| Practical Numerical Math Routines | pracma-package pracma |
| Adams-Bashford-Moulton | abm3pc |
| Accumulate Vector Elements | accumarray uniq |
| Arithmetic-geometric Mean | agmean |
| Aitken' Method | aitken |
| Univariate Akima Interpolation | akimaInterp |
| Logical AND, OR (Matlab Style) | and or |
| Andrews' Curves | andrewsplot |
| Basic Complex Functions | angle Imag Real |
| Adaptive Nelder-Mead Minimization | anms |
| Approximate and Sample Entropy | approx_entropy sample_entropy |
| Arc Length of a Curve | arclength |
| Arnoldi Iteration | arnoldi |
| Barycentric Lagrange Interpolation | barylag |
| 2-D Barycentric Lagrange Interpolation | barylag2d |
| Bernoulli Numbers and Polynomials | bernoulli |
| Bernstein Polynomials | bernstein bernsteinb |
| Rootfinding Through Bisection or Secant Rule | bisect regulaFalsi secant |
| Binary Representation | bits |
| String of Blank Carakters | blanks |
| Block Diagonal Matrix | blkdiag |
| Brent-Dekker Root Finding Algorithm | brent brentDekker |
| Brownian Motion | brown72 |
| Broyden's Method | broyden |
| Elementwise Function Application (Matlab Style) | arrayfun bsxfun |
| Bulirsch-Stoer Algorithm | bulirsch_stoer midpoint |
| Boundary Value Problems | bvp |
| Coordinate Transformations | cart2pol cart2sph pol2cart sph2cart |
| Directory Functions (Matlab style) | cd pwd what |
| Integer Functions (Matlab Style) | ceil Fix |
| Characteristic Polynomial | charpoly |
| Chebyshev Approximation | chebApprox |
| Chebyshev Polynomials | chebCoeff |
| Chebyshev Polynomials | chebPoly |
| Fitting a Circle | circlefit |
| Clear function (Matlab style) | clear ver who whos |
| Clenshaw-Curtis Quadrature Formula | clenshaw_curtis |
| Generate Combinations | combs |
| Companion Matrix | compan |
| Complex Step Derivatives | complexstep grad_csd hessian_csd jacobian_csd laplacian_csd |
| Matrix Condition | cond |
| Polynomial Convolution | conv |
| More Trigonometric Functions | acot acsc asec cot csc sec |
| Newton-Cotes Formulas | cotes |
| More Hyperbolic Functions | acoth acsch asech coth csch sech |
| Crank-Nicolson Method | cranknic |
| Vector Cross Product | cross |
| n-dimensional Vector Cross Product | crossn |
| Interpolating Cubic Spline | cubicspline |
| Parametric Curve Fit | curvefit |
| Find Cutting Points | cutpoints |
| Double and Triple Integration | dblquad triplequad |
| Deconvolution | deconv |
| Event Detection in ODE solution | deeve |
| Degrees to Radians | deg2rad rad2deg |
| Remove Linear Trends | detrend |
| Evaluate ODE Solution | deval |
| Matrix Diagonal | Diag |
| Utility functions (Matlab style) | beep disp |
| Distance Matrix | distmat pdist pdist2 |
| Scalar Product | dot |
| Eigenvalue Function (Matlab Style) | eig |
| Jacobi Eigenvalue Method | eigjacobi |
| Einstein Functions | einsteinF |
| Elliptic and Jacobi Elliptic Integrals | ellipj ellipke |
| Floating Point Relative Accuracy | eps |
| Error Functions and Inverses (Matlab Style) | erf erfc erfcinv erfcx erfi erfinv erfz |
| Plot Error Bars | errorbar |
| Dirichlet Eta Function | eta |
| Euler-Heun ODE Solver | euler_heun |
| Exponential and Logarithmic Integral | expint expint_E1 expint_Ei li |
| Matrix Exponential | expm logm |
| Some Basic Matrices | eye ones zeros |
| Contour, Surface, and Mesh Plotter | ezcontour ezmesh ezsurf |
| Easy Function Plot | ezplot fplot |
| Easy Polar Plot | ezpolar |
| Factorial Function | fact factorial2 |
| Prime Factors | factors |
| Numerical Differentiation | fderiv |
| Fibonacci Search | fibsearch |
| Control Plot Devices (Matlab Style) | figure |
| Find Interval Indices | findintervals |
| Find All Minima | findmins |
| Find Peaks | findpeaks |
| find function (Matlab Style) | finds |
| Find All Roots | findzeros |
| Fletcher-Powell Conjugate Gradient Minimization | fletcher_powell |
| Matrix Flipping (Matlab Style) | circshift flipdim fliplr flipud |
| Finding Function Minimum | fminbnd |
| Minimize Nonlinear Constrained Multivariable Function. | fmincon |
| Derivative-free Nonlinear Function Minimization | fminsearch |
| Minimize Unconstrained Multivariable Function | fminunc |
| Function Norm | fnorm |
| Fornberg's Finite Difference Approximation | fornberg |
| Formatted Printing (Matlab style) | fprintf |
| Fractal Curves | fractalcurve |
| Fresnel Integrals | fresnelC fresnelS |
| Solve System of Nonlinear Equations | fsolve |
| Root Finding Algorithm | fzero |
| Complex Root Finding | fzsolve |
| Incomplete Gamma Function | gammainc incgam |
| Complex Gamma Function | gammaz |
| Gauss-Kronrod Quadrature | gauss_kronrod |
| Gauss-Hermite Quadrature Formula | gaussHermite |
| Gauss-Laguerre Quadrature Formula | gaussLaguerre |
| Gauss-Legendre Quadrature Formula | gaussLegendre |
| Gauss-Newton Function Minimization | gaussNewton |
| GCD and LCM Integer Functions | gcd Lcm |
| Geometric Median | geo_median |
| Geometric and Harmonic Mean (Matlab Style) | geomean harmmean trimmean |
| Givens Rotation | givens |
| Generalized Minimal Residual Method | gmres |
| Golden Ratio Search | golden_ratio |
| Numerical Gradient | grad |
| Discrete Gradient (Matlab Style) | gradient |
| Gram-Schmidt | gramSchmidt |
| Hadamard Matrix | hadamard |
| Halley's Root Finding Mathod | halley |
| Hampel Filter | hampel |
| Hankel Matrix | hankel |
| Hausdorff Distance | hausdorff_dist |
| Haversine Formula | haversine |
| Hessenberg Matrix | hessenberg |
| Hessian Matrix | hessian |
| Hessian utilities | hessdiag hessvec |
| Hilbert Matrix | hilb |
| Histogram Count (Matlab style) | histc |
| Histogram Bin-width Optimization | histss |
| Hooke-Jeeves Function Minimization Method | hooke_jeeves |
| Horner's Rule | horner hornerdefl |
| Householder Reflections | householder |
| Matlab Test Functions | humps psinc sinc |
| Hurst Exponent | hurstexp |
| Hypotenuse Function | hypot |
| Inverse Fast Fourier Transformation | fftshift ifft ifftshift |
| Polygon Region | inpolygon |
| Adaptive Numerical Integration | integral |
| Numerically Evaluate Double and Triple Integrals | integral2 integral3 |
| One-dimensional Interpolation | interp1 |
| Two-dimensional Data Interpolation | interp2 |
| Matrix Inverse (Matlab Style) | inv |
| Inverse Laplacian | invlap |
| isempty Property | isempty |
| Positive Definiteness | isposdef |
| isprime Property | isprime |
| Iterative Methods | itersolve |
| Jacobian Matrix | jacobian |
| Interpolation by Kriging | kriging |
| Kronecker product (Matlab Style) | kron |
| L1 Linear Regression | L1linreg |
| Laguerre's Method | laguerre |
| Lambert's W Function | lambertWn lambertWp |
| Laplacian Operator | laplacian |
| Lebesgue Constant | lebesgue |
| Legendre Functions (Matlab Style) | legendre |
| Line integral (in the complex plane) | line_integral |
| Linear Projection onto a Subspace | affineproj linearproj |
| Linear Programming Solver | linprog |
| Linearly Spaced Sequences | linspace |
| Log-linearly Spaced Sequences | logseq logspace |
| Linear Least-Squares Fitting | lsqlin |
| Linear Least-Squares Fitting with linear constraints | lsqlincon |
| Nonlinear Least-Squares Fitting | lsqcurvefit lsqnonlin lsqnonneg lsqsep |
| LU Matrix Factorization | lu lufact lusys lu_crout |
| Magic Square | magic |
| Matlab Compatibility | matlab |
| Generate a Mesh Grid | meshgrid |
| Multi-exponential Fitting | mexpfit |
| Matlab backslash operator | mldivide mrdivide |
| Integer Division | idivide mod rem |
| Mode function (Matlab style) | Mode |
| Moler Matrix | moler |
| Moving Average Filters | movavg |
| Muller's Method | muller |
| Binomial Coefficients | nchoosek |
| Number of Dimensions | ndims |
| Nearest Symmetric Positive-definite Matrix | nearest_spd |
| Nelder-Mead Function Minimization Method | nelder_mead |
| Neville's Method | neville |
| Newmark Method | newmark |
| Newton's Root Finding Method for Polynomials. | newtonHorner |
| Lagrange and Newtons Interpolation | lagrangeInterp newtonInterp |
| Rootfinding through Newton-Raphson or Secant. | newton newtonRaphson |
| Newton Method for Nonlinear Systems | newtonsys |
| Next Power of 2 | nextpow2 |
| Nonzero Elements | nnz |
| Vector Norm | Norm |
| Estimated Matrix Norm | normest |
| Real nth Root | nthroot |
| Kernel or Nullspace | null nullspace |
| Richardson's Numerical Derivative | numderiv numdiff |
| Number of Elements | numel |
| Non-stiff (and stiff) ODE solvers | ode23 ode23s ode45 ode78 |
| Orthogonal Distance Regression | odregress |
| Range Space | orth |
| Pade Approximation | pade |
| Pascal Triangle | pascal |
| Hermitean Interpolation Polynomials | pchip pchipfun |
| Peaks Function (Matlab Style) | peaks |
| Generate Permutations | perms |
| Piecewise Linear Function | piecewise |
| Pseudoinverse or Generalized Inverse | pinv |
| Plotting Two y-Axes | plotyy |
| Poisson Disk Sampling | poisson2disk |
| Polar Coordinate Plot (Matlab Style) | polar |
| Define Polynomial by Roots | Poly |
| Print Polynomial | poly2str |
| Adding Polynomials | polyadd |
| Polynomial Approximation | polyApprox |
| Area of a Polygon | polyarea poly_center poly_crossings poly_length |
| Derivative of Polynomial | polyder |
| Fitting by Polynomial | polyfit polyfix |
| Anti-derivative of Polynomial | polyint |
| Polylogarithm Function | polylog |
| Multiplying and Dividing Polynomials | polydiv polymul |
| Polynomial Powers | polypow |
| Polynomial Transformations | polygcf polytrans |
| Evaluating a Polynomial | polyval polyvalm |
| Base 2 Power | pow2 |
| Piecewise Polynomial Fit | ppfit |
| Piecewise Polynomial Structures | mkpp ppval |
| Prime Numbers | primes |
| Solving the Procrustes Problem | kabsch procrustes |
| Psi (Polygamma) Function | psi |
| Special Quadratic Programming Solver | qpsolve qpspecial |
| LSE Solution | qrSolve |
| Adaptive Simpson Quadrature | quad |
| 2-d Gaussian Quadrature | quad2d |
| Adaptive Clenshaw-Curtis Quadrature | quadcc |
| Adaptive Gauss-Kronrod Quadrature | quadgk |
| Gaussian Quadrature with Richardson Extrapolation | quadgr |
| Infinite Integrals | quadinf |
| Adaptive Lobatto Quadrature | quadl |
| Quadratic Programming | quadprog |
| Vectorized Integration | quadv |
| Quiver or Velocity Plot | quiver |
| Create Random Matrices | rand randi randn randp rands randsample |
| Random Combination | randcomb |
| Generate Random Orthonormal or Unitary Matrix | randortho |
| Random Permutation | randperm |
| Matrix Rank | Rank |
| Continuous Fractions (Matlab Style) | rat rats |
| Rational Interpolation | ratinterp |
| Rational Function Approximation | rationalfit |
| Rectangle Intersection Areas | rectint |
| Find overlapping regular expression matches. | refindall |
| Match regular expression | regexp regexpi |
| Replace string using regular expression | regexprep |
| Replicate Matrix | repmat |
| Reshape Matrix | Reshape |
| Ridders' Root Finding Method | ridders |
| Classical Runge-Kutta | rk4 rk4sys |
| Runge-Kutta-Fehlberg | rkf54 |
| Accuracy Measures | rmserr |
| Romberg Integration | romberg |
| Polynomial Roots | polyroots roots rootsmult |
| Rosser Matrix | rosser |
| Matrix Rotation | rot90 |
| Reduced Row Echelon Form | rref |
| Runge Function | runge |
| Savitzky-Golay Smoothing | savgol |
| Segment Distance | segm_distance |
| Segment Intersection | segm_intersect |
| Semi-logarithmic Plots (Matlab Style) | loglog semilogx semilogy |
| Shooting Method | shooting |
| Shubert-Piyavskii Method | shubert |
| Sine and Cosine Integral Functions | Ci Si |
| Sigmoid Function | logit sigmoid |
| Adaptive Simpson Quadrature | simpadpt |
| Double Simpson Integration | simpson2d |
| Trigonometric Functions in Degrees | acosd acotd acscd asecd asind atan2d atand cosd cotd cscd secd sind tand |
| Size of Matrix | size |
| Soft (Inexact) Line Search | softline |
| Sorting Routines | bubbleSort heapSort insertionSort is.sorted mergeOrdered mergeSort quickSort quickSortx selectionSort shellSort testSort |
| Sort Rows of a Matrix (Matlab Style) | sortrows |
| Monotone (Shape-Preserving) Interpolation | spinterp |
| Matrix Square and p-th Roots | rootm signm sqrtm |
| Format Distance Matrix (Matlab Style) | squareform |
| Standard Deviation (Matlab Style) | std |
| Standard Error | std_err |
| Steepest Descent Minimization | steep_descent |
| Stereographic Projection | stereographic stereographic_inv |
| Converting string to number (Matlab style) | num2str str2num |
| String Concatenation | strcat |
| String Comparison | strcmp strcmpi |
| Find Substrings | findstr strfind strfindi |
| Justify character vector | strjust |
| Find and replace substring | strRep |
| Remove leading and trailing white space. | deblank strTrim |
| Angle between two subspaces | subspace |
| Alternating Series Acceleration | sumalt |
| Taylor Series Approximation | taylor |
| MATLAB timer functions | tic toc |
| Titanium Test Data | titanium |
| Toeplitz Matrix | Toeplitz |
| Matrix trace | Trace |
| Trapezoidal Integration | cumtrapz trapz trapzfun |
| Triangular Matrices (Matlab Style) | tril triu |
| Trigonometric Approximation | trigApprox |
| Trigonometric Polynomial | trigPoly |
| Gaussian Triangle Quadrature | triquad |
| Tridiagonal Linear System Solver | trisolve |
| Vandermonde matrix | vander |
| Vector Field Plotting | vectorfield |
| Whittaker Smoothing | whittaker |
| wilkinson Matrix | wilkinson |
| Riemann Zeta Function | zeta |
