def test_precond_LinearLeastSquares(self):
n = 5
_A = np.eye(n) + 0.01 * util.randn([n, n])
A = linop.MatMul([n, 1], _A)
x = util.randn([n, 1])
y = A(x)
x_lstsq = np.linalg.lstsq(_A, y, rcond=-1)[0]
p = 1 / (np.sum(abs(_A)**2, axis=0).reshape([n, 1]))
P = linop.Multiply([n, 1], p)
x_rec = app.LinearLeastSquares(A, y, show_pbar=False).run()
npt.assert_allclose(x_rec, x_lstsq, atol=1e-3)
alpha = 1 / app.MaxEig(P * A.H * A, show_pbar=False).run()
x_rec = app.LinearLeastSquares(A,
y,
solver='GradientMethod',
alpha=alpha,
max_power_iter=100,
max_iter=1000,
show_pbar=False).run()
npt.assert_allclose(x_rec, x_lstsq, atol=1e-3)
tau = p
x_rec = app.LinearLeastSquares(A,
y,
solver='PrimalDualHybridGradient',
max_iter=1000,
tau=tau,
show_pbar=False).run()
npt.assert_allclose(x_rec, x_lstsq, atol=1e-3)
def test_MaxEig(self):
n = 5
mat = util.randn([n, n])
A = linop.MatMul([n, 1], mat)
s = np.linalg.svd(mat, compute_uv=False)
npt.assert_allclose(app.MaxEig(A.H * A, max_iter=100).run(), s[0]**2, atol=1e-2)
def test_precond_LinearLeastSquares(self):
n = 5
mat = np.eye(n) + 0.1 * util.randn([n, n])
A = linop.MatMul([n, 1], mat)
x = util.randn([n, 1])
y = A(x)
x_lstsq = np.linalg.lstsq(mat, y, rcond=-1)[0]
p = 1 / (np.sum(abs(mat)**2, axis=0).reshape([n, 1]))
P = linop.Multiply([n, 1], p)
x_rec = app.LinearLeastSquares(A, y).run()
npt.assert_allclose(x_rec, x_lstsq)
alpha = p / app.MaxEig(P * A.H * A).run()
x_rec = app.LinearLeastSquares(A, y, alg_name='GradientMethod',
max_iter=1000, alpha=alpha).run()
npt.assert_allclose(x_rec, x_lstsq)
tau = p
x_rec = app.LinearLeastSquares(A, y, alg_name='PrimalDualHybridGradient',
max_iter=1000, tau=tau).run()
npt.assert_allclose(x_rec, x_lstsq)