def grid_sample(self,
resolution: math.Shape,
size,
shape: math.Shape = None):
shape = (self._shape if shape is None else shape) & resolution
for dim in channel(self._shape):
if dim.item_names[0] is None:
warnings.warn(
f"Please provide item names for Noise dim {dim} using {dim}='x,y,z'",
FutureWarning)
shape &= channel(**{dim.name: resolution.names})
rndj = math.to_complex(random_normal(shape)) + 1j * math.to_complex(
random_normal(shape)) # Note: there is no complex32
with math.NUMPY:
k = math.fftfreq(resolution) * resolution / math.tensor(
size) * math.tensor(self.scale) # in physical units
k = math.vec_squared(k)
lowest_frequency = 0.1
weight_mask = math.to_float(k > lowest_frequency)
# --- Compute 1/k ---
k._native[(0, ) * len(k.shape)] = np.inf
inv_k = 1 / k
inv_k._native[(0, ) * len(k.shape)] = 0
# --- Compute result ---
fft = rndj * inv_k**self.smoothness * weight_mask
array = math.real(math.ifft(fft))
array /= math.std(array, dim=array.shape.non_batch)
array -= math.mean(array, dim=array.shape.non_batch)
array = math.to_float(array)
return array
def test_multi_dim_tensor_from_numpy(self):
v = math.tensor(np.ones([1, 4, 3, 2]), batch('batch'), spatial('x,y'),
channel('vector'))
self.assertEqual((1, 4, 3, 2), v.shape.sizes)
v = math.tensor(np.ones([10, 4, 3, 2]), batch('batch'), spatial('x,y'),
channel('vector'))
self.assertEqual((10, 4, 3, 2), v.shape.sizes)
def points(self,
points: Tensor or Number or tuple or list,
values: Tensor or Number = None,
radius: Tensor or float or int or None = None,
extrapolation: math.Extrapolation = math.extrapolation.ZERO,
color: str or Tensor or tuple or list or None = None) -> PointCloud:
"""
Create a `phi.field.PointCloud` from the given `points`.
The created field has no channel dimensions and all points carry the value `1`.
Args:
points: point locations in physical units
values: (optional) values of the particles, defaults to 1.
radius: (optional) size of the particles
extrapolation: (optional) extrapolation to use, defaults to extrapolation.ZERO
color: (optional) color used when plotting the points
Returns:
`phi.field.PointCloud` object
"""
extrapolation = extrapolation if isinstance(extrapolation, math.Extrapolation) else self.boundaries[extrapolation]
if radius is None:
radius = math.mean(self.bounds.size) * 0.005
# --- Parse points: tuple / list ---
if isinstance(points, (tuple, list)):
if len(points) == 0: # no points
points = math.zeros(instance(points=0), channel(vector=1))
elif isinstance(points[0], Number): # single point
points = math.tensor([points], instance('points'), channel('vector'))
else:
points = math.tensor(points, instance('points'), channel('vector'))
elements = Sphere(points, radius)
if values is None:
values = math.tensor(1.)
return PointCloud(elements, values, extrapolation, add_overlapping=False, bounds=self.bounds, color=color)
def read_single_field(file: str, convert_to_backend=True) -> SampledField:
stored = np.load(file, allow_pickle=True)
ftype = stored['field_type']
implemented_types = ('CenteredGrid', 'StaggeredGrid')
if ftype in implemented_types:
data = stored['data']
dim_item_names = stored.get('dim_item_names',
(None, ) * len(data.shape))
data = NativeTensor(
data,
math.Shape(data.shape, tuple(stored['dim_names']),
tuple(stored['dim_types']), tuple(dim_item_names)))
if convert_to_backend:
data = math.tensor(data, convert=convert_to_backend)
bounds_item_names = stored.get('bounds_item_names', (None, ) *
len(stored['lower'] + stored['upper']))
lower = math.wrap(
stored['lower'], math.channel(vector=tuple(bounds_item_names))
) if stored['lower'].ndim > 0 else math.wrap(stored['lower'])
upper = math.wrap(stored['upper'],
math.channel(vector=tuple(bounds_item_names)))
extrapolation = math.extrapolation.from_dict(
stored['extrapolation'][()])
if ftype == 'CenteredGrid':
return CenteredGrid(data,
bounds=geom.Box(lower, upper),
extrapolation=extrapolation)
elif ftype == 'StaggeredGrid':
data_ = unstack_staggered_tensor(data, extrapolation)
return StaggeredGrid(data_,
bounds=geom.Box(lower, upper),
extrapolation=extrapolation)
raise NotImplementedError(f"{ftype} not implemented ({implemented_types})")
def test_np_speed_sum(self):
print()
np1, np2 = rnpv(64), rnpv(256)
t1 = math.tensor(np1, batch('batch'), spatial('x, y'), channel('vector'))
t2 = math.tensor(np2, batch('batch'), spatial('x, y'), channel('vector'))
_assert_equally_fast(lambda: np.sum(np1), lambda: math.sum(t1, dim=t1.shape), n=10000)
_assert_equally_fast(lambda: np.sum(np2), lambda: math.sum(t2, dim=t1.shape), n=10000)
def test_stacked_get(self):
t0 = math.ones(batch(batch=10) & spatial(x=4, y=3) & channel(vector=2))
tensors = t0.unstack('vector')
stacked = math.stack(tensors, channel('channel'))
self.assertEqual(tensors, stacked.channel.unstack())
assert tensors[0] is stacked.channel[0]
assert tensors[1] is stacked.channel[1:2].channel.unstack()[0]
self.assertEqual(4, len(stacked.x.unstack()))
def stagger(field: CenteredGrid,
face_function: Callable,
extrapolation: math.extrapolation.Extrapolation,
type: type = StaggeredGrid):
"""
Creates a new grid by evaluating `face_function` given two neighbouring cells.
One layer of missing cells is inferred from the extrapolation.
This method returns a Field of type `type` which must be either StaggeredGrid or CenteredGrid.
When returning a StaggeredGrid, the new values are sampled at the faces of neighbouring cells.
When returning a CenteredGrid, the new grid has the same resolution as `field`.
Args:
field: centered grid
face_function: function mapping (value1: Tensor, value2: Tensor) -> center_value: Tensor
extrapolation: extrapolation mode of the returned grid. Has no effect on the values.
type: one of (StaggeredGrid, CenteredGrid)
field: CenteredGrid:
face_function: Callable:
extrapolation: math.extrapolation.Extrapolation:
type: type: (Default value = StaggeredGrid)
Returns:
grid of type matching the `type` argument
"""
all_lower = []
all_upper = []
if type == StaggeredGrid:
for dim in field.shape.spatial.names:
lo_valid, up_valid = extrapolation.valid_outer_faces(dim)
width_lower = {dim: (int(lo_valid), int(up_valid) - 1)}
width_upper = {
dim: (int(lo_valid or up_valid) - 1, int(lo_valid
and up_valid))
}
all_lower.append(
math.pad(field.values, width_lower, field.extrapolation))
all_upper.append(
math.pad(field.values, width_upper, field.extrapolation))
all_upper = math.stack(all_upper, channel('vector'))
all_lower = math.stack(all_lower, channel('vector'))
values = face_function(all_lower, all_upper)
result = StaggeredGrid(values,
bounds=field.bounds,
extrapolation=extrapolation)
assert result.shape.spatial == field.shape.spatial
return result
elif type == CenteredGrid:
left, right = math.shift(field.values, (-1, 1),
padding=field.extrapolation,
stack_dim=channel('vector'))
values = face_function(left, right)
return CenteredGrid(values,
bounds=field.bounds,
extrapolation=extrapolation)
else:
raise ValueError(type)
def test_merge_shapes_check_item_names(self):
s1 = channel(vector='x,y,z')
s2 = channel(vector='r,g,b')
try:
math.merge_shapes(s1, s2)
self.fail('Merging incompatible shapes did not raise an error!')
except math.IncompatibleShapes:
pass
math.merge_shapes(s1, s1)
def test_subshapes(self):
s = batch(batch=10) & spatial(x=4, y=3) & channel(vector=2) & instance(points=1)
self.assertEqual(batch(batch=10), s.batch)
self.assertEqual(spatial(x=4, y=3), s.spatial)
self.assertEqual(channel(vector=2), s.channel)
self.assertEqual(instance(points=1), s.instance)
self.assertEqual(batch(batch=10), batch(s))
self.assertEqual(spatial(x=4, y=3), spatial(s))
self.assertEqual(channel(vector=2), channel(s))
self.assertEqual(instance(points=1), instance(s))
def test_np_speed_op2(self):
print()
np1, np2 = rnpv(64), rnpv(64)
t1 = math.tensor(np1, batch('batch'), spatial('x, y'), channel('vector'))
t2 = math.tensor(np2, batch('batch'), spatial('x, y'), channel('vector'))
_assert_equally_fast(lambda: np1 + np2, lambda: t1 + t2, n=10000)
np1, np2 = rnpv(256), rnpv(256)
t1 = math.tensor(np1, batch('batch'), spatial('x, y'), channel('vector'))
t2 = math.tensor(np2, batch('batch'), spatial('x, y'), channel('vector'))
_assert_equally_fast(lambda: np1 + np2, lambda: t1 + t2, n=1000)
def test_tensor_as_field(self):
t = math.random_normal(spatial(x=4, y=3), channel(vector='x,y'))
grid = field.tensor_as_field(t)
self.assertIsInstance(grid, CenteredGrid)
math.assert_close(grid.dx, 1)
math.assert_close(grid.points.x[0].y[0], 0)
t = math.random_normal(instance(points=5), channel(vector='x,y'))
points = field.tensor_as_field(t)
self.assertTrue((points.elements.bounding_radius() > 0).all)
self.assertIsInstance(points, PointCloud)
def test_convert_point_cloud(self):
loc = math.random_uniform(instance(points=4), channel(vector=2))
val = math.random_normal(instance(points=4), channel(vector=2))
points = PointCloud(Sphere(loc, radius=1), val)
for backend in BACKENDS:
converted = field.convert(points, backend)
self.assertEqual(converted.values.default_backend, backend)
self.assertEqual(converted.elements.center.default_backend,
backend)
self.assertEqual(converted.elements.radius.default_backend,
backend)
def __mul__(self, other):
if not isinstance(other, Box):
return NotImplemented
lower = self._lower.vector.unstack(
self.spatial_rank) + other._lower.vector.unstack(self.spatial_rank)
upper = self._upper.vector.unstack(
self.spatial_rank) + other._upper.vector.unstack(self.spatial_rank)
names = self._upper.vector.item_names + other._upper.vector.item_names
lower = math.stack(lower, math.channel(vector=names))
upper = math.stack(upper, math.channel(vector=names))
return Box(lower, upper)
def test_collapsed_op2(self):
# Collapsed + Collapsed
a = math.zeros(channel(vector=4))
b = math.ones(batch(batch=3))
c = a + b
self.assertIsInstance(c, CollapsedTensor)
self.assertEqual(c.shape.volume, 12)
self.assertEqual(c._inner.shape.volume, 1)
# Collapsed + Native
n = math.ones(channel(vector=3)) + (0, 1, 2)
math.assert_close(n, (1, 2, 3))
def test_boolean_mask_batched(self):
for backend in BACKENDS:
with backend:
x = math.expand(math.range(spatial('x'), 4), batch(batch=2)) * math.tensor([1, -1])
mask = math.tensor([[True, False, True, False], [False, True, False, False]], batch('batch'), spatial('x'))
selected = math.boolean_mask(x, 'x', mask)
expected_0 = math.tensor([(0, -0), (2, -2)], spatial('x'), channel('vector'))
expected_1 = math.tensor([(1, -1)], spatial('x'), channel('vector'))
math.assert_close(selected.batch[0], expected_0, msg=backend.name)
math.assert_close(selected.batch[1], expected_1, msg=backend.name)
math.assert_close(selected, x.x[mask], msg=backend.name)
def test_tensor_from_tuple_of_tensor_like(self):
native = ([1, 2, 3], math.zeros(channel(vector=3)))
for backend in BACKENDS:
with backend:
tens = wrap(native, batch(stack=2), channel(vector=3))
self.assertEqual(math.NUMPY, math.choose_backend(tens))
self.assertEqual(
batch(stack=2) & channel(vector=3), tens.shape)
tens = tensor(native, batch(stack=2), channel(vector=3))
self.assertEqual(backend, math.choose_backend(tens))
self.assertEqual(
batch(stack=2) & channel(vector=3), tens.shape)
def test_stacked_native(self):
t0 = math.ones(batch(batch=10) & spatial(x=4, y=3) & channel(vector=2))
tensors = t0.unstack('vector')
stacked = math.stack(tensors, channel('vector2'))
math.assert_close(stacked, t0)
self.assertEqual((10, 4, 3, 2), stacked.native(stacked.shape).shape)
self.assertEqual(
(4, 3, 2, 10),
stacked.native(order=('x', 'y', 'vector2', 'batch')).shape)
self.assertEqual(
(2, 10, 3, 4),
stacked.native(order=('vector2', 'batch', 'y', 'x')).shape
) # this should re-stack since only the stacked dimension position is different
def test_op2_incompatible_item_names(self):
t1 = math.random_normal(channel(vector='x,y,z'))
t2 = math.random_normal(channel(vector='r,g,b'))
self.assertEqual(('r', 'g', 'b'), t2.vector.item_names)
try:
t1 + t2
self.fail("Tensors with incompatible item names cannot be added")
except math.IncompatibleShapes:
pass
t1 + t1
t2_ = t2 + math.random_normal(channel(vector=3))
self.assertEqual(('r', 'g', 'b'), t2_.vector.item_names)
t2_ = math.random_normal(channel(vector=3)) + t2
self.assertEqual(('r', 'g', 'b'), t2_.vector.item_names)
def test_expand_copy_item_names(self):
a = math.zeros(channel(vector=2))
try:
math.expand(a, channel(vector=3))
self.fail()
except IncompatibleShapes:
pass
b = math.expand(a, channel(vector='x,y'))
self.assertEqual(('x', 'y'), b.vector.item_names)
try:
math.expand(b, channel(vector='a,b'))
self.fail()
except IncompatibleShapes:
pass
def tensor_as_field(t: Tensor):
"""
Interpret a `Tensor` as a `CenteredGrid` or `PointCloud` depending on its dimensions.
Unlike the `CenteredGrid` constructor, this function will have the values sampled at integer points for each spatial dimension.
Args:
t: `Tensor` with either `spatial` or `instance` dimensions.
Returns:
`CenteredGrid` or `PointCloud`
"""
if spatial(t):
assert not instance(
t
), f"Cannot interpret tensor as Field because it has both spatial and instance dimensions: {t.shape}"
bounds = Box(-0.5, math.wrap(spatial(t), channel('vector')) - 0.5)
return CenteredGrid(t, 0, bounds=bounds)
if instance(t):
assert not spatial(
t
), f"Cannot interpret tensor as Field because it has both spatial and instance dimensions: {t.shape}"
assert 'vector' in t.shape, f"Cannot interpret tensor as PointCloud because it has not vector dimension."
point_count = instance(t).volume
bounds = data_bounds(t)
radius = math.vec_length(
bounds.size) / (1 + point_count**(1 / t.vector.size))
return PointCloud(Sphere(t, radius=radius))
def test_meshgrid_names(self):
shape = spatial(x=2) & channel(vector='x')
indices = list(shape.meshgrid(names=True))
self.assertEqual([
dict(x=0, vector='x'),
dict(x=1, vector='x'),
], indices)
def test_dimension_types(self):
v = math.ones(batch(batch=10) & spatial(x=4, y=3) & channel(vector=2))
self.assertEqual(v.x.index, 1)
self.assertEqual(v.x.name, 'x')
self.assertEqual(('batch', 'spatial', 'spatial', 'channel'), v.shape.types)
b = v.x.as_batch()
self.assertEqual(('batch', 'batch', 'spatial', 'channel'), b.shape.types)
def vector_grid(self,
value: Field or Tensor or Number or Geometry or callable = 0.,
type: type = CenteredGrid,
extrapolation: math.Extrapolation or str = 'vector') -> CenteredGrid or StaggeredGrid:
"""
Creates a vector grid matching the resolution and bounds of the domain.
The grid is created from the given `value` which must be one of the following:
* Number (int, float, complex or zero-dimensional tensor): all grid values will be equal to `value`. This has a near-zero memory footprint.
* Field: the given value is resampled to the grid cells of this Domain.
* Tensor with spatial dimensions matcing the domain resolution: grid values will equal `value`.
* Geometry: grid values are determined from the volume overlap between grid cells and geometry. Non-overlapping = 0, fully enclosed grid cell = 1.
* function(location: Tensor) returning one of the above.
The returned grid will have a vector dimension with size equal to the rank of the domain.
Args:
value: constant, Field, Tensor or function specifying the grid values
type: class of Grid to create, must be either CenteredGrid or StaggeredGrid
extrapolation: (optional) grid extrapolation, defaults to Domain.boundaries['vector']
Returns:
Grid of specified type
"""
extrapolation = extrapolation if isinstance(extrapolation, math.Extrapolation) else self.boundaries[extrapolation]
result = type(value, resolution=self.resolution, bounds=self.bounds, extrapolation=extrapolation)
if result.shape.channel_rank == 0:
result = result.with_values(math.expand(result.values, channel(vector=self.rank)))
else:
assert result.shape.get_size('vector') == self.rank
return result
def test_indexing(self):
s = batch(batch=10) & spatial(x=4, y=3) & channel(vector=2)
self.assertEqual(batch(batch=10), s[0:1])
self.assertEqual(batch(batch=10), s[[0]])
self.assertEqual(spatial(x=4, y=3), s[1:3])
self.assertEqual(spatial(x=4), s['x'])
self.assertEqual(spatial(x=4, y=3), s['x, y'])
def test_stacked_shapes(self):
t0 = math.ones(batch(batch=10) & spatial(x=4, y=3) & channel(vector=2))
for dim in t0.shape.names:
tensors = t0.unstack(dim)
stacked = math.stack(tensors, t0.shape[dim].with_sizes([None]))
self.assertEqual(set(t0.shape.names), set(stacked.shape.names))
self.assertEqual(t0.shape.volume, stacked.shape.volume)
def test_iterate_layout(self):
a = [dict(a=1), dict(b=2)]
t = math.layout(a, channel('outer,dict'))
total = []
for d in t:
total.append(d)
self.assertEqual(total, [1, 2])
def test_layout_dict_conflict(self):
a = [dict(a=1), dict(b=2)]
t = math.layout(a, channel('outer,dict'))
self.assertEqual(None, t.shape.get_item_names('dict'))
self.assertEqual(a, t.native())
self.assertEqual([1, 2], t.dict[0].native())
self.assertEqual(2, t.dict[0].outer[1].native())
def __init__(self,
center: Tensor = None,
radius: float or Tensor = None,
**center_: float or Tensor):
"""
Args:
center: Sphere center as `Tensor` with `vector` dimension.
The spatial dimension order should be specified in the `vector` dimension via item names.
radius: Sphere radius as `float` or `Tensor`
**center_: Specifies center when the `center` argument is not given. Center position by dimension, e.g. `x=0.5, y=0.2`.
"""
if center is not None:
if not isinstance(center, Tensor):
warnings.warn(
f"constructor Sphere({type(center)}) is deprecated. Use Sphere(Tensor) or Sphere(**center_) instead.",
DeprecationWarning)
self._center = wrap(center)
else:
self._center = center
assert 'vector' in self._center.shape, f"Sphere.center must have a 'vector' dimension. Use the syntax x=0.5."
else:
self._center = math.wrap(
tuple(center_.values()),
math.channel(vector=tuple(center_.keys())))
# self._center = wrap(math.spatial(**center_), math.channel('vector'))
assert radius is not None, "radius must be specified."
self._radius = wrap(radius)
def test_slice_centered_grid(self):
g = CenteredGrid(Noise(batch(batch=10), channel(vector=2)), x=10, y=20)
s1 = g[{'vector': 0, 'batch': 1, 'x': 1}]
s2 = g.vector[0].batch[1].x[1]
self.assertIsInstance(s1, CenteredGrid)
self.assertEqual(s1.bounds, Box[1:2, 0:20])
field.assert_close(s1, s2)
def test_flip_item_names(self):
t = math.zeros(spatial(x=4, y=3), channel(vector='x,y'))
self.assertEqual(('x', 'y'), t.vector.item_names)
t_ = t.vector.flip()
self.assertEqual(('y', 'x'), t_.vector.item_names)
t_ = t.vector[::-1]
self.assertEqual(('y', 'x'), t_.vector.item_names)