Commit 8c1d9bc4 authored by Maximilian Schanner's avatar Maximilian Schanner
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Update Example_2_Integration.ipynb

parent 06db6989
......@@ -37,11 +37,11 @@
l_max=pars.l_max, scale=scale)
```
%% Cell type:markdown id: tags:
`integrate` first builds a grid over the region passed as the `bounds` argument, the `N` argument specifies the number of gridpoints per dimension. During the run an inversion for each gridpoint is performed. This way to each gridpoint there is an associated normal posterior for the quantities of interest (the magnetic field, Gauss coefficients etc.). The integration over this posteriors is performed by a weighted Riemann the sum, the weights given by the posterior probability of the gridpoint, i.e. the current choice of parameters. A sum of normal densities forms a [mixture distribution](https://en.wikipedia.org/wiki/Mixture_distribution). For later evaluation, the posterior on the grid as well as the posterior mean and covariance of the Gauss coefficients for each gridpoint is stored. The covariance for the field is too large to do so and thus along the way the mean and variance of the field-mixture are calculated and stored. `integrate` then returns an instance of the `IntegrationResult` class, which can be used to access the results and to write them to the disk. For illustration we show the posterior field and variance:
`integrate` first builds a grid over the region passed as the `bounds` argument, the `N` argument specifies the number of gridpoints per dimension. During the run an inversion for each gridpoint is performed. This way to each gridpoint an associated normal posterior for the quantities of interest (the magnetic field, Gauss coefficients etc.) is calculated. The integration over this posteriors is performed by a weighted Riemann the sum, the weights being given by the posterior probability of the gridpoint, i.e. the current choice of parameters. A sum of normal densities forms a [mixture distribution](https://en.wikipedia.org/wiki/Mixture_distribution). For later evaluation, the posterior on the grid as well as the posterior mean and covariance of the Gauss coefficients for each gridpoint are stored. The covariance for the field is too large to do so and thus along the way the mean and variance of the field-mixture are calculated and stored. `integrate` then returns an instance of the `IntegrationResult` class, which can be used to access the results and to write them to the disk. For illustration we show the posterior field and variance:
%% Cell type:code id: tags:
``` python
from matplotlib import pyplot as plt
......
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