Constrained Optimization
16.1) Given a point (x0, y0), find the closest point on the line y = ax+b by minimizing the distance d^2 = (x0 - x)^2 + (y0 - y)^2 subject to the constraint y - ax - b = 0.
16.5) Compressed sensing...
Two signals with random frequencies and amplitudes. Drawn separately:
Combined:
Code for plots here: compressed_sensing_signal_plot.py
Now sample a random subset
import numpy as np
import matplotlib.pyplot as plt
import random # for sampling
n = 100 # number of random samples
maxA = 10 # maxAmplitude
f1 = np.random.random_sample()
f2 = np.random.random_sample()
a1 = np.random.random_sample() * maxA
a2 = np.random.random_sample() * maxA
# combined signal
x = np.linspace(-5,5, 1000)
y = a1 * np.sin(2* np.pi * f1 *x) + a2 * np.sin(2* np.pi * f2 *x)
# combine x,y into 1000x2 matrix
points = np.column_stack([x,y])
# select random sample of n rows
sample = points[np.random.randint(0, points.shape[0]-1, size=n), :]
