from __future__ import print_function
from pylab import *
from pprint import pprint

# test cases, derived from doc/nasa_rotation_def.pdf

#pylint: disable=all

def euler_to_quat(phi, theta, psi):
    "Quaternion from (body 3(psi)-2(theta)-1(phi) euler angles"
    s1 = sin(psi/2)
    c1 = cos(psi/2)
    s2 = sin(theta/2)
    c2 = cos(theta/2)
    s3 = sin(phi/2)
    c3 = cos(phi/2)
    return array([
        s1*s2*s3 + c1*c2*c3,
        -s1*s2*c3 + s3*c1*c2,
        s1*s3*c2 + s2*c1*c3,
        s1*c2*c3 - s2*s3*c1
    ])

def euler_to_dcm(phi, theta, psi):
    s1 = sin(psi)
    c1 = cos(psi)
    s2 = sin(theta)
    c2 = cos(theta)
    s3 = sin(phi)
    c3 = cos(phi)
    return array([
        [c1*c2, c1*s2*s3 - s1*c3, c1*s2*c3 + s1*s3],
        [s1*c2, s1*s2*s3 + c1*c3, s1*s2*c3 - c1*s3],
        [-s2, c2*s3, c2*c3],
    ])

def quat_prod(q, r):
    "Quaternion product"
    return array([
        r[0]*q[0] - r[1]*q[1] - r[2]*q[2] - r[3]*q[3],
        r[0]*q[1] + r[1]*q[0] - r[2]*q[3] + r[3]*q[2],
        r[0]*q[2] + r[1]*q[3] + r[2]*q[0] - r[3]*q[1],
        r[0]*q[3] - r[1]*q[2] + r[2]*q[1] + r[3]*q[0]
    ])

def dcm_to_euler(dcm):
    return array([
        arctan(dcm[2,1]/ dcm[2,2]),
        arctan(-dcm[2,0]/ sqrt(1 - dcm[2,0]**2)),
        arctan(dcm[1,0]/ dcm[0,0]),
    ])

def dcm_from_quat(q):
    q1 = q[0]
    q2 = q[1]
    q3 = q[2]
    q4 = q[3]
    return array([
        [q1*q1 + q2*q2 - q3*q3 - q4*q4, 2*(q2*q3 - q1*q4), 2*(q2*q4 + q1*q3)],
        [2*(q2*q3 + q1*q4), q1*q1 - q2*q2 + q3*q3 - q4*q4, 2*(q3*q4 - q1*q2)],
        [2*(q2*q4 - q1*q3), 2*(q3*q4 + q1*q2), q1*q1 - q2*q2 - q3*q3 + q4*q4]
    ])

def quat_to_euler(q):
    "Quaternion to (body 3(psi)-2(theta)-1(phi) euler angles"
    return dcm_to_euler(dcm_from_quat(q))

def quat_to_dcm(q):
    return euler_to_dcm(quat_to_euler(q))

phi = 0.1
theta = 0.2
psi = 0.3
print('euler', phi, theta, psi)

q = euler_to_quat(phi, theta, psi)
assert(abs(norm(q) - 1) < 1e-10)
assert(abs(norm(q) - 1) < 1e-10)
assert(norm(array(quat_to_euler(q)) - array([phi, theta, psi])) < 1e-10)
print('\nq:')
pprint(q)

dcm = euler_to_dcm(phi, theta, psi)
assert(norm(dcm[:,0]) == 1)
assert(norm(dcm[:,1]) == 1)
assert(norm(dcm[:,2]) == 1)
assert(abs(dcm[:,0].dot(dcm[:,1])) < 1e-10)
assert(abs(dcm[:,0].dot(dcm[:,2])) < 1e-10)
print('\ndcm:')
pprint(dcm)


q2 = quat_prod(q, q)
pprint(q2)
print(norm(q2))

print('\nq3:')
q3 = array([1,2,3,4])
pprint(q3)
print('\nq3_norm:')
q3_norm =q3 / norm(q3)
pprint(q3_norm)

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