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unmix.py
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unmix.py
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import numpy as np
from numpy.linalg import norm
import cvxpy as cp
from scipy.optimize import *
# make global variables to pass to
# scipy objective and jacobian functions
# because scipy only supports f(x)
def FCLS_unmix(A, b):
# setup problem
n = A.shape[1]
x = cp.Variable(n)
objective = cp.Minimize(cp.sum_squares(A * x - b))
constraints = [0 <= x, cp.sum(x) == 1]
prob = cp.Problem(objective, constraints)
# find optimal solution
loss = prob.solve()
return x.value, loss
def LASSO_unmix(A, b, lam=0.01):
m = A.shape[0]
n = A.shape[1]
# setup problem
x = cp.Variable(n)
lam_cp = cp.Parameter(nonneg=True)
lam_cp.value = lam
objective = cp.Minimize(cp.sum_squares(A*x - b) + lam_cp*cp.norm(x, 1))
constraints = [0 <= x]
prob = cp.Problem(objective, constraints)
# find optimal solution
loss = prob.solve()
return x.value, loss
def SFCLS_unmix(A, b, lam=1e-6):
A = A
m = A.shape[0]
n = A.shape[1]
x = cp.Variable(n)
c = cp.Parameter(n)
objective = cp.Minimize(cp.sum_squares(A * x - b) + lam * cp.inv_pos(c*x))
constraints = [x >= 0,
cp.sum(x) == 1]
prob = cp.Problem(objective, constraints)
# iterate over n convex programs
temp_loss = np.zeros(n)
for i in range(n):
c_new = np.zeros(n)
c_new[i] = 1
c.value = c_new
temp_loss[i] = prob.solve()
# choose index with minimum loss
i_min = temp_loss.argmin()
c_new = np.zeros(n)
c_new[i_min] = 1
c.value = c_new
loss = prob.solve()
return x.value, loss
def p_norm_unmix(A, b, lam=0.01, p=0.8):
# setup problem
m = A.shape[0]
n = A.shape[1]
def func(x, A=A, b=b, lam=lam, p=p):
return np.sum((A@x - b)**2) + lam*norm(x, ord=p)
def func_deriv(x, A=A, b=b, lam=lam, p=p):
# sum of squares term
dfdx = 2*A.T@A@x - 2*A.T@b
# p norm term
for i in range(x.shape[0]):
x_i = np.clip(x[i], 1e-10, None)
dfdx[i] += lam*np.sign(x_i)*(np.abs(x_i)/norm(x, ord=p))**(p-1)
return dfdx
cons = ({'type': 'eq',
'fun': lambda x: np.ones(n).T@x - 1,
'jac': lambda x: np.ones(n)},
{'type': 'ineq',
'fun': lambda x: x,
'jac': lambda x: np.identity(n)})
x0 = np.full(n, 1/n)
res = minimize(func, x0, jac=func_deriv, constraints=cons,
method="SLSQP", options={'disp': False, 'maxiter': 500, 'ftol':1e-10})
return res.x , res
def delta_norm_unmix(A, b, lam=1e-7, delta=1e-3):
# setup problem
m = A.shape[0]
n = A.shape[1]
def func(x, A=A, b=b, lam=lam, delta=delta):
return np.sum((A@x - b)**2) + lam*[email protected](x+delta)
def func_deriv(x, A=A, b=b, lam=lam, delta=delta):
# sum of squares term
dfdx = 2*A.T@A@x - 2*A.T@b
# L0 norm term
for i in range(x.shape[0]):
dfdx[i] += lam*delta/((delta + x[i])**2)
return dfdx
cons = ({'type': 'eq',
'fun': lambda x: np.ones(n).T@x - 1,
'jac': lambda x: np.ones(n)},
{'type': 'ineq',
'fun': lambda x: x,
'jac': lambda x: np.identity(n)})
x0 = np.full(n, 1/n)
res = minimize(func, x0, jac=func_deriv, constraints=cons,
method="SLSQP", options={'disp': False, 'maxiter': 500, 'ftol':1e-9,
'eps': 1e-11})
return res.x , res
def gravitron(A, b, infty_lam=1e-7, delta_lam=1e-7, p_lam=1e-6, p=0.8, delta=1e-3):
# setup problem
m = A.shape[0]
n = A.shape[1]
def func(x, A=A, b=b, delta_lam=delta_lam, infty_lam=infty_lam,
p_lam=p_lam, p=p, delta=delta):
return np.sum((A@x - b)**2) + delta_lam*[email protected](x+delta) + infty_lam/x.max() + p_lam*norm(x, ord=p)
def func_deriv(x, A=A, b=b, infty_lam=infty_lam, delta_lam=delta_lam,
p_lam=p_lam, p=p, delta=delta):
# sum of squares term
dfdx = 2*A.T@A@x - 2*A.T@b
# L infinity norm term
max_i = np.argmax(x)
dfdx[max_i] += -infty_lam/x[max_i]**2
# delta norm and p_norm terms
for i in range(x.shape[0]):
dfdx[i] += delta_lam*delta/((delta + x[i])**2)
x_i = np.clip(x[i], 1e-10, None)
dfdx[i] += p_lam * np.sign(x_i) * (np.abs(x_i) / norm(x, ord=p)) ** (p - 1)
return dfdx
cons = ({'type': 'eq',
'fun': lambda x: np.ones(n).T@x - 1,
'jac': lambda x: np.ones(n)},
{'type': 'ineq',
'fun': lambda x: x,
'jac': lambda x: np.identity(n)})
x0 = np.full(n, 1/n)
res = minimize(func, x0, jac=func_deriv, constraints=cons,
method="SLSQP", options={'disp': False, 'maxiter': 500, 'ftol':1e-10,
'eps': 1e-11})
return res.x, res