def my_vis(ml, V, error=None, fname="", E2V=None, Pcols=None):
"""Coarse grid visualization for 2-D problems, for use with Paraview
For all levels, outputs meshes, aggregates, near nullspace modes B, and selected
prolongator basis functions. Coarse level meshes are constructed by doing a
Delaunay triangulation of interpolated fine grid vertices.
Parameters
----------
ml : {multilevel hiearchy}
defines the multilevel hierarchy to visualize
V : {array}
coordinate array (N x D)
Error : {array}
Fine grid error to plot (N x D)
fname : {string}
string to be appended to all output files, e.g. 'diffusion1'
E2V : {array}
Element index array (Nel x Nelnodes) for the finest level. If None,
then a Delaunay triangulation is done for the finest level. All coarse
levels use an internally calculated Delaunay triangulation
P_cols : {list of tuples}
Optional input list of tuples of the form [(lvl, [ints]), ...]
where lvl is an integer defining the level on which to output
the list of columns in [ints].
Returns
-------
- Writes data to .vtk files for use in paraview (xml 0.1 format)
Notes
-----
Examples
--------
"""
system('rm -f *.vtu')
##
# For the purposes of clearer plotting, perturb vertices slightly
V += rand(V.shape[0], V.shape[1])*1e-6
##
# Create a list of vertices and meshes for all levels
levels = ml.levels
Vlist = [V]
if E2V is None:
[circ_cent,edges,E2V,tri_nbs]=delaunay.delaunay(V[:,0], V[:,1])
E2Vlist = [E2V]
mesh_type_list = []
mesh_num_list = []
if E2V.shape[1] == 1:
mesh_type_list.append('vertex')
mesh_num_list.append(1)
if E2V.shape[1] == 3:
mesh_type_list.append('tri')
mesh_num_list.append(5)
if E2V.shape[1] == 4:
if vertices.shape[1] == 2:
mesh_type_list.append('quad')
mesh_num_list.append(9)
if sparse.isspmatrix_bsr(levels[0].A):
nPDEs = levels[0].A.blocksize[0]
else:
nPDEs = 1
Agglist = []
Agg = sparse.eye(levels[0].A.shape[0]/nPDEs, levels[0].A.shape[1]/nPDEs, format='csr')
for i in range(1,len(levels)):
##
# Interpolate the vertices to the next level by taking each
# aggregate's center of gravity (i.e. average x and y value).
Agg = Agg.tocsr()*levels[i-1].AggOp.tocsr()
Agg.data[:] = 1.0
Agglist.append(Agg)
AggX = scale_rows(Agg, Vlist[0][:,0], copy=True)
AggY = scale_rows(Agg, Vlist[0][:,1], copy=True)
AggX = ones((1, AggX.shape[0]))*AggX
AggY = ones((1, AggY.shape[0]))*AggY
Agg = Agg.tocsc()
count = Agg.indptr[1:]-Agg.indptr[:-1]
AggX = (ravel(AggX)/count).reshape(-1,1)
AggY = (ravel(AggY)/count).reshape(-1,1)
Vlist.append(hstack((AggX, AggY)))
[circ_cent,edges,E2Vnew,tri_nbs]=delaunay.delaunay(Vlist[i][:,0], Vlist[i][:,1])
E2Vlist.append(E2Vnew)
mesh_type_list.append('tri')
mesh_num_list.append(5)
##
# On each level, output aggregates, B, the mesh
for i in range(len(levels)):
mesh_num = mesh_num_list[i]
mesh_type = mesh_type_list[i]
vertices = Vlist[i]
elements = E2Vlist[i]
# Print mesh
write_basic_mesh(vertices, elements, mesh_type=mesh_type, \
fname=fname+"mesh_lvl"+str(i)+".vtu")
# Visualize the aggregates
if i != (len(levels)-1):
dg_vis(fname+"aggs_lvl"+str(i), Vlist[0], \
E2Vlist[0], Agglist[i], mesh_type)
# Visualize B
if sparse.isspmatrix_bsr(levels[i].A):
nPDEs = levels[i].A.blocksize[0]
else:
nPDEs = 1
cell_stuff = {mesh_num : elements}
for j in range(nPDEs):
indys = arange(j,levels[i].A.shape[0],nPDEs)
write_vtu(Verts=vertices, Cells=cell_stuff, pdata=levels[i].B[indys,:], \
fname=fname+"B_variable"+str(j)+"_lvl"+str(i)+".vtu")
##
# Output requested prolongator basis functions
if Pcols is not None:
for (lvl,cols) in Pcols:
P = levels[lvl].P.tocsc()
cell_stuff = {mesh_num_list[lvl] : E2Vlist[lvl]}
for i in cols:
Pcol = array(P[:,i].todense())
write_vtu(Verts=Vlist[lvl], Cells=cell_stuff, pdata=Pcol,
fname=fname+"P_lvl"+str(lvl)+"col"+str(i)+".vtu")
##
# Output the error on the finest level
if error is not None:
error = error.reshape(-1,1)
cell_stuff = {mesh_num_list[0] : E2Vlist[0]}
if sparse.isspmatrix_bsr(levels[0].A):
nPDEs = levels[0].A.blocksize[0]
else:
nPDEs = 1
for j in range(nPDEs):
indys = arange(j, levels[0].A.shape[0], nPDEs)
write_vtu(Verts=Vlist[0], Cells=cell_stuff, pdata=error[indys,:], \
fname=fname+"error_variable"+str(j)+".vtu")
def dg_vis(fname, Vert, E2V, Agg, mesh_type, A=None):
"""Coarse grid visualization for 2-D discontinuous Galerkin Problems, for use with Paraview
Parameters
----------
fname : {string}
file to be written, e.g. 'mymesh.vtu'
Vert : {array}
coordinate array (N x D)
E2V : {array}
element index array (Nel x Nelnodes)
Agg : {csr_matrix}
sparse matrix for the aggregate-vertex relationship (N x Nagg)
mesh_type : {string}
type of elements: tri
A : {sparse amtrix}
optional, used for better coloring
Returns
-------
- Writes data to two .vtk files for use in Paraview (xml 0.1 format)
Notes
-----
Examples
--------
"""
#----------------------
if not issubdtype(Vert.dtype,float):
raise ValueError('Vert should be of type float')
if E2V is not None:
if not issubdtype(E2V.dtype,integer):
raise ValueError('E2V should be of type integer')
if Agg.shape[1] > Agg.shape[0]:
raise ValueError('Agg should be of size Npts x Nagg')
valid_mesh_types = ('tri')
if mesh_type not in valid_mesh_types:
raise ValueError('mesh_type should be %s' % ' or '.join(valid_mesh_types))
if A is not None:
if (A.shape[0] != A.shape[1]) or (A.shape[0] != Agg.shape[0]):
raise ValueError('expected square matrix A and compatible with Agg')
#----------------------
N = Vert.shape[0]
Ndof = N
if E2V is not None:
Nel = E2V.shape[0]
Nelnodes = E2V.shape[1]
if E2V.min() != 0:
warnings.warn('element indices begin at %d' % E2V.min() )
Nagg = Agg.shape[0]
Ncolors = 16 # number of colors to use in the coloring algorithm
# ------------------
#Shrink each element in the mesh for nice plotting
#E2V, Vert = shrink_elmts(E2V, Vert)
# plot_type = 'vertex' output to .vtu --- throw point list down on mesh, so E2V becomes Nx1 array
filename = fname + "_point-aggs.vtu"
if False:#A is not None:
# color aggregates with vertex coloring
G = Agg.T * abs(A) * Agg
colors = vertex_coloring(G, method='LDF')
pdata = Agg * colors # extend aggregate colors to vertices
else:
# color aggregates in sequence
Agg = coo_matrix(Agg)
pdata = zeros(Ndof)
colors = array(range(Agg.shape[1])) % Ncolors
pdata[Agg.row] = Agg.col % Ncolors
write_basic_mesh(Vert, E2V=array(range(N)).reshape(N,1), mesh_type='vertex', pdata=pdata, fname=filename)
# plot_type = 'primal', using a global Delaunay triangulation of the shrunken mesh,
# we visualize the aggregates as if the global Delaunay triangulation defined a Continuous Galerkin
# mesh upon which our aggregates are defined.
#circum_cent, edges, tri_pts, tri_nbs = delaunay.delaunay(Vert[:,0], Vert[:,1])
#coarse_grid_vis(filename, Vert, tri_pts, Agg, A=A, plot_type='primal', mesh_type='tri')
filename = fname + "_aggs.vtu"
# Do a local Delaunay triangulation for each aggregate, and throw that down as an element in a new mesh
Agg = csc_matrix(Agg)
E2Vnew = zeros((0,),dtype=int)
colors_new = zeros((0,),dtype=int)
for i in range(Agg.shape[1]):
rowstart = Agg.indptr[i]
rowend = Agg.indptr[i+1]
#The nonzeros in column i of Agg define the dofs in Agg i
members = Agg.indices[rowstart:rowend]
if max(members.shape) > 2:
circum_cent, edges, tri_pts, tri_nbs = delaunay.delaunay(Vert[members,0], Vert[members,1])
#if i == 0:
# E2Vnew = ravel(members[ravel(tri_pts)])
# colors_new = ravel(repeat(colors[i], tri_pts.shape[0]))
#else:
E2Vnew = hstack( (E2Vnew, ravel(members[ravel(tri_pts)]) ) )
colors_new = hstack( (colors_new, ravel(repeat(colors[i], tri_pts.shape[0]))) )
if max(members.shape) == 2:
#create a dummy element, so that only a line is drawn between these two points in Paraview
#if i == 0:
# E2Vnew = array([0,members[0],members[1]])
# colors_new = array([colors[i]])
#else:
E2Vnew = hstack( (E2Vnew, array([0,members[0],members[1]]) ) )
colors_new = hstack( (colors_new, colors[i]) )
#Begin Primal plotting
E2V = E2Vnew.reshape(-1,3)
Agg = csr_matrix(Agg)
if E2V.max() >= Agg.shape[0]:
# remove elements with Dirichlet BCs
E2V = E2V[E2V.max(axis=1) < Agg.shape[0]]
# Find elements with all vertices in same aggregate
if len(Agg.indices) != Agg.shape[0]:
# account for 0 rows. Mark them as solitary aggregates
full_aggs = array(Agg.sum(axis=1),dtype=int).ravel()
full_aggs[full_aggs==1] = Agg.indices
full_aggs[full_aggs==0] = Agg.shape[1] + arange(0,Agg.shape[0]-Agg.nnz,dtype=int).ravel()
ElementAggs = full_aggs[E2V]
else:
ElementAggs = Agg.indices[E2V]
# mask[i] == True if all vertices in element i belong to the same aggregate
mask = (ElementAggs[:,:-1] == ElementAggs[:,1:]).all(axis=1)
E2V3 = E2V[mask,:]
Nel3 = E2V3.shape[0]
# 3 edges = 4 nodes. Find where the difference is 0 (bdy edge)
markedges = diff(c_[ElementAggs,ElementAggs[:,0]])
markedges[mask,:]=1
markedelements, markededges = where(markedges==0)
# now concatenate the edges (i.e. first and next one (mod 3 index)
E2V2 = c_[[E2V[markedelements,markededges],
E2V[markedelements,(markededges+1)%3]]].T
Nel2 = E2V2.shape[0]
colors2 = colors_new[markedelements] #2*ones((1,Nel2)) # color edges with twos
colors3 = colors_new[mask] #3*ones((1,Nel3)) # color triangles with threes
Cells = {3: E2V2, 5: E2V3}
cdata = {3: colors2, 5: colors3}
write_vtu(Verts=Vert, Cells=Cells, pdata=None, cdata=cdata, pvdata=None, fname=filename)
def my_vis(ml, V, error=None, fname="", E2V=None, Pcols=None):
"""Coarse grid visualization for 2-D problems, for use with Paraview
For all levels, outputs meshes, aggregates, near nullspace modes B, and selected
prolongator basis functions. Coarse level meshes are constructed by doing a
Delaunay triangulation of interpolated fine grid vertices.
Parameters
----------
ml : {multilevel hiearchy}
defines the multilevel hierarchy to visualize
V : {array}
coordinate array (N x D)
Error : {array}
Fine grid error to plot (N x D)
fname : {string}
string to be appended to all output files, e.g. 'diffusion1'
E2V : {array}
Element index array (Nel x Nelnodes) for the finest level. If None,
then a Delaunay triangulation is done for the finest level. All coarse
levels use an internally calculated Delaunay triangulation
P_cols : {list of tuples}
Optional input list of tuples of the form [(lvl, [ints]), ...]
where lvl is an integer defining the level on which to output
the list of columns in [ints].
Returns
-------
- Writes data to .vtk files for use in paraview (xml 0.1 format)
Notes
-----
Examples
--------
"""
system('rm -f *.vtu')
##
# For the purposes of clearer plotting, perturb vertices slightly
V += rand(V.shape[0], V.shape[1]) * 1e-6
##
# Create a list of vertices and meshes for all levels
levels = ml.levels
Vlist = [V]
if E2V is None:
[circ_cent, edges, E2V, tri_nbs] = delaunay.delaunay(V[:, 0], V[:, 1])
E2Vlist = [E2V]
mesh_type_list = []
mesh_num_list = []
if E2V.shape[1] == 1:
mesh_type_list.append('vertex')
mesh_num_list.append(1)
if E2V.shape[1] == 3:
mesh_type_list.append('tri')
mesh_num_list.append(5)
if E2V.shape[1] == 4:
if vertices.shape[1] == 2:
mesh_type_list.append('quad')
mesh_num_list.append(9)
if sparse.isspmatrix_bsr(levels[0].A):
nPDEs = levels[0].A.blocksize[0]
else:
nPDEs = 1
Agglist = []
Agg = sparse.eye(levels[0].A.shape[0] / nPDEs,
levels[0].A.shape[1] / nPDEs,
format='csr')
for i in range(1, len(levels)):
##
# Interpolate the vertices to the next level by taking each
# aggregate's center of gravity (i.e. average x and y value).
Agg = Agg.tocsr() * levels[i - 1].AggOp.tocsr()
Agg.data[:] = 1.0
Agglist.append(Agg)
AggX = scale_rows(Agg, Vlist[0][:, 0], copy=True)
AggY = scale_rows(Agg, Vlist[0][:, 1], copy=True)
AggX = ones((1, AggX.shape[0])) * AggX
AggY = ones((1, AggY.shape[0])) * AggY
Agg = Agg.tocsc()
count = Agg.indptr[1:] - Agg.indptr[:-1]
AggX = (ravel(AggX) / count).reshape(-1, 1)
AggY = (ravel(AggY) / count).reshape(-1, 1)
Vlist.append(hstack((AggX, AggY)))
[circ_cent, edges, E2Vnew,
tri_nbs] = delaunay.delaunay(Vlist[i][:, 0], Vlist[i][:, 1])
E2Vlist.append(E2Vnew)
mesh_type_list.append('tri')
mesh_num_list.append(5)
##
# On each level, output aggregates, B, the mesh
for i in range(len(levels)):
mesh_num = mesh_num_list[i]
mesh_type = mesh_type_list[i]
vertices = Vlist[i]
elements = E2Vlist[i]
# Print mesh
write_basic_mesh(vertices, elements, mesh_type=mesh_type, \
fname=fname+"mesh_lvl"+str(i)+".vtu")
# Visualize the aggregates
if i != (len(levels) - 1):
dg_vis(fname+"aggs_lvl"+str(i), Vlist[0], \
E2Vlist[0], Agglist[i], mesh_type)
# Visualize B
if sparse.isspmatrix_bsr(levels[i].A):
nPDEs = levels[i].A.blocksize[0]
else:
nPDEs = 1
cell_stuff = {mesh_num: elements}
for j in range(nPDEs):
indys = arange(j, levels[i].A.shape[0], nPDEs)
write_vtu(Verts=vertices, Cells=cell_stuff, pdata=levels[i].B[indys,:], \
fname=fname+"B_variable"+str(j)+"_lvl"+str(i)+".vtu")
##
# Output requested prolongator basis functions
if Pcols is not None:
for (lvl, cols) in Pcols:
P = levels[lvl].P.tocsc()
cell_stuff = {mesh_num_list[lvl]: E2Vlist[lvl]}
for i in cols:
Pcol = array(P[:, i].todense())
write_vtu(Verts=Vlist[lvl],
Cells=cell_stuff,
pdata=Pcol,
fname=fname + "P_lvl" + str(lvl) + "col" + str(i) +
".vtu")
##
# Output the error on the finest level
if error is not None:
error = error.reshape(-1, 1)
cell_stuff = {mesh_num_list[0]: E2Vlist[0]}
if sparse.isspmatrix_bsr(levels[0].A):
nPDEs = levels[0].A.blocksize[0]
else:
nPDEs = 1
for j in range(nPDEs):
indys = arange(j, levels[0].A.shape[0], nPDEs)
write_vtu(Verts=Vlist[0], Cells=cell_stuff, pdata=error[indys,:], \
fname=fname+"error_variable"+str(j)+".vtu")
def dg_vis(fname, Vert, E2V, Agg, mesh_type, A=None):
"""Coarse grid visualization for 2-D discontinuous Galerkin Problems, for use with Paraview
Parameters
----------
fname : {string}
file to be written, e.g. 'mymesh.vtu'
Vert : {array}
coordinate array (N x D)
E2V : {array}
element index array (Nel x Nelnodes)
Agg : {csr_matrix}
sparse matrix for the aggregate-vertex relationship (N x Nagg)
mesh_type : {string}
type of elements: tri
A : {sparse amtrix}
optional, used for better coloring
Returns
-------
- Writes data to two .vtk files for use in Paraview (xml 0.1 format)
Notes
-----
Examples
--------
"""
#----------------------
if not issubdtype(Vert.dtype, float):
raise ValueError('Vert should be of type float')
if E2V is not None:
if not issubdtype(E2V.dtype, integer):
raise ValueError('E2V should be of type integer')
if Agg.shape[1] > Agg.shape[0]:
raise ValueError('Agg should be of size Npts x Nagg')
valid_mesh_types = ('tri')
if mesh_type not in valid_mesh_types:
raise ValueError('mesh_type should be %s' %
' or '.join(valid_mesh_types))
if A is not None:
if (A.shape[0] != A.shape[1]) or (A.shape[0] != Agg.shape[0]):
raise ValueError(
'expected square matrix A and compatible with Agg')
#----------------------
N = Vert.shape[0]
Ndof = N
if E2V is not None:
Nel = E2V.shape[0]
Nelnodes = E2V.shape[1]
if E2V.min() != 0:
warnings.warn('element indices begin at %d' % E2V.min())
Nagg = Agg.shape[0]
Ncolors = 16 # number of colors to use in the coloring algorithm
# ------------------
#Shrink each element in the mesh for nice plotting
#E2V, Vert = shrink_elmts(E2V, Vert)
# plot_type = 'vertex' output to .vtu --- throw point list down on mesh, so E2V becomes Nx1 array
filename = fname + "_point-aggs.vtu"
if False: #A is not None:
# color aggregates with vertex coloring
G = Agg.T * abs(A) * Agg
colors = vertex_coloring(G, method='LDF')
pdata = Agg * colors # extend aggregate colors to vertices
else:
# color aggregates in sequence
Agg = coo_matrix(Agg)
pdata = zeros(Ndof)
colors = array(range(Agg.shape[1])) % Ncolors
pdata[Agg.row] = Agg.col % Ncolors
write_basic_mesh(Vert,
E2V=array(range(N)).reshape(N, 1),
mesh_type='vertex',
pdata=pdata,
fname=filename)
# plot_type = 'primal', using a global Delaunay triangulation of the shrunken mesh,
# we visualize the aggregates as if the global Delaunay triangulation defined a Continuous Galerkin
# mesh upon which our aggregates are defined.
#circum_cent, edges, tri_pts, tri_nbs = delaunay.delaunay(Vert[:,0], Vert[:,1])
#coarse_grid_vis(filename, Vert, tri_pts, Agg, A=A, plot_type='primal', mesh_type='tri')
filename = fname + "_aggs.vtu"
# Do a local Delaunay triangulation for each aggregate, and throw that down as an element in a new mesh
Agg = csc_matrix(Agg)
E2Vnew = zeros((0, ), dtype=int)
colors_new = zeros((0, ), dtype=int)
for i in range(Agg.shape[1]):
rowstart = Agg.indptr[i]
rowend = Agg.indptr[i + 1]
#The nonzeros in column i of Agg define the dofs in Agg i
members = Agg.indices[rowstart:rowend]
if max(members.shape) > 2:
circum_cent, edges, tri_pts, tri_nbs = delaunay.delaunay(
Vert[members, 0], Vert[members, 1])
#if i == 0:
# E2Vnew = ravel(members[ravel(tri_pts)])
# colors_new = ravel(repeat(colors[i], tri_pts.shape[0]))
#else:
E2Vnew = hstack((E2Vnew, ravel(members[ravel(tri_pts)])))
colors_new = hstack(
(colors_new, ravel(repeat(colors[i], tri_pts.shape[0]))))
if max(members.shape) == 2:
#create a dummy element, so that only a line is drawn between these two points in Paraview
#if i == 0:
# E2Vnew = array([0,members[0],members[1]])
# colors_new = array([colors[i]])
#else:
E2Vnew = hstack((E2Vnew, array([0, members[0], members[1]])))
colors_new = hstack((colors_new, colors[i]))
#Begin Primal plotting
E2V = E2Vnew.reshape(-1, 3)
Agg = csr_matrix(Agg)
if E2V.max() >= Agg.shape[0]:
# remove elements with Dirichlet BCs
E2V = E2V[E2V.max(axis=1) < Agg.shape[0]]
# Find elements with all vertices in same aggregate
if len(Agg.indices) != Agg.shape[0]:
# account for 0 rows. Mark them as solitary aggregates
full_aggs = array(Agg.sum(axis=1), dtype=int).ravel()
full_aggs[full_aggs == 1] = Agg.indices
full_aggs[full_aggs == 0] = Agg.shape[1] + arange(
0, Agg.shape[0] - Agg.nnz, dtype=int).ravel()
ElementAggs = full_aggs[E2V]
else:
ElementAggs = Agg.indices[E2V]
# mask[i] == True if all vertices in element i belong to the same aggregate
mask = (ElementAggs[:, :-1] == ElementAggs[:, 1:]).all(axis=1)
E2V3 = E2V[mask, :]
Nel3 = E2V3.shape[0]
# 3 edges = 4 nodes. Find where the difference is 0 (bdy edge)
markedges = diff(c_[ElementAggs, ElementAggs[:, 0]])
markedges[mask, :] = 1
markedelements, markededges = where(markedges == 0)
# now concatenate the edges (i.e. first and next one (mod 3 index)
E2V2 = c_[[
E2V[markedelements, markededges], E2V[markedelements,
(markededges + 1) % 3]
]].T
Nel2 = E2V2.shape[0]
colors2 = colors_new[
markedelements] #2*ones((1,Nel2)) # color edges with twos
colors3 = colors_new[
mask] #3*ones((1,Nel3)) # color triangles with threes
Cells = {3: E2V2, 5: E2V3}
cdata = {3: colors2, 5: colors3}
write_vtu(Verts=Vert,
Cells=Cells,
pdata=None,
cdata=cdata,
pvdata=None,
fname=filename)
use_proximity = True
if use_proximity:
thresh = step_size
print 'use proximity with thresh = %f' % thresh
DM_ = distm.euclidian(pt1, pt2) # - thresh
# DM_[DM_<0] = 0
unary += DM_ / thresh + np.power(DM_ / thresh, 3.)
print '\ncompute binary costs'
if 'connectivity' not in dir():
connectivity = 'full' #'delaunay', 'full'
if connectivity == 'delaunay':
print '(delaunay connected graph)'
pairs = delaunay.delaunay(pt1[:, 0], pt1[:, 1])[1]
elif connectivity == 'smallworld':
prop = 1
print '(small world connected graph with %d pc random edges added)' % prop
pairs = delaunay.delaunay(pt1[:, 0], pt1[:, 1])[1]
nadded = int(combination(nnodes1, 2, exact=1) * prop / 100. + 0.5)
newpairs = np.random.randint(0, nnodes1, size=(nadded, 2))
newpairs = newpairs[newpairs[:, 0] != newpairs[:, 1]]
pairs = np.r_[pairs, newpairs]
else:
print '(fully connected graph)'
pairs = np.argwhere(np.triu(np.ones((nnodes1, nnodes1)), k=1))
DM1 = distm.euclidian(pt1)
use_proximity = True
if use_proximity:
thresh = step_size
print 'use proximity with thresh = %f' %thresh
DM_ = distm.euclidian(pt1,pt2)# - thresh
# DM_[DM_<0] = 0
unary += DM_/thresh + np.power(DM_/thresh,3.)
print '\ncompute binary costs'
if 'connectivity' not in dir():
connectivity = 'full' #'delaunay', 'full'
if connectivity=='delaunay':
print '(delaunay connected graph)'
pairs = delaunay.delaunay(pt1[:,0],pt1[:,1])[1]
elif connectivity=='smallworld':
prop = 1
print '(small world connected graph with %d pc random edges added)' %prop
pairs = delaunay.delaunay(pt1[:,0],pt1[:,1])[1]
nadded = int(combination(nnodes1,2,exact=1)*prop/100. + 0.5)
newpairs = np.random.randint(0,nnodes1,size=(nadded,2))
newpairs = newpairs[newpairs[:,0]!=newpairs[:,1]]
pairs = np.r_[pairs,newpairs]
else:
print '(fully connected graph)'
pairs = np.argwhere(np.triu(np.ones((nnodes1,nnodes1)),k=1))
DM1 = distm.euclidian(pt1)