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#!/usr/bin/env python3
import sys
import numpy as np
import numpysane as nps
import os
testdir = os.path.dirname(os.path.realpath(__file__))
# I import the LOCAL mrcal since that's what I'm testing
sys.path[:0] = f"{testdir}/..",
import mrcal
from testutils import *
from test_calibration_helpers import grad,grad__r_from_R
from test_poseutils_helpers import \
R_from_r, \
r_from_R, \
compose_r
def wrap_r_unconditional(r, dr_dX = None):
'''Unwrap a Rodrigues vector r
returns r' if dr_dX is None
returns dr'_dX if dr_dX is not None
I define rotations with a Rodrigues vector r = th v. Where v is the unit
vector representing the rotation axis; and th is a scalar representing the
magnitude or this rotation, in radians. Thus rotations th v and (th + 2pi*n)
v are identical for all integer n. Furthermore the rotation (pi+th) v is
equivalent to a rotation (pi-th) (-v). So usually we have th = mag(r) in
[0,pi].
For various analyses I want to convert a rotation r to its equivalent
rotation 2*pi rad away:
r' = v (th - 2pi)
= r/magr (magr - 2pi)
= r - r/magr 2pi
= r (1 - 2pi/magr)
Let
k = 1 - 2pi/magr
So
r' = r k
As noted above, usually magr <= pi, so k < 0. Thus
magr' = -magr k
Let's apply this wrapping a second time:
r'' = r' (1 - 2pi/magr')
= r k (1 + 2pi/magr/k)
= r k (1 + (1-k) /k)
= r (k + 1 - k)
= r
So this wrapping operation switches back/forth between two modes
'''
if dr_dX is None:
if nps.mag(r) == 0:
return r
return r - r/nps.mag(r) * 2.*np.pi
if nps.mag(r) == 0:
return dr_dX
# drw_dX = d( r - r/nps.mag(r) * 2.*np.pi )/dX
# = dr_dX - 2pi (dr_dX/nps.mag(r) + r d/dx (1/magr))
# = dr_dX - 2pi (dr_dX/nps.mag(r) - r /magr^2 /2magr 2rt dr_dX )
# = dr_dX - 2pi (dr_dX - r rt /norm2(r) dr_dX ) /nps.mag(r)
# = dr_dX + 2pi /nps.mag(r) (r rt /norm2(r) - I) dr_dX
# dr_dX has shape (3,...) so r rt dr_dX also has shape (3,...) I clump
# the trailing shapes so that dr_dX.shape is (3,N), and then reshape it
# at the end
s = dr_dX.shape[1:]
# shape (3,N)
dr_dX = nps.clump(dr_dX, n = -(dr_dX.ndim-1))
drw_dX = \
dr_dX + \
2.*np.pi / nps.mag(r) * nps.matmult(nps.outer(r,r)/nps.norm2(r) - np.eye(r.size),
dr_dX)
return drw_dX.reshape((3,) + s)
def wrap_r(r,
*,
r_match_direction = None,
dr_dX = None):
'''Unwrap a Rodrigues vector r
returns r' if dr_dX is None
returns dr'_dX if dr_dX is not None
This function only wraps the argument if it needs to: if mag(r) > np.pi or
if we're pointing opposite r_match_direction
'''
if r_match_direction is not None:
if nps.inner(r, r_match_direction) > 0:
return r if dr_dX is None else dr_dX
return wrap_r_unconditional(r, dr_dX = dr_dX)
if nps.mag(r) <= np.pi:
return r if dr_dX is None else dr_dX
return wrap_r_unconditional(r, dr_dX = dr_dX)
################### Check the behavior around the th=0, th=180, th=360
################### singularities. Gradients and values should be correct
axes = \
np.array(((1., 2., 0.1),
(1., 0, 0),
(0, 0, -1.),))
axes /= nps.dummy(nps.mag(axes), -1) # normalize
for iaxis,axis in enumerate(axes):
for th0 in (-np.pi, 0, np.pi):
for dth in (-1e-4, -1e-10, 0, 1e-10, 1e-4):
r = (th0 + dth) * axis
######### R_from_r, r_from_R
if True:
R,dR_dr = mrcal.R_from_r(r, get_gradients=True)
R_ref = R_from_r(r)
dR_dr__ref = grad(R_from_r,r)
confirm_equal( R,
R_ref,
msg=f'R_from_r result near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
confirm_equal( dR_dr,
dR_dr__ref,
msg=f'R_from_r J near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
# I check R_roundtrip. The dr/dR computation assumes this
r_roundtrip,dr_dR = mrcal.r_from_R(R, get_gradients=True)
R_roundtrip,dR_dr = mrcal.R_from_r(r_roundtrip, get_gradients=True)
confirm_equal( mrcal.compose_r(r_roundtrip, -r),
0,
eps = 1e-8,
msg=f'roundtrip r result near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
confirm_equal( nps.matmult(R_roundtrip, mrcal.invert_R(R)) - np.eye(3),
0,
eps = 1e-8,
msg=f'roundtrip R result near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
dr_dR__ref = grad__r_from_R(R_ref)
confirm_equal( dr_dR,
dr_dR__ref,
relative = True,
worstcase = True,
eps = 1e-3,
reldiff_eps = 1e-5,
msg = f'r_from_R J near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
######### compose_r
if True:
r1_simple = np.array((-0.02, -1.2, 0.4),)
inv_r1_simple_r = mrcal.compose_r(-r1_simple,r)
# it isn't possible to correctly decide if we should or should
# not wrap the result for ALL cases (some cases have mag(r)=pi
# exactly, up to machine precision). So I try both, and pick the
# closer one
r_roundtrip = mrcal.compose_r( r1_simple, inv_r1_simple_r )
r_wrapped = wrap_r_unconditional(r)
confirm_equal( r_roundtrip,
r if nps.norm2(r_roundtrip-r) < nps.norm2(r_roundtrip-r_wrapped) \
else r_wrapped,
worstcase = True,
eps = 1e-6,
msg='compose()')
for (r0,r1) in ((r, r1_simple),
(r,-r),
(r, r),
(r1_simple, inv_r1_simple_r)):
###### r01
r01, dr01_dr0, dr01_dr1 = mrcal.compose_r(r0,r1, get_gradients = True)
r01_ref = compose_r(r0,r1)
confirm_equal( r01,
r01_ref,
worstcase = True,
relative = True,
eps = 1e-3,
msg=f'compose_r(r0,r1) near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
dr01_dr0__ref = grad(lambda r0: compose_r(r0,r1),
r0,
forward_differences = True,
switch = wrap_r_unconditional,
step = 1e-7)
dr01_dr1__ref = grad(lambda r1: compose_r(r0,r1),
r1,
forward_differences = True,
switch = wrap_r_unconditional,
step = 1e-7)
confirm_equal( dr01_dr0,
dr01_dr0__ref,
worstcase = True,
relative = True,
eps = 1e-2,
reldiff_eps=1e-3,
msg=f'compose_r(r0,r1) dr01_dr0 near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
confirm_equal( dr01_dr1,
dr01_dr1__ref,
worstcase = True,
relative = True,
eps = 1e-2,
reldiff_eps=1e-3,
msg=f'compose_r(r0,r1) dr01_dr1 near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
if r0 is r1: continue
###### r10
r10, dr10_dr1, dr10_dr0 = mrcal.compose_r(r1,r0, get_gradients = True)
r10_ref = compose_r(r1,r0)
if th0 == np.pi and dth == 0. and r0 is r1_simple and r1 is inv_r1_simple_r and iaxis==0:
if nps.inner(r10_ref, r10) < 0:
# This is about to fail. I'm skipping this test.
# It's the only case that fails. And it fails ONLY
# on my workstation (recent Debian/sid, Intel(R)
# Xeon(R) CPU E5-2687W). It passes on my laptops
# (same recent Debian/sid with I think identical
# packages, but older CPU: Intel(R) Core(TM)
# i7-3520M)
print("SKIPPING test case that fails on only some hardware. Everything else passes, so this is likely a subtle roundoff issue")
continue
confirm_equal( r10,
r10_ref,
worstcase = True,
relative = True,
eps = 1e-3,
msg=f'compose_r(r1,r0) near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
dr10_dr0__ref = grad(lambda r0: compose_r(r1,r0),
r0,
forward_differences = True,
switch = wrap_r_unconditional,
step = 1e-7)
dr10_dr1__ref = grad(lambda r1: compose_r(r1,r0),
r1,
forward_differences = True,
switch = wrap_r_unconditional,
step = 1e-7)
confirm_equal( dr10_dr0,
dr10_dr0__ref,
worstcase = True,
relative = True,
eps = 1e-2,
reldiff_eps=1e-3,
msg=f'compose_r(r1,r0 dr10_dr0 near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
confirm_equal( dr10_dr1,
dr10_dr1__ref,
worstcase = True,
relative = True,
eps = 1e-2,
reldiff_eps=1e-3,
msg=f'compose_r(r1,r0 dr10_dr1 near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
######### rotate_point_r
if True:
# Simple reference implementation. Should move this to
# test_poseutils_helpers.py. And test_poseutils_lib.py should
# use it
def rotate_point_r(r,p):
return nps.inner(p, R_from_r(r))
p = np.array((3., -0.2, -0.9),)
pt, dpt_dr, dpt_dp = mrcal.rotate_point_r(r,p, get_gradients = True)
pt_ref = rotate_point_r(r,p)
dpt_dr__ref = grad(lambda r: rotate_point_r(r,p),
r)
dpt_dp__ref = grad(lambda p: rotate_point_r(r,p),
p)
confirm_equal( pt,
pt_ref,
msg=f'rotate_point_r(r,p) r near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
confirm_equal(dpt_dr,
dpt_dr__ref,
msg=f'rotate_point_r(r,p) dpt_dr near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
confirm_equal(dpt_dp,
dpt_dp__ref,
msg=f'rotate_point_r(r,p) dpt_dp near a singularity. axis={axis}, th0={th0:.2f}, dth={dth}')
finish()
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