Perform gradient descent

main.cpp

@@ -119,9 +119,17 @@ int main() {
     Vector subset_differences = subset_sample_values - subset_recovered_sample_values;
     Scalar loss = subset_differences.squaredNorm();
     Vector gradient = -2 * subset_dct_matrix * subset_differences;
-
-    std::cout << loss << '\n';
-    std::cout << gradient << '\n';
+    constexpr Scalar learning_rate = 0.1;
+    while (loss > 1e-6) {
+        recovered_dct -= learning_rate * gradient;
+        recovered_sample_values = dct_matrix.transpose() * recovered_dct;
+        subset_recovered_sample_values = vector_subset(recovered_sample_values, subset_indices);
+        subset_differences = subset_sample_values - subset_recovered_sample_values;
+        loss = subset_differences.squaredNorm();
+        gradient = -2 * subset_dct_matrix * subset_differences;
+        //std::cout << loss << '\n';
+    }
+    python_print("dct_e", recovered_dct);
 
     return 0;
 }

plotter.py

@@ -7,6 +7,7 @@ dct = np.array([0.0493937, 1.53249, 0.0703373, 1.58311, 0.071832, 1.69718, 0.074
 recovered_sample_values = np.array([3.71932e-15, 0.475338, 0.917539, 1.29619, 1.5861, 1.76932, 1.83651, 1.78761, 1.6316, 1.38558, 1.0731, 0.721928, 0.361558, 0.0205522, -0.27594, -0.508314, -0.664077, -0.738727, -0.735864, -0.666533, -0.547871, -0.401193, -0.249706, -0.116065, -0.0200166, 0.0236569, 0.00668195, -0.0718098, -0.205127, -0.379618, -0.575975, -0.771114, -0.94046, -1.06042, -1.1108, -1.07697, -0.951487, -0.73516, -0.43726, -0.0750177, 0.327653, 0.742071, 1.13718, 1.48217, 1.7492, 1.91577, 1.96681, 1.89599, 1.70642, 1.41042, 1.02857, 0.588008, 0.120163, -0.341839, -0.765935, -1.12376, -1.39294, -1.5588, -1.61544, -1.56598, -1.42199, -1.20225, -0.930797, -0.634626, -0.341124, -0.0755387, 0.141293, 0.294754, 0.377636, 0.390584, 0.341783, 0.245913, 0.122481, -0.00631234, -0.117955, -0.19203, -0.212412, -0.169044, -0.0591181, 0.112454, 0.333336, 0.584794, 0.843377, 1.08309, 1.27787, 1.40408, 1.44291, 1.38232, 1.21838, 0.95598, 0.608661, 0.197701, -0.249515, -0.701696, -1.12623, -1.49192, -1.77159, -1.94442, -1.99773, -1.92798, -1.74113, -1.45207, -1.08332, -0.663067, -0.222778, 0.205515, 0.591886, 0.910992, 1.14409, 1.28044, 1.31795, 1.26307, 1.12989, 0.938508, 0.713012, 0.478999, 0.261091, 0.0805585, -0.0466774, -0.11149, -0.112311, -0.0551393, 0.0472029, 0.176484, 0.311019, 0.427974, 0.505792, 0.526522, 0.477802, 0.354329, 0.158647, -0.0988122, -0.400459, -0.722977, -1.03934, -1.32121, -1.54155, -1.67714, -1.71079, -1.63312, -1.44356, -1.15069, -0.771708, -0.33113, 0.14113, 0.6122, 1.04895, 1.42074, 1.70194, 1.87404, 1.9271, 1.86053, 1.68299, 1.41149, 1.06984, 0.686454, 0.291854, -0.0840174, -0.414358, -0.677735, -0.859784, -0.954231, -0.963144, -0.896411, -0.770496, -0.606599, -0.428405, -0.259632, -0.121617, -0.0311657, 0.00112032, -0.0281042, -0.11461, -0.247029, -0.408011, -0.575983, -0.727348, -0.838913, -0.890317, -0.866221, -0.75805, -0.565119, -0.295029, 0.0367266, 0.407896, 0.791266, 1.15696, 1.47502, 1.71807, 1.86376, 1.89685, 1.81066, 1.60779, 1.30007, 0.907671, 0.457475, -0.019091, -0.488655, -0.918654, -1.28001, -1.54948, -1.71149, -1.75931, -1.69539, -1.53092, -1.28466, -0.981105, -0.648113, -0.314394, -0.00689592, 0.25156, 0.444213, 0.561694, 0.602629, 0.573475, 0.487607, 0.363754, 0.223933, 0.0910946, -0.0133094, -0.0715908, -0.0717057, -0.00857246, 0.115302, 0.289952, 0.498828, 0.720336, 0.929905, 1.10238, 1.21454, 1.24743, 1.18842, 1.03264, 0.783761, 0.453978, 0.0632207, -0.36236, -0.792506, -1.19536, -1.54017, -1.79994, -1.95375, -1.9886, -1.9006, -1.69531, -1.38735, -0.999124, -0.559002, -0.0988865, 0.348445])
 subset_sample_times = np.array([0.000200803, 0.000240964, 0.000281124, 0.000321285, 0.000441767, 0.00064257, 0.000883534, 0.00100402, 0.00104418, 0.00116466, 0.00120482, 0.00124498, 0.00144578, 0.00148594, 0.00164659, 0.00180723, 0.00184739, 0.00192771, 0.00200803, 0.00212851, 0.00240964, 0.00248996, 0.00261044, 0.00289157, 0.00293173, 0.00305221, 0.00313253, 0.00317269, 0.00321285, 0.00325301, 0.00333333, 0.00345382, 0.00369478, 0.00373494, 0.0037751, 0.00389558, 0.00405622, 0.00413655, 0.00425703, 0.00429719, 0.00433735, 0.00437751, 0.00441767, 0.00449799, 0.00453815, 0.00465863, 0.0046988, 0.00473896, 0.00481928, 0.00485944, 0.0048996, 0.00518072, 0.00522088, 0.0053012, 0.00554217, 0.00570281, 0.00574297, 0.00586345, 0.00626506, 0.00630522, 0.00634538, 0.00646586, 0.00658635, 0.00662651, 0.00670683, 0.00674699, 0.00694779, 0.00698795, 0.00702811, 0.00706827, 0.00710843, 0.00714859, 0.00718876, 0.00726908, 0.00730924, 0.00742972, 0.0075502, 0.00763052, 0.00771084, 0.00779116, 0.00791165, 0.00799197, 0.00807229, 0.00811245, 0.00815261, 0.00819277, 0.00823293, 0.00827309, 0.00839357, 0.00843373, 0.00883534, 0.00891566, 0.00903614, 0.00923695, 0.00927711, 0.00935743, 0.00963855, 0.00975904, 0.00983936, 0.01])
 subset_sample_values = np.array([1.76932, 1.83651, 1.78761, 1.6316, 0.721928, -0.664077, -0.249706, 0.0236569, 0.00668195, -0.379618, -0.575975, -0.771114, -0.951487, -0.73516, 0.742071, 1.91577, 1.96681, 1.70642, 1.02857, -0.341839, -1.42199, -0.930797, -0.0755387, 0.122481, -0.00631234, -0.212412, -0.0591181, 0.112454, 0.333336, 0.584794, 1.08309, 1.44291, -0.249515, -0.701696, -1.12623, -1.94442, -1.45207, -0.663067, 0.591886, 0.910992, 1.14409, 1.28044, 1.31795, 1.12989, 0.938508, 0.261091, 0.0805585, -0.0466774, -0.112311, -0.0551393, 0.0472029, 0.354329, 0.158647, -0.400459, -1.71079, -0.771708, -0.33113, 1.04895, 0.291854, -0.0840174, -0.414358, -0.954231, -0.770496, -0.606599, -0.259632, -0.121617, -0.247029, -0.408011, -0.575983, -0.727348, -0.838913, -0.890317, -0.866221, -0.565119, -0.295029, 0.791266, 1.71807, 1.89685, 1.60779, 0.907671, -0.488655, -1.28001, -1.71149, -1.75931, -1.69539, -1.53092, -1.28466, -0.981105, -0.00689592, 0.25156, -0.0715908, -0.00857246, 0.498828, 1.24743, 1.18842, 0.783761, -1.79994, -1.9006, -1.38735, 0.348445])
+dct_e = np.array([-0.181725, 1.31755, 0.649338, 0.146722, 0.577319, 0.52855, -0.420861, 0.00972246, 1.34705, 2.02479, -0.45287, 1.50728, 0.11511, 2.50369, -0.860719, -1.9832, -0.188749, -1.89087, 0.895381, -0.31801, -1.49248, 1.61864, -0.740006, 1.70221, 1.18965, -3.83239, -0.595318, -1.56708, -0.0476166, -0.958164, 0.308146, 0.538959, -0.567305, -1.54234, -0.312223, -1.05125, 0.279093, -0.555883, 0.263304, -1.87512, -0.893629, 1.52954, -0.18754, 0.129317, -0.0409772, -0.481374, -0.272716, -0.40792, -0.428772, -1.23366, 0.932427, -0.284411, 0.114686, -0.175491, 0.287177, 0.321669, -0.324072, 0.163224, 0.792369, -1.01108, 1.23269, 0.226345, 0.882266, -0.0194645, 0.858726, 0.459991, -0.664407, -0.433639, 0.909784, 0.119792, 0.347188, 0.0949223, -0.223123, 0.515855, 1.06883, 0.507396, 1.05056, -0.0203115, 1.16572, 0.471133, 0.787901, -0.74391, -0.192763, 0.246201, 0.433876, 0.56428, 0.922964, 0.921105, 0.782957, 1.06646, -0.642362, -0.560816, -0.619862, 0.406475, -0.944654, 0.524438, 0.105425, 0.192224, -0.588941, 0.361894, -0.0422242, -0.039336, -0.739689, -0.431406, -0.503528, -0.476026, 0.321553, -1.01571, -0.572337, 0.309822, 0.917963, 0.861005, -0.763123, -0.260667, 0.35751, 0.803767, -0.39887, -0.580729, -0.517367, -0.134686, -0.22344, -0.263698, -0.449559, -0.882012, -0.477269, 0.705133, 0.471159, -1.19926, -0.238682, -0.554693, 0.795113, 0.0240765, 0.412576, -0.0746031, -0.56287, 0.0267437, 0.132269, -0.577963, 0.144747, -0.0134209, -0.0511658, 1.41067, -0.414959, -0.290205, 0.312317, -0.102443, -0.115503, -0.133131, -2.58108, -0.421964, 0.238911, 0.822077, -1.31384, -0.674516, 0.270687, -0.216738, 0.0403316, 0.394182, -1.24846, 0.518855, -1.11974, -0.114353, -0.105765, -0.0767365, -0.242629, 0.767938, -0.770488, 1.15386, 1.03914, -0.08044, -1.16603, 1.0451, 0.494025, -0.362372, 0.0147945, -0.1952, -0.333689, -0.507866, 1.61599, -0.814214, 0.0306287, -0.659977, 0.803305, 0.150613, 1.02249, 0.340859, 1.74513, 0.55267, -0.036223, 0.240978, 0.132654, 0.227788, 0.0112584, -0.76642, 0.941365, -0.123865, 0.579842, 1.11127, -0.478658, 0.21837, -0.213266, -0.430659, 0.953601, 0.404303, 0.593639, 0.421635, -0.771913, -0.592505, -0.627325, 0.184693, 0.317796, -0.286112, -0.478074, 0.300756, 0.0458375, 0.821987, -0.0354288, 0.459321, 0.595002, 0.190285, 0.373979, 0.365756, -0.575853, -0.492914, -0.671376, -0.0743422, 0.626893, 0.863512, -0.00458193, 1.51513, 0.183877, 0.718056, -0.512423, -0.529361, 0.0781563, 0.336743, 0.653948, 0.683846, -0.797976, 1.4012, 0.294974, -0.716314, -0.451483, 0.0356109, 1.05136, -1.26643, 0.0326029, 0.0339741, -0.294437, 0.511468])
 
 if __name__ == "__main__":
     # Part (a)
@@ -28,3 +29,8 @@ if __name__ == "__main__":
     plt.plot(subset_sample_times, subset_sample_values)
     plt.savefig("fig_d.png")
     plt.close()
+
+    # Part (e)
+    plt.plot(np.arange(len(dct)), dct_e)
+    plt.savefig("fig_e.png")
+    plt.close()