NumericalMath

Introduction

Functions from Numerical Mathematics for Julia.
[Version 0.2.1; 2014-07-23]

Functions

Linear algebra

• trisolve(d0, d1, d2, rhs) -- solves triangular systems of equations

Polynomials

• pval(p, x) -- evaluates polynomial p in x (Matlab-like order of coefficients)
• horner(p, x) -- Horner schema returning the value of polynomial p at x and the value of its derivative p' at x
• pzero(p, x0) -- finds a root of polynomial p near x0 applying Newton-Raphson
• pfit(xi, yi, n) -- polynomial fitting of data points (of order n)

Root finding

• ridders(f, a, b) -- Ridders' method for finding roots of univariate functions
• brent_dekker(f, a, b) -- root finding using the Brent-Dekker approach

Interpolation and approximation

• interp1d(xs, ys, x) -- Interpolation of data points with methods :constant, :nearest, :linear, :spline, :cubic
• pchip(xs, ys, x) -- Piecewise cubic hermitean interpolating polynomial

Differentiation

• fd_gradient(f, x0; h) -- numerical gradient of a multivariate function applying the "central difference formula"
• fd_jacobian(f, x0; h) -- Jacobian matrix of multivariate function at x0
• fd_hessian(f, x0; h) -- numerical Hessian, based on finite differences
• fd_laplacian(f, x0; h) -- numerical Laplacian, based on finite differences
• numderiv(f, x0; n, h) -- Richardson method applied to central difference
• complex_step(f, x0; h) -- complex-step derivative

Integration

• trapz(x, y) -- Trapezoidal rule for integrating discrete points (with end point correction terms)
• romberg(f, a, b) -- Romberg integration (ie., utilizes Richardson's method)

Miscellaneous

• agm(a, b) -- algebraic-geometric mean of numbers a, b
• arc_length(f, a, b) -- arc length of the curve defined by f:[a,b] --> R

Special functions

• lambertW(x) -- Lambert W function and its first derivative
• legendre(n, x) -- Legendre polynomials of degree <= n at x

Examples