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 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 drawWaveField(ax, u):
ui = u / max(pg.abs(u))
ui = pg.logDropTol(ui, 1e-2)
cMax = max(pg.abs(ui))
drawField(ax, mesh, data=ui, cMin=-cMax, cMax=cMax, cmap='RdBu',
#interpolate=0, shading='gouraud'
)
def animate(i):
i = i*5
if i > len(uI)-1:
return
print("Frame:", i, "/", len(uI))
ui = uI[i]
ui = ui / max(pg.abs(ui))
ui = pg.logDropTol(ui, 1e-2)
cMax = max(pg.abs(ui))
pg.mplviewer.setMappableData(gci, ui,
cMin=-cMax, cMax=cMax,
logScale=False)
def drawWaveField(ax, u):
ui = u / max(pg.abs(u))
ui = pg.logDropTol(ui, 1e-2)
cMax = max(pg.abs(ui))
drawField(
ax,
mesh,
data=ui,
cMin=-cMax,
cMax=cMax,
cmap='RdBu',
#interpolate=0, shading='gouraud'
)
def animate(i):
i = i * 5
if i > len(uI) - 1:
return
print("Frame:", i, "/", len(uI))
ui = uI[i]
ui = ui / max(pg.abs(ui))
ui = pg.logDropTol(ui, 1e-2)
cMax = max(pg.abs(ui))
pg.viewer.mpl.setMappableData(gci,
ui,
cMin=-cMax,
cMax=cMax,
logScale=False)
def readTOMfile(filename, ndig=2, roundto=0):
"""Read Reflex tomography (*.TOM) file"""
t, xT, zT, xR, zR = np.loadtxt(filename, usecols=(0, 2, 3, 4, 5), unpack=1)
if roundto > 0:
pT = (np.round(xT / roundto) - np.round(zT / roundto) * 1j) * roundto
pR = (np.round(xR / roundto) - np.round(zR / roundto) * 1j) * roundto
else:
pT = xT.round(ndig) - zT.round(ndig) * 1j
pR = xR.round(ndig) - zR.round(ndig) * 1j
pU = np.unique(np.hstack((pT, pR)))
iT = np.array([np.nonzero(pU == pi)[0][0] for pi in pT], dtype=float)
iR = np.array([np.nonzero(pU == pi)[0][0] for pi in pR], dtype=float)
data = pg.DataContainer()
for pp in pU:
data.createSensor(pg.RVector3(pp.real, pp.imag))
for tok in ['s', 'g']:
data.registerSensorIndex(tok)
data.resize(len(t))
data.set('t', t)
data.set('s', iT)
data.set('g', iR)
data.markValid(pg.abs(data('s') - data('g')) > 0)
return data
def readTOMfile(filename, ndig=2, roundto=0):
"""Read Reflex tomography (*.TOM) file"""
t, xT, zT, xR, zR = np.loadtxt(filename, usecols=(0, 2, 3, 4, 5), unpack=1)
if roundto > 0:
pT = (np.round(xT/roundto) - np.round(zT/roundto) * 1j) * roundto
pR = (np.round(xR/roundto) - np.round(zR/roundto) * 1j) * roundto
else:
pT = xT.round(ndig) - zT.round(ndig) * 1j
pR = xR.round(ndig) - zR.round(ndig) * 1j
pU = np.unique(np.hstack((pT, pR)))
iT = np.array([np.nonzero(pU == pi)[0][0] for pi in pT], dtype=float)
iR = np.array([np.nonzero(pU == pi)[0][0] for pi in pR], dtype=float)
data = pg.DataContainer()
for pp in pU:
data.createSensor(pg.RVector3(pp.real, pp.imag))
for tok in ['s', 'g']:
data.registerSensorIndex(tok)
data.resize(len(t))
data.set('t', t)
data.set('s', iT)
data.set('g', iR)
data.markValid(pg.abs(data('s') - data('g')) > 0)
return data
def drawSeismogramm(axes, mesh, u, ids, dt, i=None):
r"""Extract and show time series from wave field
Parameters
----------
"""
axes.set_xlim(-20., 20.)
axes.set_ylim(0., dt * len(u) * 1000)
axes.set_aspect(1)
axes.set_ylabel('Time in ms')
if i is None:
i = len(u) - 1
t = np.linspace(0, i * dt * 1000, i + 1)
for iw, n in enumerate(ids):
pos = mesh.node(n).pos()
print(pos)
axes.plot(pos[0], 0.05, '^', color='black')
trace = pg.cat(pg.RVector(0), u[:(i + 1), n])
# print(i+1, n)
# print(trace, (max(pg.abs(trace))))
# if max(pg.abs(trace)) > 1e-8:
trace *= np.exp(0.5 * t)
trace /= (max(pg.abs(trace)) * 1.5)
drawWiggle(axes, trace, t=t, xoffset=pos[0])
axes.invert_yaxis()
def drawSeismogramm(axes, mesh, u, ids, dt, i=None):
r"""Extract and show time series from wave field
Parameters
----------
"""
axes.set_xlim(-20., 20.)
axes.set_ylim(0., dt*len(u)*1000)
axes.set_aspect(1)
axes.set_ylabel('Time in ms')
if i is None:
i = len(u)-1
t = np.linspace(0, i*dt*1000, i+1)
for iw, n in enumerate(ids):
pos = mesh.node(n).pos()
print(pos)
axes.plot(pos[0], 0.05, '^', color='black')
trace = pg.cat(pg.RVector(0), u[:(i+1), n])
# print(i+1, n)
# print(trace, (max(pg.abs(trace))))
# if max(pg.abs(trace)) > 1e-8:
trace *= np.exp(0.5*t)
trace /= (max(pg.abs(trace))*1.5)
drawWiggle(axes, trace, t=t, xoffset=pos[0])
axes.invert_yaxis()
def response_mt(self, par, i=0):
"""Return response (multi threaded)."""
verbose = 1
if i == 0:
ws = self.ws
else:
ws = WorkSpace()
mesh = pg.Mesh(self.mesh())
k = self.createMappedModel(par)
ws.mesh, ws.vel, ws.p, ws.k, ws.velC = solveDarcy(mesh,
k=k,
p0=0.75,
verbose=verbose)
ws.sat = solveAdvection(ws.mesh,
ws.vel,
self.timesAdvection,
diffusion=pg.abs(ws.velC.T) * 1e-2,
verbose=verbose)
ws.meshERT, ws.scheme, ws.resis, ws.rhoa, ws.rhoaR, ws.derr = \
solveERT(ws.mesh, ws.sat[self.timesERT], verbose=verbose)
return ws.rhoaR.flatten()
def animate(i):
print(out + ": Frame:", i, "/", len(data))
pg.mplviewer.setMappableData(gci,
pg.abs(data[i]),
cMin=cMin,
cMax=cMax,
logScale=logScale)
def animate(i):
if i > 0:
tic = time.time()
i = i * 10
ax.clear()
uShow = drawWaveField(ax, u[i,:])
print(i, time.time()-tic, len(u), min(pg.abs(u[i,:])), min(u[i,:]), max(u[i,:]), dt*i)
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 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 _test_(mesh, show=False):
vTest = 0.1
u = pg.solve(mesh, a=1, f=0,
bc={'Node': [mesh.findNearestNode([0.0, 0.0]), 0.],
'Neumann': [[1, -vTest], [2, vTest]]}, verbose=0)
if show:
if mesh.dim() == 1:
pg.plt.plot(pg.x(mesh), u)
elif mesh.dim() == 2:
pg.show(grid, pg.abs(v))
pg.show(grid, v, showMesh=1)
pg.wait()
v = pg.solver.grad(mesh, u)
#print("|v|:", min(pg.abs(v)), max(pg.abs(v)), pg.mean(pg.abs(v)))
np.testing.assert_allclose(pg.abs(v), np.ones(mesh.cellCount())*vTest)
return v
def _test_(mesh, show=False):
vTest = 0.1
u = pg.solve(mesh, a=1, f=0,
bc={'Node': [mesh.findNearestNode([0.0, 0.0]), 0.],
'Neumann': [[1, -vTest], [2, vTest]]}, verbose=0)
if show:
if mesh.dim() == 1:
pg.plt.plot(pg.x(mesh), u)
elif mesh.dim() == 2:
pg.show(grid, pg.abs(v))
pg.show(grid, v, showMesh=1)
pg.wait()
v = pg.solver.grad(mesh, u)
#print("|v|:", min(pg.abs(v)), max(pg.abs(v)), pg.mean(pg.abs(v)))
np.testing.assert_allclose(pg.abs(v), np.ones(mesh.cellCount())*vTest)
return v
def calcApparentResistivities(mesh, meshERT, poro, rhoBrine):
ert = ERT(verbose=False)
meshFOP = appendTriangleBoundary(meshERT,
xbound=50, ybound=50, marker=1,
quality=34.0, smooth=False,
markerBoundary=1,
isSubSurface=False, verbose=False)
swatch = pg.Stopwatch(True)
print("res 1:", swatch.duration(True))
resis = resistivityArchie(rBrine=rhoBrine, porosity=poro, S=1.0,
mesh=mesh, meshI=meshFOP)
print("res 2:", swatch.duration(True))
ertPointsX = [pg.RVector3(x, 0) for x in np.arange(-19, 19.1, 1)]
ertScheme = ert.createData(ertPointsX, scheme="Dipole Dipole (CC-PP)")
solutionName = createCacheName('appRes', mesh) + "-" + \
str(ertScheme.size()) + "-" + str(len(rhoBrine))
try:
rhoa = np.load(solutionName + '.bmat.npy')
ertData = pb.DataContainerERT(solutionName + '.dat')
except Exception as e:
print(e)
print("Building .... ")
rhoa = np.zeros((len(resis), ertScheme.size()))
ertScheme.set('k', pb.geometricFactor(ertScheme))
ertData = ert.simulate(meshFOP, resis[0], ertScheme)
errPerc = 1
errVolt = 1e-5
voltage = ertData('rhoa') / ertData('k')
ertData.set('err', pg.abs(errVolt / voltage) + errPerc / 100.0)
print('err min:', min(ertData('err'))*100, 'max:',
max(ertData('err'))*100)
ertData.save(solutionName + '.dat', 'a b m n rhoa err k')
for i in range(0, len(resis)):
tic = time.time()
rhoa[i] = ert.fop.response(resis[i])
rand = pg.RVector(len(rhoa[i]))
pg.randn(rand)
rhoa[i] *= (1.0 + rand * ertData('err'))
print(i, "/", len(resis), " : ", time.time()-tic, "s",
"min:", min(resis[i]), "max:", max(resis[i]),
"min:", min(rhoa[i]), "max:", max(rhoa[i]))
np.save(solutionName + '.bmat', rhoa)
return meshFOP, resis, ertData, rhoa
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 invert(self, sensorPositions, gz, errAbs,
verbose=0, **kwargs):
"""
"""
self.fop.setVerbose(verbose)
self.inv.setMaxIter(kwargs.pop('maxiter', 10))
self.inv.setLambda(kwargs.pop('lambd', 10))
self.fop.setSensorPositions(sensorPositions)
mesh = kwargs.pop('mesh', None)
if mesh is None:
raise('implement me')
self.setParaMesh(mesh)
startModel = pg.RVector(self.fop.regionManager().parameterCount(), 0.0)
self.inv.setForwardOperator(self.fop)
self.fop.regionManager().setConstraintType(10)
# check err here
self.inv.setData(gz)
self.inv.setAbsoluteError(errAbs)
self.inv.setModel(startModel)
model = self.inv.run()
return model
# tl can start here
values = model
if values is not None:
if isinstance(values, pg.RVector):
values = [values]
elif isinstance(values, np.ndarray):
if values.ndim == 1:
values = [values]
allModel = pg.RMatrix(len(values)+1, len(model))
allModel[0] = model
self.inv.setVerbose(False)
for i in range(1, len(values)):
tic = time.time()
self.inv.setModel(model)
self.inv.setReferenceModel(model)
dData = pg.abs(values[i] - data)
# relModel = self.inv.invSubStep(pg.log(dData))
# allModel[i] = model * pg.exp(relModel)
relModel = self.inv.invSubStep(dData)
allModel[i] = model + relModel
print(i, "/", len(values), " : ", time.time()-tic, "s")
return allModel
return model
def animate(i):
if i > 0:
tic = time.time()
i = i * 10
ax.clear()
uShow = drawWaveField(ax, u[i, :])
print(i,
time.time() - tic, len(u), min(pg.abs(u[i, :])), min(u[i, :]),
max(u[i, :]), dt * i)
def logDropTol( p, droptol = 1e-3 ):
""""""
tmp = pg.RVector( p );
tmp = pg.abs( tmp / droptol )
tmp.setVal( 1.0, pg.find( tmp < 1.0 ) )
#for i, v in enumerate( tmp ):
#tmp[ i ] = abs( tmp[ i ] / droptol );
#if tmp[ i ] < 1.0: tmp[ i ] = 1.0;
tmp = pg.log10( tmp );
tmp *= pg.sign( p );
return tmp;
def _test_(mesh):
vTest = 0.1
u = pg.solve(mesh,
a=1,
bc={
'Node': [mesh.findNearestNode([0.0, 0.0]), 0.],
'Neumann': [[1, -vTest], [2, vTest]]
})
v = pg.solver.grad(mesh, u)
#print("|v|:", min(pg.abs(v)), max(pg.abs(v)), pg.mean(pg.abs(v)))
np.testing.assert_allclose(pg.abs(v),
np.ones(mesh.cellCount()) * vTest)
return v
def logDropTol(p, droptol=1e-3):
"""
Example
-------
>>> from pygimli.utils import logDropTol
>>> x = logDropTol((-10,-1,0,1,100))
>>> print(x.array())
[-4. -3. 0. 3. 5.]
"""
tmp = pg.RVector(p)
tmp = pg.abs(tmp / droptol)
tmp.setVal(1.0, pg.find(tmp < 1.0))
tmp = pg.log10(tmp)
tmp *= pg.sign(p)
return tmp
def drawSeismogramm(ax, mesh, u, dt, ids=None, pos=None, i=None):
r"""Extract and show time series from wave field
Parameters
----------
ids: list
List of node ids for the given mesh.
pos : list
List of positions for the given mesh. We will look for the nearest node.
"""
ax.set_xlim(mesh.xmin(), mesh.xmax())
ax.set_ylim(0., dt * len(u) * 1000)
ax.set_aspect(1)
ax.set_ylabel('Time (ms)')
ax.set_xlabel('Distance (m)')
if i is None:
i = len(u) - 1
t = np.linspace(0, i * dt * 1000, i + 1)
if ids is None and pos is not None:
ids = []
for p in pos:
ids.append(mesh.findNearestNode(p))
xDist = mesh.node(0).pos().distance(mesh.node(1).pos())
for iw, n in enumerate(ids):
pos = mesh.node(n).pos()
ax.plot(pos[0], 0.05, '^', color='black')
print(pos)
trace = pg.cat(pg.RVector(0), u[:(i + 1), n])
# print(i+1, n)
# print(trace, (max(pg.abs(trace))))
# if max(pg.abs(trace)) > 1e-8:
trace *= np.exp(1 / 1000 * t)
trace /= (max(pg.abs(trace)))
trace *= 10
drawWiggle(ax, trace, t=t, xoffset=pos[0])
ax.invert_yaxis()
def logDropTol(p, droptol=1e-3):
"""Create logarithmic scaled copy of p.
Examples
--------
>>> from pygimli.utils import logDropTol
>>> x = logDropTol((-10, -1, 0, 1, 100))
>>> print(x.array())
[-4. -3. 0. 3. 5.]
"""
tmp = pg.RVector(p)
tmp = pg.abs(tmp / droptol)
tmp.setVal(1.0, pg.find(tmp < 1.0))
tmp = pg.log10(tmp)
tmp *= pg.sign(p)
return tmp
def drawSeismogramm(ax, mesh, u, dt, ids=None, pos=None, i=None):
r"""Extract and show time series from wave field
Parameters
----------
ids: list
List of node ids for the given mesh.
pos : list
List of positions for the given mesh. We will look for the nearest node.
"""
ax.set_xlim(mesh.xmin(), mesh.xmax())
ax.set_ylim(0., dt*len(u)*1000)
ax.set_aspect(1)
ax.set_ylabel('Time (ms)')
ax.set_xlabel('Distance (m)')
if i is None:
i = len(u)-1
t = np.linspace(0, i*dt*1000, i+1)
if ids is None and pos is not None:
ids = []
for p in pos:
ids.append(mesh.findNearestNode(p))
xDist = mesh.node(0).pos().distance(mesh.node(1).pos())
for iw, n in enumerate(ids):
pos = mesh.node(n).pos()
ax.plot(pos[0], 0.05, '^', color='black')
trace = pg.cat(pg.RVector(0), u[:(i+1), n])
# print(i+1, n)
# print(trace, (max(pg.abs(trace))))
# if max(pg.abs(trace)) > 1e-8:
trace *= np.exp(1/1000 * t)
trace /= (max(pg.abs(trace)))
trace *= 10
drawWiggle(ax, trace, t=t, xoffset=pos[0])
ax.invert_yaxis()
def response_mt(self, par, i=0):
"""Return response (multi threaded)."""
verbose = 1
if i == 0:
ws = self.ws
else:
ws = WorkSpace()
mesh = pg.Mesh(self.mesh())
k = self.createMappedModel(par)
ws.mesh, ws.vel, ws.p, ws.k, ws.velC = solveDarcy(mesh, k=k, p0=0.75,
verbose=verbose)
ws.sat = solveAdvection(ws.mesh, ws.vel, self.timesAdvection,
diffusion=pg.abs(ws.velC.T) * 1e-2,
verbose=verbose)
ws.meshERT, ws.scheme, ws.resis, ws.rhoa, ws.rhoaR, ws.derr = \
solveERT(ws.mesh, ws.sat[self.timesERT], verbose=verbose)
return ws.rhoaR.flatten()
# %% # as desired for a roughness operator. Therefore, an additional matrix called # :py:func:`pg.matrix.GeostatisticalConstraintsMatrix` # was implemented where this spur is corrected for. # It is, like the correlation matrix, created by a mesh, a list of correlation # lengths I, a dip angle# that distorts the x/y plane and a strike angle # towards the third direction. # C = pg.matrix.GeostatisticConstraintsMatrix(mesh=mesh, I=5) # %% # In order to extract a certain column, we generate a vector with a single 1 vec = pg.Vector(mesh.cellCount()) vec[ind] = 1.0 pg.show(mesh, pg.log10(pg.abs(C * vec)), cMin=-6, cMax=0, cMap="magma_r") # %% # The constraints have a rather small footprint compared to the correlation # (note the logarithmic scale) but still to the whole mesh unlike the classical # constraint matrices that only include relations to neighboring cells. # %% # Such a matrix can also be defined for different ranges and a dip angle Cdip = pg.matrix.GeostatisticConstraintsMatrix(mesh=mesh, I=[10, 3], dip=-25) pg.show(mesh, pg.log10(pg.abs(Cdip * vec)), cMin=-6, cMax=0, cMap="magma_r") # %% # In order to illustrate the role of the constraints, we use a very simple # mapping forward operator that retrieves the values in the mesh at some given # positions. The constraints are therefore used as interpolation operators.
# towards the third direction. # C = pg.matrix.GeostatisticConstraintsMatrix(mesh=mesh, I=5) # %% # In order to extract a column, we generate a vector with a single 1, multiply vec = pg.Vector(mesh.cellCount()) vec[ind] = 1.0 cor = C * vec # %% # and plot it using a linear or logarithmic scale kwLin = dict(cMin=-1, cMax=1, cMap="bwr") ax, cb = pg.show(mesh, cor, **kwLin) kwLog = dict(cMin=1e-3, cMax=1, cMap="magma_r", logScale=True) ax, cb = pg.show(mesh, pg.abs(cor), **kwLog) # %% # The constraints have a rather small footprint compared to the correlation # if one considers values below a certain threshold as insignificant. # %% # Such a matrix can also be defined for different ranges and dip angles, e.g. Cdip = pg.matrix.GeostatisticConstraintsMatrix(mesh=mesh, I=[9, 2], dip=-25) ax, cb = pg.show(mesh, Cdip * vec, **kwLin) ax, cb = pg.show(mesh, pg.abs(Cdip * vec), **kwLog) # %% # Even in the linear scale, but more in the log scale one can see the # regularization footprint in the shape of an ellipsis.
x = np.arange( -10, 10, 1. );
rho = g.RVector( len( mesh.cellAttributes() ), 1. ) * 2000.0
print rho
pnts = g.stdVectorRVector3()
for i in x:
pnts.append( g.RVector3( i, 0.0001 ) )
gzNum = []
gzNum.append( g.calcGCells( pnts, mesh, rho, 0 )[0] )
#P.plot(x, gzNum[0], label = str(0) )
for i in range( 1, 10 ):
gzNum.append( g.calcGCells( pnts, mesh, rho, i )[0] )
err = g.abs(gzNum[i]/gzNum[0]-1.)*100.
P.semilogy(x, err, label = str(i) )
P.plot(x, gzNum[i], label = str(i) )
P.legend()
#P.plot(x, p1 )
test2d()
#test3d()
P.show()
from pybert.manager import ERTManager
from pygimli.physics import Refraction
from pygimli.physics.traveltime import createRAData
mesh = pg.load("mesh.bms")
sensors = np.load("sensors.npy", allow_pickle=True)
rhotrue = np.loadtxt("rhotrue.dat")
veltrue = np.loadtxt("veltrue.dat")
pg.boxprint("Simulate apparent resistivities")
# Create more realistic data set
ertScheme = pb.createData(sensors, "dd", spacings=[1, 2, 4])
k = pb.geometricFactors(ertScheme)
ertScheme.markInvalid(pg.abs(k) > 5000)
ertScheme.removeInvalid()
ert = ERTManager()
# Create suitable mesh for ert forward calculation
# NOTE: In the published results paraMaxCellSize=1.0 was used, which is
# increased here to allow testing on Continuous Integration services.
meshERTFWD = mt.createParaMesh(ertScheme,
quality=33.5,
paraMaxCellSize=2.0,
paraDX=0.2,
boundaryMaxCellSize=50,
smooth=[1, 10],
paraBoundary=30)
pg.show(meshERTFWD)
mesh = pg.meshtools.createParaMesh2dGrid(data.sensorPositions())
fop = DCMultiElectrodeModellingC(mesh, data, verbose=True)
print(dir(fop))
print(fop.jacobian())
print(fop.jacobian().rows())
#fop = pb.DCMultiElectrodeModelling(mesh, data)
fop.regionManager().region(1).setBackground(True)
fop.createRefinedForwardMesh(refine=True, pRefine=False)
cData = pb.getComplexData(data)
mag = pg.abs(cData)
phi = -pg.phase(cData)
print(pg.norm(mag-data('rhoa')))
print(pg.norm(phi-data('ip')/1000))
inv = pg.Inversion(pg.cat(mag, phi),
fop,
verbose=True, dosave=True)
dataTrans = pg.trans.TransCumulative()
datRe = pg.trans.TransLog()
datIm = pg.trans.Trans()
dataTrans.add(datRe, data.size())
dataTrans.add(datIm, data.size())
def animate(i):
print(out + ": Frame:", i, "/", len(data))
pg.mplviewer.setMappableData(gci, pg.abs(data[i]), cMin=cMin, cMax=cMax, logScale=logScale)
vel = -pg.solver.grad(mesh, p) * np.asarray([K, K, K]).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,
def _test_(mesh, p2=False, show=False):
"""
\Laplace u = 0
x = [0, -1], y, z
int_0^1 u = 0
du/dn = 1 (xMin) (inflow on -x)
du/dn = -1 (xMax) (outflow on +x)
du/dn = 0 (rest)
u = 0.5 -x linear solution, i.e., exact with p1
du/dn = -1 (xMin) (outflow -x)
du/dn = -1 (xMax) (outflow +x)
du/dn = 0 (rest)
u = -1/6 + x -x² quadratic solution, i.e., exact with p2
"""
uExact = lambda x, a, b, c: a + b * x + c * x**2
bc = {'Neumann': {1: 1.0, 2: -1.0}}
uE = uExact(pg.x(mesh), 0.5, -1.0, 0.0)
if p2 is True:
mesh = mesh.createP2()
bc['Neumann'][1] = -1.0
uE = uExact(pg.x(mesh), -1 / 6, 1.0, -1.0)
u = pg.solve(mesh, a=1, f=0, bc=bc, verbose=0)
v = pg.solver.grad(mesh, u)
if show:
if mesh.dim() == 1:
idx = np.argsort(pg.x(mesh))
fig, ax = pg.plt.subplots()
ax.plot(pg.x(mesh)[idx], uE[idx], label='exact')
ax.plot(pg.x(mesh)[idx], u[idx], 'o', label='FEM')
model, response = pg.frameworks.fit(uExact,
u[idx],
x=pg.x(mesh)[idx])
print(model)
ax.plot(pg.x(mesh)[idx], response, 'x', label='FIT')
ax.grid(True)
ax.legend()
elif mesh.dim() == 2:
pg.show(mesh, u, label='u')
ax, _ = pg.show(mesh, pg.abs(v), label='abs(grad(u))')
pg.show(mesh, v, showMesh=1, ax=ax)
pg.info("int Domain:", pg.solver.intDomain(u, mesh))
pg.info("int Domain:",
pg.solver.intDomain([1.0] * mesh.nodeCount(), mesh),
sum(mesh.cellSizes()))
pg.wait()
## test du/dn of solution and compare with Neumann BC
for m, val in bc['Neumann'].items():
for b in mesh.boundaries(mesh.boundaryMarkers() == m):
## for non Tailor Hood Elements, the gradient is only
# known at the cell center so the accuracy for the
# gradient depends on the distance boundary to cell
# center. Accuracy = du/dx(dx) = 1-2x = 2 * dx
c = b.leftCell()
dx = c.center().dist(b.center())
dudn = b.norm(c).dot(v[c.id()])
if p2:
np.testing.assert_allclose(dudn, val, atol=2 * dx)
#print(dudn, val)
else:
np.testing.assert_allclose(dudn, val)
np.testing.assert_allclose(pg.solver.intDomain([1.0]*\
mesh.nodeCount(), mesh),
sum(mesh.cellSizes()))
np.testing.assert_allclose(pg.solver.intDomain(u, mesh),
0.0,
atol=1e-8)
np.testing.assert_allclose(np.linalg.norm(u - uE), 0.0, atol=1e-8)
return v
def calcApparentResistivities(mesh, meshERT, poro, rhoBrine):
ert = ERT(verbose=False)
meshFOP = appendTriangleBoundary(meshERT,
xbound=50,
ybound=50,
marker=1,
quality=34.0,
smooth=False,
markerBoundary=1,
isSubSurface=False,
verbose=False)
swatch = pg.Stopwatch(True)
print("res 1:", swatch.duration(True))
resis = resistivityArchie(rBrine=rhoBrine,
porosity=poro,
S=1.0,
mesh=mesh,
meshI=meshFOP)
print("res 2:", swatch.duration(True))
ertPointsX = [pg.RVector3(x, 0) for x in np.arange(-19, 19.1, 1)]
ertScheme = ert.createData(ertPointsX, scheme="Dipole Dipole (CC-PP)")
solutionName = createCacheName('appRes', mesh) + "-" + \
str(ertScheme.size()) + "-" + str(len(rhoBrine))
try:
rhoa = np.load(solutionName + '.bmat.npy')
ertData = pb.DataContainerERT(solutionName + '.dat')
except Exception as e:
print(e)
print("Building .... ")
rhoa = np.zeros((len(resis), ertScheme.size()))
ertScheme.set('k', pb.geometricFactor(ertScheme))
ertData = ert.simulate(meshFOP, resis[0], ertScheme)
errPerc = 1
errVolt = 1e-5
voltage = ertData('rhoa') / ertData('k')
ertData.set('err', pg.abs(errVolt / voltage) + errPerc / 100.0)
print('err min:',
min(ertData('err')) * 100, 'max:',
max(ertData('err')) * 100)
ertData.save(solutionName + '.dat', 'a b m n rhoa err k')
for i in range(0, len(resis)):
tic = time.time()
rhoa[i] = ert.fop.response(resis[i])
rand = pg.RVector(len(rhoa[i]))
pg.randn(rand)
rhoa[i] *= (1.0 + rand * ertData('err'))
print(i, "/", len(resis), " : ",
time.time() - tic, "s", "min:", min(resis[i]), "max:",
max(resis[i]), "min:", min(rhoa[i]), "max:", max(rhoa[i]))
np.save(solutionName + '.bmat', rhoa)
return meshFOP, resis, ertData, rhoa
def invert(self, data, values=None, verbose=0, **kwargs):
"""
Invert the given data.
A parametric mesh for the inversion will be created if non is given
before.
Parameters
----------
"""
self.fop.setVerbose(verbose)
self.inv.setVerbose(verbose)
self.inv.setMaxIter(kwargs.pop('maxiter', 10))
self.inv.setLambda(kwargs.pop('lambd', 10))
if self.paraMesh is None:
self.paraMesh = createParaMesh2dGrid(data.sensorPositions(),
**kwargs)
self.setParaMesh(self.paraMesh)
if verbose:
print(self.paraMesh)
# pg.show(self.paraMesh)
err = data('err')
rhoa = data('rhoa')
startModel = pg.RVector(self.fop.regionManager().parameterCount(),
pg.median(rhoa))
self.fop.setData(data)
self.inv.setForwardOperator(self.fop)
# check err here
self.inv.setData(rhoa)
self.inv.setError(err)
self.inv.setModel(startModel)
model = self.inv.run()
if values is not None:
if isinstance(values, pg.RVector):
values = [values]
elif isinstance(values, np.ndarray):
if values.ndim == 1:
values = [values]
allModel = pg.RMatrix(len(values), len(model))
self.inv.setVerbose(False)
for i in range(len(values)):
print(i)
tic = time.time()
self.inv.setModel(model)
self.inv.setReferenceModel(model)
dData = pg.abs(values[i] / rhoa)
relModel = self.inv.invSubStep(pg.log(dData))
allModel[i] = model * pg.exp(relModel)
print(i, "/", len(values), " : ",
time.time() - tic, "s min/max: ", min(allModel[i]),
max(allModel[i]))
return allModel
return model
print('Solve Darcy equation ... ')
# Map regions to hydraulic conductivity in $m/s$
kMap = [[1, 1e-8], [2, 5e-3], [3, 1e-4], [4, 8e-4]]
# Map conductivity value per region to each cell in the given mesh
K = pg.solver.parseMapToCellArray(kMap, mesh)
# Dirichlet conditions for hydraulic potential
pBound = [[[1, 2, 3], 0.75], [[5, 6, 7], 0.0]]
# Solve for hydraulic potential
p = pg.solver.solveFiniteElements(mesh, a=K, bc={'Dirichlet': pBound})
# Solve velocity as gradient of hydraulic potential
vel = -pg.solver.grad(mesh, p) * np.asarray([K, K, K]).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, vel)
def invert(self, data, values=None, verbose=0, **kwargs):
"""
Invert the given data.
A parametric mesh for the inversion will be created if non is given
before.
Parameters
----------
"""
self.fop.setVerbose(verbose)
self.inv.setVerbose(verbose)
self.inv.setMaxIter(kwargs.pop('maxiter', 10))
self.inv.setLambda(kwargs.pop('lambd', 10))
if self.paraMesh is None:
self.paraMesh = createParaMesh2dGrid(data.sensorPositions(),
**kwargs)
self.setParaMesh(self.paraMesh)
if verbose:
print(self.paraMesh)
# pg.show(self.paraMesh)
err = data('err')
rhoa = data('rhoa')
startModel = pg.RVector(self.fop.regionManager().parameterCount(),
pg.median(rhoa))
self.fop.setData(data)
self.inv.setForwardOperator(self.fop)
# check err here
self.inv.setData(rhoa)
self.inv.setError(err)
self.inv.setModel(startModel)
model = self.inv.run()
if values is not None:
if isinstance(values, pg.RVector):
values = [values]
elif isinstance(values, np.ndarray):
if values.ndim == 1:
values = [values]
allModel = pg.RMatrix(len(values), len(model))
self.inv.setVerbose(False)
for i in range(len(values)):
print(i)
tic = time.time()
self.inv.setModel(model)
self.inv.setReferenceModel(model)
dData = pg.abs(values[i] / rhoa)
relModel = self.inv.invSubStep(pg.log(dData))
allModel[i] = model * pg.exp(relModel)
print(i, "/", len(values), " : ", time.time()-tic,
"s min/max: ", min(allModel[i]), max(allModel[i]))
return allModel
return model
# Dirichlet conditions for hydraulic potential
pBound = [[[1, 2, 3], 0.75], [[5, 6, 7], 0.0]]
# Solve for hydraulic potential
p = pg.solver.solveFiniteElements(mesh, a=K, bc={'Dirichlet': pBound})
# Solve velocity as gradient of hydraulic potential
vel = -pg.solver.grad(mesh, p) * np.asarray([K, K, K]).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.Vector(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
# %%
# as desired for a roughness operator. Therefore, an additional matrix called
# :py:mod:`pg.matrix.GeostatisticalConstraintsMatrix`
# was implemented where this spur is corrected for.
# It is, like the correlation matrix, created by a mesh, a list of correlation
# lengths I, a dip angle# that distorts the x/y plane and a strike angle
# towards the third direction.
#
C = pg.matrix.GeostatisticConstraintsMatrix(mesh=mesh, I=5)
# %%
# In order to extract a certain column, we generate a vector with a single 1
vec = pg.Vector(mesh.cellCount())
vec[ind] = 1.0
ax, cb = pg.show(mesh,
pg.log10(pg.abs(C * vec)),
cMin=-6,
cMax=0,
cMap="magma_r")
# %%
# The constraints have a rather small footprint compared to the correlation
# (note the logarithmic scale) but still to the whole mesh unlike the classical
# constraint matrices that only include relations to neighboring cells.
# %%
# Such a matrix can also be defined for different ranges and dip angles, e.g.
Cdip = pg.matrix.GeostatisticConstraintsMatrix(mesh=mesh, I=[10, 3], dip=-25)
ax, cb = pg.show(mesh,
pg.log10(pg.abs(Cdip * vec)),
cMin=-6,
mesh = pg.meshtools.createParaMesh2dGrid(data.sensorPositions())
fop = DCMultiElectrodeModellingC(mesh, data, verbose=True)
print(dir(fop))
print(fop.jacobian())
print(fop.jacobian().rows())
#fop = pb.DCMultiElectrodeModelling(mesh, data)
fop.regionManager().region(1).setBackground(True)
fop.createRefinedForwardMesh(refine=True, pRefine=False)
cData = pb.getComplexData(data)
mag = pg.abs(cData)
phi = -pg.phase(cData)
print(pg.norm(mag-data('rhoa')))
print(pg.norm(phi-data('ip')/1000))
inv = pg.RInversion(pg.cat(mag, phi),
fop,
verbose=True, dosave=True)
dataTrans = pg.RTransCumulative()
datRe = pg.RTransLog()
datIm = pg.RTrans()
dataTrans.add(datRe, data.size())
dataTrans.add(datIm, data.size())
geom = plc + cube
mesh = mt.createMesh(geom, area=4)
for bound in mesh.boundaries():
x = bound.center().x()
if x == mesh.xmin():
bound.setMarker(1)
elif x == mesh.xmax():
bound.setMarker(2)
kMap = {1: 1e-4, 2: 1e-6}
kArray = pg.solver.parseMapToCellArray(list(kMap), mesh) # dict does not work
kArray = np.column_stack([kArray] * 3)
bc = {"Dirichlet": {1: 20.0, 2: 10.0}}
h = pg.solver.solveFiniteElements(mesh, kMap, bc=bc)
vel = -pg.solver.grad(mesh, h) * kArray
pg.show(mesh, h, label="Hydraulic head (m)")
ax, _ = pg.show(mesh, hold=True, alpha=0.3)
drawStreamLines(ax, mesh, vel, radius=.1, source_radius=10)
drawSlice(ax,
mesh,
normal=[0, 1, 0],
data=pg.abs(vel),
label="Absolute velocity")
ax.show()
# We know the exact solution so we can compare it to the numerical results.
# Unfortunately, the point source singularity does not allow a good integration
# measure for the accuracy of the resulting field so we just look for the
# differences.
#
uAna = pg.Vector(
list(
map(lambda p__: uAnalytical(p__, sourcePosA, k, sigma),
mesh.positions())))
uAna -= pg.Vector(
list(
map(lambda p__: uAnalytical(p__, sourcePosB, k, sigma),
mesh.positions())))
ax = pg.show(mesh,
data=pg.abs(uAna - u),
cMap="Reds",
orientation='horizontal',
label='|$u_{exact}$ -$u$|',
logScale=True,
cMin=1e-7,
cMax=1e-1,
contourLines=False,
nCols=12,
nLevs=7,
showMesh=True)[0]
#print('l2:', pg.pf(pg.solver.normL2(uAna-u)))
print('L2:', pg.pf(pg.solver.normL2(uAna - u, mesh)))
print('H1:', pg.pf(pg.solver.normH1(uAna - u, mesh)))
np.testing.assert_approx_equal(pg.solver.normL2(uAna - u, mesh),
x = np.arange(-10, 10, 1.0)
rho = pg.RVector(len(mesh.cellAttributes()), 1.0) * 2000.0
print (rho)
pnts = pg.stdVectorRVector3()
for i in x:
pnts.append(pg.RVector3(i, 0.0001))
gzNum = []
gzNum.append(pg.calcGCells(pnts, mesh, rho, 0)[0])
# plt.plot(x, gzNum[0], label=str(0))
for i in range(1, 10):
gzNum.append(pg.calcGCells(pnts, mesh, rho, i)[0])
err = pg.abs(gzNum[i] / gzNum[0] - 1.0) * 100.0
plt.semilogy(x, err, label=str(i))
plt.plot(x, gzNum[i], label=str(i))
plt.legend()
# plt.plot(x, p1 )
test2d()
# test3d()
plt.show()
def estimateError(self,
data,
absoluteError=0.001,
relativeError=0.03,
absoluteUError=None,
absoluteCurrent=0.1):
""" Estimate error composed of an absolute and a relative part.
This is a static method and will not alter any member of the Manager
Parameters
----------
absoluteError : float [0.001]
Absolute data error in Ohm m. Need 'rhoa' values in data.
relativeError : float [0.03]
relative error level in %/100
absoluteUError : float [0.001]
Absolute potential error in V. Need 'u' values in data. Or
calculate them from 'rhoa', 'k' and absoluteCurrent if no 'i'
is given
absoluteCurrent : float [0.1]
Current level in A for reconstruction for absolute potential V
Returns
-------
error : Array
"""
if relativeError >= 0.5:
print("relativeError set to a value > 0.5 .. assuming this "
"is a percentage Error level dividing them by 100")
relativeError /= 100.0
if absoluteUError is None:
if not data.allNonZero('rhoa'):
pg.critical("We need apparent resistivity values "
"(rhoa) in the data to estimate a "
"data error.")
error = relativeError + absoluteError / data('rhoa')
else:
u = None
i = absoluteCurrent
if data.haveData("i"):
i = data('i')
if data.haveData("u"):
u = data('u')
else:
if data.haveData("r"):
u = data('r') * i
elif data.haveData("rhoa"):
if data.haveData("k"):
u = data('rhoa') / data('k') * i
else:
pg.critical("We need (rhoa) and (k) in the"
"data to estimate data error.")
else:
pg.critical("We need apparent resistivity values "
"(rhoa) or impedances (r) "
"in the data to estimate data error.")
error = pg.abs(absoluteUError / u) + relativeError
return error
print mesh.cellSizes()
x = np.arange(-10, 10, 1.)
rho = pg.RVector(len(mesh.cellAttributes()), 1.) * 2000.0
print(rho)
pnts = pg.stdVectorRVector3()
for i in x:
pnts.append(pg.RVector3(i, 0.0001))
gzNum = []
gzNum.append(pg.calcGCells(pnts, mesh, rho, 0)[0])
# plt.plot(x, gzNum[0], label=str(0))
for i in range(1, 10):
gzNum.append(pg.calcGCells(pnts, mesh, rho, i)[0])
err = pg.abs(gzNum[i] / gzNum[0] - 1.) * 100.
plt.semilogy(x, err, label=str(i))
plt.plot(x, gzNum[i], label=str(i))
plt.legend()
# plt.plot(x, p1 )
test2d()
# test3d()
plt.show()
def solveFiniteVolume(mesh,
a=1.0,
b=0.0,
f=0.0,
fn=0.0,
vel=None,
u0=0.0,
times=None,
uL=None,
relax=1.0,
ws=None,
scheme='CDS',
**kwargs):
r"""Solve partial differential equation with Finite Volumes.
This function is a syntactic sugar proxy for using the Finite Volume
functionality of the library core to solve elliptic and parabolic partial
differential of the following type:
.. math::
\frac{\partial u}{\partial t} + \mathbf{v}\cdot\nabla u & = \nabla\cdot(a \nabla u) + b u + f(\mathbf{r},t)\\
u(\mathbf{r}, t) & = u_B \quad\mathbf{r}\in\Gamma_{\text{Dirichlet}}\\
\frac{\partial u(\mathbf{r}, t)}{\partial \mathbf{n}} & = u_{\partial \text{B}} \quad\mathbf{r}\in\Gamma_{\text{Neumann}}\\
u(\mathbf{r}, t=0) & = u_0 \quad\text{with} \quad\mathbf{r}\in\Omega
The Domain :math:`\Omega` and the Boundary :math:`\Gamma` are defined
through the given mesh with appropriate boundary marker.
The solution :math:`u(\mathbf{r}, t)` is given for each cell in the mesh.
TODO:
* Refactor with solver class and Runga-Kutte solver
* non steady boundary conditions
Parameters
----------
mesh: :gimliapi:`GIMLI::Mesh`
Mesh represents spatial discretization of the calculation domain
a: value | array | callable(cell, userData)
Stiffness weighting per cell values.
b: value | array | callable(cell, userData)
Scale for mass values b
f: iterable(cell)
Load vector
fn: iterable(cell)
TODO What is fn
vel: ndarray (N,dim) | RMatrix(N,dim)
Velocity field :math:`\mathbf{v}(\mathbf{r}, t=\text{const}) = \{[v_i]_j,\}`
with :math:`i=[1\ldots 3]` for the mesh dimension
and :math:`j = [0\ldots N-1]` with N either the amount of cells,
nodes, or boundaries.
Velocities per boundary are preferred and will be interpolated
on demand.
u0: value | array | callable(cell, userData)
Starting field
times: iterable
Time steps to calculate for.
ws Workspace
This can be an empty class that will used as an Workspace to store and
cache data.
If ws is given: The system matrix is taken from ws or
calculated once and stored in ws for further usage.
The system matrix is cached in this Workspace as ws.S
The LinearSolver with the factorized matrix is cached in
this Workspace as ws.solver
The rhs vector is only stored in this Workspace as ws.rhs
scheme: str [CDS]
Finite volume scheme:
:py:mod:`pygimli.solver.diffusionConvectionKernel`
**kwargs:
* bc : Boundary Conditions dictionary, see pg.solver
* uB : Dirichlet boundary conditions DEPRECATED
* duB : Neumann boundary conditions DEPRECATED
Returns
-------
u: ndarray(nTimes, nCells)
Solution field for all time steps.
"""
verbose = kwargs.pop('verbose', False)
# The Workspace is to hold temporary data or preserve matrix rebuild
# swatch = pg.core.Stopwatch(True)
sparse = True
workspace = pg.solver.WorkSpace()
if ws:
workspace = ws
a = pg.solver.parseArgToArray(a, [mesh.cellCount(), mesh.boundaryCount()])
b = pg.solver.parseArgToArray(b, mesh.cellCount())
f = pg.solver.parseArgToArray(f, mesh.cellCount())
fn = pg.solver.parseArgToArray(fn, mesh.cellCount())
boundsDirichlet = None
boundsNeumann = None
# BEGIN check for Courant-Friedrichs-Lewy
if vel is not None:
if isinstance(vel, float):
print("Warning! .. velocity is float and no vector field")
# we need velocities for boundaries
if len(vel) is not mesh.boundaryCount():
if len(vel) == mesh.cellCount():
vel = pg.meshtools.cellDataToNodeData(mesh, vel)
if len(vel) == mesh.nodeCount():
vel = pg.meshtools.nodeDataToBoundaryData(mesh, vel)
else:
print("mesh:", mesh)
print("vel:", vel.shape)
raise Exception("Cannot determine data format for velocities")
if times is not None:
pg.solver.checkCFL(times, mesh, np.max(pg.abs(vel)))
if not hasattr(workspace, 'S'):
boundsDirichlet = []
if 'bc' in kwargs:
bct = dict(kwargs['bc'])
if 'Dirichlet' in bct:
boundsDirichlet += pg.solver.parseArgToBoundaries(
bct.pop('Dirichlet'), mesh)
if 'Node' in bct:
n = bct.pop('Node')
boundsDirichlet.append([mesh.node(n[0]), n[1]])
if 'Neumann' in bct:
boundsNeumann = pg.solver.parseArgToBoundaries(
bct.pop('Neumann'), mesh)
if 'uB' in kwargs:
pg.deprecated('use new bc dictionary')
boundsDirichlet = pg.solver.parseArgToBoundaries(
kwargs['uB'], mesh)
if 'duB' in kwargs:
pg.deprecated('use new bc dictionary')
boundsNeumann = pg.solver.parseArgToBoundaries(kwargs['duB'], mesh)
workspace.S, workspace.rhsBCScales = diffusionConvectionKernel(
mesh=mesh,
a=a,
b=b,
uB=boundsDirichlet,
duB=boundsNeumann,
# u0=u0,
fn=fn,
vel=vel,
scheme=scheme,
sparse=sparse,
userData=kwargs.pop('userData', None))
dof = len(workspace.rhsBCScales)
workspace.ap = np.zeros(dof)
# for nonlinears
if uL is not None:
for i in range(dof):
val = 0.0
if sparse:
val = workspace.S.getVal(i, i) / relax
workspace.S.setVal(i, i, val)
else:
val = workspace.S[i, i] / relax
workspace.S[i, i] = val
workspace.ap[i] = val
# print('FVM kernel 2:', swatch.duration(True))
# endif: not hasattr(workspace, 'S'):
workspace.rhs = np.zeros(len(workspace.rhsBCScales))
workspace.rhs[0:mesh.cellCount()] = f # * mesh.cellSizes()
workspace.rhs += workspace.rhsBCScales
# for nonlinear: relax progress with scaled last result
if uL is not None:
workspace.rhs += (1. - relax) * workspace.ap * uL
# print('FVM: Prep:', swatch.duration(True))
if not hasattr(times, '__len__'):
if sparse and not hasattr(workspace, 'solver'):
Sm = pg.matrix.SparseMatrix(workspace.S)
# hold Sm until we have reference counting,
# loosing Sm here will kill LinSolver later
workspace.Sm = Sm
workspace.solver = pg.core.LinSolver(Sm, verbose=verbose)
u = None
if sparse:
u = workspace.solver.solve(workspace.rhs)
else:
u = np.linalg.solve(workspace.S, workspace.rhs)
# print('FVM solve:', swatch.duration(True))
return u[0:mesh.cellCount():1]
else:
theta = kwargs.pop('theta', 0.5 + 1e-6)
if sparse:
I = pg.solver.identity(len(workspace.rhs))
else:
I = np.diag(np.ones(len(workspace.rhs)))
progress = None
if verbose:
from pygimli.utils import ProgressBar
progress = ProgressBar(its=len(times))
print("Solve timesteps with Crank-Nicolson.")
return pg.solver.crankNicolson(times,
theta,
workspace.S,
I,
f=workspace.rhs,
u0=pg.solver.cellValues(mesh, u0),
progress=progress)
