def testShapefunctions( ):
poly = g.Mesh( 3 )
n0 = poly.createNode( 0.0, 0.0, 0.0 )
n1 = poly.createNode( 1.0, 0.0, 0.0 )
n2 = poly.createNode( 0.0, 1.0, 0.0 )
n3 = poly.createNode( 0.0, 0.0, 0.5 )
poly.createTetrahedron( n0, n1, n2, n3 )
prism = poly.createP2Mesh()
u = g.RVector( prism.nodeCount(), 0.0 )
u[ 5 ] = 1.0
prism.addExportData( "u", u )
#n3 = poly.createNode( 1.0, 1.0, 0.0 )
#poly.createTriangle( n0, n1, n3 )
#prism = g.createMesh3D( poly, g.asvector( np.linspace( 0, -1, 2 ) ) )
#prism.exportVTK( "prism" )
#mesh2 = g.createMesh2D( g.asvector( np.linspace( 0, 1, 10 ) ),
#g.asvector( np.linspace( 0, 1, 10 ) ) )
#mesh2 = mesh2.createH2Mesh()
#g.interpolate( prism, mesh2 )
#ax = g.viewer.showMesh( mesh2, mesh2.exportData('u'), filled = True, showLater = True )
mesh3 = g.createMesh3D( g.asvector( np.linspace( 0, 1, 11 ) ),
g.asvector( np.linspace( 0, 1, 11 ) ),
g.asvector( np.linspace( 0, 1, 11 ) ) )
grads = g.stdVectorRVector3( )
c = prism.cell( 0 )
uc = g.RVector( mesh3.nodeCount() )
for n in mesh3.nodes():
p = c.shape().xyz( n.pos() )
if not c.shape().isInside( p ):
grads.append( g.RVector3( 0.0, 0.0, 0.0 ) )
uc[ n.id() ] = 0.0
continue
uc[ n.id() ] = c.pot( p, u )
print uc[ n.id() ]
gr = c.grad( p, u )
grads.append( gr )
g.interpolate( prism, mesh3 )
mesh3.addExportData( 'ua', uc )
mesh3.exportVTK( "prismHex", grads )
P.show()
def testShapefunctions():
poly = g.Mesh(3)
n0 = poly.createNode(0.0, 0.0, 0.0)
n1 = poly.createNode(1.0, 0.0, 0.0)
n2 = poly.createNode(0.0, 1.0, 0.0)
n3 = poly.createNode(0.0, 0.0, 0.5)
poly.createTetrahedron(n0, n1, n2, n3)
prism = poly.createP2Mesh()
u = g.RVector(prism.nodeCount(), 0.0)
u[5] = 1.0
prism.addExportData("u", u)
#n3 = poly.createNode( 1.0, 1.0, 0.0 )
#poly.createTriangle( n0, n1, n3 )
#prism = g.createMesh3D( poly, g.asvector( np.linspace( 0, -1, 2 ) ) )
#prism.exportVTK( "prism" )
#mesh2 = g.createMesh2D( g.asvector( np.linspace( 0, 1, 10 ) ),
#g.asvector( np.linspace( 0, 1, 10 ) ) )
#mesh2 = mesh2.createH2Mesh()
#g.interpolate( prism, mesh2 )
#ax = g.viewer.showMesh( mesh2, mesh2.exportData('u'), filled = True, showLater = True )
mesh3 = g.createMesh3D(g.asvector(np.linspace(0, 1, 11)),
g.asvector(np.linspace(0, 1, 11)),
g.asvector(np.linspace(0, 1, 11)))
grads = g.stdVectorRVector3()
c = prism.cell(0)
uc = g.RVector(mesh3.nodeCount())
for n in mesh3.nodes():
p = c.shape().xyz(n.pos())
if not c.shape().isInside(p):
grads.append(g.RVector3(0.0, 0.0, 0.0))
uc[n.id()] = 0.0
continue
uc[n.id()] = c.pot(p, u)
print uc[n.id()]
gr = c.grad(p, u)
grads.append(gr)
g.interpolate(prism, mesh3)
mesh3.addExportData('ua', uc)
mesh3.exportVTK("prismHex", grads)
P.show()
def FOPsmooth(self, zvec):
"""
Retrieve forward modelling operator using fixed layers
(smooth inversion)
Parameters
----------
zvec : array
???
"""
return pg.FDEM1dRhoModelling(pg.asvector(zvec),pg.asvector(self.freq()),pg.self.coilSpacing,-self.height)
def inv2D(self, nlay, lam=100., resL=1., resU=1000., thkL=1.,
thkU=100., minErr=1.0):
"""
2d LCI inversion class
"""
if isinstance(nlay, int):
modVec = pg.RVector(nlay*2 -1, 30.)
cType = 0 # no reference model
else:
modVec = nlay
cType = 10 # use this as referencemodel
nlay = (len(modVec) + 1) / 2
# init forward operator
self.f2d = self.FOP2d(nlay)
# transformations
self.tD = pg.RTrans()
self.tThk = pg.RTransLogLU(thkL, thkU)
self.tRes = pg.RTransLogLU(resL, resU)
for i in range(nlay-1): self.f2d.region(i).setTransModel(self.tThk)
for i in range(nlay-1, nlay*2-1): self.f2d.region(i).setTransModel(self.tRes)
# set constraints
self.f2d.region(0).setConstraintType(cType)
self.f2d.region(1).setConstraintType(cType)
# collect data vector
datvec = pg.RVector(0)
for i in range(len(self.x)):
datvec = pg.cat(datvec, self.datavec(i))
# collect error vector
errVec = []
for i in range(len(self.x)):
errVec.extend(np.maximum(self.ERR[i][self.activeFreq] * 0.701, minErr))
errVec.extend(np.maximum(self.ERR[i][self.activeFreq] * 0.701, minErr))
# generate starting model by repetition
model = pg.asvector(np.repeat(modVec, len(self.x)))
INV = pg.RInversion(datvec, self.f2d, self.tD)
INV.setAbsoluteError(pg.asvector(errVec))
INV.setLambda(lam)
INV.setModel(model)
INV.setReferenceModel(model)
return INV
def response( self, par ):
""" yield model response cube as vector """
nl=self.nl_
thk = par( 0, nl-1 )
wc = par( nl-1, 2*nl-1 )
t2 = par( 2*nl-1, 3*nl-1 )
zthk = np.cumsum(thk)
zv = self.zv_
lzv = len(zv)
izvec = np.zeros(nl+1,np.int32)
rzvec = np.zeros(nl+1)
for i in range(nl-1):
ii = (zv<zthk[i]).argmin()
izvec[i+1] = ii
if ii <= len(zv):
rzvec[i+1]=(zthk[i]-zv[ii-1])/(zv[ii]-zv[ii-1])
izvec[-1] = lzv-1
A = np.zeros((self.nq_,self.nt_),dtype=complex)
for i in range(nl):
wcvec = np.zeros(lzv-1)
wcvec[izvec[i]:izvec[i+1]] = wc[i]
if izvec[i+1]<lzv: wcvec[izvec[i+1]-1]=wc[i]*rzvec[i+1]
if izvec[i]>0: wcvec[izvec[i]-1]=wc[i]*(1-rzvec[i])
amps=np.dot(self.K_,wcvec)
for ii,a in enumerate(A): a += np.exp(-self.t_/t2[i])*amps[ii]
return pg.asvector( np.abs(A).ravel() )
def datavec(self, xpos=0):
"""
Extract data vector (stack in and out phase) for given pos/no
"""
ip, op, err = self.selectData(xpos)
return pg.asvector(np.hstack((ip, op)))
def grange( start, end, dx = 0, n = 0, log = False ):
'''
Return RVector from start step-wise filled with dx until end reached [start, end]\n
Or RVector is filled from start to end with n steps. [start, end] \n
If nSteps set RVector can optionaly filled with logarithmic spacing.
'''
s = float( start )
e = float( end )
d = float( dx )
if dx != 0:
if end < start and dx > 0:
print("grange: decreasing range but increasing dx, swap dx sign")
d = -d
if end > start and dx < 0:
print("grange: increasing range but decreasing dx, swap dx sign")
d = -d
ret = pg.asvector( list(range( int( floor( abs( ( e - s ) / d ) ) + 1 ))) )
ret *= d
ret += s
return ret;
elif n > 0:
if not log:
return grange( start, end, dx = ( e - s ) / ( n - 1 ) )
else:
raise Exception( 'not yet implemented.' )
else:
raise Exception( 'Either dx or nSteps have to be given.' )
def datavec(self, xpos=0):
"""
Extract data vector (stacking inphase and outphase) for given position or number
"""
ip, op, err = self.selectData(xpos)
return pg.asvector(np.hstack((ip, op)))
def response( self, par ):
"""compute response function."""
nl = self.nl_
thk = par( 0, nl-1 )
wc = par( nl-1, 2*nl-1 )
t2 = par( 2*nl-1, 3*nl-1 )
zthk = N.cumsum(thk)
zv = self.zv_
lzv = len(zv)
izvec = N.zeros( nl + 1, N.int32 )
rzvec = N.zeros( nl + 1 )
for i in range(nl-1):
ii = ( zv<zthk[i] ).argmin()
izvec[ i + 1 ] = ii
if ii <= len(zv):
rzvec[i+1] = ( zthk[i] - zv[ii-1] ) / ( zv[ii] - zv[ii-1] )
izvec[-1] = lzv - 1
A = N.zeros( (self.nq_, self.nt_), dtype=complex )
for i in range(nl):
wcvec = N.zeros(lzv-1)
wcvec[ izvec[i]:izvec[i+1] ] = wc[i]
if izvec[i+1] < lzv:
wcvec[ izvec[i+1] - 1 ] = wc[i] * rzvec[ i + 1 ]
if izvec[i] > 0:
wcvec[ izvec[i] - 1 ] = wc[i] * ( 1 - rzvec[i] )
amps = N.dot( self.KR_, wcvec ) + N.dot( self.KI_, wcvec ) * 1j
for ii, a in enumerate(A):
a += N.exp( -self.t_ / t2[i] ) * amps[ii]
return pg.asvector( N.abs(A).ravel() )
def inv2D(self,
nlay,
lam=100.,
resL=1.,
resU=1000.,
thkL=1.,
thkU=100.,
minErr=1.0):
"""2d LCI inversion class."""
if isinstance(nlay, int):
modVec = pg.RVector(nlay * 2 - 1, 30.)
cType = 0 # no reference model
else:
modVec = nlay
cType = 10 # use this as referencemodel
nlay = (len(modVec) + 1) / 2
# init forward operator
self.f2d = self.FOP2d(nlay)
# transformations
self.transData = pg.RTrans()
self.transThk = pg.RTransLogLU(thkL, thkU)
self.transRes = pg.RTransLogLU(resL, resU)
for i in range(nlay - 1):
self.f2d.region(i).setTransModel(self.transThk)
for i in range(nlay - 1, nlay * 2 - 1):
self.f2d.region(i).setTransModel(self.transRes)
# set constraints
self.f2d.region(0).setConstraintType(cType)
self.f2d.region(1).setConstraintType(cType)
# collect data vector
datvec = pg.RVector(0)
for i in range(len(self.x)):
datvec = pg.cat(datvec, self.datavec(i))
# collect error vector
if self.ERR is None:
error = 1.0
else:
error = []
for i in range(len(self.x)):
err = np.maximum(self.ERR[i][self.activeFreq] * 0.701, minErr)
error.extend(err)
# generate starting model by repetition
model = pg.asvector(np.repeat(modVec, len(self.x)))
INV = pg.RInversion(datvec, self.f2d, self.transData)
INV.setAbsoluteError(error)
INV.setLambda(lam)
INV.setModel(model)
INV.setReferenceModel(model)
return INV
def hexahedron( p2 ):
"""
"""
mesh = g.createMesh3D( g.asvector( np.linspace( 0, 1, 2 ) ),
g.asvector( np.linspace( 0, 1, 2 ) ),
g.asvector( np.linspace( 0, 1, 2 ) ) )
mesh.node(0).setPos( g.RVector3( 0.0, 0.0, 0.5 ) )
#mesh.rotate( g.RVector3( 10.0, 34.0, 45 ) )
#mesh.scale( g.RVector3( 0.9, 0.8, 0.7 ) )
#mesh.rotate( g.RVector3( 10.0, 34.0, 45 ) )
#mesh.scale( g.RVector3( 1.0, 1.0, 5.0 ) )
if p2: mesh = mesh.createP2()
show( mesh )
def DebyeDecomposition(fr,
phi,
maxfr=None,
tv=None,
verbose=False,
zero=False,
err=0.25e-3,
lam=10.,
blocky=False):
"""Debye decomposition of a phase spectrum."""
if maxfr is not None:
idx = (fr <= maxfr) & (phi >= 0.)
phi1 = phi[idx]
fr1 = fr[idx]
print("using frequencies from ", N.min(fr), " to ", N.max(fr), "Hz")
else:
phi1 = phi
fr1 = fr
if tv is None:
tmax = 1. / N.min(fr1) / 2. / N.pi * 4.
tmin = 1. / N.max(fr1) / 2. / N.pi / 8.
tvec = N.logspace(N.log10(tmin), N.log10(tmax), 30)
else:
tvec = tv
f = DebyeModelling(fr1, tvec, zero=zero)
tvec = f.t_
tm = pg.trans.TransLog()
start = pg.Vector(len(tvec), 1e-4)
if zero:
f.region(-1).setConstraintType(0) # smoothness
f.region(0).setConstraintType(1) # smoothness
f.region(1).setConstraintType(0) # min length
f.regionManager().setInterRegionConstraint(-1, 0, 1.)
f.regionManager().setInterRegionConstraint(0, 1, 1.)
f.region(-1).setTransModel(tm)
f.region(0).setTransModel(tm)
f.region(1).setTransModel(tm)
f.region(-1).setModelControl(1000.)
f.region(1).setModelControl(1000.)
else:
f.regionManager().setConstraintType(1) # smoothness
inv = pg.Inversion(pg.asvector(phi1 * 1e-3), f, verbose)
inv.setAbsoluteError(pg.Vector(len(fr1), err))
inv.setLambda(lam)
inv.setModel(start)
inv.setBlockyModel(blocky)
if zero:
inv.setReferenceModel(start)
else:
inv.setTransModel(tm)
mvec = inv.run()
resp = inv.response()
return tvec, mvec, N.array(resp) * 1e3, idx
def genMods( individual ):
""" generate MRS and VES models from unit vector """
model = pg.asvector( individual ) * ( self.lUB - self.lLB ) + self.lLB
if self.logpar:
model = pg.exp( model )
modMRS = model(0,nlay*3-1)
modVES = pg.cat(model(0,nlay-1),model(nlay*3-1,nlay*4-1))
return modMRS, modVES
def numpy2gmat(nmat):
"""convert numpy.array into pygimli RMatrix.
TODO implement correct rval
"""
gmat = pg.RMatrix()
for arr in nmat:
gmat.push_back(pg.asvector(arr))
return gmat
def testCreateTriPrismMesh():
poly = g.Mesh( 2 )
n0 = poly.createNode( 0.0, 0.0, 0. )
n1 = poly.createNode( 1.0, 0.0, 0. )
n2 = poly.createNode( 0.0, 1.0, 0. )
n3 = poly.createNode( 1.0, 1.0, 0. )
poly.createEdge( n0, n1 )
poly.createEdge( n1, n3 )
poly.createEdge( n3, n2 )
poly.createEdge( n2, n0 )
mesh2 = g.Mesh( 2 )
g.TriangleWrapper( poly, mesh2, "-pzeAfa0.01q34" );
mesh3 = g.createMesh3D( mesh2, g.asvector( np.arange(0, -1, -0.1 ) ) )
mesh3.setCellAttributes( g.asvector( range(0, mesh3.cellCount() ) ) )
mesh3.save( "prism" )
mesh3.exportVTK( "prism" )
def testCreateTriPrismMesh():
poly = g.Mesh(2)
n0 = poly.createNode(0.0, 0.0, 0.)
n1 = poly.createNode(1.0, 0.0, 0.)
n2 = poly.createNode(0.0, 1.0, 0.)
n3 = poly.createNode(1.0, 1.0, 0.)
poly.createEdge(n0, n1)
poly.createEdge(n1, n3)
poly.createEdge(n3, n2)
poly.createEdge(n2, n0)
mesh2 = g.Mesh(2)
g.TriangleWrapper(poly, mesh2, "-pzeAfa0.01q34")
mesh3 = g.createMesh3D(mesh2, g.asvector(np.arange(0, -1, -0.1)))
mesh3.setCellAttributes(g.asvector(range(0, mesh3.cellCount())))
mesh3.save("prism")
mesh3.exportVTK("prism")
def run(self,nlay=3,lam=10.,startvec=None,verbose=True,uncertainty=False,**kwargs):
''' even easier variant returning all in one call '''
if self.INV is None:
self.INV = self.createInv(nlay,lam,verbose,**kwargs)
if startvec is not None:
self.INV.setModel( pg.asvector( startvec ) )
if verbose: print("Doing inversion...")
self.model = np.array( self.INV.run() )
if uncertainty:
if verbose: print("Computing uncertainty...")
self.modelL, self.modelU = iterateBounds( self.INV, dchi2=self.INV.chi2()/2, change=1.2 )
def __init__(self, fvec, tvec=None, zero = False, verbose = False):
if tvec == None:
tvec = N.logspace(-4, 0, 5)
mesh = pg.createMesh1D(len(tvec))
if zero:
mesh.cell(0).setMarker(-1)
mesh.cell(len(tvec)-1).setMarker(1)
pg.ModellingBase.__init__(self, mesh, verbose)
self.f_ = pg.asvector(fvec)
self.t_ = tvec
self.zero_ = zero
def read1resfile(filename, readsecond=False, dellast=True):
"""read Radic instrument res file containing a single spectrum."""
f = open(filename, 'r')
line = f.readline()
fr = []
rhoa = []
phi = []
drhoa = []
dphi = []
while True:
line = f.readline()
if string.rfind(line, 'Freq') > -1:
break
if readsecond:
while True:
if string.rfind(f.readline(), 'Freq') > -1:
break
while True:
line = f.readline()
b = line.split('\t')
if len(b) < 5:
break
fr.append(string.atof(b[0]))
rhoa.append(string.atof(b[1]))
phi.append(-string.atof(b[2]) * P.pi / 180.)
drhoa.append(string.atof(b[3]))
dphi.append(string.atof(b[4]) * P.pi / 180.)
f.close()
if dellast:
fr.pop(0)
rhoa.pop(0)
phi.pop(0)
drhoa.pop(0)
dphi.pop(0)
return fr, rhoa, pg.asvector(phi), drhoa, pg.asvector(dphi)
def read1resfile(filename, readsecond=False, dellast=True):
"""read Radic instrument res file containing a single spectrum."""
f = open(filename, 'r')
line = f.readline()
fr = []
rhoa = []
phi = []
drhoa = []
dphi = []
while True:
line = f.readline()
if line.rfind('Freq') > -1:
break
if readsecond:
while True:
if f.readline().rfind('Freq') > -1:
break
while True:
line = f.readline()
b = line.split('\t')
if len(b) < 5:
break
fr.append(float(b[0]))
rhoa.append(float(b[1]))
phi.append(-float(b[2]) * P.pi / 180.)
drhoa.append(float(b[3]))
dphi.append(float(b[4]) * P.pi / 180.)
f.close()
if dellast:
fr.pop(0)
rhoa.pop(0)
phi.pop(0)
drhoa.pop(0)
dphi.pop(0)
return fr, rhoa, pg.asvector(phi), drhoa, pg.asvector(dphi)
def invBlock( self, xpos=0, nlay=2, noise=1.0, stmod=10., lam=100., lBound=1., uBound=0., verbose=False ):
"""yield gimli inversion instance for block inversion."""
""" inv(xpos,nlay) where nlay can be a FOP or a number of layers """
self.transThk = RTransLog()
self.transRes = RTransLogLU( lBound, uBound )
self.transData = RTrans()
# EM forward operator
if isinstance( nlay, FDEM1dModelling ):
self.fop = nlay
else:
self.fop = self.FOP( nlay )
data = self.datavec( xpos )
self.fop.region(0).setTransModel( self.transThk )
self.fop.region(1).setTransModel( self.transRes )
if isinstance( noise, float ):
noiseVec = RVector( len(data), noise)
else:
noiseVec = asvector( noise )
# independent EM inversion
self.inv = RInversion( data, self.fop, self.transData, verbose )
if isinstance( stmod, float): # real model given
model = RVector( nlay * 2 - 1, stmod )
model[0] = 2.
else:
if len( stmod ) == nlay*2-1:
model = asvector( stmod )
else:
model = RVector( nlay*2-1, 30. )
self.inv.setAbsoluteError( noiseVec )
self.inv.setLambda( lam )
self.inv.setMarquardtScheme( 0.8 )
self.inv.setModel( model )
self.inv.setReferenceModel( model )
return self.inv
def DebyeDecomposition(fr, phi, maxfr=None, tv=None, verbose=False,
zero=False, err=0.25e-3, lam=10., blocky=False):
"""Debye decomposition of a phase spectrum."""
if maxfr is not None:
idx = (fr <= maxfr) & (phi >= 0.)
phi1 = phi[idx]
fr1 = fr[idx]
print("using frequencies from ", N.min(fr), " to ", N.max(fr), "Hz")
else:
phi1 = phi
fr1 = fr
if tv is None:
tmax = 1. / N.min(fr1) / 2. / N.pi * 4.
tmin = 1. / N.max(fr1) / 2. / N.pi / 8.
tvec = N.logspace(N.log10(tmin), N.log10(tmax), 30)
else:
tvec = tv
f = DebyeModelling(fr1, tvec, zero=zero)
tvec = f.t_
tm = pg.RTransLog()
start = pg.RVector(len(tvec), 1e-4)
if zero:
f.region(-1).setConstraintType(0) # smoothness
f.region(0).setConstraintType(1) # smoothness
f.region(1).setConstraintType(0) # min length
f.regionManager().setInterRegionConstraint(-1, 0, 1.)
f.regionManager().setInterRegionConstraint(0, 1, 1.)
f.region(-1).setTransModel(tm)
f.region(0).setTransModel(tm)
f.region(1).setTransModel(tm)
f.region(-1).setModelControl(1000.)
f.region(1).setModelControl(1000.)
else:
f.regionManager().setConstraintType(1) # smoothness
inv = pg.RInversion(pg.asvector(phi1 * 1e-3), f, verbose)
inv.setAbsoluteError(pg.RVector(len(fr1), err))
inv.setLambda(lam)
inv.setModel(start)
inv.setBlockyModel(blocky)
if zero:
inv.setReferenceModel(start)
else:
inv.setTransModel(tm)
mvec = inv.run()
resp = inv.response()
return tvec, mvec, N.array(resp) * 1e3, idx
def ReadAndRemoveEM(filename, readsecond=False, doplot=False,
dellast=True, ePhi=0.5, ePerc=1., lam=2000.):
""" Read res1file and remove EM effects using a double-Cole-Cole model
fr,rhoa,phi,dphi = ReadAndRemoveEM(filename, readsecond/doplot bools)"""
fr, rhoa, phi, drhoa, dphi = read1resfile(filename, readsecond,
dellast=dellast)
# forward problem
mesh = pg.createMesh1D(1, 6) # 6 independent parameters
f = DoubleColeColeModelling(mesh, pg.asvector(fr) , phi[2]/abs(phi[2]))
f.regionManager().loadMap("region.control")
model = f.createStartVector()
# inversion
inv = pg.RInversion(phi, f, True, False)
inv.setAbsoluteError(phi * ePerc * 0.01 + ePhi / 1000.)
inv.setRobustData(True)
# inv.setCWeight(pg.RVector(6, 1.0)) # wozu war das denn gut?
inv.setMarquardtScheme(0.8)
inv.setLambda(lam)
inv.setModel(model)
erg = inv.run()
inv.echoStatus()
chi2 = inv.chi2()
mod0 = pg.RVector(erg)
mod0[ 0 ] = 0.0 # set IP term to zero to obtain pure EM term
emphi = f(mod0)
resid = (phi - emphi) * 1000.
if doplot:
s = "IP: m= " + str(rndig(erg[0])) + " t=" + str(rndig(erg[1])) + \
" c =" + str(rndig(erg[2]))
s = s + " EM: m= " + str(rndig(erg[3])) + " t=" + str(rndig(erg[4])) +\
" c =" + str(rndig(erg[5]))
fig = P.figure(1)
fig.clf()
ax = P.subplot(111)
P.errorbar(fr, phi*1000., yerr=dphi*1000., fmt='x-', label='measured')
ax.set_xscale('log')
P.semilogx(fr, f(mod0) * 1000., label='EM term (CC)')
P.errorbar(fr, resid, yerr=dphi*1000., label='IP term')
ax.set_yscale('log')
P.xlim((min(fr), max(fr)))
P.ylim((0.1, max(phi) * 1000.))
P.xlabel('f in Hz')
P.ylabel(r'-$\phi$ in mrad')
P.grid(True)
P.title(s)
P.legend(loc=2)#('measured','2-cole-cole','residual'))
fig.show()
return N.array(fr), N.array(rhoa), N.array(resid), N.array(phi)*1e3, dphi, chi2, N.array(emphi)*1e3
def __init__(self, fvec, tvec=None, zero=False, verbose=False):
if tvec is None:
tvec = N.logspace(-4, 0, 5)
mesh = pg.createMesh1D(len(tvec))
if zero:
mesh.cell(0).setMarker(-1)
mesh.cell(len(tvec) - 1).setMarker(1)
pg.ModellingBase.__init__(self, mesh, verbose)
self.f_ = pg.asvector(fvec)
self.t_ = tvec
self.zero_ = zero
def astausgleich(ab2org, mn2org, rhoaorg):
"""shifts the branches of a dc sounding to generate a matching curve."""
ab2 = P.asarray(ab2org)
mn2 = P.asarray(mn2org)
rhoa = P.asarray(rhoaorg)
um = P.unique(mn2)
for i in range(len(um) - 1):
r0, r1 = [], []
ac = P.intersect1d(ab2[ mn2 == um[i] ], ab2[ mn2 == um[ i + 1 ] ])
for a in ac:
r0.append(rhoa[ (ab2 == a) * (mn2 == um[i]) ][0])
r1.append(rhoa[ (ab2 == a) * (mn2 == um[i+1]) ][0])
if len(r0) > 0:
fak = P.mean(P.array(r0) / P.array(r1))
print(fak)
if P.isfinite(fak) and fak>0.:
rhoa[ mn2 == um[ i + 1 ] ] *= fak
return pg.asvector(rhoa)
def makeSlmData(ab2, mn2, rhoa=None, filename=None):
"""generate a pygimli data container from ab/2 and mn/2 array."""
data = pg.DataContainer()
data.resize(len(ab2))
pos = N.unique(N.hstack((ab2, mn2)))
for elx in N.hstack((-pos[::-1], pos)):
data.createElectrode(elx, 0., 0.)
if filename is not None:
f = open(filename, 'w')
f.write(str(len(pos) * 2) + '\n#x y z\n')
for elx in N.hstack((-pos[::-1], pos)):
f.write(str(elx) + '\t0\t0\n')
f.write(str(len(ab2)) + '\n#a\tb\tm\tn\tk\trhoa\n')
lpos = len(pos)
iab = pos.searchsorted(ab2)
imn = pos.searchsorted(mn2)
if (filename is not None) & (rhoa is None):
rhoa = N.ones(len(ab2))
for i in range(len(iab)):
# print -pos[iab[i]], -pos[imn[i]], pos[imn[i]], pos[iab[i]]
k = (ab2[i]**2 - mn2[i]**2) * N.pi / mn2[i] / 2.0
if filename is not None:
f.write(str(lpos - iab[i]) + '\t' + str(lpos + iab[i] + 1) + '\t')
f.write(str(lpos - imn[i]) + '\t' + str(lpos + imn[i] + 1) + '\t')
f.write(str(rndig(k, 4)) + '\t' + str(rhoa[i]) + '\n')
data.createFourPointData(i, int(lpos - iab[i]), int(lpos + iab[i] + 1),
int(lpos - imn[i]), int(lpos + imn[i] + 1))
if filename is not None:
f.close()
data.set('rhoa', pg.asvector(rhoa))
return data
def makeSlmData(ab2, mn2, rhoa=None, filename=None):
"""generate a pygimli data container from ab/2 and mn/2 array."""
data = pg.DataContainer()
data.resize(len(ab2))
pos = N.unique(N.hstack((ab2, mn2)))
for elx in N.hstack((-pos[::-1], pos)):
data.createElectrode(elx, 0., 0.)
if filename is not None:
f = open(filename, 'w')
f.write(str(len(pos) * 2) + '\n#x y z\n')
for elx in N.hstack((-pos[::-1], pos)):
f.write(str(elx) + '\t0\t0\n')
f.write(str(len(ab2)) + '\n#a\tb\tm\tn\tk\trhoa\n')
lpos = len(pos)
iab = pos.searchsorted(ab2)
imn = pos.searchsorted(mn2)
if (filename is not None) & (rhoa is None):
rhoa = N.ones(len(ab2))
for i in range(len(iab)):
#print -pos[iab[i]], -pos[imn[i]], pos[imn[i]], pos[iab[i]]
k = (ab2[i]**2 - mn2[i]**2) * N.pi / mn2[i] / 2.0
if filename is not None:
f.write(str(lpos - iab[i]) + '\t' + str(lpos + iab[i] + 1) + '\t')
f.write(str(lpos - imn[i]) + '\t' + str(lpos + imn[i] + 1) + '\t')
f.write(str(rndig(k, 4)) + '\t' + str(rhoa[i]) + '\n')
data.createFourPointData(i, int(lpos - iab[i]), int(lpos + iab[i] + 1),
int(lpos - imn[i]), int(lpos + imn[i] + 1))
if filename is not None:
f.close()
data.set('rhoa', pg.asvector(rhoa))
return data
def findMatrix(uN, dim, nCoeff, ptns, pascale, serendipity):
fop = g.PolynomialModelling(dim, nCoeff, pnts)
fop.setPascalsStyle(pascale)
fop.setSerendipityStyle(serendipity)
tmp = g.RPolynomialFunction(g.RVector(fop.polynomialFunction().size()))
tmp.fill(fop.startModel())
print("base:", tmp)
G = P.zeros((len(pnts), len(tmp.elements())))
for i, p in enumerate(pnts):
for j, e in enumerate(tmp.elements()):
G[i, j] = e(p)
GI = P.inv(G)
coef = P.dot(GI, uN)
print(coef)
print(P.dot(G, coef))
tmp.fill(g.asvector(coef))
print(coef, tmp)
return tmp
def findMatrix( uN, dim, nCoeff, ptns, pascale, serendipity ):
fop = g.PolynomialModelling( dim, nCoeff, pnts )
fop.setPascalsStyle( pascale )
fop.setSerendipityStyle( serendipity )
tmp = g.RPolynomialFunction( g.RVector( fop.polynomialFunction().size() ) )
tmp.fill( fop.startModel() )
print "base:", tmp
G = P.zeros( ( len( pnts), len( tmp.elements() ) ) )
for i, p in enumerate( pnts ):
for j, e in enumerate( tmp.elements() ):
G[i,j] = e( p )
GI = P.inv( G )
coef = P.dot( GI, uN )
print coef
print P.dot( G, coef )
tmp.fill( g.asvector( coef ) )
print coef, tmp
return tmp
def harmfit(y, x=None, error=None, nc=42, resample=None, lam=0.1,
window=None, verbose=False, dosave=False,
lineSearch=True, robust=False, maxiter=20):
"""HARMFIT - GIMLi based curve-fit by harmonic functions
Parameters
----------
y : 1d-array - values to be fitted
x : 1d-array(len(y)) - data abscissa data. default: [0 .. len(y))
error : 1d-array(len(y)) error of y. default (absolute error = 0.01)
nc : int - Number of harmonic coefficients
resample : 1d-array - resample y to x using fitting coeffients
window : int - just fit data inside window bounds
Returns
-------
response : 1d-array(len(resample) or len(x)) - smoothed values
coefficients : 1d-array - fitting coefficients
"""
if x is None:
x = np.arange(len(y))
# else:
# if not isinstance(x, pg.RVector):
# x = pg.asvector(x)
#
# if not isinstance(y, pg.RVector):
# y = pg.asvector(y)
xToFit = None
yToFit = None
if window is not None:
idx = pg.find((x >= window[0]) & (x < window[1]))
# idx = getIndex(x , lambda v: v > window[0] and v < window[1])
xToFit = x(idx)
yToFit = y(idx)
if error is not None:
error = error(idx)
else:
xToFit = x
yToFit = y
# print xToFit
# print yToFit
fop = pg.HarmonicModelling(nc, xToFit, verbose)
inv = pg.RInversion(yToFit, fop, verbose, dosave)
if error is not None:
inv.setAbsoluteError(error)
else:
inv.setAbsoluteError(0.01)
inv.setMarquardtScheme(0.8)
if error is not None:
inv.stopAtChi1(True)
inv.setLambda(lam)
inv.setMaxIter(maxiter)
inv.setLineSearch(lineSearch)
inv.setRobustData(robust)
# inv.setConstraintType(0)
coeff = inv.run()
print(inv.chi2())
if resample is not None:
if not isinstance(resample, pg.RVector):
resample = pg.asvector(resample)
ret = fop.response(coeff, resample)
if window is not None:
# print pg.find((resample < window[0]) | (resample >= window[1]))
ret.setVal(0.0, pg.find((resample < window[0]) |
(resample >= window[1])))
# idx = getIndex(resample,
# lambda v: v <= window[0] or v >= window[1])
# for i in idx: ret[i] = 0.0
return ret, coeff
else:
return inv.response(), coeff
def errorvec(self, xpos=0, minvalue=0.0):
"""
Extract error vector for a give position or sounding number
"""
ip, op, err = self.selectData(xpos)
return pg.asvector(np.tile(np.maximum(err * 0.7071, minvalue), 2))
surf = ax1.plot_surface(X,
Y,
Z,
rstride=1,
cstride=1,
cmap=P.cm.jet,
linewidth=0)
ax2.set_title(label + N.__str__())
fig.colorbar(surf)
e1 = [1, -1] # 1-r
e2 = [0, +1] # r
E2_1R = g.RPolynomialFunction(g.asvector(e1))
E2_2R = g.RPolynomialFunction(g.asvector(e2))
E2_1S = g.RPolynomialFunction(g.RVector(), g.asvector(e1))
E2_2S = g.RPolynomialFunction(g.RVector(), g.asvector(e2))
E2_1T = g.RPolynomialFunction(g.RVector(), g.RVector(), g.asvector(e1))
E2_2T = g.RPolynomialFunction(g.RVector(), g.RVector(), g.asvector(e2))
E3_1R = E2_1R * (E2_1R - E2_2R)
E3_2R = E2_2R * (E2_2R - E2_1R)
E3_3R = 4. * (E2_1R * E2_2R)
E3_1S = E2_1S * (E2_1S - E2_2S)
E3_2S = E2_2S * (E2_2S - E2_1S)
E3_3S = 4. * (E2_1S * E2_2S)
E3_1T = E2_1T * (E2_1T - E2_2T)
tmpNodes = pg.commonNodes(n.cellSet())
for nn in tmpNodes:
if not upTags[nn.id()] and not downTags[nn.id()]:
downwind.add(nn)
downTags[nn.id()] = 1
# start fast marching
tic = time.time()
while len(downwind) > 0:
fastMarch(mesh, downwind, times, upTags, downTags)
print(time.time() - tic, "s")
# compare with analytical solution along the x axis
x = np.arange(0., 100., 0.5)
t = pg.interpolate(mesh, times, pg.asvector(x), x * 0., x * 0.)
tdirect = x / v[0] # direct wave
alfa = asin(v[0] / v[1]) # critically refracted wave angle
xreflec = tan(alfa) * zlay * 2. # first critically refracted
trefrac = (x - xreflec) / v[1] + xreflec * v[1] / v[0]**2
tana = np.where(trefrac < tdirect, trefrac, tdirect) # minimum of both
print("min(dt)=",
min(t - tana) * 1000,
"ms max(dt)=",
max(t - tana) * 1000,
"ms")
# plot traveltime field, a few lines
fig = plt.figure()
a = fig.add_subplot(211)
drawMesh(a, mesh)
def harmfit(y, x=None, error=None, nCoefficients=42, resample=None,
window=None, verbose=False, dosave=False,
lineSearch=True, robust=False, maxiter=20):
"""
HARMFIT - GIMLi based curve-fit by harmonic functions
y .. 1d-array(len(y)) values to be fitted
x .. 1d-array(len(y)) abscissa data spacing. if not given: 1 * [0 .. len(y))
error .. 1d-array(len(y)) data error of y (fit y into the range of error). if not given (absolute err = 1%)
nCoefficients .. int Number of harmonic coefficients
resample .. 1d-array(len(resample)) resample y based on fitting coeffients
window .. just fit data inside window bounds
return response, coefficients
response .. 1d-array(len(y)) if no resample given, else 1d-array(len(resample))
coefficients .. coefficients for harmic functions that fit y
"""
if x is None:
x = pg.asvector(np.arange(len(y)))
else:
if not isinstance(x, pg.RVector):
x = pg.asvector(x)
if not isinstance(y, pg.RVector):
y = pg.asvector(y)
xToFit = None
yToFit = None
if window is not None:
idx = pg.find((x >= window[0]) & (x < window[1]))
#idx = getIndex(x , lambda v: v > window[0] and v < window[1])
xToFit = x(idx)
yToFit = y(idx)
if error is not None:
error = error(idx)
else:
xToFit = x
yToFit = y
# print xToFit
# print yToFit
fop = pg.HarmonicModelling(nCoefficients, xToFit, verbose)
inv = pg.RInversion(yToFit, fop, verbose, dosave)
if error is not None:
if not isinstance(error, pg.RVector):
error = pg.asvector(error)
inv.setRelativeError(error)
else:
inv.setAbsoluteError(0.01)
inv.setLambda(000.0)
inv.setLocalRegularization(True)
inv.setMaxIter(maxiter)
inv.setLineSearch(lineSearch)
inv.setRobustData(robust)
# inv.setConstraintType(0)
coeff = inv.run()
if resample is not None:
if not isinstance(resample, pg.RVector):
resample = pg.asvector(resample)
ret = fop.response(coeff, resample)
# print ret
if window is not None:
# print resample
# print window[0], window[1]
# print pg.find((resample < window[0]) | (resample >= window[1]))
ret.setVal(
0.0, pg.find(
(resample < window[0]) | (
resample >= window[1])))
# idx = getIndex(resample, lambda v: v <= window[0] or v >= window[1])
# for i in idx: ret[i] = 0.0
# print ret
# sys.exit
return ret, coeff
else:
return inv.response(), coeff
def invBlock(self, xpos=0, nlay=2, noise=1.0,
stmod=30., lam=100., lBound=0., uBound=0., verbose=False):
"""
Yield gimli inversion instance for block inversion
inv(xpos,nlay) where nlay can be a FOP or a number of layers
Parameters
----------
xpos : array
nLay : int
Number of layers of the model to be determined
noise : float
Absolute data err in percent
stmod : float or pg.RVector
Starting model
lam : float
Global regularization parameter lambda.
lBound : float
Lower boundary for the model
uBound : float
Upper boundary for the model. 0 means no upper booundary
verbose : bool
Be verbose
"""
self.transThk = pg.RTransLog()
self.transRes = pg.RTransLogLU(lBound, uBound)
self.transData = pg.RTrans()
# EM forward operator
if isinstance(nlay, pg.FDEM1dModelling):
self.fop = nlay
else:
self.fop = self.FOP(nlay)
data = self.datavec(xpos)
self.fop.region(0).setTransModel(self.transThk)
self.fop.region(1).setTransModel(self.transRes)
if isinstance(noise, float):
noiseVec = pg.RVector(len(data), noise)
else:
noiseVec = pg.asvector(noise)
# independent EM inversion
self.inv = pg.RInversion(data, self.fop, self.transData, verbose)
if isinstance(stmod, float): # real model given
model = pg.RVector(nlay * 2 - 1, stmod)
model[0] = 2.
else:
if len(stmod) == nlay * 2 - 1:
model = pg.asvector(stmod)
else:
model = pg.RVector(nlay * 2 - 1, 30.)
self.inv.setAbsoluteError(noiseVec)
self.inv.setLambda(lam)
self.inv.setMarquardtScheme(0.8)
self.inv.setDeltaPhiAbortPercent(0.5)
self.inv.setModel(model)
self.inv.setReferenceModel(model)
return self.inv
def response(self, par):
y = pg.RVector(self.x_.size(), par[0])
for i in range(1, self.nc_):
y += pg.pow(self.x_, i) * par[i]
return y
def startModel(self):
return pg.RVector(self.nc_, 0.5)
#!this is doku within
# evaluate f(x) = 1.1 + 2.1 * x
x = pg.asvector(np.arange(0., 10., 1))
"""
this is doku within
"""
y = 1.1 + 2.1 * x
"""
this is doku within
"""
print((x, y))
nP = 3
# two coefficients and x-vector (first data column)
fop = FunctionModelling(nP, x)
""" Let us create some synthetic data for some x values """ x = np.arange(0., 10., 1) y = 1.1 + 2.1 * x """ We now start by setting up the modelling operator, and inversion and run it. """ nP = 3 # two coefficients and x-vector (first data column) fop = FunctionModelling(nP, pg.asvector(x)) # initialize inversion with data and forward operator and set options inv = pg.RInversion(y, fop) # constant absolute error of 0.01 is 1% (not necessary, only for chi^2) inv.setAbsoluteError(0.01) # the problem is well-posed and does not need regularization inv.setLambda(0) # actual inversion run yielding coefficient model coeff = inv.run() print(coeff)
def drawShapes( ax, mesh, u ):
#ax.set_aspect( 'equal' )
N = 11
mesh3 = g.createMesh3D( g.asvector( np.linspace( 0, 1, N ) ),
g.asvector( np.linspace( 0, 1, N ) ),
g.asvector( np.linspace( 0, 1, N ) ) )
uc = g.RVector( mesh3.nodeCount( ) )
grads = g.stdVectorRVector3( )
pnts = g.stdVectorRVector3( )
c = mesh.cell( 0 )
imax=g.find( u == max( u ) )[0]
N = c.createShapeFunctions()[ imax ]
print imax, N
# print imax, c.shape().createShapeFunctions()[imax]
for i in range( c.nodeCount() ):
print c.rst( i ), N( c.rst( i ) )
# draw nodes
for i in range( c.nodeCount() ):
col = 'black'
if i == imax:
col = 'red'
#ax.plot( [c.node( i ).pos()[0], c.node( i ).pos()[0] ],
#[c.node( i ).pos()[1], c.node( i ).pos()[1] ],
#[c.node( i ).pos()[2], c.node( i ).pos()[2] ],
#'.', markersize = 15, linewidth=0, color=col )
newNode = []
for i in range( mesh3.nodeCount( ) ):
p = c.shape().xyz( mesh3.node( i ).pos() )
newNode.append( p )
#ax.plot( p[0], p[1], '.', zorder=10, color='black', markersize = 1 )
if not c.shape().isInside( p ):
uc[ i ] = -99.0
grads.append( g.RVector3( 0.0, 0.0 ) )
continue
uc[ i ] = c.pot( p, u )
gr = c.grad( p, u ).normalise()
grads.append( gr )
#ax.plot( [ p[ 0 ], p[ 0 ] + gr[ 0 ]*0.1 ],
#[ p[ 1 ], p[ 1 ] + gr[ 1 ]*0.1 ],
#[ p[ 2 ], p[ 2 ] + gr[ 2 ]*0.1 ], '-', color='black' )
#pnts.append( p )
#print len(pnts)
#Z = np.ma.masked_where( uc == -99., uc )
##ax.plot( g.x(pnts), g.y(pnts), g.z(pnts), '.' )
for i, n in enumerate( mesh3.nodes() ):
n.setPos( newNode[ i ] )
mesh3.addExportData( 'u', uc.setVal( 0.0, g.find( uc == -99 ) ) )
name = 'cell' + str( c.nodeCount() ) + '-' + str( imax )
print "write ", name
mesh3.exportVTK( name, grads )
def genMod( self, individual ):
model = pg.asvector( individual ) * ( self.lUB - self.lLB ) + self.lLB
if self.logpar:
return pg.exp( model )
else:
return model
def harmfit(y,
x=None,
error=None,
nc=42,
resample=None,
lam=0.1,
window=None,
verbose=False,
dosave=False,
lineSearch=True,
robust=False,
maxiter=20):
"""HARMFIT - GIMLi based curve-fit by harmonic functions
Parameters
----------
y : 1d-array - values to be fitted
x : 1d-array(len(y)) - data abscissa data. default: [0 .. len(y))
error : 1d-array(len(y)) error of y. default (absolute error = 0.01)
nc : int - Number of harmonic coefficients
resample : 1d-array - resample y to x using fitting coeffients
window : int - just fit data inside window bounds
Returns
-------
response : 1d-array(len(resample) or len(x)) - smoothed values
coefficients : 1d-array - fitting coefficients
"""
if x is None:
x = np.arange(len(y))
# else:
# if not isinstance(x, pg.RVector):
# x = pg.asvector(x)
#
# if not isinstance(y, pg.RVector):
# y = pg.asvector(y)
xToFit = None
yToFit = None
if window is not None:
idx = pg.find((x >= window[0]) & (x < window[1]))
# idx = getIndex(x , lambda v: v > window[0] and v < window[1])
xToFit = x(idx)
yToFit = y(idx)
if error is not None:
error = error(idx)
else:
xToFit = x
yToFit = y
# print xToFit
# print yToFit
fop = pg.HarmonicModelling(nc, xToFit, verbose)
inv = pg.RInversion(yToFit, fop, verbose, dosave)
if error is not None:
inv.setAbsoluteError(error)
else:
inv.setAbsoluteError(0.01)
inv.setMarquardtScheme(0.8)
if error is not None:
inv.stopAtChi1(True)
inv.setLambda(lam)
inv.setMaxIter(maxiter)
inv.setLineSearch(lineSearch)
inv.setRobustData(robust)
# inv.setConstraintType(0)
coeff = inv.run()
print(inv.chi2())
if resample is not None:
if not isinstance(resample, pg.RVector):
resample = pg.asvector(resample)
ret = fop.response(coeff, resample)
if window is not None:
# print pg.find((resample < window[0]) | (resample >= window[1]))
ret.setVal(
0.0, pg.find((resample < window[0]) | (resample >= window[1])))
# idx = getIndex(resample,
# lambda v: v <= window[0] or v >= window[1])
# for i in idx: ret[i] = 0.0
return ret, coeff
else:
return inv.response(), coeff
def ReadAndRemoveEM(filename, readsecond=False, doplot=False,
dellast=True, ePhi=0.5, ePerc=1., lam=2000.):
"""
Read res1file and remove EM effects using a double-Cole-Cole model
fr,rhoa,phi,dphi = ReadAndRemoveEM(filename, readsecond/doplot bools)
"""
fr, rhoa, phi, drhoa, dphi = read1resfile(filename,
readsecond,
dellast=dellast)
# forward problem
mesh = pg.createMesh1D(1, 6) # 6 independent parameters
f = DoubleColeColeModelling(mesh, pg.asvector(fr), phi[2] / abs(phi[2]))
f.regionManager().loadMap("region.control")
model = f.createStartVector()
# inversion
inv = pg.RInversion(phi, f, True, False)
inv.setAbsoluteError(phi * ePerc * 0.01 + ePhi / 1000.)
inv.setRobustData(True)
# inv.setCWeight(pg.RVector(6, 1.0)) # wozu war das denn gut?
inv.setMarquardtScheme(0.8)
inv.setLambda(lam)
inv.setModel(model)
erg = inv.run()
inv.echoStatus()
chi2 = inv.chi2()
mod0 = pg.RVector(erg)
mod0[0] = 0.0 # set IP term to zero to obtain pure EM term
emphi = f.response(mod0)
resid = (phi - emphi) * 1000.
if doplot:
s = "IP: m= " + str(rndig(erg[0])) + " t=" + str(rndig(erg[1])) + \
" c =" + str(rndig(erg[2]))
s += " EM: m= " + str(rndig(erg[3])) + " t=" + str(rndig(erg[4])) + \
" c =" + str(rndig(erg[5]))
fig = P.figure(1)
fig.clf()
ax = P.subplot(111)
P.errorbar(
fr,
phi *
1000.,
yerr=dphi *
1000.,
fmt='x-',
label='measured')
ax.set_xscale('log')
P.semilogx(fr, emphi * 1000., label='EM term (CC)')
P.errorbar(fr, resid, yerr=dphi * 1000., label='IP term')
ax.set_yscale('log')
P.xlim((min(fr), max(fr)))
P.ylim((0.1, max(phi) * 1000.))
P.xlabel('f in Hz')
P.ylabel(r'-$\phi$ in mrad')
P.grid(True)
P.title(s)
P.legend(loc=2) # ('measured','2-cole-cole','residual'))
fig.show()
return N.array(fr), N.array(rhoa), N.array(resid), N.array(
phi) * 1e3, dphi, chi2, N.array(emphi) * 1e3
def invBlock(self, xpos=0, nlay=2, noise=1.0,
stmod=30., lam=100., lBound=0., uBound=0., verbose=False):
"""Create and return Gimli inversion instance for block inversion.
Parameters
----------
xpos : array
position vector
nLay : int
Number of layers of the model to be determined OR
vector of layer numbers OR forward operator
noise : float
Absolute data err in percent
stmod : float or pg.Vector
Starting model
lam : float
Global regularization parameter lambda.
lBound : float
Lower boundary for the model
uBound : float
Upper boundary for the model. 0 means no upper booundary
verbose : bool
Be verbose
"""
self.transThk = pg.trans.TransLog()
self.transRes = pg.trans.TransLogLU(lBound, uBound)
self.transData = pg.trans.Trans()
# EM forward operator
if isinstance(nlay, pg.core.FDEM1dModelling):
self.fop = nlay
else:
self.fop = self.FOP(nlay)
data = self.datavec(xpos)
self.fop.region(0).setTransModel(self.transThk)
self.fop.region(1).setTransModel(self.transRes)
if isinstance(noise, float):
noiseVec = pg.Vector(len(data), noise)
else:
noiseVec = pg.asvector(noise)
# independent EM inversion
self.inv = pg.Inversion(data, self.fop, self.transData, verbose)
if isinstance(stmod, float): # real model given
model = pg.Vector(nlay * 2 - 1, stmod)
model[0] = 2.
else:
if len(stmod) == nlay * 2 - 1:
model = pg.asvector(stmod)
else:
model = pg.Vector(nlay * 2 - 1, 30.)
self.inv.setAbsoluteError(noiseVec)
self.inv.setLambda(lam)
self.inv.setMarquardtScheme(0.8)
self.inv.setDeltaPhiAbortPercent(0.5)
self.inv.setModel(model)
self.inv.setReferenceModel(model)
return self.inv
z[ i ] = N(p)
Z = P.ma.masked_where( z == -99., z )
Z = Z.reshape( Ny, Nx )
ax2.contourf( X, Y, Z )
ax2.set_aspect( 'equal' )
surf = ax1.plot_surface( X, Y, Z, rstride = 1, cstride = 1, cmap=P.cm.jet,linewidth=0 )
ax2.set_title( label + N.__str__() )
fig.colorbar( surf )
e1 = [ 1, -1 ] # 1-r
e2 = [ 0, 1 ] # r
E2_1R = g.RPolynomialFunction( g.asvector( e1 ) )
E2_2R = g.RPolynomialFunction( g.asvector( e2 ) )
E2_1S = g.RPolynomialFunction( g.RVector(), g.asvector( e1 ) )
E2_2S = g.RPolynomialFunction( g.RVector(), g.asvector( e2 ) )
E2_1T = g.RPolynomialFunction( g.RVector(), g.RVector(), g.asvector( e1 ) )
E2_2T = g.RPolynomialFunction( g.RVector(), g.RVector(), g.asvector( e2 ) )
E3_1R = E2_1R * ( E2_1R - E2_2R )
E3_2R = E2_2R * ( E2_2R - E2_1R )
E3_3R = 4. * ( E2_1R * E2_2R )
E3_1S = E2_1S * ( E2_1S - E2_2S )
E3_2S = E2_2S * ( E2_2S - E2_1S )
E3_3S = 4. * ( E2_1S * E2_2S )
E3_1T = E2_1T * ( E2_1T - E2_2T )
def invBlock(self, xpos=0, nlay=2, noise=1.0, show=True, stmod=30.,
lam=1000., lBound=0., uBound=0., verbose=False, **kwargs):
"""Create and return Gimli inversion instance for block inversion.
Parameters
----------
xpos : array
position vector
nLay : int
Number of layers of the model to be determined OR
vector of layer numbers OR forward operator
noise : float
Absolute data err in percent
stmod : float or pg.Vector
Starting model
lam : float
Global regularization parameter lambda.
lBound : float
Lower boundary for the model
uBound : float
Upper boundary for the model. 0 means no upper booundary
verbose : bool
Be verbose
"""
# self.transThk = pg.trans.TransLog()
# self.transRes = pg.trans.TransLogLU(lBound, uBound)
# self.transData = pg.trans.Trans()
self.transData = pg.trans.TransSymLog(tol=0.1)
self.transLog = pg.trans.TransLog()
useHEM = kwargs.pop("useHEM", False)
# EM forward operator
if isinstance(nlay, pg.core.FDEM1dModelling):
self.fop = nlay
else:
self.fop = self.FOP(nlay, useHEM=useHEM)
dataVec = self.datavec(xpos)
# self.fop.region(0).setTransModel(self.transThk)
# self.fop.region(1).setTransModel(self.transRes)
if isinstance(noise, float):
errorVec = pg.Vector(len(dataVec), noise)
else:
errorVec = pg.asvector(noise)
# independent EM inversion
if isinstance(stmod, float): # real model given
model = pg.Vector(nlay * 2 - 1, stmod)
model[0] = 2.
else:
if len(stmod) == nlay * 2 - 1:
model = stmod
else:
model = pg.Vector(nlay * 2 - 1, 30.)
print("Model", model)
if 1:
from pygimli.frameworks import MarquardtInversion
self.inv = MarquardtInversion(fop=self.fop, verbose=verbose,
debug=True)
self.inv.dataTrans = self.transData
self.inv.modelTrans = self.transLog
# self.dataTrans = self.transData
self.model1d = self.inv.run(dataVec, np.abs(errorVec/dataVec),
lam=lam, startModel=model, **kwargs)
response = self.inv.response
else:
self.inv = pg.core.RInversion(data, self.fop, self.transData,
verbose)
self.inv.setAbsoluteError(errorVec)
self.inv.setLambda(lam)
self.inv.setMarquardtScheme(0.8)
self.inv.setDeltaPhiAbortPercent(0.5)
self.inv.setModel(model)
self.model1d = self.inv.run()
response = self.inv.response()
if show:
self.plotData(xpos=xpos, response=response)
return self.model1d
