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docs: typos in documentation corrected.
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@ -26,7 +26,7 @@ print(my_new_obs) # Print the result to stdout
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# The `Obs` class
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# The `Obs` class
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`pyerrors` introduces a new datatype, `Obs`, which simplifies error propagation and estimation for auto- and cross-correlated data.
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`pyerrors` introduces a new datatype, `Obs`, which simplifies error propagation and estimation for auto- and cross-correlated data.
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An `Obs` object can be initialized with two arguments, the first is a list containing the samples for an Observable from a Monte Carlo chain.
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An `Obs` object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.
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The samples can either be provided as python list or as numpy array.
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The samples can either be provided as python list or as numpy array.
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The second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
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The second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
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@ -38,7 +38,7 @@ my_obs = pe.Obs([samples], ['ensemble_name'])
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## Error propagation
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## Error propagation
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When performing mathematical operations on `Obs` objects the correct error propagation is intrinsically taken care using a first order Taylor expansion
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When performing mathematical operations on `Obs` objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion
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$$\delta_f^i=\sum_\alpha \bar{f}_\alpha \delta_\alpha^i\,,\quad \delta_\alpha^i=a_\alpha^i-\bar{a}_\alpha\,,$$
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$$\delta_f^i=\sum_\alpha \bar{f}_\alpha \delta_\alpha^i\,,\quad \delta_\alpha^i=a_\alpha^i-\bar{a}_\alpha\,,$$
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as introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).
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as introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).
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The required derivatives $\bar{f}_\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289).
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The required derivatives $\bar{f}_\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289).
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@ -96,7 +96,7 @@ my_sum.details()
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The integrated autocorrelation time $\tau_\mathrm{int}$ and the autocorrelation function $\rho(W)$ can be monitored via the methods `pyerrors.obs.Obs.plot_tauint` and `pyerrors.obs.Obs.plot_tauint`.
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The integrated autocorrelation time $\tau_\mathrm{int}$ and the autocorrelation function $\rho(W)$ can be monitored via the methods `pyerrors.obs.Obs.plot_tauint` and `pyerrors.obs.Obs.plot_tauint`.
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If the parameter $S$ is set to zero it is assumed that dataset does not exhibit any autocorrelation and the windowsize is chosen to be zero.
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If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the windowsize is chosen to be zero.
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In this case the error estimate is identical to the sample standard error.
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In this case the error estimate is identical to the sample standard error.
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### Exponential tails
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### Exponential tails
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@ -285,7 +285,7 @@ import autograd.numpy as anp
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def func(a, x):
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def func(a, x):
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return a[1] * anp.exp(-a[0] * x)
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return a[1] * anp.exp(-a[0] * x)
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```
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```
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**It is important that numerical functions refer to `autograd.numpy` instead of `numpy` for the automatic differentiation to work properly.**
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**It is important that numerical functions refer to `autograd.numpy` instead of `numpy` for the automatic differentiation in iterative algorithms to work properly.**
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Fits can then be performed via
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Fits can then be performed via
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```python
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```python
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@ -339,7 +339,7 @@ For the full API see `pyerrors.linalg`.
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# Export data
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# Export data
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The preferred exported file format within `pyerrors` is json.gz. The exact specifications of this formats will be listed here soon.
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The preferred exported file format within `pyerrors` is json.gz. The exact specifications of this format will be listed here soon.
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## Jackknife samples
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## Jackknife samples
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For comparison with other analysis workflows `pyerrors` can generate jackknife samples from an `Obs` object or import jackknife samples into an `Obs` object.
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For comparison with other analysis workflows `pyerrors` can generate jackknife samples from an `Obs` object or import jackknife samples into an `Obs` object.
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