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<li class="toctree-l1"><a class="reference internal" href="tutorials/epsilon_tutorial.html">Epsilon Tutorial</a></li>
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<p class="caption" role="heading"><span class="caption-text">Examples</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="examples/bundle_adjustment/README.html">Bundle Adjustment</a></li>
<li class="toctree-l1"><a class="reference internal" href="examples/bundle_adjustment_fixed_size/README.html">Fixed Size Bundle Adjustment</a></li>
<li class="toctree-l1"><a class="reference internal" href="examples/bundle_adjustment_in_the_large/README.html">Bundle-Adjustment-in-the-Large</a></li>
<li class="toctree-l1"><a class="reference internal" href="examples/custom_factor_generation/README.html">Custom Factor Generation</a></li>
<li class="toctree-l1"><a class="reference internal" href="examples/robot_2d_localization/README.html">Robot 2D Localization</a></li>
<li class="toctree-l1"><a class="reference internal" href="examples/robot_3d_localization/README.html">Robot 3D Localization</a></li>
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<p class="caption" role="heading"><span class="caption-text">symforce Reference</span></p>
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<li class="toctree-l3"><a class="reference internal" href="api/symforce.codegen.geo_package_codegen.html">symforce.codegen.geo_package_codegen module</a></li>
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<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.array_lie_group_ops.html">symforce.ops.impl.array_lie_group_ops module</a></li>
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<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.class_lie_group_ops.html">symforce.ops.impl.class_lie_group_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.class_storage_ops.html">symforce.ops.impl.class_storage_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.databuffer_storage_ops.html">symforce.ops.impl.databuffer_storage_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.dataclass_group_ops.html">symforce.ops.impl.dataclass_group_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.dataclass_lie_group_ops.html">symforce.ops.impl.dataclass_lie_group_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.dataclass_storage_ops.html">symforce.ops.impl.dataclass_storage_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.nonetype_lie_group_ops.html">symforce.ops.impl.nonetype_lie_group_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.scalar_lie_group_ops.html">symforce.ops.impl.scalar_lie_group_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.sequence_group_ops.html">symforce.ops.impl.sequence_group_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.sequence_lie_group_ops.html">symforce.ops.impl.sequence_lie_group_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.sequence_storage_ops.html">symforce.ops.impl.sequence_storage_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.sym_class_lie_group_ops.html">symforce.ops.impl.sym_class_lie_group_ops module</a></li>
<li class="toctree-l4"><a class="reference internal" href="api/symforce.ops.impl.vector_class_lie_group_ops.html">symforce.ops.impl.vector_class_lie_group_ops module</a></li>
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<li class="toctree-l3"><a class="reference internal" href="api/symforce.ops.group_ops.html">symforce.ops.group_ops module</a></li>
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<li class="toctree-l3"><a class="reference internal" href="api/symforce.test_util.backend_coverage_expressions.html">symforce.test_util.backend_coverage_expressions module</a></li>
<li class="toctree-l3"><a class="reference internal" href="api/symforce.test_util.cam_cal_test_mixin.html">symforce.test_util.cam_cal_test_mixin module</a></li>
<li class="toctree-l3"><a class="reference internal" href="api/symforce.test_util.cam_test_mixin.html">symforce.test_util.cam_test_mixin module</a></li>
<li class="toctree-l3"><a class="reference internal" href="api/symforce.test_util.epsilon_handling.html">symforce.test_util.epsilon_handling module</a></li>
<li class="toctree-l3"><a class="reference internal" href="api/symforce.test_util.group_ops_test_mixin.html">symforce.test_util.group_ops_test_mixin module</a></li>
<li class="toctree-l3"><a class="reference internal" href="api/symforce.test_util.lie_group_ops_test_mixin.html">symforce.test_util.lie_group_ops_test_mixin module</a></li>
<li class="toctree-l3"><a class="reference internal" href="api/symforce.test_util.storage_ops_test_mixin.html">symforce.test_util.storage_ops_test_mixin module</a></li>
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<li class="toctree-l3"><a class="reference internal" href="api/symforce.values.values.html">symforce.values.values module</a></li>
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<li class="toctree-l2"><a class="reference internal" href="api/symforce.cc_sym.html">symforce.cc_sym module</a></li>
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<p class="caption" role="heading"><span class="caption-text">sym Python Reference</span></p>
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<li class="toctree-l1 has-children"><a class="reference internal" href="api-gen-py/sym.html">sym package</a><input class="toctree-checkbox" id="toctree-checkbox-32" name="toctree-checkbox-32" role="switch" type="checkbox"/><label for="toctree-checkbox-32"><div class="visually-hidden">Toggle navigation of sym package</div><i class="icon"><svg><use href="#svg-arrow-right"></use></svg></i></label><ul>
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<li class="toctree-l4"><a class="reference internal" href="api-gen-py/sym.ops.atan_camera_cal.lie_group_ops.html">sym.ops.atan_camera_cal.lie_group_ops module</a></li>
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<li class="toctree-l3 has-children"><a class="reference internal" href="api-gen-py/sym.ops.double_sphere_camera_cal.html">sym.ops.double_sphere_camera_cal package</a><input class="toctree-checkbox" id="toctree-checkbox-35" name="toctree-checkbox-35" role="switch" type="checkbox"/><label for="toctree-checkbox-35"><div class="visually-hidden">Toggle navigation of sym.ops.double_sphere_camera_cal package</div><i class="icon"><svg><use href="#svg-arrow-right"></use></svg></i></label><ul>
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<li class="toctree-l4"><a class="reference internal" href="api-gen-py/sym.ops.double_sphere_camera_cal.lie_group_ops.html">sym.ops.double_sphere_camera_cal.lie_group_ops module</a></li>
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<li class="toctree-l3 has-children"><a class="reference internal" href="api-gen-py/sym.ops.equirectangular_camera_cal.html">sym.ops.equirectangular_camera_cal package</a><input class="toctree-checkbox" id="toctree-checkbox-36" name="toctree-checkbox-36" role="switch" type="checkbox"/><label for="toctree-checkbox-36"><div class="visually-hidden">Toggle navigation of sym.ops.equirectangular_camera_cal package</div><i class="icon"><svg><use href="#svg-arrow-right"></use></svg></i></label><ul>
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<li class="toctree-l4"><a class="reference internal" href="api-gen-py/sym.ops.equirectangular_camera_cal.lie_group_ops.html">sym.ops.equirectangular_camera_cal.lie_group_ops module</a></li>
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<li class="toctree-l4"><a class="reference internal" href="api-gen-py/sym.ops.orthographic_camera_cal.lie_group_ops.html">sym.ops.orthographic_camera_cal.lie_group_ops module</a></li>
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<li class="toctree-l3 has-children"><a class="reference internal" href="api-gen-py/sym.ops.polynomial_camera_cal.html">sym.ops.polynomial_camera_cal package</a><input class="toctree-checkbox" id="toctree-checkbox-39" name="toctree-checkbox-39" role="switch" type="checkbox"/><label for="toctree-checkbox-39"><div class="visually-hidden">Toggle navigation of sym.ops.polynomial_camera_cal package</div><i class="icon"><svg><use href="#svg-arrow-right"></use></svg></i></label><ul>
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<p class="caption" role="heading"><span class="caption-text">sym C++ Reference</span></p>
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<li class="toctree-l1 has-children"><a class="reference internal" href="api-gen-cpp/classlist.html">Class list</a><input class="toctree-checkbox" id="toctree-checkbox-46" name="toctree-checkbox-46" role="switch" type="checkbox"/><label for="toctree-checkbox-46"><div class="visually-hidden">Toggle navigation of Class list</div><i class="icon"><svg><use href="#svg-arrow-right"></use></svg></i></label><ul>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/class/classsym_1_1ATANCameraCal.html">Class sym::ATANCameraCal</a></li>
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<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/class/classsym_1_1DoubleSphereCameraCal.html">Class sym::DoubleSphereCameraCal</a></li>
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<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/class/classsym_1_1Rot2.html">Class sym::Rot2</a></li>
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<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/class/classsym_1_1SphericalCameraCal.html">Class sym::SphericalCameraCal</a></li>
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<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/double__sphere__camera__cal_2lie__group__ops_8cc.html">File lie_group_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/double__sphere__camera__cal_2lie__group__ops_8h.html">File lie_group_ops.h</a></li>
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<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/double__sphere__reprojection__delta_8h.html">File double_sphere_reprojection_delta.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/epsilon_8cc.html">File epsilon.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/epsilon_8h.html">File epsilon.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/equirectangular__camera__cal_2group__ops_8cc.html">File group_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/equirectangular__camera__cal_2group__ops_8h.html">File group_ops.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/equirectangular__camera__cal_2lie__group__ops_8cc.html">File lie_group_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/equirectangular__camera__cal_2lie__group__ops_8h.html">File lie_group_ops.h</a></li>
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<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/equirectangular__camera__cal_8h.html">File equirectangular_camera_cal.h</a></li>
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<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/inverse__range__landmark__double__sphere__gnc__factor_8h.html">File inverse_range_landmark_double_sphere_gnc_factor.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/inverse__range__landmark__equirectangular__gnc__factor_8h.html">File inverse_range_landmark_equirectangular_gnc_factor.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/inverse__range__landmark__linear__gnc__factor_8h.html">File inverse_range_landmark_linear_gnc_factor.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/inverse__range__landmark__orthographic__gnc__factor_8h.html">File inverse_range_landmark_orthographic_gnc_factor.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/inverse__range__landmark__polynomial__gnc__factor_8h.html">File inverse_range_landmark_polynomial_gnc_factor.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/inverse__range__landmark__prior__factor_8h.html">File inverse_range_landmark_prior_factor.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/inverse__range__landmark__spherical__gnc__factor_8h.html">File inverse_range_landmark_spherical_gnc_factor.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/lie__group__ops_8h.html">File lie_group_ops.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/linear__camera__cal_2group__ops_8cc.html">File group_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/linear__camera__cal_2group__ops_8h.html">File group_ops.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/linear__camera__cal_2lie__group__ops_8cc.html">File lie_group_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/linear__camera__cal_2lie__group__ops_8h.html">File lie_group_ops.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/linear__camera__cal_2storage__ops_8cc.html">File storage_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/linear__camera__cal_2storage__ops_8h.html">File storage_ops.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/linear__camera__cal_8cc.html">File linear_camera_cal.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/linear__camera__cal_8h.html">File linear_camera_cal.h</a></li>
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<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/matrix_2group__ops_8cc.html">File group_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/matrix_2group__ops_8h.html">File group_ops.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/matrix_2lie__group__ops_8cc.html">File lie_group_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/matrix_2lie__group__ops_8h.html">File lie_group_ops.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/matrix_2storage__ops_8cc.html">File storage_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/matrix_2storage__ops_8h.html">File storage_ops.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/orthographic__camera__cal_2group__ops_8cc.html">File group_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/orthographic__camera__cal_2group__ops_8h.html">File group_ops.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/orthographic__camera__cal_2lie__group__ops_8cc.html">File lie_group_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/orthographic__camera__cal_2lie__group__ops_8h.html">File lie_group_ops.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/orthographic__camera__cal_2storage__ops_8cc.html">File storage_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/orthographic__camera__cal_2storage__ops_8h.html">File storage_ops.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/orthographic__camera__cal_8cc.html">File orthographic_camera_cal.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/orthographic__camera__cal_8h.html">File orthographic_camera_cal.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/orthographic__reprojection__delta_8h.html">File orthographic_reprojection_delta.h</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/polynomial__camera__cal_2group__ops_8cc.html">File group_ops.cc</a></li>
<li class="toctree-l2"><a class="reference internal" href="api-gen-cpp/file/polynomial__camera__cal_2group__ops_8h.html">File group_ops.h</a></li>
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<section id="symforce-cc-sym-module">
<h1>symforce.cc_sym module<a class="headerlink" href="#symforce-cc-sym-module" title="Permalink to this heading">¶</a></h1>
<span class="target" id="module-cc_sym"></span><p>This module wraps many of the C++ optimization classes.</p>
<dl class="py class">
<dt class="sig sig-object py" id="cc_sym.Factor">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Factor</span></span><a class="headerlink" href="#cc_sym.Factor" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">pybind11_object</span></code></p>
<p>A residual term for optimization.</p>
<p>Created from a function and a set of Keys that act as inputs. Given a Values as an evaluation
point, generates a linear approximation to the residual function.</p>
<dl class="py method">
<dt class="sig sig-object py" id="cc_sym.Factor.all_keys">
<span class="sig-name descname"><span class="pre">all_keys</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#cc_sym.Factor" title="cc_sym.Factor"><span class="pre">cc_sym.Factor</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="#cc_sym.Key" title="cc_sym.Key"><span class="pre">cc_sym.Key</span></a><span class="p"><span class="pre">]</span></span></span></span><a class="headerlink" href="#cc_sym.Factor.all_keys" title="Permalink to this definition">¶</a></dt>
<dd><p>Get all keys required to evaluate this factor.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="cc_sym.Factor.is_sparse">
<span class="sig-name descname"><span class="pre">is_sparse</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#cc_sym.Factor" title="cc_sym.Factor"><span class="pre">cc_sym.Factor</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.13)"><span class="pre">bool</span></a></span></span><a class="headerlink" href="#cc_sym.Factor.is_sparse" title="Permalink to this definition">¶</a></dt>
<dd><p>Does this factor use a sparse jacobian/hessian matrix?</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="cc_sym.Factor.jacobian">
<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">jacobian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#cc_sym.Factor.jacobian" title="Permalink to this definition">¶</a></dt>
<dd><p>Overloaded function.</p>
<ol class="arabic">
<li><p>jacobian(jacobian_func: Callable[[cc_sym.Values, List[lcmtypes.sym._index_entry_t.index_entry_t]], tuple], keys: List[cc_sym.Key], sparse: bool = False) -> cc_sym.Factor</p>
<blockquote>
<div><p>Create from a function that computes the jacobian. The hessian will be computed using the
Gauss Newton approximation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H</span> <span class="o">=</span> <span class="n">J</span><span class="o">.</span><span class="n">T</span> <span class="o">*</span> <span class="n">J</span>
<span class="n">rhs</span> <span class="o">=</span> <span class="n">J</span><span class="o">.</span><span class="n">T</span> <span class="o">*</span> <span class="n">b</span>
</pre></div>
</div>
<dl class="simple">
<dt>Args:</dt><dd><p>keys: The set of input arguments, in order, accepted by func.
sparse: Create a sparse factor if True, dense factor if false. Defaults to dense.</p>
</dd>
<dt>Precondition:</dt><dd><p>The jacobian returned by jacobian_func has type scipy.sparse.csc_matrix if and only if sparse = True.</p>
</dd>
</dl>
</div></blockquote>
</li>
<li><p>jacobian(jacobian_func: Callable[[cc_sym.Values, List[lcmtypes.sym._index_entry_t.index_entry_t]], tuple], keys_to_func: List[cc_sym.Key], keys_to_optimize: List[cc_sym.Key], sparse: bool = False) -> cc_sym.Factor</p>
<blockquote>
<div><p>Create from a function that computes the jacobian. The hessian will be computed using the
Gauss Newton approximation:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H</span> <span class="o">=</span> <span class="n">J</span><span class="o">.</span><span class="n">T</span> <span class="o">*</span> <span class="n">J</span>
<span class="n">rhs</span> <span class="o">=</span> <span class="n">J</span><span class="o">.</span><span class="n">T</span> <span class="o">*</span> <span class="n">b</span>
</pre></div>
</div>
<dl>
<dt>Args:</dt><dd><p>keys_to_func: The set of input arguments, in order, accepted by func.
keys_to_optimize: The set of input arguments that correspond to the derivative in func. Must be a subset of keys_to_func.
sparse: Create a sparse factor if True, dense factor if false. Defaults to dense.</p>
<dl class="simple">
<dt>Precondition:</dt><dd><p>The jacobian returned by jacobian_func has type scipy.sparse.csc_matrix if and only if sparse = True.</p>
</dd>
</dl>
</dd>
</dl>
</div></blockquote>
</li>
</ol>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="cc_sym.Factor.linearize">
<span class="sig-name descname"><span class="pre">linearize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#cc_sym.Factor" title="cc_sym.Factor"><span class="pre">cc_sym.Factor</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">arg0</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#cc_sym.Values" title="cc_sym.Values"><span class="pre">cc_sym.Values</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.13)"><span class="pre">tuple</span></a></span></span><a class="headerlink" href="#cc_sym.Factor.linearize" title="Permalink to this definition">¶</a></dt>
<dd><p>Evaluate the factor at the given linearization point and output just the numerical values of the residual and jacobian.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="cc_sym.Factor.linearized_factor">
<span class="sig-name descname"><span class="pre">linearized_factor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#cc_sym.Factor" title="cc_sym.Factor"><span class="pre">cc_sym.Factor</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">values</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#cc_sym.Values" title="cc_sym.Values"><span class="pre">cc_sym.Values</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">lcmtypes.sym._linearized_dense_factor_t.linearized_dense_factor_t</span></span></span><a class="headerlink" href="#cc_sym.Factor.linearized_factor" title="Permalink to this definition">¶</a></dt>
<dd><p>Evaluate the factor at the given linearization point and output a LinearizedDenseFactor that
contains the numerical values of the residual, jacobian, hessian, and right-hand-side.</p>
<p>This can only be called if is_sparse is false; otherwise, it will throw.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="cc_sym.Factor.optimized_keys">
<span class="sig-name descname"><span class="pre">optimized_keys</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#cc_sym.Factor" title="cc_sym.Factor"><span class="pre">cc_sym.Factor</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="#cc_sym.Key" title="cc_sym.Key"><span class="pre">cc_sym.Key</span></a><span class="p"><span class="pre">]</span></span></span></span><a class="headerlink" href="#cc_sym.Factor.optimized_keys" title="Permalink to this definition">¶</a></dt>
<dd><p>Get the optimized keys for this factor.</p>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="cc_sym.ImuPreintegrator">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ImuPreintegrator</span></span><a class="headerlink" href="#cc_sym.ImuPreintegrator" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">pybind11_object</span></code></p>
<p>Class to on-manifold preintegrate IMU measurements for usage in a SymForce optimization problem.</p>
<dl class="py method">
<dt class="sig sig-object py" id="cc_sym.ImuPreintegrator.covariance">
<span class="sig-name descname"><span class="pre">covariance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#cc_sym.ImuPreintegrator" title="cc_sym.ImuPreintegrator"><span class="pre">cc_sym.ImuPreintegrator</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v2.2)"><span class="pre">numpy.ndarray</span></a><span class="p"><span class="pre">[</span></span><span class="pre">numpy.float64</span><span class="p"><span class="pre">[</span></span><span class="m"><span class="pre">9</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="m"><span class="pre">9</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="headerlink" href="#cc_sym.ImuPreintegrator.covariance" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="cc_sym.ImuPreintegrator.integrate_measurement">
<span class="sig-name descname"><span class="pre">integrate_measurement</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#cc_sym.ImuPreintegrator" title="cc_sym.ImuPreintegrator"><span class="pre">cc_sym.ImuPreintegrator</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">measured_accel</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v2.2)"><span class="pre">numpy.ndarray</span></a><span class="p"><span class="pre">[</span></span><span class="pre">numpy.float64</span><span class="p"><span class="pre">[</span></span><span class="m"><span class="pre">3</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="m"><span class="pre">1</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">measured_gyro</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v2.2)"><span class="pre">numpy.ndarray</span></a><span class="p"><span class="pre">[</span></span><span class="pre">numpy.float64</span><span class="p"><span class="pre">[</span></span><span class="m"><span class="pre">3</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="m"><span class="pre">1</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">accel_cov</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v2.2)"><span class="pre">numpy.ndarray</span></a><span class="p"><span class="pre">[</span></span><span class="pre">numpy.float64</span><span class="p"><span class="pre">[</span></span><span class="m"><span class="pre">3</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="m"><span class="pre">1</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gyro_cov</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v2.2)"><span class="pre">numpy.ndarray</span></a><span class="p"><span class="pre">[</span></span><span class="pre">numpy.float64</span><span class="p"><span class="pre">[</span></span><span class="m"><span class="pre">3</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="m"><span class="pre">1</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dt</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)"><span class="pre">float</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">epsilon</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.13)"><span class="pre">float</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">2.220446049250313e-15</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.13)"><span class="pre">None</span></a></span></span><a class="headerlink" href="#cc_sym.ImuPreintegrator.integrate_measurement" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="cc_sym.ImuPreintegrator.preintegrated_measurements">
<span class="sig-name descname"><span class="pre">preintegrated_measurements</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#cc_sym.ImuPreintegrator" title="cc_sym.ImuPreintegrator"><span class="pre">cc_sym.ImuPreintegrator</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><a class="reference internal" href="#cc_sym.PreintegratedImuMeasurements" title="cc_sym.PreintegratedImuMeasurements"><span class="pre">cc_sym.PreintegratedImuMeasurements</span></a></span></span><a class="headerlink" href="#cc_sym.ImuPreintegrator.preintegrated_measurements" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="cc_sym.Key">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Key</span></span><a class="headerlink" href="#cc_sym.Key" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">pybind11_object</span></code></p>
<p>Key type for Values. Contains a letter plus an integral subscript and superscript. Can construct with a letter, a letter + sub, or a letter + sub + super, but not a letter + super.</p>
<dl class="py attribute">
<dt class="sig sig-object py" id="cc_sym.Key.INVALID_LETTER">
<span class="sig-name descname"><span class="pre">INVALID_LETTER</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">'\x00'</span></em><a class="headerlink" href="#cc_sym.Key.INVALID_LETTER" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="cc_sym.Key.INVALID_SUB">
<span class="sig-name descname"><span class="pre">INVALID_SUB</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">-9223372036854775808</span></em><a class="headerlink" href="#cc_sym.Key.INVALID_SUB" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py attribute">
<dt class="sig sig-object py" id="cc_sym.Key.INVALID_SUPER">
<span class="sig-name descname"><span class="pre">INVALID_SUPER</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">-9223372036854775808</span></em><a class="headerlink" href="#cc_sym.Key.INVALID_SUPER" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="cc_sym.Key.get_lcm_type">
<span class="sig-name descname"><span class="pre">get_lcm_type</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#cc_sym.Key" title="cc_sym.Key"><span class="pre">cc_sym.Key</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">lcmtypes.sym._key_t.key_t</span></span></span><a class="headerlink" href="#cc_sym.Key.get_lcm_type" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="py property">