```eval_rst
.. _data:
```

# Experimental data format
Experimental data should be provided in `.yaml` file.
In the case in which the dataset is made by multiple data points with several systematic uncertanties the sintax is the following

```yaml
dataset_name: example_dataset
num_data: 3
num_sys: 2
data_central:
- data1
- data2
- data3
statistical_error:
- sys1
- sys2
- sys3
systematics:
- - sys1_data1
  - sys1_data2
  - sys1_data3
- - sys2_data1
  - sys2_data2
  - sys2_data3
sys_names:
- CORR
- CORR
sys_type:
- MULT
- ADD
```

while if the dataset is made by a single data point

```yaml
dataset_name: example_dataset
num_data: 1
num_sys: 2
data_central: data1
statistical_error: stat1
systematics:
- sys1
- sys2
sys_names:
- CORR
- UNCORR
sys_type:
- MULT
- MULT

```
The systematic name can be ``CORR``, ``UNCORR`` to specify whether the systematic considered is correlated or uncorrelated within the dataset.
In the same way ``THEORYCORR`` and ``THEORYUNCORR`` can be used for correlated and uncorrelated theory systematics within a dataset.

For uncertainties correlated between different dataset a different name has to be used, which must be
the same for the corresponding systematic in all the datasets. For the details about the construction of the
covariance matrix from the list of statistic and systematic uncertainty see [here](./covariance.html#construction-of-the-covariance-matrix).

For some dataset only the full covariance matrix might be available. In order to use the dataset within the ``smefit`` code, the user has to decompose it in a set of correlated systematics,
see [here](./covariance.html#decomposition-of-experimental-covariance-matrix) for more details.

This can be easily done by decomposing the covariance into its eigenvectors

```math
  \text{cov}_{ij} = \sum_{k,h}\, u_{ik}\,\lambda_{k}\, \delta_{kh}\, u^T_{hj} = \sum_k \sigma^k_i \,\sigma^k_j\,,
```

with

```math
  \sigma^k_i = \sqrt{\lambda_k} \, u_{ik}\,,     \,\,\,\,\,\,\,\,\, i,k = 1,\,...\,,n_{dat}
```