# -----------------------------------------------------------------------------
# This file was autogenerated by symforce from template:
# ops/CLASS/group_ops.py.jinja
# Do NOT modify by hand.
# -----------------------------------------------------------------------------
import math
import typing as T
import numpy
import sym # pylint: disable=useless-suppression,unused-import
[docs]class GroupOps(object):
"""
Python GroupOps implementation for :py:class:`symforce.geo.unit3.Unit3`.
"""
[docs] @staticmethod
def identity():
# type: () -> sym.Unit3
# Total ops: 0
# Input arrays
# Intermediate terms (0)
# Output terms
_res = [0.0] * 4
_res[0] = 0
_res[1] = 0
_res[2] = 0
_res[3] = 1
return sym.Unit3.from_storage(_res)
[docs] @staticmethod
def inverse(a):
# type: (sym.Unit3) -> sym.Unit3
# Total ops: 3
# Input arrays
_a = a.data
# Intermediate terms (0)
# Output terms
_res = [0.0] * 4
_res[0] = -_a[0]
_res[1] = -_a[1]
_res[2] = -_a[2]
_res[3] = _a[3]
return sym.Unit3.from_storage(_res)
[docs] @staticmethod
def compose(a, b):
# type: (sym.Unit3, sym.Unit3) -> sym.Unit3
# Total ops: 28
# Input arrays
_a = a.data
_b = b.data
# Intermediate terms (0)
# Output terms
_res = [0.0] * 4
_res[0] = _a[0] * _b[3] + _a[1] * _b[2] - _a[2] * _b[1] + _a[3] * _b[0]
_res[1] = -_a[0] * _b[2] + _a[1] * _b[3] + _a[2] * _b[0] + _a[3] * _b[1]
_res[2] = _a[0] * _b[1] - _a[1] * _b[0] + _a[2] * _b[3] + _a[3] * _b[2]
_res[3] = -_a[0] * _b[0] - _a[1] * _b[1] - _a[2] * _b[2] + _a[3] * _b[3]
return sym.Unit3.from_storage(_res)
[docs] @staticmethod
def between(a, b):
# type: (sym.Unit3, sym.Unit3) -> sym.Unit3
# Total ops: 28
# Input arrays
_a = a.data
_b = b.data
# Intermediate terms (0)
# Output terms
_res = [0.0] * 4
_res[0] = -_a[0] * _b[3] - _a[1] * _b[2] + _a[2] * _b[1] + _a[3] * _b[0]
_res[1] = _a[0] * _b[2] - _a[1] * _b[3] - _a[2] * _b[0] + _a[3] * _b[1]
_res[2] = -_a[0] * _b[1] + _a[1] * _b[0] - _a[2] * _b[3] + _a[3] * _b[2]
_res[3] = _a[0] * _b[0] + _a[1] * _b[1] + _a[2] * _b[2] + _a[3] * _b[3]
return sym.Unit3.from_storage(_res)
[docs] @staticmethod
def inverse_with_jacobian(a):
# type: (sym.Unit3) -> T.Tuple[sym.Unit3, numpy.ndarray]
# Total ops: 18
# Input arrays
_a = a.data
# Intermediate terms (5)
_tmp0 = _a[0] ** 2
_tmp1 = _a[1] ** 2
_tmp2 = _a[2] ** 2 - _a[3] ** 2
_tmp3 = 2 * _a[2] * _a[3]
_tmp4 = 2 * _a[0] * _a[1]
# Output terms
_res = [0.0] * 4
_res[0] = -_a[0]
_res[1] = -_a[1]
_res[2] = -_a[2]
_res[3] = _a[3]
_res_D_a = numpy.zeros((2, 2))
_res_D_a[0, 0] = _tmp0 - _tmp1 + _tmp2
_res_D_a[1, 0] = -_tmp3 + _tmp4
_res_D_a[0, 1] = _tmp3 + _tmp4
_res_D_a[1, 1] = -_tmp0 + _tmp1 + _tmp2
return sym.Unit3.from_storage(_res), _res_D_a
[docs] @staticmethod
def compose_with_jacobians(a, b):
# type: (sym.Unit3, sym.Unit3) -> T.Tuple[sym.Unit3, numpy.ndarray, numpy.ndarray]
# Total ops: 146
# Input arrays
_a = a.data
_b = b.data
# Intermediate terms (70)
_tmp0 = _a[3] * _b[0]
_tmp1 = _a[2] * _b[1]
_tmp2 = _a[0] * _b[3]
_tmp3 = _a[1] * _b[2]
_tmp4 = _tmp0 - _tmp1 + _tmp2 + _tmp3
_tmp5 = _a[3] * _b[1]
_tmp6 = _a[2] * _b[0]
_tmp7 = _a[0] * _b[2]
_tmp8 = _a[1] * _b[3]
_tmp9 = _tmp5 + _tmp6 - _tmp7 + _tmp8
_tmp10 = _a[3] * _b[2]
_tmp11 = _a[2] * _b[3]
_tmp12 = _a[0] * _b[1]
_tmp13 = _a[1] * _b[0]
_tmp14 = _tmp10 + _tmp11 + _tmp12 - _tmp13
_tmp15 = _a[3] * _b[3]
_tmp16 = _a[2] * _b[2]
_tmp17 = _a[0] * _b[0]
_tmp18 = _a[1] * _b[1]
_tmp19 = _tmp15 - _tmp16 - _tmp17 - _tmp18
_tmp20 = (1.0 / 2.0) * _tmp10
_tmp21 = -1.0 / 2.0 * _tmp11
_tmp22 = (1.0 / 2.0) * _tmp12
_tmp23 = -_tmp22
_tmp24 = (1.0 / 2.0) * _tmp13
_tmp25 = _tmp20 + _tmp21 + _tmp23 - _tmp24
_tmp26 = 2 * _tmp14
_tmp27 = (1.0 / 2.0) * _tmp0
_tmp28 = (1.0 / 2.0) * _tmp1
_tmp29 = -_tmp28
_tmp30 = (1.0 / 2.0) * _tmp2
_tmp31 = (1.0 / 2.0) * _tmp3
_tmp32 = -_tmp31
_tmp33 = -_tmp27 + _tmp29 + _tmp30 + _tmp32
_tmp34 = 2 * _tmp4
_tmp35 = (1.0 / 2.0) * _tmp6
_tmp36 = (1.0 / 2.0) * _tmp7
_tmp37 = _tmp35 - _tmp36
_tmp38 = (1.0 / 2.0) * _tmp5
_tmp39 = -_tmp38
_tmp40 = (1.0 / 2.0) * _tmp8
_tmp41 = _tmp39 - _tmp40
_tmp42 = _tmp37 + _tmp41
_tmp43 = 2 * _tmp9
_tmp44 = (1.0 / 2.0) * _tmp16
_tmp45 = (1.0 / 2.0) * _tmp17
_tmp46 = _tmp44 + _tmp45
_tmp47 = (1.0 / 2.0) * _tmp15
_tmp48 = (1.0 / 2.0) * _tmp18
_tmp49 = -_tmp48
_tmp50 = _tmp47 + _tmp49
_tmp51 = _tmp46 + _tmp50
_tmp52 = 2 * _tmp19
_tmp53 = -_tmp47
_tmp54 = -_tmp44
_tmp55 = _tmp45 + _tmp49 + _tmp53 + _tmp54
_tmp56 = _tmp35 + _tmp36 + _tmp39 + _tmp40
_tmp57 = _tmp27 + _tmp30
_tmp58 = _tmp28 + _tmp32 + _tmp57
_tmp59 = _tmp21 + _tmp24
_tmp60 = _tmp20 + _tmp22 + _tmp59
_tmp61 = -_tmp35 + _tmp36 + _tmp41
_tmp62 = -_tmp45 + _tmp50 + _tmp54
_tmp63 = -_tmp20 + _tmp23 + _tmp59
_tmp64 = _tmp29 + _tmp31 + _tmp57
_tmp65 = -_tmp26 * _tmp63 + _tmp34 * _tmp64
_tmp66 = _tmp43 * _tmp64
_tmp67 = _tmp52 * _tmp63
_tmp68 = 2 * _tmp46 + 2 * _tmp48 + 2 * _tmp53
_tmp69 = _tmp37 + _tmp38 + _tmp40
# Output terms
_res = [0.0] * 4
_res[0] = _tmp4
_res[1] = _tmp9
_res[2] = _tmp14
_res[3] = _tmp19
_res_D_a = numpy.zeros((2, 2))
_res_D_a[0, 0] = -_tmp25 * _tmp26 + _tmp33 * _tmp34 - _tmp42 * _tmp43 + _tmp51 * _tmp52
_res_D_a[1, 0] = -_tmp25 * _tmp52 - _tmp26 * _tmp51 + _tmp33 * _tmp43 + _tmp34 * _tmp42
_res_D_a[0, 1] = -_tmp26 * _tmp55 + _tmp34 * _tmp56 - _tmp43 * _tmp58 + _tmp52 * _tmp60
_res_D_a[1, 1] = -_tmp26 * _tmp60 + _tmp34 * _tmp58 + _tmp43 * _tmp56 - _tmp52 * _tmp55
_res_D_b = numpy.zeros((2, 2))
_res_D_b[0, 0] = -_tmp43 * _tmp61 + _tmp52 * _tmp62 + _tmp65
_res_D_b[1, 0] = -_tmp26 * _tmp62 + _tmp34 * _tmp61 + _tmp66 - _tmp67
_res_D_b[0, 1] = -_tmp14 * _tmp68 + _tmp34 * _tmp69 - _tmp66 + _tmp67
_res_D_b[1, 1] = -_tmp19 * _tmp68 + _tmp43 * _tmp69 + _tmp65
return sym.Unit3.from_storage(_res), _res_D_a, _res_D_b
[docs] @staticmethod
def between_with_jacobians(a, b):
# type: (sym.Unit3, sym.Unit3) -> T.Tuple[sym.Unit3, numpy.ndarray, numpy.ndarray]
# Total ops: 107
# Input arrays
_a = a.data
_b = b.data
# Intermediate terms (55)
_tmp0 = _a[3] * _b[0]
_tmp1 = _a[2] * _b[1]
_tmp2 = _a[0] * _b[3]
_tmp3 = _a[1] * _b[2]
_tmp4 = _tmp0 + _tmp1 - _tmp2 - _tmp3
_tmp5 = _a[3] * _b[1]
_tmp6 = _a[2] * _b[0]
_tmp7 = _a[0] * _b[2]
_tmp8 = _a[1] * _b[3]
_tmp9 = _tmp5 - _tmp6 + _tmp7 - _tmp8
_tmp10 = _a[3] * _b[2]
_tmp11 = _a[2] * _b[3]
_tmp12 = _a[0] * _b[1]
_tmp13 = _a[1] * _b[0]
_tmp14 = _tmp10 - _tmp11 - _tmp12 + _tmp13
_tmp15 = _a[3] * _b[3]
_tmp16 = _a[2] * _b[2]
_tmp17 = _a[0] * _b[0]
_tmp18 = _a[1] * _b[1]
_tmp19 = _tmp15 + _tmp16 + _tmp17 + _tmp18
_tmp20 = (1.0 / 2.0) * _tmp5
_tmp21 = (1.0 / 2.0) * _tmp6
_tmp22 = (1.0 / 2.0) * _tmp7
_tmp23 = (1.0 / 2.0) * _tmp8
_tmp24 = _tmp20 - _tmp21 + _tmp22 - _tmp23
_tmp25 = 2 * _tmp9
_tmp26 = _tmp24 * _tmp25
_tmp27 = (1.0 / 2.0) * _tmp15
_tmp28 = (1.0 / 2.0) * _tmp16
_tmp29 = (1.0 / 2.0) * _tmp17
_tmp30 = (1.0 / 2.0) * _tmp18
_tmp31 = -_tmp27 - _tmp28 - _tmp29 - _tmp30
_tmp32 = 2 * _tmp19
_tmp33 = _tmp31 * _tmp32
_tmp34 = (
-1.0 / 2.0 * _tmp10 + (1.0 / 2.0) * _tmp11 + (1.0 / 2.0) * _tmp12 - 1.0 / 2.0 * _tmp13
)
_tmp35 = 2 * _tmp14
_tmp36 = -_tmp34 * _tmp35
_tmp37 = (1.0 / 2.0) * _tmp0
_tmp38 = (1.0 / 2.0) * _tmp1
_tmp39 = (1.0 / 2.0) * _tmp2
_tmp40 = (1.0 / 2.0) * _tmp3
_tmp41 = _tmp37 + _tmp38 - _tmp39 - _tmp40
_tmp42 = 2 * _tmp4
_tmp43 = _tmp36 + _tmp41 * _tmp42
_tmp44 = _tmp24 * _tmp42
_tmp45 = -_tmp31 * _tmp35
_tmp46 = _tmp25 * _tmp41
_tmp47 = _tmp32 * _tmp34
_tmp48 = _tmp46 - _tmp47
_tmp49 = _tmp27 + _tmp28 + _tmp29 + _tmp30
_tmp50 = -_tmp35 * _tmp49
_tmp51 = -_tmp37 - _tmp38 + _tmp39 + _tmp40
_tmp52 = _tmp44 + _tmp47
_tmp53 = _tmp32 * _tmp49
_tmp54 = -_tmp20 + _tmp21 - _tmp22 + _tmp23
# Output terms
_res = [0.0] * 4
_res[0] = _tmp4
_res[1] = _tmp9
_res[2] = _tmp14
_res[3] = _tmp19
_res_D_a = numpy.zeros((2, 2))
_res_D_a[0, 0] = -_tmp26 + _tmp33 + _tmp43
_res_D_a[1, 0] = _tmp44 + _tmp45 + _tmp48
_res_D_a[0, 1] = -_tmp25 * _tmp51 + _tmp50 + _tmp52
_res_D_a[1, 1] = _tmp26 + _tmp36 + _tmp42 * _tmp51 - _tmp53
_res_D_b = numpy.zeros((2, 2))
_res_D_b[0, 0] = -_tmp25 * _tmp54 + _tmp43 + _tmp53
_res_D_b[1, 0] = _tmp42 * _tmp54 + _tmp48 + _tmp50
_res_D_b[0, 1] = _tmp45 - _tmp46 + _tmp52
_res_D_b[1, 1] = _tmp26 - _tmp33 + _tmp43
return sym.Unit3.from_storage(_res), _res_D_a, _res_D_b