def test_affine_transform():
# Test affine transform
m = 20
x1d = np.arange(m)
x2d = x1d[:, None]
x22d = np.c_[x2d, x2d]
# Error if both of linear and affine components are None
assert_raises(AffineError, affine_transform, None, None)
assert_raises(AffineError, linear_transform, None)
# With linear None and 0 affine offset - identity transform
for x in (x1d, x2d, x22d):
trans = affine_transform(None, np.zeros((m, 1)))
assert_array_almost_equal(trans.affine_map(x), x)
assert_array_almost_equal(trans.linear_map(x), x)
assert_array_almost_equal(trans.adjoint_map(x), x)
# With linear eye and None affine offset - identity again
trans = affine_transform(np.eye(m), None)
assert_array_almost_equal(trans.affine_map(x), x)
assert_array_almost_equal(trans.linear_map(x), x)
assert_array_almost_equal(trans.adjoint_map(x), x)
# affine_transform as input
trans = affine_transform(trans, None)
assert_array_almost_equal(trans.affine_map(x), x)
assert_array_almost_equal(trans.linear_map(x), x)
assert_array_almost_equal(trans.adjoint_map(x), x)
# diag
trans = affine_transform(np.ones(m), None, True)
assert_array_almost_equal(trans.affine_map(x), x)
assert_array_almost_equal(trans.linear_map(x), x)
assert_array_almost_equal(trans.adjoint_map(x), x)
def test_composition2():
X1 = np.random.standard_normal((20, 30))
X2 = np.random.standard_normal((30, 10))
X3 = np.random.standard_normal((10, 20))
b1 = np.random.standard_normal(20)
b2 = np.random.standard_normal(30)
b3 = np.random.standard_normal(10)
L1 = affine_transform(X1, b1)
L2 = affine_transform(X2, b2)
L3 = affine_transform(X3, b3)
z = np.random.standard_normal(20)
w = np.random.standard_normal(20)
comp = composition(L1, L2, L3)
assert_array_almost_equal(comp.linear_map(z),
np.dot(X1, np.dot(X2, np.dot(X3, z))))
assert_array_almost_equal(comp.adjoint_map(w),
np.dot(X3.T, np.dot(X2.T, np.dot(X1.T, w))))
assert_array_almost_equal(
comp.affine_map(z),
np.dot(X1,
np.dot(X2,
np.dot(X3, z) + b3) + b2) + b1)
def test_affine_transform():
# Test affine transform
m = 20
x1d = np.arange(m)
x2d = x1d[:,None]
x22d = np.c_[x2d, x2d]
# Error if both of linear and affine components are None
assert_raises(AffineError, affine_transform, None, None)
# With linear None and 0 affine offset - identity transform
for x in (x1d, x2d, x22d):
trans = affine_transform(None, np.zeros((m,1)))
assert_array_equal(trans.affine_map(x), x)
assert_array_equal(trans.linear_map(x), x)
assert_array_equal(trans.adjoint_map(x), x)
# With linear eye and None affine offset - identity again
trans = affine_transform(np.eye(m), None)
assert_array_equal(trans.affine_map(x), x)
assert_array_equal(trans.linear_map(x), x)
assert_array_equal(trans.adjoint_map(x), x)
# affine_transform as input
trans = affine_transform(trans, None)
assert_array_equal(trans.affine_map(x), x)
assert_array_equal(trans.linear_map(x), x)
assert_array_equal(trans.adjoint_map(x), x)
# diag
trans = affine_transform(np.ones(m), None, True)
assert_array_equal(trans.affine_map(x), x)
assert_array_equal(trans.linear_map(x), x)
assert_array_equal(trans.adjoint_map(x), x)
def test_composition():
X1 = np.random.standard_normal((20,30))
X2 = np.random.standard_normal((30,10))
b1 = np.random.standard_normal(20)
b2 = np.random.standard_normal(30)
L1 = affine_transform(X1, b1)
L2 = affine_transform(X2, b2)
z = np.random.standard_normal(10)
w = np.random.standard_normal(20)
comp = composition(L1,L2)
assert_array_equal(comp.linear_map(z), np.dot(X1, np.dot(X2, z)))
assert_array_equal(comp.adjoint_map(w), np.dot(X2.T, np.dot(X1.T, w)))
assert_array_equal(comp.affine_map(z), np.dot(X1, np.dot(X2, z)+b2)+b1)
def test_subsample_cols():
X = np.random.standard_normal((50, 20))
L = ra.affine_transform(X, None)
Xs = subsample_columns(L, range(5))
Xs - X[:, range(5)]
np.testing.assert_allclose(Xs, X[:, range(5)])
def test_adjoint():
X = np.random.standard_normal((20, 30))
b = np.random.standard_normal(20)
L = affine_transform(X, b)
z = np.random.standard_normal(30)
w = np.random.standard_normal(20)
A = adjoint(L)
assert_array_almost_equal(A.linear_map(w), L.adjoint_map(w))
assert_array_almost_equal(A.affine_map(w), L.adjoint_map(w))
assert_array_almost_equal(A.adjoint_map(z), L.linear_map(z))
def test_adjoint():
X = np.random.standard_normal((20,30))
b = np.random.standard_normal(20)
L = affine_transform(X, b)
z = np.random.standard_normal(30)
w = np.random.standard_normal(20)
A = adjoint(L)
assert_array_equal(A.linear_map(w), L.adjoint_map(w))
assert_array_equal(A.affine_map(w), L.adjoint_map(w))
assert_array_equal(A.adjoint_map(z), L.linear_map(z))
def test_selector():
X = np.arange(30).reshape((6,5))
offset = np.arange(6)
transform = affine_transform(X, offset)
apply_to_first5 = selector(slice(0,5), (20,), transform)
apply_to_first5.affine_map(np.arange(20))
apply_to_first5.linear_map(np.arange(20))
apply_to_first5.adjoint_map(np.arange(6))
just_select = selector(slice(0,5), (20,))
just_select.affine_map(np.arange(20))
just_select.linear_map(np.arange(20))
just_select.adjoint_map(np.arange(5))
np.testing.assert_allclose(np.arange(5), just_select.linear_map(np.arange(20)))
def test_selector():
X = np.arange(30).reshape((6, 5))
offset = np.arange(6)
transform = affine_transform(X, offset)
apply_to_first5 = selector(slice(0, 5), (20, ), transform)
apply_to_first5.affine_map(np.arange(20))
apply_to_first5.linear_map(np.arange(20))
apply_to_first5.adjoint_map(np.arange(6))
just_select = selector(slice(0, 5), (20, ))
just_select.affine_map(np.arange(20))
just_select.linear_map(np.arange(20))
just_select.adjoint_map(np.arange(5))
np.testing.assert_allclose(np.arange(5),
just_select.linear_map(np.arange(20)))
