MathPHP\Functions\Polynomial::differentiate PHP Метод

    public function differentiate() : Polynomial
    {
        $derivativeCoefficients = [];
        // Start with empty set of coefficients
        // Iterate over each coefficient (except the last), differentiating term-by-term
        for ($i = 0; $i < $this->degree; $i++) {
            $derivativeCoefficients[] = $this->coefficients[$i] * ($this->degree - $i);
        }
        // If the array of coefficients is empty, we are differentiating a constant. Return [0].
        $derivativeCoefficients = $derivativeCoefficients !== [] ? $derivativeCoefficients : [0];
        return new Polynomial($derivativeCoefficients);
    }

 public function testSolveNonzeroError()
 {
     // f(x) = x⁴ + 8x³ -13x² -92x + 96
     $f = new Polynomial([1, 8, -13, -92, 96]);
     $f’ = $f->differentiate();
     $f⁽⁴⁾ = $f’->differentiate()->differentiate()->differentiate();
     // The error is bounded by:
     // |f(x)-p(x)| = tol <= (5/384) * h⁴ * max f⁽⁴⁾(x)
     // where h = max hᵢ
     // and max f⁽⁴⁾(x) = f⁽⁴⁾(x) for all x given a 4th-degree polynomial f(x)
     $a = 0;
     $b = 10;
     $n = 51;
     // So, tol <= (1/24) * (1/5)⁴ * 24 = (1/5)⁴
     $h = ($b - $a) / ($n - 1);
     $tol = 5 / 384 * $h ** 4 * $f⁽⁴⁾(0);
     $roundoff = 1.0E-6;
     // round off error
     $p = ClampedCubicSpline::interpolate($f, $f’, $a, $b, $n);
     // Check that p(x) agrees with f(x) at x = 0
     $target = 0;
     $expected = $f($target);
     $x = $p($target);
     $this->assertEquals($expected, $x, '', $tol + $roundoff);
     // Check that p(x) agrees with f(x) at x = 2
     $target = 2;
     $expected = $f($target);
     $x = $p($target);
     $this->assertEquals($expected, $x, '', $tol + $roundoff);
     // Check that p(x) agrees with f(x) at x = 4
     $target = 4;
     $expected = $f($target);
     $x = $p($target);
     $this->assertEquals($expected, $x, '', $tol + $roundoff);
     // Check that p(x) agrees with f(x) at x = 6
     $target = 6;
     $expected = $f($target);
     $x = $p($target);
     $this->assertEquals($expected, $x, '', $tol + $roundoff);
     // Check that p(x) agrees with f(x) at x = 8
     $target = 8;
     $expected = $f($target);
     $x = $p($target);
     $this->assertEquals($expected, $x, '', $tol + $roundoff);
     // Check that p(x) agrees with f(x) at x = 10
     $target = 10;
     $expected = $f($target);
     $x = $p($target);
     $this->assertEquals($expected, $x, '', $tol + $roundoff);
     // Check that p(x) agrees with f(x) at x = 7.32 (not a node)
     $target = 7.32;
     $expected = $f($target);
     $x = $p($target);
     $this->assertEquals($expected, $x, '', $tol + $roundoff);
 }