def parabolic_solve(self, u_in, b, a = None, u_out = None, update_matrix=True, \
imax=10000, tol=1.0e-8, atol=1.0e-8,
iprint=None, output_stats=False):
"""
Solve for u in the equation
( I + dt div a grad ) u = b
u | boundary = g
u_in, u_out, f anf g are Quantity objects
Dirichlet BC g encoded into u_in boundary_values
Initial guess for iterative scheme is given by
centroid values of u_in
Centroid values of a and b provide diffusivity and rhs
Solution u is retruned in u_out
"""
if u_out is None:
u_out = Quantity(self.domain)
if update_matrix:
self.update_elliptic_matrix(a)
self.update_elliptic_boundary_term(u_in)
self.set_parabolic_solve(True)
# Pull out arrays and a matrix operator
IdtA = self
rhs = b.centroid_values + (self.dt * self.boundary_term)
x0 = u_in.centroid_values
x, stats = conjugate_gradient(IdtA,
rhs,
x0,
imax=imax,
tol=tol,
atol=atol,
iprint=iprint,
output_stats=True)
self.set_parabolic_solve(False)
u_out.set_values(x, location='centroids')
u_out.set_boundary_values(u_in.boundary_values)
if output_stats:
return u_out, stats
else:
return u_out
def parabolic_solve(self, u_in, b, a = None, u_out = None, update_matrix=True, \
imax=10000, tol=1.0e-8, atol=1.0e-8,
iprint=None, output_stats=False):
"""
Solve for u in the equation
( I + dt div a grad ) u = b
u | boundary = g
u_in, u_out, f anf g are Quantity objects
Dirichlet BC g encoded into u_in boundary_values
Initial guess for iterative scheme is given by
centroid values of u_in
Centroid values of a and b provide diffusivity and rhs
Solution u is retruned in u_out
"""
if u_out is None:
u_out = Quantity(self.domain)
if update_matrix :
self.update_elliptic_matrix(a)
self.update_elliptic_boundary_term(u_in)
self.set_parabolic_solve(True)
# Pull out arrays and a matrix operator
IdtA = self
rhs = b.centroid_values + (self.dt * self.boundary_term)
x0 = u_in.centroid_values
x, stats = conjugate_gradient(IdtA,rhs,x0,imax=imax, tol=tol, atol=atol,
iprint=iprint, output_stats=True)
self.set_parabolic_solve(False)
u_out.set_values(x, location='centroids')
u_out.set_boundary_values(u_in.boundary_values)
if output_stats:
return u_out, stats
else:
return u_out
def fit(self,
point_coordinates_or_filename=None,
z=None,
verbose=False,
point_origin=None,
attribute_name=None,
max_read_lines=1e7):
"""Fit a smooth surface to given 1d array of data points z.
The smooth surface is computed at each vertex in the underlying
mesh using the formula given in the module doc string.
Inputs:
point_coordinates_or_filename: The co-ordinates of the data points.
A filename of a .pts file or a
List of coordinate pairs [x, y] of
data points or an nx2 numeric array or a Geospatial_data object
or points file filename
z: Single 1d vector or array of data at the point_coordinates.
"""
if isinstance(point_coordinates_or_filename, basestring):
if point_coordinates_or_filename[-4:] != ".pts":
use_blocking_option2 = False
# NOTE PADARN 29/03/13: File reading from C has been removed. Now
# the input is either a set of points, or a filename which is then
# handled by the Geospatial_data object
if verbose:
print 'Fit.fit: Initializing'
# Use blocking to load in the point info
if isinstance(point_coordinates_or_filename, basestring):
msg = "Don't set a point origin when reading from a file"
assert point_origin is None, msg
filename = point_coordinates_or_filename
G_data = Geospatial_data(filename,
max_read_lines=max_read_lines,
load_file_now=False,
verbose=verbose)
for i, geo_block in enumerate(G_data):
# Build the array
points = geo_block.get_data_points(absolute=True)
z = geo_block.get_attributes(attribute_name=attribute_name)
self._build_matrix_AtA_Atz(points, z, attribute_name, verbose)
point_coordinates = None
if verbose:
print ''
else:
point_coordinates = point_coordinates_or_filename
# This condition either means a filename was read or the function
# recieved a None as input
if point_coordinates is None:
if verbose:
log.critical('Fit.fit: Warning: no data points in fit')
msg = 'No interpolation matrix.'
assert self.AtA is not None, msg
assert self.Atz is not None
else:
point_coordinates = ensure_absolute(point_coordinates,
geo_reference=point_origin)
# if isinstance(point_coordinates,Geospatial_data) and z is None:
# z will come from the geo-ref
self._build_matrix_AtA_Atz(point_coordinates,
z,
verbose=verbose,
output='counter')
# Check sanity
m = self.mesh.number_of_nodes # Nbr of basis functions (1/vertex)
n = self.point_count
if n < m and self.alpha == 0.0:
msg = 'ERROR (least_squares): Too few data points\n'
msg += 'There are only %d data points and alpha == 0. ' % n
msg += 'Need at least %d\n' % m
msg += 'Alternatively, set smoothing parameter alpha to a small '
msg += 'positive value,\ne.g. 1.0e-3.'
raise TooFewPointsError(msg)
self._build_coefficient_matrix_B(verbose)
loners = self.mesh.get_lone_vertices()
# FIXME - make this as error message.
# test with
# Not_yet_test_smooth_att_to_mesh_with_excess_verts.
if len(loners) > 0:
msg = 'WARNING: (least_squares): \nVertices with no triangles\n'
msg += 'All vertices should be part of a triangle.\n'
msg += 'In the future this will be inforced.\n'
msg += 'The following vertices are not part of a triangle;\n'
msg += str(loners)
log.critical(msg)
#raise VertsWithNoTrianglesError(msg)
return conjugate_gradient(self.B,
self.Atz,
self.Atz,
imax=2 * len(self.Atz) + 1000,
use_c_cg=self.use_c_cg,
precon=self.cg_precon)
def fit(self, point_coordinates_or_filename=None, z=None,
verbose=False,
point_origin=None,
attribute_name=None,
max_read_lines=1e7):
"""Fit a smooth surface to given 1d array of data points z.
The smooth surface is computed at each vertex in the underlying
mesh using the formula given in the module doc string.
Inputs:
point_coordinates_or_filename: The co-ordinates of the data points.
A filename of a .pts file or a
List of coordinate pairs [x, y] of
data points or an nx2 numeric array or a Geospatial_data object
or points file filename
z: Single 1d vector or array of data at the point_coordinates.
"""
if isinstance(point_coordinates_or_filename, basestring):
if point_coordinates_or_filename[-4:] != ".pts":
use_blocking_option2 = False
# NOTE PADARN 29/03/13: File reading from C has been removed. Now
# the input is either a set of points, or a filename which is then
# handled by the Geospatial_data object
if verbose:
print 'Fit.fit: Initializing'
# Use blocking to load in the point info
if isinstance(point_coordinates_or_filename, basestring):
msg = "Don't set a point origin when reading from a file"
assert point_origin is None, msg
filename = point_coordinates_or_filename
G_data = Geospatial_data(filename,
max_read_lines=max_read_lines,
load_file_now=False,
verbose=verbose)
for i, geo_block in enumerate(G_data):
# Build the array
points = geo_block.get_data_points(absolute=True)
z = geo_block.get_attributes(attribute_name=attribute_name)
self._build_matrix_AtA_Atz(points, z, attribute_name, verbose)
point_coordinates = None
if verbose:
print ''
else:
point_coordinates = point_coordinates_or_filename
# This condition either means a filename was read or the function
# recieved a None as input
if point_coordinates is None:
if verbose:
log.critical('Fit.fit: Warning: no data points in fit')
msg = 'No interpolation matrix.'
assert self.AtA is not None, msg
assert self.Atz is not None
else:
point_coordinates = ensure_absolute(point_coordinates,
geo_reference=point_origin)
# if isinstance(point_coordinates,Geospatial_data) and z is None:
# z will come from the geo-ref
self._build_matrix_AtA_Atz(point_coordinates, z, verbose=verbose, output='counter')
# Check sanity
m = self.mesh.number_of_nodes # Nbr of basis functions (1/vertex)
n = self.point_count
if n < m and self.alpha == 0.0:
msg = 'ERROR (least_squares): Too few data points\n'
msg += 'There are only %d data points and alpha == 0. ' % n
msg += 'Need at least %d\n' % m
msg += 'Alternatively, set smoothing parameter alpha to a small '
msg += 'positive value,\ne.g. 1.0e-3.'
raise TooFewPointsError(msg)
self._build_coefficient_matrix_B(verbose)
loners = self.mesh.get_lone_vertices()
# FIXME - make this as error message.
# test with
# Not_yet_test_smooth_att_to_mesh_with_excess_verts.
if len(loners) > 0:
msg = 'WARNING: (least_squares): \nVertices with no triangles\n'
msg += 'All vertices should be part of a triangle.\n'
msg += 'In the future this will be inforced.\n'
msg += 'The following vertices are not part of a triangle;\n'
msg += str(loners)
log.critical(msg)
#raise VertsWithNoTrianglesError(msg)
return conjugate_gradient(self.B, self.Atz, self.Atz,
imax=2 * len(self.Atz)+1000, use_c_cg=self.use_c_cg,
precon=self.cg_precon)