def test():
# Two random vectors
vec_a = matrix.col((uniform(-20,20), uniform(-20,20), uniform(-20,20)))
vec_b = matrix.col((uniform(-20,20), uniform(-20,20), uniform(-20,20)))
# The test may fail if the angle between the vectors is small or close to pi
# (see gradient of acos(x) for x close to 1 or -1) but we are not interested
# in such cases anyway. Skip test if the acute angle is less than 1 degree
if vec_a.accute_angle(vec_b, deg=True) < 1: return False
a = vec_a.length()
b = vec_b.length()
a_dot_b = vec_a.dot(vec_b)
gamma = acos(a_dot_b / (a*b))
# Analytical
dg = AngleDerivativeWrtVectorElts(vec_a, vec_b)
# FD
dgFD = FDAngleDerivativeWrtVectorElts(vec_a, vec_b)
assert approx_equal(dg.dtheta_du_1(), dgFD.dtheta_du_1())
assert approx_equal(dg.dtheta_du_2(), dgFD.dtheta_du_2())
assert approx_equal(dg.dtheta_du_3(), dgFD.dtheta_du_3())
assert approx_equal(dg.dtheta_dv_1(), dgFD.dtheta_dv_1())
assert approx_equal(dg.dtheta_dv_2(), dgFD.dtheta_dv_2())
assert approx_equal(dg.dtheta_dv_3(), dgFD.dtheta_dv_3())
# Test vector version
assert approx_equal(dg.derivative_wrt_u(), matrix.col(
(dg.dtheta_du_1(), dg.dtheta_du_2(), dg.dtheta_du_3())))
assert approx_equal(dg.derivative_wrt_v(), matrix.col(
(dg.dtheta_dv_1(), dg.dtheta_dv_2(), dg.dtheta_dv_3())))
return True
print "d[a]/dp{2} analytical: {0:.5f} FD: {1:.5f}".format(da_dp, fd_grad[i]['da_dp'], i)
db_dp = 1./b * bvec.dot(dbv_dp)
print "d[b]/dp{2} analytical: {0:.5f} FD: {1:.5f}".format(db_dp, fd_grad[i]['db_dp'], i)
dc_dp = 1./c * cvec.dot(dcv_dp)
print "d[c]/dp{2} analytical: {0:.5f} FD: {1:.5f}".format(dc_dp, fd_grad[i]['dc_dp'], i)
print
print "CELL ANGLES"
# Here we know the derivatives of the angle alpha with respect to elements
# of the vectors a and b. Similarly for beta and gamma. We know these
# expressions are correct because they are tested in
# tst_angle_derivatives_wrt_vector_elts.py
dalpha_db = dalpha.derivative_wrt_u()
dalpha_dc = dalpha.derivative_wrt_v()
dbeta_da = dbeta.derivative_wrt_u()
dbeta_dc = dbeta.derivative_wrt_v()
dgamma_da = dgamma.derivative_wrt_u()
dgamma_db = dgamma.derivative_wrt_v()
#
daa_dp = RAD2DEG * (dbv_dp.dot(dalpha_db) + dcv_dp.dot(dalpha_dc))
dbb_dp = RAD2DEG * (dav_dp.dot(dbeta_da) + dcv_dp.dot(dbeta_dc))
dcc_dp = RAD2DEG * (dav_dp.dot(dgamma_da) + dbv_dp.dot(dgamma_db))
print "d[alpha]/dp{2} analytical: {0:.5f} FD: {1:.5f}".format(daa_dp, fd_grad[i]['daa_dp'], i)
print "d[beta]/dp{2} analytical: {0:.5f} FD: {1:.5f}".format(dbb_dp, fd_grad[i]['dbb_dp'], i)
print "d[gamma]/dp{2} analytical: {0:.5f} FD: {1:.5f}".format(dcc_dp, fd_grad[i]['dcc_dp'], i)
