From 5811c44cb0799ef550fd7e3684ad73f86d9f2980 Mon Sep 17 00:00:00 2001
From: Erik Strand <erik.strand@cba.mit.edu>
Date: Wed, 8 May 2019 18:40:50 -0400
Subject: [PATCH] Work on first gradient descent problem
---
compressed_sensing.py | 19 +++++++++++++++++++
1 file changed, 19 insertions(+)
diff --git a/compressed_sensing.py b/compressed_sensing.py
index 775c6bb..e3967b1 100644
--- a/compressed_sensing.py
+++ b/compressed_sensing.py
@@ -20,6 +20,18 @@ def compute_dct_matrix(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
@@ -59,3 +71,10 @@ if __name__ == "__main__":
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)
--
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