### Install SymForce

Source: https://symforce.org/index.html

Install SymForce using pip. This command installs pre-compiled C++ components for Linux and Mac.

```bash
pip install symforce
```

--------------------------------

### Setup SymForce Environment

Source: https://symforce.org/_sources/tutorials/values_tutorial.ipynb.txt

Imports necessary SymForce modules and sets the symbolic API and log level. This is a common setup for SymForce notebooks.

```python
# Setup
import symforce

symforce.set_symbolic_api("sympy")
symforce.set_log_level("warning")

import symforce.symbolic as sf
from symforce.notebook_util import display
from symforce.notebook_util import set_notebook_defaults
from symforce.values import Values

set_notebook_defaults()
```

--------------------------------

### ImuFactor Usage Example

Source: https://symforce.org/api-cpp/class/classsym_1_1ImuFactor.html

Demonstrates how to create and use ImuFactor for visual-inertial optimization. This example shows setting up variables, integrating IMU measurements between keyframes, creating ImuFactor instances, and optimizing the values.

```cpp
enum Var : char {
  POSE = 'p',        // Pose3d
  VELOCITY = 'v',    // Vector3d
  ACCEL_BIAS = 'A',  // Vector3d
  GYRO_BIAS = 'G',   // Vector3d
  GRAVITY = 'g',     // Vector3d
  EPSILON = 'e'      // Scalar
};

struct ImuMeasurement {
  Eigen::Vector3d acceleration;
  Eigen::Vector3d angular_velocity;
  double duration;
};

int main() {
  // Dummy function declarations
  std::vector<ImuMeasurement> GetMeasurementsBetween(double start_time, double end_time);
  std::vector<double> GetKeyFrameTimes();
  Eigen::Vector3d GetAccelBiasEstimate(double time);
  Eigen::Vector3d GetGyroBiasEstimate(double time);
  void AppendOtherFactors(std::vector<sym::Factord> & factors);

  // Example accelerometer and gyroscope covariances
  const Eigen::Vector3d accel_cov = Eigen::Vector3d::Constant(1e-5);
  const Eigen::Vector3d gyro_cov = Eigen::Vector3d::Constant(1e-5);

  std::vector<sym::Factord> factors;

  // GetKeyFrameTimes assumed to return at least 2 times
  std::vector<double> key_frame_times = GetKeyFrameTimes();

  // Integrating Imu measurements between keyframes, creating an ImuFactor for each
  for (int i = 0; i < static_cast<int>(key_frame_times.size()) - 1; i++) {
    const double start_time = key_frame_times[i];
    const double end_time = key_frame_times[i + 1];

    const std::vector<ImuMeasurement> measurements = GetMeasurementsBetween(start_time,
                                                                            end_time);

    // ImuPreintegrator should be initialized with the best guesses for the IMU biases
    sym::ImuPreintegrator<double> integrator(GetAccelBiasEstimate(start_time),
                                             GetGyroBiasEstimate(start_time));
    for (const ImuMeasurement& meas : measurements) {
      integrator.IntegrateMeasurement(meas.acceleration, meas.angular_velocity, accel_cov,
                                      gyro_cov, meas.duration);
    }

    factors.push_back(sym::ImuFactor<double>(integrator)
                          .Factor({{Var::POSE, i},
                                   {Var::VELOCITY, i},
                                   {Var::POSE, i + 1},
                                   {Var::VELOCITY, i + 1},
                                   {Var::ACCEL_BIAS, i},
                                   {Var::GYRO_BIAS, i},
                                   {Var::GRAVITY},
                                   {Var::EPSILON}}));
  }

  // Adding any other factors there might be for the problem
  AppendOtherFactors(factors);

  sym::Optimizerd optimizer(sym::DefaultOptimizerParams(), factors);

  // Build Values
  sym::Valuesd values;
  for (int i = 0; i < key_frame_times.size(); i++) {
    values.Set({Var::POSE, i}, sym::Pose3d());
    values.Set({Var::VELOCITY, i}, Eigen::Vector3d::Zero());
  }
  for (int i = 0; i < key_frame_times.size() - 1; i++) {
    values.Set({Var::ACCEL_BIAS, i}, GetAccelBiasEstimate(key_frame_times[i]));
    values.Set({Var::GYRO_BIAS, i}, GetGyroBiasEstimate(key_frame_times[i]));
  }
  // gravity should point towards the direction of acceleration
  values.Set({Var::GRAVITY}, Eigen::Vector3d(0.0, 0.0, -9.8));
  values.Set({Var::EPSILON}, sym::kDefaultEpsilond);
  // Initialize any other items in values ...

  optimizer.Optimize(values);
}
```

--------------------------------

### Verify SymForce Installation

Source: https://symforce.org/index.html

Verify the installation by importing the symbolic API and creating a basic symbolic type in Python.

```python
>>> import symforce.symbolic as sf
>>> sf.Rot3()
```

--------------------------------

### Get C++ SymEngine Installation Directory

Source: https://symforce.org/_modules/symforce/path_util.html

Retrieves the installation directory for the C++ SymEngine components. This path is loaded from the build manifest.

```python
from symforce.path_util import cc_sym_install_dir

cc_sym_dir = cc_sym_install_dir()
print(f"C++ SymEngine directory: {cc_sym_dir}")
```

--------------------------------

### EigenSparseSolver Usage Example

Source: https://symforce.org/api-cpp/class/classsym_1_1EigenSparseSolver.html

Demonstrates how to instantiate and use EigenSparseSolver with specific Eigen decomposition types for nonlinear solvers. This setup is typically used when configuring an optimizer.

```cpp
using LinearSolver =
    sym::EigenSparseSolver<double, Eigen::CholmodDecomposition<Eigen::SparseMatrix<double>>>;
using NonlinearSolver = sym::LevenbergMarquardtSolver<double, LinearSolver>;
using Optimizer = sym::Optimizer<double, NonlinearSolver>;

Optimizer optimizer{...};

```

--------------------------------

### symenginepy_install_dir()

Source: https://symforce.org/api/symforce.path_util.html

Returns the installation directory for SymEnginePy.

```APIDOC
def symenginepy_install_dir() -> _Path_
```

--------------------------------

### Verify SymForce Installation

Source: https://symforce.org/index.html

Verifies a successful SymForce installation by importing the library and checking the symbolic API. It also attempts to import the C++ extension module `cc_sym`. Failure to import `cc_sym` or seeing 'sympy' instead of 'symengine' indicates a broken installation.

```python
>>> import symforce
>>> symforce.get_symbolic_api()
'symengine'
>>> from symforce import cc_sym
```

--------------------------------

### symenginepy_install_dir

Source: https://symforce.org/_modules/symforce/path_util.html

Returns the installation directory for SymEnginePy.

```APIDOC
## symenginepy_install_dir

### Description
Returns the installation directory for SymEnginePy.

### Returns
- Path: The installation directory of SymEnginePy.
```

--------------------------------

### cc_sym_install_dir

Source: https://symforce.org/_modules/symforce/path_util.html

Returns the installation directory for C++ SymForce.

```APIDOC
## cc_sym_install_dir

### Description
Returns the installation directory for C++ SymForce.

### Returns
- Path: The installation directory of C++ SymForce.
```

--------------------------------

### Install SymForce with Pip

Source: https://symforce.org/index.html

Installs SymForce and its dependencies using pip. This is the recommended method for users who do not plan to modify the C++ source code frequently. For development with C++ sources, consider building with CMake directly.

```bash
pip install .
```

--------------------------------

### cc_sym_install_dir()

Source: https://symforce.org/api/symforce.path_util.html

Returns the installation directory for the C++ SymForce component.

```APIDOC
def cc_sym_install_dir() -> _Path_
```

--------------------------------

### Get All Keys

Source: https://symforce.org/api-cpp/namespace/namespacesym.html

Retrieves all keys required to evaluate this factor.

```cpp
const std::vector<Key> &AllKeys() const
```

--------------------------------

### Get SymEnginePy Installation Directory

Source: https://symforce.org/_modules/symforce/path_util.html

Retrieves the installation directory for the symenginepy package. This path is determined from the build manifest.

```python
from symforce.path_util import symenginepy_install_dir

symenginepy_dir = symenginepy_install_dir()
print(f"SymEnginePy directory: {symenginepy_dir}")
```

--------------------------------

### Key Formatting Examples

Source: https://symforce.org/api-cpp/file/key_8h.html

Demonstrates various ways to construct and format Key objects, showing the resulting string representations.

```cpp
Key('C', 13) -> "C_13"
Key('f') -> "f"
Key('f', 32, 2) -> "f_32_2"
Key('A', -2, 123) -> "A_n2_123"
Key() -> "NULLKEY"
```

--------------------------------

### Setup Test Case Environment

Source: https://symforce.org/_modules/symforce/test_util/test_case_mixin.html

Initializes the test environment by setting the default zero epsilon behavior to FAIL and creating a list to store temporary output directories.

```python
def setUp(self) -> None:
        """
        Creates list of temporary directories that will be removed before shutdown (unless debug
        mode is on)
        """
        super().setUp()

        # Set to fail on default epsilon == 0
        codegen_config.DEFAULT_ZERO_EPSILON_BEHAVIOR = codegen_config.ZeroEpsilonBehavior.FAIL

        # Storage for temporary output directories
        self.output_dirs: T.List[Path] = []
```

--------------------------------

### Get SymForce Installation Directory

Source: https://symforce.org/_modules/symforce/path_util.html

Retrieves the installation directory of the symforce Python package. This is useful for locating package resources.

```python
from symforce.path_util import symforce_dir

sym_dir = symforce_dir()
print(f"SymForce directory: {sym_dir}")
```

--------------------------------

### Setup Imports and Defaults

Source: https://symforce.org/_sources/tutorials/geometry_tutorial.ipynb.txt

Imports necessary symforce modules and sets the symbolic API to sympy and log level to warning. Also sets notebook display defaults.

```python
import symforce

symforce.set_symbolic_api("sympy")
symforce.set_log_level("warning")

import symforce.symbolic as sf
from symforce import ops
from symforce.notebook_util import display
from symforce.notebook_util import set_notebook_defaults

set_notebook_defaults()
```

--------------------------------

### Example Usage of sym::Optimizer

Source: https://symforce.org/api-cpp/class/classsym_1_1Optimizer.html

Demonstrates the creation of a sym::Optimizer, including setting up values, factors (PriorFactorRot3 and BetweenFactorRot3), optimizer parameters, and finally performing the optimization. Ensure necessary types like sym::Key, sym::Valuesd, sym::Rot3d, sym::Factord, and sym::optimizer_params_t are available.

```cpp
// Create a Values
sym::Key key0{'R', 0};
sym::Key key1{'R', 1};
sym::Valuesd values;
values.Set(key0, sym::Rot3d::Identity());
values.Set(key1, sym::Rot3d::Identity());

// Create some factors
std::vector<sym::Factord> factors;
factors.push_back(sym::Factord::Jacobian(
    [epsilon](const sym::Rot3d& rot, Eigen::Vector3d* const res,
              Eigen::Matrix3d* const jac) {
      const sym::Rot3d prior = sym::Rot3d::Random();
      const Eigen::Matrix3d sqrt_info = Eigen::Vector3d::Ones().asDiagonal();
      sym::PriorFactorRot3<double>(rot, prior, sqrt_info, epsilon, res, jac);
    },
    {key0}));
factors.push_back(sym::Factord::Jacobian(
    [epsilon](const sym::Rot3d& rot, Eigen::Vector3d* const res,
              Eigen::Matrix3d* const jac) {
      const sym::Rot3d prior = sym::Rot3d::Random();
      const Eigen::Matrix3d sqrt_info = Eigen::Vector3d::Ones().asDiagonal();
      sym::PriorFactorRot3<double>(rot, prior, sqrt_info, epsilon, res, jac);
    },
    {key1}));
factors.push_back(sym::Factord::Jacobian(
    [epsilon](const sym::Rot3d& a, const sym::Rot3d& b, Eigen::Vector3d* const res,
              Eigen::Matrix<double, 3, 6>* const jac) {
      const Eigen::Matrix3d sqrt_info = Eigen::Vector3d::Ones().asDiagonal();
      const sym::Rot3d a_T_b = sym::Rot3d::Random();
      sym::BetweenFactorRot3<double>(a, b, a_T_b, sqrt_info, epsilon, res, jac);
    },
    {key0, key1}));

// Set up the params
sym::optimizer_params_t params = sym::DefaultOptimizerParams();
params.iterations = 50;
params.early_exit_min_reduction = 0.0001;

// Optimize
sym::Optimizer<double> optimizer(params, factors);
optimizer.Optimize(values);

```

--------------------------------

### Matrix Construction Examples

Source: https://symforce.org/api/symforce.geo.matrix.html

Demonstrates various ways to construct Matrix objects, including zero initialization, initialization with data, and specifying dimensions. Use these methods to create matrices of specific sizes and with initial values.

```python
1) Matrix32()  # Zero constructed Matrix32
```

```python
2) Matrix(sm.Matrix([[1, 2], [3, 4]]))  # Matrix22 with [1, 2, 3, 4] data
```

```python
3A) Matrix([[1, 2], [3, 4]])  # Matrix22 with [1, 2, 3, 4] data
```

```python
3B) Matrix22([1, 2, 3, 4])  # Matrix22 with [1, 2, 3, 4] data (must matched fixed shape)
```

```python
3C) Matrix([1, 2, 3, 4])  # Matrix41 with [1, 2, 3, 4] data - column vector assumed
```

```python
4) Matrix(4, 3)  # Zero constructed Matrix43
```

```python
5) Matrix(2, 2, [1, 2, 3, 4])  # Matrix22 with [1, 2, 3, 4] data (first two are shape)
```

```python
6) Matrix(2, 2, lambda row, col: row + col)  # Matrix22 with [0, 1, 1, 2] data
```

```python
7) Matrix22(1, 2, 3, 4)  # Matrix22 with [1, 2, 3, 4] data (must match fixed length)
```

--------------------------------

### Install Build Dependencies with Pip

Source: https://symforce.org/index.html

Installs packages required for building and running SymForce using pip. This command installs only the essential build dependencies, not all development tools or test requirements.

```bash
pip install -r requirements/build_py3<version>.txt
```

--------------------------------

### Get Identity Element for Pose3

Source: https://symforce.org/_sources/tutorials/ops_tutorial.ipynb.txt

Demonstrates how to get the identity element for a Pose3 type using GroupOps.identity.

```python
display(GroupOps.identity(sf.Pose3))
```

--------------------------------

### Example Usage of FixedSizeOptimizer

Source: https://symforce.org/api-cpp/class/classsym_1_1FixedSizeOptimizer.html

Demonstrates how to instantiate and use the FixedSizeOptimizer with custom types. This includes setting up the nonlinear solver and calling the Optimize function.

```cpp
using LinearSolverType = sym::SparseCholeskySolver<Eigen::SparseMatrix<double>>;
using CustomNonlinearSolver = 
    sym::LevenbergMarquardtSolver<double, LinearSolverType, CustomOptimizationState>;
using CustomOptimizer = sym::FixedSizeOptimizer<double, CustomNonlinearSolver>;

CustomOptimizer optimizer(sym::DefaultOptimizerParams());
CustomValuesType custom_values{...};
optimizer.Optimize(custom_values, LinearizeCustomValues);

```

--------------------------------

### Setup SymForce Environment

Source: https://symforce.org/tutorials/values_tutorial.html

Initializes the SymForce symbolic API and logging level. Imports necessary modules for symbolic computation and notebook utilities.

```python
import symforce

symforce.set_symbolic_api("sympy")
symforce.set_log_level("warning")

import symforce.symbolic as sf
from symforce.notebook_util import display
from symforce.notebook_util import set_notebook_defaults
from symforce.values import Values

set_notebook_defaults()
```

--------------------------------

### Get Storage Dimension of Pose3

Source: https://symforce.org/_sources/tutorials/ops_tutorial.ipynb.txt

Demonstrates how to get the number of scalars required to represent a Pose3 type using StorageOps.storage_dim().

```python
# Number of scalars used to represent a Pose3 (4 quaternion + 3 position)
display(StorageOps.storage_dim(sf.Pose3))
```

--------------------------------

### _main

Source: https://symforce.org/api/symforce.test_util.test_case.html

Entry point to run all tests in scope.

```APIDOC
## static _main(* args, ** kwargs)

Call this to run all tests in scope.

Parameters:
    
  * **args** (_Any_)
  * **kwargs** (_Any_)

Return type:
    
None
```

--------------------------------

### IMU Factor Example Usage

Source: https://symforce.org/api-cpp/file/imu__factor_8h.html

Demonstrates how to use the ImuFactor within an optimization framework. It involves setting up IMU measurements, preintegration, factor creation, and optimizer initialization.

```cpp
enum Var : char {
  POSE = 'p',        // Pose3d
  VELOCITY = 'v',    // Vector3d
  ACCEL_BIAS = 'A',  // Vector3d
  GYRO_BIAS = 'G',   // Vector3d
  GRAVITY = 'g',     // Vector3d
  EPSILON = 'e'      // Scalar
};

struct ImuMeasurement {
  Eigen::Vector3d acceleration;
  Eigen::Vector3d angular_velocity;
  double duration;
};

int main() {
  // Dummy function declarations
  std::vector<ImuMeasurement> GetMeasurementsBetween(double start_time, double end_time);
  std::vector<double> GetKeyFrameTimes();
  Eigen::Vector3d GetAccelBiasEstimate(double time);
  Eigen::Vector3d GetGyroBiasEstimate(double time);
  void AppendOtherFactors(std::vector<sym::Factord> & factors);

  // Example accelerometer and gyroscope covariances
  const Eigen::Vector3d accel_cov = Eigen::Vector3d::Constant(1e-5);
  const Eigen::Vector3d gyro_cov = Eigen::Vector3d::Constant(1e-5);

  std::vector<sym::Factord> factors;

  // GetKeyFrameTimes assumed to return at least 2 times
  std::vector<double> key_frame_times = GetKeyFrameTimes();

  // Integrating Imu measurements between keyframes, creating an ImuFactor for each
  for (int i = 0; i < static_cast<int>(key_frame_times.size()) - 1; i++) {
    const double start_time = key_frame_times[i];
    const double end_time = key_frame_times[i + 1];

    const std::vector<ImuMeasurement> measurements = GetMeasurementsBetween(start_time,
                                                                            end_time);

    // ImuPreintegrator should be initialized with the best guesses for the IMU biases
    sym::ImuPreintegrator<double> integrator(GetAccelBiasEstimate(start_time),
                                             GetGyroBiasEstimate(start_time));
    for (const ImuMeasurement& meas : measurements) {
      integrator.IntegrateMeasurement(meas.acceleration, meas.angular_velocity, accel_cov,
                                      gyro_cov, meas.duration);
    }

    factors.push_back(sym::ImuFactor<double>(integrator)
                          .Factor({{Var::POSE, i}, 
                                   {Var::VELOCITY, i}, 
                                   {Var::POSE, i + 1}, 
                                   {Var::VELOCITY, i + 1}, 
                                   {Var::ACCEL_BIAS, i}, 
                                   {Var::GYRO_BIAS, i}, 
                                   {Var::GRAVITY},
                                   {Var::EPSILON}}));
  }

  // Adding any other factors there might be for the problem
  AppendOtherFactors(factors);

  sym::Optimizerd optimizer(sym::DefaultOptimizerParams(), factors);

  // Build Values
  sym::Valuesd values;
  for (int i = 0; i < key_frame_times.size(); i++) {
    values.Set({Var::POSE, i}, sym::Pose3d());
    values.Set({Var::VELOCITY, i}, Eigen::Vector3d::Zero());
  }
  for (int i = 0; i < key_frame_times.size() - 1; i++) {
    values.Set({Var::ACCEL_BIAS, i}, GetAccelBiasEstimate(key_frame_times[i]));
    values.Set({Var::GYRO_BIAS, i}, GetGyroBiasEstimate(key_frame_times[i]));
  }
  // gravity should point towards the direction of acceleration
  values.Set({Var::GRAVITY}, Eigen::Vector3d(0.0, 0.0, -9.8));
  values.Set({Var::EPSILON}, sym::kDefaultEpsilond);
  // Initialize any other items in values ...

  optimizer.Optimize(values);
}
```

--------------------------------

### Optimizer Usage Example

Source: https://symforce.org/_modules/symforce/opt/optimizer.html

Demonstrates how to use an Optimizer instance by providing an initial guess and calling the optimize method.

```python
initial_guess = Values(...)
result = optimizer.optimize(initial_guess)
print(result.optimized_values)
```

--------------------------------

### Values<Scalar> Output Format Example

Source: https://symforce.org/api-cpp/namespace/namespacesym.html

Example output format for printing a Values<Scalar> object, showing its structure and contents.

```plaintext
Valuesd entries=4 array=8 storage_dim=7 tangent_dim=6
  R_1 [0:4] --> <Rot3d [0.563679, 0.0939464, 0, 0.820634]>
  f_1 [5:6] --> 4.2
  f_2 [6:7] --> 4.3
  d_1 [7:8] --> 4.3
>

```

--------------------------------

### Get Storage Dimension of List of Pose3

Source: https://symforce.org/_sources/tutorials/ops_tutorial.ipynb.txt

Illustrates element-wise operations on containers by getting the total storage dimension for a list of Pose3 objects.

```python
# Element-wise operations on lists of objects
display(StorageOps.storage_dim([sf.Pose3, sf.Pose3]))
```

--------------------------------

### Setup SymForce Environment

Source: https://symforce.org/_sources/tutorials/ops_tutorial.ipynb.txt

Sets the symbolic API to sympy and the log level to warning. Imports necessary SymForce modules and utility functions for notebook display and default settings.

```python
import symforce

symforce.set_symbolic_api("sympy")
symforce.set_log_level("warning")

import symforce.symbolic as sf
from symforce.notebook_util import display
from symforce.notebook_util import set_notebook_defaults
from symforce.ops import GroupOps
from symforce.ops import LieGroupOps
from symforce.ops import StorageOps
from symforce.values import Values

set_notebook_defaults()
```

--------------------------------

### Matrix Construction Examples

Source: https://symforce.org/_sources/tutorials/geometry_tutorial.ipynb.txt

Provides multiple ways to construct a 2x3 matrix (sf.Matrix23) using SymForce, including from lists, specified dimensions, and aliases. Demonstrates flexibility in matrix initialization.

```python
# Matrix construction. The statements below all create the same 2x3 matrix object

# Construction from 2D list
m1 = sf.Matrix([[1, 2, 3], [4, 5, 6]])

# Construction using specified size + data
m2 = sf.Matrix(2, 3, [1, 2, 3, 4, 5, 6])

# sf.MatrixNM creates a matrix with shape NxM (defined by default for 6x6
# matrices and smaller)
m3 = sf.Matrix23(1, 2, 3, 4, 5, 6)
m4 = sf.Matrix23([1, 2, 3, 4, 5, 6])

# Construction using aliases
m5 = sf.M([[1, 2, 3], [4, 5, 6]])
m6 = sf.M(2, 3, [1, 2, 3, 4, 5, 6])
m7 = sf.M23(1, 2, 3, 4, 5, 6)
m8 = sf.M23([1, 2, 3, 4, 5, 6])

# Construction from block matrices of appropriate dimensions
m9 = sf.Matrix23.block_matrix([[sf.M13([1, 2, 3])], [sf.M13([3, 4, 5])]])
```

--------------------------------

### StorageOps for SphericalCameraCal

Source: https://symforce.org/api-gen-cpp/namespace/namespacesym.html

Provides C++ StorageOps implementation for symforce.cam.spherical_camera_cal.SphericalCameraCal. It includes methods to get storage dimension, convert to and from storage, and get the type enum.

```APIDOC
## StorageOps<SphericalCameraCal<ScalarType>>

### Description
C++ StorageOps implementation for symforce.cam.spherical_camera_cal.SphericalCameraCal.

### Public Types
- `using T = SphericalCameraCal<ScalarType>`
- `using Scalar = ScalarType`

### Public Static Functions
- `static inline constexpr int32_t StorageDim()`: Returns the dimension of the storage.
- `static void ToStorage(const T &a, ScalarType *out)`: Converts a SphericalCameraCal object to its storage representation.
- `static T FromStorage(const ScalarType *data)`: Converts storage data to a SphericalCameraCal object.
- `static inline constexpr type_t TypeEnum()`: Returns the type enum for SphericalCameraCal.
```

--------------------------------

### StorageOps for PolynomialCameraCal

Source: https://symforce.org/api-gen-cpp/namespace/namespacesym.html

Provides C++ StorageOps implementation for symforce.cam.polynomial_camera_cal.PolynomialCameraCal. It includes methods to get storage dimension, convert to and from storage, and get the type enum.

```APIDOC
## StorageOps<PolynomialCameraCal<ScalarType>>

### Description
C++ StorageOps implementation for symforce.cam.polynomial_camera_cal.PolynomialCameraCal.

### Public Types
- `using T = PolynomialCameraCal<ScalarType>`
- `using Scalar = ScalarType`

### Public Static Functions
- `static inline constexpr int32_t StorageDim()`: Returns the dimension of the storage.
- `static void ToStorage(const T &a, ScalarType *out)`: Converts a PolynomialCameraCal object to its storage representation.
- `static T FromStorage(const ScalarType *data)`: Converts storage data to a PolynomialCameraCal object.
- `static inline constexpr type_t TypeEnum()`: Returns the type enum for PolynomialCameraCal.
```

--------------------------------

### Optimize a nonlinear least-squares problem

Source: https://symforce.org/api-cpp/namespace/namespacesym.html

Example of setting up and running an optimizer for a nonlinear least-squares problem. This involves creating values, defining factors (e.g., PriorFactorRot3, BetweenFactorRot3), configuring optimizer parameters, and then calling the Optimize method. Ensure all necessary headers are included.

```cpp
#include <optimizer.h>

// Create a Values
sym::Key key0{'R', 0};
sym::Key key1{'R', 1};
sym::Valuesd values;
values.Set(key0, sym::Rot3d::Identity());
values.Set(key1, sym::Rot3d::Identity());

// Create some factors
std::vector<sym::Factord> factors;
factors.push_back(sym::Factord::Jacobian(
    [epsilon](const sym::Rot3d& rot, Eigen::Vector3d* const res,
              Eigen::Matrix3d* const jac) {
      const sym::Rot3d prior = sym::Rot3d::Random();
      const Eigen::Matrix3d sqrt_info = Eigen::Vector3d::Ones().asDiagonal();
      sym::PriorFactorRot3<double>(rot, prior, sqrt_info, epsilon, res, jac);
    },
    {key0}));
factors.push_back(sym::Factord::Jacobian(
    [epsilon](const sym::Rot3d& rot, Eigen::Vector3d* const res,
              Eigen::Matrix3d* const jac) {
      const sym::Rot3d prior = sym::Rot3d::Random();
      const Eigen::Matrix3d sqrt_info = Eigen::Vector3d::Ones().asDiagonal();
      sym::PriorFactorRot3<double>(rot, prior, sqrt_info, epsilon, res, jac);
    },
    {key1}));
factors.push_back(sym::Factord::Jacobian(
    [epsilon](const sym::Rot3d& a, const sym::Rot3d& b, Eigen::Vector3d* const res,
              Eigen::Matrix<double, 3, 6>* const jac) {
      const Eigen::Matrix3d sqrt_info = Eigen::Vector3d::Ones().asDiagonal();
      const sym::Rot3d a_T_b = sym::Rot3d::Random();
      sym::BetweenFactorRot3<double>(a, b, a_T_b, sqrt_info, epsilon, res, jac);
    },
    {key0, key1}));

// Set up the params
sym::optimizer_params_t params = sym::DefaultOptimizerParams();
params.iterations = 50;
params.early_exit_min_reduction = 0.0001;

// Optimize
sym::Optimizer<double> optimizer(params, factors);
optimizer.Optimize(values);

```

--------------------------------

### Example of Picking Generated Keys

Source: https://symforce.org/_modules/symforce/values/generated_key_selection.html

Demonstrates how variable names are mapped to generated keys, showing the logic for handling simple names, names with numbers, and names with underscores.

```python
pick_generated_keys_for_variable_names(['foo', 'foo2', 'foo_bar', 'foo_bar2', 'foo_baz'])
```

--------------------------------

### StorageOps for OrthographicCameraCal

Source: https://symforce.org/api-gen-cpp/namespace/namespacesym.html

Provides C++ StorageOps implementation for symforce.cam.orthographic_camera_cal.OrthographicCameraCal. It includes methods to get storage dimension, convert to and from storage, and get the type enum.

```APIDOC
## StorageOps<OrthographicCameraCal<ScalarType>>

### Description
C++ StorageOps implementation for symforce.cam.orthographic_camera_cal.OrthographicCameraCal.

### Public Types
- `using T = OrthographicCameraCal<ScalarType>`
- `using Scalar = ScalarType`

### Public Static Functions
- `static inline constexpr int32_t StorageDim()`: Returns the dimension of the storage.
- `static void ToStorage(const T &a, ScalarType *out)`: Converts an OrthographicCameraCal object to its storage representation.
- `static T FromStorage(const ScalarType *data)`: Converts storage data to an OrthographicCameraCal object.
- `static inline constexpr type_t TypeEnum()`: Returns the type enum for OrthographicCameraCal.
```

--------------------------------

### StorageOps for LinearCameraCal

Source: https://symforce.org/api-gen-cpp/namespace/namespacesym.html

Provides C++ StorageOps implementation for symforce.cam.linear_camera_cal.LinearCameraCal. It includes methods to get storage dimension, convert to and from storage, and get the type enum.

```APIDOC
## StorageOps<LinearCameraCal<ScalarType>>

### Description
C++ StorageOps implementation for symforce.cam.linear_camera_cal.LinearCameraCal.

### Public Types
- `using T = LinearCameraCal<ScalarType>`
- `using Scalar = ScalarType`

### Public Static Functions
- `static inline constexpr int32_t StorageDim()`: Returns the dimension of the storage.
- `static void ToStorage(const T &a, ScalarType *out)`: Converts a LinearCameraCal object to its storage representation.
- `static T FromStorage(const ScalarType *data)`: Converts storage data to a LinearCameraCal object.
- `static inline constexpr type_t TypeEnum()`: Returns the type enum for LinearCameraCal.
```

--------------------------------

### Setup Symforce Environment

Source: https://symforce.org/_sources/tutorials/codegen_tutorial.ipynb.txt

Imports necessary symforce modules and sets up the symbolic API, log level, and epsilon to a symbol for safe code generation. This is a prerequisite for most symforce operations.

```python
import numpy as np

import symforce

symforce.set_symbolic_api("symengine")
symforce.set_log_level("warning")


symforce.set_epsilon_to_symbol()

import symforce.symbolic as sf
from symforce import codegen
from symforce.codegen import codegen_util
from symforce.notebook_util import display
from symforce.notebook_util import display_code_file
from symforce.notebook_util import set_notebook_defaults
from symforce.values import Values

set_notebook_defaults()
```

--------------------------------

### StorageOps for Rot3

Source: https://symforce.org/api-gen-cpp/namespace/namespacesym.html

Provides C++ StorageOps implementation for symforce.geo.rot3.Rot3. It includes methods to get storage dimension, convert to and from storage, get the type enum, and generate random rotations.

```APIDOC
## StorageOps<Rot3<ScalarType>>

### Description
C++ StorageOps implementation for symforce.geo.rot3.Rot3.

### Public Types
- `using T = Rot3<ScalarType>`
- `using Scalar = ScalarType`

### Public Static Functions
- `static inline constexpr int32_t StorageDim()`: Returns the dimension of the storage.
- `static void ToStorage(const T &a, ScalarType *out)`: Converts a Rot3 object to its storage representation.
- `static T FromStorage(const ScalarType *data)`: Converts storage data to a Rot3 object.
- `static inline constexpr type_t TypeEnum()`: Returns the type enum for Rot3.
- `template<typename Generator> static inline T Random(Generator &gen)`: Generates a random Rot3 object using the provided generator.
```

--------------------------------

### Optimizer Creation with Single Factor

Source: https://symforce.org/_modules/symforce/opt/optimizer.html

Example of creating an Optimizer instance with a single Factor and specifying the keys to be optimized.

```python
factor = Factor(
    [my_key_0, my_key_1, my_key_2], my_residual_function
)
optimizer = Optimizer(
    factors=[factor],
    optimized_keys=[my_key_0, my_key_1],
)
```

--------------------------------

### Notebook Utilities Setup

Source: https://symforce.org/_sources/tutorials/sympy_tutorial.ipynb.txt

Import and set up utility functions for use in Jupyter notebooks, including display, expression tree printing, and default notebook settings.

```python
from symforce.notebook_util import display
from symforce.notebook_util import print_expression_tree
from symforce.notebook_util import set_notebook_defaults

set_notebook_defaults()
```

--------------------------------

### StorageOps for Rot2

Source: https://symforce.org/api-gen-cpp/namespace/namespacesym.html

Provides C++ StorageOps implementation for symforce.geo.rot2.Rot2. It includes methods to get storage dimension, convert to and from storage, get the type enum, and generate random rotations.

```APIDOC
## StorageOps<Rot2<ScalarType>>

### Description
C++ StorageOps implementation for symforce.geo.rot2.Rot2.

### Public Types
- `using T = Rot2<ScalarType>`
- `using Scalar = ScalarType`

### Public Static Functions
- `static inline constexpr int32_t StorageDim()`: Returns the dimension of the storage.
- `static void ToStorage(const T &a, ScalarType *out)`: Converts a Rot2 object to its storage representation.
- `static T FromStorage(const ScalarType *data)`: Converts storage data to a Rot2 object.
- `static inline constexpr type_t TypeEnum()`: Returns the type enum for Rot2.
- `template<typename Generator> static inline T Random(Generator &gen)`: Generates a random Rot2 object using the provided generator.
```

--------------------------------

### StorageOps for Pose3

Source: https://symforce.org/api-gen-cpp/namespace/namespacesym.html

Provides C++ StorageOps implementation for symforce.geo.pose3.Pose3. It includes methods to get storage dimension, convert to and from storage, get the type enum, and generate random poses.

```APIDOC
## StorageOps<Pose3<ScalarType>>

### Description
C++ StorageOps implementation for symforce.geo.pose3.Pose3.

### Public Types
- `using T = Pose3<ScalarType>`
- `using Scalar = ScalarType`

### Public Static Functions
- `static inline constexpr int32_t StorageDim()`: Returns the dimension of the storage.
- `static void ToStorage(const T &a, ScalarType *out)`: Converts a Pose3 object to its storage representation.
- `static T FromStorage(const ScalarType *data)`: Converts storage data to a Pose3 object.
- `static inline constexpr type_t TypeEnum()`: Returns the type enum for Pose3.
- `template<typename Generator> static inline T Random(Generator &gen)`: Generates a random Pose3 object using the provided generator.
```

--------------------------------

### StorageOps for Pose2

Source: https://symforce.org/api-gen-cpp/namespace/namespacesym.html

Provides C++ StorageOps implementation for symforce.geo.pose2.Pose2. It includes methods to get storage dimension, convert to and from storage, get the type enum, and generate random poses.

```APIDOC
## StorageOps<Pose2<ScalarType>>

### Description
C++ StorageOps implementation for symforce.geo.pose2.Pose2.

### Public Types
- `using T = Pose2<ScalarType>`
- `using Scalar = ScalarType`

### Public Static Functions
- `static inline constexpr int32_t StorageDim()`: Returns the dimension of the storage.
- `static void ToStorage(const T &a, ScalarType *out)`: Converts a Pose2 object to its storage representation.
- `static T FromStorage(const ScalarType *data)`: Converts storage data to a Pose2 object.
- `static inline constexpr type_t TypeEnum()`: Returns the type enum for Pose2.
- `template<typename Generator> static inline T Random(Generator &gen)`: Generates a random Pose2 object using the provided generator.
```

--------------------------------

### main

Source: https://symforce.org/api/symforce.benchmarks.run_benchmarks.html

The main entry point for running benchmarks, optionally specifying a particular benchmark to execute.

```APIDOC
## main

### Description
Orchestrates the execution of benchmarks. It can run all configured benchmarks or a single specified benchmark, saving the output to a designated directory.

### Parameters

* **benchmark** (str | None) - The name of a specific benchmark to run. If None, all benchmarks are executed.
* **out_dir** (str) - The directory where the benchmark outputs will be saved. Defaults to 'benchmark_outputs'.
```

--------------------------------

### Get Prettier Command

Source: https://symforce.org/_modules/symforce/codegen/format_util.html

Helper function to get the command to run prettier with necessary arguments. It checks for a local prettier binary specified in paths.json or falls back to npx/yarn.

```python
_prettier_cmd: T.Optional[T.List[str]] = None

def _get_prettier_cmd() -> T.List[str]:
    """
    Returns a command to run prettier with any necessary args
    """
    global _prettier_cmd  # noqa: PLW0603

    if _prettier_cmd is not None:
        return _prettier_cmd

    # A path to a local prettier binary can be specified in the paths.json file with they key
    # "prettier_bin_path". The path should be relative to the symforce root directory.
    # If not provided, we will use npx or yarn if installed.
    paths_file = symforce_dir() / "build" / "paths.json"

```

--------------------------------

### Editable Install SymForce with Pip

Source: https://symforce.org/index.html

Performs an editable installation of SymForce using pip. This method is useful when modifying the Python components of SymForce, as changes will be reflected without needing to reinstall.

```bash
pip install -e .
```

--------------------------------

### Install GMP Package

Source: https://symforce.org/index.html

Installs the GMP (GNU Multiple Precision Arithmetic Library) package, which is a dependency for building SymForce. Choose the command appropriate for your operating system or package manager.

```bash
apt install libgmp-dev            # Ubuntu
```

```bash
brew install gmp                  # Mac
```

```bash
conda install -c conda-forge gmp  # Conda
```

--------------------------------

### Optimizer Creation with OptimizationProblem (Symbolic Factors)

Source: https://symforce.org/_modules/symforce/opt/optimizer.html

Illustrates creating an Optimizer from an OptimizationProblem using make_symbolic_factors. Symbolic factors are converted to numeric factors upon optimizer creation, and linearization functions are generated at that time.

```python
problem = OptimizationProblem(subproblems=[...], residual_blocks=...)
factors = problem.make_symbolic_factors("my_problem")
optimizer = Optimizer(factors, problem.optimized_keys())
```

--------------------------------

### Get Memory Type of Storage or Pair

Source: https://symforce.org/_modules/symforce/caspar/memory/pair.html

Determines and returns the underlying storage type for a given Storage object, Pair, or their types. Raises an error if trying to get the type from an unannotated Pair.

```python
[docs]
def get_memtype(
    storage_or_pair: T.Union[T.Type[Storage], T.Type[Pair], Storage, Pair],
) -> T.Type[Storage]:
    if is_pair(storage_or_pair):
        if storage_or_pair is Pair:
            raise ValueError("Cannot get type from unannotated Pair")
        elif T.get_origin(storage_or_pair) is Pair:
            return T.get_args(storage_or_pair)[0]
        elif isinstance(storage_or_pair, Pair):
            return storage_or_pair.data[0].__class__
    if isinstance(storage_or_pair, type):
        storage_or_pair = T.cast(T.Type[Storage], storage_or_pair)
        return storage_or_pair
    storage_or_pair = T.cast(Storage, storage_or_pair)
    return storage_or_pair.__class__
```

--------------------------------

### Matrix Construction Examples

Source: https://symforce.org/_modules/symforce/geo/matrix.html

Demonstrates various ways to construct Matrix objects, including fixed-size types, from SymPy matrices, lists, and lambda functions. Note that fixed-size constructors require matching dimensions.

```python
Matrix32()  # Zero constructed Matrix32
```

```python
Matrix(sm.Matrix([[1, 2], [3, 4]]))  # Matrix22 with [1, 2, 3, 4] data
```

```python
Matrix([[1, 2], [3, 4]])  # Matrix22 with [1, 2, 3, 4] data
```

```python
Matrix22([1, 2, 3, 4])  # Matrix22 with [1, 2, 3, 4] data (must matched fixed shape)
```

```python
Matrix([1, 2, 3, 4])  # Matrix41 with [1, 2, 3, 4] data - column vector assumed
```

```python
Matrix(4, 3)  # Zero constructed Matrix43
```

```python
Matrix(2, 2, [1, 2, 3, 4])  # Matrix22 with [1, 2, 3, 4] data (first two are shape)
```

```python
Matrix(2, 2, lambda row, col: row + col)  # Matrix22 with [0, 1, 1, 2] data
```

```python
Matrix22(1, 2, 3, 4)  # Matrix22 with [1, 2, 3, 4] data (must match fixed length)
```

--------------------------------

### Example Usage of LevenbergMarquardtSolver

Source: https://symforce.org/api-cpp/class/classsym_1_1LevenbergMarquardtSolver.html

Demonstrates how to set up and use the LevenbergMarquardtSolver for a nonlinear least squares problem. This includes defining a linearization function, initializing values, creating the solver, and iterating until convergence.

```cpp
constexpr const int M = 9;
constexpr const int N = 5;

// Create a function that computes the residual (a linear residual for this example)
const auto J_MN = sym::RandomNormalMatrix<double, M, N>(gen);
const auto linearize_func = [&J_MN](const sym::Valuesd& values,
                                    sym::SparseLinearizationd* const linearization) {
  const auto state_vec = values.At<sym::Vector5d>('v');
  linearization->residual = J_MN * state_vec;
  linearization->hessian_lower = (J_MN.transpose() * J_MN).sparseView();
  linearization->jacobian = J_MN.sparseView();
  linearization->rhs = J_MN.transpose() * linearization->residual;
};

// Create a Values
sym::Valuesd values_init{};
values_init.Set('v', (StateVector::Ones() * 100).eval());

// Create a Solver
sym::LevenbergMarquardtSolverd solver(params, "", kEpsilon);
solver.SetIndex(values_init.CreateIndex({'v'}));
solver.Reset(values_init);

// Iterate to convergence
sym::optimization_stats_t stats;
bool should_early_exit = false;
while (!should_early_exit) {
  should_early_exit = solver.Iterate(linearize_func, &stats);
}

// Get the best values
sym::Valuesd values_final = solver.GetBestValues();

```

--------------------------------

### Retrieve SymForce Version

Source: https://symforce.org/_modules/symforce.html

Attempts to retrieve the installed version of the symforce package using importlib.metadata. If the package is not installed, it falls back to using setuptools_scm. If neither method succeeds, the __version__ attribute will not be set.

```python
# -------------------------------------------------------------------------------------------------
# Version
# -------------------------------------------------------------------------------------------------

# isort: split
from importlib.metadata import PackageNotFoundError
from importlib.metadata import version

try:
    __version__ = version("symforce")
except PackageNotFoundError:
    logger.debug(
        "symforce package is not being run from an installed context; falling back to"
        " setuptools_scm for __version__"
    )

    try:
        import setuptools_scm
    except ImportError:
        # setuptools_scm isn't required to be installed
        logger.debug("setuptools_scm not installed; __version__ will not be set")
    else:
        try:
            __version__ = setuptools_scm.get_version(root="..", relative_to=__file__)
        except LookupError:
            logger.debug("setuptools_scm failed to find version; __version__ will not be set")

```

--------------------------------

### Optimizer Creation with Numeric Factors from OptimizationProblem

Source: https://symforce.org/api/symforce.opt.optimizer.html

Shows how to create an Optimizer using numeric factors generated from an OptimizationProblem, with linearization performed with respect to the problem's optimized keys.

```python
problem = OptimizationProblem(subproblems=[...], residual_blocks=...)
factors = problem.make_numeric_factors("my_problem")
optimizer = Optimizer(factors)

```

--------------------------------

### NonlinearSolver

Source: https://symforce.org/api-cpp/class/classsym_1_1FixedSizeOptimizer.html

Get the NonlinearSolver object.

```APIDOC
## NonlinearSolver

### Description
Get the NonlinearSolver object.

### Signature
const NonlinearSolverType &NonlinearSolver() const

## NonlinearSolver

### Description
Get the NonlinearSolver object.

### Signature
NonlinearSolverType &NonlinearSolver()
```

--------------------------------

### Example Usage of pick_generated_keys_for_variable_names

Source: https://symforce.org/api/symforce.values.generated_key_selection.html

Demonstrates how to use the pick_generated_keys_for_variable_names function to map a list of variable names to generated keys. Shows the expected output format for various naming conventions.

```python
pick_generated_keys_for_variable_names(['foo', 'foo2', 'foo_bar', 'foo_bar2', 'foo_baz'])
```

```python
{
    'foo': ('f', None),
    'foo2': ('f', 2),
    'foo_bar': ('F', None),
    'foo_bar2': ('F', 2),
    'foo_baz': ('b', None)
}
```

--------------------------------

### get_scope

Source: https://symforce.org/api/symforce.internal.symbolic.html

Gets the current scope.

```APIDOC
## get_scope

### Description
Gets the current scope.

### Return Type
str
```

--------------------------------

### Initialize Optimizer with Factors

Source: https://symforce.org/index.html

Initialize an Optimizer with the defined factors and specify which keys to optimize. Debug statistics can be enabled for detailed iteration analysis.

```python
from symforce.opt.optimizer import Optimizer

optimizer = Optimizer(
    factors=factors,
    optimized_keys=[f"poses[{i}]" for i in range(num_poses)],
    # So that we save more information about each iteration, to visualize later:
    debug_stats=True,
)

```

--------------------------------

### EigenSparseSolver Usage Example

Source: https://symforce.org/api-cpp/file/eigen__sparse__solver_8h.html

Demonstrates how to use EigenSparseSolver with LevenbergMarquardtSolver and Optimizer. Requires including the eigen_sparse_solver.h header.

```cpp
using LinearSolver = 
    sym::EigenSparseSolver<double, Eigen::CholmodDecomposition<Eigen::SparseMatrix<double>>>;
using NonlinearSolver = sym::LevenbergMarquardtSolver<double, LinearSolver>;
using Optimizer = sym::Optimizer<double, NonlinearSolver>;

Optimizer optimizer{...};

```