Code generation for partial derivatives of the vectorfield #36
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enhancement idea
Suggestion or request for new features/enhancing changes
help wanted
Extra attention is needed
In its current state, PyRates generates code for a backend-specific function that evaluates the right-hand-side of a differential equation system$\dot y = f(y, \theta, t)$ .$f(y, \theta, t)$ can help to apply numerical algorithms to the DE system. For example, the Jacobian $J_{ij} = \frac{\partial f_i}{\partial y_j}$ can be required for certain gradient-based parameter optimization problems, and the partial derivatives $\frac{\partial f_i}{\partial \theta_j}$ can be used to improve the accuracy and speed of parameter continuation algorithms.
In many cases, partial derivatives of
As a new feature, I suggest to leverage the sympy-based parser of PyRates to analytically find these partial derivatives, if possible, and generate additional code that implements functionals$g(f, y, \theta)$ that compute the partial derivatives based on the current state and vectorfield of the system.
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