def GetGridInfo(self): w_nodes = self.center[0] + grid_tools.cyclic_nodes(-self.size[0]/2,self.size[0]/2,self.pts[0]) x_nodes = grid_tools.cell_centers(-self.size[1]/2,self.size[1]/2,self.pts[1]) y_nodes = grid_tools.cell_centers(-self.size[2]/2,self.size[2]/2,self.pts[2]) w_walls = grid_tools.cell_walls(w_nodes[0],w_nodes[-1],self.pts[0],self.default_band) x_walls = grid_tools.cell_walls(x_nodes[0],x_nodes[-1],self.pts[1]) y_walls = grid_tools.cell_walls(y_nodes[0],y_nodes[-1],self.pts[2]) plot_ext = np.array([w_walls[0],w_walls[-1],x_walls[0],x_walls[-1],y_walls[0],y_walls[-1]]) return w_nodes,x_nodes,y_nodes,plot_ext
def GetGridInfo(self): w_nodes = self.center[0] + grid_tools.cyclic_nodes(-self.size[0]/2,self.size[0]/2,self.pts[0]) rho_nodes = grid_tools.cell_centers(0.0,self.size[1]/2,self.pts[1]) phi_nodes = grid_tools.cyclic_nodes(-np.pi,np.pi,self.pts[2]) w_walls = grid_tools.cell_walls(w_nodes[0],w_nodes[-1],self.pts[0],self.default_band) rho_walls = grid_tools.cell_walls(rho_nodes[0],rho_nodes[-1],self.pts[1]) phi_walls = grid_tools.cell_walls(phi_nodes[0],phi_nodes[-1],self.pts[2]) plot_ext = np.array([w_walls[0],w_walls[-1],rho_walls[0],rho_walls[-1],phi_walls[0],phi_walls[-1]]) return w_nodes,rho_nodes,phi_nodes,plot_ext
def track(cl, xp, eikonal, vg, vol_dict):
'''Propagate unidirectional fully dispersive waves using eikonal data as a boundary condition.
The volume must be oriented so the polarization axis is x (linear polarization only).
:param numpy.array xp: ray phase space with shape (bundles,rays,8)
:param numpy.array eikonal: ray eikonal data with shape (bundles,4)
:param numpy.array vg: ray group velocity with shape (bundles,rays,4)
:param dictionary vol_dict: input file dictionary for the volume'''
band = vol_dict['frequency band']
size = (band[1] - band[0], ) + vol_dict['size']
N = vol_dict['wave grid']
# N[3] is the number of diagnostic planes, including the initial plane
diagnostic_steps = N[3] - 1
subcycles = vol_dict['subcycles']
steps = diagnostic_steps * subcycles
field_planes = steps + 1
powersof2 = [2**i for i in range(32)]
if N[0] - 1 not in powersof2:
raise ValueError('UPPE propagator requires 2**n+1 w-nodes')
if N[1] not in powersof2:
raise ValueError('UPPE propagator requires 2**n x-nodes')
if N[2] not in powersof2:
raise ValueError('UPPE propagator requires 2**n y-nodes')
try:
window_speed = vol_dict['window speed']
except:
window_speed = 1.0
try:
chi3 = vol_dict['chi3']
except:
chi3 = 0.0
# Capture the rays
if vol_dict['wave coordinates'] == 'cartesian':
field_tool = caustic_tools.FourierTool(N, band, (0, 0, 0), size[1:],
cl)
else:
field_tool = caustic_tools.BesselBeamTool(N, band, (0, 0, 0), size[1:],
cl)
w_nodes, x1_nodes, x2_nodes, plot_ext = field_tool.GetGridInfo()
A = np.zeros(N).astype(np.complex)
J = np.zeros(N).astype(np.complex)
ne = np.zeros(N).astype(np.complex)
A0, dom3d = field_tool.GetBoundaryFields(xp[:, 0, :], eikonal, 1)
# Setup the wave propagation domain
chi = vol_dict['dispersion inside'].chi(w_nodes)
try:
ionizer = vol_dict['ionizer']
except KeyError:
ionizer = ionization.Ionization(1.0, 1.0, 1.0, 1.0)
dens_nodes = grid_tools.cell_centers(-size[3] / 2, size[3] / 2, steps)
field_walls = grid_tools.cell_walls(dens_nodes[0], dens_nodes[-1], steps)
diagnostic_walls = np.linspace(-size[3] / 2, size[3] / 2, N[3])
dz = field_walls[1] - field_walls[0]
Dz = diagnostic_walls[1] - diagnostic_walls[0]
dom4d = np.concatenate((dom3d, [field_walls[0], field_walls[-1]]))
# Step through the domain
# Strategy to get density plane is to re-use ray gather system
# This works as long as the shape of xp is (*,*,8)
xp_eff = np.zeros((N[1], N[2], 8))
if vol_dict['wave coordinates'] == 'cartesian':
xp_eff[..., 1] = np.outer(x1_nodes, np.ones(N[2]))
xp_eff[..., 2] = np.outer(np.ones(N[1]), x2_nodes)
else:
xp_eff[..., 1] = np.outer(x1_nodes, np.cos(x2_nodes))
xp_eff[..., 2] = np.outer(x1_nodes, np.sin(x2_nodes))
A[..., 0] = A0
J[..., 0] = 0.0
ne[..., 0] = 0.0
for k in range(diagnostic_steps):
print('Advancing to diagnostic plane', k + 1)
rhs_evals = 0
for s in range(subcycles):
if subcycles > 1:
if s == 0:
print(' subcycling .', end='', flush=True)
else:
print('.', end='', flush=True)
xp_eff[..., 3] = dens_nodes[k * subcycles + s]
dens = vol_dict['object'].GetDensity(xp_eff)
A0, J0, ne0, evals = propagator(cl, field_tool, window_speed, A0,
chi, chi3, dens, ionizer, dz)
A0[:4, ...] = 0.0
rhs_evals += evals
print('', rhs_evals, 'evaluations of j(w,kx,ky)')
A[..., k + 1] = A0
J[..., k + 1] = J0
ne[..., k + 1] = ne0
# Finish by relaunching rays and returning UPPE data
field_tool.RelaunchRays(xp, eikonal, vg, A[..., -1], size[3])
return A, J, ne, dom4d
def track(xp, eikonal, vg, vol_dict):
'''Propagate unidirectional fully dispersive waves using eikonal data as a boundary condition.
The volume must be oriented so the polarization axis is x (linear polarization only).
:param numpy.array xp: ray phase space with shape (bundles,rays,8)
:param numpy.array eikonal: ray eikonal data with shape (bundles,4)
:param numpy.array vg: ray group velocity with shape (bundles,rays,4)
:param dictionary vol_dict: input file dictionary for the volume'''
band = vol_dict['frequency band']
size = (band[1] - band[0], ) + vol_dict['size']
N = vol_dict['wave grid']
# N[3] is the number of diagnostic planes, including the initial plane
diagnostic_steps = N[3] - 1
subcycles = vol_dict['subcycles']
steps = diagnostic_steps * subcycles
field_planes = steps + 1
Vol = vol_dict['object']
try:
window_speed = vol_dict['window speed']
except:
window_speed = 1.0
try:
chi3 = vol_dict['chi3']
except:
chi3 = 0.0
# Capture the rays
if vol_dict['wave coordinates'] == 'cartesian':
field_tool = caustic_tools.FourierTool(N, band, (0, 0, 0), size[1:],
Vol.queue, Vol.transform_k)
else:
field_tool = caustic_tools.BesselBeamTool(N, band, (0, 0, 0), size[1:],
Vol.queue, Vol.transform_k)
w_nodes, x1_nodes, x2_nodes, plot_ext = field_tool.GetGridInfo()
A = np.zeros(N).astype(np.complex)
J = np.zeros(N).astype(np.complex)
ne = np.zeros(N).astype(np.complex)
A0, dom3d = field_tool.GetBoundaryFields(xp[:, 0, :], eikonal, 1)
# Setup the wave propagation domain
chi = vol_dict['dispersion inside'].chi(w_nodes)
try:
ionizer = vol_dict['ionizer']
except KeyError:
ionizer = ionization.Ionization(1.0, 1.0, 1.0, 1.0)
dens_nodes = grid_tools.cell_centers(-size[3] / 2, size[3] / 2, steps)
field_walls = grid_tools.cell_walls(dens_nodes[0], dens_nodes[-1], steps)
diagnostic_walls = np.linspace(-size[3] / 2, size[3] / 2, N[3])
dz = field_walls[1] - field_walls[0]
Dz = diagnostic_walls[1] - diagnostic_walls[0]
dom4d = np.concatenate((dom3d, [field_walls[0], field_walls[-1]]))
# Step through the domain
# Strategy to get density plane is to re-use ray gather system
# This works as long as the shape of xp is (*,*,8)
xp_eff = np.zeros((N[1], N[2], 8))
if vol_dict['wave coordinates'] == 'cartesian':
xp_eff[..., 1] = np.outer(x1_nodes, np.ones(N[2]))
xp_eff[..., 2] = np.outer(np.ones(N[1]), x2_nodes)
else:
xp_eff[..., 1] = np.outer(x1_nodes, np.cos(x2_nodes))
xp_eff[..., 2] = np.outer(x1_nodes, np.sin(x2_nodes))
A[..., 0] = A0
J[..., 0] = 0.0
ne[..., 0] = 0.0
for k in range(diagnostic_steps):
print('Advancing to diagnostic plane', k + 1)
for s in range(subcycles):
xp_eff[..., 3] = dens_nodes[k * subcycles + s]
dens = vol_dict['object'].GetDensity(xp_eff)
A0, J0, ne0 = propagator(field_tool, window_speed, A0, chi, chi3,
dens, ionizer, dz)
try:
A0 *= vol_dict['damping filter'](w_nodes)[:, np.newaxis,
np.newaxis]
except KeyError:
A0 = A0
A[..., k + 1] = A0
J[..., k + 1] = J0
ne[..., k + 1] = ne0
# Return the wave amplitude
# Rays are re-launched externally
return A, J, ne, dom4d
def track(cl, xp, eikonal, vg, vol_dict):
'''Propagate unidirectional fully dispersive waves using eikonal data as a boundary condition.
The volume must be oriented so the polarization axis is x (linear polarization only).
:param numpy.array xp: ray phase space with shape (bundles,rays,8)
:param numpy.array eikonal: ray eikonal data with shape (bundles,4)
:param numpy.array vg: ray group velocity with shape (bundles,rays,4)
:param dictionary vol_dict: input file dictionary for the volume'''
band = vol_dict['frequency band']
NL_band = vol_dict['nonlinear band']
size = (band[1] - band[0], ) + vol_dict['size']
N = vol_dict['wave grid']
# N[3] is the number of diagnostic planes, including the initial plane
diagnostic_steps = N[3] - 1
subcycles = vol_dict['subcycles']
steps = diagnostic_steps * subcycles
field_planes = steps + 1
powersof2 = [2**i for i in range(32)]
if N[0] - 1 not in powersof2:
raise ValueError('UPPE propagator requires 2**n+1 w-nodes')
if N[1] not in powersof2:
raise ValueError('UPPE propagator requires 2**n x-nodes')
if N[2] not in powersof2:
raise ValueError('UPPE propagator requires 2**n y-nodes')
try:
window_speed = vol_dict['window speed']
except KeyError:
window_speed = 1.0
try:
chi3 = vol_dict['chi3']
except KeyError:
chi3 = 0.0
try:
full_relaunch = vol_dict['full relaunch']
except KeyError:
full_relaunch = False
# Capture the rays
if vol_dict['wave coordinates'] == 'cartesian':
field_tool = caustic_tools.FourierTool(N, band, (0, 0, 0), size[1:],
cl)
else:
field_tool = caustic_tools.BesselBeamTool(N, band, (0, 0, 0), size[1:],
cl, vol_dict['radial modes'])
warnings.warn(
'Polarization information is lost upon entering paraxial region.')
w_nodes, x1_nodes, x2_nodes, plot_ext = field_tool.GetGridInfo()
A = np.zeros(N).astype(np.complex)
J = np.zeros(N).astype(np.complex)
ne = np.zeros(N).astype(np.complex)
A[..., 0], dom3d = field_tool.GetBoundaryFields(xp[:, 0, :], eikonal, 1)
# Setup the wave propagation medium
chi = vol_dict['dispersion inside'].chi(w_nodes).astype(np.complex)
try:
ionizer = ionization.Ionizer(vol_dict['ionizer'])
except KeyError:
ionizer = None
mat = Material(cl.q, field_tool, N, vol_dict['wave coordinates'],
vol_dict['object'], chi, chi3,
vol_dict['density reference'], window_speed)
# Setup the wave propagation domain
dens_nodes = grid_tools.cell_centers(-size[3] / 2, size[3] / 2, steps)
field_walls = grid_tools.cell_walls(dens_nodes[0], dens_nodes[-1], steps)
diagnostic_walls = np.linspace(-size[3] / 2, size[3] / 2, N[3])
dzmin = vol_dict['minimum step']
Dz = diagnostic_walls[1] - diagnostic_walls[0]
dom4d = np.concatenate((dom3d, [field_walls[0], field_walls[-1]]))
# Step through the domain
A0 = np.copy(A[..., 0])
for k in range(diagnostic_steps):
zi = diagnostic_walls[k]
zf = diagnostic_walls[k + 1]
print('Advancing to diagnostic plane', k + 1)
A0, J0, ne0, evals = propagator(cl, field_tool, window_speed, A0, mat,
ionizer, NL_band, subcycles, zi, zf,
dzmin)
print('', evals, 'evaluations of j(w,kx,ky)')
A[..., k + 1] = A0
J[..., k + 1] = J0
ne[..., k + 1] = ne0
# Finish by relaunching rays and returning UPPE data
if full_relaunch:
field_tool.RelaunchRays1(xp, eikonal, vg, A[..., -1], size[3],
vol_dict['dispersion inside'])
else:
field_tool.RelaunchRays(xp, eikonal, vg, A[..., -1], size[3],
vol_dict['dispersion inside'])
return A, J, ne, dom4d
def test_normal(self):
nodes = grid_tools.cell_centers(0.0, 5.0, 5)
assert np.allclose(nodes, [0.5, 1.5, 2.5, 3.5, 4.5])
walls = grid_tools.cell_walls(0.5, 4.5, 5)
assert np.allclose(walls, [0.0, 1.0, 2.0, 3.0, 4.0, 5.0])
def track(cl, xp, eikonal, vg, vol_dict):
'''Propagate paraxial waves using eikonal data as a boundary condition.
The volume must be oriented so the polarization axis is x (linear polarization only).
:param numpy.array xp: ray phase space with shape (bundles,rays,8)
:param numpy.array eikonal: ray eikonal data with shape (bundles,4)
:param numpy.array vg: ray group velocity with shape (bundles,rays,4)
:param dictionary vol_dict: input file dictionary for the volume'''
band = vol_dict['frequency band']
size = (band[1] - band[0], ) + vol_dict['size']
N = vol_dict['wave grid']
# N[3] is the number of diagnostic planes, including the initial plane
diagnostic_steps = N[3] - 1
subcycles = vol_dict['subcycles']
steps = diagnostic_steps * subcycles
field_planes = steps + 1
Vol = vol_dict['object']
powersof2 = [2**i for i in range(32)]
if N[0] not in powersof2:
raise ValueError('Paraxial propagator requires 2**n w-nodes')
if N[1] not in powersof2:
raise ValueError('Paraxial propagator requires 2**n x-nodes')
if N[2] not in powersof2:
raise ValueError('Paraxial propagator requires 2**n y-nodes')
try:
window_speed = vol_dict['window speed']
except:
window_speed = 1.0
try:
chi3 = vol_dict['chi3']
except:
chi3 = 0.0
# Capture the rays
if vol_dict['wave coordinates'] == 'cartesian':
field_tool = caustic_tools.FourierTool(N, band, (0, 0, 0), size[1:],
cl)
else:
field_tool = caustic_tools.BesselBeamTool(N, band, (0, 0, 0), size[1:],
cl)
w_nodes, x1_nodes, x2_nodes, plot_ext = field_tool.GetGridInfo()
A = np.zeros(N).astype(np.complex)
A0, dom3d = field_tool.GetBoundaryFields(xp[:, 0, :], eikonal, 1)
n0 = np.mean(
np.sqrt(np.einsum('...i,...i', xp[:, 0, 5:8], xp[:, 0, 5:8])) /
xp[:, 0, 4])
ng = 1.0 / np.mean(
np.sqrt(np.einsum('...i,...i', vg[:, 0, 1:4], vg[:, 0, 1:4])))
# Setup the wave propagation domain
chi = vol_dict['dispersion inside'].chi(w_nodes)
dens_nodes = grid_tools.cell_centers(-size[3] / 2, size[3] / 2, steps)
field_walls = grid_tools.cell_walls(dens_nodes[0], dens_nodes[-1], steps)
diagnostic_walls = np.linspace(-size[3] / 2, size[3] / 2, N[3])
dz = field_walls[1] - field_walls[0]
Dz = diagnostic_walls[1] - diagnostic_walls[0]
dom4d = np.concatenate((dom3d, [field_walls[0], field_walls[-1]]))
# Step through the domain
# Strategy to get density plane is to re-use ray gather system
# This works as long as the shape of xp is (*,*,8)
xp_eff = np.zeros((N[1], N[2], 8))
if vol_dict['wave coordinates'] == 'cartesian':
xp_eff[..., 1] = np.outer(x1_nodes, np.ones(N[2]))
xp_eff[..., 2] = np.outer(np.ones(N[1]), x2_nodes)
else:
xp_eff[..., 1] = np.outer(x1_nodes, np.cos(x2_nodes))
xp_eff[..., 2] = np.outer(x1_nodes, np.sin(x2_nodes))
A[..., 0] = A0
for k in range(diagnostic_steps):
print('Advancing to diagnostic plane', k + 1)
for s in range(subcycles):
xp_eff[..., 3] = dens_nodes[k * subcycles + s]
dens = vol_dict['object'].GetDensity(xp_eff)
A0 = propagator(field_tool, A0, chi, dens, n0, ng, dz, True)
try:
A0 *= vol_dict['damping filter'](w_nodes)[:, np.newaxis,
np.newaxis]
except KeyError:
A0 = A0
A[..., k + 1] = A0
# Finish by relaunching rays and returning wave data
field_tool.RelaunchRays(xp, eikonal, vg, A[..., -1], size[3])
return A, dom4d