Roots of a function: Difference between revisions

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=={{header|OCaml}}==

A general root finder using the False Position (~~regula~~ ~~falsi~~) method, which will find all simple roots given a small step size.

A general root finder using the False Position (Regula Falsi) method, which will find all simple roots given a small step size.

let bracket u v =

~~let~~ ~~zcross u v =~~ ((u > 0.0) && (v < 0.0)) || ((u < 0.0) && (v > 0.0));;

((u > 0.0) && (v < 0.0)) || ((u < 0.0) && (v > 0.0));;

let ~~tol~~ a b = (a = b);; (* or use a ~~weaker~~ ~~tolerance~~ *)

let xtol a b = (a = b);; (* or use |a-b| < epsilon *)

let rec regula_falsi a b fa fb f =

if ~~tol~~ a b then (a, fa) else

if xtol a b then (a, fa) else

let c = (fb*.a -. fa*.b)/.(fb-.fa) in

let c = (fb*.a -. fa*.b) /. (fb -. fa) in

let fc = f c in

if fc = 0.0 then (c, fc) else

if ~~zcross~~ fa fc then

if bracket fa fc then

regula_falsi a c fa fc f

else

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let rec next x fx =

if x > hi then [] else

let y = x+.step in

let y = x +. step in

let fy = f y in

if fx = 0.0 then

(x,fx) :: next y fy

else if bracket fx fy then

(regula_falsi x y fx fy f) :: next y fy

else

if ~~zcross fx~~ fy ~~then~~

next y fy in

(regula_falsi x y fx fy f) :: next y fy

else

next y fy in

next lo (f lo);;

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</pre>

Note these roots are exact with floating-point ~~accuracy~~.

Note these roots are exact solutions with floating-point calculation.

=={{header|Octave}}==