import numpy as np


def rms(errors):
    """
        root mean square calculation
    """

    # slow pure python way for reference:
    # r = 0.0
    # for i in errors:
    #     r += np.power(i, 2)
    # r = np.sqrt(r / len(errors))
    # return r

    return np.sqrt((errors ** 2).mean())


def baker_exact_2D(X):
    """
        the exact function (2D) used from baker's article (for testing,
        slightly modified)
    """
    x, y = X

    answer = np.power((np.sin(x * np.pi) * np.cos(y * np.pi)), 2)
    return answer


def friendly_exact_2D(X):
    """
        A friendlier 2D func
    """
    x, y = X
    answer = 1.0 + x * x + y * y
    return answer


def baker_exact_3D(X):
    """
        the exact function (3D) used from baker's article (for testing)
    """
    x, y, z = X
    answer = np.power((np.sin(x * np.pi / 2.0) * np.sin(y * np.pi / 2.0) *
                            np.sin(z * np.pi / 2.0)), 2)
    return answer


def exact_me(points, f):
    a = np.array([f(i) for i in points])
    return a


def friendly_exact_3D(X):
    x, y, z = X
    return 1 + x * x + y * y + z * z


def scipy_exact_2D(X):
    x, y = X
    return x * (1 - x) * np.cos(4 * np.pi * x) *\
            np.sin(4 * np.pi * y ** 2) ** 2


def improved_answer(answer, exact):
    if not answer.error:
        # was probably just a linear interpolation
        return False

    if np.abs(answer.final - exact) <= np.abs(answer.qlin - exact):
        return True
    else:
        return False


def identical_points(a, b):
    return all(set(j[i] for j in a) \
             == set(j[i] for j in b) for i in xrange(len(a[0])))


def improved(qlin, err, final, exact):
    if np.abs(final - exact) <= np.abs(qlin - exact):
        return True
    else:
        return False