solve_survival.py

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High-level description

This code implements a numerical solver for the generating function of a branching process, assuming diffusive changes in fitness over time. It provides solutions for the lineage propagator, considering the non-sampling constraint.

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Code Structure

The code defines a class survival_gen_func that encapsulates the logic for solving the generating function and lineage propagator. It uses numerical integration methods like integrate_rk4 (a 4th order Runge-Kutta implementation) and scipy.integrate.odeint. The class stores precomputed solutions in the phi_solutions dictionary for efficiency.

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Symbols

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survival_gen_func

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Description

This class provides methods to solve for the generating function of a branching process and the lineage propagator, considering non-branching.

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Inputs

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Outputs

The class itself does not return any output. Its methods return the computed solutions.

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Internal Logic

The class initializes with a fitness grid and precomputes values for numerical efficiency. It stores solutions in the phi_solutions dictionary. The main methods are:

• integrate_phi: Solves the generating function equation for given parameters.
• dphi: Computes the time derivative of the generating function.
• integrate_prop_odeint: Integrates the lineage propagator using scipy.integrate.odeint.
• integrate_prop: Integrates the lineage propagator using the custom integrate_rk4 method.
• dprop_backward: Computes the time derivative of the propagator.

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integrate_rk4

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Description

This function implements a 4th order Runge-Kutta integration scheme with a fixed time step.

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Inputs

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Outputs

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non_negativity_cutoff

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Description

A global variable defining the minimum allowed value for the solutions, used to avoid numerical issues with very small or negative values.

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Error Handling

The code uses np.maximum to ensure non-negativity of the solutions, replacing values below non_negativity_cutoff with the cutoff value. It also includes checks for valid time ranges within the dprop_backward method and prints warning messages if necessary.

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Performance Considerations

The code uses a custom integrate_rk4 implementation instead of scipy.integrate.odeint for the lineage propagator integration, claiming better performance for systems with different convergence criteria. The phi_solutions dictionary stores precomputed generating function solutions to avoid redundant computations.