Bisection
===================

.. plot::
    :include-source: False

    import openturns as ot
    from matplotlib import pyplot as plt
    from openturns.viewer import View

    xMin = 0.0
    xMax= 3.0
    f = ot.MemoizeFunction(ot.SymbolicFunction("x", "x^3-2*x^2-1"))
    solver = ot.Bisection()
    root = solver.solve(f, 0.0, xMin, xMax)
    x = f.getInputHistory()
    y = f.getOutputHistory()
    g = f.draw(xMin, xMax)
    c = ot.Cloud(x, y)
    c.setColor("red")
    c.setPointStyle("bullet")
    g.add(c)
    data = ot.Sample(0, 2)
    msg = ot.Description(0)
    for i in range(len(x)-1):
    	data.add([x[i, 0], y[i, 0]])
        data.add([x[i+1, 0], y[i, 0]])
        data.add([x[i+1, 0], y[i+1, 0]])
        if abs(x[i, 0] - x[i+1, 0]) + abs(y[i, 0] - y[i+1, 0]) > 0.4:
            msg.add(r"$x_"+str(i)+r"$")
        else:
            msg.add("")
    msg.add(r"$x_\infty$")
    c = ot.Curve(data)
    c.setColor("green")
    g.add(c)
    z = ot.Curve([[xMin, 0.0], [xMax, 0.0]])
    z.setColor("black")
    z.setLineStyle("dashed")
    g.add(z)
    t = ot.Text(x, y, msg)
    t.setColor("black")
    t.setLegend(r"$x_\infty$="+str(root))
    g.add(t)
    g.setTitle("Root finding using " + solver.getClassName())
    fig = plt.figure()
    ax = fig.add_subplot(111)
    View(g, figure=fig)
    plt.xlabel(r'$x$')
    plt.ylabel(r'$f(x)$')
    plt.grid()

.. currentmodule:: openturns

.. autoclass:: Bisection

   
   .. automethod:: __init__