def tensors_scalarproduct(dec_x, dec_y, dec_z, tilt_x, tilt_y, tilt_z,
directions1, directions2, tensor1, tensor2):
"""
Vectors/tensors have same contractions in different coordinate systems.
"""
system = LocalCoordinates(name="1",
decx=100.*(2.*dec_x-1.),
decy=100.*(2.*dec_y-1.),
decz=100.*(2.*dec_z-1.),
tiltx=2.*math.pi*tilt_x,
tilty=2.*math.pi*tilt_y,
tiltz=2.*math.pi*tilt_z)
global_directions1 = system.returnLocalToGlobalDirections(directions1)
global_directions2 = system.returnLocalToGlobalDirections(directions2)
global_tensor1 = system.returnLocalToGlobalTensors(tensor1)
global_tensor2 = system.returnLocalToGlobalTensors(tensor2)
# check whether a transformation between coordinate
# systems changes indeed the components
# assert np.any(t1glob - t1loc != 0) FIXME: currently breaks
# assert np.any(t2glob - t2loc != 0) FIXME: currently breaks
# assert np.any(v1glob - v1loc != 0) FIXME: currently breaks
# assert np.any(v2glob - v2loc != 0) FIXME: currently breaks
# test trace of tensor
assert np.allclose((np.trace(global_tensor1, axis1=0, axis2=1)-
np.trace(tensor1, axis1=0, axis2=1)),
0)
# test t1 t2 tensor contraction
assert np.allclose((np.einsum('ij...,ij...',
global_tensor1, global_tensor2)-
np.einsum('ij...,ij...', tensor1, tensor2)),
0)
# test v1 t1 v2
assert np.allclose((np.einsum('i...,ij...,j...',
global_directions1,
global_tensor1,
global_directions2)-
np.einsum('i...,ij...,j...',
directions1,
tensor1,
directions2)),
0)
# test v1 t1 t2 v2
assert np.allclose((np.einsum('i...,ij...,jk...,k...',
global_directions1,
global_tensor1,
global_tensor2,
global_directions2)-
np.einsum('i...,ij...,jk...,k...',
directions1,
tensor1,
tensor2,
directions2)),
0)
def transform_directions(dec_x, dec_y, dec_z, tilt_x, tilt_y, tilt_z,
local_directions):
"""
Sequential local/global and back transformation yields original vector.
"""
system = LocalCoordinates(name="1",
decx=100. * (2. * dec_x - 1.),
decy=100. * (2. * dec_y - 1.),
decz=100. * (2. * dec_z - 1.),
tiltx=2. * math.pi * tilt_x,
tilty=2. * math.pi * tilt_y,
tiltz=2. * math.pi * tilt_z)
global_directions = system.returnLocalToGlobalDirections(local_directions)
local_directions2 = system.returnGlobalToLocalDirections(global_directions)
assert np.allclose(local_directions2 - local_directions, 0)
def transform_directions(dec_x, dec_y, dec_z, tilt_x, tilt_y, tilt_z,
local_directions):
"""
Sequential local/global and back transformation yields original vector.
"""
system = LocalCoordinates(name="1",
decx=100.*(2.*dec_x-1.),
decy=100.*(2.*dec_y-1.),
decz=100.*(2.*dec_z-1.),
tiltx=2.*math.pi*tilt_x,
tilty=2.*math.pi*tilt_y,
tiltz=2.*math.pi*tilt_z)
global_directions = system.returnLocalToGlobalDirections(local_directions)
local_directions2 = system.returnGlobalToLocalDirections(global_directions)
assert np.allclose(local_directions2-local_directions, 0)
def directions_scalarproduct(dec_x, dec_y, dec_z, tilt_x, tilt_y, tilt_z,
local1, local2):
"""
Two vectors have same scalar product in two different coordinate systems.
"""
system = LocalCoordinates(name="1",
decx=100. * (2. * dec_x - 1.),
decy=100. * (2. * dec_y - 1.),
decz=100. * (2. * dec_z - 1.),
tiltx=2. * math.pi * tilt_x,
tilty=2. * math.pi * tilt_y,
tiltz=2. * math.pi * tilt_z)
global1 = system.returnLocalToGlobalDirections(local1)
global2 = system.returnLocalToGlobalDirections(local2)
scalarproduct_local = np.einsum('i...,i...', local1, local2)
scalarproduct_global = np.einsum('i...,i...', global1, global2)
assert np.allclose(scalarproduct_local - scalarproduct_global, 0)
def directions_scalarproduct(dec_x, dec_y, dec_z, tilt_x, tilt_y, tilt_z,
local1, local2):
"""
Two vectors have same scalar product in two different coordinate systems.
"""
system = LocalCoordinates(name="1",
decx=100.*(2.*dec_x-1.),
decy=100.*(2.*dec_y-1.),
decz=100.*(2.*dec_z-1.),
tiltx=2.*math.pi*tilt_x,
tilty=2.*math.pi*tilt_y,
tiltz=2.*math.pi*tilt_z)
global1 = system.returnLocalToGlobalDirections(local1)
global2 = system.returnLocalToGlobalDirections(local2)
scalarproduct_local = np.einsum('i...,i...', local1, local2)
scalarproduct_global = np.einsum('i...,i...', global1, global2)
assert np.allclose(scalarproduct_local-scalarproduct_global, 0)
def tensors_scalarproduct(dec_x, dec_y, dec_z, tilt_x, tilt_y, tilt_z,
directions1, directions2, tensor1, tensor2):
"""
Vectors/tensors have same contractions in different coordinate systems.
"""
system = LocalCoordinates(name="1",
decx=100. * (2. * dec_x - 1.),
decy=100. * (2. * dec_y - 1.),
decz=100. * (2. * dec_z - 1.),
tiltx=2. * math.pi * tilt_x,
tilty=2. * math.pi * tilt_y,
tiltz=2. * math.pi * tilt_z)
global_directions1 = system.returnLocalToGlobalDirections(directions1)
global_directions2 = system.returnLocalToGlobalDirections(directions2)
global_tensor1 = system.returnLocalToGlobalTensors(tensor1)
global_tensor2 = system.returnLocalToGlobalTensors(tensor2)
# check whether a transformation between coordinate
# systems changes indeed the components
# assert np.any(t1glob - t1loc != 0) FIXME: currently breaks
# assert np.any(t2glob - t2loc != 0) FIXME: currently breaks
# assert np.any(v1glob - v1loc != 0) FIXME: currently breaks
# assert np.any(v2glob - v2loc != 0) FIXME: currently breaks
# test trace of tensor
assert np.allclose((np.trace(global_tensor1, axis1=0, axis2=1) -
np.trace(tensor1, axis1=0, axis2=1)), 0)
# test t1 t2 tensor contraction
assert np.allclose(
(np.einsum('ij...,ij...', global_tensor1, global_tensor2) -
np.einsum('ij...,ij...', tensor1, tensor2)), 0)
# test v1 t1 v2
assert np.allclose(
(np.einsum('i...,ij...,j...', global_directions1, global_tensor1,
global_directions2) -
np.einsum('i...,ij...,j...', directions1, tensor1, directions2)), 0)
# test v1 t1 t2 v2
assert np.allclose(
(np.einsum('i...,ij...,jk...,k...', global_directions1, global_tensor1,
global_tensor2, global_directions2) -
np.einsum('i...,ij...,jk...,k...', directions1, tensor1, tensor2,
directions2)), 0)
