function

Tests.RuleChecks.fdSo3InverseJacobian

Central difference of SO(3) inverse, right-trivialized on both sides

Public declarations

Explicit source declarations; dimensions, modifications and defaults are shown as written, without evaluation.

Role	Name	Type	Dimensions / attributes / default	Description
input	`q`	`Real`	`[4]`	Unit quaternion
input	`step`	`Real`		Central-difference step
output	`J`	`Real`	`[3, 3]`

Modelica declarations and implementation

Show parameters, interfaces and source

Parameters, inputs, outputs, defaults and equations from the source file.

function fdSo3InverseJacobian
  "Central difference of SO(3) inverse, right-trivialized on both sides"
  input Real q[4] "Unit quaternion";
  input Real step "Central-difference step";
  output Real J[3, 3];
protected
  Real basis[3, 3];
  Real forward[3];
  Real backward[3];
algorithm
  basis := identity(3);
  for j in 1:3 loop
    forward := LieGroups.SO3.Quat.log_map(LieGroups.SO3.Quat.product(
      q, LieGroups.SO3.Quat.inverse(LieGroups.SO3.Quat.product(
        q, LieGroups.SO3.Quat.exp_map(step * basis[:, j])))));
    backward := LieGroups.SO3.Quat.log_map(LieGroups.SO3.Quat.product(
      q, LieGroups.SO3.Quat.inverse(LieGroups.SO3.Quat.product(
        q, LieGroups.SO3.Quat.exp_map(-step * basis[:, j])))));
    J[:, j] := (forward - backward) / (2.0 * step);
  end for;
end fdSo3InverseJacobian;