bisect

Parameters

f F

The function.

predicate bool delegate

(

T

,

R

)

The predicate, which must take a point and the function value at that point and return a boolean.

xTrue T

A point where the predicate is true.

xFalse T

A point where the predicate is false.

xTolerance T

Success: When the absolute distance between xTrue and xFalse is less than this number, the function returns.

maxIterations int

Failure: When the algorithm has failed to produce a result after maxIterations bisections, an exception is thrown.

Return Value

f(xTrue) == fTrue
f(xFalse) == fFalse
predicate(xTrue, fTrue) == true
predicate(xFalse, fFalse) == false
abs(xTrue-xFalse) <= xTolerance

Examples

// Find a root by bisection
auto r = bisect(
    (real x) { return x^^3; },
    (real x, real fx) { return fx < 0; },
    -1.0L, 1.5L, 1e-10L
    );

// Let's check if we got the right answer.
enum root = 0.0L;
assert (abs(r.xTrue - root) <= 1e-10);
assert (abs(r.xFalse - root) <= 1e-10);

assert (r.fTrue < 0);
assert (r.fFalse >= 0);
assert (abs(r.xTrue - r.xFalse) <= 1e-10);
assert (r.xNaN < 0);
assert (abs(r.xValid - r.xNan) <= 1e-6);

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