findIntersection - Tries to find the first intersection of functions $f and $g within a given interval

find-intersection.php

<?php

/**
 * Tries to find the first intersection of functions $f and $g within a given
 * interval
 *
 * $discardExceptions allows $f and $g to reject/skip certain values (e. g.
 * because of division by zero) by throwing an exception without having to stop
 * the whole calculation.
 *
 * In theory, all intersections in the interval could be returned, not just the
 * first one. But I couldn't be bothered to figure out whether the next
 * intersection really is a *new* intersection and what to do when $f and $g
 * have the same definition.
 *
 * @param Closure $f
 * @param Closure $g
 * @param int|float $from
 * @param int|float $to
 * @param int|float $step
 * @param int|float $epsilon
 * @param bool $discardExceptions
 * @return array
 * @throws InvalidArgumentException
 * @throws Exception
 */
function findIntersection(Closure $f, Closure $g, $from, $to, $step, $epsilon = 0.00001, $discardExceptions = true)
{
    $info = new ReflectionFunction($f);
    if ($info->getNumberOfParameters() !== 1) {
        throw new InvalidArgumentException('$f must accept exactly one parameter');
    }

    $info = new ReflectionFunction($g);
    if ($info->getNumberOfParameters() !== 1) {
        throw new InvalidArgumentException('$g must accept exactly one parameter');
    }

    if (!is_int($from) && !is_float($from)) {
        throw new InvalidArgumentException('$from must be int|float');
    }

    if (!is_int($to) && !is_float($to)) {
        throw new InvalidArgumentException('$to must be int|float');
    }

    if (!is_int($step) && !is_float($step)) {
        throw new InvalidArgumentException('$step must be int|float');
    }

    if ((float) $step === 0.0) {
        throw new InvalidArgumentException('$step cannot be 0');
    }

    if (
        $from - $to > 0 && $step > 0
        || $from - $to < 0 && $step < 0
    ) {
        throw new InvalidArgumentException('Stepping in the wrong direction');
    }

    if (!is_int($epsilon) && !is_float($epsilon)) {
        throw new InvalidArgumentException('$epsilon must be int|float');
    }

    if (!is_bool($discardExceptions)) {
        throw new InvalidArgumentException('$discardExceptions must be bool');
    }

    $ignoreActiveIteration = false;

    $tmpf = 0;
    $tmpg = 0;

    $intersections = array();

    $x = (float) $from;

    do {
        try {
            $tmpf = $f($x);
            $tmpg = $g($x);
        } catch (Exception $e) {
            if ($discardExceptions) {
                $ignoreActiveIteration = true;
            } else {
                throw $e;
            }
        }

        if ($ignoreActiveIteration) {
            // reset for next iteration
            $ignoreActiveIteration = false;
        } elseif (abs($tmpf - $tmpg) <= $epsilon) {
            $intersections[] = $x;
            break;
        }

        $x += $step;

        if ($x > $to) {
            break;
        }
    } while (true);

    return $intersections;
}

$f = function ($x) { return pow($x, 2) - 1; };
$g = function ($x) { return sin($x);        };

var_dump(findIntersection($f, $g, -2, 2, 0.001, 0.001));

// http://www.wolframalpha.com/input/?i=x^2+-1+%3D+sin+x

// array(1) {
//   [0]=>
//   float(-0.63700000000011)
// }