Practical Numerical Math Functions
Control Plot Devices (Matlab Style)
find function (Matlab Style)
Find Interval Indices
Find All Minima
Gauss-Hermite Quadrature Formula
Adams-Bashford-Moulton
Accumulate Vector Elements
Arithmetic-geometric Mean
Aitken' Method
Univariate Akima Interpolation
Logical AND, OR (Matlab Style)
Andrews' Curves
Basic Complex Functions
Adaptive Nelder-Mead Minimization
Arc Length of a Curve
Arnoldi Iteration
Barycentric Lagrange Interpolation
2-D Barycentric Lagrange Interpolation
Utility functions (Matlab style)
Bernoulli Numbers and Polynomials
Bernstein Polynomials
Rootfinding Through Bisection or Secant Rule
Binary Representation
String of Blank Carakters
Block Diagonal Matrix
Brent-Dekker Root Finding Algorithm
Broyden's Method
Elementwise Function Application (Matlab Style)
Boundary Value Problems
Coordinate Transformations
Directory Functions (Matlab style)
Integer Functions (Matlab Style)
Characteristic Polynomial
Chebyshev Approximation
Chebyshev Polynomials
Chebyshev Polynomials
Fitting a Circle
Clear function (Matlab style)
Clenshaw-Curtis Quadrature Formula
Generate Combinations
Companion Matrix
Complex Step Derivatives
Matrix Condition
Polynomial Convolution
Newton-Cotes Formulas
Crank-Nicolson Method
Vector Cross Product
n-dimensional Vector Cross Product
Interpolating Cubic Spline
Parametric Curve Fit
Find Cutting Points
Double and Triple Integration
Deconvolution
Event Detection in ODE solution
Degrees to Radians
Remove Linear Trends
Evaluate ODE Solution
Matrix Diagonal
Distance Matrix
Scalar Product
Eigenvalue Function (Matlab Style)
Jacobi Eigenvalue Method
Einstein Functions
Elliptic and Jacobi Elliptic Integrals
Approximate and Sample Entropy
Floating Point Relative Accuracy
Error Functions and Inverses (Matlab Style)
Plot Error Bars
Dirichlet Eta Function
Euler-Heun ODE Solver
Exponential and Logarithmic Integral
Matrix Exponential
Some Basic Matrices
Contour, Surface, and Mesh Plotter
Easy Function Plot
Easy Polar Plot
Factorial Function
Prime Factors
Numerical Differentiation
Fibonacci Search
Find Peaks
Find All Roots
Fletcher-Powell Conjugate Gradient Minimization
Matrix Flipping (Matlab Style)
Finding Function Minimum
Minimize Nonlinear Constrained Multivariable Function.
Derivative-free Nonlinear Function Minimization
Minimize Unconstrained Multivariable Function
Function Norm
Fornberg's Finite Difference Approximation
Formatted Printing (Matlab style)
Fractal Curves
Fresnel Integrals
Solve System of Nonlinear Equations
Root Finding Algorithm
Complex Root Finding
Incomplete Gamma Function
Complex Gamma Function
Gauss-Kronrod Quadrature
Gauss-Laguerre Quadrature Formula
Gauss-Legendre Quadrature Formula
Gauss-Newton Function Minimization
GCD and LCM Integer Functions
Geometric Median
Givens Rotation
Generalized Minimal Residual Method
Golden Ratio Search
Numerical Gradient
Discrete Gradient (Matlab Style)
Gram-Schmidt
Hadamard Matrix
Halley's Root Finding Mathod
Hampel Filter
Hankel Matrix
Hausdorff Distance
Haversine Formula
Hessenberg Matrix
Hessian Matrix
Hessian utilities
Hilbert Matrix
Histogram Count (Matlab style)
Histogram Bin-width Optimization
Hooke-Jeeves Function Minimization Method
Horner's Rule
Householder Reflections
Matlab Test Functions
Hurst Exponent
More Hyperbolic Functions
Hypotenuse Function
Inverse Fast Fourier Transformation
Polygon Region
Adaptive Numerical Integration
Numerically Evaluate Double and Triple Integrals
One-dimensional Interpolation
Two-dimensional Data Interpolation
Matrix Inverse (Matlab Style)
Inverse Laplacian
isempty Property
Positive Definiteness
isprime Property
Iterative Methods
Jacobian Matrix
Interpolation by Kriging
Kronecker product (Matlab Style)
L1 Linear Regression
Laguerre's Method
Lambert's W Function
Laplacian Operator
Lebesgue Constant
Legendre Functions (Matlab Style)
Line integral (in the complex plane)
Linear Projection onto a Subspace
Linear Programming Solver
Linearly Spaced Sequences
Log-linearly Spaced Sequences
Linear Least-Squares Fitting
Linear Least-Squares Fitting with linear constraints
Nonlinear Least-Squares Fitting
LU Matrix Factorization
Magic Square
Matlab Compatibility
Geometric and Harmonic Mean (Matlab Style)
Generate a Mesh Grid
Multi-exponential Fitting
Bulirsch-Stoer Algorithm
Matlab backslash operator
Integer Division
Mode function (Matlab style)
Moler Matrix
Moving Average Filters
Muller's Method
Binomial Coefficients
Number of Dimensions
Nearest Symmetric Positive-definite Matrix
Nelder-Mead Function Minimization Method
Neville's Method
Newmark Method
Newton's Root Finding Method for Polynomials.
Lagrange and Newtons Interpolation
Rootfinding through Newton-Raphson or Secant.
Newton Method for Nonlinear Systems
Next Power of 2
Nonzero Elements
Vector Norm
Estimated Matrix Norm
Real nth Root
Kernel or Nullspace
Richardson's Numerical Derivative
Number of Elements
Non-stiff (and stiff) ODE solvers
Orthogonal Distance Regression
Range Space
Pade Approximation
Pascal Triangle
Hermitean Interpolation Polynomials
Peaks Function (Matlab Style)
Generate Permutations
Piecewise Linear Function
Pseudoinverse or Generalized Inverse
Plotting Two y-Axes
Poisson Disk Sampling
Polar Coordinate Plot (Matlab Style)
Define Polynomial by Roots
Print Polynomial
Adding Polynomials
Polynomial Approximation
Area of a Polygon
Derivative of Polynomial
Fitting by Polynomial
Anti-derivative of Polynomial
Polylogarithm Function
Multiplying and Dividing Polynomials
Polynomial Powers
Polynomial Transformations
Evaluating a Polynomial
Base 2 Power
Piecewise Polynomial Structures
Piecewise Polynomial Fit
Practical Numerical Math Routines
Prime Numbers
Solving the Procrustes Problem
Psi (Polygamma) Function
Special Quadratic Programming Solver
LSE Solution
Adaptive Simpson Quadrature
2-d Gaussian Quadrature
Adaptive Clenshaw-Curtis Quadrature
Adaptive Gauss-Kronrod Quadrature
Gaussian Quadrature with Richardson Extrapolation
Infinite Integrals
Adaptive Lobatto Quadrature
Quadratic Programming
Vectorized Integration
Quiver or Velocity Plot
Create Random Matrices
Random Combination
Generate Random Orthonormal or Unitary Matrix
Random Permutation
Matrix Rank
Continuous Fractions (Matlab Style)
Rational Interpolation
Rational Function Approximation
Rectangle Intersection Areas
Find overlapping regular expression matches.
Match regular expression
Replace string using regular expression
Replicate Matrix
Reshape Matrix
Ridders' Root Finding Method
Classical Runge-Kutta
Runge-Kutta-Fehlberg
Accuracy Measures
Romberg Integration
Polynomial Roots
Rosser Matrix
Matrix Rotation
Reduced Row Echelon Form
Runge Function
Savitzky-Golay Smoothing
Segment Distance
Segment Intersection
Semi-logarithmic Plots (Matlab Style)
Shooting Method
Shubert-Piyavskii Method
Sine and Cosine Integral Functions
Sigmoid Function
Adaptive Simpson Quadrature
Double Simpson Integration
Trigonometric Functions in Degrees
Size of Matrix
Soft (Inexact) Line Search
Sorting Routines
Sort Rows of a Matrix (Matlab Style)
Monotone (Shape-Preserving) Interpolation
Matrix Square and p-th Roots
Format Distance Matrix (Matlab Style)
Standard Deviation (Matlab Style)
Standard Error
Steepest Descent Minimization
Stereographic Projection
Converting string to number (Matlab style)
String Concatenation
String Comparison
Find Substrings
Justify character vector
Find and replace substring
Remove leading and trailing white space.
Angle between two subspaces
Alternating Series Acceleration
Taylor Series Approximation
MATLAB timer functions
Toeplitz Matrix
Matrix trace
Trapezoidal Integration
Triangular Matrices (Matlab Style)
Trigonometric Approximation
More Trigonometric Functions
Trigonometric Polynomial
Gaussian Triangle Quadrature
Tridiagonal Linear System Solver
Vandermonde matrix
Vector Field Plotting
Whittaker Smoothing
wilkinson Matrix
Riemann Zeta Function
Provides a large number of functions from numerical analysis and linear algebra, numerical optimization, differential equations, time series, plus some well-known special mathematical functions. Uses 'MATLAB' function names where appropriate to simplify porting.