grad_g = lambda x: np.dot(A.T, np.dot(A, x) - y)
L = lin.norm(A, 2)**2 # Lipschitz constant
# context
maxiter = 1000
ctx = Context(full_output=True, maxiter=maxiter)
ctx.callback = lambda x: F(x) + G(x)
res = np.zeros((maxiter, len(methods)))
i = 0
for method in methods:
t1 = time.time()
x, fx = forward_backward(prox_f,
grad_g,
np.zeros((n, 1)),
L,
method=method,
context=ctx)
t2 = time.time()
print ("[" + method + "]: Performed 1000 iterations in " \
+ str(t2 - t1) + "seconds.")
res[:, i] = fx
i += 1
e = np.min(res.flatten())
plt.loglog(res[:(maxiter // 10), :] - e)
plt.legend(methods)
plt.grid(True, which="both", ls="-")
plt.tight_layout()
plt.show()
grad_g = lambda x: np.dot(A.T, np.dot(A, x) - y)
L = lin.norm(A, 2)**2 # Lipschitz constant
callback = lambda x: F(x) + G(x)
maxiter = 1000
res = np.zeros((maxiter, len(methods)))
i = 0
for method in methods:
t1 = time.time()
x, fx = forward_backward(prox_f,
grad_g,
np.zeros((n, 1)),
L,
maxiter=maxiter,
method=method,
full_output=1,
retall=0,
callback=callback)
t2 = time.time()
print "[" + method + "]: Performed 1000 iterations in " \
+ str(t2 - t1) + "seconds."
res[:, i] = fx
i += 1
e = np.min(res.flatten())
pl.loglog(res[:(maxiter // 10), :] - e)
pl.legend(methods)
pl.grid(True, which="both", ls="-")
F = lambda x: la * lin.norm(x, 1)
G = lambda x: 1 / 2 * lin.norm(y - np.dot(A, x)) ** 2
prox_f = lambda x, tau: soft_thresholding(x, la * tau)
grad_g = lambda x: np.dot(A.T, np.dot(A, x) - y)
L = lin.norm(A, 2) ** 2 # Lipschitz constant
callback = lambda x: F(x) + G(x)
maxiter = 1000
res = np.zeros((maxiter, len(methods)))
i = 0
for method in methods:
t1 = time.time()
x, fx = forward_backward(prox_f, grad_g, np.zeros((n, 1)), L,
maxiter=maxiter, method=method,
full_output=1, retall=0, callback=callback)
t2 = time.time()
print "[" + method + "]: Performed 1000 iterations in " \
+ str(t2 - t1) + "seconds."
res[:, i] = fx
i += 1
e = np.min(res.flatten())
pl.loglog(res[:(maxiter // 10), :] - e)
pl.legend(methods)
pl.grid(True, which="both", ls="-")
pl.tight_layout()
pl.show()
F = lambda x: la*np.linalg.norm(x,1)
G = lambda x: 1/2*np.linalg.norm(y - np.dot(A,x)) ** 2
ProxF = lambda x,tau: soft_thresholding(x, la*tau)
GradG = lambda x: np.dot(A.T,np.dot(A,x) - y)
L = np.linalg.norm(A, 2) ** 2 #Lipschitz constant
callback = lambda x: F(x) + G(x)
maxiter = 1000
res = np.zeros((maxiter,len(methods)))
i = 0
for method in methods:
t1 = time.time()
x, fx = forward_backward(ProxF, GradG, np.zeros((n,1)), L,
maxiter=maxiter, method=method,
full_output=1, retall=0, callback=callback)
t2 = time.time()
print "[" + method + "]: Performed 1000 iterations in " \
+ str(t2-t1) +"seconds."
res[:,i] = fx
i += 1
e = np.min(res.flatten())
plt.loglog(res[:(maxiter // 10),:] - e)
plt.legend(methods)
plt.grid(True,which="both",ls="-")
plt.tight_layout()
plt.show()
