Delete old Python file

compressed_sensing.py

-import numpy as np
-import scipy
-import matplotlib.pyplot as plt
-
-
-def sample_two_sins(f1, f2, sample_times):
-    sample_rads = 2 * np.pi * sample_times
-    return np.sin(f1 * sample_rads) + np.sin(f2 * sample_rads)
-
-
-def compute_dct_matrix(n_samples):
-    dct_matrix = np.zeros((n_samples, n_samples))
-    root_one_over_n = np.sqrt(1.0 / n_samples)
-    root_two_over_n = np.sqrt(2.0 / n_samples)
-    for j in range(0, n_samples):
-        dct_matrix[0, j] = root_one_over_n
-    for i in range(1, n_samples):
-        for j in range(0, n_samples):
-            dct_matrix[i, j] = root_two_over_n * np.cos(np.pi * (2 * j + 1) * i / (2 * n_samples))
-    return dct_matrix
-
-
-def compute_differences(recovered_dct, inverse_dct_matrix, sample_values):
-    return sample_values - np.matmul(inverse_dct_matrix, recovered_dct)
-
-
-def loss_e(differences, subset_indices):
-    return np.linalg.norm(differences[subset_indices])
-
-
-def grad_e(differences, dct_matrix, subset_indices):
-    return -2 * np.matmul(dct_matrix[:,subset_indices], differences[subset_indices])
-
-
-if __name__ == "__main__":
-    f1 = 697 # Hz
-    f2 = 1209 # Hz
-
-    # Part (a)
-    sample_period = 0.01
-    n_samples = 250
-    sample_times = (sample_period / n_samples) * np.arange(n_samples)
-    sample_values = sample_two_sins(f1, f2, sample_times)
-    plt.plot(sample_times, sample_values)
-    plt.savefig("fig_a.png")
-    plt.close()
-
-    # Part (b)
-    dct_matrix = compute_dct_matrix(n_samples)
-    dct = np.matmul(dct_matrix, sample_values)
-    plt.plot(np.arange(n_samples), dct)
-    plt.savefig("fig_b.png")
-    plt.close()
-
-    # Part (c)
-    inverse_dct_matrix = np.transpose(dct_matrix)
-    recovered_sample_values = np.matmul(inverse_dct_matrix, dct)
-    plt.plot(sample_times, recovered_sample_values)
-    plt.savefig("fig_c.png")
-    plt.close()
-
-    # Part (d)
-    n_subsamples = 100
-    np.random.seed(7250147)
-    subset_indices = np.arange(n_samples)
-    np.random.shuffle(subset_indices)
-    subset_indices = subset_indices[:n_subsamples]
-    subset_indices = np.sort(subset_indices)
-    subset_sample_times = sample_times[subset_indices]
-    subset_sample_values = sample_values[subset_indices]
-    plt.plot(subset_sample_times, subset_sample_values)
-    plt.savefig("fig_d.png")
-    plt.close()
-
-    # Part (e)
-    recovered_dct = np.random.normal(0.0, 1.0, (n_samples))
-    differences = compute_differences(recovered_dct, inverse_dct_matrix, sample_values)
-    loss = loss_e(differences, subset_indices)
-    grad = grad_e(differences, dct_matrix, subset_indices)
-    print(grad)