def computeRT(item_path, xp=np):
with open(item_path, 'r') as f:
LINES = [line.strip("';\n") for line in f]
param = {}
for index, args in enumerate(LINES):
name = args[:15].replace(" ", "")
name = name[:].replace("=", "")
val = args[15:]
val = xp.asarray(val.strip("[]").split(","), dtype=xp.float64)
param[name] = val
cam_dir = param["cam_dir"]
cam_pos = param["cam_pos"]
cam_up = param["cam_up"]
z = cam_dir / xp.linalg.norm(cam_dir)
x = xp.cross(cam_up, z)
x = x / xp.linalg.norm(x)
y = xp.cross(z, x)
x = xp.expand_dims(x, axis=1)
y = xp.expand_dims(y, axis=1)
z = xp.expand_dims(z, axis=1)
R = xp.concatenate([x, y, z], axis=1)
T = xp.expand_dims(cam_pos, axis=1)
R_T = xp.concatenate([R, T], axis=1)
return R_T
def view_dirs(norm: cp.ndarray) -> cp.ndarray:
dir_0 = cp.asarray([-float(norm[1]), float(norm[0]), 0.])
dir_1 = cp.cross(norm, dir_0)
dir_0 = unitize(dir_0) * FOV
dir_1 = unitize(dir_1) * FOV
dirs = cp.tile(
unitize(norm) +
dir_0 * cp.linspace(-1, 1, RESOLUTION)[..., cp.newaxis],
(RESOLUTION, 1)).reshape(RESOLUTION, RESOLUTION, 3)
dirs += (dir_1 *
cp.linspace(-1, 1, RESOLUTION)[..., cp.newaxis])[:, cp.newaxis]
return dirs
def locate_points(
mesh_prefix: str = None,
pts_prefix: str = None,
chunk_size: int = None,
bounding_box: dict = None) -> [cp.ndarray, cp.ndarray, cp.ndarray]:
#
# Load data
tris, verts, vert_normals = load_mesh(mesh_prefix)
all_pts = load_query_points(pts_prefix)
vertices = verts[tris[:, :]]
#
# Fix common dimensions
num_verts = vertices.shape[0]
#
# Compute static information about
# the triangles
#
# ====================
# EDGE ORDER
# [:, 0, :] = v
# [:, 1, :] = -u
# [:, 2, :] = -w
# ====================
edges = cp.roll(vertices, 1, axis=1) - vertices # (p3-p1, p1-p2, p2-p3)
#
# Correct edge signs and ordering
edges[:, 1, :] = edges[:, 1, :] * -1
edges[:, 2, :] = edges[:, 2, :] * -1
edges = cp.roll(edges, 2, axis=1)
tmp = edges[:, 1, :].copy()
edges[:, 1, :] = edges[:, 2, :]
edges[:, 2, :] = tmp
#
# Compute normals and lengths
normals = cp.cross(edges[:, 0], edges[:, 1])
norms = cp.linalg.norm(normals, axis=1)
normssq = cp.square(norms)
#
return _locate_points(all_pts=all_pts,
vertices=vertices,
edges=edges,
normals=normals,
norms=norms,
normssq=normssq,
chunk_size=chunk_size,
num_verts=num_verts,
tris=tris,
vertex_normals=vert_normals,
bounding_box=bounding_box)
"""
Array API compatible wrapper for :py:func:`np.cross <numpy.cross>`.
See its docstring for more information.
"""
if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
raise TypeError('Only numeric dtypes are allowed in cross')
# Note: this is different from np.cross(), which broadcasts
if x1.shape != x2.shape:
raise ValueError('x1 and x2 must have the same shape')
if x1.ndim == 0:
raise ValueError('cross() requires arrays of dimension at least 1')
# Note: this is different from np.cross(), which allows dimension 2
if x1.shape[axis] != 3:
raise ValueError('cross() dimension must equal 3')
return Array._new(np.cross(x1._array, x2._array, axis=axis))
def det(x: Array, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.linalg.det <numpy.linalg.det>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.det.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in det')
return Array._new(np.linalg.det(x._array))
def evaluate_chunks(
results: [cp.ndarray, cp.ndarray,
cp.ndarray], # closest triangle, distance, projection
all_pts: cp.ndarray = None,
vertices: cp.ndarray = None,
edges: cp.ndarray = None,
edge_norms: cp.ndarray = None,
edge_normssq: cp.ndarray = None,
normals: cp.ndarray = None,
norms: cp.ndarray = None,
normssq: cp.ndarray = None,
zero_tensor: cp.ndarray = None,
one_tensor: cp.ndarray = None,
tris: cp.ndarray = None,
vertex_normals: cp.ndarray = None,
bounding_box: dict = None,
chunk_size: int = None,
num_verts: int = None) -> None:
#
# Expand vertex normals if non empty
if vertex_normals is not None:
vertex_normals = vertex_normals[tris]
vertex_normals = cp.tile(cp.expand_dims(vertex_normals, axis=2),
(1, 1, chunk_size, 1))
# begin = time.time()
#
# Load and extend the batch
num_chunks = all_pts.shape[0] // chunk_size
for i in range(num_chunks):
#
# Get subset of the query points
start_index = i * chunk_size
end_index = (i + 1) * chunk_size
pts = all_pts[start_index:end_index, :]
#
# Match the dimensions to those assumed above.
# REPEATED REPEATED
# [triangle_index, vert_index, querypoint_index, coordinates]
pts = cp.tile(cp.expand_dims(pts, axis=(0, 1)), (num_verts, 3, 1, 1))
#
# Compute the differences between
# vertices on each triangle and the
# points of interest
#
# [triangle_index, vert_index, querypoint_index, coordinates]
# ===================
# [:,0,:,:] = p - p1
# [:,1,:,:] = p - p2
# [:,2,:,:] = p - p3
diff_vectors = pts - vertices
#
# Compute alpha, beta, gamma
barycentric = cp.empty(diff_vectors.shape)
#
# gamma = u x (p - p1)
barycentric[:, 2, :, :] = cp.cross(edges[:, 0, :, :],
diff_vectors[:, 0, :, :])
# beta = (p - p1) x v
barycentric[:, 1, :, :] = cp.cross(diff_vectors[:, 0, :, :],
edges[:, 1, :, :])
# alpha = w x (p - p2)
barycentric[:, 0, :, :] = cp.cross(edges[:, 2, :, :],
diff_vectors[:, 1, :, :])
barycentric = cp.divide(
cp.sum(cp.multiply(barycentric, normals), axis=3), normssq)
#
# Test conditions
less_than_one = cp.less_equal(barycentric, one_tensor)
more_than_zero = cp.greater_equal(barycentric, zero_tensor)
#
# if 0 <= gamma and gamma <= 1
# and 0 <= beta and beta <= 1
# and 0 <= alpha and alpha <= 1:
cond1 = cp.logical_and(less_than_one, more_than_zero)
#
# if gamma <= 0:
cond2 = cp.logical_not(more_than_zero[:, 2, :])
cond2 = cp.tile(cp.expand_dims(cond2, axis=1), (1, 3, 1))
#
# if beta <= 0:
cond3 = cp.logical_not(more_than_zero[:, 1, :])
cond3 = cp.tile(cp.expand_dims(cond3, axis=1), (1, 3, 1))
#
# if alpha <= 0:
cond4 = cp.logical_not(more_than_zero[:, 0, :])
cond4 = cp.tile(cp.expand_dims(cond4, axis=1), (1, 3, 1))
#
# Get the projections for each case
xi = cp.empty(barycentric.shape)
barycentric_ext = cp.tile(cp.expand_dims(barycentric, axis=3),
(1, 1, 1, 3))
proj = cp.sum(cp.multiply(barycentric_ext, vertices), axis=1)
#
# if 0 <= gamma and gamma <= 1
# and 0 <= beta and beta <= 1
# and 0 <= alpha and alpha <= 1:
xi[cond1] = barycentric[cond1]
#
# if gamma <= 0:
# x = p - p1
# u = p2 - p1
# a = p1
# b = p2
t2 = cp.divide(
#
# u.dot(x)
cp.sum(cp.multiply(edges[:, 0, :, :], diff_vectors[:, 0, :, :]),
axis=2),
edge_normssq[:, 0])
xi2 = cp.zeros((t2.shape[0], 3, t2.shape[1]))
xi2[:, 0, :] = -t2 + 1
xi2[:, 1, :] = t2
#
t2 = cp.tile(cp.expand_dims(t2, axis=2), (1, 1, 3))
lz = cp.less(t2, cp.zeros(t2.shape))
go = cp.greater(t2, cp.ones(t2.shape))
proj2 = vertices[:, 0, :, :] + cp.multiply(t2, edges[:, 0, :, :])
proj2[lz] = vertices[:, 0, :, :][lz]
proj2[go] = vertices[:, 1, :, :][go]
#
xi[cond2] = xi2[cond2]
proj[cp.swapaxes(cond2, 1, 2)] = proj2[cp.swapaxes(cond2, 1, 2)]
#
# if beta <= 0:
# x = p - p1
# v = p3 - p1
# a = p1
# b = p3
t3 = cp.divide(
#
# v.dot(x)
cp.sum(cp.multiply(edges[:, 1, :, :], diff_vectors[:, 0, :, :]),
axis=2),
edge_normssq[:, 1])
xi3 = cp.zeros((t3.shape[0], 3, t3.shape[1]))
xi3[:, 0, :] = -t3 + 1
xi3[:, 2, :] = t3
#
t3 = cp.tile(cp.expand_dims(t3, axis=2), (1, 1, 3))
lz = cp.less(t3, cp.zeros(t3.shape))
go = cp.greater(t3, cp.ones(t3.shape))
proj3 = vertices[:, 0, :, :] + cp.multiply(t3, edges[:, 1, :, :])
proj3[lz] = vertices[:, 0, :, :][lz]
proj3[go] = vertices[:, 2, :, :][go]
#
xi[cond3] = xi3[cond3]
proj[cp.swapaxes(cond3, 1, 2)] = proj3[cp.swapaxes(cond3, 1, 2)]
#
# if alpha <= 0:
# y = p - p2
# w = p3 - p2
# a = p2
# b = p3
t4 = cp.divide(
#
# w.dot(y)
cp.sum(cp.multiply(edges[:, 2, :, :], diff_vectors[:, 1, :, :]),
axis=2),
edge_normssq[:, 2])
xi4 = cp.zeros((t4.shape[0], 3, t4.shape[1]))
xi4[:, 1, :] = -t4 + 1
xi4[:, 2, :] = t4
#
t4 = cp.tile(cp.expand_dims(t4, axis=2), (1, 1, 3))
lz = cp.less(t4, cp.zeros(t4.shape))
go = cp.greater(t4, cp.ones(t4.shape))
proj4 = vertices[:, 1, :, :] + cp.multiply(t4, edges[:, 2, :, :])
proj4[lz] = vertices[:, 1, :, :][lz]
proj4[go] = vertices[:, 2, :, :][go]
#
xi[cond4] = xi4[cond4]
proj[cp.swapaxes(cond4, 1, 2)] = proj4[cp.swapaxes(cond4, 1, 2)]
vec_to_point = pts[:, 0, :, :] - proj
distances = cp.linalg.norm(vec_to_point, axis=2)
# n = "\n"
# print(f"{pts[:,0,:,:]=}")
# print(f"{proj=}")
# print(f"{pts[:,0,:,:] - proj=}")
# print(f"{distances=}")
min_distances = cp.min(distances, axis=0)
closest_triangles = cp.argmin(distances, axis=0)
projections = proj[closest_triangles, np.arange(chunk_size), :]
#
# Distinguish close triangles
is_close = cp.isclose(distances, min_distances)
#
# Determine sign
signed_normal = normals[:, 0, :, :]
if vertex_normals is not None:
signed_normal = cp.sum(vertex_normals.transpose() * xi.transpose(),
axis=2).transpose()
is_negative = cp.less_equal(
cp.sum(cp.multiply(vec_to_point, signed_normal), axis=2), 0.)
#
# Combine
is_close_and_negative = cp.logical_and(is_close, is_negative)
#
# Determine if inside
is_inside = cp.all(cp.logical_or(is_close_and_negative,
cp.logical_not(is_close)),
axis=0)
#
# Overwrite the signs of points
# that are outside of the box
if bounding_box is not None:
#
# Extract
rotation_matrix = cp.asarray(bounding_box['rotation_matrix'])
translation_vector = cp.asarray(bounding_box['translation_vector'])
size = cp.asarray(bounding_box['size'])
#
# Transform
transformed_pts = cp.dot(
all_pts[start_index:end_index, :] - translation_vector,
rotation_matrix)
#
# Determine if outside bbox
inside_bbox = cp.all(cp.logical_and(
cp.less_equal(0., transformed_pts),
cp.less_equal(transformed_pts, size)),
axis=1)
#
# Treat points outside bbox as
# being outside of lumen
print(f"{inside_bbox=}")
is_inside = cp.logical_and(is_inside, inside_bbox)
#
# Apply sign to indicate whether the distance is
# inside or outside the mesh.
min_distances[is_inside] = -1 * min_distances[is_inside]
#
# Emplace results
# [triangle_index, vert_index, querypoint_index, coordinates]
results[0][start_index:end_index] = closest_triangles
results[1][start_index:end_index] = min_distances
results[2][start_index:end_index, :] = projections
def cross(self, v: Vec3) -> Vec3:
return Vec3(*cp.cross(self.e, v.e))
def llgs(t, m, H_eff):
beta = (gamma*hbar*J_mtj)/(2*q_e*M_s*t_mtj)
return -(gamma*mu_0)/(1+alpha**2) * cp.cross(m, H_eff) \
- alpha*(gamma*mu_0)/(1+alpha**2) * cp.cross(m, cp.cross(m,H_eff)) \
+ beta/(1+alpha**2) * cp.cross(m, cp.cross(m, m_p)) \
+ alpha*beta/(1+alpha**2) * cp.cross(m,m_p)
def llgsSmallNoise2(m):
return - (v_sd*gamma*mu_0)/(1+alpha**2)*m*I_sf \
+ (v_sd*gamma*mu_0)/(1+alpha**2)*cp.cross(m, alpha*m)
def llgsSmallNoise4(m):
return -(v_sd*gamma*mu_0)/(1+alpha**2)*cp.cross(m, I_sf+alpha*m)
def cross(self, v):
return Vec3(*cp.cross(self.e, v.e))