All functions

abm3pc()

Adams-Bashford-Moulton

accumarray() uniq()

Accumulate Vector Elements

agmean()

Arithmetic-geometric Mean

aitken()

Aitken' Method

akimaInterp()

Univariate Akima Interpolation

and() or()

Logical AND, OR (Matlab Style)

andrewsplot()

Andrews' Curves

Real() Imag() angle()

Basic Complex Functions

anms()

Adaptive Nelder-Mead Minimization

arclength()

Arc Length of a Curve

arnoldi()

Arnoldi Iteration

barylag()

Barycentric Lagrange Interpolation

barylag2d()

2-D Barycentric Lagrange Interpolation

disp() beep()

Utility functions (Matlab style)

bernoulli()

Bernoulli Numbers and Polynomials

bernstein() bernsteinb()

Bernstein Polynomials

bisect() secant() regulaFalsi()

Rootfinding Through Bisection or Secant Rule

bits()

Binary Representation

blanks()

String of Blank Carakters

blkdiag()

Block Diagonal Matrix

brentDekker() brent()

Brent-Dekker Root Finding Algorithm

brown72

Brownian Motion

broyden()

Broyden's Method

bsxfun() arrayfun()

Elementwise Function Application (Matlab Style)

bvp()

Boundary Value Problems

cart2sph() sph2cart() cart2pol() pol2cart()

Coordinate Transformations

cd() pwd() what()

Directory Functions (Matlab style)

ceil() Fix()

Integer Functions (Matlab Style)

charpoly()

Characteristic Polynomial

chebApprox()

Chebyshev Approximation

chebCoeff()

Chebyshev Polynomials

chebPoly()

Chebyshev Polynomials

circlefit()

Fitting a Circle

clear() ver() who() whos()

Clear function (Matlab style)

clenshaw_curtis()

Clenshaw-Curtis Quadrature Formula

combs()

Generate Combinations

compan()

Companion Matrix

complexstep() grad_csd() jacobian_csd() hessian_csd() laplacian_csd()

Complex Step Derivatives

cond()

Matrix Condition

conv()

Polynomial Convolution

cotes()

Newton-Cotes Formulas

cranknic()

Crank-Nicolson Method

cross()

Vector Cross Product

crossn()

n-dimensional Vector Cross Product

cubicspline()

Interpolating Cubic Spline

curvefit()

Parametric Curve Fit

cutpoints()

Find Cutting Points

dblquad() triplequad()

Double and Triple Integration

deconv()

Deconvolution

deeve()

Event Detection in ODE solution

deg2rad() rad2deg()

Degrees to Radians

detrend()

Remove Linear Trends

deval()

Evaluate ODE Solution

Diag()

Matrix Diagonal

distmat() pdist() pdist2()

Distance Matrix

dot()

Scalar Product

eig()

Eigenvalue Function (Matlab Style)

eigjacobi()

Jacobi Eigenvalue Method

einsteinF()

Einstein Functions

ellipke() ellipj()

Elliptic and Jacobi Elliptic Integrals

approx_entropy() sample_entropy()

Approximate and Sample Entropy

eps()

Floating Point Relative Accuracy

erf() erfinv() erfc() erfcinv() erfcx() erfz() erfi()

Error Functions and Inverses (Matlab Style)

errorbar()

Plot Error Bars

eta()

Dirichlet Eta Function

euler_heun()

Euler-Heun ODE Solver

expint() expint_E1() expint_Ei() li()

Exponential and Logarithmic Integral

expm() logm()

Matrix Exponential

eye() ones() zeros()

Some Basic Matrices

ezcontour() ezsurf() ezmesh()

Contour, Surface, and Mesh Plotter

fplot() ezplot()

Easy Function Plot

ezpolar()

Easy Polar Plot

fact() factorial2()

Factorial Function

factors()

Prime Factors

fderiv()

Numerical Differentiation

fibsearch()

Fibonacci Search

figure()

Control Plot Devices (Matlab Style)

finds()

find function (Matlab Style)

findintervals()

Find Interval Indices

findmins()

Find All Minima

findpeaks()

Find Peaks

findzeros()

Find All Roots

fletcher_powell()

Fletcher-Powell Conjugate Gradient Minimization

flipdim() flipud() fliplr() circshift()

Matrix Flipping (Matlab Style)

fminbnd()

Finding Function Minimum

fmincon()

Minimize Nonlinear Constrained Multivariable Function.

fminsearch()

Derivative-free Nonlinear Function Minimization

fminunc()

Minimize Unconstrained Multivariable Function

fnorm()

Function Norm

fornberg()

Fornberg's Finite Difference Approximation

fprintf()

Formatted Printing (Matlab style)

fractalcurve()

Fractal Curves

fresnelS() fresnelC()

Fresnel Integrals

fsolve()

Solve System of Nonlinear Equations

fzero()

Root Finding Algorithm

fzsolve()

Complex Root Finding

gammainc() incgam()

Incomplete Gamma Function

gammaz()

Complex Gamma Function

gaussHermite()

Gauss-Hermite Quadrature Formula

gaussLaguerre()

Gauss-Laguerre Quadrature Formula

gaussLegendre()

Gauss-Legendre Quadrature Formula

gaussNewton()

Gauss-Newton Function Minimization

gauss_kronrod()

Gauss-Kronrod Quadrature

gcd() Lcm()

GCD and LCM Integer Functions

geo_median()

Geometric Median

givens()

Givens Rotation

gmres()

Generalized Minimal Residual Method

golden_ratio()

Golden Ratio Search

grad()

Numerical Gradient

gradient()

Discrete Gradient (Matlab Style)

gramSchmidt()

Gram-Schmidt

hadamard()

Hadamard Matrix

halley()

Halley's Root Finding Mathod

hampel()

Hampel Filter

hankel()

Hankel Matrix

hausdorff_dist()

Hausdorff Distance

haversine()

Haversine Formula

hessenberg()

Hessenberg Matrix

hessian()

Hessian Matrix

hessvec() hessdiag()

Hessian utilities

hilb()

Hilbert Matrix

histc()

Histogram Count (Matlab style)

histss()

Histogram Bin-width Optimization

hooke_jeeves()

Hooke-Jeeves Function Minimization Method

horner() hornerdefl()

Horner's Rule

householder()

Householder Reflections

humps() sinc() psinc()

Matlab Test Functions

hurstexp()

Hurst Exponent

coth() csch() sech() acoth() acsch() asech()

More Hyperbolic Functions

hypot()

Hypotenuse Function

ifft() ifftshift() fftshift()

Inverse Fast Fourier Transformation

inpolygon()

Polygon Region

integral()

Adaptive Numerical Integration

integral2() integral3()

Numerically Evaluate Double and Triple Integrals

interp1()

One-dimensional Interpolation

interp2()

Two-dimensional Data Interpolation

inv()

Matrix Inverse (Matlab Style)

invlap()

Inverse Laplacian

isempty()

isempty Property

isposdef()

Positive Definiteness

isprime()

isprime Property

itersolve()

Iterative Methods

jacobian()

Jacobian Matrix

kriging()

Interpolation by Kriging

kron()

Kronecker product (Matlab Style)

L1linreg()

L1 Linear Regression

laguerre()

Laguerre's Method

lambertWp() lambertWn()

Lambert's W Function

laplacian()

Laplacian Operator

lebesgue()

Lebesgue Constant

legendre()

Legendre Functions (Matlab Style)

line_integral()

Line integral (in the complex plane)

linearproj() affineproj()

Linear Projection onto a Subspace

linprog()

Linear Programming Solver

linspace()

Linearly Spaced Sequences

logspace() logseq()

Log-linearly Spaced Sequences

lsqlin()

Linear Least-Squares Fitting

lsqlincon()

Linear Least-Squares Fitting with linear constraints

lsqnonlin() lsqnonneg() lsqsep() lsqcurvefit()

Nonlinear Least-Squares Fitting

lu() lu_crout() lufact() lusys()

LU Matrix Factorization

magic()

Magic Square

matlab()

Matlab Compatibility

geomean() harmmean() trimmean()

Geometric and Harmonic Mean (Matlab Style)

meshgrid()

Generate a Mesh Grid

mexpfit()

Multi-exponential Fitting

bulirsch_stoer() midpoint()

Bulirsch-Stoer Algorithm

mldivide() mrdivide()

Matlab backslash operator

mod() rem() idivide()

Integer Division

Mode()

Mode function (Matlab style)

moler()

Moler Matrix

movavg()

Moving Average Filters

muller()

Muller's Method

nchoosek()

Binomial Coefficients

ndims()

Number of Dimensions

nearest_spd()

Nearest Symmetric Positive-definite Matrix

nelder_mead()

Nelder-Mead Function Minimization Method

neville()

Neville's Method

newmark()

Newmark Method

newtonHorner()

Newton's Root Finding Method for Polynomials.

newtonInterp() lagrangeInterp()

Lagrange and Newtons Interpolation

newtonRaphson() newton()

Rootfinding through Newton-Raphson or Secant.

newtonsys()

Newton Method for Nonlinear Systems

nextpow2()

Next Power of 2

nnz()

Nonzero Elements

Norm()

Vector Norm

normest()

Estimated Matrix Norm

nthroot()

Real nth Root

nullspace() null()

Kernel or Nullspace

numderiv() numdiff()

Richardson's Numerical Derivative

numel()

Number of Elements

ode23() ode23s() ode45() ode78()

Non-stiff (and stiff) ODE solvers

odregress()

Orthogonal Distance Regression

orth()

Range Space

pade()

Pade Approximation

pascal()

Pascal Triangle

pchip() pchipfun()

Hermitean Interpolation Polynomials

peaks()

Peaks Function (Matlab Style)

perms()

Generate Permutations

piecewise()

Piecewise Linear Function

pinv()

Pseudoinverse or Generalized Inverse

plotyy()

Plotting Two y-Axes

poisson2disk()

Poisson Disk Sampling

polar()

Polar Coordinate Plot (Matlab Style)

Poly()

Define Polynomial by Roots

poly2str()

Print Polynomial

polyApprox()

Polynomial Approximation

polyadd()

Adding Polynomials

polyarea() poly_length() poly_center() poly_crossings()

Area of a Polygon

polyder()

Derivative of Polynomial

polyfit() polyfix()

Fitting by Polynomial

polyint()

Anti-derivative of Polynomial

polylog()

Polylogarithm Function

polymul() polydiv()

Multiplying and Dividing Polynomials

polypow()

Polynomial Powers

polytrans() polygcf()

Polynomial Transformations

polyval() polyvalm()

Evaluating a Polynomial

pow2()

Base 2 Power

mkpp() ppval()

Piecewise Polynomial Structures

ppfit()

Piecewise Polynomial Fit

pracma-package pracma

Practical Numerical Math Routines

primes()

Prime Numbers

procrustes() kabsch()

Solving the Procrustes Problem

psi()

Psi (Polygamma) Function

qpspecial() qpsolve()

Special Quadratic Programming Solver

qrSolve()

LSE Solution

quad()

Adaptive Simpson Quadrature

quad2d()

2-d Gaussian Quadrature

quadcc()

Adaptive Clenshaw-Curtis Quadrature

quadgk()

Adaptive Gauss-Kronrod Quadrature

quadgr()

Gaussian Quadrature with Richardson Extrapolation

quadinf()

Infinite Integrals

quadl()

Adaptive Lobatto Quadrature

quadprog()

Quadratic Programming

quadv()

Vectorized Integration

quiver()

Quiver or Velocity Plot

rand() randn() randi() randsample() rands() randp()

Create Random Matrices

randcomb()

Random Combination

randortho()

Generate Random Orthonormal or Unitary Matrix

randperm()

Random Permutation

Rank()

Matrix Rank

rat() rats()

Continuous Fractions (Matlab Style)

ratinterp()

Rational Interpolation

rationalfit()

Rational Function Approximation

rectint()

Rectangle Intersection Areas

refindall()

Find overlapping regular expression matches.

regexp() regexpi()

Match regular expression

regexprep()

Replace string using regular expression

repmat()

Replicate Matrix

Reshape()

Reshape Matrix

ridders()

Ridders' Root Finding Method

rk4() rk4sys()

Classical Runge-Kutta

rkf54()

Runge-Kutta-Fehlberg

rmserr()

Accuracy Measures

romberg()

Romberg Integration

roots() polyroots() rootsmult()

Polynomial Roots

rosser()

Rosser Matrix

rot90()

Matrix Rotation

rref()

Reduced Row Echelon Form

runge()

Runge Function

savgol()

Savitzky-Golay Smoothing

segm_distance()

Segment Distance

segm_intersect()

Segment Intersection

semilogx() semilogy() loglog()

Semi-logarithmic Plots (Matlab Style)

shooting()

Shooting Method

shubert()

Shubert-Piyavskii Method

Si() Ci()

Sine and Cosine Integral Functions

sigmoid() logit()

Sigmoid Function

simpadpt()

Adaptive Simpson Quadrature

simpson()

Simpson Integration

simpson2d()

Double Simpson Integration

sind() cosd() tand() cotd() asind() acosd() atand() acotd() secd() cscd() asecd() acscd() atan2d()

Trigonometric Functions in Degrees

size()

Size of Matrix

softline()

Soft (Inexact) Line Search

is.sorted() testSort() bubbleSort() insertionSort() selectionSort() shellSort() heapSort() mergeSort() mergeOrdered() quickSort() quickSortx()

Sorting Routines

sortrows()

Sort Rows of a Matrix (Matlab Style)

spinterp()

Monotone (Shape-Preserving) Interpolation

sqrtm() signm() rootm()

Matrix Square and p-th Roots

squareform()

Format Distance Matrix (Matlab Style)

std()

Standard Deviation (Matlab Style)

std_err()

Standard Error

steep_descent()

Steepest Descent Minimization

stereographic() stereographic_inv()

Stereographic Projection

str2num() num2str()

Converting string to number (Matlab style)

strcat()

String Concatenation

strcmp() strcmpi()

String Comparison

strfind() strfindi() findstr()

Find Substrings

strjust()

Justify character vector

strRep()

Find and replace substring

strTrim() deblank()

Remove leading and trailing white space.

subspace()

Angle between two subspaces

sumalt()

Alternating Series Acceleration

taylor()

Taylor Series Approximation

tic() toc()

MATLAB timer functions

titanium

Titanium Test Data

Toeplitz()

Toeplitz Matrix

Trace()

Matrix trace

trapz() cumtrapz() trapzfun()

Trapezoidal Integration

tril() triu()

Triangular Matrices (Matlab Style)

trigApprox()

Trigonometric Approximation

trigPoly()

Trigonometric Polynomial

cot() csc() sec() acot() acsc() asec()

More Trigonometric Functions

triquad()

Gaussian Triangle Quadrature

trisolve()

Tridiagonal Linear System Solver

vander()

Vandermonde matrix

vectorfield()

Vector Field Plotting

whittaker()

Whittaker Smoothing

wilkinson()

wilkinson Matrix

zeta()

Riemann Zeta Function