# Copyright 2020 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""timecast/utils/pcr.py"""
import jax.numpy as jnp
import numpy as np


def compute_projection(X: np.ndarray, k: int, center=False) -> np.ndarray:
    """Compute PCA projection"""

    if center:
        X = X - X.mean(axis=0)
        # X /= X.shape[0] - 1

    # Compute SVD
    # X: (steps - history_len + 1, history_len * input_dim) -> (H, d)
    # U: (H, H), but because full_matrices=False, (H, d)
    # S: (min(H, d),)
    # VT: (d, d)
    U, S, VT = jnp.linalg.svd(X, full_matrices=False, compute_uv=True)

    # Get index of top K eigen values
    top_k = (-jnp.square(S)).argsort()[:k]

    # Get projection
    # projection: (d, k)
    projection = VT[top_k].T

    return projection
