# Using line search with PARAFACΒΆ

Example on how to use `tensorly.decomposition.parafac` with line search to accelerate convergence.

```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()