Using line search with PARAFAC

import matplotlib.pyplot as plt

from time import time
import numpy as np
import tensorly as tl
from tensorly.random import random_cp
from tensorly.decomposition import CP, parafac

tol = np.logspace(-1, -9)
err = np.empty_like(tol)
err_ls = np.empty_like(tol)
tt = np.empty_like(tol)
tt_ls = np.empty_like(tol)
tensor = random_cp((10, 10, 10), 3, random_state=1234, full=True)

# Get a high-accuracy decomposition for comparison
fac = parafac(tensor, rank=3, n_iter_max=2000000, tol=1.0e-15, linesearch=True)
err_min = tl.norm(tl.cp_to_tensor(fac) - tensor)

for ii, toll in enumerate(tol):
    # Run PARAFAC decomposition without line search and time
    start = time()
    cp = CP(rank=3, n_iter_max=2000000, tol=toll, linesearch=False)
    fac = cp.fit_transform(tensor)
    tt[ii] = time() - start
    err[ii] = tl.norm(tl.cp_to_tensor(fac) - tensor)

# Run PARAFAC decomposition with line search and time
for ii, toll in enumerate(tol):
    start = time()
    cp = CP(rank=3, n_iter_max=2000000, tol=toll, linesearch=True)
    fac_ls = cp.fit_transform(tensor)
    tt_ls[ii] = time() - start

    # Calculate the error of both decompositions
    err_ls[ii] = tl.norm(tl.cp_to_tensor(fac_ls) - tensor)


fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.loglog(tt, err - err_min, ".", label="No line search")
ax.loglog(tt_ls, err_ls - err_min, ".r", label="Line search")
ax.legend()
ax.set_ylabel("Time")
ax.set_xlabel("Error")

plt.show()