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Add function and class (OOP) examples to Python lesson (#108)
* Minor text edits * Add module with an example funtion * Add example class to model diffusion * Remove lint * Update example to pass doctest * Rename advanced Python section * Swap the order of the last two topics
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| Original file line number | Diff line number | Diff line change |
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| """Modeling the one-dimensional diffusion equation.""" | ||
| import numpy as np | ||
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| class Diffusion: | ||
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| """Model one-dimensional diffusion with fixed boundary conditions. | ||
| Examples | ||
| -------- | ||
| >>> import numpy as np | ||
| >>> from diffusion import Diffusion | ||
| >>> m = Diffusion(diffusivity=0.25) | ||
| >>> m.concentration = np.zeros(m.shape) | ||
| >>> m.concentration[int(m.shape/2)] = 5 | ||
| >>> m.concentration | ||
| array([ 0.0, 0.0, 0.0, 0.0, 0.0, 5.0, 0.0, 0.0, 0.0, | ||
| 0.0]) | ||
| >>> m.time | ||
| 0.0 | ||
| >>> m.update() | ||
| >>> m.time | ||
| 1.0 | ||
| >>> m.concentration | ||
| array([ 0.0, 0.0, 0.0, 0.0, 1.2, 2.5, 1.2, 0.0, 0.0, | ||
| 0.0]) | ||
| """ | ||
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| def __init__(self, shape=10, spacing=1.0, diffusivity=1.0): | ||
| """Create a new diffusion model. | ||
| Parameters | ||
| --------- | ||
| shape : int, optional | ||
| The number of nodes in the solution grid. | ||
| spacing : float, optional | ||
| Grid spacing. | ||
| diffusivity : float, optional | ||
| Diffusivity. | ||
| """ | ||
| self.shape = shape | ||
| self.spacing = spacing | ||
| self.diffusivity = diffusivity | ||
| self.time = 0.0 | ||
| self.time_step = self.spacing**2 / (4.0 * self.diffusivity) | ||
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| self.concentration = np.random.random(self.shape) | ||
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| def solve(self): | ||
| """Solve the 1D diffusion equation.""" | ||
| flux = -self.diffusivity * np.diff(self.concentration) / self.spacing | ||
| self.concentration[1:-1] -= self.time_step * np.diff(flux) / self.spacing | ||
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| def update(self): | ||
| """Calculate concentration at the next time step.""" | ||
| self.solve() | ||
| self.time += self.time_step |
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| """A solver for the one-dimensional diffusion equation.""" | ||
| import numpy as np | ||
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| np.set_printoptions(formatter={"float": "{: 5.1f}".format}) | ||
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| def solve1d(concentration, spacing=1.0, time_step=1.0, diffusivity=1.0): | ||
| """Solve the one-dimensional diffusion equation with fixed boundary conditions. | ||
| Parameters | ||
| ---------- | ||
| concentration : ndarray | ||
| The quantity being diffused. | ||
| spacing : float (optional) | ||
| Grid spacing. | ||
| time_step : float (optional) | ||
| Time step. | ||
| alpha : float (optional) | ||
| Diffusivity. | ||
| Returns | ||
| ------- | ||
| result : ndarray | ||
| The temperatures after time *time_step*. | ||
| Examples | ||
| -------- | ||
| >>> import numpy as np | ||
| >>> from solver import solve1d | ||
| >>> z = np.zeros(5) | ||
| >>> z[2] = 5 | ||
| >>> solve1d(z, diffusivity=0.25) | ||
| array([ 0.0, 1.2, 2.5, 1.2, 0.0]) | ||
| """ | ||
| flux = -diffusivity * np.diff(concentration) / spacing | ||
| concentration[1:-1] -= time_step * np.diff(flux) / spacing | ||
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| return concentration | ||
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| def _run_example(): | ||
| """An example of running solve1d.""" | ||
| print(_run_example.__doc__) | ||
| D = 100 | ||
| Lx = 10 | ||
| dx = 0.5 | ||
| C1 = 500 | ||
| C2 = 0 | ||
| C = np.empty(Lx) | ||
| C[: int(Lx / 2)] = C1 | ||
| C[int(Lx / 2) :] = C2 | ||
| dt = dx * dx / D / 2.1 | ||
| print("Time = 0\n", C) | ||
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| for t in range(1, 3): | ||
| solve1d(C, dx, dt, D) | ||
| print(f"Time = {t}\n", C) | ||
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| if __name__ == "__main__": | ||
| _run_example() |