perms(a) = reverse(collect(permutations(a)))
perms (generic function with 1 method)

julia> perms([2,4,6])
6-element Array{Array{Int64,1},1}:
 [6, 4, 2]
 [6, 2, 4]
 [4, 6, 2]
 [4, 2, 6]
 [2, 6, 4]
 [2, 4, 6]

`rat` Rational fraction approximation, `rats` Rational output

There doesn't appear to be a direct Julia equivalent of these, but note that unlike Matlab, Julia has a native Rational Number type .

Polynomials

See the Polynomials.jl package. Note that this package provides a proper type for polynomials, Polynomials.Poly, while in Matlab a polynomial of degree $n$ is represented by a vector of length $n+1$ whose elements are the coefficients in descending powers of the polynomial.

`poly` Polynomial with specified roots or characteristic polynomial

`polyeig` Polynomial eigenvalue problem

`polyfit` Polynomial curve fitting

Polynomials.polyfit provides comparable basic functionality--the single output argument form of the Matlab function--although it lacks the additional error estimate and centering/scaling features.

`residue` Partial fraction expansion (partial fraction decomposition)

`roots` Polynomial roots

Polynomials.roots provides roots with multiplicity.

`polyval` Polynomial evaluation

See Base.Math.@evalpoly in the Julia Manual.

`polyvalm` Matrix polynomial evaluation

`conv` Convolution and polynomial multiplication

`deconv` Deconvolution and polynomial division

`polyint` Polynomial integration

`polyder` Polynomial differentiation

Special Functions

`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

`betaincinv` Beta inverse cumulative distribution function

`betaln` Logarithm of beta function

`ellipj` Jacobi elliptic functions

`ellipke` Complete elliptic integrals of first and second kind

`erf` Error function

`erfc` Complementary error function

`erfcinv` Inverse complementary error function

`erfcx` Scaled complementary error function

`erfinv` Inverse error function

`expint` Exponential integral

`gamma` Gamma function

`gammainc` Incomplete gamma function

`gammaincinv` Inverse incomplete gamma function

`gammaln` Logarithm of gamma function

`legendre` Associated Legendre functions

`psi` Psi (polygamma) function

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

Constants and Test Matrices

Constants

See General Number Functions and Constants in the Julia manual.

`eps` Floating-point relative accuracy

`flintmax` Largest consecutive integer in floating-point format

`i`, `j` Imaginary unit

In Julia, im is equivalent; this allows i and j to be used as e.g. loop indices without conflict.

`Inf` Infinity

`pi` Ratio of circle's circumference to its diameter

Also available as pi in Julia as well as \piTab ↹ → $\pi$

`NaN` Not-a-Number

`isfinite` Array elements that are finite

`isinf` Array elements that are infinite

`isnan` Array elements that are NaN

`compan` Companion matrix

Test Matrices

See the MatrixDepot.jl package; most of the matrices in gallery and all the rest below are available in that package, plus some additional ones.

`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

See Linear Algebra in the Julia manual.

`mldivide` Solve systems of linear equations $xA=B$ for $x$

`mrdivide` Solve systems of linear equations $Ax=B$ for $x$

`decomposition` Matrix decomposition for solving linear systems

`lsqminnorm` Minimum norm least-squares solution to linear equation

`linsolve` Solve linear system of equations

`inv` Matrix inverse

`pinv` Moore-Penrose pseudoinverse

`lscov` Least-squares solution in presence of known covariance

`lsqnonneg` Solve nonnegative linear least-squares problem

`sylvester` Solve Sylvester equation $AX+XB=C$ for $X$

`eig` Eigenvalues and eigenvectors

`eigs` Subset of eigenvalues and eigenvectors

`balance` Diagonal scaling to improve eigenvalue accuracy

`svd` Singular value decomposition

`svds` Subset of singular values and vectors

`gsvd` Generalized singular value decomposition

`ordeig` Eigenvalues of quasitriangular matrices

`ordqz` Reorder eigenvalues in QZ factorization

`ordschur` Reorder eigenvalues in Schur factorization

`polyeig` Polynomial eigenvalue problem

`qz` QZ factorization for generalized eigenvalues

`hess` Hessenberg form of matrix

`schur` Schur decomposition

`rsf2csf` Convert real Schur form to complex Schur form

`cdf2rdf` Convert complex diagonal form to real block diagonal form

`lu` LU matrix factorization

`ldl` Block LDL' factorization for Hermitian indefinite matrices

`chol` Cholesky factorization

`cholupdate` Rank 1 update to Cholesky factorization

`qr` Orthogonal-triangular decomposition

`qrdelete` Remove column or row from QR factorization

`qrinsert` Insert column or row into QR factorization

`qrupdate` Rank 1 update to QR factorization

`planerot` Givens plane rotation

`transpose` Transpose vector or matrix

`ctranspose` Complex conjugate transpose

`mtimes` Matrix Multiplication

`mpower` Matrix power

`sqrtm` Matrix square root

`expm` Matrix exponential

`logm` Matrix logarithm

`funm` Evaluate general matrix function

`kron` Kronecker tensor product

`cross` Cross product

`dot` Dot product

`bandwidth` Lower and upper matrix bandwidth

`tril` Lower triangular part of matrix

`triu` Upper triangular part of matrix

`isbanded` Determine if matrix is within specific bandwidth

`isdiag` Determine if matrix is diagonal

`ishermitian` Determine if matrix is Hermitian or skew-Hermitian

`issymmetric` Determine if matrix is symmetric or skew-symmetric

`istril` Determine if matrix is lower triangular

`istriu` Determine if matrix is upper triangular

`norm` Vector and matrix norms

`normest` 2-norm estimate

`vecnorm` Vector-wise norm

`cond` Condition number for inversion

`condest` 1-norm condition number estimate

`rcond` Reciprocal condition number

`condeig` Condition number with respect to eigenvalues

`det` Matrix determinant

`null` Null space

`orth` Orthonormal basis for range of matrix

`rank` Rank of matrix

`rref` Reduced row echelon form (Gauss-Jordan elimination)

`trace` Sum of diagonal elements

`subspace` Angle between two subspaces

Random Number Generation

`rand` Uniformly distributed random numbers

`randn` Normally distributed random numbers

`randi` Uniformly distributed pseudorandom integers

`randperm` Random permutation

`rng` Control random number generation

`randStream` Random number stream

Interpolation

`interp1` 1-D data interpolation (table lookup)

`interp2` Interpolation for 2-D gridded data in meshgrid format

`interp3` Interpolation for 3-D gridded data in meshgrid format

`interpn` Interpolation for 1-D, 2-D, 3-D, and N-D gridded data in ndgrid format

`gRiddedinterpolant` Gridded data interpolation

`pchip` Piecewise Cubic Hermite Interpolating Polynomial (PCHIP)

`spline` Cubic spline data interpolation

`ppval` Evaluate piecewise polynomial

`mkpp` Make piecewise polynomial

`unmkpp` Extract piecewise polynomial details

`padecoef` Padé approximation of time delays

`interpft` 1-D interpolation (FFT method)

`ndgrid` Rectangular grid in N-D space

`meshgrid` 2-D and 3-D grids

`griddata` Interpolate 2-D or 3-D scattered data

`griddatan` Interpolate N-D scattered data

`scaTteredinterpolant` Interpolate 2-D or 3-D scattered data

Optimization

`fminbnd` Find minimum of single-variable function on fixed interval

`fminsearch` Find minimum of unconstrained multivariable function using derivative-free method

`lsqnonneg` Solve nonnegative linear least-squares problem

`fzero` Root of nonlinear function

`optimget` Optimization options values

`optimset` Create or edit optimization options structure

Numerical Integration and Differential Equations

See DifferentialEquations.jl. In particular see the section Translations from MATLAB/Python/R.

Ordinary Differential Equations

`ode45` Solve nonstiff differential equations — medium order method

`ode23` Solve nonstiff differential equations — low order method

`ode113` Solve nonstiff differential equations — variable order method

`ode15s` Solve stiff differential equations and DAEs — variable order method

`ode23s` Solve stiff differential equations — low order method

`ode23t` Solve moderately stiff ODEs and DAEs — trapezoidal rule

`ode23tb` Solve stiff differential equations — trapezoidal rule + backward differentiation formula

`ode15i` Solve fully implicit differential equations — variable order method

`decic` Compute consistent initial conditions for ode15i

`odeget` Extract ODE option values

`odeset` Create or modify options structure for ODE solvers

`deval` Evaluate differential equation solution structure

`odextend` Extend solution to ODE

Boundary Value Problems

`bvp4c` Solve boundary value problems for ordinary differential equations

`bvp5c` Solve boundary value problems for ordinary differential equations

`bvpinit` Form initial guess for BVP solvers

`bvpxtend` Form guess structure for extending boundary value solutions

`bvpget` Extract properties from options structure created with bvpset

`bvpset` Create or alter options structure of boundary value problem

`deval` Evaluate differential equation solution structure

Delay Differential Equations

`dde23` Solve delay differential equations (DDEs) with constant delays

`ddesd` Solve delay differential equations (DDEs) with general delays

`ddensd` Solve delay differential equations (DDEs) of neutral type

`ddeget` Extract properties from delay differential equations options structure

`ddeset` Create or alter delay differential equations options structure

`deval` Evaluate differential equation solution structure

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

Numerical Integration and Differentiation

`integral` Numerical integration

`integral2` Numerically evaluate double integral

`integral3` Numerically evaluate triple integral

`quadgk` Numerically evaluate integral, adaptive Gauss-Kronrod quadrature

`quad2d` Numerically evaluate double integral, tiled method

`cumtrapz` Cumulative trapezoidal numerical integration

`trapz` Trapezoidal numerical integration

`polyint` Polynomial integration

`del2` Discrete Laplacian

`diff` Differences and Approximate Derivatives

`gradient` Numerical gradient

`polyder` Polynomial differentiation

Fourier Analysis and Filtering

`fft` Fast Fourier transform

`fft2` 2-D fast Fourier transform

`fftn` N-D fast Fourier transform

`fftshift` Shift zero-frequency component to center of spectrum

`fftw` Define method for determining FFT algorithm

`ifft` Inverse fast Fourier transform

`ifft2` 2-D inverse fast Fourier transform

`ifftn` Multidimensional inverse fast Fourier transform

`ifftshift` Inverse zero-frequency shift

`nextpow2` Exponent of next higher power of 2

`interpft` 1-D interpolation (FFT method)

`conv` Convolution and polynomial multiplication

`conv2` 2-D convolution

`convn` N-D convolution

`deconv` Deconvolution and polynomial division

`filter` 1-D digital filter

`filter2` 2-D digital filter

`ss2tf` Convert state-space representation to transfer function

`padecoef` Padé approximation of time delays

Sparse Matrices

`spalloc` Allocate space for sparse matrix

`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

`sparse` Create sparse matrix

`spconvert` Import from sparse matrix external format

`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

`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

`find` Find indices and values of nonzero elements

`full` Convert sparse matrix to full matrix

`dissect` Nested dissection permutation

`amd` Approximate minimum degree permutation

`colamd` Column approximate minimum degree permutation

`colperm` Sparse column permutation based on nonzero count

`dmperm` Dulmage-Mendelsohn decomposition

`randperm` Random permutation

`symamd` Symmetric approximate minimum degree permutation

`symrcm` Sparse reverse Cuthill-McKee ordering

`pcg` Preconditioned conjugate gradients method

`minres` Minimum residual method

`symmlq` Symmetric LQ method

`gmres` Generalized minimum residual method (with restarts)

`bicg` Biconjugate gradients method

`bicgstab` Biconjugate gradients stabilized method

`bicgstabl` Biconjugate gradients stabilized (l) method

`cgs` Conjugate gradients squared method

`qmr` Quasi-minimal residual method

`tfqmr` Transpose-free quasi-minimal residual method

`lsqr` LSQR method

`ichol` Incomplete Cholesky factorization

`ilu` Incomplete LU factorization

`eigs` Subset of eigenvalues and eigenvectors

`svds` Subset of singular values and vectors

`normest` 2-norm estimate

`condest` 1-norm condition number estimate

`sprank` Structural rank

`etree` Elimination tree

`symbfact` Symbolic factorization analysis

`spaugment` Form least-squares augmented system

`dmperm` Dulmage-Mendelsohn decomposition

`etreeplot` Plot elimination tree

`treelayout` Lay out tree or forest

`treeplot` Plot picture of tree

`gplot` Plot nodes and links representing adjacency matrix

`unmesh` Convert edge matrix to coordinate and Laplacian matrices

Graph and Network Algorithms

`graph` Graph with undirected edges

`digraph` Graph with directed edges

`addnode` Add new node to graph

`rmnode` Remove node from graph

`addedge` Add new edge to graph

`rmedge` Remove edge from graph

`flipedge` Reverse edge directions

`numnodes` Number of nodes in graph

`numedges` Number of edges in graph

`findnode` Locate node in graph

`findedge` Locate edge in graph

`edgecount` Number of edges between two nodes

`reordernodes` Reorder graph nodes

`subgraph` Extract subgraph

`bfsearch` Breadth-first graph search

`dfsearch` Depth-first graph search

`centrality` Measure node importance

`maxflow` Maximum flow in graph

`conncomp` Connected graph components

`biconncomp` Biconnected graph components

`condensation` Graph condensation

`bctree` Block-cut tree graph

`minspantree` Minimum spanning tree of graph

`toposort` Topological order of directed acyclic graph

`isdag` Determine if graph is acyclic

`transclosure` Transitive closure

`transreduction` Transitive reduction

`isisomorphic` Determine whether two graphs are isomorphic

`isomorphism` Compute isomorphism between two graphs

`ismultigraph` Determine whether graph has multiple edges

`simplify` Reduce multigraph to simple graph

`shortestpath` Shortest path between two single nodes

`shortestpathtree` Shortest path tree from node

`distances` Shortest path distances of all node pairs

`adjacency` Graph adjacency matrix

`incidence` Graph incidence matrix

`laplacian` Graph Laplacian matrix

`degree` Degree of graph nodes

`neighbors` Neighbors of graph node

`nearest` Nearest neighbors within radius

`indegree` In-degree of nodes

`outdegree` Out-degree of nodes

`predecessors` Node predecessors

`successors` Node successors

`inedges` Incoming edges to node

`outedges` Outgoing edges from node

`plot` Plot graph nodes and edges

`labeledge` Label graph edges

`labelnode` Label graph nodes

`layout` Change layout of graph plot

`highlight` Highlight nodes and edges in plotted graph

`graphPlot` Graph plot for directed and undirected graphs

Computational Geometry

See the JuliaGeometry GitHub organization.

Triangulation Representation

`triangulation` Triangulation in 2-D or 3-D

`tetramesh` Tetrahedron mesh plot

`trimesh` Triangular mesh plot

`triplot` 2-D triangular plot

`trisurf` Triangular surface plot

Delaunay Triangulation

`deLaunaytriangulation` Delaunay triangulation in 2-D and 3-D

`delaunay` Delaunay triangulation

`delaunayn` N-D Delaunay triangulation

`tetramesh` Tetrahedron mesh plot

`trimesh` Triangular mesh plot

`triplot` 2-D triangular plot

`trisurf` Triangular surface plot

Spatial Search

`triangulation` Triangulation in 2-D or 3-D

`deLaunaytriangulation` Delaunay triangulation in 2-D and 3-D

`dsearchn` N-D nearest point search

`tsearchn` N-D closest simplex search

`delaunay` Delaunay triangulation

`delaunayn` N-D Delaunay triangulation

Bounding Regions

`boundary` Boundary of a set of points in 2-D or 3-D

`alphaShape` Polygons and polyhedra from points in 2-D and 3-D

`convhull` Convex hull

`convhulln` N-D convex hull

Voronoi Diagram

`patch` Create one or more filled polygons

`voronoi` Voronoi diagram

`voronoin` N-D Voronoi diagram

Elementary Polygons

The Julia package GeometricalPredicates.jl provides some similar functionality.

`inpolygon` Points located inside or on edge of polygonal region

`nsidedpoly` Regular polygon

`polyarea` Area of polygon

`polybuffer` Create buffer around points or lines

`rectint` Rectangle intersection area

`polyshape` 2-D polygons

`addboundary` Add polyshape boundary

`rmboundary` Remove polyshape boundary

`rmholes` Remove holes in polyshape

`rmslivers` Remove polyshape boundary outliers

`simplify` Simplify polyshape boundaries

`boundary` Vertex coordinates of polyshape boundary

`isequal` Determine if polyshape objects are equal

`ishole` Determine if polyshape boundary is a hole

`isinterior` Query points inside polyshape

`issimplified` Determine if polyshape is well-defined

`nearestvertex` Query nearest polyshape vertex

`numboundaries` Number of polyshape boundaries

`numsides` Number of polyshape sides

`overlaps` Determine whether polyshape objects overlap

`area` Area of polyshape

`boundingbox` Bounding box of polyshape

`centroid` Centroid of polyshape

`convhull` Convex hull of polyshape

`perimeter` Perimeter of polyshape

`triangulation` Triangulate polyshape

`turningdist` Compute turning distance between polyshape objects

`intersect` Intersection of polyshape objects

`subtract` Difference of two polyshape objects

`union` Union of polyshape objects

`xor` Exclusive OR of two polyshape objects

`polybuffer` Buffer polyshape

`rotate` Rotate polyshape

`scale` Scale polyshape

`translate` Translate polyshape

`holes` Convert polyshape hole boundaries to array of polyshape objects

`plot` Plot polyshape

`regions` Access polyshape regions

`sortboundaries` Sort polyshape boundaries

`sortregions` Sort polyshape regions

Mathematics

Elementary Math

Arithmetic

plus Addition

uplus Unary plus

minus Subtraction

uminus Unary minus

times Element-wise multiplication

rdivide Right array division

ldivide Left array division

power Element-wise power

mtimes Matrix Multiplication

mrdivide Solve systems of linear equations x A = B {\displaystyle xA=B} for x {\displaystyle x}

mldivide Solve systems of linear equations A x = B {\displaystyle Ax=B} for x {\displaystyle x}

mpower Matrix power

cumprod Cumulative product

cumsum Cumulative sum

diff Differences and Approximate Derivatives

movsum Moving sum

prod Product of array elements

sum Sum of array elements

ceil Round toward positive infinity

fix Round toward zero

floor Round toward negative infinity

idivide Integer division with rounding option

mod Remainder after division (modulo operation)

rem Remainder after division

round Round to nearest decimal or integer

bsxfun Apply element-wise operation to two arrays with implicit expansion enabled

Trigonometry

sin Sine of argument in radians

sind Sine of argument in degrees

asin Inverse sine in radians

asind Inverse sine in degrees

sinh Hyperbolic sine of argument in radians

asinh Inverse hyperbolic sine

cos Cosine of argument in radians

cosd Cosine of argument in degrees

acos Inverse cosine in radians

acosd Inverse cosine in degrees

cosh Hyperbolic cosine

acosh Inverse hyperbolic cosine

tan Tangent of argument in radians

tand Tangent of argument in degrees

atan Inverse tangent in radians

atand Inverse tangent in degrees

atan2 Four-quadrant inverse tangent

atan2d Four-quadrant inverse tangent in degrees

tanh Hyperbolic tangent

atanh Inverse hyperbolic tangent

csc Cosecant of input angle in radians

cscd Cosecant of argument in degrees

acsc Inverse cosecant in radians

acscd Inverse cosecant in degrees

csch Hyperbolic cosecant

acsch Inverse hyperbolic cosecant

sec Secant of angle in radians

secd Secant of argument in degrees

asec Inverse secant in radians

asecd Inverse secant in degrees

sech Hyperbolic secant

asech Inverse hyperbolic secant

cot Cotangent of angle in radians

cotd Cotangent of argument in degrees

acot Inverse cotangent in radians

acotd Inverse cotangent in degrees

coth Hyperbolic cotangent

acoth Inverse hyperbolic cotangent

hypot Square root of sum of squares (hypotenuse)

deg2rad Convert angle from degrees to radians

rad2deg Convert angle from radians to degrees

Exponents and Logarithms

exp Exponential

expm1 Compute e x − 1 {\displaystyle e^{x}-1} accurately for small values of x

log Natural logarithm

log10 Common logarithm (base 10)

log1p Compute log(1+x) accurately for small values of x

log2 Base 2 logarithm and floating-point number dissection

nextpow2 Exponent of next higher power of 2

nthroot Real nth root of real numbers

`plus` Addition

`uplus` Unary plus

`minus` Subtraction

`uminus` Unary minus

`times` Element-wise multiplication

`rdivide` Right array division

`ldivide` Left array division

`power` Element-wise power

`mtimes` Matrix Multiplication

`mrdivide` Solve systems of linear equations $xA=B$ for $x$

`mldivide` Solve systems of linear equations $Ax=B$ for $x$

`mpower` Matrix power

`cumprod` Cumulative product

`cumsum` Cumulative sum

`diff` Differences and Approximate Derivatives

`movsum` Moving sum

`prod` Product of array elements

`sum` Sum of array elements

`ceil` Round toward positive infinity

`fix` Round toward zero

`floor` Round toward negative infinity

`idivide` Integer division with rounding option

`mod` Remainder after division (modulo operation)

`rem` Remainder after division

`round` Round to nearest decimal or integer

`bsxfun` Apply element-wise operation to two arrays with implicit expansion enabled

`sin` Sine of argument in radians

`sind` Sine of argument in degrees

`asin` Inverse sine in radians

`asind` Inverse sine in degrees

`sinh` Hyperbolic sine of argument in radians

`asinh` Inverse hyperbolic sine

`cos` Cosine of argument in radians

`cosd` Cosine of argument in degrees

`acos` Inverse cosine in radians

`acosd` Inverse cosine in degrees

`cosh` Hyperbolic cosine

`acosh` Inverse hyperbolic cosine

`tan` Tangent of argument in radians

`tand` Tangent of argument in degrees

`atan` Inverse tangent in radians

`atand` Inverse tangent in degrees

`atan2` Four-quadrant inverse tangent

`atan2d` Four-quadrant inverse tangent in degrees

`tanh` Hyperbolic tangent

`atanh` Inverse hyperbolic tangent

`csc` Cosecant of input angle in radians

`cscd` Cosecant of argument in degrees

`acsc` Inverse cosecant in radians

`acscd` Inverse cosecant in degrees

`csch` Hyperbolic cosecant

`acsch` Inverse hyperbolic cosecant

`sec` Secant of angle in radians

`secd` Secant of argument in degrees

`asec` Inverse secant in radians

`asecd` Inverse secant in degrees

`sech` Hyperbolic secant

`asech` Inverse hyperbolic secant

`cot` Cotangent of angle in radians

`cotd` Cotangent of argument in degrees

`acot` Inverse cotangent in radians

`acotd` Inverse cotangent in degrees

`coth` Hyperbolic cotangent

`acoth` Inverse hyperbolic cotangent

`hypot` Square root of sum of squares (hypotenuse)

`deg2rad` Convert angle from degrees to radians

`rad2deg` Convert angle from radians to degrees

`exp` Exponential

`expm1` Compute $e^{x}-1$ accurately for small values of x

`log` Natural logarithm

`log10` Common logarithm (base 10)

`log1p` Compute log(1+x) accurately for small values of x

`log2` Base 2 logarithm and floating-point number dissection

`nextpow2` Exponent of next higher power of 2

`nthroot` Real nth 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