def simulate(mesh, res, scheme, verbose=False, **kwargs):
"""Forward calculation vor given mesh, data and resistivity."""
fop = ERTModelling(verbose=verbose)
# fop = ERTManager.createFOP(verbose=verbose)
fop.setData(scheme)
fop.setMesh(mesh, ignoreRegionManager=True)
if not scheme.allNonZero('k'):
if min(pg.y(scheme)) != max(pg.y(scheme)) or min(pg.z(scheme)) != max(pg.z(scheme)):
pg.info("Non flat earth topography found. "
"We will set geometric factors to -1 to emulate "
"electrical impedance tomography (EIT). If you want to "
"use ERT will full topography support. "
"Please consider the use of pyBERT.")
scheme.set('k', pg.RVector(scheme.size(), -1))
else:
scheme.set('k', fop.calcGeometricFactors(scheme))
rhoa = None
isArrayData = None
if hasattr(res[0], '__iter__'):
isArrayData = True
rhoa = np.zeros((len(res), scheme.size()))
for i, r in enumerate(res):
rhoa[i] = fop.response(r)
else:
rhoa = fop.response(res)
pg.renameKwarg('noisify', 'noiseLevel', kwargs)
noiseLevel = kwargs.pop('noiseLevel', 0.0)
if noiseLevel > 0:
noiseAbs = kwargs.pop('noiseAbs', 1e-4)
err = noiseLevel + noiseAbs / rhoa
scheme.set('err', err)
if verbose:
pg.info("Set noise (" + str(noiseLevel*100) + "% + " + str(noiseAbs) + " V) min:",
min(err), "max:", max(err))
rhoa *= 1. + pg.randn(scheme.size()) * err
if isArrayData is None:
scheme.set('rhoa', rhoa)
if kwargs.pop('returnArray', False):
return rhoa
return scheme
def create_mesh_and_data(n):
nc = np.linspace(-2.0, 0.0, n)
mesh = pg.createMesh2D(nc, nc)
mcx = pg.x(mesh.cellCenter())
mcy = pg.y(mesh.cellCenter())
data = np.cos(1.5 * mcx) * np.sin(1.5 * mcy)
return mesh, data
def checkData(self):
"""Check data
w.r.t. shot/geophone identity and zero/negative
traveltimes, plus check y/z sensor positions
"""
oldsize = self.dataContainer.size()
self.dataContainer.markInvalid(pg.abs(self.dataContainer('s') -
self.dataContainer('g')) < 1)
self.dataContainer.markInvalid(self.dataContainer('t') <= 0.)
self.dataContainer.removeInvalid()
newsize = self.dataContainer.size()
if newsize < oldsize:
if self.verbose:
print('Removed ' + str(oldsize - newsize) + ' values.')
maxyabs = max(pg.abs(pg.y(self.dataContainer.sensorPositions())))
maxzabs = max(pg.abs(pg.z(self.dataContainer.sensorPositions())))
if maxzabs > 0 and maxyabs == 0:
for i in range(self.dataContainer.sensorCount()):
pos = self.dataContainer.sensorPosition(i).rotateX(-pi / 2)
self.dataContainer.setSensorPosition(i, pos)
if self.verbose:
print(self.dataContainer)
def cellDataToCellGrad(mesh, v, CtB):
if len(v) != mesh.cellCount():
print(len(v), mesh.cellCount())
raise
div = mesh.boundaryDataToCellGradient(CtB * v)
return np.vstack([pg.x(div), pg.y(div), pg.z(div)]).T
vF = cellDataToBoundaryData(mesh, v)
gC = np.zeros((mesh.cellCount(), 3))
for b in mesh.boundaries():
leftCell = b.leftCell()
rightCell = b.rightCell()
vec = b.norm() * vF[b.id()] * b.size()
if leftCell:
gC[leftCell.id(), 0] += vec[0]
gC[leftCell.id(), 1] += vec[1]
gC[leftCell.id(), 2] += vec[2]
if rightCell:
gC[rightCell.id(), 0] -= vec[0]
gC[rightCell.id(), 1] -= vec[1]
gC[rightCell.id(), 2] -= vec[2]
gC[:, 0] /= mesh.cellSizes()
gC[:, 1] /= mesh.cellSizes()
gC[:, 2] /= mesh.cellSizes()
return gC
def cellDataToBoundaryGrad(mesh, v, vGrad):
"""
"""
if len(v) != mesh.cellCount() or len(vGrad) != mesh.cellCount():
raise
gB = mesh.cellDataToBoundaryGradient(v, vGrad)
return np.vstack([pg.x(gB), pg.y(gB), pg.z(gB)]).T
gB = np.zeros((mesh.boundaryCount(), 3))
for b in mesh.boundaries():
leftCell = b.leftCell()
rightCell = b.rightCell()
gr = pg.RVector3(0.0, 0.0, 0.0)
t = (b.node(1).pos() - b.node(0).pos()).norm()
if leftCell and rightCell:
df1 = b.center().distance(leftCell.center())
df2 = b.center().distance(rightCell.center())
gr = b.norm() * \
(v[rightCell.id()] - v[leftCell.id()]) / (df1 + df2)
grL = t * t.dot(vGrad[leftCell.id()])
grR = t * t.dot(vGrad[rightCell.id()])
gr += (grL + grR) * 0.5
elif leftCell:
gr = t * t.dot(vGrad[leftCell.id()])
gB[b.id(), 0] = gr[0]
gB[b.id(), 1] = gr[1]
gB[b.id(), 2] = gr[2]
return gB
def showVAold(self, vals=None, ax=None, usepos=True, name='va'):
"""show apparent velocity as image plot (old style)"""
va = self.getVA(t=vals)
data = self.dataContainer
A = np.ones((data.sensorCount(), data.sensorCount())) * np.nan
for i in range(data.size()):
A[int(data('s')[i]), int(data('g')[i])] = va[i]
if ax is None:
fig, ax = plt.subplots()
self.figs[name] = fig
gci = ax.imshow(A, interpolation='nearest')
ax.grid(True)
if usepos:
xt = np.linspace(0, data.sensorCount()-1, 7)
xt.round()
px = pg.abs(pg.y(self.dataContainer.sensorPositions()))
ax.set_xticks(xt)
ax.set_xticklabels([str(int(px[int(xti)])) for xti in xt])
ax.set_yticks(xt)
ax.set_yticklabels([str(int(px[int(xti)])) for xti in xt])
plt.colorbar(gci, ax=ax)
return va
def transform2DMeshTo3D(mesh, x, y, z=None):
"""
Transform a 2D mesh into 3D coordinates using a point list (e.g. from GPS)
Parameters
----------
mesh: GIMLi::Mesh
x,y: array of x/y positions along 2d profile
z: optional height to add (topographical correction if computed flat earth)
See Also
--------
References
----------
"""
# get mesh node positions
mt, mz = pg.x( mesh.positions() ), pg.y( mesh.positions() ) # mesh tape and z
# compute length of reference points along tape
pt = np.hstack( (0., np.cumsum( np.sqrt( np.diff( x )**2 + np.diff( y )**2 ) ) ) )
# interpolate node positions from tape to x/y using tape positions
mx = np.interp( mt, pt, x )
my = np.interp( mt, pt, y )
# compute z offset by interpolating z
if z is None:
oz = np.zeros( len(mt) )
else:
oz = np.interp( mt, pt, z )
# set the positions in the mesh
for i, node in enumerate( mesh.nodes() ):
node.setPos( pg.RVector3( mx[i], my[i], mz[i]+oz[i] ) )
def createCoarsePoly( coarseData ):
boundary = 1250.0
mesh = g.Mesh()
x = g.x( coarseData )
y = g.y( coarseData )
z = g.z( coarseData )
xMin = min( x ); xMax = max( x )
yMin = min( y ); yMax = max( y )
zMin = min( z ); zMax = max( z )
print(xMin, xMax, yMin, yMax)
border = max( (xMax - xMin) * boundary / 100.0, (yMax - yMin) * boundary / 100.0);
n1 = mesh.createNode( xMin - border, yMin - border, zMin, 1 )
n2 = mesh.createNode( xMax + border, yMin - border, zMin, 2 )
n3 = mesh.createNode( xMax + border, yMax + border, zMin, 3 )
n4 = mesh.createNode( xMin - border, yMax + border, zMin, 4 )
mesh.createEdge( n1, n2, 12 );
mesh.createEdge( n2, n3, 23 );
mesh.createEdge( n3, n4, 34 );
mesh.createEdge( n4, n1, 41 );
for p in coarseData:
mesh.createNode( p )
return mesh
def cellDataToBoundaryGrad(mesh, v, vGrad):
"""TODO Documentme."""
if len(v) != mesh.cellCount() or len(vGrad) != mesh.cellCount():
raise BaseException("len(v) dismatch mesh.cellCount()")
gB = mesh.cellDataToBoundaryGradient(v, vGrad)
return np.vstack([pg.x(gB), pg.y(gB), pg.z(gB)]).T
def cellDataToCellGrad(mesh, v, CtB):
"""TODO Documentme."""
if len(v) != mesh.cellCount():
print(len(v), mesh.cellCount())
raise BaseException("len of v missmatch mesh.cellCount()")
div = mesh.boundaryDataToCellGradient(CtB * v)
return np.vstack([pg.x(div), pg.y(div), pg.z(div)]).T
def showVA(self, t=None, ax=None, usepos=True, name='va', squeeze=True):
"""show apparent velocity as image plot"""
# va = self.getVA(vals=vals)
xvec = self.dataContainer('g')
yvec = self.dataContainer('s')
if usepos:
pz = pg.y(self.dataContainer.sensorPositions())
if squeeze:
xvec = pz[xvec]
yvec = pz[yvec]
else:
pz = pg.y(self.dataContainer.sensorPositions())
raise Exception('Implement ME')
# xvec = px[xvec]*1000 + pz[xvec]
# xvec = px[yvec]*1000 + pz[yvec]
plotVecMatrix(xvec, yvec, vals=t, squeeze=squeeze, ax=ax, name=name)
def ani(i):
axGra.clear()
axGra.plot(pg.x(gravPoints), dz[i])
axGra.plot(pg.x(gravPoints), pg.y(gravPoints), 'v', color='black')
axGra.set_ylabel('Grav in mGal')
axGra.set_xlim((-20, 20))
axGra.set_ylim((0, 0.001))
axGra.grid()
pg.mplviewer.setMappableData(gciDDe, abs(dDens[i]),
cMin=0, cMax=20,
logScale=False)
def createGradientModel2D(data, mesh, VTop, VBot):
"""
Create 2D velocity gradient model.
Creates a smooth, linear, starting model that takes the slope
of the topography into account. This is done by fitting a straight line
and using the distance to that as the depth value.
Known as "The Marcus method"
Parameters
----------
data : pygimli DataContainer
The topography list is in here.
mesh : pygimli.Mesh
The parametric mesh used for the inversion
VTop : float
The velocity at the surface of the mesh
VBot : float
The velocity at the bottom of the mesh
Returns
-------
model : pygimli Vector, length M
A numpy array with slowness values that can be used to start
the inversion.
"""
p = np.polyfit(pg.x(data.sensorPositions()), pg.y(data.sensorPositions()),
deg=1) # slope-intercept form
n = np.asarray([-p[0], 1.0]) # normal vector
nLen = np.sqrt(np.dot(n, n))
x = pg.x(mesh.cellCenters())
z = pg.y(mesh.cellCenters())
pos = np.column_stack((x, z))
d = np.array([np.abs(np.dot(pos[i, :], n) - p[1]) / nLen
for i in range(pos.shape[0])])
return np.interp(d, [min(d), max(d)], [1.0 / VTop, 1.0 / VBot])
def createGradientModel2D(data, mesh, vTop, vBot):
"""Create 2D velocity gradient model.
Creates a smooth, linear, starting model that takes the slope
of the topography into account. This is done by fitting a straight line
and using the distance to that as the depth value.
Known as "The Marcus method"
Parameters
----------
data : pygimli DataContainer
The topography list is in here.
mesh : pygimli.Mesh
The parametric mesh used for the inversion
vTop : float
The velocity at the surface of the mesh
vBot : float
The velocity at the bottom of the mesh
Returns
-------
model : pygimli Vector, length M
A numpy array with slowness values that can be used to start
the inversion.
"""
p = np.polyfit(pg.x(data.sensorPositions()), pg.y(data.sensorPositions()),
deg=1) # slope-intercept form
n = np.asarray([-p[0], 1.0]) # normal vector
nLen = np.sqrt(np.dot(n, n))
x = pg.x(mesh.cellCenters())
z = pg.y(mesh.cellCenters())
pos = np.column_stack((x, z))
d = np.array([np.abs(np.dot(pos[i, :], n) - p[1]) / nLen
for i in range(pos.shape[0])])
return 1. / np.interp(d, [min(d), max(d)], [vTop, vBot])
def ani(i):
axGra.clear()
axGra.plot(pg.x(gravPoints), dz[i])
axGra.plot(pg.x(gravPoints), pg.y(gravPoints), 'v', color='black')
axGra.set_ylabel('Grav in mGal')
axGra.set_xlim((-20, 20))
axGra.set_ylim((0, 0.001))
axGra.grid()
pg.mplviewer.setMappableData(gciDDe,
abs(dDens[i]),
cMin=0,
cMax=20,
logScale=False)
def createTriangles(mesh, data=None):
"""
What is this?
"""
x = pg.x(mesh.positions())
# x.round(1e-1)
y = pg.y(mesh.positions())
# y.round(1e-1)
triCount = 0
for c in mesh.cells():
if c.shape().nodeCount() == 4:
triCount = triCount + 2
else:
triCount = triCount + 1
triangles = np.zeros((triCount, 3))
dataIdx = list(range(triCount))
triCount = 0
for c in mesh.cells():
if c.shape().nodeCount() == 4:
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(1).id()
triangles[triCount, 2] = c.node(2).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(2).id()
triangles[triCount, 2] = c.node(3).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
else:
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(1).id()
triangles[triCount, 2] = c.node(2).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
z = None
if data is not None:
if len(data) == mesh.cellCount():
# strange behavior if we just use these slice
z = np.array(data[dataIdx])
else:
z = np.array(data)
return x, y, triangles, z, dataIdx
def cellDataToBoundaryData(mesh, vec):
"""
DOCUMENT_ME
"""
if len(data) != mesh.cellCount():
raise BaseException("Dimension mismatch, expecting cellCount(): "
+ str(mesh.cellCount())
+ "got: " + str(len(vec)), str(len(vec[0])))
CtB = mesh.cellToBoundaryInterpolation()
if type(vec) == pg.R3Vector():
return np.array([CtB*pg.x(vec), CtB*pg.y(vec), CtB*pg.z(vec)]).T
else:
return CtB*vec
def calcGeometricFactor(self, data):
"""Calculate geometry factors for a given dataset."""
if pg.y(data.sensorPositions()) == pg.z(data.sensorPositions()):
k = np.zeros(data.size())
for i in range(data.size()):
a = data.sensorPosition(data('a')[i])
b = data.sensorPosition(data('b')[i])
m = data.sensorPosition(data('m')[i])
n = data.sensorPosition(data('n')[i])
k[i] = 1. / (2. * np.pi) * (1. / a.dist(m) - 1. / a.dist(n) -
1. / b.dist(m) + 1. / b.dist(n))
return k
else:
raise BaseException("Please use BERT for non-standard "
"data sets" + str(data))
def cellDataToBoundaryData(mesh, data):
""" TODO DOCUMENT_ME """
if len(data) != mesh.cellCount():
raise BaseException(
"Dimension mismatch, expecting cellCount(): " +
str(mesh.cellCount()) + "got: " + str(len(data)),
str(len(data[0])))
CtB = mesh.cellToBoundaryInterpolation()
if isinstance(data, pg.R3Vector()):
return np.array([CtB * pg.x(data), CtB * pg.y(data),
CtB * pg.z(data)]).T
else:
return CtB * data
def cellDataToBoundaryData(mesh, data):
""" TODO DOCUMENT_ME """
if len(data) != mesh.cellCount():
raise BaseException("Dimension mismatch, expecting cellCount(): " +
str(mesh.cellCount()) +
"got: " + str(len(data)), str(len(data[0])))
CtB = mesh.cellToBoundaryInterpolation()
if isinstance(data, pg.R3Vector()):
return np.array([CtB * pg.x(data),
CtB * pg.y(data),
CtB * pg.z(data)]).T
else:
return CtB * data
def createTriangles(mesh, data=None):
"""TODO Documentme."""
x = pg.x(mesh.positions())
# x.round(1e-1)
y = pg.y(mesh.positions())
# y.round(1e-1)
triCount = 0
for c in mesh.cells():
if c.shape().nodeCount() == 4:
triCount = triCount + 2
else:
triCount = triCount + 1
triangles = np.zeros((triCount, 3))
dataIdx = list(range(triCount))
triCount = 0
for c in mesh.cells():
if c.shape().nodeCount() == 4:
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(1).id()
triangles[triCount, 2] = c.node(2).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(2).id()
triangles[triCount, 2] = c.node(3).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
else:
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(1).id()
triangles[triCount, 2] = c.node(2).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
z = None
if data is not None:
if len(data) == mesh.cellCount():
# strange behavior if we just use these slice
z = np.array(data[dataIdx])
else:
z = np.array(data)
return x, y, triangles, z, dataIdx
def calcGeometricFactors(self, data):
"""Calculate geometry factors for a given dataset."""
if pg.y(data) == pg.z(data):
k = np.zeros(data.size())
for i in range(data.size()):
a = data.sensorPosition(data('a')[i])
b = data.sensorPosition(data('b')[i])
m = data.sensorPosition(data('m')[i])
n = data.sensorPosition(data('n')[i])
k[i] = 2.*np.pi * 1./(1./a.dist(m) - 1./a.dist(n) -
1./b.dist(m) + 1./b.dist(n))
return k
else:
raise BaseException("Please use BERT for non-standard "
"data sets" + str(data))
def exportHDF5Mesh(mesh,
exportname,
group='mesh',
indices='cell_indices',
pos='coordinates',
cells='topology',
marker='values'):
"""Writes given :gimliapi:`GIMLI::Mesh` in a hdf5 format file.
3D tetrahedron meshes only! Boundary markers are ignored.
Keywords are explained in :py:mod:`pygimli.meshtools.readHDFS`
"""
h5py = pg.optImport('h5py', requiredFor='export mesh in .h5 data format')
if not isinstance(mesh, pg.Mesh):
mesh = pg.Mesh(mesh)
# prepare output for writing in hdf data container
pg_pos = mesh.positions()
mesh_pos = np.array((np.array(pg.x(pg_pos)), np.array(pg.y(pg_pos)),
np.array(pg.z(pg_pos)))).T
mesh_cells = np.zeros((mesh.cellCount(), 4)) # hard coded for tetrahedrons
for i, cell in enumerate(mesh.cells()):
mesh_cells[i] = cell.ids()
mesh_indices = np.arange(0, mesh.cellCount() + 1, 1, dtype=np.int64)
mesh_markers = np.array(mesh.cellMarkers())
with h5py.File(exportname, 'w') as out:
for grp in np.atleast_1d(group): # can use more than one group
# writing indices
idx_name = '{}/{}'.format(grp, indices)
out.create_dataset(idx_name, data=mesh_indices, dtype=int)
# writing node positions
pos_name = '{}/{}'.format(grp, pos)
out.create_dataset(pos_name, data=mesh_pos, dtype=float)
# writing cells via indices
cells_name = '{}/{}'.format(grp, cells)
out.create_dataset(cells_name, data=mesh_cells, dtype=int)
# writing marker
marker_name = '{}/{}'.format(grp, marker)
out.create_dataset(marker_name, data=mesh_markers, dtype=int)
out[grp][cells].attrs['celltype'] = np.string_('tetrahedron')
out[grp][cells].attrs.create('partition', [0])
return True
def solveDarcy(mesh, k=None, p0=1, verbose=False):
"""Darcy flow."""
if verbose:
print("Solve Darcy equation ...")
uDir = [[2, p0], # left aquiver
[3, p0], # left bedrock
# [4, 0], # bottom (paper)
[5, 0], # right bedrock
[6, 0], # right aquiver
[7, 0], # right top
]
p = pg.solver.solve(mesh, a=k, bc={'Dirichlet': uDir}, verbose=True)
vel = -pg.solver.grad(mesh, p) * np.asarray([k, k, k]).T
mvel = mt.cellDataToNodeData(mesh, vel)
return mesh, mvel, p, k, np.asarray([pg.x(vel), pg.y(vel)])
def createFinePoly( coarseMesh, ePos ):
paraBoundary = 10
mesh = g.Mesh()
n1 = None; n2 = None; n3 = None; n4 = None
for n in coarseMesh.nodes():
if n.marker() == 1:
n1 = mesh.createNode( n.pos(), 1 )
elif n.marker() == 2:
n2 = mesh.createNode( n.pos(), 2 )
elif n.marker() == 3:
n3 = mesh.createNode( n.pos(), 3 )
elif n.marker() == 4:
n4 = mesh.createNode( n.pos(), 4 )
mesh.createEdge( n1, n2, 12 );
mesh.createEdge( n2, n3, 23 );
mesh.createEdge( n3, n4, 34 );
mesh.createEdge( n4, n1, 41 );
x = g.x( ePos )
y = g.y( ePos )
z = g.z( ePos )
xMin = min( x ); xMax = max( x )
yMin = min( y ); yMax = max( y )
zMin = min( z ); zMax = max( z )
maxSpan = max( xMax - xMin, yMax - yMin );
borderPara = maxSpan * paraBoundary / 100.0;
n5 = mesh.createNode( xMin - borderPara, yMin - borderPara , 0.0, 5 );
n6 = mesh.createNode( xMax + borderPara, yMin - borderPara , 0.0, 6 );
n7 = mesh.createNode( xMax + borderPara, yMax + borderPara , 0.0, 7 );
n8 = mesh.createNode( xMin - borderPara, yMax + borderPara , 0.0, 8 );
mesh.createEdge( n5, n6, 56 );
mesh.createEdge( n6, n7, 67 );
mesh.createEdge( n7, n8, 78 );
mesh.createEdge( n8, n5, 85 );
for p in ePos:
mesh.createNode( p )
return mesh;
def exportHDF5Mesh(mesh,
exportname,
group='mesh',
indices='cell_indices',
pos='coordinates',
cells='topology',
marker='values'):
'''
3D tetrahedron meshes only! Boundary markers are ignored.
Keywords are explained in "readH5"
'''
h5py = pg.io.opt_import('h5py',
requiredTo='export mesh in .h5 data format')
if not isinstance(mesh, pg.Mesh):
mesh = pg.Mesh(mesh)
# prepare output for writing in hdf data container
pg_pos = mesh.positions()
mesh_pos = np.array((np.array(pg.x(pg_pos)), np.array(pg.y(pg_pos)),
np.array(pg.z(pg_pos)))).T
mesh_cells = np.zeros((mesh.cellCount(), 4)) # hard coded for tetrahedrons
for i, cell in enumerate(mesh.cells()):
mesh_cells[i] = cell.ids()
mesh_indices = np.arange(0, mesh.cellCount() + 1, 1, dtype=np.int64)
mesh_markers = np.array(mesh.cellMarkers())
with h5py.File(exportname, 'w') as out:
# writing indices
idx_name = '{}/{}'.format(group, indices)
out.create_dataset(idx_name, data=mesh_indices, dtype=np.int64)
# writing node positions
pos_name = '{}/{}'.format(group, pos)
out.create_dataset(pos_name, data=mesh_pos, dtype=float)
# writing cells via indices
cells_name = '{}/{}'.format(group, cells)
out.create_dataset(cells_name, data=mesh_cells, dtype=np.int64)
# writing marker
marker_name = '{}/{}'.format(group, marker)
out.create_dataset(marker_name, data=mesh_markers, dtype=np.uint64)
out[group][cells].attrs['celltype'] = np.array(('tetrahedron'))
out[group][cells].attrs['partition'] = np.array([0], dtype=np.uint64)
return True
def rst_cov(mesh, cov):
""" Simplify refraction coverage with convex hull. """
points_all = np.column_stack((
pg.x(mesh.cellCenters()),
pg.y(mesh.cellCenters()),
))
points = points_all[np.nonzero(cov)[0]]
hull = ConvexHull(points)
hull_path = Path(points[hull.vertices])
covs = []
for cell in mesh.cells():
if hull_path.contains_point(points_all[cell.id()]):
covs.append(1)
else:
covs.append(0)
return np.array(covs)
def checkData(self):
""" check data w.r.t. shot/geophone identity and zero/negative
traveltimes, plus check y/z sensor positions """
oldsize = self.data.size()
self.data.markInvalid(pg.abs(self.data("s") - self.data("g")) < 1)
self.data.markInvalid(self.data("t") <= 0.0)
self.data.removeInvalid()
newsize = self.data.size()
if newsize < oldsize:
print("Removed " + str(oldsize - newsize) + " values.")
maxyabs = max(pg.abs(pg.y(self.data.sensorPositions())))
maxzabs = max(pg.abs(pg.z(self.data.sensorPositions())))
if maxzabs > 0 and maxyabs == 0:
for i in range(self.data.sensorCount()):
pos = self.data.sensorPosition(i).rotateX(-pi / 2)
self.data.setSensorPosition(i, pos)
print(self.data)
def solveDarcy(mesh, k=None, p0=1, verbose=False):
"""Darcy flow."""
if verbose:
print("Solve Darcy equation ...")
uDir = [
[2, p0], # left aquiver
[3, p0], # left bedrock
# [4, 0], # bottom (paper)
[5, 0], # right bedrock
[6, 0], # right aquiver
[7, 0], # right top
]
p = pg.solver.solve(mesh, a=k, uB=uDir)
vel = -pg.solver.grad(mesh, p) * np.asarray([k, k, k]).T
mvel = mt.cellDataToNodeData(mesh, vel)
return mesh, mvel, p, k, np.asarray([pg.x(vel), pg.y(vel)])
def drawRayPaths(self, ax, model=None, **kwargs):
"""Draw the the ray paths for model or last model.
If model is not specifies, the last calculated Jacobian is used.
Parameters
----------
model : array
Velocity model for which to calculate and visualize ray paths (the
default is model for last Jacobian calculation in self.velocity).
ax : matplotlib.axes object
To draw the model and the path into.
**kwargs : type
Additional arguments passed to LineCollection (alpha, linewidths,
color, linestyles).
Returns
-------
lc : matplotlib.LineCollection
"""
if model is not None:
if self.fop.jacobian().size() == 0 or model != self.model:
self.fop.createJacobian(1/model)
else:
model = self.model
_ = kwargs.setdefault("color", "w")
_ = kwargs.setdefault("alpha", 0.5)
_ = kwargs.setdefault("linewidths", 0.8)
shots = self.fop.data.id("s")
recei = self.fop.data.id("g")
segs = []
for s, g in zip(shots, recei):
wi = self.fop.way(s, g)
points = self.fop._core.mesh().positions(withSecNodes=True)[wi]
segs.append(np.column_stack((pg.x(points), pg.y(points))))
lc = LineCollection(segs, **kwargs)
ax.add_collection(lc)
return lc
def exportHDF5Mesh(mesh, exportname, group='mesh', indices='cell_indices',
pos='coordinates', cells='topology', marker='values'):
"""Writes given :gimliapi:`GIMLI::Mesh` in a hdf5 format file.
3D tetrahedron meshes only! Boundary markers are ignored.
Keywords are explained in :py:mod:`pygimli.meshtools.readHDFS`
"""
h5py = pg.optImport('h5py',
requiredFor='export mesh in .h5 data format')
if not isinstance(mesh, pg.Mesh):
mesh = pg.Mesh(mesh)
# prepare output for writing in hdf data container
pg_pos = mesh.positions()
mesh_pos = np.array((np.array(pg.x(pg_pos)), np.array(pg.y(pg_pos)),
np.array(pg.z(pg_pos)))).T
mesh_cells = np.zeros((mesh.cellCount(), 4)) # hard coded for tetrahedrons
for i, cell in enumerate(mesh.cells()):
mesh_cells[i] = cell.ids()
mesh_indices = np.arange(0, mesh.cellCount() + 1, 1, dtype=np.int64)
mesh_markers = np.array(mesh.cellMarkers())
with h5py.File(exportname, 'w') as out:
for grp in np.atleast_1d(group): # can use more than one group
# writing indices
idx_name = '{}/{}'.format(grp, indices)
out.create_dataset(idx_name, data=mesh_indices, dtype=int)
# writing node positions
pos_name = '{}/{}'.format(grp, pos)
out.create_dataset(pos_name, data=mesh_pos, dtype=float)
# writing cells via indices
cells_name = '{}/{}'.format(grp, cells)
out.create_dataset(cells_name, data=mesh_cells, dtype=int)
# writing marker
marker_name = '{}/{}'.format(grp, marker)
out.create_dataset(marker_name, data=mesh_markers, dtype=int)
out[grp][cells].attrs['celltype'] = np.string_('tetrahedron')
out[grp][cells].attrs.create('partition', [0])
return True
def createMesh(self, quality=34.6, maxarea=0.1, addpoints=None):
"""Create (inversion) mesh by circumventing PLC"""
data = self.dataContainer
sx = list(pg.x(data.sensorPositions()))
sz = list(pg.y(data.sensorPositions()))
if addpoints is not None:
for po in addpoints:
sx.append(po[0])
sz.append(po[1])
iS = np.argsort(np.arctan2(sx-np.mean(sx), sz-np.mean(sz)))
plc = pg.Mesh(2)
nodes = [plc.createNode(sx[i], sz[i], 0) for i in iS]
for i in range(len(nodes)-1):
plc.createEdge(nodes[i], nodes[i+1])
plc.createEdge(nodes[-1], nodes[0])
tri = pg.TriangleWrapper(plc)
tri.setSwitches("-pzFq"+str(quality)+"a"+str(maxarea))
self.setMesh(tri.generate())
def createMesh(self, quality=34.6, maxarea=0.1, addpoints=None):
"""Create (inversion) mesh by circumventing PLC"""
data = self.dataContainer
sx = list(pg.x(data.sensorPositions()))
sz = list(pg.y(data.sensorPositions()))
if addpoints is not None:
for po in addpoints:
sx.append(po[0])
sz.append(po[1])
iS = np.argsort(np.arctan2(sx - np.mean(sx), sz - np.mean(sz)))
plc = pg.Mesh(2)
nodes = [plc.createNode(sx[i], sz[i], 0) for i in iS]
for i in range(len(nodes) - 1):
plc.createEdge(nodes[i], nodes[i + 1])
plc.createEdge(nodes[-1], nodes[0])
tri = pg.TriangleWrapper(plc)
tri.setSwitches("-pzFq" + str(quality) + "a" + str(maxarea))
self.setMesh(tri.generate())
def showVA(self, data=None, t=None, name='va', pseudosection=False,
squeeze=True, full=True, ax=None, cmap=None, **kwargs):
"""Show apparent velocity as image plot.
TODO showXXX commands need to return ax and cbar .. if there is one
"""
if data is None:
data = self.dataContainer
if ax is None:
fig, ax = plt.subplots()
self.figs[name] = fig
self.axs[name] = ax
if t is None:
t = data('t')
px = pg.x(data.sensorPositions())
py = pg.y(data.sensorPositions())
if len(np.unique(py)) > len(np.unique(px)): # probably crosshole
px = py
gx = np.array([px[int(g)] for g in data("g")])
sx = np.array([px[int(s)] for s in data("s")])
offset = self.getOffset(data=data, full=full)
kwargs.setdefault('vals', offset / t)
if pseudosection:
midpoint = (gx + sx) / 2
_, cb = showVecMatrix(midpoint, offset, squeeze=True, ax=ax,
label='Apparent slowness [s/m]', cmap=cmap,
**kwargs)
else:
_, cb = showVecMatrix(gx, sx, squeeze=squeeze, ax=ax,
label='Apparent velocity [m/s]', cmap=cmap,
**kwargs)
ax.figure.show()
return ax, cb
def transform2DMeshTo3D(mesh, x, y, z=None):
"""2D mesh into 3D coordinates.
Transform a 2D mesh into 3D coordinates using a point list (e.g. from GPS)
Parameters
----------
mesh: :gimliapi:`GIMLI::Mesh`
x,y: [float]
array of x/y positions along 2d profile
z: [float]
optional height to add (topographical correction on top of flat earth)
See Also
--------
References
----------
"""
# get mesh node positions
mt, mz = pg.x(mesh.positions()), pg.y(mesh.positions()) # mesh tape and z
# compute length of reference points along tape
pt = np.hstack((0., np.cumsum(np.sqrt(np.diff(x)**2 + np.diff(y)**2))))
# interpolate node positions from tape to x/y using tape positions
mx = np.interp(mt, pt, x)
my = np.interp(mt, pt, y)
# compute z offset by interpolating z
if z is None:
oz = np.zeros(len(mt))
else:
oz = np.interp(mt, pt, z)
# set the positions in the mesh
for i, node in enumerate(mesh.nodes()):
node.setPos(pg.RVector3(mx[i], my[i], mz[i] + oz[i]))
def checkData(self):
"""check data w.r.t. shot/geophone identity and zero/negative
traveltimes, plus check y/z sensor positions """
oldsize = self.dataContainer.size()
self.dataContainer.markInvalid(
pg.abs(self.dataContainer('s') - self.dataContainer('g')) < 1)
self.dataContainer.markInvalid(self.dataContainer('t') <= 0.)
self.dataContainer.removeInvalid()
newsize = self.dataContainer.size()
if newsize < oldsize:
if self.verbose:
print('Removed ' + str(oldsize - newsize) + ' values.')
maxyabs = max(pg.abs(pg.y(self.dataContainer.sensorPositions())))
maxzabs = max(pg.abs(pg.z(self.dataContainer.sensorPositions())))
if maxzabs > 0 and maxyabs == 0:
for i in range(self.dataContainer.sensorCount()):
pos = self.dataContainer.sensorPosition(i).rotateX(-pi / 2)
self.dataContainer.setSensorPosition(i, pos)
if self.verbose:
print(self.dataContainer)
def testShowVariants():
# Create geometry definition for the modelling domain
world = mt.createWorld(start=[-10, 0],
end=[10, -16],
layers=[-8],
worldMarker=False)
# Create a heterogeneous block
block = mt.createRectangle(start=[-6, -3.5],
end=[6, -6.0],
marker=4,
boundaryMarker=10,
area=0.1)
circ = mt.createCircle(pos=[0, -11],
radius=2,
boundaryMarker=11,
isHole=True)
# Merge geometrical entities
geom = world + block + circ
mesh = mt.createMesh(geom)
fig, axs = plt.subplots(3, 5)
pg.show(geom, ax=axs[0][0])
axs[0][0].set_title('plc, (default)')
pg.show(geom, fillRegion=False, ax=axs[0][1])
axs[0][1].set_title('plc, fillRegion=False')
pg.show(geom, showBoundary=False, ax=axs[0][2])
axs[0][2].set_title('plc, showBoundary=False')
pg.show(geom, markers=True, ax=axs[0][3])
axs[0][3].set_title('plc, markers=True')
pg.show(mesh, ax=axs[0][4], showBoundary=False)
axs[0][4].set_title('mesh, showBoundary=False')
pg.show(mesh, ax=axs[1][0])
axs[1][0].set_title('mesh, (default)')
pg.show(mesh, mesh.cellMarkers(), label='Cell markers', ax=axs[1][1])
axs[1][1].set_title('mesh, cells, (default)')
pg.show(mesh, markers=True, ax=axs[1][2])
axs[1][2].set_title('mesh, cells, markers=True')
pg.show(mesh,
mesh.cellMarkers(),
label='Cell markers',
showMesh=True,
ax=axs[1][3])
axs[1][3].set_title('mesh, cells, showMesh=True')
pg.show(mesh,
mesh.cellMarkers(),
label='Cell markers',
showBoundary=False,
ax=axs[1][4])
axs[1][4].set_title('mesh, cells, showBoundary=False')
pg.show(mesh, pg.x(mesh), label='Nodes (x)', ax=axs[2][0])
axs[2][0].set_title('mesh, nodes, (default)')
pg.show(mesh, pg.x(mesh), label='Nodes (x)', showMesh=True, ax=axs[2][1])
axs[2][1].set_title('mesh, nodes, showMesh=True')
pg.show(mesh,
pg.x(mesh),
label='Nodes (x)',
showBoundary=True,
ax=axs[2][2])
axs[2][2].set_title('mesh, nodes, showBoundary=True')
pg.show(mesh,
pg.y(mesh.cellCenters()),
label='Cell center (y)',
tri=True,
shading='flat',
ax=axs[2][3])
axs[2][3].set_title('mesh, cells, tri=True, shading=flat')
pg.show(mesh,
pg.y(mesh.cellCenters()),
label='Cell center (y)',
tri=True,
shading='gouraud',
ax=axs[2][4])
axs[2][4].set_title('mesh, cells, tri=True, shading=gouraud')
##pg.show(mesh, mesh.cellMarker(), label(markers), axs[1][1])
axs[2][4].figure.tight_layout()
fig.tight_layout()
def testCoverage():
grid = pg.createGrid(10, 10)
cov = pg.y(grid.cellCenters()).array()
cov[-9:] = 0 # remove first row
data = pg.Vector(grid.cellCount(), 1.0)
pg.show(grid, data, coverage=cov)
def createTriangles(mesh, data=None):
"""Generate triangle objects for later drawing.
Parameters
----------
mesh : :gimliapi:`GIMLI::Mesh`
pyGimli mesh to plot
data : iterable [None]
cell-based values to plot
Returns
-------
x : numpy array
x position of nodes
y : numpy array
x position of nodes
triangles : numpy array Cx3
cell indices for each triangle
z : numpy array
data for given indices
dataIdx : list of int
list of indices into array to plot
"""
x = pg.x(mesh.positions())
# x.round(1e-1)
y = pg.y(mesh.positions())
# y.round(1e-1)
triCount = 0
for c in mesh.cells():
if c.shape().nodeCount() == 4:
triCount = triCount + 2
else:
triCount = triCount + 1
triangles = np.zeros((triCount, 3))
dataIdx = list(range(triCount))
triCount = 0
for c in mesh.cells():
if c.shape().nodeCount() == 4:
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(1).id()
triangles[triCount, 2] = c.node(2).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(2).id()
triangles[triCount, 2] = c.node(3).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
else:
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(1).id()
triangles[triCount, 2] = c.node(2).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
z = None
if data is not None:
if len(data) == mesh.cellCount():
# strange behavior if we just use these slice
z = np.array(data[dataIdx])
else:
z = np.array(data)
return x, y, triangles, z, dataIdx
axs[1][3].set_title('mesh, cells, showMesh=True')
pg.show(mesh,
mesh.cellMarkers(),
label='Cell markers',
showBoundary=False,
ax=axs[1][4])
axs[1][4].set_title('mesh, cells, showBoundary=False')
pg.show(mesh, pg.x(mesh), label='Nodes (x)', ax=axs[2][0])
axs[2][0].set_title('mesh, nodes, (default)')
pg.show(mesh, pg.x(mesh), label='Nodes (x)', showMesh=True, ax=axs[2][1])
axs[2][1].set_title('mesh, nodes, showMesh=True')
pg.show(mesh, pg.x(mesh), label='Nodes (x)', showBoundary=True, ax=axs[2][2])
axs[2][2].set_title('mesh, nodes, showBoundary=True')
pg.show(mesh,
pg.y(mesh.cellCenters()),
label='Cell center (y)',
tri=True,
shading='flat',
ax=axs[2][3])
axs[2][3].set_title('mesh, cells, tri=True, shading=flat')
pg.show(mesh,
pg.y(mesh.cellCenters()),
label='Cell center (y)',
tri=True,
shading='gouraud',
ax=axs[2][4])
axs[2][4].set_title('mesh, cells, tri=True, shading=gouraud')
##pg.show(mesh, mesh.cellMarker(), label(markers), axs[1][1])
pg.wait()
def covarianceMatrixPos(pos, **kwargs):
"""Position (R3Vector) based covariance matrix"""
return covarianceMatrixVec(np.array(pg.x(pos)), np.array(pg.y(pos)),
np.array(pg.z(pos)), **kwargs)
def test2d():
mesh = pg.Mesh("mesh/world2d.bms")
print (mesh)
xMin = mesh.boundingBox().min()[0]
yMax = mesh.boundingBox().max()[0]
x = np.arange(xMin, yMax, 1.0)
mesh.createNeighbourInfos()
rho = pg.RVector(len(mesh.cellAttributes()), 1.0) * 2000.0
rho.setVal(0.0, pg.find(mesh.cellAttributes() == 1.0))
swatch = pg.Stopwatch(True)
pnts = []
spnts = pg.stdVectorRVector3()
for i in x:
pnts.append(pg.RVector3(i, 0.0001))
spnts.append(pg.RVector3(i, 0.0001))
# gzC, GC = calcGCells(pnts, mesh, rho, 1)
gzC = pg.calcGCells(spnts, mesh, rho, 1)
print ("calcGCells", swatch.duration(True))
# gzB, GB = calcGBounds(pnts, mesh, rho)
# gzB = pg.calcGBounds(spnts, mesh, rho)
# print("calcGBounds", swatch.duration(True))
gZ_Mesh = gzC
ax1, ax2 = getaxes()
# sphere analytical solution
gAna = analyticalCircle2D(spnts, radius=2.0, pos=pg.RVector3(0.0, -5.0), dDensity=2000)
gAna2 = analyticalCircle2D(spnts, radius=2.0, pos=pg.RVector3(5.0, -5.0), dDensity=2000)
gAna = gAna + gAna2
ax1.plot(x, gAna, "-x", label="analytical")
ax1.plot(x, gZ_Mesh, label="WonBevis1987-mesh")
print (gAna / gZ_Mesh)
# rho=GB[0]/mesh.cellSizes()
drawModel(ax2, mesh, rho)
for i in (0, 1):
drawSelectedMeshBoundaries(ax2, mesh.findBoundaryByMarker(i), color=(1.0, 1.0, 1.0, 1.0), linewidth=0.3)
# sphere polygone
radius = 2.0
depth = 5.0
poly1 = pg.stdVectorRVector3()
poly2 = pg.stdVectorRVector3()
nSegment = 124
for i in range(nSegment):
xp = np.sin((i + 1) * (2.0 * np.pi) / nSegment)
yp = np.cos((i + 1) * (2.0 * np.pi) / nSegment)
poly1.append(pg.RVector3(xp * radius, yp * radius - depth))
poly2.append(pg.RVector3(xp * radius + 5.0, yp * radius - depth))
gZ_Poly = calcPolydgdz(spnts, poly1, 2000)
gZ_Poly += calcPolydgdz(spnts, poly2, 2000)
ax1.plot(x, gZ_Poly, label="WonBevis1987-Poly")
ax2.plot(pg.x(poly1), pg.y(poly1), color="red")
ax2.plot(pg.x(poly2), pg.y(poly2), color="red")
ax2.plot(pg.x(spnts), pg.y(spnts), marker="x", color="black")
# test some special case
for i, p in enumerate(poly1):
poly1[i] = pg.RVector3(poly1[i] - pg.RVector3(5.0, -6.0))
ax2.plot(pg.x(poly1), pg.y(poly1), color="green")
gz = calcPolydgdz(spnts, poly1, 2000)
ax1.plot(x, gz, label="Special Case", color="green")
ax1.set_ylabel("dg/dz [mGal]")
ax2.set_ylabel("Tiefe [m]")
ax1.legend()
ax2.set_xlim([x[0], x[-1]])
ax2.grid()
def drawStreams(ax, mesh, data, startStream=3, **kwargs):
"""Draw streamlines based on an unstructured mesh.
Every cell contains only one streamline and every new stream line
starts in the center of a cell. You can alternatively provide a second mesh
with coarser mesh to draw streams for.
Parameters
----------
ax : matplotlib.ax
ax to draw into
mesh : :gimliapi:`GIMLI::Mesh`
2d Mesh to draw the streamline
data : iterable float | [float, float] | pg.R3Vector
If data is an array (per cell or node) gradients are calculated
otherwise the data will be interpreted as vector field.
startStream : int
variate the start stream drawing, try values from 1 to 3 what every
you like more.
**kwargs: forward to drawStreamLine_
* coarseMesh
Instead of draw a stream for every cell in mesh, draw a streamline
segment for each cell in coarseMesh.
* quiver: bool
Draw arrows instead of streamlines.
Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import pygimli as pg
>>> from pygimli.mplviewer import drawStreams
>>> n = np.linspace(0, 1, 10)
>>> mesh = pg.createGrid(x=n, y=n)
>>> nx = pg.x(mesh.positions())
>>> ny = pg.y(mesh.positions())
>>> data = np.cos(1.5 * nx) * np.sin(1.5 * ny)
>>> fig, ax = plt.subplots()
>>> drawStreams(ax, mesh, data, color='red')
>>> drawStreams(ax, mesh, data, dropTol=0.9)
>>> drawStreams(ax, mesh, pg.solver.grad(mesh, data),
... color='green', quiver=True)
>>> ax.set_aspect('equal')
>>> pg.wait()
"""
viewMesh = None
dataMesh = None
quiver = kwargs.pop('quiver', False)
if quiver:
x = None
y = None
u = None
v = None
if len(data) == mesh.nodeCount():
x = pg.x(mesh.positions())
y = pg.y(mesh.positions())
elif len(data) == mesh.cellCount():
x = pg.x(mesh.cellCenters())
y = pg.y(mesh.cellCenters())
elif len(data) == mesh.boundaryCount():
x = pg.x(mesh.boundaryCenters())
y = pg.y(mesh.boundaryCenters())
if isinstance(data, pg.R3Vector):
u = pg.x(data)
v = pg.y(data)
else:
u = data[:, 0]
v = data[:, 1]
ax.quiver(x, y, u, v, **kwargs)
updateAxes_(ax)
return
if 'coarseMesh' in kwargs:
viewMesh = kwargs['coarseMesh']
dataMesh = mesh
dataMesh.createNeighbourInfos()
del kwargs['coarseMesh']
else:
viewMesh = mesh
viewMesh.createNeighbourInfos()
for c in viewMesh.cells():
c.setValid(True)
if startStream == 1:
# start a stream from each boundary cell
for y in np.linspace(viewMesh.ymin(), viewMesh.ymax(), 100):
c = viewMesh.findCell(
[(viewMesh.xmax() - viewMesh.xmax()) / 2.0, y])
if c is not None:
if c.valid():
drawStreamLine_(ax, viewMesh, c, data, dataMesh, **kwargs)
elif startStream == 2:
# start a stream from each boundary cell
for x in np.linspace(viewMesh.xmin(), viewMesh.xmax(), 100):
c = viewMesh.findCell(
[x, (viewMesh.ymax() - viewMesh.ymax()) / 2.0])
if c is not None:
if c.valid():
drawStreamLine_(ax, viewMesh, c, data, dataMesh, **kwargs)
elif startStream == 3:
# start a stream from each boundary cell
for b in viewMesh.findBoundaryByMarker(1, 99):
c = b.leftCell()
if c is None:
c = b.rightCell()
if c.valid():
drawStreamLine_(ax, viewMesh, c, data, dataMesh, **kwargs)
# start a stream from each unused cell
for c in viewMesh.cells():
if c.valid():
drawStreamLine_(ax, viewMesh, c, data, dataMesh, **kwargs)
for c in viewMesh.cells():
c.setValid(True)
updateAxes_(ax)
def show(obj=None, data=None, **kwargs):
"""Mesh and model visualization.
Syntactic sugar to show a obj with data. Forwards to
a known visualization for obj. Typical is
:py:mod:`pygimli.viewer.showMesh` or
:py:mod:`pygimli.viewer.mayaview.showMesh3D` to show most of the typical 2D
and 3D content.
See tutorials and examples for usage hints. An empty show
call creates an empty ax window.
Parameters
----------
obj: obj
obj can be so far.
* :gimliapi:`GIMLI::Mesh` or list of meshes
* DataContainer
* pg.core.Sparse[Map]Matrix
data: iterable
Optionally data to visualize. See appropriate show function.
Keyword Arguments
-----------------
**kwargs
Additional kwargs forward to appropriate show functions.
* ax : axe [None]
Matplotlib axes object. Create a new if necessary.
* fitView : bool [True]
Scale x and y limits to match the view.
Returns
-------
Return the results from the showMesh* functions. Usually the axe object
and a colorbar.
See Also
--------
showMesh
"""
if "axes" in kwargs: # remove me in 1.2 #20200515
print("Deprecation Warning: Please use keyword `ax` instead of `axes`")
kwargs['ax'] = kwargs.pop('axes', None)
### Empty call just to create a axes
if obj is None and not 'mesh' in kwargs.keys():
ax = kwargs.pop('ax', None)
if ax is None:
ax = plt.subplots(figsize=kwargs.pop('figsize', None))[1]
return ax, None
### try to interprete obj containes a mesh
if hasattr(obj, 'mesh'):
return pg.show(obj.mesh, obj, **kwargs)
### try to interprete obj as ERT Data
if isinstance(obj, pg.DataContainerERT):
from pygimli.physics.ert import showERTData
return showERTData(obj, vals=kwargs.pop('vals', data), **kwargs)
### try to interprete obj as matrices
if isinstance(obj, pg.core.MatrixBase) or \
(isinstance(obj, np.ndarray) and obj.ndim == 2):
return showMatrix(obj, **kwargs)
try:
from scipy.sparse import spmatrix
if isinstance(obj, spmatrix):
return showMatrix(obj, **kwargs)
except ImportError:
pass
### try to interprete obj as mesh or list of meshes
mesh = kwargs.pop('mesh', obj)
fitView = kwargs.get('fitView', True)
if isinstance(mesh, list):
ax = kwargs.pop('ax', None)
ax, cBar = show(mesh[0],
data,
hold=1,
ax=ax,
fitView=fitView,
**kwargs)
for m in mesh[1:]:
ax, cBar = show(m, data, ax=ax, hold=1, fitView=False, **kwargs)
if fitView is not False:
ax.autoscale(enable=True, axis='both', tight=True)
ax.set_aspect('equal')
return ax, cBar
if isinstance(mesh, pg.Mesh):
if mesh.dim() == 2:
if pg.zero(pg.y(mesh)):
pg.info("swap z<->y coordinates for visualization.")
meshSwap = pg.Mesh(mesh)
for n in meshSwap.nodes():
n.pos()[1] = n.pos()[2]
return showMesh(meshSwap, data, **kwargs)
return showMesh(mesh, data, **kwargs)
elif mesh.dim() == 3:
from .vistaview import showMesh3D
return showMesh3D(mesh, data, **kwargs)
else:
pg.error("ERROR: Mesh not valid.", mesh)
pg.error("Can't interprete obj: {0} to show.".format(obj))
return None, None
def interpolateAlongCurve(curve, t, **kwargs):
"""Interpolate along curve.
Return curve coordinates for a piecewise linear curve :math:`C(t) = {x_i,y_i,z_i}`
at positions :math:`t`.
Curve and :math:`t` values are expected to be sorted along distance from the
origin of the curve.
Parameters
----------
curve : [[x,z]] | [[x,y,z]] | [:gimliapi:`GIMLI::RVector3`] | :gimliapi:`GIMLI::R3Vector`
Discrete curve for 2D :math:`x,z` curve=[[x,z]], 3D :math:`x,y,z`
t : 1D iterable
Query positions along the curve in absolute distance
kwargs :
If kwargs are given an additional curve smoothing is applied using
:py:mod:`pygimli.meshtools.interpolate`. The kwargs will be delegated.
Returns
-------
p : np.array
Curve positions at query points :math:`t`.
Dimension of p match the size of curve the coordinates.
Examples
--------
>>> # no need to import matplotlib. pygimli's show does
>>> import numpy as np
>>> import pygimli as pg
>>> import pygimli.meshtools as mt
>>> fig, axs = pg.plt.subplots(2,2)
>>> topo = np.array([[-2., 0.], [-1., 0.], [0.5, 0.], [3., 2.], [4., 2.], [6., 1.], [10., 1.], [12., 1.]])
>>> t = np.arange(15.0)
>>> p = mt.interpolateAlongCurve(topo, t)
>>> _= axs[0,0].plot(topo[:,0], topo[:,1], '-x', mew=2)
>>> _= axs[0,1].plot(p[:,0], p[:,1], 'o', color='red') #doctest: +ELLIPSIS
>>>
>>> p = mt.interpolateAlongCurve(topo, t, method='spline')
>>> _= axs[1,0].plot(p[:,0], p[:,1], '-o', color='black') #doctest: +ELLIPSIS
>>>
>>> p = mt.interpolateAlongCurve(topo, t, method='harmonic', nc=3)
>>> _= axs[1,1].plot(p[:,0], p[:,1], '-o', color='green') #doctest: +ELLIPSIS
>>>
>>> pg.plt.show()
>>> pg.wait()
"""
xC = np.zeros(len(curve))
yC = np.zeros(len(curve))
zC = np.zeros(len(curve))
tCurve = kwargs.pop('tCurve', None)
if tCurve is None:
tCurve = pg.utils.cumDist(curve)
dim = 3
## extrapolate starting overlaps
if min(t) < min(tCurve):
d = pg.RVector3(curve[1]) - pg.RVector3(curve[0])
#d[2] = 0.0
d.normalise()
curve = np.insert(curve, [0], [
curve[0] - np.array(d * (min(tCurve) - min(t)))[0:curve.shape[1]]
],
axis=0)
tCurve = np.insert(tCurve, 0, min(t), axis=0)
## extrapolate ending overlaps
if max(t) > max(tCurve):
d = pg.RVector3(curve[-2]) - pg.RVector3(curve[-1])
#d[2] = 0.0
d.normalise()
curve = np.append(curve, [
curve[-1] - np.array(d * (max(t) - max(tCurve)))[0:curve.shape[1]]
],
axis=0)
tCurve = np.append(tCurve, max(t))
if isinstance(curve, pg.R3Vector) or isinstance(curve,
pg.stdVectorRVector3):
xC = pg.x(curve)
yC = pg.y(curve)
zC = pg.z(curve)
else:
if curve.shape[1] == 2:
xC = curve[:, 0]
zC = curve[:, 1]
dim = 2
else:
xC = curve[:, 0]
yC = curve[:, 1]
zC = curve[:, 2]
if len(kwargs.keys()) > 0:
#interpolate more curve points to get a smooth line
dTi = min(pg.utils.dist(pg.utils.diff(curve))) / 10.
ti = np.arange(min(tCurve), max(tCurve) + dTi, dTi)
xC = pg.interpolate(ti, tCurve, xC, **kwargs)
zC = pg.interpolate(ti, tCurve, zC, **kwargs)
if dim == 3:
yC = pg.interpolate(ti, tCurve, yC, **kwargs)
tCurve = ti
xt = interpolate(t, tCurve, xC)
zt = interpolate(t, tCurve, zC)
if dim == 2:
return np.vstack([xt, zt]).T
yt = interpolate(t, tCurve, yC)
return np.vstack([xt, yt, zt]).T
#ax, _ = pg.show(mesh, data=K, label='Hydraulic conductivity $K$ in m$/$s',
#cMin=1e-5, cMax=1e-2, nLevs=4, cmap='viridis')
#ax, _ = pg.show(mesh, data=pg.abs(vel), logScale=0, label='Velocity $v$ in m$/$s')
#ax, _ = pg.show(mesh, data=vel, ax=ax, color='black', linewidth=0.5, dropTol=1e-6)
print('Solve Advection-diffusion equation ...')
S = pg.RVector(mesh.cellCount(), 0.0)
# Fill injection source vector for a fixed injection position
sourceCell = mesh.findCell([-19.1, -4.6])
S[sourceCell.id()] = 1.0 / sourceCell.size() #g/(l s)
# Choose 800 time steps for 6 days in seconds
t = pg.utils.grange(0, 6 * 24 * 3600, n=800)
# Create dispersitivity, depending on the absolute velocity
dispersion = pg.abs(vel) * 1e-2
# Solve for injection time, but we need velocities on cell nodes
vel = mt.cellDataToNodeData(mesh, np.asarray([pg.x(vel), pg.y(vel)]).T).T
c1 = pg.solver.solveFiniteVolume(mesh,
a=dispersion,
f=S,
vel=vel,
times=t,
uB=[1, 0],
scheme='PS',
verbose=0)
# Solve without injection starting with last result
c2 = pg.solver.solveFiniteVolume(mesh,
a=dispersion,
f=0,
vel=vel,
u0=c1[-1],
times=t,
def drawStreams(ax, mesh, data, startStream=3, **kwargs):
"""Draw streamlines based on an unstructured mesh.
Every cell contains only one streamline and every new stream line
starts in the center of a cell. You can alternatively provide a second mesh
with coarser mesh to draw streams for.
Parameters
----------
ax : matplotlib.ax
ax to draw into
mesh : :gimliapi:`GIMLI::Mesh`
2d Mesh to draw the streamline
data : iterable float | [float, float] | pg.R3Vector
If data is an array (per cell or node) gradients are calculated
otherwise the data will be interpreted as vector field.
startStream : int
variate the start stream drawing, try values from 1 to 3 what every
you like more.
**kwargs: forward to drawStreamLine_
* coarseMesh
Instead of draw a stream for every cell in mesh, draw a streamline
segment for each cell in coarseMesh.
* quiver: bool
Draw arrows instead of streamlines.
Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import pygimli as pg
>>> from pygimli.mplviewer import drawStreams
>>> n = np.linspace(0, 1, 10)
>>> mesh = pg.createGrid(x=n, y=n)
>>> nx = pg.x(mesh.positions())
>>> ny = pg.y(mesh.positions())
>>> data = np.cos(1.5 * nx) * np.sin(1.5 * ny)
>>> fig, ax = plt.subplots()
>>> drawStreams(ax, mesh, data, color='red')
>>> drawStreams(ax, mesh, data, dropTol=0.9)
>>> drawStreams(ax, mesh, pg.solver.grad(mesh, data),
... color='green', quiver=True)
>>> ax.set_aspect('equal')
>>> pg.wait()
"""
viewMesh = None
dataMesh = None
quiver = kwargs.pop('quiver', False)
if quiver:
x = None
y = None
u = None
v = None
if len(data) == mesh.nodeCount():
x = pg.x(mesh.positions())
y = pg.y(mesh.positions())
elif len(data) == mesh.cellCount():
x = pg.x(mesh.cellCenters())
y = pg.y(mesh.cellCenters())
elif len(data) == mesh.boundaryCount():
x = pg.x(mesh.boundaryCenters())
y = pg.y(mesh.boundaryCenters())
if isinstance(data, pg.R3Vector):
u = pg.x(data)
v = pg.y(data)
else:
u = data[:, 0]
v = data[:, 1]
ax.quiver(x, y, u, v, **kwargs)
updateAxes_(ax)
return
if 'coarseMesh' in kwargs:
viewMesh = kwargs['coarseMesh']
dataMesh = mesh
dataMesh.createNeighbourInfos()
del kwargs['coarseMesh']
else:
viewMesh = mesh
viewMesh.createNeighbourInfos()
for c in viewMesh.cells():
c.setValid(True)
if startStream == 1:
# start a stream from each boundary cell
for y in np.linspace(viewMesh.ymin(), viewMesh.ymax(), 100):
c = viewMesh.findCell(
[(viewMesh.xmax() - viewMesh.xmax()) / 2.0, y])
if c is not None:
if c.valid():
drawStreamLine_(ax, viewMesh, c, data, dataMesh, **kwargs)
elif startStream == 2:
# start a stream from each boundary cell
for x in np.linspace(viewMesh.xmin(), viewMesh.xmax(), 100):
c = viewMesh.findCell(
[x, (viewMesh.ymax() - viewMesh.ymax()) / 2.0])
if c is not None:
if c.valid():
drawStreamLine_(ax, viewMesh, c, data, dataMesh, **kwargs)
elif startStream == 3:
# start a stream from each boundary cell
for b in viewMesh.findBoundaryByMarker(1, 99):
c = b.leftCell()
if c is None:
c = b.rightCell()
if c.valid():
drawStreamLine_(ax, viewMesh, c, data, dataMesh, **kwargs)
# start a stream from each unused cell
for c in viewMesh.cells():
if c.valid():
drawStreamLine_(ax, viewMesh, c, data, dataMesh, **kwargs)
for c in viewMesh.cells():
c.setValid(True)
updateAxes_(ax)
drawField(ax, mesh, times, cmap='Spectral', fillContour=True)
drawStreamLines(ax, mesh, -times, nx=50, ny=50)
###############################################################################
# We compare the result with the analytical solution along the x axis
x = np.arange(0., 140., 0.5)
tFMM = pg.interpolate(mesh, times, x, x * 0., x * 0.)
tAna = analyticalSolution2Layer(x)
print("min(dt)={} ms max(dt)={} ms".format(
min(tFMM - tAna) * 1000,
max(tFMM - tAna) * 1000))
###############################################################################
# In order to use the Dijkstra, we extract the surface positions >0
mx = pg.x(mesh.positions())
my = pg.y(mesh.positions())
fi = pg.find((my == 0.0) & (mx >= 0))
px = np.sort(mx(fi))
###############################################################################
# A data container with index arrays named s (shot) and g (geophones) is
# created and filled with the positions and shot/geophone indices.
data = pg.DataContainer()
data.registerSensorIndex('s')
data.registerSensorIndex('g')
for pxi in px:
data.createSensor(pg.RVector3(pxi, 0.0))
ndata = len(px) - 1
data.resize(ndata)
data.set('s', pg.RVector(ndata, 0)) # only one shot at first sensor
pg.show(mesh, axes=a, data=l[0])
cells = fwd.mesh().cells()
active_cells = [cells[i] for i in range(mesh.cellCount()) if l[0][i]]
# active_cells.append(cells[2044])
for c in active_cells:
pos = c.center()
gradient = 2000 * c.grad(pos, fwd.timefields[0])
dx, dy = gradient.x(), gradient.y()
a.text(pos.x(), pos.y(), str(c.id()))
a.arrow(pos.x(), pos.y(), dx, dy)
ray = fwd.poslist
a.plot(
pg.x(ray),
pg.y(ray),
'm-*',
)
plt.show()
# look at if next gradient contradicts the previous
# if so, then follow the interface instead (line segment to next node)
# this will stop when the gradients are more aligned.
# drawMesh(a, mesh)
# drawField(a, mesh, fwd.timefields[0], True, 'Spectral')
# drawStreamLines(a, mesh, fwd.timefields[0], nx=50, ny=50)
# some stats:
delta_t = np.array(data("t")) - t_fmm
diff_rms = np.sqrt(np.sum(delta_t**2) / len(delta_t))
def covarianceMatrixPos(pos, **kwargs):
"""Position (R3Vector) based covariance matrix"""
return covarianceMatrixVec(np.array(pg.x(pos)), np.array(pg.y(pos)),
np.array(pg.z(pos)), **kwargs)
def show(mesh=None, data=None, **kwargs):
"""Mesh and model visualization.
Syntactic sugar to show a mesh with data. Forwards to
:py:mod:`pygimli.viewer.showMesh` or
:py:mod:`pygimli.viewer.mayaview.showMesh3D` to show most of the typical 2D
and 3D content. See tutorials and examples for usage hints. An empty show
call create an empty ax window.
Parameters
----------
mesh : :gimliapi:`GIMLI::Mesh` or list of meshes
2D or 3D GIMLi mesh
**kwargs :
* fitView : bool [True]
Scale x and y limits to match the view.
* ax : axe [None]
Matplotlib axes object. Create a new if necessary.
* Will be forwarded to the appropriate show functions.
Returns
-------
Return the results from the showMesh* functions.
See Also
--------
showMesh
"""
if "axes" in kwargs:
print("Deprecation Warning: Please use keyword `ax` instead of `axes`")
kwargs['ax'] = kwargs.pop('axes', None)
if isinstance(mesh, list):
ax = kwargs.pop('ax', None)
fitView = kwargs.pop('fitView', True)
ax, cbar = show(mesh[0],
data,
hold=1,
ax=ax,
fitView=fitView,
**kwargs)
xmin = mesh[0].xmin()
xmax = mesh[0].xmax()
ymin = mesh[0].ymin()
ymax = mesh[0].ymax()
for m in mesh[1:]:
ax, cbar = show(m, data, ax=ax, hold=1, fitView=False, **kwargs)
xmin = min(xmin, m.xmin())
xmax = max(xmax, m.xmax())
ymin = min(ymin, m.ymin())
ymax = max(ymax, m.ymax())
# ax.relim()
# ax.autoscale_view(tight=True)
if fitView is not False:
ax.set_xlim([xmin, xmax])
ax.set_ylim([ymin, ymax])
# print(ax.get_data_interval())
return ax, cbar
if isinstance(mesh, pg.Mesh):
if mesh.dim() == 2:
if pg.zero(pg.y(mesh)):
pg.info("swap z<->y coordinates for visualization.")
meshSwap = pg.Mesh(mesh)
for n in meshSwap.nodes():
n.pos()[1] = n.pos()[2]
return showMesh(meshSwap, data, **kwargs)
return showMesh(mesh, data, **kwargs)
elif mesh.dim() == 3:
from .mayaview import showMesh3D
return showMesh3D(mesh, data, **kwargs)
else:
pg.error("ERROR: Mesh not valid.", mesh)
ax = kwargs.pop('ax', None)
if ax is None:
ax = plt.subplots()[1]
return ax, None
def maillage_SWMS2D(geometry):
"""Définition du maillage triangulaire pour SWMS_2D"""
xmin=geometry.xmin
xmax=geometry.xmax
emin=geometry.emin
emax=geometry.emax
dtrou=geometry.dtrou
etrou=geometry.etrou
r=geometry.r
dx=geometry.dx
zaff=geometry.zaff
eaff=geometry.eaff
#waff=geometry.waff
assert dtrou + zaff < emax
xtrou_reg = np.arange(xmin, r + dx, dx, 'float')
# xtrou_reg = np.arange(xmin, r + zaff, dx, 'float')
etrou_reg = np.arange(etrou, emax +dx, dx, 'float')
efin_reg = np.arange(eaff, etrou+dx, dx, 'float')
#A présent on crée une zone grâce à un polygone
poly = pg.Mesh(2) # empty 2d mesh
nStart = poly.createNode(0.0, 0.0, 0.0) # On crée un noeud de départ, on travaille en 2D donc le dernier terme vaut 0.0
nA = nStart # noeud de départ
for e in efin_reg[0:len(efin_reg)]: # On démarre de 1 et on se balade sur l'axe des x en créant un noeud à chaque fois
nB = poly.createNode(0, e, 0.0)
poly.createEdge(nA, nB) # On définit un côté entre le noeud précédemment créé et le nouveau
nA = nB # On remplace le noeud de départ par le noeud nouvellement créé
#Définir les noeuds au fond du trou
for x in xtrou_reg[1:len(xtrou_reg)]:
nB = poly.createNode(x, etrou, 0.0)
poly.createEdge(nA, nB) #On définit un côté entre le noeud précédemment crée et le nouveau
nA = nB #On remplace le noeud de départ par le noeud nouvellement crée
#Définir les noeuds le long du trou
for f in etrou_reg[1:len(etrou_reg)]: # On démarre du haut et on se balade sur l'axe des z en créant un noeud à chaque fois
nB = poly.createNode(r, f, 0.0)
poly.createEdge(nA, nB) # On définit un côté entre le noeud précédemment créé et le nouveau
nA = nB # On remplace le noeud de départ par le noeud nouvellement crée
nC=nB
nD = poly.createNode(xmax, emax, 0.0)
poly.createEdge(nC, nD)
nE = poly.createNode(xmax, emin, 0.0)
poly.createEdge(nD, nE)
poly.createEdge(nE, nStart) #On ferme le polygone!
mesh=pg.meshtools.createMesh(poly, quality=geometry.quality, area=geometry.area, smooth=geometry.smooth)
pg_pos = mesh.positions()
mesh_pos = np.array((np.array(pg.x(pg_pos)), np.array(pg.y(pg_pos)), np.array(pg.z(pg_pos)))).T #On crée une matrice contenant la position des noeuds
mesh_cells = np.zeros((mesh.cellCount(), 3)) #Matrice vide de la taille du nombre de cellules
for i, cell in enumerate(mesh.cells()): #On rentre les cellules das une matrice
mesh_cells[i] = cell.ids()
return mesh, pg_pos, mesh_pos, mesh_cells
def createTriangles(mesh, data=None):
"""Generate triangle objects for later drawing.
Parameters
----------
mesh : :gimliapi:`GIMLI::Mesh`
pyGimli mesh to plot
data : iterable [None]
cell-based values to plot
Returns
-------
x : numpy array
x position of nodes
y : numpy array
x position of nodes
triangles : numpy array Cx3
cell indices for each triangle
z : numpy array
data for given indices
dataIdx : list of int
list of indices into array to plot
"""
x = pg.x(mesh.positions())
# x.round(1e-1)
y = pg.y(mesh.positions())
# y.round(1e-1)
triCount = 0
for c in mesh.cells():
if c.shape().nodeCount() == 4:
triCount = triCount + 2
else:
triCount = triCount + 1
triangles = np.zeros((triCount, 3))
dataIdx = list(range(triCount))
triCount = 0
for c in mesh.cells():
if c.shape().nodeCount() == 4:
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(1).id()
triangles[triCount, 2] = c.node(2).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(2).id()
triangles[triCount, 2] = c.node(3).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
else:
triangles[triCount, 0] = c.node(0).id()
triangles[triCount, 1] = c.node(1).id()
triangles[triCount, 2] = c.node(2).id()
dataIdx[triCount] = c.id()
triCount = triCount + 1
z = None
if data is not None:
if len(data) == mesh.cellCount():
# strange behavior if we just use these slice
z = np.array(data[dataIdx])
else:
z = np.array(data)
return x, y, triangles, z, dataIdx
def show(mesh=None, data=None, **kwargs):
"""Mesh and model visualization.
Syntactic sugar to show a mesh with data. Forwards to
:py:mod:`pygimli.viewer.showMesh` or
:py:mod:`pygimli.viewer.mayaview.showMesh3D` to show most of the typical 2D
and 3D content. See tutorials and examples for usage hints. An empty show
call creates an empty ax window.
Parameters
----------
mesh : :gimliapi:`GIMLI::Mesh` or list of meshes
2D or 3D GIMLi mesh
**kwargs :
* fitView : bool [True]
Scale x and y limits to match the view.
* ax : axe [None]
Matplotlib axes object. Create a new if necessary.
* Will be forwarded to the appropriate show functions.
Returns
-------
Return the results from the showMesh* functions.
See Also
--------
showMesh
"""
if "axes" in kwargs:
print("Deprecation Warning: Please use keyword `ax` instead of `axes`")
kwargs['ax'] = kwargs.pop('axes', None)
if isinstance(mesh, list):
ax = kwargs.pop('ax', None)
fitView = kwargs.pop('fitView', True)
ax, cbar = show(mesh[0], data, hold=1, ax=ax, fitView=fitView, **kwargs)
xmin = mesh[0].xmin()
xmax = mesh[0].xmax()
ymin = mesh[0].ymin()
ymax = mesh[0].ymax()
for m in mesh[1:]:
ax, cbar = show(m, data, ax=ax, hold=1, fitView=False, **kwargs)
xmin = min(xmin, m.xmin())
xmax = max(xmax, m.xmax())
ymin = min(ymin, m.ymin())
ymax = max(ymax, m.ymax())
# ax.relim()
# ax.autoscale_view(tight=True)
if fitView is not False:
ax.set_xlim([xmin, xmax])
ax.set_ylim([ymin, ymax])
# print(ax.get_data_interval())
return ax, cbar
if isinstance(mesh, pg.Mesh):
if mesh.dim() == 2:
if pg.zero(pg.y(mesh)):
pg.info("swap z<->y coordinates for visualization.")
meshSwap = pg.Mesh(mesh)
for n in meshSwap.nodes():
n.pos()[1] = n.pos()[2]
return showMesh(meshSwap, data, **kwargs)
return showMesh(mesh, data, **kwargs)
elif mesh.dim() == 3:
from .mayaview import showMesh3D
return showMesh3D(mesh, data, **kwargs)
else:
pg.error("ERROR: Mesh not valid.", mesh)
ax = kwargs.pop('ax', None)
if ax is None:
ax = plt.subplots()[1]
return ax, None
def test2d():
mesh = g.Mesh( 'mesh/world2d.bms' )
print mesh
xMin = mesh.boundingBox( ).min()[0]
yMax = mesh.boundingBox( ).max()[0]
x = P.arange( xMin, yMax, 1. );
mesh.createNeighbourInfos()
rho = g.RVector( len( mesh.cellAttributes() ), 1. ) * 2000.0
rho.setVal( 0.0, g.find( mesh.cellAttributes() == 1.0 ) )
swatch = g.Stopwatch( True )
pnts = []
spnts = g.stdVectorRVector3()
for i in x:
pnts.append( g.RVector3( i, 0.0001 ) )
spnts.append( g.RVector3( i, 0.0001 ) )
#gzC, GC = calcGCells( pnts, mesh, rho, 1 )
gzC = g.calcGCells( spnts , mesh, rho, 1 )
print "calcGCells", swatch.duration( True )
#gzB, GB = calcGBounds( pnts, mesh, rho )
gzB = g.calcGBounds( spnts , mesh, rho )
print "calcGBounds", swatch.duration( True )
gZ_Mesh = gzC
ax1, ax2 = getaxes()
# sphere analytical solution
gAna = analyticalCircle2D( spnts, radius = 2.0, pos = g.RVector3( 0.0, -5.0 ), dDensity = 2000 )
gAna2 = analyticalCircle2D( spnts, radius = 2.0, pos = g.RVector3( 5.0, -5.0 ), dDensity = 2000 )
gAna = gAna + gAna2
ax1.plot( x, gAna, '-x', label= 'Analytisch' )
ax1.plot( x, gZ_Mesh, label= 'WonBevis1987-mesh' )
print gAna / gZ_Mesh
#rho=GB[0]/mesh.cellSizes()
gci = drawModel( ax2, mesh, rho )
drawSelectedMeshBoundaries( ax2, mesh.findBoundaryByMarker( 0 )
, color = ( 1.0, 1.0, 1.0, 1.0 )
, linewidth = 0.3 )
drawSelectedMeshBoundaries( ax2, mesh.findBoundaryByMarker( 1 )
, color = ( 1.0, 1.0, 1.0, 1.0 )
, linewidth = 0.3 )
# sphere polygone
radius = 2.
depth = 5.
poly1 = g.stdVectorRVector3()
poly2 = g.stdVectorRVector3()
nSegment=124
for i in range( nSegment ):
xp = np.sin( (i+1) * ( 2. * np.pi ) / nSegment )
yp = np.cos( (i+1) * ( 2. * np.pi ) / nSegment )
poly1.append( g.RVector3( xp * radius, yp * radius - depth ) )
poly2.append( g.RVector3( xp * radius + 5., yp * radius - depth ) )
gZ_Poly = calcPolydgdz( spnts, poly1, 2000 )
gZ_Poly += calcPolydgdz( spnts, poly2, 2000 )
ax1.plot( x, gZ_Poly, label= 'WonBevis1987-Poly' )
ax2.plot( g.x( poly1 ), g.y( poly1 ), color = 'red' )
ax2.plot( g.x( poly2 ), g.y( poly2 ), color = 'red' )
ax2.plot( g.x( spnts ), g.y( spnts ), marker = 'x', color = 'black' )
# test some special case
for i, p in enumerate( poly1 ):
poly1[i] = g.RVector3( poly1[i] - g.RVector3( 5.0, -6. ) )
ax2.plot( g.x( poly1 ), g.y( poly1 ), color = 'green' )
gz = calcPolydgdz( spnts, poly1, 2000 )
ax1.plot( x, gz, label= 'Special Case', color = 'green' )
ax1.set_ylabel( 'dg/dz [mGal]' )
ax2.set_ylabel( 'Tiefe [m]' )
ax1.legend()
ax2.set_xlim( [ x[0], x[-1] ] )
ax2.grid()
def show(obj=None, data=None, **kwargs):
"""Mesh and model visualization.
Syntactic sugar to show a obj with data. Forwards to
a known visualization for obj. Typical is
:py:mod:`pygimli.viewer.showMesh` or
:py:mod:`pygimli.viewer.mayaview.showMesh3D` to show most of the typical 2D
and 3D content.
See tutorials and examples for usage hints. An empty show
call creates an empty ax window.
Parameters
----------
obj: obj
obj can be so far.
* :gimliapi:`GIMLI::Mesh` or list of meshes
* DataContainer
* pg.core.Sparse[Map]Matrix
data: iterable
Optionally data to visualize. See appropriate show function.
Keyword Arguments
-----------------
**kwargs
Additional kwargs forward to appropriate show functions.
* ax : axe [None]
Matplotlib axes object. Create a new if necessary.
* fitView : bool [True]
Scale x and y limits to match the view.
Returns
-------
Return the results from the showMesh* functions. Usually the axe object
and a colorbar.
See Also
--------
showMesh
"""
if "axes" in kwargs:
print("Deprecation Warning: Please use keyword `ax` instead of `axes`")
kwargs['ax'] = kwargs.pop('axes', None)
if isinstance(obj, pg.DataContainerERT):
from pygimli.physics.ert import showERTData
return showERTData(obj, vals=kwargs.pop('vals', data), **kwargs)
if isinstance(obj, pg.core.MatrixBase):
ax, _ = pg.show()
return drawMatrix(ax, obj, **kwargs)
mesh = kwargs.pop('mesh', obj)
if isinstance(mesh, list):
ax = kwargs.pop('ax', None)
fitView = kwargs.pop('fitView', ax is None)
ax, cBar = show(mesh[0],
data,
hold=1,
ax=ax,
fitView=fitView,
**kwargs)
xMin = mesh[0].xMin()
xMax = mesh[0].xMax()
yMin = mesh[0].yMin()
yMax = mesh[0].yMax()
for m in mesh[1:]:
ax, cBar = show(m, data, ax=ax, hold=1, fitView=False, **kwargs)
xMin = min(xMin, m.xMin())
xMax = max(xMax, m.xMax())
yMin = min(yMin, m.yMin())
yMax = max(yMax, m.yMax())
# ax.relim()
# ax.autoscale_view(tight=True)
if fitView is not False:
ax.set_xlim([xMin, xMax])
ax.set_ylim([yMin, yMax])
# print(ax.get_data_interval())
return ax, cBar
if isinstance(mesh, pg.Mesh):
if mesh.dim() == 2:
if pg.zero(pg.y(mesh)):
pg.info("swap z<->y coordinates for visualization.")
meshSwap = pg.Mesh(mesh)
for n in meshSwap.nodes():
n.pos()[1] = n.pos()[2]
return showMesh(meshSwap, data, **kwargs)
return showMesh(mesh, data, **kwargs)
elif mesh.dim() == 3:
from .vistaview import showMesh3D
return showMesh3D(mesh, data, **kwargs)
else:
pg.error("ERROR: Mesh not valid.", mesh)
ax = kwargs.pop('ax', None)
if ax is None:
ax = plt.subplots()[1]
return ax, None
def interpolate(*args, **kwargs):
r"""Interpolation convinience function.
Convenience function to interpolate different kind of data.
Currently supported interpolation schemes are:
* Interpolate mesh based data from one mesh to another
(syntactic sugar for the core based interpolate (see below))
Parameters:
args: :gimliapi:`GIMLI::Mesh`, :gimliapi:`GIMLI::Mesh`, iterable
`outData = interpolate(outMesh, inMesh, vals)`
Interpolate values based on inMesh to outMesh.
Values can be of length inMesh.cellCount() interpolated to
outMesh.cellCenters() or inMesh.nodeCount() which are interpolated tp
outMesh.positions().
Returns:
Interpolated values.
* Mesh based values to arbitrary points, based on finite element
interpolation (from gimli core).
Parameters:
args: :gimliapi:`GIMLI::Mesh`, ...
Arguments forwarded to :gimliapi:`GIMLI::interpolate`
kwargs:
Arguments forwarded to :gimliapi:`GIMLI::interpolate`
`interpolate(srcMesh, destMesh)`
All data from inMesh are interpolated to outMesh
Returns:
Interpolated values
* Interpolate along curve.
Forwarded to :py:mod:`pygimli.meshtools.interpolateAlongCurve`
Parameters:
args: curve, t
kwargs:
Arguments forwarded to
:py:mod:`pygimli.meshtools.interpolateAlongCurve`
* 1D point set :math:`u(x)` for ascending :math:`x`.
Find interpolation function :math:`I = u(x)` and
returns :math:`u_{\text{i}} = I(x_{\text{i}})`
(interpolation methods are [**linear** via matplotlib,
cubic **spline** via scipy, fit with **harmonic** functions' via pygimli])
Note, for 'linear' and 'spline' the interpolate contains all original
coordinates while 'harmonic' returns an approximate best fit.
The amount of harmonic coefficients can be specfied with the 'nc' keyword.
Parameters:
args: xi, x, u
* :math:`x_{\text{i}}` - target sample points
* :math:`x` - function sample points
* :math:`u` - function values
kwargs:
* method : string
Specify interpolation method 'linear, 'spline', 'harmonic'
* nc : int
Number of harmonic coefficients for the 'harmonic' method.
Returns:
ui: array of length xi
:math:`u_{\text{i}} = I(x_{\text{i}})`, with :math:`I = u(x)`
To use the core functions :gimliapi:`GIMLI::interpolate` start with a
mesh instance as first argument or use the appropriate keyword arguments.
TODO
* 2D parametric to points (method=['linear, 'spline', 'harmonic'])
* 2D/3D point cloud to points/grids ('Delauney', 'linear, 'spline', 'harmonic')
* Mesh to points based on nearest neighbour values (pg.core)
Examples
--------
>>> # no need to import matplotlib. pygimli's show does
>>> import numpy as np
>>> import pygimli as pg
>>> fig, ax = pg.plt.subplots(1, 1, figsize=(10, 5))
>>> u = np.array([1.0, 12.0, 3.0, -4.0, 5.0, 6.0, -1.0])
>>> xu = np.array(range(len(u)))
>>> xi = np.linspace(xu[0], xu[-1], 1000)
>>> _= ax.plot(xu, u, 'o')
>>> _= ax.plot(xi, pg.interpolate(xi, xu, u, method='linear'),
... color='blue', label='linear')
>>> _= ax.plot(xi, pg.interpolate(xi, xu, u, method='spline'),
... color='red', label='spline')
>>> _= ax.plot(xi, pg.interpolate(xi, xu, u, method='harmonic'),
... color='green', label='harmonic')
>>> _= ax.legend()
"""
pgcore = False
if 'srcMesh' in kwargs:
pgcore = True
elif len(args) > 0:
if isinstance(args[0], pg.Mesh):
if len(args) == 2 and isinstance(args[1], pg.Mesh):
return pg.core._pygimli_.interpolate(args[0], args[1],
**kwargs)
if len(args) == 3 and isinstance(args[1], pg.Mesh):
pgcore = False # (outMesh, inMesh, vals)
else:
pgcore = True
if pgcore:
if len(args) == 3: # args: outData = (inMesh, inData, outPos)
if args[1].ndim == 2: # outData = (inMesh, mat, vR3)
outMat = pg.Matrix()
pg.core._pygimli_.interpolate(args[0],
inMat=np.array(args[1]),
destPos=args[2],
outMat=outMat,
**kwargs)
return np.array(outMat)
if len(args) == 4: # args: (inMesh, inData, outPos, outData)
if args[1].ndim == 1 and args[2].ndim == 1 and args[3].ndim == 1:
return pg.core._pygimli_.interpolate(args[0],
inVec=args[1],
x=args[2],
y=args[3],
**kwargs)
if isinstance(args[1], pg.RMatrix) and \
isinstance(args[3], pg.RMatrix):
return pg.core._pygimli_.interpolate(args[0],
inMat=args[1],
destPos=args[2],
outMat=args[3],
**kwargs)
if isinstance(args[1], pg.RVector) and \
isinstance(args[3], pg.RVector):
return pg.core._pygimli_.interpolate(args[0],
inVec=args[1],
destPos=args[2],
outVec=args[3],
**kwargs)
if len(args) == 5:
if args[1].ndim == 1 and args[2].ndim == 1 and \
args[3].ndim == 1 and args[4].ndim == 1:
return pg.core._pygimli_.interpolate(args[0],
inVec=args[1],
x=args[2],
y=args[3],
z=args[4],
**kwargs)
return pg.core._pygimli_.interpolate(*args, **kwargs)
# end if pg.core:
if len(args) == 3:
if isinstance(args[0], pg.Mesh): # args: (outMesh, inMesh, data)
outMesh = args[0]
inMesh = args[1]
data = args[2]
if isinstance(data, pg.R3Vector) or isinstance(
data, pg.stdVectorRVector3):
x = pg.interpolate(outMesh, inMesh, pg.x(data))
y = pg.interpolate(outMesh, inMesh, pg.y(data))
z = pg.interpolate(outMesh, inMesh, pg.z(data))
return np.vstack([x, y, z]).T
if isinstance(data, np.ndarray):
if data.ndim == 2 and data.shape[1] == 3:
x = pg.interpolate(outMesh, inMesh, data[:, 0])
y = pg.interpolate(outMesh, inMesh, data[:, 1])
z = pg.interpolate(outMesh, inMesh, data[:, 2])
return np.vstack([x, y, z]).T
if len(data) == inMesh.cellCount():
return pg.interpolate(srcMesh=inMesh,
inVec=data,
destPos=outMesh.cellCenters())
elif len(data) == inMesh.nodeCount():
return pg.interpolate(srcMesh=inMesh,
inVec=data,
destPos=outMesh.positions())
else:
print(inMesh)
print(outMesh)
raise Exception("Don't know how to interpolate data of size",
str(len(data)))
print("data: ", data)
raise Exception("Cannot interpret data: ", str(len(data)))
else: #args: xi, x, u
xi = args[0]
x = args[1]
u = args[2]
method = kwargs.pop('method', 'linear')
if 'linear' in method:
return np.interp(xi, x, u)
if 'harmonic' in method:
coeff = kwargs.pop('nc', int(np.ceil(np.sqrt(len(x)))))
from pygimli.frameworks import harmfitNative
return harmfitNative(u, x=x, nc=coeff, xc=xi, err=None)[0]
if 'spline' in method:
if pg.optImport("scipy",
requiredFor="use interpolate splines."):
from scipy import interpolate
tck = interpolate.splrep(x, u, s=0)
return interpolate.splev(xi, tck, der=0)
else:
return xi * 0.
if len(args) == 2: # args curve, t
curve = args[0]
t = args[1]
return interpolateAlongCurve(curve, t, **kwargs)
def midconfERT(data, ind=None, rnum=1, circular=False):
"""Return the midpoint and configuration key for ERT data.
Return the midpoint and configuration key for ERT data.
Parameters
----------
data : DataContainerERT
data container with sensorPositions and a/b/m/n fields
ind : []
Documentme
rnum : []
Documentme
circular : bool
Return midpoint in degree (rad) instead if meter.
Returns
-------
mid : np.array of float
representative midpoint (middle of MN, AM depending on array)
conf : np.array of float
configuration/array key consisting of
1) array type (Wenner-alpha/beta, Schlumberger, PP, PD, DD, MG)
00000: pole-pole
10000: pole-dipole or dipole-pole
30000: Wenner-alpha
40000: Schlumberger or Gradient
50000: dipole-dipole or Wenner-beta
2) potential dipole length (in electrode spacings)
.XX..: dipole length
3) separation factor (current dipole length or (di)pole separation)
...XX: pole/dipole separation (PP,PD,DD,GR) or separation
"""
# xe = np.hstack((pg.x(data.sensorPositions()), np.nan)) # not used anymore
x0 = data.sensorPosition(0).x()
xe = pg.x(data.sensorPositions()) - x0
ux = pg.unique(xe)
if len(ux) * 2 > data.sensorCount(): # 2D with topography case
dx = np.array(pg.utils.diff(pg.utils.cumDist(data.sensorPositions())))
dxM = pg.mean(dx)
if min(pg.y(data)) != max(pg.y(data)) or \
min(pg.z(data)) != max(pg.z(data)):
# Topography case
if (max(abs(dx - dxM)) < dxM * 0.9):
# if the maximum spacing < meanSpacing/2 we assume equidistant
# spacing and no missing electrodes
dx = np.ones(len(dx)) * dxM
else:
# topography with probably missing electrodes
dx = np.floor(dx / np.round(dxM)) * dxM
pass
if max(dx) < 0.5:
print("Detecting small distances, using mm accuracy")
rnum = 3
xe = np.hstack((0., np.cumsum(np.round(dx, rnum)), np.nan))
de = np.median(np.diff(xe[:-1])).round(rnum)
ne = np.round(xe / de)
else: # 3D (without topo) case => take positions directly
de = np.median(np.diff(ux)).round(1)
ne = np.array(xe / de, dtype=int)
# a, b, m, n = data('a'), data('b'), data('m'), data('n')
# check if xe[a]/a is better suited (has similar size)
if circular:
# for circle geometry
center = np.mean(data.sensorPositions(), axis=0)
r = data.sensors()[0].distance(center)
s0 = data.sensors()[0] - center
s1 = data.sensors()[1] - center
p0 = np.arctan2(s0[1], s0[0])
p1 = np.arctan2(s1[1], s1[0])
if p1 > p0:
# rotate left
x = np.cos(np.linspace(0, 2 * pi,
data.sensorCount() + 1) + p0)[:-1] * r
y = np.sin(np.linspace(0, 2 * pi,
data.sensorCount() + 1) + p0)[:-1] * r
else:
x = np.cos(np.linspace(2 * pi, 0,
data.sensorCount() + 1) + p0)[:-1] * r
y = np.sin(np.linspace(2 * pi, 0,
data.sensorCount() + 1) + p0)[:-1] * r
a = np.array([np.arctan2(y[i], x[i]) for i in data['a']])
b = np.array([np.arctan2(y[i], x[i]) for i in data['b']])
m = np.array([np.arctan2(y[i], x[i]) for i in data['m']])
n = np.array([np.arctan2(y[i], x[i]) for i in data['n']])
a = np.unwrap(a) % (np.pi * 2)
b = np.unwrap(b) % (np.pi * 2)
m = np.unwrap(m) % (np.pi * 2)
n = np.unwrap(n) % (np.pi * 2)
else:
a = np.array([ne[int(i)] for i in data('a')])
b = np.array([ne[int(i)] for i in data('b')])
m = np.array([ne[int(i)] for i in data('m')])
n = np.array([ne[int(i)] for i in data('n')])
if ind is not None:
a = a[ind]
b = b[ind]
m = m[ind]
n = n[ind]
anan = np.isnan(a)
a[anan] = b[anan]
b[anan] = np.nan
ab, am, an = np.abs(a - b), np.abs(a - m), np.abs(a - n)
bm, bn, mn = np.abs(b - m), np.abs(b - n), np.abs(m - n)
if circular:
for v in [ab, mn, bm, an]:
v[v > pi] = 2 * pi - v[v > pi]
# 2-point (default) 00000
sep = np.abs(a - m)
mid = (a + m) / 2
# 3-point (PD, DP) (now only b==-1 or n==-<1, check also for a and m)
imn = np.isfinite(n) * np.isnan(b)
mid[imn] = (m[imn] + n[imn]) / 2
sep[imn] = np.minimum(am[imn], an[imn]) + 10000 + 100 * (mn[imn]-1) + \
(np.sign(a[imn]-m[imn])/2+0.5) * 10000
iab = np.isfinite(b) * np.isnan(n)
mid[iab] = (a[iab] + b[iab]) / 2 # better 20000 or -10000?
sep[iab] = np.minimum(am[iab], bm[iab]) + 10000 + 100 * (ab[iab]-1) + \
(np.sign(a[iab]-n[iab])/2+0.5) * 10000
# + 10000*(a-m)
# 4-point alpha: 30000 (WE) or 4000 (SL)
iabmn = np.isfinite(a) & np.isfinite(b) & np.isfinite(m) & np.isfinite(n)
ialfa = np.copy(iabmn)
ialfa[iabmn] = (ab[iabmn] >= mn[iabmn] + 2) # old
mnmid = (m[iabmn] + n[iabmn]) / 2
ialfa[iabmn] = np.sign((a[iabmn] - mnmid) * (b[iabmn] - mnmid)) < 0
mid[ialfa] = (m[ialfa] + n[ialfa]) / 2
spac = np.minimum(bn[ialfa], bm[ialfa])
abmn3 = np.round((3 * mn[ialfa] - ab[ialfa]) * 10000) / 10000
sep[ialfa] = spac + (mn[ialfa]-1)*100*(abmn3 != 0) + \
30000 + (abmn3 < 0)*10000
# gradient
# %% 4-point beta
ibeta = np.copy(iabmn)
ibeta[iabmn] = (bm[iabmn] >= mn[iabmn]) & (~ialfa[iabmn])
if circular:
# print(ab[ibeta])
ibeta = np.copy(iabmn)
def _averageAngle(vs):
sumsin = 0
sumcos = 0
for v in vs:
sumsin += np.sin(v)
sumcos += np.cos(v)
return np.arctan2(sumsin, sumcos)
abC = _averageAngle([a[ibeta], b[ibeta]])
mnC = _averageAngle([m[ibeta], n[ibeta]])
mid[ibeta] = _averageAngle([abC, mnC])
# special case when dipoles are completely opposite
iOpp = abs(abs((mnC - abC)) - np.pi) < 1e-3
mid[iOpp] = _averageAngle([b[iOpp], m[iOpp]])
minAb = min(ab[ibeta])
sep[ibeta] = 50000 + (np.round(ab[ibeta]/minAb)) * 100 + \
np.round(np.minimum(np.minimum(am[ibeta], an[ibeta]),
np.minimum(bm[ibeta], bn[ibeta])) / minAb)
else:
mid[ibeta] = (a[ibeta] + b[ibeta] + m[ibeta] + n[ibeta]) / 4
sep[ibeta] = 50000 + (ab[ibeta] - 1) * 100 + np.minimum(
np.minimum(am[ibeta], an[ibeta]), np.minimum(bm[ibeta], bn[ibeta]))
# %% 4-point gamma
# multiply with electrode distance and add first position
if not circular:
mid *= de
mid += x0
return mid, sep
def showRayPaths(self, model=None, ax=None, **kwargs):
"""Show ray paths for `model` or last model for which the Jacobian was
calculated.
Parameters
----------
model : array
Velocity model for which to calculate and visualize ray paths (the
default is model for last Jacobian calculation in self.velocity).
ax : matplotlib.axes
Axes for the plot (the default is None).
**kwargs : type
Additional arguments passed to LineCollection (alpha, linewidths,
color, linestyles).
Returns
-------
ax : matplotlib.axes object
cb : matplotlib.colorbar object (only if model is provided)
Examples
--------
>>> # No reason to import matplotlib
>>> import pygimli as pg
>>> from pygimli.physics import Refraction
>>> from pygimli.physics.traveltime import createRAData
>>>
>>> x, y = 8, 6
>>> mesh = pg.createGrid(x, y)
>>> data = createRAData([(0,0)] + [(x, i) for i in range(y)], shotdistance=y+1)
>>> data.set("t", pg.RVector(data.size(), 1.0))
>>> rst = Refraction()
>>> rst.setDataContainer(data)
Data: Sensors: 7 data: 6
>>> rst.setMesh(mesh, 5)
>>> ax, cb = rst.showRayPaths()
"""
cbar = None
if model is None and self.velocity is None:
pg.info("No previous inversion result found and no model given.",
"Using homogeneous slowness model.")
self.velocity = pg.RVector(self.mesh.cellCount(), 1.0)
self.fop.createJacobian(1. / self.velocity)
if model is not None:
if self.velocity is not None:
if not np.allclose(model, self.velocity):
self.fop.createJacobian(1 / model)
ax, cbar = self.showResult(ax=ax, val=model)
_ = kwargs.setdefault("color", "w")
_ = kwargs.setdefault("alpha", 0.5)
_ = kwargs.setdefault("linewidths", 0.8)
else:
ax = self.showMesh(ax=ax)
# Due to different numbering scheme of way matrix
_, shots = np.unique(self.dataContainer("s"), return_inverse=True)
_, receivers = np.unique(self.dataContainer("g"), return_inverse=True)
# Collecting way segments for all shot/receiver combinations
segs = []
for s, g in zip(shots, receivers):
wi = self.fop.way(s, g)
points = self.fop.mesh().positions(withSecNodes=True)[wi]
segs.append(np.column_stack((pg.x(points), pg.y(points))))
line_segments = LineCollection(segs, **kwargs)
ax.add_collection(line_segments)
return ax, cbar
fig, a = plt.subplots()
drawMesh(a, mesh)
pg.show(mesh, axes=a, data=l[0])
cells = fwd.mesh().cells()
active_cells = [cells[i] for i in range(mesh.cellCount()) if l[0][i]]
# active_cells.append(cells[2044])
for c in active_cells:
pos = c.center()
gradient = 2000*c.grad(pos, fwd.timefields[0])
dx, dy = gradient.x(), gradient.y()
a.text(pos.x(), pos.y(), str(c.id()))
a.arrow(pos.x(), pos.y(), dx, dy)
ray = fwd.poslist
a.plot(pg.x(ray), pg.y(ray), 'm-*', )
plt.show()
# look at if next gradient contradicts the previous
# if so, then follow the interface instead (line segment to next node)
# this will stop when the gradients are more aligned.
# drawMesh(a, mesh)
# drawField(a, mesh, fwd.timefields[0], True, 'Spectral')
# drawStreamLines(a, mesh, fwd.timefields[0], nx=50, ny=50)
# some stats:
diff_rms = np.sqrt(np.sum(delta_t**2)/len(delta_t))
print("RMS of difference: {}".format(diff_rms))
print("Mean of difference: {}".format(np.mean(delta_t)))
print("Standard dev of difference: {}".format(np.std(delta_t)))