def _make_iterator(repeat, n_row, n_col):
ii = 0
for ij, iric in enumerate(cycle((n_row, n_col))):
ir, ic = iric
if ij < len(repeat):
for ik in xrange(repeat[ij]):
yield ii, ir, ic
ii += 1
def make_axes(self):
self.fig.clf()
self.ax = []
n_col = min(5.0, nm.fix(nm.sqrt(self.n_gr)))
if int(n_col) == 0:
n_row = 0
else:
n_row = int(nm.ceil(self.n_gr / n_col))
n_col = int(n_col)
for ii, (ir, ic) in enumerate(cycle((n_col, n_row))):
if ii == self.n_gr: break
self.ax.append(self.fig.add_subplot(n_row, n_col, ii+1))
self.vlines.setdefault(ii, [])
def make_axes(self):
self.fig.clf()
self.ax = []
n_col = min(5.0, nm.fix(nm.sqrt(self.n_gr)))
if int(n_col) == 0:
n_row = 0
else:
n_row = int(nm.ceil(self.n_gr / n_col))
n_col = int(n_col)
for ii, (ir, ic) in enumerate(cycle((n_col, n_row))):
if ii == self.n_gr: break
self.ax.append(self.fig.add_subplot(n_row, n_col, ii + 1))
self.vlines.setdefault(ii, [])
def read_spline_box_hdf5(filename):
if not pt.isHDF5File(filename):
raise ValueError, 'not a HDF5 file! (%s)' % filename
fd = pt.openFile(filename, mode='r')
boxes = fd.listNodes('/box')
n_box = len(boxes)
dim = len(fd.listNodes(boxes[0].ax))
sp_boxes = SplineBoxes(dim=dim,
n_box=n_box,
n_vertex=0,
spbs=OneTypeList(SplineBox))
for box in boxes:
spb = SplineBox()
sp_boxes.spbs.append(spb)
spb.ib = int(box._v_name)
spb.cpi = nm.asarray(box.cpi.read()) - 1
spb.gpi = nm.asarray(box.gpi.read()) - 1
spb.cxyz = nm.asarray(box.cxyz.read()).transpose()
spb.cxyz0 = spb.cxyz.copy()
spb.ax = []
for axi in fd.listNodes(box.ax):
spb.ax.append(nm.asarray(axi.bsc.read()))
sp_boxes.n_vertex = max(sp_boxes.n_vertex, nm.amax(spb.gpi) + 1)
print nm.amin(spb.gpi), nm.amax(spb.gpi)
##
# Fix cpi by rebuilding :).
off = 0
n0, n1, n2 = spb.cpi.shape
aux = nm.arange(n0 * n1).reshape(n1, n0).transpose()
for ii in xrange(n2):
spb.cpi[:, :, ii] = aux + off
off += n0 * n1
fd.close()
for perm in cycle([n_box] * 2):
if perm[0] == perm[1]: continue
gpi1 = sp_boxes.spbs[perm[0]].gpi
gpi2 = sp_boxes.spbs[perm[1]].gpi
assert_(len(nm.intersect1d(gpi1, gpi2)) == 0)
return sp_boxes
def read_spline_box_hdf5( filename ):
if not pt.isHDF5File( filename ):
raise ValueError, 'not a HDF5 file! (%s)' % filename
fd = pt.openFile( filename, mode = 'r' )
boxes = fd.listNodes( '/box' )
n_box = len( boxes )
dim = len( fd.listNodes( boxes[0].ax ) )
sp_boxes = SplineBoxes( dim = dim, n_box = n_box, n_vertex = 0,
spbs = OneTypeList( SplineBox ) )
for box in boxes:
spb = SplineBox()
sp_boxes.spbs.append( spb )
spb.ib = int( box._v_name )
spb.cpi = nm.asarray( box.cpi.read() ) - 1
spb.gpi = nm.asarray( box.gpi.read() ) - 1
spb.cxyz = nm.asarray( box.cxyz.read() ).transpose()
spb.cxyz0 = spb.cxyz.copy()
spb.ax = []
for axi in fd.listNodes( box.ax ):
spb.ax.append( nm.asarray( axi.bsc.read() ) )
sp_boxes.n_vertex = max( sp_boxes.n_vertex, nm.amax( spb.gpi ) + 1 )
print nm.amin( spb.gpi ), nm.amax( spb.gpi )
##
# Fix cpi by rebuilding :).
off = 0
n0, n1, n2 = spb.cpi.shape
aux = nm.arange( n0 * n1 ).reshape( n1, n0 ).transpose()
for ii in xrange( n2 ):
spb.cpi[:,:,ii] = aux + off
off += n0 * n1
fd.close()
for perm in cycle( [n_box] * 2 ):
if perm[0] == perm[1]: continue
gpi1 = sp_boxes.spbs[perm[0]].gpi
gpi2 = sp_boxes.spbs[perm[1]].gpi
assert_( len( nm.intersect1d( gpi1, gpi2 ) ) == 0 )
return sp_boxes
def __call__(self, u=None, v=None, w=None, field=None):
"""
Igakit-like interface for NURBS evaluation.
"""
pars = [u]
if v is not None: pars += [v]
if w is not None: pars += [w]
indices = []
uks = []
rcs = []
for ia, par in enumerate(pars):
uk, indx, rc = self._get_ref_coors_1d(par, ia)
indices.append(indx)
uks.append(uk)
rcs.append(rc)
shape = [len(ii) for ii in pars]
n_vals = nm.prod(shape)
if field is None:
out = nm.zeros((n_vals, self.dim), dtype=nm.float64)
else:
out = nm.zeros((n_vals, field.shape[1]), dtype=nm.float64)
for ip, igrid in enumerate(cycle(shape)):
iis = [indices[ii][igrid[ii]] for ii in xrange(self.dim)]
ie = iga.get_raveled_index(iis, self.n_els)
rc = [rcs[ii][igrid[ii]] for ii in xrange(self.dim)]
bf, bfg, det = iga.eval_nurbs_basis_tp(rc, ie, self.cps,
self.weights, self.degrees,
self.cs, self.conn)
ec = self.conn[ie]
if field is None:
out[ip, :] = nm.dot(bf, self.cps[ec])
else:
out[ip, :] = nm.dot(bf, field[ec])
return out
def main():
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-b', '--basis', metavar='name',
action='store', dest='basis',
default='lagrange', help=help['basis'])
parser.add_option('-d', '--derivative', metavar='d', type=int,
action='store', dest='derivative',
default=0, help=help['derivative'])
parser.add_option('-n', '--max-order', metavar='order', type=int,
action='store', dest='max_order',
default=2, help=help['max_order'])
parser.add_option('-g', '--geometry', metavar='name',
action='store', dest='geometry',
default='2_4', help=help['geometry'])
parser.add_option('-m', '--mesh', metavar='mesh',
action='store', dest='mesh',
default=None, help=help['mesh'])
parser.add_option('', '--permutations', metavar='permutations',
action='store', dest='permutations',
default=None, help=help['permutations'])
parser.add_option('', '--dofs', metavar='dofs',
action='store', dest='dofs',
default=None, help=help['dofs'])
parser.add_option('-l', '--lin-options', metavar='options',
action='store', dest='lin_options',
default='min_level=2,max_level=5,eps=1e-3',
help=help['lin_options'])
parser.add_option('', '--plot-dofs',
action='store_true', dest='plot_dofs',
default=False, help=help['plot_dofs'])
options, args = parser.parse_args()
if len(args) == 1:
output_dir = args[0]
else:
parser.print_help(),
return
output('polynomial space:', options.basis)
output('max. order:', options.max_order)
lin = Struct(kind='adaptive', min_level=2, max_level=5, eps=1e-3)
for opt in options.lin_options.split(','):
key, val = opt.split('=')
setattr(lin, key, eval(val))
if options.mesh is None:
dim, n_ep = int(options.geometry[0]), int(options.geometry[2])
output('reference element geometry:')
output(' dimension: %d, vertices: %d' % (dim, n_ep))
gel = GeometryElement(options.geometry)
gps = PolySpace.any_from_args(None, gel, 1,
base=options.basis)
ps = PolySpace.any_from_args(None, gel, options.max_order,
base=options.basis)
n_digit, _format = get_print_info(ps.n_nod, fill='0')
name_template = os.path.join(output_dir, 'bf_%s.vtk' % _format)
for ip in get_dofs(options.dofs, ps.n_nod):
output('shape function %d...' % ip)
def eval_dofs(iels, rx):
if options.derivative == 0:
bf = ps.eval_base(rx).squeeze()
rvals = bf[None, :, ip:ip+1]
else:
bfg = ps.eval_base(rx, diff=True)
rvals = bfg[None, ..., ip]
return rvals
def eval_coors(iels, rx):
bf = gps.eval_base(rx).squeeze()
coors = nm.dot(bf, gel.coors)[None, ...]
return coors
(level, coors, conn,
vdofs, mat_ids) = create_output(eval_dofs, eval_coors, 1,
ps, min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
out = {
'bf' : Struct(name='output_data',
mode='vertex', data=vdofs,
var_name='bf', dofs=None)
}
mesh = Mesh.from_data('bf_mesh', coors, None, [conn], [mat_ids],
[options.geometry])
name = name_template % ip
ensure_path(name)
mesh.write(name, out=out)
output('...done (%s)' % name)
else:
mesh = Mesh.from_file(options.mesh)
output('mesh geometry:')
output(' dimension: %d, vertices: %d, elements: %d'
% (mesh.dim, mesh.n_nod, mesh.n_el))
if options.permutations:
if options.permutations == 'all':
from sfepy.linalg import cycle
gel = GeometryElement(mesh.descs[0])
n_perms = gel.get_conn_permutations().shape[0]
all_permutations = [ii for ii in cycle(mesh.n_el * [n_perms])]
else:
all_permutations = [int(ii)
for ii in options.permutations.split(',')]
all_permutations = nm.array(all_permutations)
np = len(all_permutations)
all_permutations.shape = (np / mesh.n_el, mesh.n_el)
output('using connectivity permutations:\n', all_permutations)
else:
all_permutations = [None]
for ip, permutations in enumerate(all_permutations):
if permutations is None:
suffix = ''
else:
suffix = '_' + '_'.join('%d' % ii for ii in permutations)
save_basis_on_mesh(mesh, options, output_dir, lin, permutations,
suffix)
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nnfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def gen_block_mesh(dims, shape, centre, name='block'):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
name : string
Mesh name.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
grid = nm.zeros(shape, dtype = nm.int32)
n_nod = nm.prod(shape)
coors = nm.zeros((n_nod, dim), dtype = nm.float64)
bar = MyBar(" nodes:")
bar.init(n_nod)
for ii, ic in enumerate(cycle(shape)):
grid[tuple(ic)] = ii
coors[ii] = x0 + ic * dd
if not (ii % 100):
bar.update(ii)
bar.update(ii + 1)
n_el = nm.prod(shape - 1)
mat_id = nm.zeros((n_el,), dtype = nm.int32)
if (dim == 2):
conn = nm.zeros((n_el, 4), dtype = nm.int32)
bar = MyBar(" elements:")
bar.init(n_el)
for ii, (ix, iy) in enumerate(cycle(shape - 1)):
conn[ii,:] = [grid[ix ,iy], grid[ix+1,iy ],
grid[ix+1,iy+1], grid[ix ,iy+1]]
if not (ii % 100):
bar.update(ii)
bar.update(ii + 1)
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype = nm.int32)
bar = MyBar(" elements:")
bar.init(n_el)
for ii, (ix, iy, iz) in enumerate(cycle(shape - 1)):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
if not (ii % 100):
bar.update(ii)
bar.update(ii + 1)
desc = '3_8'
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def compose_periodic_mesh(mesh_in, scale, repeat, eps, check_mvd=False):
"""
Create a new mesh from a periodic mesh by scaling it and repeating
along each axis,
Parameters
----------
mesh_in : Mesh instance
The input periodic mesh.
scale : float
The scale parameter.
repeat : array
The number of repetitions of `mesh_in` along each axis.
eps : float
Tolerance for finding matching mesh vertices.
check_mvd : bool
If True, verify periodicity by checking approximate minimum
vertex distance and minimum edge length.
Returns
-------
mesh_out : Mesh instance
The composed periodic mesh.
"""
dim = mesh_in.dim
bbox = mesh_in.get_bounding_box()
mscale = bbox[1] - bbox[0]
output('bbox:\n', bbox)
centre0 = 0.5 * (bbox[1] + bbox[0])
output('centre:\n', centre0)
scale = float(scale)
if repeat is None:
repeat = [scale] * dim
repeat = nm.asarray(repeat)
# Normalize original coordinates.
coor0 = (mesh_in.coors - centre0) / (mscale)
aux = fix_double_nodes(coor0, mesh_in.ngroups, mesh_in.conns, eps)
coor0, ngroups0, mesh_in.conns = aux
if check_mvd:
mes0 = get_min_edge_size(coor0, mesh_in.conns)
mvd0 = get_min_vertex_distance(coor0, mes0)
if mes0 > (mvd0 + eps):
output(' original min. "edge" length: %.5e' % mes0)
output('original approx. min. vertex distance: %.5e' % mvd0)
output('-> still double nodes in input mesh!')
output('try increasing eps')
raise ValueError('cannot fix double nodes!')
output('composing periodic mesh...')
for indx in cycle(repeat):
aindx = nm.array(indx, dtype=nm.float64)
centre = 0.5 * (2.0 * aindx - repeat + 1.0)
output(indx, centre)
if aindx.sum() == 0:
coor = coor0 + centre
ngroups = ngroups0
conns = mesh_in.conns
else:
coor1 = coor0 + centre
ngroups1 = ngroups0
conns1 = mesh_in.conns
cmap = find_map(coor, coor1, eps=eps)
if not cmap.size:
raise ValueError('non-periodic mesh!')
else:
output(cmap.size / 2)
coor, ngroups, conns = merge_mesh(coor, ngroups, conns,
coor1, ngroups1, conns1,
cmap, eps=eps)
if check_mvd:
mes = get_min_edge_size( coor, conns )
mvd = get_min_vertex_distance( coor, mes0 )
output(' original min. "edge" length: %.5e' % mes0)
output(' final min. "edge" length: %.5e' % mes)
output('original approx. min. vertex distance: %.5e' % mvd0)
output(' final approx. min. vertex distance: %.5e' % mvd)
if mvd < 0.99999 * mvd0:
if mvd0 < (mes0 - eps):
output('-> probably non-periodic input mesh!')
output(' - adjacent sides were not connected!')
output(' try increasing eps')
else:
output('-> input mesh might be periodic')
output(' try increasing eps')
else:
output('-> input mesh looks periodic')
else:
output('non-periodic input mesh detection skipped!')
# Renormalize.
coor = (coor * mscale) / scale
mesh_out = make_mesh(coor, ngroups, conns, mesh_in)
output('...done')
return mesh_out
def main():
parser = OptionParser(usage=usage, version="%prog 42")
parser.add_option(
"-s", "--scale", type=int, metavar="scale", action="store", dest="scale", default=2, help=help["scale"]
)
parser.add_option(
"-e", "--eps", type=float, metavar="eps", action="store", dest="eps", default=1e-8, help=help["eps"]
)
parser.add_option("-t", "--test", action="store_true", dest="test", default=False, help=help["test"])
parser.add_option("-n", "--no-mvd", action="store_true", dest="nomvd", default=False, help=help["nomvd"])
(options, args) = parser.parse_args()
if options.test:
test()
return
if len(args) == 2:
filename_in = args[0]
filename_out = args[1]
else:
parser.print_help()
return
print "scale:", options.scale
print "eps:", options.eps
mesh_in = Mesh.from_file(filename_in)
bbox = mesh_in.get_bounding_box()
print "bbox:\n", bbox
mscale = bbox[1] - bbox[0]
centre0 = 0.5 * (bbox[1] + bbox[0])
print "centre:\n", centre0
scale = nm.array(options.scale, dtype=nm.float64)
# Normalize original coordinates.
coor0 = (mesh_in.coors - centre0) / (mscale)
dim = mesh_in.dim
aux = fix_double_nodes(coor0, mesh_in.ngroups, mesh_in.conns, options.eps)
coor0, ngroups0, mesh_in.conns = aux
if not options.nomvd:
mes0 = get_min_edge_size(coor0, mesh_in.conns)
mvd0 = get_min_vertex_distance(coor0, mes0)
if mes0 > (mvd0 + options.eps):
print ' original min. "edge" length: %.5e' % mes0
print "original approx. min. vertex distance: %.5e" % mvd0
print "-> still double nodes in input mesh!"
print "try increasing eps..."
raise ValueError
for indx in cycle([options.scale] * dim):
aindx = nm.array(indx, dtype=nm.float64)
centre = 0.5 * (2.0 * aindx - scale + 1.0)
print indx, centre
if aindx.sum() == 0:
coor = coor0 + centre
ngroups = ngroups0
conns = mesh_in.conns
else:
coor1 = coor0 + centre
ngroups1 = ngroups0
conns1 = mesh_in.conns
cmap = find_map(coor, coor1, eps=options.eps)
if not cmap.size:
print "non-periodic mesh!"
# raise ValueError
else:
print cmap.size / 2
coor, ngroups, conns = merge_mesh(coor, ngroups, conns, coor1, ngroups1, conns1, cmap, eps=options.eps)
if not options.nomvd:
mes = get_min_edge_size(coor, conns)
mvd = get_min_vertex_distance(coor, mes0)
print ' original min. "edge" length: %.5e' % mes0
print ' final min. "edge" length: %.5e' % mes
print "original approx. min. vertex distance: %.5e" % mvd0
print " final approx. min. vertex distance: %.5e" % mvd
if mvd < 0.99999 * mvd0:
if mvd0 < (mes0 - options.eps):
print "-> probably non-periodic input mesh!"
print " ... adjacent sides were not connected!"
print " try increasing eps..."
else:
print "-> input mesh might be periodic"
print " try increasing eps..."
else:
print "-> input mesh looks periodic"
else:
print "non-periodic input mesh detection skipped!"
print "renormalizing..."
coor = (coor * mscale) / scale
print "saving..."
mesh_out = make_mesh(coor, ngroups, conns, mesh_in)
mesh_out.write(filename_out, io="auto")
print "done."