from openmdao.api import ImplicitComponent

class QuadraticComp(ImplicitComponent):
    """
    A Simple Implicit Component representing a Quadratic Equation.

    R(a, b, c, x) = ax^2 + bx + c

    Solution via Quadratic Formula:
    x = (-b + sqrt(b^2 - 4ac)) / 2a
    """

    def setup(self):
        self.add_input('a', val=1.)
        self.add_input('b', val=1.)
        self.add_input('c', val=1.)
        self.add_output('x', val=0.)

        self.declare_partials(of='x', wrt='*')

    def apply_nonlinear(self, inputs, outputs, residuals):
        a = inputs['a']
        b = inputs['b']
        c = inputs['c']
        x = outputs['x']
        residuals['x'] = a * x ** 2 + b * x + c

    def solve_nonlinear(self, inputs, outputs):
        a = inputs['a']
        b = inputs['b']
        c = inputs['c']
        outputs['x'] = (-b + (b ** 2 - 4 * a * c) ** 0.5) / (2 * a)

    def linearize(self, inputs, outputs, partials):
        a = inputs['a']
        b = inputs['b']
        c = inputs['c']
        x = outputs['x']

        partials['x', 'a'] = x ** 2
        partials['x', 'b'] = x
        partials['x', 'c'] = 1.0
        partials['x', 'x'] = 2 * a * x + b

        self.inv_jac = 1.0 / (2 * a * x + b)

