68 lines
4.1 KiB
Plaintext
68 lines
4.1 KiB
Plaintext
{
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{
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"cell_type": "markdown",
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"id": "59407eaf",
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"metadata": {},
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"source": [
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"# ExpressionFactor 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 `ExpressionFactor` class in GTSAM is a template class designed to work with factor graphs in the context of nonlinear optimization. It represents a factor that can be constructed from an expression, allowing for flexible and efficient computation of error terms in optimization problems.\n",
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"\n",
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"## Key Features\n",
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"\n",
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"- **Expression-Based Factor**: The `ExpressionFactor` class allows users to define factors based on expressions, which can represent complex mathematical relationships between variables.\n",
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"- **Error Calculation**: It computes the error based on the difference between the predicted and observed values, typically used in least-squares optimization.\n",
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"- **Jacobian Computation**: The class can compute the Jacobian matrix, which is essential for gradient-based optimization methods.\n",
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"\n",
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"## Main Methods\n",
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"\n",
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"### Constructor\n",
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"\n",
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"The `ExpressionFactor` class provides constructors that allow for the initialization of the factor with a specific expression and measurement. The constructors are designed to handle various types of expressions and measurements, making the class versatile for different applications.\n",
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"\n",
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"### `evaluateError`\n",
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"\n",
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"This method calculates the error vector for the factor. The error is typically defined as the difference between the predicted value from the expression and the actual measurement. Mathematically, this can be represented as:\n",
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"\n",
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"$$\n",
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"\\text{error} = \\text{measurement} - \\text{expression}\n",
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"$$\n",
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"\n",
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"where `measurement` is the observed value, and `expression` is the predicted value based on the current estimate of the variables.\n",
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"\n",
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"### `linearize`\n",
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"\n",
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"The `linearize` method is used to linearize the factor around a given linearization point. This involves computing the Jacobian matrix, which represents the partial derivatives of the error with respect to the variables. The Jacobian is crucial for iterative optimization algorithms such as Gauss-Newton or Levenberg-Marquardt.\n",
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"\n",
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"### `clone`\n",
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"\n",
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"The `clone` method creates a deep copy of the factor. This is useful when factors need to be duplicated, ensuring that changes to one copy do not affect the other.\n",
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"\n",
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"## Mathematical Background\n",
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"\n",
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"The `ExpressionFactor` class is grounded in the principles of nonlinear optimization, particularly in the context of factor graphs. Factor graphs are bipartite graphs used to represent the factorization of a function, often used in probabilistic graphical models and optimization problems.\n",
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"\n",
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"In the context of GTSAM, factors represent constraints or relationships between variables. The `ExpressionFactor` allows these relationships to be defined using mathematical expressions, providing a flexible and powerful tool for modeling complex systems.\n",
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"\n",
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"## Usage\n",
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"\n",
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"The `ExpressionFactor` class is typically used in scenarios where the relationships between variables can be naturally expressed as mathematical expressions. This includes applications in robotics, computer vision, and other fields where optimization problems are prevalent.\n",
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"\n",
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"By leveraging the power of expressions, users can define custom factors that capture the nuances of their specific problem, leading to more accurate and efficient optimization solutions.\n",
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"\n",
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"---\n",
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"\n",
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"This documentation provides a high-level overview of the `ExpressionFactor` class, highlighting its main features and methods. For detailed usage and examples, users should refer to the GTSAM library documentation and source code."
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