def test_fspace_one(out_shape):
"""Check one element."""
fspace = FunctionSpace(odl.IntervalProd(0, 1),
out_dtype=(float, out_shape))
points = _points(fspace.domain, 4)
mesh_shape = (5, )
mesh = _meshgrid(fspace.domain, mesh_shape)
point = 0.5
values_points_shape = out_shape + (4, )
values_point_shape = out_shape
values_mesh_shape = out_shape + mesh_shape
f_one = fspace.one()
assert all_equal(f_one(points), np.ones(values_points_shape))
if not out_shape:
assert f_one(point) == 1.0
else:
assert all_equal(f_one(point), np.ones(values_point_shape))
assert all_equal(f_one(mesh), np.ones(values_mesh_shape))
out_points = np.empty(values_points_shape)
out_mesh = np.empty(values_mesh_shape)
f_one(points, out=out_points)
f_one(mesh, out=out_mesh)
assert all_equal(out_points, np.ones(values_points_shape))
assert all_equal(out_mesh, np.ones(values_mesh_shape))
def test_fspace_elem_power(power, out_shape):
"""Check taking powers of fspace elements."""
# Make sure test functions don't take negative values
intv = odl.IntervalProd([1, 0], [2, 1])
fspace = FunctionSpace(intv, out_dtype=(float, out_shape))
points = _points(fspace.domain, 4)
ndim = len(out_shape)
with np.errstate(all='ignore'):
if ndim == 0:
f_elem = fspace.element(func_nd_oop)
true_result = func_nd_ref(points)**power
elif ndim == 1:
f_elem = fspace.element(func_vec_nd_oop)
true_result = func_vec_nd_ref(points)**power
elif ndim == 2:
f_elem = fspace.element(func_tens_oop)
true_result = func_tens_ref(points)**power
else:
assert False
# Out-of-place power
f_elem_pow = f_elem**power
assert all_almost_equal(f_elem_pow(points), true_result)
out_arr = np.empty(out_shape + (4, ))
f_elem_pow(points, out_arr)
assert all_almost_equal(out_arr, true_result)
# In-place power
f_elem_pow = f_elem.copy()
f_elem_pow **= power
assert all_almost_equal(f_elem_pow(points), true_result)
out_arr = np.empty(out_shape + (4, ))
f_elem_pow(points, out_arr)
assert all_almost_equal(out_arr, true_result)
def test_fspace_elem_real_imag_conj(out_shape):
"""Check taking real/imaginary parts of fspace elements."""
fspace = FunctionSpace(odl.IntervalProd(0, 1),
out_dtype=(complex, out_shape))
ndim = len(out_shape)
if ndim == 0:
f_elem = fspace.element(func_complex_nd_oop)
elif ndim == 1:
f_elem = fspace.element(func_vec_complex_nd_oop)
elif ndim == 2:
f_elem = fspace.element(func_tens_complex_oop)
else:
assert False
points = _points(fspace.domain, 4)
mesh_shape = (5, )
mesh = _meshgrid(fspace.domain, mesh_shape)
point = 0.5
values_points_shape = out_shape + (4, )
values_mesh_shape = out_shape + mesh_shape
result_points = f_elem(points)
result_point = f_elem(point)
result_mesh = f_elem(mesh)
assert all_almost_equal(f_elem.real(points), result_points.real)
assert all_almost_equal(f_elem.real(point), result_point.real)
assert all_almost_equal(f_elem.real(mesh), result_mesh.real)
assert all_almost_equal(f_elem.imag(points), result_points.imag)
assert all_almost_equal(f_elem.imag(point), result_point.imag)
assert all_almost_equal(f_elem.imag(mesh), result_mesh.imag)
assert all_almost_equal(f_elem.conj()(points), result_points.conj())
assert all_almost_equal(f_elem.conj()(point), np.conj(result_point))
assert all_almost_equal(f_elem.conj()(mesh), result_mesh.conj())
out_points = np.empty(values_points_shape, dtype=float)
out_mesh = np.empty(values_mesh_shape, dtype=float)
f_elem.real(points, out=out_points)
f_elem.real(mesh, out=out_mesh)
assert all_almost_equal(out_points, result_points.real)
assert all_almost_equal(out_mesh, result_mesh.real)
f_elem.imag(points, out=out_points)
f_elem.imag(mesh, out=out_mesh)
assert all_almost_equal(out_points, result_points.imag)
assert all_almost_equal(out_mesh, result_mesh.imag)
out_points = np.empty(values_points_shape, dtype=complex)
out_mesh = np.empty(values_mesh_shape, dtype=complex)
f_elem.conj()(points, out=out_points)
f_elem.conj()(mesh, out=out_mesh)
assert all_almost_equal(out_points, result_points.conj())
assert all_almost_equal(out_mesh, result_mesh.conj())
def test_addition():
fspace = FunctionSpace(odl.Interval(0, pi))
sine = fspace.element(np.sin)
cosine = fspace.element(np.cos)
sum_func = sine + cosine
for x in [0.0, 0.2, 1.0]:
assert almost_equal(sum_func(x), np.sin(x) + np.cos(x))
def test_fspace_vector_eval_complex():
rect, points, mg = _standard_setup_2d()
fspace = FunctionSpace(rect, field=odl.ComplexNumbers())
f_novec = fspace.element(cfunc_2d_novec, vectorized=False)
f_vec_oop = fspace.element(cfunc_2d_vec_oop, vectorized=True)
f_vec_ip = fspace.element(cfunc_2d_vec_ip, vectorized=True)
f_vec_dual = fspace.element(cfunc_2d_vec_dual, vectorized=True)
true_arr = cfunc_2d_vec_oop(points)
true_mg = cfunc_2d_vec_oop(mg)
# Out-of-place
assert f_novec([0.5, 1.5]) == cfunc_2d_novec([0.5, 1.5])
assert f_vec_oop([0.5, 1.5]) == cfunc_2d_novec([0.5, 1.5])
assert all_equal(f_vec_oop(points), true_arr)
assert all_equal(f_vec_oop(mg), true_mg)
# In-place standard implementation
out_arr = np.empty((5,), dtype='complex128')
out_mg = np.empty((2, 3), dtype='complex128')
f_vec_oop(points, out=out_arr)
f_vec_oop(mg, out=out_mg)
assert all_equal(out_arr, true_arr)
assert all_equal(out_mg, true_mg)
with pytest.raises(TypeError): # ValueError: invalid vectorized input
f_vec_oop(points[0])
# In-place only
out_arr = np.empty((5,), dtype='complex128')
out_mg = np.empty((2, 3), dtype='complex128')
f_vec_ip(points, out=out_arr)
f_vec_ip(mg, out=out_mg)
assert all_equal(out_arr, true_arr)
assert all_equal(out_mg, true_mg)
# Standard out-of-place evaluation
assert f_vec_ip([0.5, 1.5]) == cfunc_2d_novec([0.5, 1.5])
assert all_equal(f_vec_ip(points), true_arr)
assert all_equal(f_vec_ip(mg), true_mg)
# Dual use
assert f_vec_dual([0.5, 1.5]) == cfunc_2d_novec([0.5, 1.5])
assert all_equal(f_vec_dual(points), true_arr)
assert all_equal(f_vec_dual(mg), true_mg)
out_arr = np.empty((5,), dtype='complex128')
out_mg = np.empty((2, 3), dtype='complex128')
f_vec_dual(points, out=out_arr)
f_vec_dual(mg, out=out_mg)
assert all_equal(out_arr, true_arr)
assert all_equal(out_mg, true_mg)
def test_fspace_simple_attributes():
intv = odl.IntervalProd(0, 1)
fspace = FunctionSpace(intv)
fspace_r = FunctionSpace(intv, field=odl.RealNumbers())
fspace_c = FunctionSpace(intv, field=odl.ComplexNumbers())
assert fspace.domain == intv
assert fspace.range == odl.RealNumbers()
assert fspace_r.range == odl.RealNumbers()
assert fspace_c.range == odl.ComplexNumbers()
def test_fspace_vector_equality():
rect = odl.IntervalProd([0, 0], [1, 2])
fspace = FunctionSpace(rect)
f_novec = fspace.element(func_2d_novec, vectorized=False)
f_vec_oop = fspace.element(func_2d_vec_oop, vectorized=True)
f_vec_oop_2 = fspace.element(func_2d_vec_oop, vectorized=True)
f_vec_ip = fspace.element(func_2d_vec_ip, vectorized=True)
f_vec_ip_2 = fspace.element(func_2d_vec_ip, vectorized=True)
f_vec_dual = fspace.element(func_2d_vec_dual, vectorized=True)
f_vec_dual_2 = fspace.element(func_2d_vec_dual, vectorized=True)
assert f_novec == f_novec
assert f_novec != f_vec_oop
assert f_novec != f_vec_ip
assert f_novec != f_vec_dual
assert f_vec_oop == f_vec_oop
assert f_vec_oop == f_vec_oop_2
assert f_vec_oop != f_vec_ip
assert f_vec_oop != f_vec_dual
assert f_vec_ip == f_vec_ip
assert f_vec_ip == f_vec_ip_2
assert f_vec_ip != f_vec_dual
assert f_vec_dual == f_vec_dual
assert f_vec_dual == f_vec_dual_2
def test_fspace_lincomb_vec_tens(a, b, out_shape):
"""Check linear combination in function spaces."""
if out_shape == ():
return
intv = odl.IntervalProd([0, 0], [1, 1])
fspace = FunctionSpace(intv, out_dtype=(float, out_shape))
points = _points(fspace.domain, 4)
ndim = len(out_shape)
if ndim == 1:
f_elem1 = fspace.element(func_vec_nd_oop)
f_elem2 = fspace.element(func_vec_nd_other)
true_result = (a * func_vec_nd_ref(points) +
b * func_vec_nd_other(points))
elif ndim == 2:
f_elem1 = fspace.element(func_tens_oop)
f_elem2 = fspace.element(func_tens_other)
true_result = a * func_tens_ref(points) + b * func_tens_other(points)
else:
assert False
out_func = fspace.element()
fspace.lincomb(a, f_elem1, b, f_elem2, out_func)
assert all_equal(out_func(points), true_result)
out_arr = np.empty(out_shape + (4, ))
out_func(points, out=out_arr)
assert all_equal(out_arr, true_result)
def test_fspace_equality():
intv = odl.Interval(0, 1)
intv2 = odl.Interval(-1, 1)
fspace = FunctionSpace(intv)
fspace_r = FunctionSpace(intv, field=odl.RealNumbers())
fspace_c = FunctionSpace(intv, field=odl.ComplexNumbers())
fspace_intv2 = FunctionSpace(intv2)
assert fspace == fspace_r
assert fspace != fspace_c
assert fspace != fspace_intv2
def test_fspace_vector_ufunc():
intv = odl.IntervalProd(0, 1)
points = _points(intv, num=5)
mg = _meshgrid(intv, shape=(5, ))
fspace = FunctionSpace(intv)
f_vec = fspace.element(np.sin)
assert f_vec(0.5) == np.sin(0.5)
assert all_equal(f_vec(points), np.sin(points.squeeze()))
assert all_equal(f_vec(mg), np.sin(mg[0]))
def test_fspace_vector_ufunc():
intv = odl.Interval(0, 1)
points = _points(intv, num=5)
mg = _meshgrid(intv, shape=(5,))
fspace = FunctionSpace(intv)
f_vec = fspace.element(np.sin)
assert f_vec(0.5) == np.sin(0.5)
assert all_equal(f_vec(points), np.sin(points.squeeze()))
assert all_equal(f_vec(mg), np.sin(mg[0]))
def test_interval(exponent):
fspace = FunctionSpace(odl.Interval(0, pi))
lpdiscr = odl.uniform_discr(fspace, 10, exponent=exponent)
if exponent == float("inf"):
sine = fspace.element(np.sin)
discr_sine = lpdiscr.element(sine)
assert discr_sine.norm() <= 1
else:
sine_p = fspace.element(lambda x: np.sin(x) ** (1 / exponent))
discr_sine_p = lpdiscr.element(sine_p)
assert almost_equal(discr_sine_p.norm(), 2 ** (1 / exponent), places=2)
def test_rectangle(exponent):
fspace = FunctionSpace(odl.Rectangle((0, 0), (pi, 2 * pi)))
n, m = 10, 10
lpdiscr = odl.uniform_discr(fspace, (n, m), exponent=exponent)
if exponent == float("inf"):
sine2 = fspace.element(lambda x, y: np.sin(x) * np.sin(y))
discr_sine = lpdiscr.element(sine2)
assert discr_sine.norm() <= 1
else:
sine_p = fspace.element(lambda x, y: (np.sin(x) * np.sin(y)) ** (1 / exponent))
discr_sine_p = lpdiscr.element(sine_p)
assert almost_equal(discr_sine_p.norm(), 4 ** (1 / exponent), places=2)
def test_fspace_vector_real_imag():
rect, _, mg = _standard_setup_2d()
cspace = FunctionSpace(rect, field=odl.ComplexNumbers())
f = cspace.element(cfunc_2d_vec_oop)
# real / imag on complex functions
assert all_equal(f.real(mg), cfunc_2d_vec_oop(mg).real)
assert all_equal(f.imag(mg), cfunc_2d_vec_oop(mg).imag)
out_mg = np.empty((2, 3))
f.real(mg, out=out_mg)
assert all_equal(out_mg, cfunc_2d_vec_oop(mg).real)
f.imag(mg, out=out_mg)
assert all_equal(out_mg, cfunc_2d_vec_oop(mg).imag)
# real / imag on real functions, should be the function itself / zero
rspace = FunctionSpace(rect)
f = rspace.element(func_2d_vec_oop)
assert all_equal(f.real(mg), f(mg))
assert all_equal(f.imag(mg), rspace.zero()(mg))
# Complex conjugate
f = cspace.element(cfunc_2d_vec_oop)
fbar = f.conj()
assert all_equal(fbar(mg), cfunc_2d_vec_oop(mg).conj())
out_mg = np.empty((2, 3), dtype='complex128')
fbar(mg, out=out_mg)
assert all_equal(out_mg, cfunc_2d_vec_oop(mg).conj())
def test_fspace_vector_equality():
rect = odl.Rectangle([0, 0], [1, 2])
fspace = FunctionSpace(rect)
f_novec = fspace.element(func_2d_novec, vectorized=False)
f_vec_oop = fspace.element(func_2d_vec_oop, vectorized=True)
f_vec_oop_2 = fspace.element(func_2d_vec_oop, vectorized=True)
f_vec_ip = fspace.element(func_2d_vec_ip, vectorized=True)
f_vec_ip_2 = fspace.element(func_2d_vec_ip, vectorized=True)
f_vec_dual = fspace.element(func_2d_vec_dual, vectorized=True)
f_vec_dual_2 = fspace.element(func_2d_vec_dual, vectorized=True)
assert f_novec == f_novec
assert f_novec != f_vec_oop
assert f_novec != f_vec_ip
assert f_novec != f_vec_dual
assert f_vec_oop == f_vec_oop
assert f_vec_oop == f_vec_oop_2
assert f_vec_oop != f_vec_ip
assert f_vec_oop != f_vec_dual
assert f_vec_ip == f_vec_ip
assert f_vec_ip == f_vec_ip_2
assert f_vec_ip != f_vec_dual
assert f_vec_dual == f_vec_dual
assert f_vec_dual == f_vec_dual_2
def test_fspace_vector_arithmetic(variant, op):
if variant == 'sv' and '=' in op: # makes no sense, quit
return
# Setup
rect, points, mg = _standard_setup_2d()
point = points.T[0]
fspace = FunctionSpace(rect)
a = -1.5
b = 2.0
array_out = np.empty((5, ), dtype=float)
mg_out = np.empty((2, 3), dtype=float)
# Initialize a bunch of elements
f_novec = fspace.element(func_2d_novec, vectorized=False)
f_vec = fspace.element(func_2d_vec_dual, vectorized=True)
g_novec = fspace.element(other_func_2d_novec, vectorized=False)
g_vec = fspace.element(other_func_2d_vec_dual, vectorized=True)
out_novec = fspace.element(vectorized=False)
out_vec = fspace.element(vectorized=True)
if variant[0] == 'v':
true_l_novec = func_2d_novec(point)
true_l_arr = func_2d_vec_oop(points)
true_l_mg = func_2d_vec_oop(mg)
test_l_novec = f_novec
test_l_vec = f_vec
else: # 's'
true_l_novec = true_l_arr = true_l_mg = a
test_l_novec = test_l_vec = a
if variant[1] == 'v':
true_r_novec = other_func_2d_novec(point)
true_r_arr = other_func_2d_vec_oop(points)
true_r_mg = other_func_2d_vec_oop(mg)
test_r_novec = g_novec
test_r_vec = g_vec
else: # 's'
true_r_novec = true_r_arr = true_r_mg = b
test_r_novec = test_r_vec = b
true_novec = _op(true_l_novec, op, true_r_novec)
true_arr = _op(true_l_arr, op, true_r_arr)
true_mg = _op(true_l_mg, op, true_r_mg)
out_novec = _op(test_l_novec, op, test_r_novec)
out_vec = _op(test_l_vec, op, test_r_vec)
assert almost_equal(out_novec(point), true_novec)
assert all_equal(out_vec(points), true_arr)
out_vec(points, out=array_out)
assert all_equal(array_out, true_arr)
assert all_equal(out_vec(mg), true_mg)
out_vec(mg, out=mg_out)
assert all_equal(mg_out, true_mg)
def test_fspace_vector_copy():
fspace = FunctionSpace(odl.IntervalProd(0, 1))
f_novec = fspace.element(func_1d_oop, vectorized=False)
f_vec_ip = fspace.element(func_1d_ip, vectorized=True)
f_vec_dual = fspace.element(func_1d_dual, vectorized=True)
f_out = f_novec.copy()
assert f_out == f_novec
f_out = f_vec_ip.copy()
assert f_out == f_vec_ip
f_out = f_vec_dual.copy()
assert f_out == f_vec_dual
def test_equals():
"""Test equality check and hash."""
intv = odl.IntervalProd(0, 1)
intv2 = odl.IntervalProd(-1, 1)
fspace = FunctionSpace(intv)
fspace_r = FunctionSpace(intv, field=odl.RealNumbers())
fspace_c = FunctionSpace(intv, field=odl.ComplexNumbers())
fspace_intv2 = FunctionSpace(intv2)
_test_eq(fspace, fspace)
_test_eq(fspace, fspace_r)
_test_eq(fspace_c, fspace_c)
_test_neq(fspace, fspace_c)
_test_neq(fspace, fspace_intv2)
def test_fspace_vector_copy():
fspace = FunctionSpace(odl.Interval(0, 1))
f_novec = fspace.element(func_1d_oop, vectorized=False)
f_vec_ip = fspace.element(func_1d_ip, vectorized=True)
f_vec_dual = fspace.element(func_1d_dual, vectorized=True)
f_out = f_novec.copy()
assert f_out == f_novec
f_out = f_vec_ip.copy()
assert f_out == f_vec_ip
f_out = f_vec_dual.copy()
assert f_out == f_vec_dual
def test_fspace_elem_eval_unusual_dtypes():
"""Check evaluation with unusual data types (int and string)."""
str3 = odl.Strings(3)
fspace = FunctionSpace(str3, out_dtype=int)
strings = np.array(['aa', 'b', 'cab', 'aba'])
out_vec = np.empty((4, ), dtype=int)
# Vectorized for arrays only
func_elem = fspace.element(
lambda s: np.array([str(si).count('a') for si in s]))
true_values = [2, 0, 1, 2]
assert func_elem('abc') == 1
assert all_equal(func_elem(strings), true_values)
func_elem(strings, out=out_vec)
assert all_equal(out_vec, true_values)
def test_fspace_attributes():
"""Check attribute access and correct values."""
intv = odl.IntervalProd(0, 1)
# Scalar-valued function spaces
fspace = FunctionSpace(intv)
fspace_r = FunctionSpace(intv, out_dtype=float)
fspace_c = FunctionSpace(intv, out_dtype=complex)
fspace_s = FunctionSpace(intv, out_dtype='U1')
scalar_spaces = (fspace, fspace_r, fspace_c, fspace_s)
assert fspace.domain == intv
assert fspace.field == odl.RealNumbers()
assert fspace_r.field == odl.RealNumbers()
assert fspace_c.field == odl.ComplexNumbers()
assert fspace_s.field is None
assert fspace.out_dtype == float
assert fspace_r.out_dtype == float
assert fspace_r.real_out_dtype == float
assert fspace_r.complex_out_dtype == complex
assert fspace_c.out_dtype == complex
assert fspace_c.real_out_dtype == float
assert fspace_c.complex_out_dtype == complex
assert fspace_s.out_dtype == np.dtype('U1')
assert fspace.is_real
assert not fspace.is_complex
assert fspace_r.is_real
assert not fspace_r.is_complex
assert fspace_c.is_complex
assert not fspace_c.is_real
with pytest.raises(AttributeError):
fspace_s.real_out_dtype
with pytest.raises(AttributeError):
fspace_s.complex_out_dtype
assert all(spc.scalar_out_dtype == spc.out_dtype for spc in scalar_spaces)
assert all(spc.out_shape == () for spc in scalar_spaces)
assert all(not spc.tensor_valued for spc in scalar_spaces)
# Vector-valued function space
fspace_vec = FunctionSpace(intv, out_dtype=(float, (2, )))
assert fspace_vec.field == odl.RealNumbers()
assert fspace_vec.out_dtype == np.dtype((float, (2, )))
assert fspace_vec.scalar_out_dtype == float
assert fspace_vec.out_shape == (2, )
assert fspace_vec.tensor_valued
def test_fspace_out_dtype():
rect = odl.IntervalProd([0, 0], [3, 5])
points = np.array([[0, 1], [0, 3], [3, 4], [2, 5]], dtype='int').T
vec1 = np.array([0, 1, 3])[:, None]
vec2 = np.array([1, 2, 4, 5])[None, :]
mg = (vec1, vec2)
true_arr = func_2d_vec_oop(points)
true_mg = func_2d_vec_oop(mg)
fspace = FunctionSpace(rect, out_dtype='int')
f_vec = fspace.element(func_2d_vec_oop)
assert all_equal(f_vec(points), true_arr)
assert all_equal(f_vec(mg), true_mg)
assert f_vec(points).dtype == np.dtype('int')
assert f_vec(mg).dtype == np.dtype('int')
def test_fspace_out_dtype():
rect = odl.Rectangle([0, 0], [3, 5])
points = np.array([[0, 1], [0, 3], [3, 4], [2, 5]], dtype='int').T
vec1 = np.array([0, 1, 3])[:, None]
vec2 = np.array([1, 2, 4, 5])[None, :]
mg = (vec1, vec2)
true_arr = func_2d_vec_oop(points)
true_mg = func_2d_vec_oop(mg)
fspace = FunctionSpace(rect, out_dtype='int')
f_vec = fspace.element(func_2d_vec_oop)
assert all_equal(f_vec(points), true_arr)
assert all_equal(f_vec(mg), true_mg)
assert f_vec(points).dtype == np.dtype('int')
assert f_vec(mg).dtype == np.dtype('int')
def test_equals():
"""Test equality check and hash."""
intv = odl.IntervalProd(0, 1)
intv2 = odl.IntervalProd(-1, 1)
fspace = FunctionSpace(intv)
fspace_r = FunctionSpace(intv, out_dtype=float)
fspace_c = FunctionSpace(intv, out_dtype=complex)
fspace_intv2 = FunctionSpace(intv2)
fspace_vec = FunctionSpace(intv, out_dtype=(float, (2, )))
_test_eq(fspace, fspace)
_test_eq(fspace, fspace_r)
_test_eq(fspace_c, fspace_c)
_test_neq(fspace, fspace_c)
_test_neq(fspace, fspace_intv2)
_test_neq(fspace_r, fspace_vec)
def test_fspace_elem_vectorized_init(vectorized):
"""Check init of fspace elements with(out) vectorization."""
intv = odl.IntervalProd(0, 1)
fspace_scal = FunctionSpace(intv)
fspace_scal.element(func_nd_oop, vectorized=vectorized)
fspace_vec = FunctionSpace(intv, out_dtype=(float, (2, )))
fspace_vec.element(func_vec_nd_oop, vectorized=vectorized)
fspace_vec.element(func_nd_oop_seq, vectorized=vectorized)
def test_fspace_one():
rect, points, mg = _standard_setup_2d()
# real
fspace = FunctionSpace(rect)
one_vec = fspace.one()
assert one_vec([0.5, 1.5]) == 1.0
assert all_equal(one_vec(points), np.ones(5, dtype=float))
assert all_equal(one_vec(mg), np.ones((2, 3), dtype=float))
# complex
fspace = FunctionSpace(rect, field=odl.ComplexNumbers())
one_vec = fspace.one()
assert one_vec([0.5, 1.5]) == 1.0 + 1j * 0.0
assert all_equal(one_vec(points), np.ones(5, dtype=complex))
assert all_equal(one_vec(mg), np.ones((2, 3), dtype=complex))
def test_fspace_vec_elem_eval(func_vec_nd, out_dtype):
"""Check evaluation of scalar-valued function elements."""
intv = odl.IntervalProd([0, 0], [1, 1])
fspace_vec = FunctionSpace(intv, out_dtype=(float, (2, )))
points = _points(fspace_vec.domain, 3)
mesh_shape = (2, 3)
mesh = _meshgrid(fspace_vec.domain, mesh_shape)
point = [0.5, 0.5]
values_points_shape = (2, 3)
values_mesh_shape = (2, 2, 3)
func_ref, func = func_vec_nd
true_values_points = func_ref(points)
true_values_mesh = func_ref(mesh)
true_value_point = func_ref(point)
func_elem = fspace_vec.element(func)
# Out of place
result_points = func_elem(points)
result_mesh = func_elem(mesh)
assert all_almost_equal(result_points, true_values_points)
assert all_almost_equal(result_mesh, true_values_mesh)
assert result_points.dtype == fspace_vec.scalar_out_dtype
assert result_mesh.dtype == fspace_vec.scalar_out_dtype
assert result_points.flags.writeable
assert result_mesh.flags.writeable
# In place
out_points = np.empty(values_points_shape,
dtype=fspace_vec.scalar_out_dtype)
out_mesh = np.empty(values_mesh_shape, dtype=fspace_vec.scalar_out_dtype)
func_elem(points, out=out_points)
func_elem(mesh, out=out_mesh)
assert all_almost_equal(out_points, true_values_points)
assert all_almost_equal(out_mesh, true_values_mesh)
# Single point evaluation
result_point = func_elem(point)
assert all_almost_equal(result_point, true_value_point)
out_point = np.empty((2, ), dtype=fspace_vec.scalar_out_dtype)
func_elem(point, out=out_point)
assert all_almost_equal(out_point, true_value_point)
def test_fspace_vector_arithmetic(variant, op):
if variant == 'sv' and '=' in op: # makes no sense, quit
return
# Setup
rect, points, mg = _standard_setup_2d()
point = points.T[0]
fspace = FunctionSpace(rect)
a = -1.5
b = 2.0
array_out = np.empty((5,), dtype=float)
mg_out = np.empty((2, 3), dtype=float)
# Initialize a bunch of elements
f_novec = fspace.element(func_2d_novec, vectorized=False)
f_vec = fspace.element(func_2d_vec_dual, vectorized=True)
g_novec = fspace.element(other_func_2d_novec, vectorized=False)
g_vec = fspace.element(other_func_2d_vec_dual, vectorized=True)
out_novec = fspace.element(vectorized=False)
out_vec = fspace.element(vectorized=True)
if variant[0] == 'v':
true_l_novec = func_2d_novec(point)
true_l_arr = func_2d_vec_oop(points)
true_l_mg = func_2d_vec_oop(mg)
test_l_novec = f_novec
test_l_vec = f_vec
else: # 's'
true_l_novec = true_l_arr = true_l_mg = a
test_l_novec = test_l_vec = a
if variant[1] == 'v':
true_r_novec = other_func_2d_novec(point)
true_r_arr = other_func_2d_vec_oop(points)
true_r_mg = other_func_2d_vec_oop(mg)
test_r_novec = g_novec
test_r_vec = g_vec
else: # 's'
true_r_novec = true_r_arr = true_r_mg = b
test_r_novec = test_r_vec = b
true_novec = _op(true_l_novec, op, true_r_novec)
true_arr = _op(true_l_arr, op, true_r_arr)
true_mg = _op(true_l_mg, op, true_r_mg)
out_novec = _op(test_l_novec, op, test_r_novec)
out_vec = _op(test_l_vec, op, test_r_vec)
assert almost_equal(out_novec(point), true_novec)
assert all_equal(out_vec(points), true_arr)
out_vec(points, out=array_out)
assert all_equal(array_out, true_arr)
assert all_equal(out_vec(mg), true_mg)
out_vec(mg, out=mg_out)
assert all_equal(mg_out, true_mg)
def test_fspace_elem_eval_vec_1d(func_vec_1d):
"""Test evaluation in 1d since it's a corner case regarding shapes."""
intv = odl.IntervalProd(0, 1)
fspace_vec = FunctionSpace(intv, out_dtype=(float, (2, )))
points = _points(fspace_vec.domain, 3)
mesh_shape = (4, )
mesh = _meshgrid(fspace_vec.domain, mesh_shape)
point1 = 0.5
point2 = [0.5]
values_points_shape = (2, 3)
values_mesh_shape = (2, 4)
value_point_shape = (2, )
func_ref, func = func_vec_1d
true_result_points = np.array(func_ref(points))
true_result_mesh = np.array(func_ref(mesh))
true_result_point = np.array(func_ref(np.array([point1]))).squeeze()
func_elem = fspace_vec.element(func)
result_points = func_elem(points)
result_mesh = func_elem(mesh)
result_point1 = func_elem(point1)
result_point2 = func_elem(point2)
assert all_almost_equal(result_points, true_result_points)
assert all_almost_equal(result_mesh, true_result_mesh)
assert all_almost_equal(result_point1, true_result_point)
assert all_almost_equal(result_point2, true_result_point)
out_points = np.empty(values_points_shape, dtype=float)
out_mesh = np.empty(values_mesh_shape, dtype=float)
out_point1 = np.empty(value_point_shape, dtype=float)
out_point2 = np.empty(value_point_shape, dtype=float)
func_elem(points, out=out_points)
func_elem(mesh, out=out_mesh)
func_elem(point1, out=out_point1)
func_elem(point2, out=out_point2)
assert all_almost_equal(out_points, true_result_points)
assert all_almost_equal(out_mesh, true_result_mesh)
assert all_almost_equal(out_point1, true_result_point)
assert all_almost_equal(out_point2, true_result_point)
def test_fspace_power(power):
rect, points, mg = _standard_setup_2d()
point = points.T[0]
out_arr = np.empty(5)
out_mg = np.empty((2, 3))
fspace = FunctionSpace(rect)
# Not vectorized
true_novec = func_2d_novec(point)**power
f_novec = fspace.element(func_2d_novec, vectorized=False)
pow_novec = f_novec**power
assert almost_equal(pow_novec(point), true_novec)
pow_novec = f_novec.copy()
pow_novec **= power
assert almost_equal(pow_novec(point), true_novec)
# Vectorized
true_arr = func_2d_vec_oop(points)**power
true_mg = func_2d_vec_oop(mg)**power
f_vec = fspace.element(func_2d_vec_dual, vectorized=True)
pow_vec = f_vec**power
assert all_almost_equal(pow_vec(points), true_arr)
assert all_almost_equal(pow_vec(mg), true_mg)
pow_vec = f_vec.copy()
pow_vec **= power
assert all_almost_equal(pow_vec(points), true_arr)
assert all_almost_equal(pow_vec(mg), true_mg)
pow_vec(points, out=out_arr)
pow_vec(mg, out=out_mg)
assert all_almost_equal(out_arr, true_arr)
assert all_almost_equal(out_mg, true_mg)
def test_fspace_power(power):
rect, points, mg = _standard_setup_2d()
point = points.T[0]
out_arr = np.empty(5)
out_mg = np.empty((2, 3))
fspace = FunctionSpace(rect)
# Not vectorized
true_novec = func_2d_novec(point) ** power
f_novec = fspace.element(func_2d_novec, vectorized=False)
pow_novec = f_novec ** power
assert almost_equal(pow_novec(point), true_novec)
pow_novec = f_novec.copy()
pow_novec **= power
assert almost_equal(pow_novec(point), true_novec)
# Vectorized
true_arr = func_2d_vec_oop(points) ** power
true_mg = func_2d_vec_oop(mg) ** power
f_vec = fspace.element(func_2d_vec_dual, vectorized=True)
pow_vec = f_vec ** power
assert all_almost_equal(pow_vec(points), true_arr)
assert all_almost_equal(pow_vec(mg), true_mg)
pow_vec = f_vec.copy()
pow_vec **= power
assert all_almost_equal(pow_vec(points), true_arr)
assert all_almost_equal(pow_vec(mg), true_mg)
pow_vec(points, out=out_arr)
pow_vec(mg, out=out_mg)
assert all_almost_equal(out_arr, true_arr)
assert all_almost_equal(out_mg, true_mg)
def test_fspace_vector_real_imag():
rect, _, mg = _standard_setup_2d()
cspace = FunctionSpace(rect, field=odl.ComplexNumbers())
f = cspace.element(cfunc_2d_vec_oop)
# real / imag on complex functions
assert all_equal(f.real(mg), cfunc_2d_vec_oop(mg).real)
assert all_equal(f.imag(mg), cfunc_2d_vec_oop(mg).imag)
out_mg = np.empty((2, 3))
f.real(mg, out=out_mg)
assert all_equal(out_mg, cfunc_2d_vec_oop(mg).real)
f.imag(mg, out=out_mg)
assert all_equal(out_mg, cfunc_2d_vec_oop(mg).imag)
# real / imag on real functions, should be the function itself / zero
rspace = FunctionSpace(rect)
f = rspace.element(func_2d_vec_oop)
assert all_equal(f.real(mg), f(mg))
assert all_equal(f.imag(mg), rspace.zero()(mg))
# Complex conjugate
f = cspace.element(cfunc_2d_vec_oop)
fbar = f.conj()
assert all_equal(fbar(mg), cfunc_2d_vec_oop(mg).conj())
out_mg = np.empty((2, 3), dtype='complex128')
fbar(mg, out=out_mg)
assert all_equal(out_mg, cfunc_2d_vec_oop(mg).conj())
def test_fspace_astype():
rspace = FunctionSpace(odl.Interval(0, 1))
cspace = FunctionSpace(odl.Interval(0, 1), field=odl.ComplexNumbers())
rspace_s = FunctionSpace(odl.Interval(0, 1), out_dtype='float32')
cspace_s = FunctionSpace(odl.Interval(0, 1), out_dtype='complex64')
assert rspace.astype('complex64') == cspace_s
assert rspace.astype('complex128') == cspace
assert rspace.astype('complex128') is rspace._complex_space
assert rspace.astype('float32') == rspace_s
assert rspace.astype('float64') is rspace._real_space
assert cspace.astype('float32') == rspace_s
assert cspace.astype('float64') == rspace
assert cspace.astype('float64') is cspace._real_space
assert cspace.astype('complex64') == cspace_s
assert cspace.astype('complex128') is cspace._complex_space
def test_fspace_tens_eval(func_tens):
"""Test tensor-valued function evaluation."""
intv = odl.IntervalProd([0, 0], [1, 1])
fspace_tens = FunctionSpace(intv, out_dtype=(float, (2, 3)))
points = _points(fspace_tens.domain, 4)
mesh_shape = (4, 5)
mesh = _meshgrid(fspace_tens.domain, mesh_shape)
point = [0.5, 0.5]
values_points_shape = (2, 3, 4)
values_mesh_shape = (2, 3, 4, 5)
value_point_shape = (2, 3)
func_ref, func = func_tens
true_result_points = np.array(func_ref(points))
true_result_mesh = np.array(func_ref(mesh))
true_result_point = np.array(func_ref(np.array(point)[:, None])).squeeze()
func_elem = fspace_tens.element(func)
result_points = func_elem(points)
result_mesh = func_elem(mesh)
result_point = func_elem(point)
assert all_almost_equal(result_points, true_result_points)
assert all_almost_equal(result_mesh, true_result_mesh)
assert all_almost_equal(result_point, true_result_point)
assert result_points.flags.writeable
assert result_mesh.flags.writeable
assert result_point.flags.writeable
out_points = np.empty(values_points_shape, dtype=float)
out_mesh = np.empty(values_mesh_shape, dtype=float)
out_point = np.empty(value_point_shape, dtype=float)
func_elem(points, out=out_points)
func_elem(mesh, out=out_mesh)
func_elem(point, out=out_point)
assert all_almost_equal(out_points, true_result_points)
assert all_almost_equal(out_mesh, true_result_mesh)
assert all_almost_equal(out_point, true_result_point)
def test_fspace_vector_eval_complex():
rect, points, mg = _standard_setup_2d()
fspace = FunctionSpace(rect, field=odl.ComplexNumbers())
f_novec = fspace.element(cfunc_2d_novec, vectorized=False)
f_vec_oop = fspace.element(cfunc_2d_vec_oop, vectorized=True)
f_vec_ip = fspace.element(cfunc_2d_vec_ip, vectorized=True)
f_vec_dual = fspace.element(cfunc_2d_vec_dual, vectorized=True)
true_arr = cfunc_2d_vec_oop(points)
true_mg = cfunc_2d_vec_oop(mg)
# Out-of-place
assert f_novec([0.5, 1.5]) == cfunc_2d_novec([0.5, 1.5])
assert f_vec_oop([0.5, 1.5]) == cfunc_2d_novec([0.5, 1.5])
assert all_equal(f_vec_oop(points), true_arr)
assert all_equal(f_vec_oop(mg), true_mg)
# In-place standard implementation
out_arr = np.empty((5, ), dtype='complex128')
out_mg = np.empty((2, 3), dtype='complex128')
f_vec_oop(points, out=out_arr)
f_vec_oop(mg, out=out_mg)
assert all_equal(out_arr, true_arr)
assert all_equal(out_mg, true_mg)
with pytest.raises(TypeError): # ValueError: invalid vectorized input
f_vec_oop(points[0])
# In-place-only
out_arr = np.empty((5, ), dtype='complex128')
out_mg = np.empty((2, 3), dtype='complex128')
f_vec_ip(points, out=out_arr)
f_vec_ip(mg, out=out_mg)
assert all_equal(out_arr, true_arr)
assert all_equal(out_mg, true_mg)
# Standard out-of-place evaluation
assert f_vec_ip([0.5, 1.5]) == cfunc_2d_novec([0.5, 1.5])
assert all_equal(f_vec_ip(points), true_arr)
assert all_equal(f_vec_ip(mg), true_mg)
# Dual use
assert f_vec_dual([0.5, 1.5]) == cfunc_2d_novec([0.5, 1.5])
assert all_equal(f_vec_dual(points), true_arr)
assert all_equal(f_vec_dual(mg), true_mg)
out_arr = np.empty((5, ), dtype='complex128')
out_mg = np.empty((2, 3), dtype='complex128')
f_vec_dual(points, out=out_arr)
f_vec_dual(mg, out=out_mg)
assert all_equal(out_arr, true_arr)
assert all_equal(out_mg, true_mg)
def test_fspace_vector_assign():
fspace = FunctionSpace(odl.Interval(0, 1))
f_novec = fspace.element(func_1d_oop, vectorized=False)
f_vec_ip = fspace.element(func_1d_ip, vectorized=True)
f_vec_dual = fspace.element(func_1d_dual, vectorized=True)
f_out = fspace.element()
f_out.assign(f_novec)
assert f_out == f_novec
f_out = fspace.element()
f_out.assign(f_vec_ip)
assert f_out == f_vec_ip
f_out = fspace.element()
f_out.assign(f_vec_dual)
assert f_out == f_vec_dual
def test_fspace_init():
"""Check if all initialization patterns work."""
intv = odl.IntervalProd(0, 1)
FunctionSpace(intv)
FunctionSpace(intv, out_dtype=float)
FunctionSpace(intv, out_dtype=complex)
FunctionSpace(intv, out_dtype=(float, (2, 3)))
str3 = odl.Strings(3)
FunctionSpace(str3, out_dtype=int)
# Make sure repr shows something
assert repr(FunctionSpace(intv, out_dtype=(float, (2, 3))))
def test_fspace_vector_assign():
fspace = FunctionSpace(odl.IntervalProd(0, 1))
f_novec = fspace.element(func_1d_oop, vectorized=False)
f_vec_ip = fspace.element(func_1d_ip, vectorized=True)
f_vec_dual = fspace.element(func_1d_dual, vectorized=True)
f_out = fspace.element()
f_out.assign(f_novec)
assert f_out == f_novec
f_out = fspace.element()
f_out.assign(f_vec_ip)
assert f_out == f_vec_ip
f_out = fspace.element()
f_out.assign(f_vec_dual)
assert f_out == f_vec_dual
def test_fspace_elem_arithmetic(odl_arithmetic_op, out_shape):
"""Test arithmetic of fspace elements."""
op = odl_arithmetic_op
intv = odl.IntervalProd([1, 0], [2, 1])
fspace = FunctionSpace(intv, out_dtype=(float, out_shape))
points = _points(fspace.domain, 4)
ndim = len(out_shape)
if ndim == 0:
f_elem1 = fspace.element(func_nd_oop)
f_elem2 = fspace.element(func_nd_other)
elif ndim == 1:
f_elem1 = fspace.element(func_vec_nd_oop)
f_elem2 = fspace.element(func_vec_nd_other)
elif ndim == 2:
f_elem1 = fspace.element(func_tens_oop)
f_elem2 = fspace.element(func_tens_other)
else:
assert False
result1 = f_elem1(points)
result1_cpy = result1.copy()
result2 = f_elem2(points)
true_result_func = op(result1, result2)
true_result_scal = op(result1_cpy, -2.0)
f_elem1_cpy = f_elem1.copy()
func_arith_func = op(f_elem1, f_elem2)
func_arith_scal = op(f_elem1_cpy, -2.0)
assert all_almost_equal(func_arith_func(points), true_result_func)
assert all_almost_equal(func_arith_scal(points), true_result_scal)
out_arr_func = np.empty(out_shape + (4, ))
out_arr_scal = np.empty(out_shape + (4, ))
func_arith_func(points, out=out_arr_func)
func_arith_scal(points, out=out_arr_scal)
assert all_almost_equal(out_arr_func, true_result_func)
assert all_almost_equal(out_arr_scal, true_result_scal)
def test_fspace_one():
rect, points, mg = _standard_setup_2d()
# real
fspace = FunctionSpace(rect)
one_vec = fspace.one()
assert one_vec([0.5, 1.5]) == 1.0
assert all_equal(one_vec(points), np.ones(5, dtype=float))
assert all_equal(one_vec(mg), np.ones((2, 3), dtype=float))
# complex
fspace = FunctionSpace(rect, field=odl.ComplexNumbers())
one_vec = fspace.one()
assert one_vec([0.5, 1.5]) == 1.0 + 1j * 0.0
assert all_equal(one_vec(points), np.ones(5, dtype=complex))
assert all_equal(one_vec(mg), np.ones((2, 3), dtype=complex))
def test_fspace_scal_elem_with_param_eval(func_param_nd):
"""Check evaluation of scalar-valued function elements with parameters."""
intv = odl.IntervalProd([0, 0], [1, 1])
fspace_scal = FunctionSpace(intv)
points = _points(fspace_scal.domain, 3)
mesh_shape = (2, 3)
mesh = _meshgrid(fspace_scal.domain, mesh_shape)
func_ref, func = func_param_nd
true_values_points = func_ref(points, c=2.5)
true_values_mesh = func_ref(mesh, c=2.5)
func_elem = fspace_scal.element(func)
# Out of place
result_points = func_elem(points, c=2.5)
result_mesh = func_elem(mesh, c=2.5)
assert all_almost_equal(result_points, true_values_points)
assert all_almost_equal(result_mesh, true_values_mesh)
# In place
out_points = np.empty(3, dtype=fspace_scal.scalar_out_dtype)
out_mesh = np.empty(mesh_shape, dtype=fspace_scal.scalar_out_dtype)
func_elem(points, out=out_points, c=2.5)
func_elem(mesh, out=out_mesh, c=2.5)
assert all_almost_equal(out_points, true_values_points)
assert all_almost_equal(out_mesh, true_values_mesh)
# Complex output
fspace_complex = FunctionSpace(intv, out_dtype=complex)
true_values_points = func_ref(points, c=2j)
true_values_mesh = func_ref(mesh, c=2j)
func_elem = fspace_complex.element(func)
result_points = func_elem(points, c=2j)
result_mesh = func_elem(mesh, c=2j)
assert all_almost_equal(result_points, true_values_points)
assert all_almost_equal(result_mesh, true_values_mesh)
def test_fspace_lincomb_scalar(a, b):
"""Check linear combination in function spaces.
Note: Special cases and more alignment options are tested later in the
special methods like ``__add__``.
"""
intv = odl.IntervalProd([0, 0], [1, 1])
fspace = FunctionSpace(intv)
points = _points(fspace.domain, 4)
true_result = a * func_nd_oop(points) + b * func_nd_bcast_ref(points)
# Non-vectorized evaluation, checking with `out` array and without.
f_elem1_novec = fspace.element(func_nd_oop, vectorized=False)
f_elem2_novec = fspace.element(func_nd_bcast_oop, vectorized=False)
out_novec = fspace.element(vectorized=False)
fspace.lincomb(a, f_elem1_novec, b, f_elem2_novec, out_novec)
assert all_equal(out_novec(points), true_result)
out_arr = np.empty(4)
out_novec(points, out=out_arr)
assert all_equal(out_arr, true_result)
# Vectorized evaluation with definition from out-of-place (oop),
# in-place (ip) and dual-use (dual) versions of Python functions.
# Checking evaluation with `out` array and without.
# out-of-place
f_elem1_oop = fspace.element(func_nd_oop)
f_elem2_oop = fspace.element(func_nd_bcast_oop)
out_oop = fspace.element()
fspace.lincomb(a, f_elem1_oop, b, f_elem2_oop, out_oop)
assert all_equal(out_oop(points), true_result)
out_arr = np.empty(4)
out_oop(points, out=out_arr)
assert all_equal(out_arr, true_result)
# in-place
f_elem1_ip = fspace.element(func_nd_ip)
f_elem2_ip = fspace.element(func_nd_bcast_ip)
out_ip = fspace.element()
fspace.lincomb(a, f_elem1_ip, b, f_elem2_ip, out_ip)
assert all_equal(out_ip(points), true_result)
out_arr = np.empty(4)
out_ip(points, out=out_arr)
assert all_equal(out_arr, true_result)
# dual
f_elem1_dual = fspace.element(func_nd_dual)
f_elem2_dual = fspace.element(func_nd_bcast_dual)
out_dual = fspace.element()
fspace.lincomb(a, f_elem1_dual, b, f_elem2_dual, out_dual)
assert all_equal(out_dual(points), true_result)
out_arr = np.empty(4)
out_dual(points, out=out_arr)
assert all_equal(out_arr, true_result)
# Check mixing vectorized and non-vectorized functions
out = fspace.element()
fspace.lincomb(a, f_elem1_oop, b, f_elem2_novec, out)
assert all_equal(out(points), true_result)
out_arr = np.empty(4)
out(points, out=out_arr)
assert all_equal(out_arr, true_result)
# Alignment options
# out = a * out + b * f2, out = f1.copy() -> same as before
out = f_elem1_oop.copy()
fspace.lincomb(a, out, b, f_elem2_oop, out)
true_result_aligned = true_result
assert all_equal(out(points), true_result_aligned)
# out = a * f1 + b * out, out = f2.copy() -> same as before
out = f_elem2_oop.copy()
fspace.lincomb(a, f_elem1_oop, b, out, out)
true_result_aligned = true_result
assert all_equal(out(points), true_result_aligned)
# out = a * out + b * out
out = f_elem1_oop.copy()
fspace.lincomb(a, out, b, out, out)
true_result_aligned = (a + b) * f_elem1_oop(points)
assert all_equal(out(points), true_result_aligned)
# out = a * f1 + b * f1
out = fspace.element()
fspace.lincomb(a, f_elem1_oop, b, f_elem1_oop, out)
true_result_aligned = (a + b) * f_elem1_oop(points)
assert all_equal(out(points), true_result_aligned)
def test_fspace_elem_copy(out_shape):
"""Check copying of fspace elements."""
fspace = FunctionSpace(odl.IntervalProd(0, 1),
out_dtype=(float, out_shape))
ndim = len(out_shape)
if ndim == 0:
f_oop = fspace.element(func_nd_oop)
f_ip = fspace.element(func_nd_ip)
f_dual = fspace.element(func_nd_dual)
elif ndim == 1:
f_oop = fspace.element(func_vec_nd_oop)
f_ip = fspace.element(func_vec_nd_ip)
f_dual = fspace.element(func_vec_nd_dual)
elif ndim == 2:
f_oop = fspace.element(func_tens_oop)
f_ip = fspace.element(func_tens_ip)
f_dual = fspace.element(func_tens_dual)
else:
assert False
f_out = f_oop.copy()
assert f_out == f_oop
f_out = f_ip.copy()
assert f_out == f_ip
f_out = f_dual.copy()
assert f_out == f_dual
def fspace_scal(domain_ndim, out_dtype):
"""Fixture returning a function space with given properties."""
domain = odl.IntervalProd([0] * domain_ndim, [1] * domain_ndim)
return FunctionSpace(domain, out_dtype=out_dtype)
def test_fspace_vector_init():
# 1d, real
intv = odl.Interval(0, 1)
fspace = FunctionSpace(intv)
fspace.element(func_1d_oop)
fspace.element(func_1d_oop, vectorized=False)
fspace.element(func_1d_oop, vectorized=True)
fspace.element(func_1d_ip, vectorized=True)
fspace.element(func_1d_dual, vectorized=True)
# 2d, real
rect = odl.Rectangle([0, 0], [1, 2])
fspace = FunctionSpace(rect)
fspace.element(func_2d_novec, vectorized=False)
fspace.element(func_2d_vec_oop)
fspace.element(func_2d_vec_oop, vectorized=True)
fspace.element(func_2d_vec_ip, vectorized=True)
fspace.element(func_2d_vec_dual, vectorized=True)
# 2d, complex
fspace = FunctionSpace(rect, field=odl.ComplexNumbers())
fspace.element(cfunc_2d_novec, vectorized=False)
fspace.element(cfunc_2d_vec_oop)
fspace.element(cfunc_2d_vec_oop, vectorized=True)
fspace.element(cfunc_2d_vec_ip, vectorized=True)
fspace.element(cfunc_2d_vec_dual, vectorized=True)
def test_fspace_lincomb(a, b):
rect, points, mg = _standard_setup_2d()
point = points.T[0]
fspace = FunctionSpace(rect)
# Note: Special cases and alignment are tested later in the magic methods
# Not vectorized
true_novec = a * func_2d_novec(point) + b * other_func_2d_novec(point)
f_novec = fspace.element(func_2d_novec, vectorized=False)
g_novec = fspace.element(other_func_2d_novec, vectorized=False)
out_novec = fspace.element(vectorized=False)
fspace.lincomb(a, f_novec, b, g_novec, out_novec)
assert almost_equal(out_novec(point), true_novec)
# Vectorized
true_arr = (a * func_2d_vec_oop(points) +
b * other_func_2d_vec_oop(points))
true_mg = (a * func_2d_vec_oop(mg) + b * other_func_2d_vec_oop(mg))
# Out-of-place
f_vec_oop = fspace.element(func_2d_vec_oop, vectorized=True)
g_vec_oop = fspace.element(other_func_2d_vec_oop, vectorized=True)
out_vec = fspace.element()
fspace.lincomb(a, f_vec_oop, b, g_vec_oop, out_vec)
assert all_equal(out_vec(points), true_arr)
assert all_equal(out_vec(mg), true_mg)
assert almost_equal(out_vec(point), true_novec)
out_arr = np.empty((5,), dtype=float)
out_mg = np.empty((2, 3), dtype=float)
out_vec(points, out=out_arr)
out_vec(mg, out=out_mg)
assert all_equal(out_arr, true_arr)
assert all_equal(out_mg, true_mg)
# In-place
f_vec_ip = fspace.element(func_2d_vec_ip, vectorized=True)
g_vec_ip = fspace.element(other_func_2d_vec_ip, vectorized=True)
out_vec = fspace.element()
fspace.lincomb(a, f_vec_ip, b, g_vec_ip, out_vec)
assert all_equal(out_vec(points), true_arr)
assert all_equal(out_vec(mg), true_mg)
assert almost_equal(out_vec(point), true_novec)
out_arr = np.empty((5,), dtype=float)
out_mg = np.empty((2, 3), dtype=float)
out_vec(points, out=out_arr)
out_vec(mg, out=out_mg)
assert all_equal(out_arr, true_arr)
assert all_equal(out_mg, true_mg)
# Dual use
f_vec_dual = fspace.element(func_2d_vec_dual, vectorized=True)
g_vec_dual = fspace.element(other_func_2d_vec_dual, vectorized=True)
out_vec = fspace.element()
fspace.lincomb(a, f_vec_dual, b, g_vec_dual, out_vec)
assert all_equal(out_vec(points), true_arr)
assert all_equal(out_vec(mg), true_mg)
assert almost_equal(out_vec(point), true_novec)
out_arr = np.empty((5,), dtype=float)
out_mg = np.empty((2, 3), dtype=float)
out_vec(points, out=out_arr)
out_vec(mg, out=out_mg)
assert all_equal(out_arr, true_arr)
assert all_equal(out_mg, true_mg)
# Mix of vectorized and non-vectorized -> manual vectorization
fspace.lincomb(a, f_vec_dual, b, g_novec, out_vec)
assert all_equal(out_vec(points), true_arr)
assert all_equal(out_vec(mg), true_mg)