66 lines
3.6 KiB
Plaintext
66 lines
3.6 KiB
Plaintext
{
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"# LinearContainerFactor Class Documentation\n",
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"\n",
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"*Disclaimer: This documentation was generated by AI and may require human revision for accuracy and completeness.*\n",
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"\n",
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"## Overview\n",
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"\n",
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"The `LinearContainerFactor` class in GTSAM is a specialized factor that encapsulates a linear factor within a nonlinear factor graph. This class allows for the seamless integration of linear factors into a nonlinear optimization problem, providing flexibility in problem modeling and solution.\n",
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"\n",
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"## Key Features\n",
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"\n",
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"- **Encapsulation of Linear Factors**: The primary function of the `LinearContainerFactor` is to store a linear factor and its associated values, enabling it to be used within a nonlinear context.\n",
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"- **Error Calculation**: It provides mechanisms to compute the error of the factor given a set of values.\n",
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"- **Jacobian Computation**: The class can compute the Jacobian matrix, which is essential for optimization processes.\n",
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"\n",
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"## Key Methods\n",
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"\n",
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"### Constructor\n",
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"\n",
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"- **LinearContainerFactor**: This constructor initializes the `LinearContainerFactor` with a linear factor and optionally with values. It serves as the entry point for creating an instance of this class.\n",
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"\n",
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"### Error Evaluation\n",
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"\n",
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"- **error**: This method calculates the error of the factor given a set of values. The error is typically defined as the difference between the predicted and observed measurements, and it plays a crucial role in optimization.\n",
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"\n",
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"### Jacobian Computation\n",
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"\n",
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"- **linearize**: This method computes the Jacobian matrix of the factor. The Jacobian is a matrix of partial derivatives that describes how the error changes with respect to changes in the variables. It is a critical component in gradient-based optimization algorithms.\n",
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"\n",
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"### Accessors\n",
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"\n",
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"- **keys**: This method returns the keys associated with the factor. Keys are identifiers for the variables involved in the factor, and they are essential for understanding the structure of the factor graph.\n",
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"\n",
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"### Utility Methods\n",
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"\n",
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"- **equals**: This method checks for equality between two `LinearContainerFactor` instances. It is useful for testing and validation purposes.\n",
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"\n",
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"## Mathematical Background\n",
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"\n",
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"The `LinearContainerFactor` operates within the context of factor graphs, where the goal is to minimize the total error across all factors. The error for a linear factor can be expressed as:\n",
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"\n",
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"$$ e(x) = A \\cdot x - b $$\n",
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"\n",
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"where $A$ is the coefficient matrix, $x$ is the vector of variables, and $b$ is the measurement vector. The optimization process aims to find the values of $x$ that minimize the sum of squared errors:\n",
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"\n",
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"$$ \\text{minimize} \\quad \\sum e(x)^T \\cdot e(x) $$\n",
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"\n",
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"The Jacobian matrix, which is derived from the linearization of the error function, is crucial for iterative optimization techniques such as Gauss-Newton or Levenberg-Marquardt.\n",
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"\n",
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"## Conclusion\n",
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"\n",
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"The `LinearContainerFactor` class is a powerful tool in GTSAM for integrating linear factors into nonlinear optimization problems. By providing mechanisms for error evaluation and Jacobian computation, it facilitates the efficient solution of complex estimation problems in robotics and computer vision."
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