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150 lines
3.5 KiB
Python
150 lines
3.5 KiB
Python
from __future__ import print_function
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from pylab import *
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from pprint import pprint
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import scipy.linalg
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# test cases, derived from doc/nasa_rotation_def.pdf
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#pylint: disable=all
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def euler_to_quat(phi, theta, psi):
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"Quaternion from (body 3(psi)-2(theta)-1(phi) euler angles"
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s1 = sin(psi/2)
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c1 = cos(psi/2)
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s2 = sin(theta/2)
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c2 = cos(theta/2)
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s3 = sin(phi/2)
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c3 = cos(phi/2)
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return array([
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s1*s2*s3 + c1*c2*c3,
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-s1*s2*c3 + s3*c1*c2,
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s1*s3*c2 + s2*c1*c3,
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s1*c2*c3 - s2*s3*c1
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])
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def euler_to_dcm(phi, theta, psi):
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s1 = sin(psi)
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c1 = cos(psi)
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s2 = sin(theta)
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c2 = cos(theta)
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s3 = sin(phi)
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c3 = cos(phi)
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return array([
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[c1*c2, c1*s2*s3 - s1*c3, c1*s2*c3 + s1*s3],
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[s1*c2, s1*s2*s3 + c1*c3, s1*s2*c3 - c1*s3],
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[-s2, c2*s3, c2*c3],
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])
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def quat_prod(q, r):
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"Quaternion product"
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return array([
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r[0]*q[0] - r[1]*q[1] - r[2]*q[2] - r[3]*q[3],
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r[0]*q[1] + r[1]*q[0] - r[2]*q[3] + r[3]*q[2],
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r[0]*q[2] + r[1]*q[3] + r[2]*q[0] - r[3]*q[1],
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r[0]*q[3] - r[1]*q[2] + r[2]*q[1] + r[3]*q[0]
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])
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def dcm_to_euler(dcm):
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return array([
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arctan(dcm[2,1]/ dcm[2,2]),
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arctan(-dcm[2,0]/ sqrt(1 - dcm[2,0]**2)),
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arctan(dcm[1,0]/ dcm[0,0]),
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])
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def dcm_from_quat(q):
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q1 = q[0]
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q2 = q[1]
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q3 = q[2]
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q4 = q[3]
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return array([
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[q1*q1 + q2*q2 - q3*q3 - q4*q4, 2*(q2*q3 - q1*q4), 2*(q2*q4 + q1*q3)],
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[2*(q2*q3 + q1*q4), q1*q1 - q2*q2 + q3*q3 - q4*q4, 2*(q3*q4 - q1*q2)],
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[2*(q2*q4 - q1*q3), 2*(q3*q4 + q1*q2), q1*q1 - q2*q2 - q3*q3 + q4*q4]
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])
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def quat_to_euler(q):
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"Quaternion to (body 3(psi)-2(theta)-1(phi) euler angles"
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return dcm_to_euler(dcm_from_quat(q))
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def quat_to_dcm(q):
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return euler_to_dcm(quat_to_euler(q))
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phi = 0.1
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theta = 0.2
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psi = 0.3
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print('euler', phi, theta, psi)
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q = euler_to_quat(phi, theta, psi)
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assert(abs(norm(q) - 1) < FLT_EPSILON)
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assert(abs(norm(q) - 1) < FLT_EPSILON)
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assert(norm(array(quat_to_euler(q)) - array([phi, theta, psi])) < FLT_EPSILON)
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print('\nq:')
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pprint(q)
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dcm = euler_to_dcm(phi, theta, psi)
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assert(norm(dcm[:,0]) == 1)
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assert(norm(dcm[:,1]) == 1)
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assert(norm(dcm[:,2]) == 1)
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assert(abs(dcm[:,0].dot(dcm[:,1])) < FLT_EPSILON)
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assert(abs(dcm[:,0].dot(dcm[:,2])) < FLT_EPSILON)
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print('\ndcm:')
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pprint(dcm)
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print('\nq*q', quat_prod(q, q))
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q2 = quat_prod(q, q)
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pprint(q2)
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print(norm(q2))
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print('\nq3:')
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q3 = array([1,2,3,4])
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pprint(q3)
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print('\nq3_norm:')
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q3_norm =q3 / norm(q3)
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pprint(q3_norm)
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print('\ninverse')
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A = array([[0,2,3], [4,5,6], [7,8,10]])
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pprint(A)
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pprint(inv(A))
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print('\nmatrix exponential')
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A = 0.01*array([[1.0,2.0,3.0], [4.0,5.0,6.0], [7.0,8.0,10.0]])
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eA_check = scipy.linalg.expm(A)
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pprint(eA_check)
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eA_approx = eye(3)
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k = 1.0
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A_pow = A
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for i in range(1,3):
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k *= i
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# print(i, k, '\n', A_pow/k, '\n')
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eA_approx += A_pow/k
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A_pow = A_pow.dot(A)
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print(eA_approx)
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print('\nqr decomposition 4x4')
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A = array([[20.0, -10.0, -13.0, 21.0], [ 17.0, 16.0, -18.0, -14], [0.7, -0.8, 0.9, -0.5], [-1.0, -1.1, -1.2, -1.3]])
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b = array([[2.], [3.], [4.], [5.]])
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x = scipy.linalg.lstsq(A,b)[0]
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print('A:')
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pprint(A)
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print('b:')
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pprint(b)
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print('x:')
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pprint(scipy.linalg.lstsq(A,b)[0])
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print('\nqr decomposition 4x3')
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A = array([[20.0, -10.0, -13.0], [ 17.0, 16.0, -18.0], [0.7, -0.8, 0.9], [-1.0, -1.1, -1.2]])
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b = array([[2.], [3.], [4.], [5.]])
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x = scipy.linalg.lstsq(A,b)[0]
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print('A:')
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pprint(A)
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print('b:')
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pprint(b)
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print('x:')
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pprint(x)
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# vim: set et ft=python fenc=utf-8 ff=unix sts=4 sw=4 ts=8 :
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