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gevp_time.py
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gevp_time.py
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#
# We are interested in how much time GEVP solve takes on relevant 1d meshes
#
from dolfin import Mesh, MeshFunction, UnitSquareMesh, EdgeFunction, CompiledSubDomain
from dolfin import FunctionSpace, TrialFunction, TestFunction, DirichletBC
from dolfin import inner, grad, Constant, dx, assemble_system
from mesh_extraction import interval_mesh_from_edge_f
from scipy.linalg import eigh
from dolfin import Timer
import numpy as np
from lapack_stegr import s3d_eig
from eigw import lump, cpu_type, mem_total
def get_1d_matrices(mesh_, N, root=''):
'''Given mesh construct 1d matrices for GEVP.'''
if not isinstance(N, (int, float)):
assert root
return all([get_1d_matrices(mesh_, n, root) == 0 for n in N])
mesh_dir = '../plate-beam/py/fem_new/meshes'
# Zig zag mesh
if mesh_ == 'nonuniform':
mesh = 'Pb_zig_zag_bif'
mesh2d = '%s/%s_%d.xml.gz' % (mesh_dir, mesh, N)
# mesh1d = '%s/%s_%d_facet_region.xml.gz' % (mesh_dir, mesh, N)
mesh2d = Mesh(mesh2d)
# Constructing facet function can be too expensive so here's and
# alternative
# mesh1d = get_marked_facets(mesh1d)
# Structured meshes
elif mesh_ == 'uniform':
mesh = mesh_
N = int(N)
mesh2d = UnitSquareMesh(N, N)
# mesh1d = EdgeFunction('size_t', mesh2d, 0)
# Beam at y = 0.5
# CompiledSubDomain('near(x[1], 0.5, 1E-10)').mark(mesh1d, 1)
# Use the above here as well
# from dolfin import SubsetIterator
# mesh1d = [e.index() for e in SubsetIterator(mesh1d, 1)]
mesh1d = '%s/%s_%d_edgelist' % (mesh_dir, mesh, N)
mesh1d = map(int, np.loadtxt(mesh1d))
print FunctionSpace(mesh2d, 'CG', 1).dim()
# Extract 1d
import sys; sys.setrecursionlimit(20000);
mesh = interval_mesh_from_edge_f(mesh2d, mesh1d, 1)[0].pop()
# Assemble
V = FunctionSpace(mesh, 'CG', 1)
u = TrialFunction(V)
v = TestFunction(V)
bc = DirichletBC(V, Constant(0), 'on_boundary')
a = inner(grad(u), grad(v))*dx
m = inner(u, v)*dx
L = inner(Constant(0), v)*dx
A, _ = assemble_system(a, L, bc)
M, _ = assemble_system(m, L, bc)
A, M = A.array(), M.array()
if root:
dA = np.diagonal(A, 0)
uA = np.r_[np.diagonal(A, 1), 0]
A = np.c_[dA, uA]
dM = np.diagonal(M, 0)
uM = np.r_[np.diagonal(M, 1), 0]
M = np.c_[dM, uM]
header = 'main and upper diagonals of A, M'
f = '_'.join([mesh_, str(N)])
import os
f = os.path.join(root, f)
np.savetxt(f, np.c_[A, M], header=header)
return 0
else:
return A, M
def read_matrices(mesh, root):
import os
from scipy.sparse import diags
files = os.listdir(root)
files = filter(lambda f: f.startswith(mesh), files)
files = sorted(files, key=lambda v: int(v.split('_')[-1]))
for f in files:
data = np.loadtxt(os.path.join(root, f))
d, u = data[:, 0], data[:-1, 1]
A = diags([u, d, u], [-1, 0, 1]).toarray()
d, u = data[:, 2], data[:-1, 3]
M = diags([u, d, u], [-1, 0, 1]).toarray()
yield A, M
def python_timings(mesh, Nrange, read_matrix=False):
'''Run across meshes solving lumped EVP and recording their sizes and exec time.'''
# We know from julia that this idea(lumping) works.
# So we are only after timing
data = []
if read_matrix:
matrices = read_matrices(mesh, root='./jl_matrices')
else:
matrices = (get_1d_matrices(mesh, N) for N in Nrange)
for A, M in matrices:
row = [A.shape[0]]
M0 = lump(M, -0.5) #
A0 = M0.dot(A.dot(M0)) #
d, u = np.diagonal(A0, 0), np.diagonal(A0, 1) #
t = Timer('EVP')
eigw, eigv = s3d_eig(d, u)
row.append(t.stop())
# Assembling the preconditioner
t = Timer('ASSEMBLE')
H = eigv.dot(np.diag(eigw**-0.5).dot(eigv.T))
row.append(t.stop())
# Action of preconditioner(matrix)
x = np.random.rand(H.shape[1])
t = Timer('ACTION')
y = H*x
row.append(t.stop())
# The original GEVP
t = Timer('GEVP')
eigw, eigv = eigh(A, M)
row.append(t.stop())
print row
data.append(row)
return data
# ----------------------------------------------------------------------------
if __name__ == '__main__':
# Generate uniform matrices for julia
mesh, Ns = 'uniform', [2**i for i in range(2, 12)] + [2**i for i in (11.5, 11.7)]
print get_1d_matrices(mesh, Ns, root='./jl_matrices')
# Generate nonuniform matrices for julia
mesh, Ns = 'nonuniform', range(8)
print get_1d_matrices(mesh, Ns, root='./jl_matrices')
read_matrix = False
if False:
data = python_timings('uniform',
[2**i for i in range(2, 12)] + [2**i for i in (11.5, 11.7)],
read_matrix)
np.savetxt('./data/py_uniform_%d_@%s_%.2f_evp' % (read_matrix, cpu_type(), mem_total()),
data,
header='size, EVP, ASSEMBLE, ACTION, GEVP. Julia has c, C')
if False:
data = python_timings('nonuniform', range(8), read_matrix)
np.savetxt('./data/py_nonuniform_%d_@%s_%.2f_evp' % (read_matrix, cpu_type(), mem_total()),
data,
header='size, EVP, ASSEMBLE, ACTION, GEVP. Julia has c, C')