def set_prior_prob(self, map_, energy=False):
"""Sets the prior probability attribute of the sampler.
It is possible to provide prior probability values (`energy=False`) or
probability energy values (`energy=True`). In the latter case, the
values are transformed to un-normalized probability measures by::
prior_prob.values = exp(-map_.values)
where `exp` denotes the exponential function.
Args:
map_ (LatticeMap): Prior map
energy (bool): Indicates if the prior map represents probability
values (false) or probability energy (true).
Returns:
None
"""
# Minor consistency checks
if self._lattice != map_.lattice:
raise ValueError(msg.err3000(self._lattice, map_.lattice))
# If the map represents the energy, transform it to probability values
values = np.copy(map_.values)
if energy:
values = np.exp(-values)
# Set value within self
self._prior_prob = LatticeMap(self._lattice, values)
def __init__(self, lattice):
# Also accept objects that can be used to generate a lattice
if not isinstance(lattice, Lattice):
lattice = Lattice(lattice)
self._lattice = lattice
# Make default prior maps (all equal probability, all allowed)
ones = np.ones(lattice.nnodes_dim)
self._prior_prob = LatticeMap(lattice, ones, dtype=int)
self._prior_cond = LatticeMap(lattice, ones, dtype=bool)
def test_LatticeMap2D_print(self):
lattice = Lattice(self.nodes2D)
values = np.random.randn(lattice.nnodes)
latticemap = LatticeMap(lattice, values)
self.assertTrue(hasattr(latticemap, '__repr__'))
self.assertTrue(latticemap.__repr__())
self.assertTrue(hasattr(latticemap, '__str__'))
self.assertTrue(latticemap.__str__())
def test_LatticeMap3D_print(self):
lattice = Lattice(self.nodes3D)
values = np.random.randn(lattice.nnodes)
latticemap = LatticeMap(lattice, values)
# Force the implementation of __repr__() and __str__()
self.assertTrue(hasattr(latticemap, '__repr__'))
self.assertTrue(latticemap.__repr__())
self.assertTrue(hasattr(latticemap, '__str__'))
self.assertTrue(latticemap.__str__())
def test_LatticeMap2D_normalize_sum(self):
nodes = [[0, 1, 2, 3, 4], [-3, -2, -1, 0]]
vals = np.random.rand(20)
map_ = LatticeMap(nodes, vals)
vals_nrm = map_.normalize_sum().values
self.assertTrue(np.allclose(vals_nrm, vals / np.sum(vals)))
vals_nrm = map_.normalize_sum(axis=0).values
sum_vals_nrm = np.sum(vals_nrm.reshape((5, 4), order=NP_ORDER), axis=0)
self.assertTrue(np.allclose(sum_vals_nrm, 1))
vals_nrm = map_.normalize_sum(axis=1).values
sum_vals_nrm = np.sum(vals_nrm.reshape((5, 4), order=NP_ORDER), axis=1)
self.assertTrue(np.allclose(sum_vals_nrm, 1))
def test_LatticeMap3D__eq__(self):
lattice = Lattice(self.nodes3D)
values = np.random.randn(lattice.nnodes)
latticemap = LatticeMap(lattice, values)
latticemap_is = latticemap
latticemap_eq = LatticeMap(lattice, values)
latticemap_non_eq = LatticeMap(lattice, values + 1)
self.assertTrue(latticemap is latticemap_is)
self.assertTrue(latticemap == latticemap_eq)
self.assertEqual(latticemap, latticemap_eq)
self.assertFalse(latticemap is latticemap_eq)
self.assertFalse(latticemap == latticemap_non_eq)
def test_Trajectory_to_latticemap(self):
nodes = [[-2, -1, 0, 1, 2], [-3, 1, 5, 9]]
lattice = Lattice(nodes)
pts = [(-2, 1), (-1, -4), (0, 3), (1, 4), (2, 8.8)]
values = np.array([
0,
1,
0,
0,
0,
1,
0,
1,
0,
0,
0,
0,
0,
1,
0,
0,
0,
0,
0,
1,
],
dtype=bool)
map_test = Trajectory(pts).to_latticemap(lattice)
map_true = LatticeMap(lattice, values)
self.assertEqual(map_true, map_test)
def test_LatticeMap3D__mul__(self):
lattice = Lattice(self.nodes3D)
num = -25.89
values = np.random.randn(lattice.nnodes)
latticemap = LatticeMap(lattice, values)
latticmap_mul = LatticeMap(lattice, values * num)
latticemap_squared = LatticeMap(lattice, values**2)
self.assertEqual(latticmap_mul, latticemap * num)
self.assertTrue(latticmap_mul == latticemap * num)
self.assertEqual(latticmap_mul, num * latticemap)
self.assertTrue(latticmap_mul == num * latticemap)
self.assertEqual(latticemap * latticemap, latticemap_squared)
with self.assertRaises(TypeError):
latticemap * 'foobar'
def _cond_map_from_point(self, components):
"""Generate a conditioning lattice map from a conditioning point."""
# Initialization
nodes = self._lattice.nodes
nnodes_dim = self._lattice.nnodes_dim
# Generate array with lowest dimension corresponding to the gantry
dim = (nnodes_dim[DIM_GANTRY], nnodes_dim[DIM_TABLE])
values = np.zeros(dim, dtype=bool)
# Conical opening for the permitted area of the trajectory
center = components[DIM_TABLE]
con_rat = 2 * self._ratio # The conical opening is symmetric
pts = nodes[DIM_TABLE]
# Loop in gantry direction through the lattice
for inode, node in enumerate(nodes[DIM_GANTRY]):
dist = abs(node - components[DIM_GANTRY])
allowed = utl.within_conical_opening(center, dist, con_rat, pts)
values[inode, allowed] = True
# Correct dimension ordering if needed
if DIM_GANTRY > DIM_TABLE:
values = values.transpose()
values = values.ravel(order=NP_ORDER)
return LatticeMap(self._lattice, values)
def test_LatticeMap2D_slice(self):
nodes = [[-1.5, 1.5, 5, 8, 9], [1, 2, 3, 4, 5, 6]]
lattice = Lattice(nodes)
values = [
0.51,
0.52,
0.53,
0.54,
0.55,
0.61,
0.62,
0.63,
0.64,
0.65,
0.71,
0.72,
0.73,
0.74,
0.75,
0.71,
0.72,
0.73,
0.74,
0.75,
0.61,
0.62,
0.63,
0.64,
0.65,
0.51,
0.52,
0.53,
0.54,
0.55,
]
latticemap = LatticeMap(lattice, values=values)
lattice_slice_0 = Lattice([[1, 2, 3, 4, 5, 6]])
values_slice_0 = [0.52, 0.62, 0.72, 0.72, 0.62, 0.52]
latticemap_slice_0 = LatticeMap(lattice_slice_0, values_slice_0)
lattice_slice_1 = Lattice([[-1.5, 1.5, 5, 8, 9]])
values_slice_1 = [0.71, 0.72, 0.73, 0.74, 0.75]
latticemap_slice_1 = LatticeMap(lattice_slice_1, values_slice_1)
self.assertEqual(latticemap_slice_0, latticemap.slice(0, 1))
self.assertEqual(latticemap_slice_1, latticemap.slice(1, 3))
def test_LatticeMap3D__getitem__(self):
lattice = Lattice(self.nodes3D)
nodes = lattice.nodes
nnodes_dim = lattice.nnodes_dim
values = np.random.randn(lattice.nnodes)
latticemap = LatticeMap(lattice, values)
nx_st, nx_end = 2, 4
ny_st, ny_end = 0, 3
nz_st, nz_end = 2, 3
ind_x = np.arange(nx_st, nx_end)
ind_y = np.arange(ny_st, ny_end)
ind_z = np.arange(nz_st, nz_end)
latticemap_z = latticemap[:, :, nz_st]
lin_ind_z = np.array([
ix + iy * nnodes_dim[0] + nz_st * nnodes_dim[0] * nnodes_dim[1]
for iy in range(nnodes_dim[1]) for ix in range(nnodes_dim[0])
])
latticemap_zslice = latticemap[:, :, nz_st:nz_end]
lin_ind_zslice = np.array([
ix + iy * nnodes_dim[0] + iz * nnodes_dim[0] * nnodes_dim[1]
for iz in ind_z for iy in range(nnodes_dim[1])
for ix in range(nnodes_dim[0])
])
latticemap_xyzslice = latticemap[nx_st:nx_end, ny_st:ny_end,
nz_st:nz_end]
lin_ind_xyzslice = np.array([
ix + iy * nnodes_dim[0] + iz * nnodes_dim[0] * nnodes_dim[1]
for iz in ind_z for iy in ind_y for ix in ind_x
])
self.assertTrue(latticemap_z == LatticeMap(lattice=lattice[:, :,
nz_st],
values=values[lin_ind_z]))
self.assertTrue(latticemap_zslice == LatticeMap(
lattice=lattice[:, :,
nz_st:nz_end], values=values[lin_ind_zslice]))
self.assertTrue(
latticemap_xyzslice == LatticeMap(lattice=lattice[nx_st:nx_end,
ny_st:ny_end,
nz_st:nz_end],
values=values[lin_ind_xyzslice]))
def test_LatticeMap3D_ndim(self):
ndim = 3
lattice = Lattice(self.nodes3D)
values = np.random.randn(lattice.nnodes)
latticemap = LatticeMap(lattice, values)
self.assertTrue(hasattr(latticemap, 'ndim'))
self.assertEqual(latticemap.ndim, ndim)
self.assertTrue(isinstance(latticemap.ndim, int))
def test_LatticeMap2D_make_latticemap_from_txt(self):
nodes = [[-1.5, 1.5, 5, 8, 9], [1, 2, 3, 4, 5, 6]]
lattice = Lattice(nodes)
values = [
0.5,
0.5,
0.5,
0.5,
0.5,
0.6,
0.6,
0.6,
0.6,
0.6,
0.7,
0.7,
0.7,
0.7,
0.7,
0.7,
0.7,
0.7,
0.7,
0.7,
0.6,
0.6,
0.6,
0.6,
0.6,
0.5,
0.5,
0.5,
0.5,
0.5,
]
latticemap_true = LatticeMap(lattice, values)
file = PATH_TESTFILES + 'latticemap2d_simple.txt'
latticemap_test = LatticeMap.from_txt(file)
self.assertTrue(isinstance(latticemap_test, LatticeMap))
self.assertEqual(latticemap_true, latticemap_test)
def test_LatticeMap3D__add__(self):
lattice = Lattice(self.nodes3D)
nodes_short = [self.x_short, self.y, self.z]
lattice_short = Lattice(nodes_short)
num = -25.89
values_left = np.random.randn(lattice.nnodes)
values_right = np.random.randn(lattice.nnodes)
values_short = np.random.randn(lattice_short.nnodes)
latticemap_left = LatticeMap(lattice, values_left)
latticemap_right = LatticeMap(lattice, values_right)
latticemap_short = LatticeMap(lattice_short, values_short)
latticmap_sum = LatticeMap(lattice, values_left + values_right)
latticmap_sum_num = LatticeMap(lattice, values_left + num)
self.assertEqual(latticmap_sum, latticemap_left + latticemap_right)
self.assertTrue(latticmap_sum == latticemap_left + latticemap_right)
self.assertEqual(latticmap_sum_num, latticemap_left + num)
self.assertTrue(latticmap_sum_num == latticemap_left + num)
with self.assertRaises(ValueError):
latticemap_left + latticemap_short
with self.assertRaises(TypeError):
latticemap_left + 'foobar'
def test_LatticeMap3D_make_latticemap_from_txt(self):
nodes = [[-1.5, 1.5], [5, 8, 9], [-2, 3]]
lattice = Lattice(nodes)
values = [
0.5,
0.5,
0.8,
0.8,
0.1,
0.1,
0.6,
0.6,
0.9,
0.9,
0.2,
0.2,
]
latticemap_true = LatticeMap(lattice, values)
file = PATH_TESTFILES + 'latticemap3d_simple.txt'
latticemap_test = LatticeMap.from_txt(file)
self.assertTrue(isinstance(latticemap_test, LatticeMap))
self.assertEqual(latticemap_true, latticemap_test)
def test_readfile_latticemap_2D(self):
nodes = [[-1.5, 1.5, 5, 8, 9], [1, 2, 3, 4, 5, 6]]
values = np.asarray([
[0.5, 0.5, 0.5, 0.5, 0.5],
[0.6, 0.6, 0.6, 0.6, 0.6],
[0.7, 0.7, 0.7, 0.7, 0.7],
[0.7, 0.7, 0.7, 0.7, 0.7],
[0.6, 0.6, 0.6, 0.6, 0.6],
[0.5, 0.5, 0.5, 0.5, 0.5],
]).ravel(order='C')
latticemap_true = LatticeMap(nodes, values)
file = PATH_TESTFILES + 'latticemap2d_simple.txt'
latticemap_test = readfile_latticemap(file)
self.assertEqual(latticemap_true, latticemap_test)
def test_utils_readfile_latticemap3D(self):
nodes = [[-1.5, 1.5], [5, 8, 9], [-2, 3]]
values = np.asarray([
[0.5, 0.5],
[0.8, 0.8],
[0.1, 0.1],
[0.6, 0.6],
[0.9, 0.9],
[0.2, 0.2],
]).ravel(order='C')
latticemap_true = LatticeMap(nodes, values)
file = PATH_TESTFILES + 'latticemap3d_simple.txt'
latticemap_test = readfile_latticemap(file)
self.assertEqual(latticemap_true, latticemap_test)
def compute_condition_map(self, conditions=None, validate=False):
"""Computes a lattice map representing the union of a set of
conditions.
Args:
conditions (list, optional): Set of conditions of either strings
(that indicate the path of a conditioning file), array_like
objects (that represent conditioning points), or conditioning
lattice maps.
validate (bool, optional): Inspect the given conditioning with
respect to the sampler settings and if necessary correct it.
Returns:
LatticeMap: Conditioning map.
"""
if not conditions:
ones = np.ones(self._lattice.nnodes_dim, dtype=bool)
return LatticeMap(self._lattice, ones)
# Iteratively transform all conditions into lattice maps
cond_maps = []
for cond in conditions:
if isinstance(cond, str): # conditioning FILE
file = cond
cond_map = self._cond_map_from_str(file)
elif isinstance(cond, LatticeMap): # conditioning MAP
cond_map = cond
elif len(cond) == self._lattice.ndim: # conditioning POINT
components = np.asarray(cond)
cond_map = self._cond_map_from_point(components)
else:
raise ValueError(msg.err3004(cond))
cond_maps.append(cond_map)
# Reduce set of conditioning by multplication of all maps
map_ = functools.reduce(lambda a, b: a * b, cond_maps)
# Validate final conditioning map
if validate:
self._validate_conditioning(map_)
return map_
def _cond_map_from_str(self, file):
"""Loads a conditioning map from a saved file.
!!! ATTENTION !!!
This map invertes the values. AMS is used to indicate blocked nodes
by `1` and allowed nodes by `0`. However, for the sampling it is more
convenient to use it the other way around. Therefore, the values are
inverted withing this function.
"""
# Read the conditioning file
nodes, values = readfile_nodes_values(file)
# Invert the values (c.f. docstring)
values = utl.ams_val_map_to_bool_map(values)
# Check consistency of the lattices
if Lattice(nodes) != self._lattice:
raise ValueError(msg.err3001(file, self._lattice))
return LatticeMap(nodes, values)
def to_latticemap(self, lattice, dtype=None):
"""Generates a boolean lattice map indicating the trajectory.
Args:
lattice (Lattice): Object defining the computational lattice.
dtype (data-type, optional): The desired data-type for the map values.
If not given, then the type will be determined as the minimum
requirement by `numpy`.
Returns:
LatticeMap: Boolean trajectory according to a lattice grid.
"""
values = np.zeros(lattice.nnodes, dtype=bool)
# Make similar (closest node) computation iteratively for each point
for components in self:
linear_index = lattice.linear_index_from_point(components)
values[linear_index] = True
return LatticeMap(lattice, values, dtype=dtype)
def test_LatticeMap2D__getitem__(self):
lattice = Lattice(self.nodes2D)
nodes = lattice.nodes
nnodes_dim = lattice.nnodes_dim
values = np.random.randn(lattice.nnodes)
latticemap = LatticeMap(lattice, values)
nx_st, nx_end = 2, 4
ny_st, ny_end = 0, 3
ind_x = np.arange(nx_st, nx_end)
ind_y = np.arange(ny_st, ny_end)
latticemap_x = latticemap[nx_st, :]
lin_ind_x = np.array(
[nx_st + iy * nnodes_dim[0] for iy in range(nnodes_dim[1])])
latticemap_xslice = latticemap[nx_st:nx_end, :]
lin_ind_xslice = np.array([
ix + iy * nnodes_dim[0] for iy in range(nnodes_dim[1])
for ix in ind_x
])
latticemap_y = latticemap[:, ny_st]
lin_ind_y = np.array(
[ix + ny_st * nnodes_dim[0] for ix in range(nnodes_dim[0])])
latticemap_yslice = latticemap[:, ny_st:ny_end]
lin_ind_yslice = np.array([
ix + iy * nnodes_dim[0] for iy in ind_y
for ix in range(nnodes_dim[0])
])
latticemap_xyslice = latticemap[nx_st:nx_end, ny_st:ny_end]
lin_ind_xyslice = np.array(
[ix + iy * nnodes_dim[0] for iy in ind_y for ix in ind_x])
self.assertTrue(latticemap_x == LatticeMap(lattice=lattice[nx_st, :],
values=values[lin_ind_x]))
self.assertTrue(latticemap_xslice == LatticeMap(
lattice=lattice[nx_st:nx_end, :], values=values[lin_ind_xslice]))
self.assertTrue(latticemap_y == LatticeMap(lattice=lattice[:, ny_st],
values=values[lin_ind_y]))
self.assertTrue(latticemap_yslice == LatticeMap(
lattice=lattice[:, ny_st:ny_end], values=values[lin_ind_yslice]))
self.assertTrue(
latticemap_xyslice == LatticeMap(lattice=lattice[nx_st:nx_end,
ny_st:ny_end],
values=values[lin_ind_xyslice]))
def test_GantryDominant2D_set_prior_cond_with_str(self):
nodes = [[1, 2, 3], [4, 5, 6, 7, 8, 9, 10]]
lattice = Lattice(nodes)
conditions = [PATH_TESTFILES + 'condmap2d_simple.txt']
values_true = np.array([
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
0,
0,
0,
0,
0,
0,
0,
0,
],
dtype=bool)
prior_cond_true = LatticeMap(nodes, values_true)
ratio = 1.0
sampler = GantryDominant2D(lattice, ratio=ratio)
sampler.set_prior_cond(conditions)
self.assertEqual(sampler._prior_cond, prior_cond_true)
def test_LatticeMap2D_gen(self):
lattice = Lattice(self.nodes2D)
values = np.random.randn(lattice.nnodes)
latticemap = LatticeMap(lattice, values)
self.assertTrue(isinstance(latticemap, LatticeMap))
self.assertTrue(np.all(values == latticemap.values))
with self.assertRaises(ValueError):
LatticeMap(lattice, values[:-1])
with self.assertRaises(ValueError):
LatticeMap(lattice, [])
latticemap = LatticeMap(self.nodes2D, values)
self.assertTrue(isinstance(latticemap, LatticeMap))
self.assertTrue(np.all(values == latticemap.values))
with self.assertRaises(ValueError):
LatticeMap(self.nodes2D, values[:-1])
with self.assertRaises(ValueError):
LatticeMap(self.nodes2D, [])
class GantryDominant2D(Sampler):
"""`GantryDominant2D` is a 2D gantry dominated trajectory sampler.
It is designed to sample trajectories in two-dimensional domains as e.g.::
--------------------------------------
| **** 0000000000 |
| *** ** * 0000000000 |
** ****** * 000000 |
| * 00 |
DIM_TABLE | 00 * |
| 000000 ***** **** Trajectory
| 0000000000 *** *** |
| 0000000000 ** |
--------------------------------------
DIM_GANTRY
where the zeros indicate prior conditioning. The trajectories are guided
by a prior probability map describing higher and lower passage frequencies.
Notes
If the ratio is too small, the trajectory can not jump to upper or
lower neighbors but only straight right (or left). Consider the
following setup::
________________________________
| | | | |
| | B | E | H |
|_______|_______|_______|_______|
| | | | |
DIM_TABLE | A | C | F | I |
|_______|_______|_______|_______|
| | | | |
| | D | G | J |
|_______|_______|_______|_______|
DIM_GANTRY
where the nodes are chosen to have horizontal and vertical spread of
1.0. Let us fix a ratio value of 0.5. This means that when moving from
the first row to the second (distance=1.0) the trajectory is free to
move up or down anything between +0.5 and -0.5 (distance*ratio = 0.5).
We observe that in this case, it is not possible to jump from A to B or
D, because the vertical difference is 1.0 which is higher than 0.5.
Therefore, from A it is only possible to move to C.
Considering the spread across two rows (distance=2.0), we have a
vertical freedom of 1.0. This would technically allow to
start at A and end on E. However, due to the discretization of the grid
it would request to go the path A-C-E or A-B-E what would violate at
least once the maximum ratio of 0.5.
In such cases it is better to adapt the grid and design it more
according to the desired ratio as e.g::
________________________________
| | |
| | B |
|_______________|_______________|
| | |
| A | C |
|_______________|_______________|
| | |
| | D |
|_______________|_______________|
In the latter setup we can keep a ratio of 0.5 and it would be allowed
to jump from A to B or from A to D.
Args
lattice (Lattice or list of array_like): Object defining the
computational lattice.
ratio (float): Ratio describing the agility of the table with respect
to the gantry.
order (str {'random', 'max_val', 'max_random'}, optional): Order in
which the trajectory points are sampled. 'random' randomly selects
one gantry position after the other. 'max_val' treats the gantry
positions according to the maximum value in the prior probability
map. 'max_random' samples positions according to their maximum
value in the prior probability map.
"""
def __call__(self, conditions=None, validate=False, seed=None):
logging.info(f'Start Path Sampling')
# Set the random seed for reproducibility and write it to the logger
if seed is None:
seed = np.random.get_state()[1][0]
np.random.seed(seed)
logging.info(f'Numpy seed is {seed}')
# Sample path and generate a `Trajectory` object
points = self._compute_trajectory_points(conditions, validate)
return Trajectory(points)
def __init__(self, lattice, ratio=1.0, order='random'):
# Check the ratio with respect to the lattice, for more information
# consult the docstring in :meth:`_check_ratio`
self._validate_ratio(lattice, ratio)
# Initialize the values
super().__init__(lattice)
self._ratio = ratio
if order not in ['random', 'max_val', 'max_random']:
raise ValueError(msg.err3005(order))
self._order = order
self._graph = None
def __repr__(self):
cls_name = type(self).__name__
return f'{cls_name}(lattice={self._lattice}, ' \
f'ratio={repr(self._ratio)})'
def __str__(self):
return self.__repr__()
# Public Methods
def compute_adjacency_graph(self):
"""Computes and stores the adjacency graph of the sampler.
Not that we consider a directed graph where the edges always go from
the lower to the higher nodes such that the graph::
2---3
/ \ |
/ \ |
/ \|
1---4---5
would give the adjacency matrix::
| 1 2 3 4 5
--|--------------------
1 | * *
2 | * *
3 | *
4 | *
5 |
In this matrix, the rows represent 'arriving' and the columns
'departing' edges.
"""
graph = self._adjacency_graph()
self._graph = graph
def compute_condition_map(self, conditions=None, validate=False):
"""Computes a lattice map representing the union of a set of
conditions.
Args:
conditions (list, optional): Set of conditions of either strings
(that indicate the path of a conditioning file), array_like
objects (that represent conditioning points), or conditioning
lattice maps.
validate (bool, optional): Inspect the given conditioning with
respect to the sampler settings and if necessary correct it.
Returns:
LatticeMap: Conditioning map.
"""
if not conditions:
ones = np.ones(self._lattice.nnodes_dim, dtype=bool)
return LatticeMap(self._lattice, ones)
# Iteratively transform all conditions into lattice maps
cond_maps = []
for cond in conditions:
if isinstance(cond, str): # conditioning FILE
file = cond
cond_map = self._cond_map_from_str(file)
elif isinstance(cond, LatticeMap): # conditioning MAP
cond_map = cond
elif len(cond) == self._lattice.ndim: # conditioning POINT
components = np.asarray(cond)
cond_map = self._cond_map_from_point(components)
else:
raise ValueError(msg.err3004(cond))
cond_maps.append(cond_map)
# Reduce set of conditioning by multplication of all maps
map_ = functools.reduce(lambda a, b: a * b, cond_maps)
# Validate final conditioning map
if validate:
self._validate_conditioning(map_)
return map_
def set_prior_cond(self, conditions=None, validate=False):
"""Sets the prior conditioning map of the sampler with the possibility
to validate it.
The prior probability map is updated whenever a new prior conditioning
map is set.
Args:
conditions (list, optional): Set of conditions of either strings
(that indicate the path of a conditioning file), array_like
objects (that represent conditioning points), or conditioning
lattice maps.
validate (bool, optional): Inspect the given conditioning with
respect to the sampler settings and if necessary correct it.
Returns:
None
"""
# Get conditioning map
map_ = self.compute_condition_map(conditions, validate)
# Minor consistency check
if self._lattice != map_.lattice:
raise ValueError(msg.err3000(self._lattice, map_.lattice))
# Set value within self
self._prior_cond = map_
def set_prior_prob(self, map_, energy=False):
"""Sets the prior probability attribute of the sampler.
It is possible to provide prior probability values (`energy=False`) or
probability energy values (`energy=True`). In the latter case, the
values are transformed to un-normalized probability measures by::
prior_prob.values = exp(-map_.values)
where `exp` denotes the exponential function.
Args:
map_ (LatticeMap): Prior map
energy (bool): Indicates if the prior map represents probability
values (false) or probability energy (true).
Returns:
None
"""
# Minor consistency checks
if self._lattice != map_.lattice:
raise ValueError(msg.err3000(self._lattice, map_.lattice))
# If the map represents the energy, transform it to probability values
values = np.copy(map_.values)
if energy:
values = np.exp(-values)
# Set value within self
self._prior_prob = LatticeMap(self._lattice, values)
# Private Methods
def _adjacency_graph(self):
"""Computes an adjacency graph based on a computational lattice.
The entry (i, j) of the graph matrix is non-zero if there is a
connection starting from node i and joining j. For more information see
docstring of :meth:`compute_adjacency_graph`.
Returns
ndarray: Matrix representing the directed graph
"""
# Gantry/Table nodes
lattice = self._lattice
nodes_gantry = lattice.nodes[DIM_GANTRY]
nodes_table = lattice.nodes[DIM_TABLE]
# Get an array containing the linear indices
lin_ind = self._linear_indices()
shape, dim = lin_ind.shape, (len(nodes_gantry), len(nodes_table))
if shape != dim:
raise ValueError(msg.err3002(shape, dim))
# Iteratively go through the nodes and generate adjacency graph
ratio = 2 * self._ratio # The opening is symmetric
pts = nodes_table
graph = np.zeros((lattice.nnodes, ) * 2, dtype=bool)
for igan, node_g in enumerate(nodes_gantry[:-1]):
# Conical opening for the permitted area of the trajectory
dist = abs(node_g - nodes_gantry[igan + 1])
for itab, node_t in enumerate(nodes_table):
cntr = node_t
allowed = utl.within_conical_opening(cntr, dist, ratio, pts)
from_node = lin_ind[igan, itab]
to_nodes = lin_ind[igan + 1, allowed]
graph[from_node, to_nodes] = True
return graph
def _compute_trajectory_points(self, conditions=None, validate=False):
"""Samples the trajectory points to generate a trajectory reaching
through the gantry dimension of the lattice.
Args:
conditions (list, optional): Set of conditions of either strings
(that indicate the path of a conditioning file), array_like
objects (that represent conditioning points), or conditioning
lattice maps.
validate (bool, optional): Inspect the given conditioning with
respect to the sampler settings and if necessary correct it.
Returns:
list of tuples: List of sampled points
"""
# Initialization
nodes_gantry = self._lattice.nodes[DIM_GANTRY]
nodes_table = self._lattice.nodes[DIM_TABLE]
points = [
None,
] * len(nodes_gantry)
# Compute (and eventually validate) the global condition map
if not conditions:
conditions = []
conditions.append(self.prior_cond)
cond_map = self.compute_condition_map(conditions, validate)
# Iteratively sample the points following a given gantry order
for ipos in self._sampling_indices():
# Compute the distribution in the slice at position `ipos`
prior_slice = self._prior_prob.slice(DIM_GANTRY, ipos)
cond_slice = cond_map.slice(DIM_GANTRY, ipos)
distribution = prior_slice * cond_slice
# Normalize the distribution values
try:
distribution = distribution.normalize_sum()
except (ValueError, TypeError) as e:
# Write logging file entry
logging.error(f'No possible path passage at ipos={ipos}')
# Save current permission map to a text file
map_ = self._prior_prob * cond_map
map_.to_txt(os.path.join(_LOC_FOLDER, LOG_MAP_NAME))
raise e
# Select table trajectory point according to the distribution
p_choice = distribution.values
pos_table = np.random.choice(nodes_table, p=p_choice)
# Generate and set new trajectory point
new_point = [
None,
] * self._lattice.ndim
new_point[DIM_GANTRY] = nodes_gantry[ipos]
new_point[DIM_TABLE] = pos_table
points[ipos] = tuple(new_point)
# Update the restriction map by conditioning the new point
cond_map *= self._cond_map_from_point(new_point)
return points
def _cond_map_from_point(self, components):
"""Generate a conditioning lattice map from a conditioning point."""
# Initialization
nodes = self._lattice.nodes
nnodes_dim = self._lattice.nnodes_dim
# Generate array with lowest dimension corresponding to the gantry
dim = (nnodes_dim[DIM_GANTRY], nnodes_dim[DIM_TABLE])
values = np.zeros(dim, dtype=bool)
# Conical opening for the permitted area of the trajectory
center = components[DIM_TABLE]
con_rat = 2 * self._ratio # The conical opening is symmetric
pts = nodes[DIM_TABLE]
# Loop in gantry direction through the lattice
for inode, node in enumerate(nodes[DIM_GANTRY]):
dist = abs(node - components[DIM_GANTRY])
allowed = utl.within_conical_opening(center, dist, con_rat, pts)
values[inode, allowed] = True
# Correct dimension ordering if needed
if DIM_GANTRY > DIM_TABLE:
values = values.transpose()
values = values.ravel(order=NP_ORDER)
return LatticeMap(self._lattice, values)
def _cond_map_from_str(self, file):
"""Loads a conditioning map from a saved file.
!!! ATTENTION !!!
This map invertes the values. AMS is used to indicate blocked nodes
by `1` and allowed nodes by `0`. However, for the sampling it is more
convenient to use it the other way around. Therefore, the values are
inverted withing this function.
"""
# Read the conditioning file
nodes, values = readfile_nodes_values(file)
# Invert the values (c.f. docstring)
values = utl.ams_val_map_to_bool_map(values)
# Check consistency of the lattices
if Lattice(nodes) != self._lattice:
raise ValueError(msg.err3001(file, self._lattice))
return LatticeMap(nodes, values)
def _linear_indices(self):
"""Returns the two dimensional array of the linear indices. The lower
dimension of the produced array always considers the GANTRY dimension.
The setting (DIM_GANTRY < DIM_TABLE and NP_ORDER='F') then produces the
same outcome as (DIM_GANTRY > DIM_TABLE and NP_ORDER='C') because in
both cases, the linear counter first considers (and increases) along
the gantry dimension.
Similar reasoning goes for the two settings (DIM_GANTRY > DIM_TABLE and
NP_ORDER='F') and (DIM_GANTRY < DIM_TABLE and NP_ORDER='C') because the
linear counter first considers (and increases) along the table
dimension.
"""
linear_indices = self._lattice.linear_indices()
# As mentioned in the docstring, lower dimension corresponds to gantry
if DIM_GANTRY > DIM_TABLE:
linear_indices = linear_indices.transpose()
return linear_indices
def _sampling_indices(self):
"""This method is used to define the order in which the trajectory
points are sampled.
There are the following possibilities:
- 'random': Randomly choose positions indices,
- 'max_val': For each position, compute the maximum value in the
prior probability map (i.e. np.max(..., axis=DIM_TABLE) and
sort positions indices accordingly in descending order,
- 'max_random': As above, but rather than ordering, we sample
position indices according to these values.
Returns:
ndarray: Position indices.
"""
order = self._order
lattice = self._lattice
def _max_vals():
"""Computing the maximum probability values in table direction.
"""
values = (self._prior_prob * self.prior_cond).values
values = values.reshape(lattice.nnodes_dim, order=NP_ORDER)
return np.max(values, axis=DIM_TABLE)
if order == 'random':
pos = np.arange(lattice.nnodes_dim[DIM_GANTRY])
np.random.shuffle(pos)
elif order == 'max_val':
pos = np.argsort(_max_vals())[::-1]
elif order == 'max_random':
prob = _max_vals()
prob /= np.sum(prob)
npos = lattice.nnodes_dim[DIM_GANTRY]
pos = np.arange(npos)
pos = np.random.choice(pos, size=npos, replace=False, p=prob)
else:
raise ValueError(msg.err3005(order))
return pos
def _validate_conditioning(self, map_):
"""Checks if a given conditioning map is valid with respect to the
sampler settings.
For doing so, we check if each node is potentially reachable by a
trajectory that goes through the entire gantry range. If not, the node
is set to be 'blocked'.
Args:
map_ (LatticeMap): Conditioning map
"""
# The validity of the conditioning us checked by using an adjacency
# graph to see if all nodes can be reached f
if not self._graph:
self.compute_adjacency_graph()
graph = np.array(self._graph, copy=True)
# Make the changes to an shallow copy of map_.values
values = map_.values
# Initialize set of nodes to be checked
inodes_control = set(np.where(np.logical_not(values))[0])
# Boundary nodes
lin_ind = self._linear_indices()
no_out = lin_ind[-1, :] # boundary nodes with no outgoing edges
no_in = lin_ind[0, :] # boundary nodes with no incoming edges
# Loop until there is no potential issue anymore
while len(inodes_control) > 0:
# Pop next node index to be checked
inode = inodes_control.pop()
# Get incoming and outgoing edges for the given node index `inode`
outgoing = np.where(graph[inode, :])[0]
incoming = np.where(graph[:, inode])[0]
# Block node if there is no path passing through it
issue_out = len(outgoing) == 0 and inode not in no_out
issue_in = len(incoming) == 0 and inode not in no_in
if not values[inode] or issue_out or issue_in:
# Block the specific node
values[inode] = False
# Remove node edges from graph
graph[inode, :] = False
graph[:, inode] = False
# Add the modified nodes to the control set
inodes_control = inodes_control.union(outgoing)
inodes_control = inodes_control.union(incoming)
@staticmethod
def _validate_ratio(lattice, ratio):
"""Checks if the ratio corresponds well with the lattice definitions.
For mor information see the docstring of this class. The ratio can be
interpreted as:
ratio = d_table / d_gantry.
In this function we test if the given ratio is sufficient to make
the largest table gap when facing the smallest gantry gap.
"""
nodes = lattice.nodes
spacing_gantry = nodes[DIM_GANTRY][1:] - nodes[DIM_GANTRY][:-1]
spacing_table = nodes[DIM_TABLE][1:] - nodes[DIM_TABLE][:-1]
ratio_max = np.max(spacing_table) / np.min(spacing_gantry)
if ratio < ratio_max:
raise ValueError(msg.err3003)
def test_GantryDominant2D_set_prior_cond_with_map(self):
nodes = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5]]
lattice = Lattice(nodes)
values = np.array([
1,
1,
1,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
1,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
1,
],
dtype=bool)
conditions = [LatticeMap(nodes, values)]
values_true = np.array([
1,
1,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
1,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
1,
],
dtype=bool)
prior_cond_true = LatticeMap(nodes, values_true)
ratio = 2.0
sampler = GantryDominant2D(lattice, ratio=ratio)
sampler.set_prior_cond(conditions, validate=True)
self.assertEqual(sampler._prior_cond, prior_cond_true)
values_true = np.array([
1,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
0,
0,
0,
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
1,
0,
1,
1,
1,
1,
1,
1,
1,
1,
0,
0,
0,
1,
1,
1,
1,
1,
1,
0,
0,
0,
0,
0,
],
dtype=bool)
prior_cond_true = LatticeMap(nodes, values_true)
ratio = 1.0
sampler = GantryDominant2D(lattice, ratio=ratio)
sampler.set_prior_cond(conditions, validate=True)
self.assertEqual(sampler._prior_cond, prior_cond_true)
def test_GantryDominant2D__cond_map_from_point(self):
nodes = [[-2, -1, 0, 1, 2], [-2, 0, 2]]
lattice = Lattice(nodes)
conditions = [(0, 0)]
values_true = np.array([
1,
1,
0,
1,
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
1,
],
dtype=bool)
prior_cond_true = LatticeMap(nodes, values_true)
ratio = 2.0
sampler = GantryDominant2D(lattice, ratio=ratio)
sampler.set_prior_cond(conditions)
self.assertEqual(sampler._prior_cond, prior_cond_true)
conditions = [(-2, -2)]
values_true = np.array([
1,
1,
1,
1,
1,
0,
1,
1,
1,
1,
0,
0,
1,
1,
1,
],
dtype=bool)
prior_cond_true = LatticeMap(nodes, values_true)
ratio = 2.0
sampler = GantryDominant2D(lattice, ratio=ratio)
sampler.set_prior_cond(conditions)
self.assertEqual(sampler._prior_cond, prior_cond_true)
conditions = [(1, -2)]
values_true = np.array([
1,
1,
1,
1,
1,
1,
1,
1,
0,
1,
1,
1,
1,
0,
1,
],
dtype=bool)
prior_cond_true = LatticeMap(nodes, values_true)
ratio = 4.0
sampler = GantryDominant2D(lattice, ratio=ratio)
sampler.set_prior_cond(conditions)
self.assertEqual(sampler._prior_cond, prior_cond_true)