diff --git a/examples/plot_cv_vs_cp_path_lowrank.py b/examples/plot_cv_vs_cp_path_lowrank.py
new file mode 100644
index 0000000..be59c5d
--- /dev/null
+++ b/examples/plot_cv_vs_cp_path_lowrank.py
@@ -0,0 +1,99 @@
+"""
+=========================================
+Compare CV and CP for Low rank completion
+=========================================
+
+Compare explicit and implicit for low rank matrix completion.
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from numpy.linalg import norm
+from celer.plot_utils import configure_plt
+
+from iterreg.low_rank.solvers import dual_primal_low_rank
+from sklearn.model_selection import train_test_split
+# configure_plt()
+
+
+d = 50
+np.random.seed(0)
+observed = np.zeros([d, d], dtype=bool)
+idx = np.random.choice(d ** 2, int(0.6 * d ** 2), replace=False)
+observed.flat[idx] = True
+# rank = d // 10
+rank = 5
+Y_true = np.random.randn(d, rank) @ np.random.randn(rank, d)
+Y_true /= norm(Y_true, ord="fro")
+noise = np.random.randn(*Y_true.shape)
+noise /= norm(noise)
+Y_true += 0.3 * noise
+
+Y = Y_true.copy()
+Y[~observed] = 0
+
+idx_train, idx_test = train_test_split(idx, test_size=0.25)
+
+observed_train = np.zeros_like(observed)
+observed_train.flat[idx_train] = True
+Y_train = Y.copy()
+Y_train[~observed_train] = 0
+observed_test = np.zeros_like(observed)
+observed_test.flat[idx_test] = True
+Y_test = Y.copy()
+Y_test[~observed_test] = 0
+
+
+def pgd_nucnorm(Y, alpha, max_iter=10_000, tol=1e-6, X_init=None):
+    norm_Y = norm(Y)
+    if X_init is None:
+        X = Y.copy()
+    else:
+        X = X_init.copy()
+    for it in range(max_iter):
+        X_old = X.copy()
+        X -= observed * (X - Y)
+        U, s, VT = np.linalg.svd(X)
+        s = np.sign(s) * np.maximum(np.abs(s) - alpha, 0)
+        X = U @ (s[:, np.newaxis] * VT)
+        delta = norm(X - X_old)
+        if it % 100 == 0:
+            print(f"Iter {it}, delta={delta:.2e}")
+        if delta <= tol * norm_Y:
+            print(f"Early exit at iter {it}.")
+            break
+    return X
+
+
+x, _, _, all_x = dual_primal_low_rank(
+    observed, Y_train, max_iter=100, f_store=1, retall=True)
+
+losses_cp = [norm((Y_test - x)[observed_test]) / norm(Y_test) for x in all_x]
+
+
+alpha_max = np.linalg.norm(Y, ord=2)
+X = Y_train.copy()
+rhos = np.geomspace(1, 1e-3, 20)
+all_X_cv = []
+for idx, rho in enumerate(rhos):
+    X = pgd_nucnorm(Y_train, alpha=rho * alpha_max, X_init=X)
+    all_X_cv.append(X.copy())
+all_X_cv = np.array(all_X_cv)
+
+losses_cv = [norm((Y_test - x)[observed_test]) / norm(Y_test) for x in all_X_cv]
+
+
+plt.close('all')
+fig, axarr = plt.subplots(
+    1, 2, constrained_layout=True, sharey=True, figsize=(7.4, 2))
+ax = axarr[0]
+ax.semilogx(rhos, losses_cv)
+ax.invert_xaxis()
+ax.set_xlabel(r"$\lambda / \lambda_{\mathrm{max}}$")
+ax.set_ylabel(r"Loss on left out indices")
+
+ax = axarr[1]
+ax.plot(np.arange(len(losses_cp)), losses_cp)
+ax.set_xlabel("Chambolle-Pock iteration")
+
+plt.show(block=False)
diff --git a/examples/plot_sparse_recovery.py b/examples/plot_sparse_recovery.py
index 0a4e326..c6306a8 100644
--- a/examples/plot_sparse_recovery.py
+++ b/examples/plot_sparse_recovery.py
@@ -31,7 +31,7 @@ def plot_varying_sigma(corr, density, snr, max_iter=100):
     supp = np.random.choice(n_features, size=int(density * n_features),
                             replace=False)
     w_true = np.zeros(n_features)
-    w_true[supp] = 1
+    w_true[supp] = np.random.uniform(low=0.5, high=1.5, size=len(supp))
     X_, y_, w_true = make_correlated_data(
         n_samples=int(n_samples * 4 / 3.), n_features=n_features,
         w_true=w_true,
diff --git a/examples/plot_stopping_lowrank.py b/examples/plot_stopping_lowrank.py
index b147570..749401e 100644
--- a/examples/plot_stopping_lowrank.py
+++ b/examples/plot_stopping_lowrank.py
@@ -16,7 +16,7 @@
 configure_plt()
 
 
-d = 100
+d = 200
 np.random.seed(0)
 mask = np.zeros([d, d], dtype=bool)
 idx = np.random.choice(d ** 2, d ** 2 // 5, replace=False)
@@ -55,7 +55,7 @@
     distances[delta] = dist
 
 plt.close('all')
-fig1, ax = plt.subplots(1, 1, constrained_layout=True, figsize=(3.8, 2.2))
+fig1, ax = plt.subplots(1, 1, constrained_layout=True, figsize=(8., 4))
 n_points = 100
 for delta in deltas:
     x_plt = f_store * np.arange(len(distances[delta]))
diff --git a/iterreg/low_rank/solvers.py b/iterreg/low_rank/solvers.py
index 141db66..8a59adb 100644
--- a/iterreg/low_rank/solvers.py
+++ b/iterreg/low_rank/solvers.py
@@ -6,7 +6,7 @@
 
 def dual_primal_low_rank(
         mask, Y, max_iter=1000, f_store=10, sigma=None, limit=None,
-        stop_crit=1e-10, verbose=False):
+        stop_crit=1e-10, verbose=False, retall=False):
     """Lowest nuclear norm matrix equal to Y on mask.
     mask and Y are np.arrays, shape (d, d).
     """
@@ -17,9 +17,12 @@ def dual_primal_low_rank(
         tau = 1.
     else:
         tau = 0.99 / sigma
+    print(sigma, tau)
     Theta = np.zeros((d, d))
     Theta_old = Theta.copy()
     distances = np.zeros(max_iter // f_store)
+    if retall:
+        all_W = []
     W = Theta.copy()
 
     for k in range(max_iter):
@@ -32,6 +35,8 @@ def dual_primal_low_rank(
         if k % f_store == 0:
             if limit is not None:
                 distances[k // f_store] = norm(W - limit)
+            if retall:
+                all_W.append(W.copy())
             feasability = norm((W - Y)[mask])
             if verbose:
                 print(f"Iter {k}, feasability: {feasability:.1e}")
@@ -40,4 +45,6 @@ def dual_primal_low_rank(
                     f"Feasability {feasability:.1e} < {stop_crit:.1e}, exit.")
                 break
 
+    if retall:
+        return W, Theta, distances, np.array(all_W)
     return W, Theta, distances