# Numpy metrics#

mae(y_hat: , y: , mask: = None, reduction: Literal['mean', 'sum', 'none'] = 'mean', nan_to_zero: bool = False) [source]#

Compute the Mean Absolute Error (MAE) between the estimate $$\hat{y}$$ and the true value $$y$$, i.e.

$\text{MAE} = \frac{\sum_{i=1}^n |\hat{y}_i - y_i|}{n}$
Parameters:
• y_hat (FrameArray) – The estimated variable.

• y (FrameArray) – The ground-truth variable.

• mask (FrameArray, optional) – If provided, compute the metric using only the values at valid indices (with mask set to True). If mask is not None and reduction is 'none', masked indices are set to nan (see nan_to_zero). (default: None)

• reduction (str) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. (default: 'mean')

• nan_to_zero (bool) – If True, then masked values in output are converted to 0. This has an effect only when mask is not None and reduction is 'none'. (default: False)

Returns:

The Mean Absolute Error.

Return type:

float | np.ndarray

nmae(y_hat: , y: , mask: = None, reduction: Literal['mean', 'sum', 'none'] = 'mean', nan_to_zero: bool = False) [source]#

Compute the Normalized Mean Absolute Error (NMAE) between the estimate $$\hat{y}$$ and the true value $$y$$. The NMAE is the Mean Absolute Error (MAE) scaled by the max-min range of the target data, i.e.

$\text{NMAE} = \frac{\frac{1}{N} \sum_{i=1}^n |\hat{y}_i - y_i|} {\max(y) - \min(y)}$
Parameters:
• y_hat (FrameArray) – The estimated variable.

• y (FrameArray) – The ground-truth variable.

• mask (FrameArray, optional) – If provided, compute the metric using only the values at valid indices (with mask set to True). If mask is not None and reduction is 'none', masked indices are set to nan (see nan_to_zero). (default: None)

• reduction (str) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. (default: 'mean')

• nan_to_zero (bool) – If True, then masked values in output are converted to 0. This has an effect only when mask is not None and reduction is 'none'. (default: False)

Returns:

The Normalized Mean Absolute Error

Return type:

float | np.ndarray

mape(y_hat: , y: , mask: = None, reduction: Literal['mean', 'sum', 'none'] = 'mean', nan_to_zero: bool = False) [source]#

Compute the Mean Absolute Percentage Error (MAPE). between the estimate $$\hat{y}$$ and the true value $$y$$, i.e.

$\text{MAPE} = \frac{1}{n} \sum_{i=1}^n \frac{|\hat{y}_i - y_i|} {y_i}$
Parameters:
• y_hat (FrameArray) – The estimated variable.

• y (FrameArray) – The ground-truth variable.

• mask (FrameArray, optional) – If provided, compute the metric using only the values at valid indices (with mask set to True). If mask is not None and reduction is 'none', masked indices are set to nan (see nan_to_zero). (default: None)

• reduction (str) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. (default: 'mean')

• nan_to_zero (bool) – If True, then masked values in output are converted to 0. This has an effect only when mask is not None and reduction is 'none'. (default: False)

Returns:

The Mean Absolute Percentage Error.

Return type:

float | np.ndarray

mse(y_hat: , y: , mask: = None, reduction: Literal['mean', 'sum', 'none'] = 'mean', nan_to_zero: bool = False) [source]#

Compute the Mean Squared Error (MSE) between the estimate $$\hat{y}$$ and the true value $$y$$, i.e.

$\text{MSE} = \frac{\sum_{i=1}^n (\hat{y}_i - y_i)^2}{n}$
Parameters:
• y_hat (FrameArray) – The estimated variable.

• y (FrameArray) – The ground-truth variable.

• mask (FrameArray, optional) – If provided, compute the metric using only the values at valid indices (with mask set to True). If mask is not None and reduction is 'none', masked indices are set to nan (see nan_to_zero). (default: None)

• reduction (str) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. (default: 'mean')

• nan_to_zero (bool) – If True, then masked values in output are converted to 0. This has an effect only when mask is not None and reduction is 'none'. (default: False)

Returns:

The Mean Squared Error.

Return type:

float | np.ndarray

rmse(y_hat: , y: , mask: = None, reduction: Literal['mean', 'sum', 'none'] = 'mean') [source]#

Compute the Root Mean Squared Error (RMSE) between the estimate $$\hat{y}$$ and the true value $$y$$, i.e.

$\text{RMSE} = \sqrt{\frac{\sum_{i=1}^n (\hat{y}_i - y_i)^2}{n}}$
Parameters:
• y_hat (FrameArray) – The estimated variable.

• y (FrameArray) – The ground-truth variable.

• mask (FrameArray, optional) – If provided, compute the metric using only the values at valid indices (with mask set to True). (default: None)

• reduction (str) – Specifies the reduction to apply to the output: 'mean' | 'sum'. 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. (default: 'mean')

Returns:

The Root Mean Squared Error.

Return type:

float

nrmse(y_hat: , y: , mask: = None, reduction: Literal['mean', 'sum', 'none'] = 'mean') [source]#

Compute the Normalized Root Mean Squared Error (NRMSE) between the estimate $$\hat{y}$$ and the true value $$y$$, i.e. Normalization is by the max-min range of the data

$\text{NRMSE} = \frac{\sqrt{\frac{\sum_{i=1}^n (\hat{y}_i - y_i)^2} {n}} }{\max y - \min y}$
Parameters:
• y_hat (FrameArray) – The estimated variable.

• y (FrameArray) – The ground-truth variable.

• mask (FrameArray, optional) – If provided, compute the metric using only the values at valid indices (with mask set to True).

• reduction (str) – Specifies the reduction to apply to the output: 'mean' | 'sum'. 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. (default: 'mean')

Returns:

The range-normalzized NRMSE

Return type:

float

nrmse_2(y_hat: , y: , mask: = None, reduction: Literal['mean', 'sum', 'none'] = 'mean') [source]#

Compute the Normalized Root Mean Squared Error (NRMSE) between the estimate $$\hat{y}$$ and the true value $$y$$, i.e. Normalization is by the power of the true signal $$y$$

$\text{NRMSE}_2 = \frac{\sqrt{\frac{\sum_{i=1}^n (\hat{y}_i - y_i)^2}{n}} }{\sum_{i=1}^n y_i^2}$
Parameters:
• y_hat (FrameArray) – The estimated variable.

• y (FrameArray) – The ground-truth variable.

• mask (FrameArray, optional) – If provided, compute the metric using only the values at valid indices (with mask set to True).

• reduction (str) – Specifies the reduction to apply to the output: 'mean' | 'sum'. 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. (default: 'mean')

Returns:

The power-normalzized NRMSE.

Return type:

float

r2(y_hat: , y: , mask: = None, reduction: Literal['mean', 'sum', 'none'] = 'mean', nan_to_zero: bool = False, mean_axis: = None) [source]#

Compute the coefficient of determination $$R^2$$ between the estimate $$\hat{y}$$ and the true value $$y$$, i.e.

$R^{2} = 1 - \frac{\sum_{i} (\hat{y}_i - y_i)^2} {\sum_{i} (\bar{y} - y_i)^2}$

where $$\bar{y}=\frac{1}{n}\sum_{i=1}^n y_i$$ is the mean of $$y$$.

Parameters:
• y_hat (FrameArray) – The estimated variable.

• y (FrameArray) – The ground-truth variable.

• mask (FrameArray, optional) – If provided, compute the metric using only the values at valid indices (with mask set to True).

• reduction (str) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the sum of the output will be divided by the number of elements in the output, 'sum': the output will be summed. (default: 'mean')

• nan_to_zero (bool) – If True, then masked values in output are converted to 0. This has an effect only when mask is not None and reduction is 'none'. (default: False)

• mean_axis (int, Tuple, optional) – the axis along which the mean of y is computed, to compute the variance of y needed in the denominator of the R2 formula.

Returns:

The $$R^2$$.

Return type:

float | np.ndarray

mre(y_hat: , y: , mask: = None) [source]#

Compute the MAE normalized by the L1-norm of the true signal $$y$$, i.e.

$\text{MRE} = \frac{\sum_{i=1}^n |\hat{y}_i - y_i|}{\sum_{i=1}^n |y_i|}$
Parameters:
• y_hat (FrameArray) – The estimated variable.

• y (tFrameArray) – The ground-truth variable.

• mask (FrameArray, optional) – If provided, compute the metric using only the values at valid indices (with mask set to True). (default: None)

Returns:

The computed MRE value.

Return type:

float