MathPHP\NumericalAnalysis\Interpolation\ClampedCubicSplineTest::testSolveZeroError PHP Метод

    public function testSolveZeroError()
    {
        // f(x) = 8x³ -13x² -92x + 96
        $f = new Polynomial([8, -13, -92, 96]);
        $f’ = $f->differentiate();
        // The error in the Cubic Spline Interpolating Polynomial is proportional
        // to the max value of the 4th derivative. Thus, if our input Function
        // is a 3rd-degree polynomial, the fourth derivative will be zero, and
        // thus we will have zero error.
        $a = 0;
        $b = 10;
        $n = 50;
        $tol = 0;
        $roundoff = 0.0001;
        // round off error
        $p = ClampedCubicSpline::interpolate($f, $f’, $a, $b, $n);
        // Check that p(x) agrees with f(x) at x = 0
        $expected = $f(0);
        $actual = $p(0);
        $this->assertEquals($expected, $actual, '', $tol + $roundoff);
        // Check that p(x) agrees with f(x) at x = 2
        $expected = $f(2);
        $actual = $p(2);
        $this->assertEquals($expected, $actual, '', $tol + $roundoff);
        // Check that p(x) agrees with f(x) at x = 4
        $expected = $f(4);
        $actual = $p(4);
        $this->assertEquals($expected, $actual, '', $tol + $roundoff);
        // Check that p(x) agrees with f(x) at x = 6
        $expected = $f(6);
        $actual = $p(6);
        $this->assertEquals($expected, $actual, '', $tol + $roundoff);
        // Check that p(x) agrees with f(x) at x = 8
        $expected = $f(8);
        $actual = $p(8);
        $this->assertEquals($expected, $actual, '', $tol + $roundoff);
        // Check that p(x) agrees with f(x) at x = 10
        $expected = $f(10);
        $actual = $p(10);
        $this->assertEquals($expected, $actual, '', $tol + $roundoff);
        // Check that p(x) agrees with f(x) at x = 7.32 (not a node)
        $expected = $f(10);
        $actual = $p(10);
        $this->assertEquals($expected, $actual, '', $tol + $roundoff);
    }