Metric(评价指标) 模块¶

`ppsci.metric` ¶

`Metric` ¶

Bases: Layer

Base class for metric.

Source code in ppsci/metric/base.py

class Metric(nn.Layer):
    """Base class for metric."""

    def __init__(self, keep_batch: bool = False):
        super().__init__()
        self.keep_batch = keep_batch

`FunctionalMetric` ¶

Bases: Metric

Functional metric class, which allows to use custom metric computing function from given metric_expr for complex computation cases.

Parameters:

Name	Type	Description	Default
`metric_expr`	`Callable`	Expression of metric calculation.	required
`keep_batch`	`bool`	Whether keep batch axis. Defaults to False.	`False`

Examples:

>>> import paddle
>>> from ppsci.metric import FunctionalMetric
>>> def metric_expr(output_dict, *args):
...     rel_l2 = 0
...     for key in output_dict:
...         length = int(len(output_dict[key])/2)
...         out_dict = output_dict[key][:length]
...         label_dict = output_dict[key][length:]
...         rel_l2 += paddle.norm(out_dict - label_dict) / paddle.norm(label_dict)
...     return {"rel_l2": rel_l2}
>>> metric_dict = FunctionalMetric(metric_expr)
>>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3], [-0.2, 1.5], [-0.1, -0.3]]),
...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3], [-1.8, 1.0], [-0.2, 2.5]])}
>>> result = metric_dict(output_dict)
>>> print(result)
{'rel_l2': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       2.59985542)}

Source code in ppsci/metric/func.py

class FunctionalMetric(base.Metric):
    r"""Functional metric class, which allows to use custom metric computing function from given metric_expr for complex computation cases.

    Args:
        metric_expr (Callable): Expression of metric calculation.
        keep_batch (bool, optional): Whether keep batch axis. Defaults to False.

    Examples:
        >>> import paddle
        >>> from ppsci.metric import FunctionalMetric
        >>> def metric_expr(output_dict, *args):
        ...     rel_l2 = 0
        ...     for key in output_dict:
        ...         length = int(len(output_dict[key])/2)
        ...         out_dict = output_dict[key][:length]
        ...         label_dict = output_dict[key][length:]
        ...         rel_l2 += paddle.norm(out_dict - label_dict) / paddle.norm(label_dict)
        ...     return {"rel_l2": rel_l2}
        >>> metric_dict = FunctionalMetric(metric_expr)
        >>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3], [-0.2, 1.5], [-0.1, -0.3]]),
        ...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3], [-1.8, 1.0], [-0.2, 2.5]])}
        >>> result = metric_dict(output_dict)
        >>> print(result)
        {'rel_l2': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               2.59985542)}
    """

    def __init__(
        self,
        metric_expr: Callable,
        keep_batch: bool = False,
    ):
        super().__init__(keep_batch)
        self.metric_expr = metric_expr

    def forward(self, output_dict, label_dict=None) -> Dict[str, "paddle.Tensor"]:
        return self.metric_expr(output_dict, label_dict)

`MAE` ¶

Bases: Metric

Mean absolute error.

\[ metric = \dfrac{1}{N} \Vert \mathbf{x} - \mathbf{y} \Vert_1 \]

\[ \mathbf{x}, \mathbf{y} \in \mathcal{R}^{N} \]

Parameters:

Name	Type	Description	Default
`keep_batch`	`bool`	Whether keep batch axis. Defaults to False.	`False`

Examples:

>>> import paddle
>>> from ppsci.metric import MAE
>>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]]),
...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]])}
>>> label_dict = {'u': paddle.to_tensor([[-1.8, 1.0], [-0.2, 2.5]]),
...               'v': paddle.to_tensor([[0.1, 0.1], [0.1, 0.1]])}
>>> loss = MAE()
>>> result = loss(output_dict, label_dict)
>>> print(result)
{'u': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       1.87500000), 'v': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       0.89999998)}
>>> loss = MAE(keep_batch=True)
>>> result = loss(output_dict, label_dict)
>>> print(result)
{'u': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       [1.20000005, 2.54999995]), 'v': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       [0.59999996, 1.20000005])}

Source code in ppsci/metric/mae.py

class MAE(base.Metric):
    r"""Mean absolute error.

    $$
    metric = \dfrac{1}{N} \Vert \mathbf{x} - \mathbf{y} \Vert_1
    $$

    $$
    \mathbf{x}, \mathbf{y} \in \mathcal{R}^{N}
    $$

    Args:
        keep_batch (bool, optional): Whether keep batch axis. Defaults to False.

    Examples:
        >>> import paddle
        >>> from ppsci.metric import MAE
        >>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]]),
        ...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]])}
        >>> label_dict = {'u': paddle.to_tensor([[-1.8, 1.0], [-0.2, 2.5]]),
        ...               'v': paddle.to_tensor([[0.1, 0.1], [0.1, 0.1]])}
        >>> loss = MAE()
        >>> result = loss(output_dict, label_dict)
        >>> print(result)
        {'u': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               1.87500000), 'v': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               0.89999998)}
        >>> loss = MAE(keep_batch=True)
        >>> result = loss(output_dict, label_dict)
        >>> print(result)
        {'u': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               [1.20000005, 2.54999995]), 'v': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               [0.59999996, 1.20000005])}
    """

    def __init__(self, keep_batch: bool = False):
        super().__init__(keep_batch)

    @paddle.no_grad()
    def forward(self, output_dict, label_dict) -> Dict[str, "paddle.Tensor"]:
        metric_dict = {}
        for key in label_dict:
            mae = F.l1_loss(output_dict[key], label_dict[key], "none")
            if self.keep_batch:
                metric_dict[key] = mae.mean(axis=tuple(range(1, mae.ndim)))
            else:
                metric_dict[key] = mae.mean()

        return metric_dict

`MSE` ¶

Bases: Metric

Mean square error

\[ metric = \dfrac{1}{N} \Vert \mathbf{x} - \mathbf{y} \Vert_2^2 \]

\[ \mathbf{x}, \mathbf{y} \in \mathcal{R}^{N} \]

Parameters:

Name	Type	Description	Default
`keep_batch`	`bool`	Whether keep batch axis. Defaults to False.	`False`

Examples:

>>> import paddle
>>> from ppsci.metric import MSE
>>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]]),
...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]])}
>>> label_dict = {'u': paddle.to_tensor([[-1.8, 1.0], [-0.2, 2.5]]),
...               'v': paddle.to_tensor([[0.1, 0.1], [0.1, 0.1]])}
>>> loss = MSE()
>>> result = loss(output_dict, label_dict)
>>> print(result)
{'u': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       5.35750008), 'v': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       0.94000000)}
>>> loss = MSE(keep_batch=True)
>>> result = loss(output_dict, label_dict)
>>> print(result)
{'u': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       [2.65000010, 8.06499958]), 'v': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       [0.39999998, 1.48000002])}

Source code in ppsci/metric/mse.py

class MSE(base.Metric):
    r"""Mean square error

    $$
    metric = \dfrac{1}{N} \Vert \mathbf{x} - \mathbf{y} \Vert_2^2
    $$

    $$
    \mathbf{x}, \mathbf{y} \in \mathcal{R}^{N}
    $$

    Args:
        keep_batch (bool, optional): Whether keep batch axis. Defaults to False.

    Examples:
        >>> import paddle
        >>> from ppsci.metric import MSE
        >>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]]),
        ...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]])}
        >>> label_dict = {'u': paddle.to_tensor([[-1.8, 1.0], [-0.2, 2.5]]),
        ...               'v': paddle.to_tensor([[0.1, 0.1], [0.1, 0.1]])}
        >>> loss = MSE()
        >>> result = loss(output_dict, label_dict)
        >>> print(result)
        {'u': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               5.35750008), 'v': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               0.94000000)}
        >>> loss = MSE(keep_batch=True)
        >>> result = loss(output_dict, label_dict)
        >>> print(result)
        {'u': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               [2.65000010, 8.06499958]), 'v': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               [0.39999998, 1.48000002])}
    """

    def __init__(self, keep_batch: bool = False):
        super().__init__(keep_batch)

    @paddle.no_grad()
    def forward(self, output_dict, label_dict) -> Dict[str, "paddle.Tensor"]:
        metric_dict = {}
        for key in label_dict:
            mse = F.mse_loss(output_dict[key], label_dict[key], "none")
            if self.keep_batch:
                metric_dict[key] = mse.mean(axis=tuple(range(1, mse.ndim)))
            else:
                metric_dict[key] = mse.mean()

        return metric_dict

`RMSE` ¶

Bases: Metric

Root mean square error

\[ metric = \sqrt{\dfrac{1}{N} \Vert \mathbf{x} - \mathbf{y} \Vert_2^2} \]

\[ \mathbf{x}, \mathbf{y} \in \mathcal{R}^{N} \]

Parameters:

Name	Type	Description	Default
`keep_batch`	`bool`	Whether keep batch axis. Defaults to False.	`False`

Examples:

>>> import paddle
>>> from ppsci.metric import RMSE
>>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]]),
...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]])}
>>> label_dict = {'u': paddle.to_tensor([[-1.8, 1.0], [-0.2, 2.5]]),
...               'v': paddle.to_tensor([[0.1, 0.1], [0.1, 0.1]])}
>>> loss = RMSE()
>>> result = loss(output_dict, label_dict)
>>> print(result)
{'u': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       2.31462741), 'v': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       0.96953595)}

Source code in ppsci/metric/rmse.py

class RMSE(base.Metric):
    r"""Root mean square error

    $$
    metric = \sqrt{\dfrac{1}{N} \Vert \mathbf{x} - \mathbf{y} \Vert_2^2}
    $$

    $$
    \mathbf{x}, \mathbf{y} \in \mathcal{R}^{N}
    $$

    Args:
        keep_batch (bool, optional): Whether keep batch axis. Defaults to False.

    Examples:
        >>> import paddle
        >>> from ppsci.metric import RMSE
        >>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]]),
        ...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]])}
        >>> label_dict = {'u': paddle.to_tensor([[-1.8, 1.0], [-0.2, 2.5]]),
        ...               'v': paddle.to_tensor([[0.1, 0.1], [0.1, 0.1]])}
        >>> loss = RMSE()
        >>> result = loss(output_dict, label_dict)
        >>> print(result)
        {'u': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               2.31462741), 'v': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               0.96953595)}
    """

    def __init__(self, keep_batch: bool = False):
        if keep_batch:
            raise ValueError(f"keep_batch should be False, but got {keep_batch}.")
        super().__init__(keep_batch)

    @paddle.no_grad()
    def forward(self, output_dict, label_dict) -> Dict[str, "paddle.Tensor"]:
        metric_dict = {}
        for key in label_dict:
            rmse = F.mse_loss(output_dict[key], label_dict[key], "mean") ** 0.5
            metric_dict[key] = rmse

        return metric_dict

`L2Rel` ¶

Bases: Metric

Class for l2 relative error.

NOTE: This metric API is slightly different from MeanL2Rel, difference is as below:

L2Rel regards the input sample as a whole and calculates the l2 relative error of the whole;
MeanL2Rel will calculate L2Rel separately for each input sample and return the average of l2 relative error for all samples.

\[ metric = \dfrac{\Vert \mathbf{x} - \mathbf{y} \Vert_2}{\max(\Vert \mathbf{y} \Vert_2, \epsilon)} \]

\[ \mathbf{x}, \mathbf{y} \in \mathcal{R}^{N} \]

Parameters:

Name	Type	Description	Default
`keep_batch`	`bool`	Whether keep batch axis. Defaults to False.	`False`

Examples:

>>> import paddle
>>> from ppsci.metric import L2Rel
>>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]]),
...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]])}
>>> label_dict = {'u': paddle.to_tensor([[-1.8, 1.0], [-0.2, 2.5]]),
...               'v': paddle.to_tensor([[0.1, 0.1], [0.1, 0.1]])}
>>> loss = L2Rel()
>>> result = loss(output_dict, label_dict)
>>> print(result)
{'u': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       1.42658269), 'v': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       9.69535923)}

Source code in ppsci/metric/l2_rel.py

class L2Rel(base.Metric):
    r"""Class for l2 relative error.

    NOTE: This metric API is slightly different from `MeanL2Rel`, difference is as below:

    - `L2Rel` regards the input sample as a whole and calculates the l2 relative error of the whole;
    - `MeanL2Rel` will calculate L2Rel separately for each input sample and return the average of l2 relative error for all samples.

    $$
    metric = \dfrac{\Vert \mathbf{x} - \mathbf{y} \Vert_2}{\max(\Vert \mathbf{y} \Vert_2, \epsilon)}
    $$

    $$
    \mathbf{x}, \mathbf{y} \in \mathcal{R}^{N}
    $$

    Args:
        keep_batch (bool, optional): Whether keep batch axis. Defaults to False.

    Examples:
        >>> import paddle
        >>> from ppsci.metric import L2Rel
        >>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]]),
        ...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]])}
        >>> label_dict = {'u': paddle.to_tensor([[-1.8, 1.0], [-0.2, 2.5]]),
        ...               'v': paddle.to_tensor([[0.1, 0.1], [0.1, 0.1]])}
        >>> loss = L2Rel()
        >>> result = loss(output_dict, label_dict)
        >>> print(result)
        {'u': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               1.42658269), 'v': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               9.69535923)}
    """

    # NOTE: Avoid divide by zero in result
    # see https://github.com/scikit-learn/scikit-learn/pull/15007
    EPS: float = np.finfo(np.float32).eps

    def __init__(self, keep_batch: bool = False):
        if keep_batch:
            raise ValueError(f"keep_batch should be False, but got {keep_batch}.")
        super().__init__(keep_batch)

    @paddle.no_grad()
    def forward(self, output_dict, label_dict) -> Dict[str, "paddle.Tensor"]:
        metric_dict = {}
        for key in label_dict:
            rel_l2 = paddle.norm(label_dict[key] - output_dict[key], p=2) / paddle.norm(
                label_dict[key], p=2
            ).clip(min=self.EPS)
            metric_dict[key] = rel_l2

        return metric_dict

`MeanL2Rel` ¶

Bases: Metric

Class for mean l2 relative error.

NOTE: This metric API is slightly different from L2Rel, difference is as below:

MeanL2Rel will calculate L2Rel separately for each input sample and return the average of l2 relative error for all samples.
L2Rel regards the input sample as a whole and calculates the l2 relative error of the whole;

\[ metric = \dfrac{1}{M} \sum_{i=1}^{M}\dfrac{\Vert \mathbf{x_i} - \mathbf{y_i} \Vert_2}{\max(\Vert \mathbf{y_i} \Vert_2, \epsilon) } \]

\[ \mathbf{x_i}, \mathbf{y_i} \in \mathcal{R}^{N} \]

Parameters:

Name	Type	Description	Default
`keep_batch`	`bool`	Whether keep batch axis. Defaults to False.	`False`

Examples:

>>> import paddle
>>> from ppsci.metric import MeanL2Rel
>>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]]),
...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]])}
>>> label_dict = {'u': paddle.to_tensor([[-1.8, 1.0], [-0.2, 2.5]]),
...               'v': paddle.to_tensor([[0.1, 0.1], [0.1, 0.1]])}
>>> loss = MeanL2Rel()
>>> result = loss(output_dict, label_dict)
>>> print(result)
{'u': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       1.35970235), 'v': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       9.24504089)}
>>> loss = MeanL2Rel(keep_batch=True)
>>> result = loss(output_dict, label_dict)
>>> print(result)
{'u': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       [1.11803389, 1.60137081]), 'v': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
       [6.32455540 , 12.16552544])}

Source code in ppsci/metric/l2_rel.py

class MeanL2Rel(base.Metric):
    r"""Class for mean l2 relative error.

    NOTE: This metric API is slightly different from `L2Rel`, difference is as below:

    - `MeanL2Rel` will calculate L2Rel separately for each input sample and return the average of l2 relative error for all samples.
    - `L2Rel` regards the input sample as a whole and calculates the l2 relative error of the whole;

    $$
    metric = \dfrac{1}{M} \sum_{i=1}^{M}\dfrac{\Vert \mathbf{x_i} - \mathbf{y_i} \Vert_2}{\max(\Vert \mathbf{y_i} \Vert_2, \epsilon) }
    $$

    $$
    \mathbf{x_i}, \mathbf{y_i} \in \mathcal{R}^{N}
    $$

    Args:
        keep_batch (bool, optional): Whether keep batch axis. Defaults to False.

    Examples:
        >>> import paddle
        >>> from ppsci.metric import MeanL2Rel
        >>> output_dict = {'u': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]]),
        ...                'v': paddle.to_tensor([[0.5, 0.9], [1.1, -1.3]])}
        >>> label_dict = {'u': paddle.to_tensor([[-1.8, 1.0], [-0.2, 2.5]]),
        ...               'v': paddle.to_tensor([[0.1, 0.1], [0.1, 0.1]])}
        >>> loss = MeanL2Rel()
        >>> result = loss(output_dict, label_dict)
        >>> print(result)
        {'u': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               1.35970235), 'v': Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               9.24504089)}
        >>> loss = MeanL2Rel(keep_batch=True)
        >>> result = loss(output_dict, label_dict)
        >>> print(result)
        {'u': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               [1.11803389, 1.60137081]), 'v': Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True,
               [6.32455540 , 12.16552544])}
    """

    # NOTE: Avoid divide by zero in result
    # see https://github.com/scikit-learn/scikit-learn/pull/15007
    EPS: float = np.finfo(np.float32).eps

    def __init__(self, keep_batch: bool = False):
        super().__init__(keep_batch)

    @paddle.no_grad()
    def forward(self, output_dict, label_dict) -> Dict[str, "paddle.Tensor"]:
        metric_dict = {}
        for key in label_dict:
            rel_l2 = paddle.norm(
                label_dict[key] - output_dict[key], p=2, axis=1
            ) / paddle.norm(label_dict[key], p=2, axis=1).clip(min=self.EPS)
            if self.keep_batch:
                metric_dict[key] = rel_l2
            else:
                metric_dict[key] = rel_l2.mean()

        return metric_dict

`LatitudeWeightedACC` ¶

Bases: Metric

Latitude weighted anomaly correlation coefficient.

\[ metric = \dfrac{\sum\limits_{m,n}{L_mX_{mn}Y_{mn}}}{\sqrt{\sum\limits_{m,n}{L_mX_{mn}^{2}}\sum\limits_{m,n}{L_mY_{mn}^{2}}}} \]

\[ L_m = N_{lat}\dfrac{\cos(lat_m)}{\sum\limits_{j=1}^{N_{lat}}\cos(lat_j)} \]

\(lat_m\) is the latitude at m. \(N_{lat}\) is the number of latitude set by num_lat.

Parameters:

Name	Type	Description	Default
`num_lat`	`int`	Number of latitude.	required
`mean`	`Optional[Union[array, Tuple[float, ...]]]`	Mean of training data. Defaults to None.	required
`keep_batch`	`bool`	Whether keep batch axis. Defaults to False.	`False`
`variable_dict`	`Optional[Dict[str, int]]`	Variable dictionary, the key is the name of a variable and the value is its index. Defaults to None.	`None`
`unlog`	`bool`	Whether calculate expm1 for all elements in the array. Defaults to False.	`False`
`scale`	`float`	The scale value used after expm1. Defaults to 1e-5.	`1e-05`

Examples:

>>> import numpy as np
>>> import ppsci
>>> mean = np.random.randn(20, 720, 1440)
>>> metric = ppsci.metric.LatitudeWeightedACC(720, mean=mean)

Source code in ppsci/metric/anomaly_coef.py

class LatitudeWeightedACC(base.Metric):
    r"""Latitude weighted anomaly correlation coefficient.

    $$
    metric =
        \dfrac{\sum\limits_{m,n}{L_mX_{mn}Y_{mn}}}{\sqrt{\sum\limits_{m,n}{L_mX_{mn}^{2}}\sum\limits_{m,n}{L_mY_{mn}^{2}}}}
    $$

    $$
    L_m = N_{lat}\dfrac{\cos(lat_m)}{\sum\limits_{j=1}^{N_{lat}}\cos(lat_j)}
    $$

    $lat_m$ is the latitude at m.
    $N_{lat}$ is the number of latitude set by `num_lat`.

    Args:
        num_lat (int): Number of latitude.
        mean (Optional[Union[np.array, Tuple[float, ...]]]): Mean of training data. Defaults to None.
        keep_batch (bool, optional): Whether keep batch axis. Defaults to False.
        variable_dict (Optional[Dict[str, int]]): Variable dictionary, the key is the name of a variable and
            the value is its index. Defaults to None.
        unlog (bool, optional): Whether calculate expm1 for all elements in the array. Defaults to False.
        scale (float, optional): The scale value used after expm1. Defaults to 1e-5.

    Examples:
        >>> import numpy as np
        >>> import ppsci
        >>> mean = np.random.randn(20, 720, 1440)
        >>> metric = ppsci.metric.LatitudeWeightedACC(720, mean=mean)
    """

    def __init__(
        self,
        num_lat: int,
        mean: Optional[Union[np.array, Tuple[float, ...]]],
        keep_batch: bool = False,
        variable_dict: Optional[Dict[str, int]] = None,
        unlog: bool = False,
        scale: float = 1e-5,
    ):
        super().__init__(keep_batch)
        self.num_lat = num_lat
        self.mean = (
            None if mean is None else paddle.to_tensor(mean, paddle.get_default_dtype())
        )
        self.variable_dict = variable_dict
        self.unlog = unlog
        self.scale = scale

        self.weight = self.get_latitude_weight(num_lat)

    def get_latitude_weight(self, num_lat: int = 720):
        lat_t = paddle.linspace(start=0, stop=1, num=num_lat)
        lat_t = paddle.cos(3.1416 * (0.5 - lat_t))
        weight = num_lat * lat_t / paddle.sum(lat_t)
        weight = weight.reshape((1, 1, -1, 1))
        return weight

    def scale_expm1(self, x: paddle.Tensor):
        return self.scale * paddle.expm1(x)

    @paddle.no_grad()
    def forward(self, output_dict, label_dict) -> Dict[str, "paddle.Tensor"]:
        metric_dict = {}

        for key in label_dict:
            output = (
                self.scale_expm1(output_dict[key]) if self.unlog else output_dict[key]
            )
            label = self.scale_expm1(label_dict[key]) if self.unlog else label_dict[key]

            if self.mean is not None:
                output = output - self.mean
                label = label - self.mean

            rmse = paddle.sum(
                self.weight * output * label, axis=(-1, -2)
            ) / paddle.sqrt(
                paddle.sum(self.weight * output**2, axis=(-1, -2))
                * paddle.sum(self.weight * label**2, axis=(-1, -2))
            )

            if self.variable_dict is not None:
                for variable_name, idx in self.variable_dict.items():
                    if self.keep_batch:
                        metric_dict[f"{key}.{variable_name}"] = rmse[:, idx]
                    else:
                        metric_dict[f"{key}.{variable_name}"] = rmse[:, idx].mean()
            else:
                if self.keep_batch:
                    metric_dict[key] = rmse.mean(axis=1)
                else:
                    metric_dict[key] = rmse.mean()

        return metric_dict

`LatitudeWeightedRMSE` ¶

Bases: Metric

Latitude weighted root mean square error.

\[ metric =\sqrt{\dfrac{1}{MN}\sum\limits_{m=1}^{M}\sum\limits_{n=1}^{N}L_m(X_{mn}-Y_{mn})^{2}} \]

\[ L_m = N_{lat}\dfrac{\cos(lat_m)}{\sum\limits_{j=1}^{N_{lat}}\cos(lat_j)} \]

\(lat_m\) is the latitude at m. \(N_{lat}\) is the number of latitude set by num_lat.

Parameters:

Name	Type	Description	Default
`num_lat`	`int`	Number of latitude.	required
`std`	`Optional[Union[array, Tuple[float, ...]]]`	Standard Deviation of training dataset. Defaults to None.	`None`
`keep_batch`	`bool`	Whether keep batch axis. Defaults to False.	`False`
`variable_dict`	`Optional[Dict[str, int]]`	Variable dictionary, the key is the name of a variable and the value is its index. Defaults to None.	`None`
`unlog`	`bool`	Whether calculate expm1 for all elements in the array. Defaults to False.	`False`
`scale`	`float`	The scale value used after expm1. Defaults to 1e-5.	`1e-05`

Examples:

>>> import numpy as np
>>> import ppsci
>>> std = np.random.randn(20, 1, 1)
>>> metric = ppsci.metric.LatitudeWeightedRMSE(720, std=std)

Source code in ppsci/metric/rmse.py

class LatitudeWeightedRMSE(base.Metric):
    r"""Latitude weighted root mean square error.

    $$
    metric =\sqrt{\dfrac{1}{MN}\sum\limits_{m=1}^{M}\sum\limits_{n=1}^{N}L_m(X_{mn}-Y_{mn})^{2}}
    $$

    $$
    L_m = N_{lat}\dfrac{\cos(lat_m)}{\sum\limits_{j=1}^{N_{lat}}\cos(lat_j)}
    $$

    $lat_m$ is the latitude at m.
    $N_{lat}$ is the number of latitude set by `num_lat`.

    Args:
        num_lat (int): Number of latitude.
        std (Optional[Union[np.array, Tuple[float, ...]]]): Standard Deviation of training dataset. Defaults to None.
        keep_batch (bool, optional): Whether keep batch axis. Defaults to False.
        variable_dict (Optional[Dict[str, int]]): Variable dictionary, the key is the name of a variable and
            the value is its index. Defaults to None.
        unlog (bool, optional): Whether calculate expm1 for all elements in the array. Defaults to False.
        scale (float, optional): The scale value used after expm1. Defaults to 1e-5.

    Examples:
        >>> import numpy as np
        >>> import ppsci
        >>> std = np.random.randn(20, 1, 1)
        >>> metric = ppsci.metric.LatitudeWeightedRMSE(720, std=std)
    """

    def __init__(
        self,
        num_lat: int,
        std: Optional[Union[np.array, Tuple[float, ...]]] = None,
        keep_batch: bool = False,
        variable_dict: Dict[str, int] = None,
        unlog: bool = False,
        scale: float = 1e-5,
    ):
        super().__init__(keep_batch)
        self.num_lat = num_lat
        self.std = (
            None
            if std is None
            else paddle.to_tensor(std, paddle.get_default_dtype()).reshape((1, -1))
        )
        self.variable_dict = variable_dict
        self.unlog = unlog
        self.scale = scale
        self.weight = self.get_latitude_weight(num_lat)

    def get_latitude_weight(self, num_lat: int = 720):
        lat_t = paddle.linspace(start=0, stop=1, num=num_lat)
        lat_t = paddle.cos(3.1416 * (0.5 - lat_t))
        weight = num_lat * lat_t / paddle.sum(lat_t)
        weight = weight.reshape((1, 1, -1, 1))
        return weight

    def scale_expm1(self, x: paddle.Tensor):
        return self.scale * paddle.expm1(x)

    @paddle.no_grad()
    def forward(self, output_dict, label_dict) -> Dict[str, "paddle.Tensor"]:
        metric_dict = {}
        for key in label_dict:
            output = (
                self.scale_expm1(output_dict[key]) if self.unlog else output_dict[key]
            )
            label = self.scale_expm1(label_dict[key]) if self.unlog else label_dict[key]

            mse = F.mse_loss(output, label, "none")
            rmse = (mse * self.weight).mean(axis=(-1, -2)) ** 0.5
            if self.std is not None:
                rmse = rmse * self.std
            if self.variable_dict is not None:
                for variable_name, idx in self.variable_dict.items():
                    metric_dict[f"{key}.{variable_name}"] = (
                        rmse[:, idx] if self.keep_batch else rmse[:, idx].mean()
                    )
            else:
                metric_dict[key] = rmse.mean(axis=1) if self.keep_batch else rmse.mean()

        return metric_dict

Metric(评价指标) 模块¶

ppsci.metric ¶

Metric ¶

FunctionalMetric ¶

MAE ¶

MSE ¶

RMSE ¶

L2Rel ¶

MeanL2Rel ¶

LatitudeWeightedACC ¶

LatitudeWeightedRMSE ¶

`ppsci.metric` ¶

`Metric` ¶

`FunctionalMetric` ¶

`MAE` ¶

`MSE` ¶

`RMSE` ¶

`L2Rel` ¶

`MeanL2Rel` ¶

`LatitudeWeightedACC` ¶

`LatitudeWeightedRMSE` ¶