def build_sparse_solver(self): if self.sparse_solver == 'scipy_slu': print "Using scipy superlu solver..." luobj = ssl.splu(self.Asel.tocsc()) elif self.sparse_solver == 'PyKLU': print "Using klu solver..." try: import PyKLU.klu as klu luobj = klu.Klu(self.Asel.tocsc()) except StandardError, e: print "Got exception: ", e print "Falling back on scipy superlu solver:" luobj = ssl.splu(self.Asel.tocsc())
def build_sparse_solver(self):
if self.sparse_solver == 'scipy_slu':
print("Using scipy superlu solver...")
luobj = ssl.splu(self.Asel.tocsc())
elif self.sparse_solver == 'PyKLU':
print("Using klu solver...")
try:
import PyKLU.klu as klu
luobj = klu.Klu(self.Asel.tocsc())
except Exception as e:
print("Got exception: ", e)
print("Falling back on scipy superlu solver:")
luobj = ssl.splu(self.Asel.tocsc())
else:
raise ValueError(
'Solver not recognized!!!!\nsparse_solver must be "scipy_slu" or "PyKLU"\n'
)
self.luobj = luobj
def __init__(self,
mesh,
context,
laplacian_stencil=laplacian_3D_7stencil,
symmetrize=True):
'''Assumes that the mesh can accommodate all particles
on its nodes. Dirichlet boundaries will overwrite all boundary
nodes for the charge density rho with 0!
'''
self.symmetrize = symmetrize
self.mesh = mesh
self._context = context
self._cusolver_handle = curf.cusolverRfCreate()
self.mesh_inner = gpuarray.to_gpu(~mesh.boundary_nodes())
lapl_data, lapl_rows, lapl_cols = self.assemble_laplacian(
mesh, laplacian_stencil)
A = sps.coo_matrix((lapl_data, (lapl_rows, lapl_cols)),
shape=(mesh.n_nodes, mesh.n_nodes),
dtype=np.float64).tocsc()
if symmetrize:
"""Remove all trivial equations (rows of the matrix where the
only non-zero element is a 1 on the diagonal. This symmetrizes
the matrix"""
N_full = A.shape[0]
diagonal = A.diagonal()
indices_non_boundary = np.where(diagonal != 1.)[0]
N_sel = len(indices_non_boundary)
Msel = sps.lil_matrix((N_full, N_sel))
for ii, ind in enumerate(indices_non_boundary):
Msel[ind, ii] = 1.
Msel = Msel.tocsc()
A = (Msel.T * A * Msel).tocsc()
self.Msel = Msel
self.MselT = Msel.T
self.lu_obj = klu.Klu(A.tocsc())
def __init__(self, chamb, Dh, sparse_solver = 'scipy_slu', remove_external_nodes_from_mat=True, include_solver = True):
print('Start PIC init.:')
print('Finite Differences, Square Grid')
self.Dh = Dh
if hasattr(chamb, 'x_min') and hasattr(chamb, 'x_max') and hasattr(chamb, 'y_min') and hasattr(chamb, 'y_max'):
super(FiniteDifferences_Staircase_SquareGrid, self).__init__(dx = self.Dh, dy = self.Dh,
x_min = chamb.x_min, x_max = chamb.x_max, y_min = chamb.y_min, y_max = chamb.y_max)
else:
super(FiniteDifferences_Staircase_SquareGrid, self).__init__(chamb.x_aper, chamb.y_aper, self.Dh, self.Dh)
Nyg, Nxg = self.Nyg, self.Nxg
[xn, yn]=np.meshgrid(self.xg,self.yg)
xn=xn.T
xn=xn.flatten()
yn=yn.T
yn=yn.flatten()
#% xn and yn are stored such that the external index is on x
flag_outside_n=chamb.is_outside(xn,yn)
flag_inside_n=~(flag_outside_n)
flag_outside_n_mat=np.reshape(flag_outside_n,(Nyg,Nxg),'F');
flag_outside_n_mat=flag_outside_n_mat.T
[gx,gy]=np.gradient(np.double(flag_outside_n_mat));
gradmod=abs(gx)+abs(gy);
flag_border_mat=np.logical_and((gradmod>0), flag_outside_n_mat);
flag_border_n = flag_border_mat.flatten()
if include_solver:
A=scsp.lil_matrix((Nxg*Nyg,Nxg*Nyg)); #allocate a sparse matrix
list_internal_force_zero = []
# Build A matrix
for u in range(0,Nxg*Nyg):
if np.mod(u, Nxg*Nyg//20)==0:
print(('Mat. assembly %.0f'%(float(u)/ float(Nxg*Nyg)*100)+"""%"""))
if flag_inside_n[u]:
A[u,u] = -(4./(Dh*Dh))
A[u,u-1]=1./(Dh*Dh); #phi(i-1,j)nx
A[u,u+1]=1./(Dh*Dh); #phi(i+1,j)
A[u,u-Nyg]=1./(Dh*Dh); #phi(i,j-1)
A[u,u+Nyg]=1./(Dh*Dh); #phi(i,j+1)
else:
# external nodes
A[u,u]=1.
A=A.tocsr() #convert to csr format
#Remove trivial equtions
if remove_external_nodes_from_mat:
diagonal = A.diagonal()
N_full = len(diagonal)
indices_non_id = np.where(diagonal!=1.)[0]
N_sel = len(indices_non_id)
Msel = scsp.lil_matrix((N_full, N_sel))
for ii, ind in enumerate(indices_non_id):
Msel[ind, ii] =1.
else:
diagonal = A.diagonal()
N_full = len(diagonal)
Msel = scsp.lil_matrix((N_full, N_full))
for ii in range(N_full):
Msel[ii, ii] =1.
Msel = Msel.tocsc()
Asel = Msel.T*A*Msel
Asel=Asel.tocsc()
if sparse_solver == 'scipy_slu':
print("Using scipy superlu solver...")
luobj = ssl.splu(Asel.tocsc())
elif sparse_solver == 'PyKLU':
print("Using klu solver...")
try:
import PyKLU.klu as klu
luobj = klu.Klu(Asel.tocsc())
except Exception as e:
print("Got exception: ", e)
print("Falling back on scipy superlu solver:")
luobj = ssl.splu(Asel.tocsc())
else:
raise ValueError('Solver not recognized!!!!\nsparse_solver must be "scipy_slu" or "PyKLU"\n')
self.xn = xn
self.yn = yn
self.flag_inside_n = flag_inside_n
self.flag_outside_n = flag_outside_n
self.flag_outside_n_mat = flag_outside_n_mat
self.flag_inside_n_mat = np.logical_not(flag_outside_n_mat)
self.flag_border_mat = flag_border_mat
self.Asel = Asel
self.luobj = luobj
self.U_sc_eV_stp=0.;
self.sparse_solver = sparse_solver
self.Msel = Msel.tocsc()
self.Msel_T = (Msel.T).tocsc()
self.flag_border_n = flag_border_n
print('Done PIC init.')
else:
self.solve = self._solve_for_states
self.rho = np.zeros((self.Nxg,self.Nyg));
self.phi = np.zeros((self.Nxg,self.Nyg));
self.efx = np.zeros((self.Nxg,self.Nyg));
self.efy = np.zeros((self.Nxg,self.Nyg));
self.chamb = chamb
def __init__(self,chamb, Dh, sparse_solver = 'scipy_slu'):
print 'Start PIC init.:'
print 'Finite Differences, Square Grid'
super(FiniteDifferences_Staircase_SquareGrid, self).__init__(chamb.x_aper, chamb.y_aper, Dh)
Nyg, Nxg = self.Nyg, self.Nxg
[xn, yn]=np.meshgrid(self.xg,self.yg)
xn=xn.T
xn=xn.flatten()
yn=yn.T
yn=yn.flatten()
#% xn and yn are stored such that the external index is on x
flag_outside_n=chamb.is_outside(xn,yn)
flag_inside_n=~(flag_outside_n)
flag_outside_n_mat=np.reshape(flag_outside_n,(Nyg,Nxg),'F');
flag_outside_n_mat=flag_outside_n_mat.T
[gx,gy]=np.gradient(np.double(flag_outside_n_mat));
gradmod=abs(gx)+abs(gy);
flag_border_mat=np.logical_and((gradmod>0), flag_outside_n_mat);
flag_border_n = flag_border_mat.flatten()
A=scsp.lil_matrix((Nxg*Nyg,Nxg*Nyg)); #allocate a sparse matrix
list_internal_force_zero = []
# Build A matrix
for u in range(0,Nxg*Nyg):
if np.mod(u, Nxg*Nyg/20)==0:
print ('Mat. assembly %.0f'%(float(u)/ float(Nxg*Nyg)*100)+"""%""")
if flag_inside_n[u]:
A[u,u] = -(4./(Dh*Dh))
A[u,u-1]=1./(Dh*Dh); #phi(i-1,j)nx
A[u,u+1]=1./(Dh*Dh); #phi(i+1,j)
A[u,u-Nyg]=1./(Dh*Dh); #phi(i,j-1)
A[u,u+Nyg]=1./(Dh*Dh); #phi(i,j+1)
else:
# external nodes
A[u,u]=1.
A=A.tocsr() #convert to csr format
#Remove trivial equtions
diagonal = A.diagonal()
N_full = len(diagonal)
indices_non_id = np.where(diagonal!=1.)[0]
N_sel = len(indices_non_id)
Msel = scsp.lil_matrix((N_full, N_sel))
for ii, ind in enumerate(indices_non_id):
Msel[ind, ii] =1.
Msel = Msel.tocsc()
Asel = Msel.T*A*Msel
Asel=Asel.tocsc()
if sparse_solver == 'scipy_slu':
print "Using scipy superlu solver..."
luobj = ssl.splu(Asel.tocsc())
elif sparse_solver == 'PyKLU':
print "Using klu solver..."
try:
import PyKLU.klu as klu
luobj = klu.Klu(Asel.tocsc())
except StandardError, e:
print "Got exception: ", e
print "Falling back on scipy superlu solver:"
luobj = ssl.splu(Asel.tocsc())
def __init__(self,
chamb,
Dh,
sparse_solver='scipy_slu',
ext_boundary=False):
# mimics the super() call in the old version
params = compute_new_mesh_properties(chamb.x_aper,
chamb.y_aper,
Dh,
ext_boundary=ext_boundary)
self.Dh, self.xg, self.Nxg, self.bias_x, self.yg, self.Nyg, self.bias_y = params
self.chamb = chamb
[xn, yn] = np.meshgrid(self.xg, self.yg)
xn = xn.T
xn = xn.flatten()
self.xn = xn
yn = yn.T
yn = yn.flatten()
self.yn = yn
#% xn and yn are stored such that the external index is on x
self.flag_outside_n = chamb.is_outside(xn, yn)
self.flag_inside_n = ~(self.flag_outside_n)
flag_outside_n_mat = np.reshape(self.flag_outside_n,
(self.Nyg, self.Nxg), 'F')
flag_outside_n_mat = flag_outside_n_mat.T
[gx, gy] = np.gradient(np.double(flag_outside_n_mat))
gradmod = abs(gx) + abs(gy)
self.flag_border_mat = np.logical_and((gradmod > 0),
flag_outside_n_mat)
self.flag_border_n = self.flag_border_mat.flatten()
A = self.assemble_laplacian()
diagonal = A.diagonal()
N_full = len(diagonal)
indices_non_id = np.where(diagonal != 1.)[0]
N_sel = len(indices_non_id)
Msel = sps.lil_matrix((N_full, N_sel))
for ii, ind in enumerate(indices_non_id):
Msel[ind, ii] = 1.
Msel = Msel.tocsc()
Asel = Msel.T * A * Msel
Asel = Asel.tocsc()
if sparse_solver == 'scipy_slu':
print("Using scipy superlu solver...")
self.luobj = spl.splu(Asel.tocsc())
elif sparse_solver == 'PyKLU':
print("Using klu solver...")
try:
import PyKLU.klu as klu
self.luobj = klu.Klu(Asel.tocsc())
except Exception as e:
print(("Got exception: " + str(e)))
print("Falling back on scipy superlu solver:")
self.luobj = spl.splu(Asel.tocsc())
else:
raise ValueError(
'Solver not recognized!!!!\nsparse_solver must be "scipy_klu" or "PyKLU"\n'
)
self.Msel = Msel.tocsc()
self.Msel_T = (Msel.T).tocsc()
print('Done PIC init.')
def __init__(self, chamb, Dh, sparse_solver='scipy_slu'):
print 'Start PIC init.:'
print 'Finite Differences, Shortley-Weller, Square Grid'
print 'Using Shortley-Weller boundary approx.'
super(FiniteDifferences_ShortleyWeller_SquareGrid,
self).__init__(chamb.x_aper, chamb.y_aper, Dh)
Nyg, Nxg = self.Nyg, self.Nxg
[xn, yn] = np.meshgrid(self.xg, self.yg)
xn = xn.T
xn = xn.flatten()
yn = yn.T
yn = yn.flatten()
#% xn and yn are stored such that the external index is on x
flag_outside_n = chamb.is_outside(xn, yn)
flag_inside_n = ~(flag_outside_n)
#flag_inside_n=(((xn/x_aper)**2 + (yn/y_aper)**2)<1);
#flag_outside_n= ~(flag_inside_n);
flag_outside_n_mat = np.reshape(flag_outside_n, (Nyg, Nxg), 'F')
flag_outside_n_mat = flag_outside_n_mat.T
[gx, gy] = np.gradient(np.double(flag_outside_n_mat))
gradmod = abs(gx) + abs(gy)
flag_border_mat = np.logical_and((gradmod > 0), flag_outside_n_mat)
flag_border_n = flag_border_mat.flatten()
A = scsp.lil_matrix((Nxg * Nyg, Nxg * Nyg))
#allocate a sparse matrix
Dx = scsp.lil_matrix((Nxg * Nyg, Nxg * Nyg))
#allocate a sparse matrix
Dy = scsp.lil_matrix((Nxg * Nyg, Nxg * Nyg))
#allocate a sparse matrix
list_internal_force_zero = []
# Build A Dx Dy matrices
for u in range(0, Nxg * Nyg):
if np.mod(u, Nxg * Nyg / 20) == 0:
print(
'Mat. assembly %.0f' %
(float(u) / float(Nxg * Nyg) * 100) + """%""")
if flag_inside_n[u]:
#Compute Shortley-Weller coefficients
if flag_inside_n[u - 1]: #phi(i-1,j)
hw = Dh
else:
x_int, y_int, z_int, Nx_int, Ny_int, i_found_int = chamb.impact_point_and_normal(
na(xn[u]),
na(yn[u]),
na(0.),
na(xn[u - 1]),
na(yn[u - 1]),
na(0.),
resc_fac=.995,
flag_robust=False)
hw = np.abs(y_int[0] - yn[u])
if flag_inside_n[u + 1]: #phi(i+1,j)
he = Dh
else:
x_int, y_int, z_int, Nx_int, Ny_int, i_found_int = chamb.impact_point_and_normal(
na(xn[u]),
na(yn[u]),
na(0.),
na(xn[u + 1]),
na(yn[u + 1]),
na(0.),
resc_fac=.995,
flag_robust=False)
he = np.abs(y_int[0] - yn[u])
if flag_inside_n[u - Nyg]: #phi(i,j-1)
hs = Dh
else:
x_int, y_int, z_int, Nx_int, Ny_int, i_found_int = chamb.impact_point_and_normal(
na(xn[u]),
na(yn[u]),
na(0.),
na(xn[u - Nyg]),
na(yn[u - Nyg]),
na(0.),
resc_fac=.995,
flag_robust=False)
hs = np.abs(x_int[0] - xn[u])
#~ print hs
if flag_inside_n[u + Nyg]: #phi(i,j+1)
hn = Dh
else:
x_int, y_int, z_int, Nx_int, Ny_int, i_found_int = chamb.impact_point_and_normal(
na(xn[u]),
na(yn[u]),
na(0.),
na(xn[u + Nyg]),
na(yn[u + Nyg]),
na(0.),
resc_fac=.995,
flag_robust=False)
hn = np.abs(x_int[0] - xn[u])
#~ print hn
# Build A matrix
if hn < Dh / 100. or hs < Dh / 100. or hw < Dh / 100. or he < Dh / 100.: # nodes very close to the bounday
A[u, u] = 1.
list_internal_force_zero.append(u)
#print u, xn[u], yn[u]
else:
A[u, u] = -(2. / (he * hw) + 2 / (hs * hn))
A[u, u - 1] = 2. / (hw * (hw + he))
#phi(i-1,j)nx
A[u, u + 1] = 2. / (he * (hw + he))
#phi(i+1,j)
A[u, u - Nyg] = 2. / (hs * (hs + hn))
#phi(i,j-1)
A[u, u + Nyg] = 2. / (hn * (hs + hn))
#phi(i,j+1)
# Build Dx matrix
if hn < Dh / 100.:
if hs >= Dh / 100.:
Dx[u, u] = -1. / hs
Dx[u, u - Nyg] = 1. / hs
elif hs < Dh / 100.:
if hn >= Dh / 100.:
Dx[u, u] = 1. / hn
Dx[u, u + Nyg] = -1. / hn
else:
Dx[u, u] = (1. / (2 * hn) - 1. / (2 * hs))
Dx[u, u - Nyg] = 1. / (2 * hs)
Dx[u, u + Nyg] = -1. / (2 * hn)
# Build Dy matrix
if he < Dh / 100.:
if hw >= Dh / 100.:
Dy[u, u] = -1. / hw
Dy[u, u - 1] = 1. / hw
elif hw < Dh / 100.:
if he >= Dh / 100.:
Dy[u, u] = 1. / he
Dy[u, u + 1] = -1. / (he)
else:
Dy[u, u] = (1. / (2 * he) - 1. / (2 * hw))
Dy[u, u - 1] = 1. / (2 * hw)
Dy[u, u + 1] = -1. / (2 * he)
else:
# external nodes
A[u, u] = 1.
if flag_border_n[u]:
handle_border(u, flag_inside_n, Nxg, Nyg, xn, yn, chamb,
Dh, Dx, Dy)
for u in list_internal_force_zero:
handle_border(u, flag_inside_n, Nxg, Nyg, xn, yn, chamb, Dh, Dx,
Dy)
#~ A = A.tocsc()
#~ Dx = Dx.tocsc()
#~ Dy = Dy.tocsc()
flag_force_zero = flag_outside_n.copy()
for ind in list_internal_force_zero:
flag_force_zero[ind] = True
flag_force_zero_mat = np.reshape(flag_force_zero, (Nyg, Nxg), 'F')
flag_force_zero_mat = flag_force_zero_mat.T
[gxc, gyc] = np.gradient(np.double(flag_force_zero_mat))
gradmodc = abs(gxc) + abs(gyc)
flag_border_mat_c = np.logical_and((gradmodc > 0), flag_force_zero_mat)
sumcurr = np.sum(flag_border_mat_c, axis=0)
jj_max_border = np.max((np.where(sumcurr > 0))[0])
jj_min_border = np.min((np.where(sumcurr > 0))[0])
sumcurr = np.sum(
flag_border_mat_c, axis=1
) # corrected in version 4.05. I it was: sumcurr = np.sum(flag_border_mat_c, axis=1)
ii_max_border = np.max((np.where(sumcurr > 0))[0])
ii_min_border = np.min((np.where(sumcurr > 0))[0])
print 'Internal nodes with 0 potential'
print list_internal_force_zero
A = A.tocsr() #convert to csr format
#Remove trivial equtions
diagonal = A.diagonal()
N_full = len(diagonal)
indices_non_id = np.where(diagonal != 1.)[0]
N_sel = len(indices_non_id)
Msel = scsp.lil_matrix((N_full, N_sel))
for ii, ind in enumerate(indices_non_id):
Msel[ind, ii] = 1.
Msel = Msel.tocsc()
Asel = Msel.T * A * Msel
Asel = Asel.tocsc()
if sparse_solver == 'scipy_slu':
print "Using scipy superlu solver..."
luobj = ssl.splu(Asel.tocsc())
elif sparse_solver == 'PyKLU':
print "Using klu solver..."
try:
import PyKLU.klu as klu
luobj = klu.Klu(Asel.tocsc())
except StandardError, e:
print "Got exception: ", e
print "Falling back on scipy superlu solver:"
luobj = ssl.splu(Asel.tocsc())