import numpy as np
# For testing whether a number is close to zero
_FLOAT_EPS = np.finfo(np.float64).eps
_EPS4 = _FLOAT_EPS * 4.0


def mulQuat(qa, qb):
    res = np.zeros(4)
    res[0] = qa[0]*qb[0] - qa[1]*qb[1] - qa[2]*qb[2] - qa[3]*qb[3]
    res[1] = qa[0]*qb[1] + qa[1]*qb[0] + qa[2]*qb[3] - qa[3]*qb[2]
    res[2] = qa[0]*qb[2] - qa[1]*qb[3] + qa[2]*qb[0] + qa[3]*qb[1]
    res[3] = qa[0]*qb[3] + qa[1]*qb[2] - qa[2]*qb[1] + qa[3]*qb[0]
    return res

def negQuat(quat):
    return np.array([quat[0], -quat[1], -quat[2], -quat[3]])

def quat2Vel(quat, dt=1):
    axis = quat[1:].copy()
    sin_a_2 = np.sqrt(np.sum(axis**2))
    axis = axis/(sin_a_2+1e-8)
    speed = 2*np.arctan2(sin_a_2, quat[0])/dt
    return speed, axis

def quatDiff2Vel(quat1, quat2, dt):
    neg = negQuat(quat1)
    diff = mulQuat(quat2, neg)
    return quat2Vel(diff, dt)


def axis_angle2quat(axis, angle):
    c = np.cos(angle/2)
    s = np.sin(angle/2)
    return np.array([c, s*axis[0], s*axis[1], s*axis[2]])

def euler2mat(euler):
    """ Convert Euler Angles to Rotation Matrix.  See rotation.py for notes """
    euler = np.asarray(euler, dtype=np.float64)
    assert euler.shape[-1] == 3, "Invalid shaped euler {}".format(euler)

    ai, aj, ak = -euler[..., 2], -euler[..., 1], -euler[..., 0]
    si, sj, sk = np.sin(ai), np.sin(aj), np.sin(ak)
    ci, cj, ck = np.cos(ai), np.cos(aj), np.cos(ak)
    cc, cs = ci * ck, ci * sk
    sc, ss = si * ck, si * sk

    mat = np.empty(euler.shape[:-1] + (3, 3), dtype=np.float64)
    mat[..., 2, 2] = cj * ck
    mat[..., 2, 1] = sj * sc - cs
    mat[..., 2, 0] = sj * cc + ss
    mat[..., 1, 2] = cj * sk
    mat[..., 1, 1] = sj * ss + cc
    mat[..., 1, 0] = sj * cs - sc
    mat[..., 0, 2] = -sj
    mat[..., 0, 1] = cj * si
    mat[..., 0, 0] = cj * ci
    return mat


def euler2quat(euler):
    """ Convert Euler Angles to Quaternions.  See rotation.py for notes """
    euler = np.asarray(euler, dtype=np.float64)
    assert euler.shape[-1] == 3, "Invalid shape euler {}".format(euler)

    ai, aj, ak = euler[..., 2] / 2, -euler[..., 1] / 2, euler[..., 0] / 2
    si, sj, sk = np.sin(ai), np.sin(aj), np.sin(ak)
    ci, cj, ck = np.cos(ai), np.cos(aj), np.cos(ak)
    cc, cs = ci * ck, ci * sk
    sc, ss = si * ck, si * sk

    quat = np.empty(euler.shape[:-1] + (4,), dtype=np.float64)
    quat[..., 0] = cj * cc + sj * ss
    quat[..., 3] = cj * sc - sj * cs
    quat[..., 2] = -(cj * ss + sj * cc)
    quat[..., 1] = cj * cs - sj * sc
    return quat


def mat2euler(mat):
    """ Convert Rotation Matrix to Euler Angles.  See rotation.py for notes """
    mat = np.asarray(mat, dtype=np.float64)
    assert mat.shape[-2:] == (3, 3), "Invalid shape matrix {}".format(mat)

    cy = np.sqrt(mat[..., 2, 2] * mat[..., 2, 2] + mat[..., 1, 2] * mat[..., 1, 2])
    condition = cy > _EPS4
    euler = np.empty(mat.shape[:-1], dtype=np.float64)
    euler[..., 2] = np.where(condition,
                             -np.arctan2(mat[..., 0, 1], mat[..., 0, 0]),
                             -np.arctan2(-mat[..., 1, 0], mat[..., 1, 1]))
    euler[..., 1] = np.where(condition,
                             -np.arctan2(-mat[..., 0, 2], cy),
                             -np.arctan2(-mat[..., 0, 2], cy))
    euler[..., 0] = np.where(condition,
                             -np.arctan2(mat[..., 1, 2], mat[..., 2, 2]),
                             0.0)
    return euler


def mat2quat(mat):
    """ Convert Rotation Matrix to Quaternion.  See rotation.py for notes """
    mat = np.asarray(mat, dtype=np.float64)
    assert mat.shape[-2:] == (3, 3), "Invalid shape matrix {}".format(mat)

    Qxx, Qyx, Qzx = mat[..., 0, 0], mat[..., 0, 1], mat[..., 0, 2]
    Qxy, Qyy, Qzy = mat[..., 1, 0], mat[..., 1, 1], mat[..., 1, 2]
    Qxz, Qyz, Qzz = mat[..., 2, 0], mat[..., 2, 1], mat[..., 2, 2]
    # Fill only lower half of symmetric matrix
    K = np.zeros(mat.shape[:-2] + (4, 4), dtype=np.float64)
    K[..., 0, 0] = Qxx - Qyy - Qzz
    K[..., 1, 0] = Qyx + Qxy
    K[..., 1, 1] = Qyy - Qxx - Qzz
    K[..., 2, 0] = Qzx + Qxz
    K[..., 2, 1] = Qzy + Qyz
    K[..., 2, 2] = Qzz - Qxx - Qyy
    K[..., 3, 0] = Qyz - Qzy
    K[..., 3, 1] = Qzx - Qxz
    K[..., 3, 2] = Qxy - Qyx
    K[..., 3, 3] = Qxx + Qyy + Qzz
    K /= 3.0
    # TODO: vectorize this -- probably could be made faster
    q = np.empty(K.shape[:-2] + (4,))
    it = np.nditer(q[..., 0], flags=['multi_index'])
    while not it.finished:
        # Use Hermitian eigenvectors, values for speed
        vals, vecs = np.linalg.eigh(K[it.multi_index])
        # Select largest eigenvector, reorder to w,x,y,z quaternion
        q[it.multi_index] = vecs[[3, 0, 1, 2], np.argmax(vals)]
        # Prefer quaternion with positive w
        # (q * -1 corresponds to same rotation as q)
        if q[it.multi_index][0] < 0:
            q[it.multi_index] *= -1
        it.iternext()
    return q


def quat2euler(quat):
    """ Convert Quaternion to Euler Angles.  See rotation.py for notes """
    return mat2euler(quat2mat(quat))


def quat2mat(quat):
    """ Convert Quaternion to Euler Angles.  See rotation.py for notes """
    quat = np.asarray(quat, dtype=np.float64)
    assert quat.shape[-1] == 4, "Invalid shape quat {}".format(quat)

    w, x, y, z = quat[..., 0], quat[..., 1], quat[..., 2], quat[..., 3]
    Nq = np.sum(quat * quat, axis=-1)
    s = 2.0 / Nq
    X, Y, Z = x * s, y * s, z * s
    wX, wY, wZ = w * X, w * Y, w * Z
    xX, xY, xZ = x * X, x * Y, x * Z
    yY, yZ, zZ = y * Y, y * Z, z * Z

    mat = np.empty(quat.shape[:-1] + (3, 3), dtype=np.float64)
    mat[..., 0, 0] = 1.0 - (yY + zZ)
    mat[..., 0, 1] = xY - wZ
    mat[..., 0, 2] = xZ + wY
    mat[..., 1, 0] = xY + wZ
    mat[..., 1, 1] = 1.0 - (xX + zZ)
    mat[..., 1, 2] = yZ - wX
    mat[..., 2, 0] = xZ - wY
    mat[..., 2, 1] = yZ + wX
    mat[..., 2, 2] = 1.0 - (xX + yY)
    return np.where((Nq > _FLOAT_EPS)[..., np.newaxis, np.newaxis], mat, np.eye(3))