Crate roots

A set of functions to find real roots of numerical equations.

This crate contains various algorithms for numerical and analytical solving of 1-variable equations like f(x)=0. Only real roots are calculated. Multiple (double etc.) roots are considered as one root.

Use

Functions find_root_* try to find a root of any given closure function by iterative approximations. Conditions for success/failure can be customized by implementing the Convergency trait. Functions find_roots_* return all roots of several simple equations at once.

Structs

DebugConvergency	Convergency provider for debugging. It will print out the error at each iteration.
Interval	Interval between two samples, including these samples
Parabola	Definition of the quadratic equation ax^2 + bx + c
Sample	Pair of the independent variable x and the function value y=F(x)
SimpleConvergency	A very basic convergency rules that must be sufficient for many cases. The absolute precision is the same for x and y axes, no relative precision.

Enums

Roots

Sorted and unique list of roots of an equation.

Traits

Convergency	The way to check if the algorithm has finished by either finding a root or reaching the iteration limit.
FloatType	Generic type that lists functions and constants needed in calculations. Default implementations for f32 and f64 are provided.

Functions

find_root_brent	Find a root of the function f(x) = 0 using the Brent method.
find_root_inverse_quadratic	Find a root of the function f(x) = 0 using inverse quadratic approximation.
find_root_newton_raphson	Find a root of the function f(x) = 0 using the Newton-Raphson method.
find_root_regula_falsi	Find a root of the function f(x) = 0 using the Illinois modification of the regula falsi method.
find_root_secant	Find a root of the function f(x) = 0 using the secant method.
find_roots_biquadratic	Solves a bi-quadratic equation a4x^4 + a2x^2 + a0 = 0.
find_roots_cubic	Solves a cubic equation a3x^3 + a2x^2 + a1*x + a0 = 0.
find_roots_cubic_depressed	Solves a depressed cubic equation x^3 + a1*x + a0 = 0.
find_roots_cubic_normalized	Solves a normalized cubic equation x^3 + a2x^2 + a1x + a0 = 0.
find_roots_eigen	Find all roots of the normalized polynomial by finding eigen numbers of the corresponding matrix. (Converted from Java by stiv-yakovenko)
find_roots_linear	Solves a linear equation a1*x + a0 = 0.
find_roots_quadratic	Solves a quadratic equation a2x^2 + a1x + a0 = 0.
find_roots_quartic	Solves a quartic equation a4x^4 + a3x^3 + a2x^2 + a1x + a0 = 0.
find_roots_quartic_depressed	Solves a depressed quartic equation x^4 + a2x^2 + a1x + a0 = 0.
find_roots_sturm	Find all roots of the normalized polynomial x^n + a[0]*x^(n-1) + a[1]*x^(n-2) + ... + a[n-1] = 0 using the Sturm's theorem recursively.