01 hotova

hod_1/data/pca_first.py

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+#!/usr/bin/env python3
+import argparse
+
+import numpy as np
+import torch
+
+import npfl138
+from npfl138.datasets.mnist import MNIST
+npfl138.require_version("2526.1")
+
+parser = argparse.ArgumentParser()
+# These arguments will be set appropriately by ReCodEx, even if you change them.
+parser.add_argument("--examples", default=256, type=int, help="MNIST examples to use.")
+parser.add_argument("--iterations", default=100, type=int, help="Iterations of the power algorithm.")
+parser.add_argument("--recodex", default=False, action="store_true", help="Evaluation in ReCodEx.")
+parser.add_argument("--seed", default=42, type=int, help="Random seed.")
+parser.add_argument("--threads", default=1, type=int, help="Maximum number of threads to use.")
+# If you add more arguments, ReCodEx will keep them with your default values.
+
+
+def main(args: argparse.Namespace) -> tuple[float, float]:
+    # Set the random seed and the number of threads.
+    npfl138.startup(args.seed, args.threads, args.recodex)
+    npfl138.global_keras_initializers()
+
+    # Prepare the data.
+    mnist = MNIST()
+
+    data_indices = np.random.choice(len(mnist.train), size=args.examples, replace=False)
+    data = mnist.train.data["images"][data_indices].to(torch.float32) / 255
+
+    # TODO: Data has shape [args.examples, MNIST.C, MNIST.H, MNIST.W].
+    # We want to reshape it to [args.examples, MNIST.C * MNIST.H * MNIST.W].
+    # We can do so using `torch.reshape(data, new_shape)` with new shape
+    # `[data.shape[0], data.shape[1] * data.shape[2] * data.shape[3]]`.
+    data = ...
+
+    # TODO: Now compute mean of every feature. Use `torch.mean`, and set
+    # `dim` (or `axis`) argument to zero -- therefore, the mean will be
+    # computed across the first dimension, so across examples.
+    #
+    # Note that for compatibility with Numpy/TF/Keras, all `dim` arguments
+    # in PyTorch can be also called `axis`.
+    mean = ...
+
+    # TODO: Compute the covariance matrix. The covariance matrix is
+    #   (data - mean)^T @ (data - mean) / data.shape[0]
+    # where transpose can be computed using `torch.transpose` or `torch.t` and
+    # matrix multiplication using either Python operator @ or `torch.matmul`.
+    cov = ...
+
+    # TODO: Compute the total variance, which is the sum of the diagonal
+    # of the covariance matrix. To extract the diagonal use `torch.diagonal`,
+    # and to sum a tensor use `torch.sum`.
+    total_variance = ...
+
+    # TODO: Now run `args.iterations` of the power iteration algorithm.
+    # Start with a vector of `cov.shape[0]` ones of type `torch.float32` using `torch.ones`.
+    v = ...
+    for i in range(args.iterations):
+        # TODO: In the power iteration algorithm, we compute
+        # 1. v = cov v
+        #    The matrix-vector multiplication can be computed as regular matrix multiplication
+        #    or using `torch.mv`.
+        # 2. s = l2_norm(v)
+        #    The l2_norm can be computed using for example `torch.linalg.vector_norm`.
+        # 3. v = v / s
+        ...
+
+    # The `v` is now approximately the eigenvector of the largest eigenvalue, `s`.
+    # We now compute the explained variance, which is the ratio of `s` and `total_variance`.
+    explained_variance = s / total_variance
+
+    # Return the total and explained variance for ReCodEx to validate
+    return total_variance, 100 * explained_variance
+
+
+if __name__ == "__main__":
+    main_args = parser.parse_args([] if "__file__" not in globals() else None)
+    total_variance, explained_variance = main(main_args)
+    print(f"Total variance: {total_variance:.2f}")
+    print(f"Explained variance: {explained_variance:.2f}%")