import numpy as np
import cvxpy as cp


## PROBLEM 3
# Create data
m = 30
n = 10
np.random.seed(2020)
A = np.random.randn(m, n)
y = np.random.randn(m)

# Set up CVX problem
x = cp.Variable(n)
objective = cp.Minimize(0.5*cp.norm(A@x - y,2))
constraints = [0 <= x]
prob = cp.Problem(objective, constraints)

# The optimal objective value is returned by `prob.solve()`
result = prob.solve()
# The optimal value for x is stored in `x.value`
xstar = x.value
# The optimal Lagrange multiplier for a constraint is stored in
# `constraint.dual_value`
lambdastar = constraints[0].dual_value
    


## PROBLEM 4
# Create data
from sklearn import datasets 
np.random.seed(2020) # Set random seed so results are repeatable
x,y = datasets.make_circles(n_samples=100,noise=.05,factor=.5 )


# Create a function h, where h takes as input a vector x and outputs a the
# result of an SVM classifier with a quadratic kernel trained on the data above


# Plot the decision boundary. 
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap

# Begin by creating the mesh [x_min, x_max]x[y_min, y_max].
h = .02  # step size in the mesh
x_delta = (x[:,0].max() - x[:,0].min())*0.05 # add 5% white space to border
y_delta = (x[:,1].max() - x[:,1].min())*0.05
x_min, x_max = x[:,0].min() - x_delta, x[:,0].max() + x_delta
y_min, y_max = x[:,1].min() - y_delta, x[:,1].max() + y_delta
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))


#Z = h(np.c_[xx.ravel(), yy.ravel()]) 

# Create color maps
cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA'])
cmap_bold = ListedColormap(['#FF0000', '#00FF00'])

plt.figure()
# Put the classifier results
#Z = Z.reshape(xx.shape)
#plt.pcolormesh(xx, yy, Z, cmap=cmap_light)

# Plot the training points
plt.scatter(x[:,0], x[:,1], c=y, cmap=cmap_bold)

# Show the plot
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.title("SVM classifier")
plt.show()



## PROBLEM 5
# Construct the problem
N = 1000 # Population size
S = 10 # Number of infected individuals
M = 100 # Number of tests
K = 10 # Number of splits of each sample

# Define x0
ind0 = np.random.choice(N,S,0) # index subset 
x0 = np.zeros(N) 
x0[ind0] = np.random.rand(S)

# Define A
A = np.zeros((M,N))
for i in np.arange(N):
    ind = np.random.choice(M,K,0)
    A[ind,i] = 1
    
y = A @ x0