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@ -30,8 +30,49 @@ my_obs = pe.Obs([samples], ['ensemble_name'])
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## Multiple ensembles/replica
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Error propagation for multiple ensemblesi (Markov chains with different simulation parameters) are automatically handled.
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**Example:**
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```python
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import pyerrors as pe
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obs1 = pe.Obs([samples1], ['ensemble1'])
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obs2 = pe.Obs([samples1], ['ensemble2'])
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my_sum = obs1 + obs2
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my_sum.details()
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> Result 2.00596631e+00 +/- 0.00000000e+00 +/- 0.00000000e+00 (0.000%)
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> 1500 samples in 2 ensembles:
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> ensemble1: ['ensemble1']
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> ensemble2: ['ensemble2']
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```
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`pyerrors` identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar `|` in the name of the dataset.
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**Example:**
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```python
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import pyerrors as pe
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obs1 = pe.Obs([samples1], ['ensemble1|r01'])
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obs2 = pe.Obs([samples1], ['ensemble1|r02'])
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my_sum = obs1 + obs2
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my_sum.details()
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> Result 2.00596631e+00 +/- 0.00000000e+00 +/- 0.00000000e+00 (0.000%)
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> 1500 samples in 1 ensemble:
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> ensemble1: ['ensemble1|r01', 'ensemble1|r02']
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```
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## Irregular Monte Carlo chains
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```python
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import pyerrors as pe
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obs1 = pe.Obs([samples1], ['ensemble1|r01'])
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obs2 = pe.Obs([samples1], ['ensemble1|r02'])
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my_sum = obs1 + obs2
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```
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# Error propagation
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Automatic differentiation, cite Alberto,
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