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11847606997

Pull #744

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Merge da1a22bdd into 7a0d42be3
Pull Request #744: Update release notes

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/src/scores/continuous/correlation/correlation_impl.py
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"""
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This module contains functions to calculate the correlation.
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"""
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from typing import Optional




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import xarray as xr




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import scores.utils




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from scores.typing import FlexibleDimensionTypes




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def pearsonr(




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    fcst: xr.DataArray,










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    obs: xr.DataArray,










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    *,  # Force keywords arguments to be keyword-only










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    reduce_dims: Optional[FlexibleDimensionTypes] = None,










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    preserve_dims: Optional[FlexibleDimensionTypes] = None,










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) -> xr.DataArray:










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    """










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    Calculates the Pearson's correlation coefficient between two xarray DataArrays










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    .. math::










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        \\rho = \\frac{\\sum_{i=1}^{n}{(x_i - \\bar{x})(y_i - \\bar{y})}}










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        {\\sqrt{\\sum_{i=1}^{n}{(x_i-\\bar{x})^2}\\sum_{i=1}^{n}{(y_i - \\bar{y})^2}}}










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    where:










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        - :math:`\\rho` = Pearson's correlation coefficient










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        - :math:`x_i` = the values of x in a sample (i.e. forecast values)










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        - :math:`\\bar{x}` = the mean value of the forecast sample










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        - :math:`y_i` = the values of y in a sample (i.e. observed values)










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        - :math:`\\bar{y}` = the mean value of the observed sample value










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    Args:










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        fcst: Forecast or predicted variables










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        obs: Observed variables.










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        reduce_dims: Optionally specify which dimensions to reduce when










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            calculating the Pearson's correlation coefficient.










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            All other dimensions will be preserved.










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        preserve_dims: Optionally specify which dimensions to preserve when










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            calculating the Pearson's correlation coefficient. All other dimensions will










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            be reduced. As a special case, 'all' will allow all dimensions to be










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            preserved. In this case, the result will be in the same shape/dimensionality










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            as the forecast, and the errors will be the absolute error at each










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            point (i.e. single-value comparison against observed), and the










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            forecast and observed dimensions must match precisely.










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    Returns:










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        xr.DataArray: An xarray object with Pearson's correlation coefficient values










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    Note:










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        This function isn't set up to take weights.










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    Reference:










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        https://en.wikipedia.org/wiki/Pearson_correlation_coefficient










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    """










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    reduce_dims = scores.utils.gather_dimensions(




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        fcst.dims, obs.dims, reduce_dims=reduce_dims, preserve_dims=preserve_dims










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    )










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    return xr.corr(fcst, obs, reduce_dims)




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