test: added test to compare PG and GPG

Author: mrava87

examples/pyprox_deconv_pgm_compare.ipynb

@@ -264,7 +264,7 @@ def ProximalGradient(proxf, proxg, x0, tau=None, beta=0.5,
         if show:
             if iiter < 10 or niter - iiter < 10 or iiter % (niter // 10) == 0:
                 pf, pg = proxf(x), proxg(x)
-                msg = '%6g  %12.5e  %10.3e  %10.3e  %10.3e' % \
+                msg = '%6g  %12.5e  %10.3e  %10.3e  %10.3e  %10.3e' % \
                       (iiter + 1, np.real(to_numpy(x[0])) if x.ndim == 1 else np.real(to_numpy(x[0, 0])),
                        pf, pg[0] if epsg_print == 'Multi' else pg,
                        pf + np.sum(epsg * pg),

pyproximal/optimization/primal.py

@@ -0,0 +1,49 @@
+import pytest
+
+import numpy as np
+from numpy.testing import assert_array_almost_equal
+from pylops.basicoperators import MatrixMult
+from pyproximal.proximal import L1, L2
+from pyproximal.optimization.primal import ProximalGradient, GeneralizedProximalGradient
+
+par1 = {'n': 8, 'm': 10,  'dtype': 'float32'}  # float64
+par2 = {'n': 8, 'm': 10,  'dtype': 'float64'}  # float32
+
+
+@pytest.mark.parametrize("par", [(par1), (par2)])
+def test_PG_GPG(par):
+    """Check equivalency of ProximalGradient and GeneralizedProximalGradient when using
+    a single regularization term
+    """
+    np.random.seed(0)
+    n, m = par['n'], par['m']
+
+    # Define sparse model
+    x = np.zeros(m)
+    x[2], x[4] = 1, 0.5
+
+    # Random mixing matrix
+    R = np.random.normal(0., 1., (n, m))
+    Rop = MatrixMult(R)
+
+    y = Rop @ x
+
+    # Step size
+    L = (Rop.H * Rop).eigs(1).real
+    tau = 0.99 / L
+
+    # PG
+    l2 = L2(Op=Rop, b=y, niter=10, warm=True)
+    l1 = L1(sigma=5e-1)
+    xpg = ProximalGradient(l2, l1, x0=np.zeros(m),
+                           tau=tau, niter=100,
+                           acceleration='fista')
+
+    # GPG
+    l2 = L2(Op=Rop, b=y, niter=10, warm=True)
+    l1 = L1(sigma=5e-1)
+    xgpg = GeneralizedProximalGradient([l2, ], [l1, ], x0=np.zeros(m),
+                                       tau=tau, niter=100,
+                                       acceleration='fista')
+
+    assert_array_almost_equal(xpg, xgpg, decimal=2)