from typing import Union, Optional, Callable, Dict, Any
from typing_extensions import Literal

import numpy as np

from alibi_detect.base import outlier_prediction_dict
from alibi_detect.base import BaseDetector, ThresholdMixin, FitMixin
from alibi_detect.od.pytorch import KernelPCATorch, LinearPCATorch
from alibi_detect.utils.frameworks import BackendValidator
from alibi_detect.version import __version__
from alibi_detect.exceptions import _catch_error as catch_error
from alibi_detect.utils._types import TorchDeviceType


backends = {
    'pytorch': (KernelPCATorch, LinearPCATorch)
}


class PCA(BaseDetector, ThresholdMixin, FitMixin):
    def __init__(
        self,
        n_components: int,
        kernel: Optional[Callable] = None,
        backend: Literal['pytorch'] = 'pytorch',
        device: TorchDeviceType = None,
    ) -> None:
        """Principal Component Analysis (PCA) outlier detector.

        The detector is based on the Principal Component Analysis (PCA) algorithm. There are two variants of PCA:
        linear PCA and kernel PCA. Linear PCA computes the eigenvectors of the covariance matrix of the data. Kernel
        PCA computes the eigenvectors of the kernel matrix of the data.

        When scoring a test instance using the linear variant compute the distance to the principal subspace spanned
        by the first `n_components` eigenvectors.

        When scoring a test instance using the kernel variant we project it onto the largest eigenvectors and
        compute its score using the L2 norm.

        If a threshold is fitted we use this to determine whether the instance is an outlier or not.

        Parameters
        ----------
        n_components:
            The number of dimensions in the principal subspace. For linear pca should have
            ``1 <= n_components < dim(data)``. For kernel pca should have ``1 <= n_components < len(data)``.
        kernel
            Kernel function to use for outlier detection. If ``None``, linear PCA is used instead of the
            kernel variant.
        backend
            Backend used for outlier detection. Defaults to ``'pytorch'``. Options are ``'pytorch'``.
        device
            Device type used. The default tries to use the GPU and falls back on CPU if needed.
            Can be specified by passing either ``'cuda'``, ``'gpu'``, ``'cpu'`` or an instance of
            ``torch.device``.

        Raises
        ------
        NotImplementedError
            If choice of `backend` is not implemented.
        ValueError
            If `n_components` is less than 1.
        """
        super().__init__()

        backend_str: str = backend.lower()
        BackendValidator(
            backend_options={'pytorch': ['pytorch']},
            construct_name=self.__class__.__name__
        ).verify_backend(backend_str)

        kernel_backend_cls, linear_backend_cls = backends[backend]

        self.backend: Union[KernelPCATorch, LinearPCATorch]
        if kernel is not None:
            self.backend = kernel_backend_cls(
                n_components=n_components,
                device=device,
                kernel=kernel
            )
        else:
            self.backend = linear_backend_cls(
                n_components=n_components,
                device=device,
            )

        # set metadata
        self.meta['detector_type'] = 'outlier'
        self.meta['data_type'] = 'numeric'
        self.meta['online'] = False

    def fit(self, x_ref: np.ndarray) -> None:
        """Fit the detector on reference data.

        In the linear case we compute the principal components of the reference data using the
        covariance matrix and then remove the largest `n_components` eigenvectors. The remaining
        eigenvectors correspond to the invariant dimensions of the data. Changes in these
        dimensions are used to compute the outlier score which is the distance to the principal
        subspace spanned by the first `n_components` eigenvectors.

        In the kernel case we compute the principal components of the reference data using the
        kernel matrix and then return the largest `n_components` eigenvectors. These are then
        normalized to have length equal to `1/eigenvalue`. Note that this differs from the
        linear case where we remove the largest eigenvectors.

        In both cases we then store the computed components to use later when we score test
        instances.

        Parameters
        ----------
        x_ref
            Reference data used to fit the detector.

        Raises
        ------
        ValueError
            If using linear pca variant and `n_components` is greater than or equal to number of
            features or if using kernel pca variant and `n_components` is greater than or equal
            to number of instances.
        """
        self.backend.fit(self.backend._to_backend_dtype(x_ref))

    @catch_error('NotFittedError')
    def score(self, x: np.ndarray) -> np.ndarray:
        """Score `x` instances using the detector.

        Project `x` onto the eigenvectors and compute the score using the L2 norm.

        Parameters
        ----------
        x
            Data to score. The shape of `x` should be `(n_instances, n_features)`.

        Returns
        -------
        Outlier scores. The shape of the scores is `(n_instances,)`. The higher the score, the more anomalous the \
        instance.

        Raises
        ------
        NotFittedError
            If called before detector has been fit.
        """
        score = self.backend.score(self.backend._to_backend_dtype(x))
        return self.backend._to_frontend_dtype(score)

    @catch_error('NotFittedError')
    def infer_threshold(self, x: np.ndarray, fpr: float) -> None:
        """Infer the threshold for the PCA detector.

        The threshold is computed so that the outlier detector would incorrectly classify `fpr` proportion of the
        reference data as outliers.

        Parameters
        ----------
        x
            Reference data used to infer the threshold.
        fpr
            False positive rate used to infer the threshold. The false positive rate is the proportion of
            instances in `x` that are incorrectly classified as outliers. The false positive rate should
            be in the range ``(0, 1)``.

        Raises
        ------
        ValueError
            Raised if `fpr` is not in ``(0, 1)``.
        NotFittedError
            If called before detector has been fit.
        """
        self.backend.infer_threshold(self.backend._to_backend_dtype(x), fpr)

    @catch_error('NotFittedError')
    def predict(self, x: np.ndarray) -> Dict[str, Any]:
        """Predict whether the instances in `x` are outliers or not.

        Scores the instances in `x` and if the threshold was inferred, returns the outlier labels and p-values as well.

        Parameters
        ----------
        x
            Data to predict. The shape of `x` should be `(n_instances, n_features)`.

        Returns
        -------
        Dictionary with keys 'data' and 'meta'. 'data' contains the outlier scores. If threshold inference was  \
        performed, 'data' also contains the threshold value, outlier labels and p-vals . The shape of the scores is \
        `(n_instances,)`. The higher the score, the more anomalous the instance. 'meta' contains information about \
        the detector.

        Raises
        ------
        NotFittedError
            If called before detector has been fit.
        """
        outputs = self.backend.predict(self.backend._to_backend_dtype(x))
        output = outlier_prediction_dict()
        output['data'] = {
            **output['data'],
            **self.backend._to_frontend_dtype(outputs)
        }
        output['meta'] = {
            **output['meta'],
            'name': self.__class__.__name__,
            'detector_type': 'outlier',
            'online': False,
            'version': __version__,
        }
        return output

372971f696683155aff1bb72f69bd473e367d736
<mask token>


class PCA(BaseDetector, ThresholdMixin, FitMixin):

    def __init__(self, n_components: int, kernel: Optional[Callable]=None,
        backend: Literal['pytorch']='pytorch', device: TorchDeviceType=None
        ) ->None:
        """Principal Component Analysis (PCA) outlier detector.

        The detector is based on the Principal Component Analysis (PCA) algorithm. There are two variants of PCA:
        linear PCA and kernel PCA. Linear PCA computes the eigenvectors of the covariance matrix of the data. Kernel
        PCA computes the eigenvectors of the kernel matrix of the data.

        When scoring a test instance using the linear variant compute the distance to the principal subspace spanned
        by the first `n_components` eigenvectors.

        When scoring a test instance using the kernel variant we project it onto the largest eigenvectors and
        compute its score using the L2 norm.

        If a threshold is fitted we use this to determine whether the instance is an outlier or not.

        Parameters
        ----------
        n_components:
            The number of dimensions in the principal subspace. For linear pca should have
            ``1 <= n_components < dim(data)``. For kernel pca should have ``1 <= n_components < len(data)``.
        kernel
            Kernel function to use for outlier detection. If ``None``, linear PCA is used instead of the
            kernel variant.
        backend
            Backend used for outlier detection. Defaults to ``'pytorch'``. Options are ``'pytorch'``.
        device
            Device type used. The default tries to use the GPU and falls back on CPU if needed.
            Can be specified by passing either ``'cuda'``, ``'gpu'``, ``'cpu'`` or an instance of
            ``torch.device``.

        Raises
        ------
        NotImplementedError
            If choice of `backend` is not implemented.
        ValueError
            If `n_components` is less than 1.
        """
        super().__init__()
        backend_str: str = backend.lower()
        BackendValidator(backend_options={'pytorch': ['pytorch']},
            construct_name=self.__class__.__name__).verify_backend(backend_str)
        kernel_backend_cls, linear_backend_cls = backends[backend]
        self.backend: Union[KernelPCATorch, LinearPCATorch]
        if kernel is not None:
            self.backend = kernel_backend_cls(n_components=n_components,
                device=device, kernel=kernel)
        else:
            self.backend = linear_backend_cls(n_components=n_components,
                device=device)
        self.meta['detector_type'] = 'outlier'
        self.meta['data_type'] = 'numeric'
        self.meta['online'] = False

    def fit(self, x_ref: np.ndarray) ->None:
        """Fit the detector on reference data.

        In the linear case we compute the principal components of the reference data using the
        covariance matrix and then remove the largest `n_components` eigenvectors. The remaining
        eigenvectors correspond to the invariant dimensions of the data. Changes in these
        dimensions are used to compute the outlier score which is the distance to the principal
        subspace spanned by the first `n_components` eigenvectors.

        In the kernel case we compute the principal components of the reference data using the
        kernel matrix and then return the largest `n_components` eigenvectors. These are then
        normalized to have length equal to `1/eigenvalue`. Note that this differs from the
        linear case where we remove the largest eigenvectors.

        In both cases we then store the computed components to use later when we score test
        instances.

        Parameters
        ----------
        x_ref
            Reference data used to fit the detector.

        Raises
        ------
        ValueError
            If using linear pca variant and `n_components` is greater than or equal to number of
            features or if using kernel pca variant and `n_components` is greater than or equal
            to number of instances.
        """
        self.backend.fit(self.backend._to_backend_dtype(x_ref))

    @catch_error('NotFittedError')
    def score(self, x: np.ndarray) ->np.ndarray:
        """Score `x` instances using the detector.

        Project `x` onto the eigenvectors and compute the score using the L2 norm.

        Parameters
        ----------
        x
            Data to score. The shape of `x` should be `(n_instances, n_features)`.

        Returns
        -------
        Outlier scores. The shape of the scores is `(n_instances,)`. The higher the score, the more anomalous the         instance.

        Raises
        ------
        NotFittedError
            If called before detector has been fit.
        """
        score = self.backend.score(self.backend._to_backend_dtype(x))
        return self.backend._to_frontend_dtype(score)
    <mask token>
    <mask token>

<mask token>


class PCA(BaseDetector, ThresholdMixin, FitMixin):

    def __init__(self, n_components: int, kernel: Optional[Callable]=None,
        backend: Literal['pytorch']='pytorch', device: TorchDeviceType=None
        ) ->None:
        """Principal Component Analysis (PCA) outlier detector.

        The detector is based on the Principal Component Analysis (PCA) algorithm. There are two variants of PCA:
        linear PCA and kernel PCA. Linear PCA computes the eigenvectors of the covariance matrix of the data. Kernel
        PCA computes the eigenvectors of the kernel matrix of the data.

        When scoring a test instance using the linear variant compute the distance to the principal subspace spanned
        by the first `n_components` eigenvectors.

        When scoring a test instance using the kernel variant we project it onto the largest eigenvectors and
        compute its score using the L2 norm.

        If a threshold is fitted we use this to determine whether the instance is an outlier or not.

        Parameters
        ----------
        n_components:
            The number of dimensions in the principal subspace. For linear pca should have
            ``1 <= n_components < dim(data)``. For kernel pca should have ``1 <= n_components < len(data)``.
        kernel
            Kernel function to use for outlier detection. If ``None``, linear PCA is used instead of the
            kernel variant.
        backend
            Backend used for outlier detection. Defaults to ``'pytorch'``. Options are ``'pytorch'``.
        device
            Device type used. The default tries to use the GPU and falls back on CPU if needed.
            Can be specified by passing either ``'cuda'``, ``'gpu'``, ``'cpu'`` or an instance of
            ``torch.device``.

        Raises
        ------
        NotImplementedError
            If choice of `backend` is not implemented.
        ValueError
            If `n_components` is less than 1.
        """
        super().__init__()
        backend_str: str = backend.lower()
        BackendValidator(backend_options={'pytorch': ['pytorch']},
            construct_name=self.__class__.__name__).verify_backend(backend_str)
        kernel_backend_cls, linear_backend_cls = backends[backend]
        self.backend: Union[KernelPCATorch, LinearPCATorch]
        if kernel is not None:
            self.backend = kernel_backend_cls(n_components=n_components,
                device=device, kernel=kernel)
        else:
            self.backend = linear_backend_cls(n_components=n_components,
                device=device)
        self.meta['detector_type'] = 'outlier'
        self.meta['data_type'] = 'numeric'
        self.meta['online'] = False

    def fit(self, x_ref: np.ndarray) ->None:
        """Fit the detector on reference data.

        In the linear case we compute the principal components of the reference data using the
        covariance matrix and then remove the largest `n_components` eigenvectors. The remaining
        eigenvectors correspond to the invariant dimensions of the data. Changes in these
        dimensions are used to compute the outlier score which is the distance to the principal
        subspace spanned by the first `n_components` eigenvectors.

        In the kernel case we compute the principal components of the reference data using the
        kernel matrix and then return the largest `n_components` eigenvectors. These are then
        normalized to have length equal to `1/eigenvalue`. Note that this differs from the
        linear case where we remove the largest eigenvectors.

        In both cases we then store the computed components to use later when we score test
        instances.

        Parameters
        ----------
        x_ref
            Reference data used to fit the detector.

        Raises
        ------
        ValueError
            If using linear pca variant and `n_components` is greater than or equal to number of
            features or if using kernel pca variant and `n_components` is greater than or equal
            to number of instances.
        """
        self.backend.fit(self.backend._to_backend_dtype(x_ref))

    @catch_error('NotFittedError')
    def score(self, x: np.ndarray) ->np.ndarray:
        """Score `x` instances using the detector.

        Project `x` onto the eigenvectors and compute the score using the L2 norm.

        Parameters
        ----------
        x
            Data to score. The shape of `x` should be `(n_instances, n_features)`.

        Returns
        -------
        Outlier scores. The shape of the scores is `(n_instances,)`. The higher the score, the more anomalous the         instance.

        Raises
        ------
        NotFittedError
            If called before detector has been fit.
        """
        score = self.backend.score(self.backend._to_backend_dtype(x))
        return self.backend._to_frontend_dtype(score)

    @catch_error('NotFittedError')
    def infer_threshold(self, x: np.ndarray, fpr: float) ->None:
        """Infer the threshold for the PCA detector.

        The threshold is computed so that the outlier detector would incorrectly classify `fpr` proportion of the
        reference data as outliers.

        Parameters
        ----------
        x
            Reference data used to infer the threshold.
        fpr
            False positive rate used to infer the threshold. The false positive rate is the proportion of
            instances in `x` that are incorrectly classified as outliers. The false positive rate should
            be in the range ``(0, 1)``.

        Raises
        ------
        ValueError
            Raised if `fpr` is not in ``(0, 1)``.
        NotFittedError
            If called before detector has been fit.
        """
        self.backend.infer_threshold(self.backend._to_backend_dtype(x), fpr)

    @catch_error('NotFittedError')
    def predict(self, x: np.ndarray) ->Dict[str, Any]:
        """Predict whether the instances in `x` are outliers or not.

        Scores the instances in `x` and if the threshold was inferred, returns the outlier labels and p-values as well.

        Parameters
        ----------
        x
            Data to predict. The shape of `x` should be `(n_instances, n_features)`.

        Returns
        -------
        Dictionary with keys 'data' and 'meta'. 'data' contains the outlier scores. If threshold inference was          performed, 'data' also contains the threshold value, outlier labels and p-vals . The shape of the scores is         `(n_instances,)`. The higher the score, the more anomalous the instance. 'meta' contains information about         the detector.

        Raises
        ------
        NotFittedError
            If called before detector has been fit.
        """
        outputs = self.backend.predict(self.backend._to_backend_dtype(x))
        output = outlier_prediction_dict()
        output['data'] = {**output['data'], **self.backend.
            _to_frontend_dtype(outputs)}
        output['meta'] = {**output['meta'], 'name': self.__class__.__name__,
            'detector_type': 'outlier', 'online': False, 'version': __version__
            }
        return output

<mask token>
backends = {'pytorch': (KernelPCATorch, LinearPCATorch)}


class PCA(BaseDetector, ThresholdMixin, FitMixin):

    def __init__(self, n_components: int, kernel: Optional[Callable]=None,
        backend: Literal['pytorch']='pytorch', device: TorchDeviceType=None
        ) ->None:
        """Principal Component Analysis (PCA) outlier detector.

        The detector is based on the Principal Component Analysis (PCA) algorithm. There are two variants of PCA:
        linear PCA and kernel PCA. Linear PCA computes the eigenvectors of the covariance matrix of the data. Kernel
        PCA computes the eigenvectors of the kernel matrix of the data.

        When scoring a test instance using the linear variant compute the distance to the principal subspace spanned
        by the first `n_components` eigenvectors.

        When scoring a test instance using the kernel variant we project it onto the largest eigenvectors and
        compute its score using the L2 norm.

        If a threshold is fitted we use this to determine whether the instance is an outlier or not.

        Parameters
        ----------
        n_components:
            The number of dimensions in the principal subspace. For linear pca should have
            ``1 <= n_components < dim(data)``. For kernel pca should have ``1 <= n_components < len(data)``.
        kernel
            Kernel function to use for outlier detection. If ``None``, linear PCA is used instead of the
            kernel variant.
        backend
            Backend used for outlier detection. Defaults to ``'pytorch'``. Options are ``'pytorch'``.
        device
            Device type used. The default tries to use the GPU and falls back on CPU if needed.
            Can be specified by passing either ``'cuda'``, ``'gpu'``, ``'cpu'`` or an instance of
            ``torch.device``.

        Raises
        ------
        NotImplementedError
            If choice of `backend` is not implemented.
        ValueError
            If `n_components` is less than 1.
        """
        super().__init__()
        backend_str: str = backend.lower()
        BackendValidator(backend_options={'pytorch': ['pytorch']},
            construct_name=self.__class__.__name__).verify_backend(backend_str)
        kernel_backend_cls, linear_backend_cls = backends[backend]
        self.backend: Union[KernelPCATorch, LinearPCATorch]
        if kernel is not None:
            self.backend = kernel_backend_cls(n_components=n_components,
                device=device, kernel=kernel)
        else:
            self.backend = linear_backend_cls(n_components=n_components,
                device=device)
        self.meta['detector_type'] = 'outlier'
        self.meta['data_type'] = 'numeric'
        self.meta['online'] = False

    def fit(self, x_ref: np.ndarray) ->None:
        """Fit the detector on reference data.

        In the linear case we compute the principal components of the reference data using the
        covariance matrix and then remove the largest `n_components` eigenvectors. The remaining
        eigenvectors correspond to the invariant dimensions of the data. Changes in these
        dimensions are used to compute the outlier score which is the distance to the principal
        subspace spanned by the first `n_components` eigenvectors.

        In the kernel case we compute the principal components of the reference data using the
        kernel matrix and then return the largest `n_components` eigenvectors. These are then
        normalized to have length equal to `1/eigenvalue`. Note that this differs from the
        linear case where we remove the largest eigenvectors.

        In both cases we then store the computed components to use later when we score test
        instances.

        Parameters
        ----------
        x_ref
            Reference data used to fit the detector.

        Raises
        ------
        ValueError
            If using linear pca variant and `n_components` is greater than or equal to number of
            features or if using kernel pca variant and `n_components` is greater than or equal
            to number of instances.
        """
        self.backend.fit(self.backend._to_backend_dtype(x_ref))

    @catch_error('NotFittedError')
    def score(self, x: np.ndarray) ->np.ndarray:
        """Score `x` instances using the detector.

        Project `x` onto the eigenvectors and compute the score using the L2 norm.

        Parameters
        ----------
        x
            Data to score. The shape of `x` should be `(n_instances, n_features)`.

        Returns
        -------
        Outlier scores. The shape of the scores is `(n_instances,)`. The higher the score, the more anomalous the         instance.

        Raises
        ------
        NotFittedError
            If called before detector has been fit.
        """
        score = self.backend.score(self.backend._to_backend_dtype(x))
        return self.backend._to_frontend_dtype(score)

    @catch_error('NotFittedError')
    def infer_threshold(self, x: np.ndarray, fpr: float) ->None:
        """Infer the threshold for the PCA detector.

        The threshold is computed so that the outlier detector would incorrectly classify `fpr` proportion of the
        reference data as outliers.

        Parameters
        ----------
        x
            Reference data used to infer the threshold.
        fpr
            False positive rate used to infer the threshold. The false positive rate is the proportion of
            instances in `x` that are incorrectly classified as outliers. The false positive rate should
            be in the range ``(0, 1)``.

        Raises
        ------
        ValueError
            Raised if `fpr` is not in ``(0, 1)``.
        NotFittedError
            If called before detector has been fit.
        """
        self.backend.infer_threshold(self.backend._to_backend_dtype(x), fpr)

    @catch_error('NotFittedError')
    def predict(self, x: np.ndarray) ->Dict[str, Any]:
        """Predict whether the instances in `x` are outliers or not.

        Scores the instances in `x` and if the threshold was inferred, returns the outlier labels and p-values as well.

        Parameters
        ----------
        x
            Data to predict. The shape of `x` should be `(n_instances, n_features)`.

        Returns
        -------
        Dictionary with keys 'data' and 'meta'. 'data' contains the outlier scores. If threshold inference was          performed, 'data' also contains the threshold value, outlier labels and p-vals . The shape of the scores is         `(n_instances,)`. The higher the score, the more anomalous the instance. 'meta' contains information about         the detector.

        Raises
        ------
        NotFittedError
            If called before detector has been fit.
        """
        outputs = self.backend.predict(self.backend._to_backend_dtype(x))
        output = outlier_prediction_dict()
        output['data'] = {**output['data'], **self.backend.
            _to_frontend_dtype(outputs)}
        output['meta'] = {**output['meta'], 'name': self.__class__.__name__,
            'detector_type': 'outlier', 'online': False, 'version': __version__
            }
        return output

from typing import Union, Optional, Callable, Dict, Any
from typing_extensions import Literal
import numpy as np
from alibi_detect.base import outlier_prediction_dict
from alibi_detect.base import BaseDetector, ThresholdMixin, FitMixin
from alibi_detect.od.pytorch import KernelPCATorch, LinearPCATorch
from alibi_detect.utils.frameworks import BackendValidator
from alibi_detect.version import __version__
from alibi_detect.exceptions import _catch_error as catch_error
from alibi_detect.utils._types import TorchDeviceType
backends = {'pytorch': (KernelPCATorch, LinearPCATorch)}


class PCA(BaseDetector, ThresholdMixin, FitMixin):

    def __init__(self, n_components: int, kernel: Optional[Callable]=None,
        backend: Literal['pytorch']='pytorch', device: TorchDeviceType=None
        ) ->None:
        """Principal Component Analysis (PCA) outlier detector.

        The detector is based on the Principal Component Analysis (PCA) algorithm. There are two variants of PCA:
        linear PCA and kernel PCA. Linear PCA computes the eigenvectors of the covariance matrix of the data. Kernel
        PCA computes the eigenvectors of the kernel matrix of the data.

        When scoring a test instance using the linear variant compute the distance to the principal subspace spanned
        by the first `n_components` eigenvectors.

        When scoring a test instance using the kernel variant we project it onto the largest eigenvectors and
        compute its score using the L2 norm.

        If a threshold is fitted we use this to determine whether the instance is an outlier or not.

        Parameters
        ----------
        n_components:
            The number of dimensions in the principal subspace. For linear pca should have
            ``1 <= n_components < dim(data)``. For kernel pca should have ``1 <= n_components < len(data)``.
        kernel
            Kernel function to use for outlier detection. If ``None``, linear PCA is used instead of the
            kernel variant.
        backend
            Backend used for outlier detection. Defaults to ``'pytorch'``. Options are ``'pytorch'``.
        device
            Device type used. The default tries to use the GPU and falls back on CPU if needed.
            Can be specified by passing either ``'cuda'``, ``'gpu'``, ``'cpu'`` or an instance of
            ``torch.device``.

        Raises
        ------
        NotImplementedError
            If choice of `backend` is not implemented.
        ValueError
            If `n_components` is less than 1.
        """
        super().__init__()
        backend_str: str = backend.lower()
        BackendValidator(backend_options={'pytorch': ['pytorch']},
            construct_name=self.__class__.__name__).verify_backend(backend_str)
        kernel_backend_cls, linear_backend_cls = backends[backend]
        self.backend: Union[KernelPCATorch, LinearPCATorch]
        if kernel is not None:
            self.backend = kernel_backend_cls(n_components=n_components,
                device=device, kernel=kernel)
        else:
            self.backend = linear_backend_cls(n_components=n_components,
                device=device)
        self.meta['detector_type'] = 'outlier'
        self.meta['data_type'] = 'numeric'
        self.meta['online'] = False

    def fit(self, x_ref: np.ndarray) ->None:
        """Fit the detector on reference data.

        In the linear case we compute the principal components of the reference data using the
        covariance matrix and then remove the largest `n_components` eigenvectors. The remaining
        eigenvectors correspond to the invariant dimensions of the data. Changes in these
        dimensions are used to compute the outlier score which is the distance to the principal
        subspace spanned by the first `n_components` eigenvectors.

        In the kernel case we compute the principal components of the reference data using the
        kernel matrix and then return the largest `n_components` eigenvectors. These are then
        normalized to have length equal to `1/eigenvalue`. Note that this differs from the
        linear case where we remove the largest eigenvectors.

        In both cases we then store the computed components to use later when we score test
        instances.

        Parameters
        ----------
        x_ref
            Reference data used to fit the detector.

        Raises
        ------
        ValueError
            If using linear pca variant and `n_components` is greater than or equal to number of
            features or if using kernel pca variant and `n_components` is greater than or equal
            to number of instances.
        """
        self.backend.fit(self.backend._to_backend_dtype(x_ref))

    @catch_error('NotFittedError')
    def score(self, x: np.ndarray) ->np.ndarray:
        """Score `x` instances using the detector.

        Project `x` onto the eigenvectors and compute the score using the L2 norm.

        Parameters
        ----------
        x
            Data to score. The shape of `x` should be `(n_instances, n_features)`.

        Returns
        -------
        Outlier scores. The shape of the scores is `(n_instances,)`. The higher the score, the more anomalous the         instance.

        Raises
        ------
        NotFittedError
            If called before detector has been fit.
        """
        score = self.backend.score(self.backend._to_backend_dtype(x))
        return self.backend._to_frontend_dtype(score)

    @catch_error('NotFittedError')
    def infer_threshold(self, x: np.ndarray, fpr: float) ->None:
        """Infer the threshold for the PCA detector.

        The threshold is computed so that the outlier detector would incorrectly classify `fpr` proportion of the
        reference data as outliers.

        Parameters
        ----------
        x
            Reference data used to infer the threshold.
        fpr
            False positive rate used to infer the threshold. The false positive rate is the proportion of
            instances in `x` that are incorrectly classified as outliers. The false positive rate should
            be in the range ``(0, 1)``.

        Raises
        ------
        ValueError
            Raised if `fpr` is not in ``(0, 1)``.
        NotFittedError
            If called before detector has been fit.
        """
        self.backend.infer_threshold(self.backend._to_backend_dtype(x), fpr)

    @catch_error('NotFittedError')
    def predict(self, x: np.ndarray) ->Dict[str, Any]:
        """Predict whether the instances in `x` are outliers or not.

        Scores the instances in `x` and if the threshold was inferred, returns the outlier labels and p-values as well.

        Parameters
        ----------
        x
            Data to predict. The shape of `x` should be `(n_instances, n_features)`.

        Returns
        -------
        Dictionary with keys 'data' and 'meta'. 'data' contains the outlier scores. If threshold inference was          performed, 'data' also contains the threshold value, outlier labels and p-vals . The shape of the scores is         `(n_instances,)`. The higher the score, the more anomalous the instance. 'meta' contains information about         the detector.

        Raises
        ------
        NotFittedError
            If called before detector has been fit.
        """
        outputs = self.backend.predict(self.backend._to_backend_dtype(x))
        output = outlier_prediction_dict()
        output['data'] = {**output['data'], **self.backend.
            _to_frontend_dtype(outputs)}
        output['meta'] = {**output['meta'], 'name': self.__class__.__name__,
            'detector_type': 'outlier', 'online': False, 'version': __version__
            }
        return output

from typing import Union, Optional, Callable, Dict, Any
from typing_extensions import Literal

import numpy as np

from alibi_detect.base import outlier_prediction_dict
from alibi_detect.base import BaseDetector, ThresholdMixin, FitMixin
from alibi_detect.od.pytorch import KernelPCATorch, LinearPCATorch
from alibi_detect.utils.frameworks import BackendValidator
from alibi_detect.version import __version__
from alibi_detect.exceptions import _catch_error as catch_error
from alibi_detect.utils._types import TorchDeviceType


backends = {
    'pytorch': (KernelPCATorch, LinearPCATorch)
}


class PCA(BaseDetector, ThresholdMixin, FitMixin):
    def __init__(
        self,
        n_components: int,
        kernel: Optional[Callable] = None,
        backend: Literal['pytorch'] = 'pytorch',
        device: TorchDeviceType = None,
    ) -> None:
        """Principal Component Analysis (PCA) outlier detector.

        The detector is based on the Principal Component Analysis (PCA) algorithm. There are two variants of PCA:
        linear PCA and kernel PCA. Linear PCA computes the eigenvectors of the covariance matrix of the data. Kernel
        PCA computes the eigenvectors of the kernel matrix of the data.

        When scoring a test instance using the linear variant compute the distance to the principal subspace spanned
        by the first `n_components` eigenvectors.

        When scoring a test instance using the kernel variant we project it onto the largest eigenvectors and
        compute its score using the L2 norm.

        If a threshold is fitted we use this to determine whether the instance is an outlier or not.

        Parameters
        ----------
        n_components:
            The number of dimensions in the principal subspace. For linear pca should have
            ``1 <= n_components < dim(data)``. For kernel pca should have ``1 <= n_components < len(data)``.
        kernel
            Kernel function to use for outlier detection. If ``None``, linear PCA is used instead of the
            kernel variant.
        backend
            Backend used for outlier detection. Defaults to ``'pytorch'``. Options are ``'pytorch'``.
        device
            Device type used. The default tries to use the GPU and falls back on CPU if needed.
            Can be specified by passing either ``'cuda'``, ``'gpu'``, ``'cpu'`` or an instance of
            ``torch.device``.

        Raises
        ------
        NotImplementedError
            If choice of `backend` is not implemented.
        ValueError
            If `n_components` is less than 1.
        """
        super().__init__()

        backend_str: str = backend.lower()
        BackendValidator(
            backend_options={'pytorch': ['pytorch']},
            construct_name=self.__class__.__name__
        ).verify_backend(backend_str)

        kernel_backend_cls, linear_backend_cls = backends[backend]

        self.backend: Union[KernelPCATorch, LinearPCATorch]
        if kernel is not None:
            self.backend = kernel_backend_cls(
                n_components=n_components,
                device=device,
                kernel=kernel
            )
        else:
            self.backend = linear_backend_cls(
                n_components=n_components,
                device=device,
            )

        # set metadata
        self.meta['detector_type'] = 'outlier'
        self.meta['data_type'] = 'numeric'
        self.meta['online'] = False

    def fit(self, x_ref: np.ndarray) -> None:
        """Fit the detector on reference data.

        In the linear case we compute the principal components of the reference data using the
        covariance matrix and then remove the largest `n_components` eigenvectors. The remaining
        eigenvectors correspond to the invariant dimensions of the data. Changes in these
        dimensions are used to compute the outlier score which is the distance to the principal
        subspace spanned by the first `n_components` eigenvectors.

        In the kernel case we compute the principal components of the reference data using the
        kernel matrix and then return the largest `n_components` eigenvectors. These are then
        normalized to have length equal to `1/eigenvalue`. Note that this differs from the
        linear case where we remove the largest eigenvectors.

        In both cases we then store the computed components to use later when we score test
        instances.

        Parameters
        ----------
        x_ref
            Reference data used to fit the detector.

        Raises
        ------
        ValueError
            If using linear pca variant and `n_components` is greater than or equal to number of
            features or if using kernel pca variant and `n_components` is greater than or equal
            to number of instances.
        """
        self.backend.fit(self.backend._to_backend_dtype(x_ref))

    @catch_error('NotFittedError')
    def score(self, x: np.ndarray) -> np.ndarray:
        """Score `x` instances using the detector.

        Project `x` onto the eigenvectors and compute the score using the L2 norm.

        Parameters
        ----------
        x
            Data to score. The shape of `x` should be `(n_instances, n_features)`.

        Returns
        -------
        Outlier scores. The shape of the scores is `(n_instances,)`. The higher the score, the more anomalous the \
        instance.

        Raises
        ------
        NotFittedError
            If called before detector has been fit.
        """
        score = self.backend.score(self.backend._to_backend_dtype(x))
        return self.backend._to_frontend_dtype(score)

    @catch_error('NotFittedError')
    def infer_threshold(self, x: np.ndarray, fpr: float) -> None:
        """Infer the threshold for the PCA detector.

        The threshold is computed so that the outlier detector would incorrectly classify `fpr` proportion of the
        reference data as outliers.

        Parameters
        ----------
        x
            Reference data used to infer the threshold.
        fpr
            False positive rate used to infer the threshold. The false positive rate is the proportion of
            instances in `x` that are incorrectly classified as outliers. The false positive rate should
            be in the range ``(0, 1)``.

        Raises
        ------
        ValueError
            Raised if `fpr` is not in ``(0, 1)``.
        NotFittedError
            If called before detector has been fit.
        """
        self.backend.infer_threshold(self.backend._to_backend_dtype(x), fpr)

    @catch_error('NotFittedError')
    def predict(self, x: np.ndarray) -> Dict[str, Any]:
        """Predict whether the instances in `x` are outliers or not.

        Scores the instances in `x` and if the threshold was inferred, returns the outlier labels and p-values as well.

        Parameters
        ----------
        x
            Data to predict. The shape of `x` should be `(n_instances, n_features)`.

        Returns
        -------
        Dictionary with keys 'data' and 'meta'. 'data' contains the outlier scores. If threshold inference was  \
        performed, 'data' also contains the threshold value, outlier labels and p-vals . The shape of the scores is \
        `(n_instances,)`. The higher the score, the more anomalous the instance. 'meta' contains information about \
        the detector.

        Raises
        ------
        NotFittedError
            If called before detector has been fit.
        """
        outputs = self.backend.predict(self.backend._to_backend_dtype(x))
        output = outlier_prediction_dict()
        output['data'] = {
            **output['data'],
            **self.backend._to_frontend_dtype(outputs)
        }
        output['meta'] = {
            **output['meta'],
            'name': self.__class__.__name__,
            'detector_type': 'outlier',
            'online': False,
            'version': __version__,
        }
        return output
