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+1
-1
@@ -1,4 +1,4 @@
|
||||
[bumpversion]
|
||||
current_version = 0.1.12
|
||||
current_version = 0.1.10
|
||||
files = setup.py SimPEG/__init__.py docs/conf.py
|
||||
|
||||
|
||||
@@ -39,5 +39,3 @@ nosetests.xml
|
||||
*.sublime-workspace
|
||||
docs/_build/
|
||||
Makefile
|
||||
docs/warnings.txt
|
||||
.DS_Store
|
||||
|
||||
+3
-26
@@ -24,25 +24,18 @@ env:
|
||||
- TEST_DIR=tests/examples
|
||||
- TEST_DIR=tests/em/fdem/inverse/adjoint
|
||||
- TEST_DIR=tests/em/fdem/forward
|
||||
- TEST_DIR=tests/docs;
|
||||
GAE_PYTHONPATH=${HOME}/.cache/google_appengine;
|
||||
PATH=$PATH:${HOME}/google-cloud-sdk/bin;
|
||||
PYTHONPATH=${PYTHONPATH}:${GAE_PYTHONPATH};
|
||||
CLOUDSDK_CORE_DISABLE_PROMPTS=1
|
||||
|
||||
# Setup anaconda
|
||||
before_install:
|
||||
# Install packages
|
||||
- if [ ${TRAVIS_PYTHON_VERSION:0:1} == "2" ]; then wget http://repo.continuum.io/miniconda/Miniconda-3.8.3-Linux-x86_64.sh
|
||||
-O miniconda.sh; else wget http://repo.continuum.io/miniconda/Miniconda3-3.8.3-Linux-x86_64.sh
|
||||
-O miniconda.sh; fi
|
||||
- if [ ${TRAVIS_PYTHON_VERSION:0:1} == "2" ]; then wget http://repo.continuum.io/miniconda/Miniconda-3.8.3-Linux-x86_64.sh -O miniconda.sh; else wget http://repo.continuum.io/miniconda/Miniconda3-3.8.3-Linux-x86_64.sh -O miniconda.sh; fi
|
||||
- chmod +x miniconda.sh
|
||||
- ./miniconda.sh -b
|
||||
- export PATH=/home/travis/anaconda/bin:/home/travis/miniconda/bin:$PATH
|
||||
- conda update --yes conda
|
||||
|
||||
# Install packages
|
||||
install:
|
||||
- conda install --yes pip python=$TRAVIS_PYTHON_VERSION numpy scipy matplotlib cython ipython nose vtk sphinx
|
||||
- conda install --yes pip python=$TRAVIS_PYTHON_VERSION numpy scipy matplotlib cython ipython nose vtk
|
||||
- pip install nose-cov python-coveralls
|
||||
|
||||
- git clone https://github.com/rowanc1/pymatsolver.git
|
||||
@@ -53,28 +46,12 @@ install:
|
||||
|
||||
# Run test
|
||||
script:
|
||||
# test docs
|
||||
- nosetests $TEST_DIR --with-cov --cov SimPEG --cov-config .coveragerc -v -s
|
||||
|
||||
# Calculate coverage
|
||||
after_success:
|
||||
- coveralls --config_file .coveragerc
|
||||
|
||||
- if [ "$TRAVIS_BRANCH" = "master" -a "$TRAVIS_PULL_REQUEST" = "false" ]; then
|
||||
if [ ${TEST_DIR} == "tests/docs" ]; then
|
||||
python scripts/fetch_gae_sdk.py $(dirname "${GAE_PYTHONPATH}");
|
||||
openssl aes-256-cbc -K $encrypted_93066031461c_key -iv $encrypted_93066031461c_iv
|
||||
-in docs/credentials.tar.gz.enc -out credentials.tar.gz -d ;
|
||||
if [ ! -d ${HOME}/google-cloud-sdk ]; then curl https://sdk.cloud.google.com | bash; fi ;
|
||||
tar -xzf credentials.tar.gz ;
|
||||
gcloud auth activate-service-account --key-file client-secret.json ;
|
||||
gcloud config set project simpegdocs;
|
||||
gcloud -q components update gae-python;
|
||||
gcloud -q preview app deploy ./docs/app.yaml --version ${TRAVIS_COMMIT} --promote;
|
||||
fi;
|
||||
fi
|
||||
|
||||
|
||||
notifications:
|
||||
email:
|
||||
- rowanc1@gmail.com
|
||||
|
||||
+1
-1
@@ -1,4 +1,4 @@
|
||||
.. image:: https://raw.github.com/simpeg/simpeg/master/docs/images/simpeg-logo.png
|
||||
.. image:: https://raw.github.com/simpeg/simpeg/master/docs/simpeg-logo.png
|
||||
:alt: SimPEG Logo
|
||||
|
||||
======
|
||||
|
||||
@@ -162,8 +162,8 @@ class ProblemDC_CC(Problem.BaseProblem):
|
||||
"""
|
||||
Makes the matrix A(m) for the DC resistivity problem.
|
||||
|
||||
:param numpy.ndarray m: model
|
||||
:rtype: scipy.sparse.csc_matrix
|
||||
:param numpy.array m: model
|
||||
:rtype: scipy.csc_matrix
|
||||
:return: A(m)
|
||||
|
||||
.. math::
|
||||
|
||||
@@ -71,7 +71,7 @@ class ProblemIP(Problem.BaseProblem):
|
||||
Makes the matrix A(m) for the DC resistivity problem.
|
||||
|
||||
:param numpy.array m: model
|
||||
:rtype: scipy.sparse.csc_matrix
|
||||
:rtype: scipy.csc_matrix
|
||||
:return: A(m)
|
||||
|
||||
.. math::
|
||||
|
||||
+58
-132
@@ -144,7 +144,6 @@ class BetaSchedule(InversionDirective):
|
||||
if self.debug: print 'BetaSchedule is cooling Beta. Iteration: %d' % self.opt.iter
|
||||
self.invProb.beta /= self.coolingFactor
|
||||
|
||||
|
||||
class TargetMisfit(InversionDirective):
|
||||
|
||||
chifact = 1.
|
||||
@@ -167,7 +166,7 @@ class TargetMisfit(InversionDirective):
|
||||
|
||||
|
||||
|
||||
class SaveEveryIteration(InversionDirective):
|
||||
class _SaveEveryIteration(InversionDirective):
|
||||
@property
|
||||
def name(self):
|
||||
if getattr(self, '_name', None) is None:
|
||||
@@ -188,7 +187,7 @@ class SaveEveryIteration(InversionDirective):
|
||||
self._fileName = value
|
||||
|
||||
|
||||
class SaveModelEveryIteration(SaveEveryIteration):
|
||||
class SaveModelEveryIteration(_SaveEveryIteration):
|
||||
"""SaveModelEveryIteration"""
|
||||
|
||||
def initialize(self):
|
||||
@@ -198,7 +197,7 @@ class SaveModelEveryIteration(SaveEveryIteration):
|
||||
np.save('%03d-%s' % (self.opt.iter, self.fileName), self.opt.xc)
|
||||
|
||||
|
||||
class SaveOutputEveryIteration(SaveEveryIteration):
|
||||
class SaveOutputEveryIteration(_SaveEveryIteration):
|
||||
"""SaveModelEveryIteration"""
|
||||
|
||||
def initialize(self):
|
||||
@@ -212,7 +211,7 @@ class SaveOutputEveryIteration(SaveEveryIteration):
|
||||
f.write(' %3d %1.4e %1.4e %1.4e %1.4e\n'%(self.opt.iter, self.invProb.beta, self.invProb.phi_d, self.invProb.phi_m, self.opt.f))
|
||||
f.close()
|
||||
|
||||
class SaveOutputDictEveryIteration(SaveEveryIteration):
|
||||
class SaveOutputDictEveryIteration(_SaveEveryIteration):
|
||||
"""SaveOutputDictEveryIteration"""
|
||||
|
||||
def initialize(self):
|
||||
@@ -243,6 +242,12 @@ class SaveOutputDictEveryIteration(SaveEveryIteration):
|
||||
# Save the file as a npz
|
||||
np.savez('{:03d}-{:s}'.format(self.opt.iter,self.fileName), iter=self.opt.iter, beta=self.invProb.beta, phi_d=self.invProb.phi_d, phi_m=self.invProb.phi_m, phi_ms=phi_ms, phi_mx=phi_mx, phi_my=phi_my, phi_mz=phi_mz,f=self.opt.f, m=self.invProb.curModel,dpred=self.invProb.dpred)
|
||||
|
||||
|
||||
# class UpdateReferenceModel(Parameter):
|
||||
|
||||
# mref0 = None
|
||||
|
||||
# def nextIter(self):
|
||||
# mref = getattr(self, 'm_prev', None)
|
||||
# if mref is None:
|
||||
# if self.debug: print 'UpdateReferenceModel is using mref0'
|
||||
@@ -253,151 +258,56 @@ class SaveOutputDictEveryIteration(SaveEveryIteration):
|
||||
class Update_IRLS(InversionDirective):
|
||||
|
||||
eps_min = None
|
||||
eps = None
|
||||
norms = [2.,2.,2.,2.]
|
||||
factor = None
|
||||
gamma = None
|
||||
phi_m_last = None
|
||||
phi_d_last = None
|
||||
f_old = None
|
||||
f_min_change = 1e-2
|
||||
beta_tol = 5e-2
|
||||
prctile = 95
|
||||
|
||||
# Solving parameter for IRLS (mode:2)
|
||||
IRLSiter = 0
|
||||
minGNiter = 5
|
||||
maxIRLSiter = 10
|
||||
iterStart = 0
|
||||
|
||||
# Beta schedule
|
||||
coolingFactor = 2.
|
||||
coolingRate = 1
|
||||
|
||||
mode = 1
|
||||
|
||||
@property
|
||||
def target(self):
|
||||
if getattr(self, '_target', None) is None:
|
||||
self._target = self.survey.nD*0.5
|
||||
return self._target
|
||||
@target.setter
|
||||
def target(self, val):
|
||||
self._target = val
|
||||
|
||||
def initialize(self):
|
||||
|
||||
if self.mode == 1:
|
||||
self.reg.norms = [2., 2., 2., 2.]
|
||||
# Scale the regularization for changes in norm
|
||||
if getattr(self, 'phi_m_last', None) is not None:
|
||||
|
||||
self.reg.curModel = self.invProb.curModel
|
||||
self.reg.gamma = 1.
|
||||
phim_new = self.reg.eval(self.invProb.curModel)
|
||||
self.gamma = self.phi_m_last / phim_new
|
||||
|
||||
self.reg.curModel = self.invProb.curModel
|
||||
self.reg.gamma = self.gamma
|
||||
|
||||
if getattr(self, 'phi_d_last', None) is None:
|
||||
self.phi_d_last = self.invProb.phi_d
|
||||
|
||||
def endIter(self):
|
||||
# Cool the threshold parameter if required
|
||||
if getattr(self, 'factor', None) is not None:
|
||||
eps = self.reg.eps / self.factor
|
||||
|
||||
# After reaching target misfit with l2-norm, switch to IRLS (mode:2)
|
||||
if self.invProb.phi_d < self.target and self.mode == 1:
|
||||
print "Convergence with smooth l2-norm regularization: Start IRLS steps..."
|
||||
|
||||
self.mode = 2
|
||||
|
||||
# Either use the supplied epsilon, or fix base on distribution of
|
||||
# model values
|
||||
if getattr(self, 'reg.eps', None) is None:
|
||||
self.reg.eps_p = np.percentile(np.abs(self.invProb.curModel),self.prctile)
|
||||
else:
|
||||
self.reg.eps_p = self.eps[0]
|
||||
|
||||
if getattr(self, 'reg.eps', None) is None:
|
||||
self.reg.eps_q = np.percentile(np.abs(self.reg.regmesh.cellDiffxStencil*(self.reg.mapping * self.invProb.curModel)),self.prctile)
|
||||
else:
|
||||
self.reg.eps_q = self.eps[1]
|
||||
|
||||
print "L[p qx qy qz]-norm : " + str(self.reg.norms)
|
||||
print "eps_p: " + str(self.reg.eps_p) + " eps_q: " + str(self.reg.eps_q)
|
||||
|
||||
self.reg.norms = self.norms
|
||||
self.coolingFactor = 1.
|
||||
self.coolingRate = 1
|
||||
self.iterStart = self.opt.iter
|
||||
self.phi_d_last = self.invProb.phi_d
|
||||
self.phi_m_last = self.invProb.phi_m_last
|
||||
|
||||
self.reg.l2model = self.invProb.curModel
|
||||
self.reg.curModel = self.invProb.curModel
|
||||
|
||||
if getattr(self, 'f_old', None) is None:
|
||||
self.f_old = self.reg.eval(self.invProb.curModel)#self.invProb.evalFunction(self.invProb.curModel, return_g=False, return_H=False)
|
||||
|
||||
# Beta Schedule
|
||||
if self.opt.iter > 0 and self.opt.iter % self.coolingRate == 0:
|
||||
if self.debug: print 'BetaSchedule is cooling Beta. Iteration: %d' % self.opt.iter
|
||||
self.invProb.beta /= self.coolingFactor
|
||||
|
||||
|
||||
# Only update after GN iterations
|
||||
if (self.opt.iter-self.iterStart) % self.minGNiter == 0 and self.mode==2:
|
||||
|
||||
self.IRLSiter += 1
|
||||
|
||||
phim_new = self.reg.eval(self.invProb.curModel)
|
||||
self.f_change = np.abs(self.f_old - phim_new) / self.f_old
|
||||
|
||||
print "Regularization decrease: %6.3e" % (self.f_change)
|
||||
|
||||
# Check for maximum number of IRLS cycles
|
||||
if self.IRLSiter == self.maxIRLSiter:
|
||||
print "Reach maximum number of IRLS cycles: %i" % self.maxIRLSiter
|
||||
self.opt.stopNextIteration = True
|
||||
return
|
||||
|
||||
# Check if the function has changed enough
|
||||
if self.f_change < self.f_min_change and self.IRLSiter > 1:
|
||||
print "Minimum decrease in regularization. End of IRLS"
|
||||
self.opt.stopNextIteration = True
|
||||
return
|
||||
if getattr(self, 'eps_min', None) is not None:
|
||||
self.reg.eps = np.max([self.eps_min,eps])
|
||||
else:
|
||||
self.f_old = phim_new
|
||||
self.reg.eps = eps
|
||||
|
||||
# # Cool the threshold parameter if required
|
||||
# if getattr(self, 'factor', None) is not None:
|
||||
# eps = self.reg.eps / self.factor
|
||||
#
|
||||
# if getattr(self, 'eps_min', None) is not None:
|
||||
# self.reg.eps = np.max([self.eps_min,eps])
|
||||
# else:
|
||||
# self.reg.eps = eps
|
||||
# Get phi_m at the end of current iteration
|
||||
self.phi_m_last = self.invProb.phi_m_last
|
||||
|
||||
# Get phi_m at the end of current iteration
|
||||
self.phi_m_last = self.invProb.phi_m_last
|
||||
# Update the model used for the IRLS weights
|
||||
self.reg.curModel = self.invProb.curModel
|
||||
|
||||
# Reset the regularization matrices so that it is
|
||||
# recalculated for current model
|
||||
self.reg._Wsmall = None
|
||||
self.reg._Wx = None
|
||||
self.reg._Wy = None
|
||||
self.reg._Wz = None
|
||||
# Temporarely set gamma to 1. to get raw phi_m
|
||||
self.reg.gamma = 1.
|
||||
|
||||
# Update the model used for the IRLS weights
|
||||
self.reg.curModel = self.invProb.curModel
|
||||
# Compute new model objective function value
|
||||
phim_new = self.reg.eval(self.invProb.curModel)
|
||||
|
||||
# Temporarely set gamma to 1. to get raw phi_m
|
||||
self.reg.gamma = 1.
|
||||
# Update gamma to scale the regularization between IRLS iterations
|
||||
self.reg.gamma = self.phi_m_last / phim_new
|
||||
|
||||
# Compute new model objective function value
|
||||
phim_new = self.reg.eval(self.invProb.curModel)
|
||||
|
||||
# Update gamma to scale the regularization between IRLS iterations
|
||||
self.reg.gamma = self.phi_m_last / phim_new
|
||||
|
||||
# Reset the regularization matrices again for new gamma
|
||||
self.reg._Wsmall = None
|
||||
self.reg._Wx = None
|
||||
self.reg._Wy = None
|
||||
self.reg._Wz = None
|
||||
|
||||
# Check if misfit is within the tolerance, otherwise scale beta
|
||||
val = self.invProb.phi_d / (self.survey.nD*0.5)
|
||||
|
||||
if np.abs(1.-val) > self.beta_tol:
|
||||
self.invProb.beta = self.invProb.beta * self.survey.nD*0.5 / self.invProb.phi_d
|
||||
# Set the weighting matrix to None so that it is recomputed next time
|
||||
# it is called in the inversion
|
||||
self.reg._W = None
|
||||
|
||||
class Update_lin_PreCond(InversionDirective):
|
||||
"""
|
||||
@@ -450,3 +360,19 @@ class Update_Wj(InversionDirective):
|
||||
JtJdiag = JtJdiag / max(JtJdiag)
|
||||
|
||||
self.reg.wght = JtJdiag
|
||||
|
||||
class Scale_Beta(InversionDirective):
|
||||
"""
|
||||
Instead of a linear cooling schedule, beta is allowed to change based
|
||||
on the ratio between the target misfit and the current data misfit. The
|
||||
update is done only if the misfit is outside some threshold bounds.
|
||||
"""
|
||||
tol = 0.05
|
||||
|
||||
def endIter(self):
|
||||
|
||||
# Check if misfit is within the tolerance, otherwise adjust beta
|
||||
val = self.invProb.phi_d / (self.survey.nD*0.5)
|
||||
|
||||
if np.abs(1.-val) > self.tol:
|
||||
self.invProb.beta = self.invProb.beta * self.survey.nD*0.5 / self.invProb.phi_d
|
||||
|
||||
@@ -1,302 +0,0 @@
|
||||
from __future__ import division
|
||||
import numpy as np
|
||||
from scipy.constants import mu_0, pi, epsilon_0
|
||||
from scipy.special import erf
|
||||
from SimPEG import Utils
|
||||
|
||||
omega = lambda f: 2.*np.pi*f
|
||||
# TODO:
|
||||
# r = lambda dx, dy, dz: np.sqrt( dx**2. + dy**2. + dz**2.)
|
||||
# k = lambda f, mu, epsilon, sig: np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
|
||||
|
||||
def E_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=0., epsr=1.):
|
||||
|
||||
"""
|
||||
Computing Analytic Electric fields from Electrical Dipole in a Wholespace
|
||||
TODO:
|
||||
Add description of parameters
|
||||
"""
|
||||
mu = mu_0*(1+kappa)
|
||||
epsilon = epsilon_0*epsr
|
||||
sig_hat = sig + 1j*omega(f)*epsilon
|
||||
|
||||
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
|
||||
# Check
|
||||
if XYZ.shape[0] > 1 & f.shape[0] > 1:
|
||||
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
|
||||
|
||||
dx = XYZ[:,0]-srcLoc[0]
|
||||
dy = XYZ[:,1]-srcLoc[1]
|
||||
dz = XYZ[:,2]-srcLoc[2]
|
||||
|
||||
r = np.sqrt( dx**2. + dy**2. + dz**2.)
|
||||
# k = np.sqrt( -1j*2.*np.pi*f*mu*sig )
|
||||
k = np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
|
||||
|
||||
front = current * length / (4.*np.pi*sig_hat* r**3) * np.exp(-1j*k*r)
|
||||
mid = -k**2 * r**2 + 3*1j*k*r + 3
|
||||
|
||||
if orientation.upper() == 'X':
|
||||
Ex = front*((dx**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
|
||||
Ey = front*(dx*dy / r**2)*mid
|
||||
Ez = front*(dx*dz / r**2)*mid
|
||||
return Ex, Ey, Ez
|
||||
|
||||
elif orientation.upper() == 'Y':
|
||||
# x--> y, y--> z, z-->x
|
||||
Ey = front*((dy**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
|
||||
Ez = front*(dy*dz / r**2)*mid
|
||||
Ex = front*(dy*dx / r**2)*mid
|
||||
return Ex, Ey, Ez
|
||||
|
||||
elif orientation.upper() == 'Z':
|
||||
# x --> z, y --> x, z --> y
|
||||
Ez = front*((dz**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
|
||||
Ex = front*(dz*dx / r**2)*mid
|
||||
Ey = front*(dz*dy / r**2)*mid
|
||||
return Ex, Ey, Ez
|
||||
|
||||
|
||||
def E_galvanic_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
|
||||
|
||||
"""
|
||||
Computing Galvanic portion of Electric fields from Electrical Dipole in a Wholespace
|
||||
TODO:
|
||||
Add description of parameters
|
||||
"""
|
||||
mu = mu_0*(1+kappa)
|
||||
epsilon = epsilon_0*epsr
|
||||
sig_hat = sig + 1j*omega(f)*epsilon
|
||||
|
||||
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
|
||||
# Check
|
||||
if XYZ.shape[0] > 1 & f.shape[0] > 1:
|
||||
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
|
||||
|
||||
dx = XYZ[:,0]-srcLoc[0]
|
||||
dy = XYZ[:,1]-srcLoc[1]
|
||||
dz = XYZ[:,2]-srcLoc[2]
|
||||
|
||||
r = np.sqrt( dx**2. + dy**2. + dz**2.)
|
||||
# k = np.sqrt( -1j*2.*np.pi*f*mu*sig )
|
||||
k = np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
|
||||
|
||||
front = current * length / (4.*np.pi*sig_hat* r**3) * np.exp(-1j*k*r)
|
||||
mid = -k**2 * r**2 + 3*1j*k*r + 3
|
||||
|
||||
if orientation.upper() == 'X':
|
||||
Ex_galvanic = front*((dx**2 / r**2)*mid + (-1j*k*r-1.))
|
||||
Ey_galvanic = front*(dx*dy / r**2)*mid
|
||||
Ez_galvanic = front*(dx*dz / r**2)*mid
|
||||
return Ex_galvanic, Ey_galvanic, Ez_galvanic
|
||||
|
||||
elif orientation.upper() == 'Y':
|
||||
# x--> y, y--> z, z-->x
|
||||
Ey_galvanic = front*((dy**2 / r**2)*mid + (-1j*k*r-1.))
|
||||
Ez_galvanic = front*(dy*dz / r**2)*mid
|
||||
Ex_galvanic = front*(dy*dx / r**2)*mid
|
||||
return Ex_galvanic, Ey_galvanic, Ez_galvanic
|
||||
|
||||
elif orientation.upper() == 'Z':
|
||||
# x --> z, y --> x, z --> y
|
||||
Ez_galvanic = front*((dz**2 / r**2)*mid + (-1j*k*r-1.))
|
||||
Ex_galvanic = front*(dz*dx / r**2)*mid
|
||||
Ey_galvanic = front*(dz*dy / r**2)*mid
|
||||
return Ex_galvanic, Ey_galvanic, Ez_galvanic
|
||||
|
||||
|
||||
def E_inductive_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
|
||||
|
||||
"""
|
||||
Computing Inductive portion of Electric fields from Electrical Dipole in a Wholespace
|
||||
TODO:
|
||||
Add description of parameters
|
||||
"""
|
||||
mu = mu_0*(1+kappa)
|
||||
epsilon = epsilon_0*epsr
|
||||
sig_hat = sig + 1j*omega(f)*epsilon
|
||||
|
||||
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
|
||||
# Check
|
||||
if XYZ.shape[0] > 1 & f.shape[0] > 1:
|
||||
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
|
||||
|
||||
dx = XYZ[:,0]-srcLoc[0]
|
||||
dy = XYZ[:,1]-srcLoc[1]
|
||||
dz = XYZ[:,2]-srcLoc[2]
|
||||
|
||||
r = np.sqrt( dx**2. + dy**2. + dz**2.)
|
||||
# k = np.sqrt( -1j*2.*np.pi*f*mu*sig )
|
||||
k = np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
|
||||
|
||||
front = current * length / (4.*np.pi*sig_hat* r**3) * np.exp(-1j*k*r)
|
||||
|
||||
if orientation.upper() == 'X':
|
||||
Ex_inductive = front*(k**2 * r**2)
|
||||
Ey_inductive = np.zeros_like(Ex_inductive)
|
||||
Ez_inductive = np.zeros_like(Ex_inductive)
|
||||
return Ex_inductive, Ey_inductive, Ez_inductive
|
||||
|
||||
elif orientation.upper() == 'Y':
|
||||
# x--> y, y--> z, z-->x
|
||||
Ey_inductive = front*(k**2 * r**2)
|
||||
Ez_inductive = np.zeros_like(Ey_inductive)
|
||||
Ex_inductive = np.zeros_like(Ey_inductive)
|
||||
return Ex_inductive, Ey_inductive, Ez_inductive
|
||||
|
||||
elif orientation.upper() == 'Z':
|
||||
# x --> z, y --> x, z --> y
|
||||
Ez_inductive = front*(k**2 * r**2)
|
||||
Ex_inductive = np.zeros_like(Ez_inductive)
|
||||
Ey_inductive = np.zeros_like(Ez_inductive)
|
||||
return Ex_inductive, Ey_inductive, Ez_inductive
|
||||
|
||||
|
||||
def J_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
|
||||
|
||||
"""
|
||||
Computing Current densities from Electrical Dipole in a Wholespace
|
||||
TODO:
|
||||
Add description of parameters
|
||||
"""
|
||||
|
||||
Ex, Ey, Ez = E_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=current, length=length, orientation=orientation, kappa=kappa, epsr=epsr)
|
||||
Jx = sig*Ex
|
||||
Jy = sig*Ey
|
||||
Jz = sig*Ez
|
||||
return Jx, Jy, Jz
|
||||
|
||||
|
||||
def J_galvanic_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
|
||||
|
||||
"""
|
||||
Computing Galvanic portion of Current densities from Electrical Dipole in a Wholespace
|
||||
TODO:
|
||||
Add description of parameters
|
||||
"""
|
||||
|
||||
Ex_galvanic, Ey_galvanic, Ez_galvanic = E_galvanic_from_ElectricDipoleWholeSpaced(XYZ, srcLoc, sig, f, current=current, length=length, orientation=orientation, kappa=kappa, epsr=epsr)
|
||||
Jx_galvanic = sig*Ex_galvanic
|
||||
Jy_galvanic = sig*Ey_galvanic
|
||||
Jz_galvanic = sig*Ez_galvanic
|
||||
return Jx_galvanic, Jy_galvanic, Jz_galvanic
|
||||
|
||||
|
||||
def J_inductive_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
|
||||
|
||||
"""
|
||||
Computing Inductive portion of Current densities from Electrical Dipole in a Wholespace
|
||||
TODO:
|
||||
Add description of parameters
|
||||
"""
|
||||
|
||||
Ex_inductive, Ey_inductive, Ez_inductive = E_inductive_from_ElectricDipoleWholeSpaced(XYZ, srcLoc, sig, f, current=current, length=length, orientation=orientation, kappa=kappa, epsr=epsr)
|
||||
Jx_inductive = sig*Ex_inductive
|
||||
Jy_inductive = sig*Ey_inductive
|
||||
Jz_inductive = sig*Ez_inductive
|
||||
return Jx_inductive, Jy_inductive, Jz_inductive
|
||||
|
||||
|
||||
def H_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
|
||||
|
||||
"""
|
||||
Computing Magnetic fields from Electrical Dipole in a Wholespace
|
||||
TODO:
|
||||
Add description of parameters
|
||||
"""
|
||||
mu = mu_0*(1+kappa)
|
||||
epsilon = epsilon_0*epsr
|
||||
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
|
||||
# Check
|
||||
if XYZ.shape[0] > 1 & f.shape[0] > 1:
|
||||
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
|
||||
|
||||
dx = XYZ[:,0]-srcLoc[0]
|
||||
dy = XYZ[:,1]-srcLoc[1]
|
||||
dz = XYZ[:,2]-srcLoc[2]
|
||||
|
||||
r = np.sqrt( dx**2. + dy**2. + dz**2.)
|
||||
# k = np.sqrt( -1j*2.*np.pi*f*mu*sig )
|
||||
k = np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
|
||||
|
||||
front = current * length / (4.*np.pi* r**2) * (-1j*k*r + 1) * np.exp(-1j*k*r)
|
||||
|
||||
if orientation.upper() == 'X':
|
||||
Hy = front*(-dz / r)
|
||||
Hz = front*(dy / r)
|
||||
Hx = np.zeros_like(Hy)
|
||||
return Hx, Hy, Hz
|
||||
|
||||
elif orientation.upper() == 'Y':
|
||||
Hx = front*(dz / r)
|
||||
Hz = front*(-dx / r)
|
||||
Hy = np.zeros_like(Hx)
|
||||
return Hx, Hy, Hz
|
||||
|
||||
elif orientation.upper() == 'Z':
|
||||
Hx = front*(-dy / r)
|
||||
Hy = front*(dx / r)
|
||||
Hz = np.zeros_like(Hx)
|
||||
return Hx, Hy, Hz
|
||||
|
||||
|
||||
def B_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
|
||||
|
||||
"""
|
||||
Computing Magnetic flux densites from Electrical Dipole in a Wholespace
|
||||
TODO:
|
||||
Add description of parameters
|
||||
"""
|
||||
|
||||
Hx, Hy, Hz = H_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=current, length=length, orientation=orientation, kappa=kappa, epsr=epsr)
|
||||
Bx = mu*Hx
|
||||
By = mu*Hy
|
||||
Bz = mu*Hz
|
||||
return Bx, By, Bz
|
||||
|
||||
|
||||
def A_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
|
||||
|
||||
"""
|
||||
Computing Electric vector potentials from Electrical Dipole in a Wholespace
|
||||
TODO:
|
||||
Add description of parameters
|
||||
"""
|
||||
mu = mu_0*(1+kappa)
|
||||
epsilon = epsilon_0*epsr
|
||||
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
|
||||
# Check
|
||||
if XYZ.shape[0] > 1 & f.shape[0] > 1:
|
||||
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
|
||||
|
||||
dx = XYZ[:,0]-srcLoc[0]
|
||||
dy = XYZ[:,1]-srcLoc[1]
|
||||
dz = XYZ[:,2]-srcLoc[2]
|
||||
|
||||
r = np.sqrt( dx**2. + dy**2. + dz**2.)
|
||||
k = np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
|
||||
|
||||
front = current * length / (4.*np.pi*r)
|
||||
|
||||
if orientation.upper() == 'X':
|
||||
Ax = front*np.exp(-1j*k*r)
|
||||
Ay = np.zeros_like(Ax)
|
||||
Az = np.zeros_like(Ax)
|
||||
return Ax, Ay, Az
|
||||
|
||||
elif orientation.upper() == 'Y':
|
||||
Ay = front*np.exp(-1j*k*r)
|
||||
Ax = np.zeros_like(Ay)
|
||||
Az = np.zeros_like(Ay)
|
||||
return Ax, Ay, Az
|
||||
|
||||
elif orientation.upper() == 'Z':
|
||||
Az = front*np.exp(-1j*k*r)
|
||||
Ax = np.zeros_like(Ay)
|
||||
Ay = np.zeros_like(Ay)
|
||||
return Ax, Ay, Az
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
@@ -2,4 +2,3 @@ from TDEM import hzAnalyticDipoleT
|
||||
from FDEM import hzAnalyticDipoleF
|
||||
from FDEMcasing import *
|
||||
from DC import DCAnalyticHalf, DCAnalyticSphere
|
||||
from FDEMDipolarfields import *
|
||||
|
||||
+3
-4
@@ -20,10 +20,10 @@ class BaseEMProblem(Problem.BaseProblem):
|
||||
Problem.BaseProblem.__init__(self, mesh, **kwargs)
|
||||
|
||||
|
||||
surveyPair = Survey.BaseSurvey #: The survey to pair with.
|
||||
dataPair = Survey.Data #: The data to pair with.
|
||||
surveyPair = Survey.BaseSurvey
|
||||
dataPair = Survey.Data
|
||||
|
||||
PropMap = EMPropMap #: The property mapping
|
||||
PropMap = EMPropMap
|
||||
|
||||
Solver = SimpegSolver
|
||||
solverOpts = {}
|
||||
@@ -217,7 +217,6 @@ class BaseEMSurvey(Survey.BaseSurvey):
|
||||
def eval(self, f):
|
||||
"""
|
||||
Project fields to receiver locations
|
||||
|
||||
:param Fields u: fields object
|
||||
:rtype: numpy.ndarray
|
||||
:return: data
|
||||
|
||||
@@ -6,11 +6,11 @@ from SimPEG.EM.Utils import omega
|
||||
from SimPEG.Utils import Zero, Identity, sdiag
|
||||
|
||||
|
||||
class FieldsFDEM(SimPEG.Problem.Fields):
|
||||
class Fields(SimPEG.Problem.Fields):
|
||||
"""
|
||||
|
||||
Fancy Field Storage for a FDEM survey. Only one field type is stored for
|
||||
each problem, the rest are computed. The fields object acts like an array and is indexed by
|
||||
each problem, the rest are computed. The fields obejct acts like an array and is indexed by
|
||||
|
||||
.. code-block:: python
|
||||
|
||||
@@ -92,7 +92,7 @@ class FieldsFDEM(SimPEG.Problem.Fields):
|
||||
"""
|
||||
Total derivative of e with respect to the inversion model. Returns :math:`d\mathbf{e}/d\mathbf{m}` for forward and (:math:`d\mathbf{e}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
|
||||
|
||||
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: source
|
||||
:param Src src: sorce
|
||||
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
|
||||
:param numpy.ndarray v: vector to take sensitivity product with
|
||||
:param bool adjoint: adjoint?
|
||||
@@ -110,7 +110,7 @@ class FieldsFDEM(SimPEG.Problem.Fields):
|
||||
"""
|
||||
Total derivative of b with respect to the inversion model. Returns :math:`d\mathbf{b}/d\mathbf{m}` for forward and (:math:`d\mathbf{b}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
|
||||
|
||||
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: source
|
||||
:param Src src: sorce
|
||||
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
|
||||
:param numpy.ndarray v: vector to take sensitivity product with
|
||||
:param bool adjoint: adjoint?
|
||||
@@ -128,7 +128,7 @@ class FieldsFDEM(SimPEG.Problem.Fields):
|
||||
"""
|
||||
Total derivative of h with respect to the inversion model. Returns :math:`d\mathbf{h}/d\mathbf{m}` for forward and (:math:`d\mathbf{h}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
|
||||
|
||||
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: source
|
||||
:param Src src: sorce
|
||||
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
|
||||
:param numpy.ndarray v: vector to take sensitivity product with
|
||||
:param bool adjoint: adjoint?
|
||||
@@ -146,7 +146,7 @@ class FieldsFDEM(SimPEG.Problem.Fields):
|
||||
"""
|
||||
Total derivative of j with respect to the inversion model. Returns :math:`d\mathbf{j}/d\mathbf{m}` for forward and (:math:`d\mathbf{j}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
|
||||
|
||||
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: source
|
||||
:param Src src: sorce
|
||||
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
|
||||
:param numpy.ndarray v: vector to take sensitivity product with
|
||||
:param bool adjoint: adjoint?
|
||||
@@ -160,12 +160,12 @@ class FieldsFDEM(SimPEG.Problem.Fields):
|
||||
return self._jDeriv_u(src, v, adjoint), self._jDeriv_m(src, v, adjoint)
|
||||
return np.array(self._jDeriv_u(src, du_dm_v, adjoint) + self._jDeriv_m(src, v, adjoint), dtype = complex)
|
||||
|
||||
class Fields3D_e(FieldsFDEM):
|
||||
class Fields3D_e(Fields):
|
||||
"""
|
||||
Fields object for Problem3D_e.
|
||||
|
||||
:param BaseMesh mesh: mesh
|
||||
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
|
||||
:param Mesh mesh: mesh
|
||||
:param Survey survey: survey
|
||||
"""
|
||||
|
||||
knownFields = {'eSolution':'E'}
|
||||
@@ -180,6 +180,9 @@ class Fields3D_e(FieldsFDEM):
|
||||
'h' : ['eSolution','CCV','_h'],
|
||||
}
|
||||
|
||||
def __init__(self, mesh, survey, **kwargs):
|
||||
Fields.__init__(self, mesh, survey, **kwargs)
|
||||
|
||||
def startup(self):
|
||||
self.prob = self.survey.prob
|
||||
self._edgeCurl = self.survey.prob.mesh.edgeCurl
|
||||
@@ -254,7 +257,7 @@ class Fields3D_e(FieldsFDEM):
|
||||
"""
|
||||
|
||||
# assuming primary does not depend on the model
|
||||
return Zero()
|
||||
return src.ePrimaryDeriv(self.prob, v, adjoint) #Zero()
|
||||
|
||||
def _bPrimary(self, eSolution, srcList):
|
||||
"""
|
||||
@@ -423,12 +426,12 @@ class Fields3D_e(FieldsFDEM):
|
||||
|
||||
|
||||
|
||||
class Fields3D_b(FieldsFDEM):
|
||||
class Fields3D_b(Fields):
|
||||
"""
|
||||
Fields object for Problem3D_b.
|
||||
|
||||
:param BaseMesh mesh: mesh
|
||||
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
|
||||
:param Mesh mesh: mesh
|
||||
:param Survey survey: survey
|
||||
"""
|
||||
|
||||
knownFields = {'bSolution':'F'}
|
||||
@@ -443,6 +446,9 @@ class Fields3D_b(FieldsFDEM):
|
||||
'h' : ['bSolution','CCV','_h'],
|
||||
}
|
||||
|
||||
def __init__(self,mesh,survey,**kwargs):
|
||||
Fields.__init__(self,mesh,survey,**kwargs)
|
||||
|
||||
def startup(self):
|
||||
self.prob = self.survey.prob
|
||||
self._edgeCurl = self.survey.prob.mesh.edgeCurl
|
||||
@@ -594,8 +600,8 @@ class Fields3D_b(FieldsFDEM):
|
||||
|
||||
|
||||
if adjoint:
|
||||
return self._MeSigmaIDeriv(w).T * v - self._MeSigmaI.T * s_eDeriv
|
||||
return self._MeSigmaIDeriv(w) * v - self._MeSigmaI * s_eDeriv
|
||||
return self._MeSigmaIDeriv(w).T * v - self._MeSigmaI.T * s_eDeriv + src.ePrimaryDeriv(self.prob, v, adjoint)
|
||||
return self._MeSigmaIDeriv(w) * v - self._MeSigmaI * s_eDeriv + src.ePrimaryDeriv(self.prob, v, adjoint)
|
||||
|
||||
def _j(self, bSolution, srcList):
|
||||
"""
|
||||
@@ -687,12 +693,12 @@ class Fields3D_b(FieldsFDEM):
|
||||
return Zero()
|
||||
|
||||
|
||||
class Fields3D_j(FieldsFDEM):
|
||||
class Fields3D_j(Fields):
|
||||
"""
|
||||
Fields object for Problem3D_j.
|
||||
|
||||
:param BaseMesh mesh: mesh
|
||||
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
|
||||
:param Mesh mesh: mesh
|
||||
:param Survey survey: survey
|
||||
"""
|
||||
|
||||
knownFields = {'jSolution':'F'}
|
||||
@@ -707,6 +713,9 @@ class Fields3D_j(FieldsFDEM):
|
||||
'b' : ['jSolution','CCV','_b'],
|
||||
}
|
||||
|
||||
def __init__(self,mesh,survey,**kwargs):
|
||||
Fields.__init__(self,mesh,survey,**kwargs)
|
||||
|
||||
def startup(self):
|
||||
self.prob = self.survey.prob
|
||||
self._edgeCurl = self.survey.prob.mesh.edgeCurl
|
||||
@@ -979,12 +988,12 @@ class Fields3D_j(FieldsFDEM):
|
||||
return 1./(1j * omega(src.freq)) * VI * (self._aveE2CCV * ( s_mDeriv(v) - self._edgeCurl.T * ( self._MfRhoDeriv(jSolution) * v ) ) )
|
||||
|
||||
|
||||
class Fields3D_h(FieldsFDEM):
|
||||
class Fields3D_h(Fields):
|
||||
"""
|
||||
Fields object for Problem3D_h.
|
||||
|
||||
:param BaseMesh mesh: mesh
|
||||
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
|
||||
:param Mesh mesh: mesh
|
||||
:param Survey survey: survey
|
||||
"""
|
||||
|
||||
knownFields = {'hSolution':'E'}
|
||||
@@ -999,6 +1008,9 @@ class Fields3D_h(FieldsFDEM):
|
||||
'b' : ['hSolution','CCV','_b'],
|
||||
}
|
||||
|
||||
def __init__(self,mesh,survey,**kwargs):
|
||||
Fields.__init__(self,mesh,survey,**kwargs)
|
||||
|
||||
def startup(self):
|
||||
self.prob = self.survey.prob
|
||||
self._edgeCurl = self.survey.prob.mesh.edgeCurl
|
||||
|
||||
@@ -1,7 +1,7 @@
|
||||
from SimPEG import Problem, Utils, np, sp, Solver as SimpegSolver
|
||||
from scipy.constants import mu_0
|
||||
from SurveyFDEM import Survey as SurveyFDEM
|
||||
from FieldsFDEM import FieldsFDEM, Fields3D_e, Fields3D_b, Fields3D_h, Fields3D_j
|
||||
from FieldsFDEM import Fields, Fields3D_e, Fields3D_b, Fields3D_h, Fields3D_j
|
||||
from SimPEG.EM.Base import BaseEMProblem
|
||||
from SimPEG.EM.Utils import omega
|
||||
|
||||
@@ -31,11 +31,10 @@ class BaseFDEMProblem(BaseEMProblem):
|
||||
if using the H-J formulation (:code:`Problem3D_j` or :code:`Problem3D_h`). Note that here, :math:`\mathbf{s_m}` is an integrated quantity.
|
||||
|
||||
The problem performs the elimination so that we are solving the system for \\\(\\\mathbf{e},\\\mathbf{b},\\\mathbf{j} \\\) or \\\(\\\mathbf{h}\\\)
|
||||
|
||||
"""
|
||||
|
||||
surveyPair = SurveyFDEM
|
||||
fieldsPair = FieldsFDEM
|
||||
fieldsPair = Fields
|
||||
|
||||
def fields(self, m):
|
||||
"""
|
||||
@@ -65,7 +64,7 @@ class BaseFDEMProblem(BaseEMProblem):
|
||||
|
||||
:param numpy.array m: inversion model (nP,)
|
||||
:param numpy.array v: vector which we take sensitivity product with (nP,)
|
||||
:param SimPEG.EM.FDEM.FieldsFDEM.FieldsFDEM u: fields object
|
||||
:param SimPEG.EM.FDEM.Fields u: fields object
|
||||
:rtype numpy.array:
|
||||
:return: Jv (ndata,)
|
||||
"""
|
||||
@@ -75,7 +74,8 @@ class BaseFDEMProblem(BaseEMProblem):
|
||||
|
||||
self.curModel = m
|
||||
|
||||
Jv = self.dataPair(self.survey)
|
||||
# Jv = self.dataPair(self.survey)
|
||||
Jv = []
|
||||
|
||||
for freq in self.survey.freqs:
|
||||
A = self.getA(freq)
|
||||
@@ -90,9 +90,9 @@ class BaseFDEMProblem(BaseEMProblem):
|
||||
for rx in src.rxList:
|
||||
df_dmFun = getattr(f, '_{0}Deriv'.format(rx.projField), None)
|
||||
df_dm_v = df_dmFun(src, du_dm_v, v, adjoint=False)
|
||||
Jv[src, rx] = rx.evalDeriv(src, self.mesh, f, df_dm_v)
|
||||
Jv.append(rx.evalDeriv(src, self.mesh, f, df_dm_v))
|
||||
Ainv.clean()
|
||||
return Utils.mkvc(Jv)
|
||||
return np.hstack(Jv)
|
||||
|
||||
def Jtvec(self, m, v, f=None):
|
||||
"""
|
||||
@@ -100,7 +100,7 @@ class BaseFDEMProblem(BaseEMProblem):
|
||||
|
||||
:param numpy.array m: inversion model (nP,)
|
||||
:param numpy.array v: vector which we take adjoint product with (nP,)
|
||||
:param SimPEG.EM.FDEM.FieldsFDEM.FieldsFDEM u: fields object
|
||||
:param SimPEG.EM.FDEM.Fields u: fields object
|
||||
:rtype numpy.array:
|
||||
:return: Jv (ndata,)
|
||||
"""
|
||||
@@ -154,8 +154,8 @@ class BaseFDEMProblem(BaseEMProblem):
|
||||
Evaluates the sources for a given frequency and puts them in matrix form
|
||||
|
||||
:param float freq: Frequency
|
||||
:rtype: tuple
|
||||
:return: (s_m, s_e) (nE or nF, nSrc)
|
||||
:rtype: (numpy.ndarray, numpy.ndarray)
|
||||
:return: s_m, s_e (nE or nF, nSrc)
|
||||
"""
|
||||
Srcs = self.survey.getSrcByFreq(freq)
|
||||
if self._formulation is 'EB':
|
||||
@@ -167,7 +167,6 @@ class BaseFDEMProblem(BaseEMProblem):
|
||||
|
||||
for i, src in enumerate(Srcs):
|
||||
smi, sei = src.eval(self)
|
||||
#Why are you adding?
|
||||
s_m[:,i] = s_m[:,i] + smi
|
||||
s_e[:,i] = s_e[:,i] + sei
|
||||
|
||||
@@ -195,7 +194,7 @@ class Problem3D_e(BaseFDEMProblem):
|
||||
|
||||
which we solve for :math:`\mathbf{e}`.
|
||||
|
||||
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
|
||||
:param SimPEG.Mesh mesh: mesh
|
||||
"""
|
||||
|
||||
_solutionType = 'eSolution'
|
||||
@@ -270,7 +269,7 @@ class Problem3D_e(BaseFDEMProblem):
|
||||
Derivative of the right hand side with respect to the model
|
||||
|
||||
:param float freq: frequency
|
||||
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
|
||||
:param SimPEG.EM.FDEM.Src src: FDEM source
|
||||
:param numpy.ndarray v: vector to take product with
|
||||
:param bool adjoint: adjoint?
|
||||
:rtype: numpy.ndarray
|
||||
@@ -306,7 +305,7 @@ class Problem3D_b(BaseFDEMProblem):
|
||||
.. note ::
|
||||
The inverse problem will not work with full anisotropy
|
||||
|
||||
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
|
||||
:param SimPEG.Mesh mesh: mesh
|
||||
"""
|
||||
|
||||
_solutionType = 'bSolution'
|
||||
@@ -401,7 +400,7 @@ class Problem3D_b(BaseFDEMProblem):
|
||||
Derivative of the right hand side with respect to the model
|
||||
|
||||
:param float freq: frequency
|
||||
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
|
||||
:param SimPEG.EM.FDEM.Src src: FDEM source
|
||||
:param numpy.ndarray v: vector to take product with
|
||||
:param bool adjoint: adjoint?
|
||||
:rtype: numpy.ndarray
|
||||
@@ -445,7 +444,6 @@ class Problem3D_j(BaseFDEMProblem):
|
||||
|
||||
\mathbf{h} = \\frac{1}{i \omega} \mathbf{M_{\mu}^e}^{-1} \\left(-\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{j} + \mathbf{M^e} \mathbf{s_m} \\right)
|
||||
|
||||
|
||||
and solve for \\\(\\\mathbf{j}\\\) using
|
||||
|
||||
.. math ::
|
||||
@@ -455,7 +453,7 @@ class Problem3D_j(BaseFDEMProblem):
|
||||
.. note::
|
||||
This implementation does not yet work with full anisotropy!!
|
||||
|
||||
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
|
||||
:param SimPEG.Mesh mesh: mesh
|
||||
"""
|
||||
|
||||
_solutionType = 'jSolution'
|
||||
@@ -531,8 +529,8 @@ class Problem3D_j(BaseFDEMProblem):
|
||||
\mathbf{RHS} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1}\mathbf{s_m} -i\omega \mathbf{s_e}
|
||||
|
||||
:param float freq: Frequency
|
||||
:rtype: numpy.ndarray
|
||||
:return: RHS (nE, nSrc)
|
||||
:rtype: numpy.ndarray (nE, nSrc)
|
||||
:return: RHS
|
||||
"""
|
||||
|
||||
s_m, s_e = self.getSourceTerm(freq)
|
||||
@@ -551,7 +549,7 @@ class Problem3D_j(BaseFDEMProblem):
|
||||
Derivative of the right hand side with respect to the model
|
||||
|
||||
:param float freq: frequency
|
||||
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
|
||||
:param SimPEG.EM.FDEM.Src src: FDEM source
|
||||
:param numpy.ndarray v: vector to take product with
|
||||
:param bool adjoint: adjoint?
|
||||
:rtype: numpy.ndarray
|
||||
@@ -593,7 +591,7 @@ class Problem3D_h(BaseFDEMProblem):
|
||||
|
||||
\\left(\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{s_e}
|
||||
|
||||
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
|
||||
:param SimPEG.Mesh mesh: mesh
|
||||
"""
|
||||
|
||||
_solutionType = 'hSolution'
|
||||
@@ -610,11 +608,9 @@ class Problem3D_h(BaseFDEMProblem):
|
||||
.. math::
|
||||
\mathbf{A} = \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}
|
||||
|
||||
|
||||
:param float freq: Frequency
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:return: A
|
||||
|
||||
"""
|
||||
|
||||
MeMu = self.MeMu
|
||||
@@ -657,7 +653,6 @@ class Problem3D_h(BaseFDEMProblem):
|
||||
:param float freq: Frequency
|
||||
:rtype: numpy.ndarray
|
||||
:return: RHS (nE, nSrc)
|
||||
|
||||
"""
|
||||
|
||||
s_m, s_e = self.getSourceTerm(freq)
|
||||
@@ -671,7 +666,7 @@ class Problem3D_h(BaseFDEMProblem):
|
||||
Derivative of the right hand side with respect to the model
|
||||
|
||||
:param float freq: frequency
|
||||
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
|
||||
:param SimPEG.EM.FDEM.Src src: FDEM source
|
||||
:param numpy.ndarray v: vector to take product with
|
||||
:param bool adjoint: adjoint?
|
||||
:rtype: numpy.ndarray
|
||||
|
||||
@@ -25,10 +25,10 @@ class BaseRx(SimPEG.Survey.BaseRx):
|
||||
|
||||
def eval(self, src, mesh, f):
|
||||
"""
|
||||
Project fields to receivers to get data.
|
||||
Project fields to recievers to get data.
|
||||
|
||||
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
|
||||
:param BaseMesh mesh: mesh used
|
||||
:param Source src: FDEM source
|
||||
:param Mesh mesh: mesh used
|
||||
:param Fields f: fields object
|
||||
:rtype: numpy.ndarray
|
||||
:return: fields projected to recievers
|
||||
@@ -44,8 +44,8 @@ class BaseRx(SimPEG.Survey.BaseRx):
|
||||
"""
|
||||
Derivative of projected fields with respect to the inversion model times a vector.
|
||||
|
||||
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
|
||||
:param BaseMesh mesh: mesh used
|
||||
:param Source src: FDEM source
|
||||
:param Mesh mesh: mesh used
|
||||
:param Fields f: fields object
|
||||
:param numpy.ndarray v: vector to multiply
|
||||
:rtype: numpy.ndarray
|
||||
|
||||
+227
-29
@@ -23,8 +23,8 @@ class BaseSrc(Survey.BaseSrc):
|
||||
- :math:`s_m` : magnetic source term
|
||||
- :math:`s_e` : electric source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:rtype: tuple
|
||||
:param Problem prob: FDEM Problem
|
||||
:rtype: (numpy.ndarray, numpy.ndarray)
|
||||
:return: tuple with magnetic source term and electric source term
|
||||
"""
|
||||
s_m = self.s_m(prob)
|
||||
@@ -37,10 +37,10 @@ class BaseSrc(Survey.BaseSrc):
|
||||
- :code:`s_mDeriv` : derivative of the magnetic source term
|
||||
- :code:`s_eDeriv` : derivative of the electric source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:param numpy.ndarray v: vector to take product with
|
||||
:param bool adjoint: adjoint?
|
||||
:rtype: tuple
|
||||
:rtype: (numpy.ndarray, numpy.ndarray)
|
||||
:return: tuple with magnetic source term and electric source term derivatives times a vector
|
||||
"""
|
||||
if v is not None:
|
||||
@@ -52,7 +52,7 @@ class BaseSrc(Survey.BaseSrc):
|
||||
"""
|
||||
Primary magnetic flux density
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic flux density
|
||||
"""
|
||||
@@ -60,11 +60,23 @@ class BaseSrc(Survey.BaseSrc):
|
||||
return Zero()
|
||||
return self._bPrimary
|
||||
|
||||
def bPrimaryDeriv(self, prob, v, adjoint=False):
|
||||
"""
|
||||
Derivative of the primary magnetic flux density
|
||||
|
||||
:param Problem prob: FDEM Problem
|
||||
:param numpy.ndarray v: vector
|
||||
:param bool adjoint: adjoint?
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic flux density
|
||||
"""
|
||||
return Zero()
|
||||
|
||||
def hPrimary(self, prob):
|
||||
"""
|
||||
Primary magnetic field
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -72,11 +84,23 @@ class BaseSrc(Survey.BaseSrc):
|
||||
return Zero()
|
||||
return self._hPrimary
|
||||
|
||||
def hPrimaryDeriv(self, prob, v, adjoint=False):
|
||||
"""
|
||||
Derivative of the primary magnetic field
|
||||
|
||||
:param Problem prob: FDEM Problem
|
||||
:param numpy.ndarray v: vector
|
||||
:param bool adjoint: adjoint?
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic flux density
|
||||
"""
|
||||
return Zero()
|
||||
|
||||
def ePrimary(self, prob):
|
||||
"""
|
||||
Primary electric field
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary electric field
|
||||
"""
|
||||
@@ -84,11 +108,23 @@ class BaseSrc(Survey.BaseSrc):
|
||||
return Zero()
|
||||
return self._ePrimary
|
||||
|
||||
def ePrimaryDeriv(self, prob, v, adjoint=False):
|
||||
"""
|
||||
Derivative of the primary electric field
|
||||
|
||||
:param Problem prob: FDEM Problem
|
||||
:param numpy.ndarray v: vector
|
||||
:param bool adjoint: adjoint?
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic flux density
|
||||
"""
|
||||
return Zero()
|
||||
|
||||
def jPrimary(self, prob):
|
||||
"""
|
||||
Primary current density
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary current density
|
||||
"""
|
||||
@@ -96,11 +132,23 @@ class BaseSrc(Survey.BaseSrc):
|
||||
return Zero()
|
||||
return self._jPrimary
|
||||
|
||||
def jPrimaryDeriv(self, prob, v, adjoint=False):
|
||||
"""
|
||||
Derivative of the primary current density
|
||||
|
||||
:param Problem prob: FDEM Problem
|
||||
:param numpy.ndarray v: vector
|
||||
:param bool adjoint: adjoint?
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic flux density
|
||||
"""
|
||||
return Zero()
|
||||
|
||||
def s_m(self, prob):
|
||||
"""
|
||||
Magnetic source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: magnetic source term on mesh
|
||||
"""
|
||||
@@ -110,7 +158,7 @@ class BaseSrc(Survey.BaseSrc):
|
||||
"""
|
||||
Electric source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: electric source term on mesh
|
||||
"""
|
||||
@@ -120,7 +168,7 @@ class BaseSrc(Survey.BaseSrc):
|
||||
"""
|
||||
Derivative of magnetic source term with respect to the inversion model
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:param numpy.ndarray v: vector to take product with
|
||||
:param bool adjoint: adjoint?
|
||||
:rtype: numpy.ndarray
|
||||
@@ -133,7 +181,7 @@ class BaseSrc(Survey.BaseSrc):
|
||||
"""
|
||||
Derivative of electric source term with respect to the inversion model
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:param numpy.ndarray v: vector to take product with
|
||||
:param bool adjoint: adjoint?
|
||||
:rtype: numpy.ndarray
|
||||
@@ -162,7 +210,7 @@ class RawVec_e(BaseSrc):
|
||||
"""
|
||||
Electric source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: electric source term on mesh
|
||||
"""
|
||||
@@ -191,7 +239,7 @@ class RawVec_m(BaseSrc):
|
||||
"""
|
||||
Magnetic source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: magnetic source term on mesh
|
||||
"""
|
||||
@@ -220,7 +268,7 @@ class RawVec(BaseSrc):
|
||||
"""
|
||||
Magnetic source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: magnetic source term on mesh
|
||||
"""
|
||||
@@ -232,7 +280,7 @@ class RawVec(BaseSrc):
|
||||
"""
|
||||
Electric source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM Problem
|
||||
:param Problem prob: FDEM Problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: electric source term on mesh
|
||||
"""
|
||||
@@ -301,7 +349,7 @@ class MagDipole(BaseSrc):
|
||||
"""
|
||||
The primary magnetic flux density from a magnetic vector potential
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -339,7 +387,7 @@ class MagDipole(BaseSrc):
|
||||
"""
|
||||
The primary magnetic field from a magnetic vector potential
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -350,7 +398,7 @@ class MagDipole(BaseSrc):
|
||||
"""
|
||||
The magnetic source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -364,7 +412,7 @@ class MagDipole(BaseSrc):
|
||||
"""
|
||||
The electric source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -416,7 +464,7 @@ class MagDipole_Bfield(BaseSrc):
|
||||
"""
|
||||
The primary magnetic flux density from the analytic solution for magnetic fields from a dipole
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -455,7 +503,7 @@ class MagDipole_Bfield(BaseSrc):
|
||||
"""
|
||||
The primary magnetic field from a magnetic vector potential
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -466,7 +514,7 @@ class MagDipole_Bfield(BaseSrc):
|
||||
"""
|
||||
The magnetic source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -479,7 +527,7 @@ class MagDipole_Bfield(BaseSrc):
|
||||
"""
|
||||
The electric source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -530,7 +578,7 @@ class CircularLoop(BaseSrc):
|
||||
"""
|
||||
The primary magnetic flux density from a magnetic vector potential
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -555,7 +603,7 @@ class CircularLoop(BaseSrc):
|
||||
a = MagneticLoopVectorPotential(self.loc, gridY, 'y', moment=self.radius, mu=self.mu)
|
||||
|
||||
else:
|
||||
srcfct = MagneticDipoleVectorPotential
|
||||
srcfct = MagneticLoopVectorPotential
|
||||
ax = srcfct(self.loc, gridX, 'x', self.radius, mu=self.mu)
|
||||
ay = srcfct(self.loc, gridY, 'y', self.radius, mu=self.mu)
|
||||
az = srcfct(self.loc, gridZ, 'z', self.radius, mu=self.mu)
|
||||
@@ -567,7 +615,7 @@ class CircularLoop(BaseSrc):
|
||||
"""
|
||||
The primary magnetic field from a magnetic vector potential
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -578,7 +626,7 @@ class CircularLoop(BaseSrc):
|
||||
"""
|
||||
The magnetic source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -591,7 +639,7 @@ class CircularLoop(BaseSrc):
|
||||
"""
|
||||
The electric source term
|
||||
|
||||
:param BaseFDEMProblem prob: FDEM problem
|
||||
:param Problem prob: FDEM problem
|
||||
:rtype: numpy.ndarray
|
||||
:return: primary magnetic field
|
||||
"""
|
||||
@@ -614,5 +662,155 @@ class CircularLoop(BaseSrc):
|
||||
return -C.T * (MMui_s * self.bPrimary(prob))
|
||||
|
||||
|
||||
class PrimSecSigma(BaseSrc):
|
||||
|
||||
def __init__(self, rxList, freq, sigBack, ePrimary, **kwargs):
|
||||
self.sigBack = sigBack
|
||||
|
||||
BaseSrc.__init__(self, rxList, freq=freq, _ePrimary=ePrimary, **kwargs)
|
||||
|
||||
def s_e(self, prob):
|
||||
return (prob.MeSigma - prob.mesh.getEdgeInnerProduct(self.sigBack)) * self.ePrimary(prob)
|
||||
|
||||
def s_eDeriv(self, prob, v, adjoint=False):
|
||||
if adjoint:
|
||||
return prob.MeSigmaDeriv(self.ePrimary(prob)).T * v
|
||||
return prob.MeSigmaDeriv(self.ePrimary(prob)) * v
|
||||
|
||||
|
||||
class PrimSecMappedSigma(BaseSrc):
|
||||
|
||||
"""
|
||||
Primary-Secondary Source in which a mapping is provided to put the current model
|
||||
onto the primary mesh. This is solved on every model update.
|
||||
|
||||
There are a lot of layers to the derivatives here!
|
||||
|
||||
**Required**
|
||||
:param list rxList: Receiver List
|
||||
:param float freq: frequency
|
||||
:param ProblemFDEM primaryProblem: FDEM primary problem
|
||||
:param SurveyFDEM primarySurvey: FDEM primary survey
|
||||
|
||||
**Optional**
|
||||
:param Mapping map2meshSecondary: mapping current model to act as primary model on the secondary mesh
|
||||
|
||||
"""
|
||||
|
||||
def __init__(self, rxList, freq, primaryProblem, primarySurvey, map2meshSecondary = None ,**kwargs):
|
||||
|
||||
self.primaryProblem = primaryProblem
|
||||
self.primarySurvey = primarySurvey
|
||||
|
||||
if self.primaryProblem.ispaired is False:
|
||||
self.primaryProblem.pair(self.primarySurvey)
|
||||
|
||||
self.map2meshSecondary = map2meshSecondary
|
||||
|
||||
BaseSrc.__init__(self, rxList, freq=freq, **kwargs)
|
||||
|
||||
def _ProjPrimary(self, prob):
|
||||
# if getattr(self, '__ProjPrimary', None) is None:
|
||||
return self.primaryProblem.mesh.getInterpolationMatCartMesh(prob.mesh, locType='F', locTypeTo='E')
|
||||
# return self.__ProjPrimary
|
||||
|
||||
|
||||
def _primaryFields(self, prob, fieldType=None):
|
||||
|
||||
# TODO: cache and check if prob.curModel has changed
|
||||
fields = self.primaryProblem.fields(prob.curModel.sigmaModel)
|
||||
|
||||
if fieldType is not None:
|
||||
return fields[:,fieldType]
|
||||
return fields
|
||||
|
||||
def _primaryFieldsDeriv(self, prob, v, adjoint=False, f=None):
|
||||
if adjoint:
|
||||
raise NotImplementedError
|
||||
|
||||
# TODO: this should not be hard-coded for j
|
||||
# jp = self._primaryFields(prob)[:,'j']
|
||||
|
||||
# TODO: pull apart Jvec so that don't have to copy paste this code in
|
||||
# A = self.primaryProblem.getA(self.freq)
|
||||
# Ainv = self.primaryProblem.Solver(A, **self.primaryProblem.solverOpts) # create the concept of Ainv (actually a solve)
|
||||
|
||||
if f is None:
|
||||
f = self._primaryFields(prob.curModel.sigmaModel)
|
||||
|
||||
freq = self.freq
|
||||
|
||||
A = self.primaryProblem.getA(freq)
|
||||
Ainv = self.primaryProblem.Solver(A, **self.primaryProblem.solverOpts) # create the concept of Ainv (actually a solve)
|
||||
|
||||
src = self.primarySurvey.srcList[0]
|
||||
# for src in self.survey.getSrcByFreq(freq):
|
||||
u_src = Utils.mkvc(f[src, self.primaryProblem._solutionType])
|
||||
dA_dm_v = self.primaryProblem.getADeriv(freq, u_src, v)
|
||||
dRHS_dm_v = self.primaryProblem.getRHSDeriv(freq, src, v)
|
||||
du_dm_v = Ainv * ( - dA_dm_v + dRHS_dm_v )
|
||||
|
||||
df_dmFun = getattr(f, '_{0}Deriv'.format('j'), None)
|
||||
df_dm_v = df_dmFun(src, du_dm_v, v, adjoint=False)
|
||||
# Jv[src, rx] = rx.evalDeriv(src, self.mesh, f, df_dm_v)
|
||||
Ainv.clean()
|
||||
|
||||
return df_dm_v
|
||||
|
||||
# return self.primaryProblem.Jvec(prob.curModel, v, f=f)
|
||||
|
||||
def ePrimary(self, prob, f=None):
|
||||
if f is None:
|
||||
f = self._primaryFields(prob)
|
||||
|
||||
ep = self._ProjPrimary(prob) * (
|
||||
self.primaryProblem.MfI * (
|
||||
self.primaryProblem.MfRho * f[:,'j'])
|
||||
)
|
||||
|
||||
return Utils.mkvc(ep)
|
||||
|
||||
def ePrimaryDeriv(self, prob, v, adjoint=False, f=None):
|
||||
|
||||
if adjoint is True:
|
||||
raise NotImplementedError
|
||||
|
||||
if f is None:
|
||||
f = self._primaryFields(prob)
|
||||
|
||||
epDeriv = self._ProjPrimary(prob) * (
|
||||
self.primaryProblem.MfI * (
|
||||
(self.primaryProblem.MfRhoDeriv(f[:,'j']) * v)
|
||||
+
|
||||
(self.primaryProblem.MfRho * self._primaryFieldsDeriv(prob, v, f=f))
|
||||
)
|
||||
)
|
||||
|
||||
return Utils.mkvc(epDeriv)
|
||||
|
||||
|
||||
def s_e(self, prob):
|
||||
sigmaPrimary = self.map2meshSecondary * prob.curModel.sigmaModel
|
||||
|
||||
return Utils.mkvc((prob.MeSigma - prob.mesh.getEdgeInnerProduct(sigmaPrimary)) * self.ePrimary(prob))
|
||||
|
||||
|
||||
def s_eDeriv(self, prob, v, adjoint=False):
|
||||
if adjoint:
|
||||
raise NotImplementedError
|
||||
return prob.MeSigmaDeriv(self.ePrimary(prob)).T * v
|
||||
|
||||
sigmaPrimary = self.map2meshSecondary * prob.curModel.sigmaModel
|
||||
sigmaPrimaryDeriv = self.map2meshSecondary.deriv(prob.curModel.sigmaModel)
|
||||
|
||||
f = self._primaryFields(prob)
|
||||
ePrimary = self.ePrimary(prob,f=f)
|
||||
|
||||
return (prob.MeSigmaDeriv(ePrimary) * v
|
||||
- prob.mesh.getEdgeInnerProductDeriv(sigmaPrimary)(ePrimary) * sigmaPrimaryDeriv * v
|
||||
+ (prob.MeSigma - prob.mesh.getEdgeInnerProduct(sigmaPrimary)) * self.ePrimaryDeriv(prob, v, None, f=f)
|
||||
)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
@@ -43,7 +43,14 @@ class BaseRx(SimPEG.Survey.BaseRx):
|
||||
elif adjoint:
|
||||
return P.T*v
|
||||
|
||||
# DC.Rx.Dipole(locs)
|
||||
# DC.Rx.Pole(locs)
|
||||
class Pole(BaseRx):
|
||||
|
||||
def __init__(self, locs, rxType = 'phi', **kwargs):
|
||||
BaseRx.__init__(self, locs, rxType)
|
||||
|
||||
|
||||
# DC.Rx.Dipole(locsM, locsN)
|
||||
class Dipole(BaseRx):
|
||||
|
||||
def __init__(self, locsM, locsN, rxType = 'phi', **kwargs):
|
||||
|
||||
@@ -112,7 +112,7 @@ class BaseTDEMProblem(BaseTimeProblem, BaseEMProblem):
|
||||
"""
|
||||
:param numpy.array m: Conductivity model
|
||||
:param numpy.ndarray v: vector (model object)
|
||||
:param FieldsTDEM f: Fields resulting from m
|
||||
:param simpegEM.TDEM.FieldsTDEM f: Fields resulting from m
|
||||
:rtype: numpy.ndarray
|
||||
:return: w (data object)
|
||||
|
||||
@@ -136,8 +136,8 @@ class BaseTDEMProblem(BaseTimeProblem, BaseEMProblem):
|
||||
def Jtvec(self, m, v, f=None):
|
||||
"""
|
||||
:param numpy.array m: Conductivity model
|
||||
:param numpy.ndarray v: vector (or a :class:`SimPEG.Survey.Data` object)
|
||||
:param FieldsTDEM u: Fields resulting from m
|
||||
:param numpy.ndarray,SimPEG.Survey.Data v: vector (data object)
|
||||
:param simpegEM.TDEM.FieldsTDEM u: Fields resulting from m
|
||||
:rtype: numpy.ndarray
|
||||
:return: w (model object)
|
||||
|
||||
|
||||
+13
-13
@@ -87,8 +87,8 @@ class ProblemTDEM_b(BaseTDEMProblem):
|
||||
"""
|
||||
:param numpy.array m: Conductivity model
|
||||
:param numpy.array vec: vector (like a model)
|
||||
:param FieldsTDEM u: Fields resulting from m
|
||||
:rtype: FieldsTDEM
|
||||
:param simpegEM.TDEM.FieldsTDEM u: Fields resulting from m
|
||||
:rtype: simpegEM.TDEM.FieldsTDEM
|
||||
:return: f
|
||||
|
||||
Multiply G by a vector
|
||||
@@ -125,9 +125,9 @@ class ProblemTDEM_b(BaseTDEMProblem):
|
||||
"""
|
||||
:param numpy.array m: Conductivity model
|
||||
:param numpy.array vec: vector (like a fields)
|
||||
:param FieldsTDEM u: Fields resulting from m
|
||||
:rtype: numpy.ndarray
|
||||
:return: p (like a model)
|
||||
:param simpegEM.TDEM.FieldsTDEM u: Fields resulting from m
|
||||
:rtype: np.ndarray (like a model)
|
||||
:return: p
|
||||
|
||||
Multiply G.T by a vector
|
||||
"""
|
||||
@@ -153,8 +153,8 @@ class ProblemTDEM_b(BaseTDEMProblem):
|
||||
def solveAh(self, m, p):
|
||||
"""
|
||||
:param numpy.array m: Conductivity model
|
||||
:param FieldsTDEM p: Fields object
|
||||
:rtype: FieldsTDEM
|
||||
:param simpegEM.TDEM.FieldsTDEM p: Fields object
|
||||
:rtype: simpegEM.TDEM.FieldsTDEM
|
||||
:return: y
|
||||
|
||||
Solve the block-matrix system \\\(\\\hat{A} \\\hat{y} = \\\hat{p}\\\):
|
||||
@@ -200,8 +200,8 @@ class ProblemTDEM_b(BaseTDEMProblem):
|
||||
def solveAht(self, m, p):
|
||||
"""
|
||||
:param numpy.array m: Conductivity model
|
||||
:param FieldsTDEM p: Fields object
|
||||
:rtype: FieldsTDEM
|
||||
:param simpegEM.TDEM.FieldsTDEM p: Fields object
|
||||
:rtype: simpegEM.TDEM.FieldsTDEM
|
||||
:return: y
|
||||
|
||||
Solve the block-matrix system \\\(\\\hat{A}^\\\\top \\\hat{y} = \\\hat{p}\\\):
|
||||
@@ -270,8 +270,8 @@ class ProblemTDEM_b(BaseTDEMProblem):
|
||||
def _AhVec(self, m, vec):
|
||||
"""
|
||||
:param numpy.array m: Conductivity model
|
||||
:param FieldsTDEM vec: Fields object
|
||||
:rtype: FieldsTDEM
|
||||
:param simpegEM.TDEM.FieldsTDEM vec: Fields object
|
||||
:rtype: simpegEM.TDEM.FieldsTDEM
|
||||
:return: f
|
||||
|
||||
Multiply the matrix \\\(\\\hat{A}\\\) by a fields vector where
|
||||
@@ -315,8 +315,8 @@ class ProblemTDEM_b(BaseTDEMProblem):
|
||||
def _AhtVec(self, m, vec):
|
||||
"""
|
||||
:param numpy.array m: Conductivity model
|
||||
:param FieldsTDEM vec: Fields object
|
||||
:rtype: FieldsTDEM
|
||||
:param simpegEM.TDEM.FieldsTDEM vec: Fields object
|
||||
:rtype: simpegEM.TDEM.FieldsTDEM
|
||||
:return: f
|
||||
|
||||
Multiply the matrix \\\(\\\hat{A}\\\) by a fields vector where
|
||||
|
||||
@@ -1,7 +1,7 @@
|
||||
from SimPEG import *
|
||||
import SimPEG.EM.Static.DC as DC
|
||||
import SimPEG.DCIP as DC
|
||||
|
||||
def run(plotIt=True):
|
||||
def run(plotIt=False):
|
||||
cs = 25.
|
||||
hx = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
|
||||
hy = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
|
||||
@@ -21,10 +21,10 @@ def run(plotIt=True):
|
||||
# ax.plot(xyz_rxP[:,0],xyz_rxP[:,1], 'w.')
|
||||
# ax.plot(xyz_rxN[:,0],xyz_rxN[:,1], 'r.', ms = 3)
|
||||
|
||||
rx = DC.Rx.Dipole(xyz_rxP, xyz_rxN)
|
||||
src = DC.Src.Dipole([rx], np.r_[-200, 0, -12.5], np.r_[+200, 0, -12.5])
|
||||
survey = DC.Survey([src])
|
||||
problem = DC.Problem3D_CC(mesh)
|
||||
rx = DC.RxDipole(xyz_rxP, xyz_rxN)
|
||||
src = DC.SrcDipole([rx], [-200, 0, -12.5], [+200, 0, -12.5])
|
||||
survey = DC.SurveyDC([src])
|
||||
problem = DC.ProblemDC_CC(mesh)
|
||||
problem.pair(survey)
|
||||
try:
|
||||
from pymatsolver import MumpsSolver
|
||||
@@ -65,4 +65,4 @@ def run(plotIt=True):
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
print run()
|
||||
print run(plotIt=True)
|
||||
|
||||
@@ -19,13 +19,10 @@ def run(plotIt=True):
|
||||
Morrison Casing Model, and the results are used in a 2016 SEG abstract by
|
||||
Yang et al.
|
||||
|
||||
.. code-block:: text
|
||||
|
||||
Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
|
||||
- Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
|
||||
|
||||
|
||||
The model consists of:
|
||||
|
||||
- Air: Conductivity 1e-8 S/m, above z = 0
|
||||
- Background: conductivity 1e-2 S/m, below z = 0
|
||||
- Casing: conductivity 1e6 S/m
|
||||
@@ -218,7 +215,7 @@ def run(plotIt=True):
|
||||
# ------------ Problem and Survey ---------------
|
||||
survey = FDEM.Survey(sg_p + dg_p)
|
||||
mapping = [('sigma', Maps.IdentityMap(mesh))]
|
||||
problem = FDEM.Problem3D_h(mesh, mapping=mapping, Solver=solver)
|
||||
problem = FDEM.Problem3D_h(mesh, mapping=mapping)
|
||||
problem.pair(survey)
|
||||
|
||||
# ------------- Solve ---------------------------
|
||||
|
||||
+31
-12
@@ -1,25 +1,22 @@
|
||||
from SimPEG import Mesh, Utils, np, SolverLU
|
||||
|
||||
## 2D DC forward modeling example with Tensor and Curvilinear Meshes
|
||||
|
||||
def run(plotIt=True):
|
||||
|
||||
"""
|
||||
Mesh: Basic Forward 2D DC Resistivity
|
||||
=====================================
|
||||
|
||||
2D DC forward modeling example with Tensor and Curvilinear Meshes
|
||||
"""
|
||||
|
||||
# Step1: Generate Tensor and Curvilinear Mesh
|
||||
sz = [40,40]
|
||||
# Tensor Mesh
|
||||
tM = Mesh.TensorMesh(sz)
|
||||
# Curvilinear Mesh
|
||||
rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz,'rotate'))
|
||||
|
||||
# Step2: Direct Current (DC) operator
|
||||
def DCfun(mesh, pts):
|
||||
D = mesh.faceDiv
|
||||
G = D.T
|
||||
sigma = 1e-2*np.ones(mesh.nC)
|
||||
MsigI = mesh.getFaceInnerProduct(sigma, invProp=True, invMat=True)
|
||||
A = -D*MsigI*D.T
|
||||
Msigi = mesh.getFaceInnerProduct(1./sigma)
|
||||
MsigI = Utils.sdInv(Msigi)
|
||||
A = D*MsigI*G
|
||||
A[-1,-1] /= mesh.vol[-1] # Remove null space
|
||||
rhs = np.zeros(mesh.nC)
|
||||
txind = Utils.meshutils.closestPoints(mesh, pts)
|
||||
@@ -40,17 +37,39 @@ def run(plotIt=True):
|
||||
if not plotIt: return
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
import matplotlib
|
||||
from matplotlib.mlab import griddata
|
||||
|
||||
#Step4: Making Figure
|
||||
fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
|
||||
label = ["(a)", "(b)"]
|
||||
opts = {}
|
||||
vmin, vmax = phitM.min(), phitM.max()
|
||||
dat = tM.plotImage(phitM, ax=axes[0], clim=(vmin, vmax), grid=True)
|
||||
dat = rM.plotImage(phirM, ax=axes[1], clim=(vmin, vmax), grid=True)
|
||||
|
||||
#TODO: At the moment Curvilinear Mesh do not have plotimage
|
||||
|
||||
Xi = tM.gridCC[:,0].reshape(sz[0], sz[1], order='F')
|
||||
Yi = tM.gridCC[:,1].reshape(sz[0], sz[1], order='F')
|
||||
PHIrM = griddata(rM.gridCC[:,0], rM.gridCC[:,1], phirM, Xi, Yi, interp='linear')
|
||||
axes[1].contourf(Xi, Yi, PHIrM, 100, vmin=vmin, vmax=vmax)
|
||||
|
||||
cb = plt.colorbar(dat[0], ax=axes[0]); cb.set_label("Voltage (V)")
|
||||
cb = plt.colorbar(dat[0], ax=axes[1]); cb.set_label("Voltage (V)")
|
||||
|
||||
tM.plotGrid(ax=axes[0], **opts)
|
||||
axes[0].set_title('TensorMesh')
|
||||
rM.plotGrid(ax=axes[1], **opts)
|
||||
axes[1].set_title('CurvilinearMesh')
|
||||
for i in range(2):
|
||||
axes[i].set_xlim(0.025, 0.975)
|
||||
axes[i].set_ylim(0.025, 0.975)
|
||||
axes[i].text(0., 1.0, label[i], fontsize=20)
|
||||
if i==0:
|
||||
axes[i].set_ylabel("y")
|
||||
else:
|
||||
axes[i].set_ylabel(" ")
|
||||
axes[i].set_xlabel("x")
|
||||
plt.show()
|
||||
|
||||
|
||||
@@ -1,7 +1,7 @@
|
||||
from SimPEG import *
|
||||
|
||||
|
||||
def run(N=100, plotIt=True):
|
||||
def run(N=200, plotIt=True):
|
||||
"""
|
||||
Inversion: Linear Problem
|
||||
=========================
|
||||
@@ -18,8 +18,6 @@ def run(N=100, plotIt=True):
|
||||
mesh = Mesh.TensorMesh([N])
|
||||
|
||||
m0 = np.ones(mesh.nC) * 1e-4
|
||||
mref = np.zeros(mesh.nC)
|
||||
|
||||
nk = 10
|
||||
jk = np.linspace(1.,nk,nk)
|
||||
p = -2.
|
||||
@@ -42,35 +40,67 @@ def run(N=100, plotIt=True):
|
||||
survey = Survey.LinearSurvey()
|
||||
survey.pair(prob)
|
||||
survey.dobs = prob.fields(mtrue) + std_noise * np.random.randn(nk)
|
||||
#survey.makeSyntheticData(mtrue, std=std_noise)
|
||||
|
||||
wd = np.ones(nk) * std_noise
|
||||
|
||||
#print survey.std[0]
|
||||
#M = prob.mesh
|
||||
# Distance weighting
|
||||
wr = np.sum(prob.G**2.,axis=0)**0.5
|
||||
wr = ( wr/np.max(wr) )
|
||||
|
||||
reg = Regularization.Simple(mesh)
|
||||
reg.wght = wr
|
||||
|
||||
dmis = DataMisfit.l2_DataMisfit(survey)
|
||||
dmis.Wd = 1./wd
|
||||
|
||||
opt = Optimization.ProjectedGNCG(maxIter=30,lower=-2.,upper=2., maxIterCG= 20, tolCG = 1e-4)
|
||||
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
|
||||
invProb.curModel = m0
|
||||
|
||||
beta = Directives.BetaSchedule(coolingFactor=2, coolingRate=1)
|
||||
target = Directives.TargetMisfit()
|
||||
|
||||
betaest = Directives.BetaEstimate_ByEig()
|
||||
inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest, target])
|
||||
|
||||
|
||||
mrec = inv.run(m0)
|
||||
ml2 = mrec
|
||||
print "Final misfit:" + str(invProb.dmisfit.eval(mrec))
|
||||
|
||||
# Switch regularization to sparse
|
||||
phim = invProb.phi_m_last
|
||||
phid = invProb.phi_d
|
||||
|
||||
reg = Regularization.Sparse(mesh)
|
||||
reg.mref = mref
|
||||
reg.cell_weights = wr
|
||||
|
||||
#==============================================================================
|
||||
# fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
|
||||
# dmdx = reg.mesh.cellDiffxStencil * mrec
|
||||
# plt.plot(np.sort(dmdx))
|
||||
#==============================================================================
|
||||
|
||||
#reg.recModel = mrec
|
||||
reg.wght = np.ones(mesh.nC)
|
||||
reg.mref = np.zeros(mesh.nC)
|
||||
|
||||
reg.eps_p = 5e-2
|
||||
reg.eps_q = 1e-2
|
||||
reg.norms = [0., 0., 2., 2.]
|
||||
reg.wght = wr
|
||||
|
||||
opt = Optimization.ProjectedGNCG(maxIter=100 ,lower=-2.,upper=2., maxIterLS = 20, maxIterCG= 10, tolCG = 1e-3)
|
||||
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
|
||||
update_Jacobi = Directives.Update_lin_PreCond()
|
||||
|
||||
# Set the IRLS directive, penalize the lowest 25 percentile of model values
|
||||
# Start with an l2-l2, then switch to lp-norms
|
||||
norms = [0., 0., 2., 2.]
|
||||
IRLS = Directives.Update_IRLS( norms=norms, prctile = 25, maxIRLSiter = 15, minGNiter=3)
|
||||
opt = Optimization.ProjectedGNCG(maxIter=10 ,lower=-2.,upper=2., maxIterLS = 20, maxIterCG= 20, tolCG = 1e-3)
|
||||
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta = invProb.beta*2.)
|
||||
beta = Directives.BetaSchedule(coolingFactor=1, coolingRate=1)
|
||||
#betaest = Directives.BetaEstimate_ByEig()
|
||||
target = Directives.TargetMisfit()
|
||||
IRLS =Directives.Update_IRLS( phi_m_last = phim, phi_d_last = phid )
|
||||
|
||||
inv = Inversion.BaseInversion(invProb, directiveList=[IRLS,betaest,update_Jacobi])
|
||||
inv = Inversion.BaseInversion(invProb, directiveList=[beta,IRLS])
|
||||
|
||||
m0 = mrec
|
||||
|
||||
# Run inversion
|
||||
mrec = inv.run(m0)
|
||||
@@ -87,7 +117,7 @@ def run(N=100, plotIt=True):
|
||||
axes[0].set_title('Columns of matrix G')
|
||||
|
||||
axes[1].plot(mesh.vectorCCx, mtrue, 'b-')
|
||||
axes[1].plot(mesh.vectorCCx, reg.l2model, 'r-')
|
||||
axes[1].plot(mesh.vectorCCx, ml2, 'r-')
|
||||
#axes[1].legend(('True Model', 'Recovered Model'))
|
||||
axes[1].set_ylim(-1.0,1.25)
|
||||
|
||||
|
||||
@@ -7,7 +7,7 @@ import matplotlib.pyplot as plt
|
||||
def run(plotIt=True):
|
||||
"""
|
||||
MT: 1D: Inversion
|
||||
=================
|
||||
=======================
|
||||
|
||||
Forward model 1D MT data.
|
||||
Setup and run a MT 1D inversion.
|
||||
@@ -50,7 +50,7 @@ def run(plotIt=True):
|
||||
m_0 = np.log(sigma_0[active])
|
||||
|
||||
# Set the mapping
|
||||
actMap = simpeg.Maps.InjectActiveCells(m1d, active, np.log(1e-8), nC=m1d.nCx)
|
||||
actMap = simpeg.Maps.ActiveCells(m1d, active, np.log(1e-8), nC=m1d.nCx)
|
||||
mappingExpAct = simpeg.Maps.ExpMap(m1d) * actMap
|
||||
|
||||
## Setup the layout of the survey, set the sources and the connected receivers
|
||||
@@ -76,7 +76,7 @@ def run(plotIt=True):
|
||||
survey.dobs = survey.dtrue + 0.025*abs(survey.dtrue)*np.random.randn(*survey.dtrue.shape)
|
||||
|
||||
if plotIt:
|
||||
fig = MT.Utils.dataUtils.plotMT1DModelData(problem, [m_0])
|
||||
fig = MT.Utils.dataUtils.plotMT1DModelData(problem)
|
||||
fig.suptitle('Target - smooth true')
|
||||
|
||||
|
||||
|
||||
@@ -12,7 +12,7 @@ except:
|
||||
def run(plotIt=True, nFreq=1):
|
||||
"""
|
||||
MT: 3D: Forward
|
||||
===============
|
||||
=======================
|
||||
|
||||
Forward model 3D MT data.
|
||||
|
||||
@@ -46,15 +46,16 @@ def run(plotIt=True, nFreq=1):
|
||||
survey = MT.Survey(srcList)
|
||||
|
||||
## Setup the problem object
|
||||
problem = MT.Problem3D.eForm_ps(M, sigmaPrimary=sigBG, Solver=Solver)
|
||||
problem = MT.Problem3D.eForm_ps(M, sigmaPrimary=sigBG)
|
||||
problem.pair(survey)
|
||||
problem.Solver = Solver
|
||||
|
||||
# Calculate the data
|
||||
fields = problem.fields(sig)
|
||||
dataVec = survey.eval(fields)
|
||||
|
||||
# Make the data
|
||||
mtData = MT.Data(survey, dataVec)
|
||||
mtData = MT.Data(survey,dataVec)
|
||||
# Add plots
|
||||
if plotIt:
|
||||
pass
|
||||
|
||||
@@ -1,62 +0,0 @@
|
||||
from SimPEG import Mesh, Maps, np
|
||||
|
||||
def run(plotIt=True):
|
||||
"""
|
||||
|
||||
Maps: ComboMaps
|
||||
===============
|
||||
|
||||
We will use an example where we want a 1D layered earth as
|
||||
our model, but we want to map this to a 2D discretization to do our forward
|
||||
modeling. We will also assume that we are working in log conductivity still,
|
||||
so after the transformation we want to map to conductivity space.
|
||||
To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.SurjectVertical1D`),
|
||||
which does the first part of what we just described. The second part will be
|
||||
done by the :class:`SimPEG.Maps.ExpMap` described above.
|
||||
|
||||
.. code-block:: python
|
||||
:linenos:
|
||||
|
||||
M = Mesh.TensorMesh([7,5])
|
||||
v1dMap = Maps.SurjectVertical1D(M)
|
||||
expMap = Maps.ExpMap(M)
|
||||
myMap = expMap * v1dMap
|
||||
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
|
||||
sig = myMap * m
|
||||
|
||||
If you noticed, it was pretty easy to combine maps. What is even cooler is
|
||||
that the derivatives also are made for you (if everything goes right).
|
||||
Just to be sure that the derivative is correct, you should always run the test
|
||||
on the mapping that you create.
|
||||
|
||||
"""
|
||||
|
||||
|
||||
M = Mesh.TensorMesh([7,5])
|
||||
v1dMap = Maps.SurjectVertical1D(M)
|
||||
expMap = Maps.ExpMap(M)
|
||||
myMap = expMap * v1dMap
|
||||
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
|
||||
sig = myMap * m
|
||||
|
||||
if not plotIt: return
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
figs, axs = plt.subplots(1,2)
|
||||
axs[0].plot(m, M.vectorCCy, 'b-o')
|
||||
axs[0].set_title('Model')
|
||||
axs[0].set_ylabel('Depth, y')
|
||||
axs[0].set_xlabel('Value, $m_i$')
|
||||
axs[0].set_xlim(0,3)
|
||||
axs[0].set_ylim(0,1)
|
||||
clbar = plt.colorbar(M.plotImage(sig,ax=axs[1],grid=True,gridOpts=dict(color='grey'))[0])
|
||||
axs[1].set_title('Physical Property')
|
||||
axs[1].set_ylabel('Depth, y')
|
||||
clbar.set_label('$\sigma = \exp(\mathbf{P}m)$')
|
||||
plt.tight_layout()
|
||||
plt.show()
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
run()
|
||||
|
||||
@@ -1,41 +0,0 @@
|
||||
from SimPEG import Mesh, Maps, Utils
|
||||
|
||||
def run(plotIt=True):
|
||||
"""
|
||||
|
||||
Maps: Mesh2Mesh
|
||||
===============
|
||||
|
||||
This mapping allows you to go from one mesh to another.
|
||||
|
||||
"""
|
||||
|
||||
M = Mesh.TensorMesh([100,100])
|
||||
h1 = Utils.meshTensor([(6,7,-1.5),(6,10),(6,7,1.5)])
|
||||
h1 = h1/h1.sum()
|
||||
M2 = Mesh.TensorMesh([h1,h1])
|
||||
V = Utils.ModelBuilder.randomModel(M.vnC, seed=79, its=50)
|
||||
v = Utils.mkvc(V)
|
||||
modh = Maps.Mesh2Mesh([M,M2])
|
||||
modH = Maps.Mesh2Mesh([M2,M])
|
||||
H = modH * v
|
||||
h = modh * H
|
||||
|
||||
if not plotIt: return
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
ax = plt.subplot(131)
|
||||
M.plotImage(v, ax=ax)
|
||||
ax.set_title('Fine Mesh (Original)')
|
||||
ax = plt.subplot(132)
|
||||
M2.plotImage(H,clim=[0,1],ax=ax)
|
||||
ax.set_title('Course Mesh')
|
||||
ax = plt.subplot(133)
|
||||
M.plotImage(h,clim=[0,1],ax=ax)
|
||||
ax.set_title('Fine Mesh (Interpolated)')
|
||||
plt.show()
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
run()
|
||||
|
||||
@@ -2,12 +2,8 @@ from SimPEG import *
|
||||
from SimPEG.Utils import surface2ind_topo
|
||||
|
||||
|
||||
def run(plotIt=True, nx=5, ny=5):
|
||||
def run(plotIt=False, nx = 5, ny = 5):
|
||||
"""
|
||||
|
||||
Utils: surface2ind_topo
|
||||
=======================
|
||||
|
||||
Here we show how to use :code:`Utils.surface2ind_topo` to identify cells below
|
||||
a topographic surface.
|
||||
|
||||
@@ -17,25 +13,27 @@ def run(plotIt=True, nx=5, ny=5):
|
||||
xtopo = np.linspace(mesh.gridN[:,0].min(), mesh.gridN[:,0].max())
|
||||
topo = 0.4*np.sin(xtopo*5) # define a topographic surface
|
||||
|
||||
Topo = np.hstack([Utils.mkvc(xtopo,2), Utils.mkvc(topo,2)]) #make it an array
|
||||
Topo = np.hstack([Utils.mkvc(xtopo,2),Utils.mkvc(topo,2)]) #make it an array
|
||||
|
||||
indcc = surface2ind_topo(mesh, Topo, 'CC')
|
||||
indcc = surface2ind_topo(mesh, Topo,'CC')
|
||||
|
||||
if plotIt:
|
||||
from matplotlib.pylab import plt
|
||||
from scipy.interpolate import interp1d
|
||||
fig, ax = plt.subplots(1,1, figsize=(6,6))
|
||||
fig, ax = plt.subplots(1,1,figsize=(6,6))
|
||||
mesh.plotGrid(ax=ax, nodes=True, centers=True)
|
||||
ax.plot(xtopo,topo,'k',linewidth=1)
|
||||
# ax.plot(mesh.vectorNx, interp1d(xtopo,topo)(mesh.vectorNx),'--k',linewidth=3)
|
||||
ax.plot(mesh.vectorCCx, interp1d(xtopo,topo)(mesh.vectorCCx),'--k',linewidth=3)
|
||||
|
||||
|
||||
aveN2CC = Utils.sdiag(mesh.aveN2CC.T.sum(1))*mesh.aveN2CC.T
|
||||
a = aveN2CC * indcc
|
||||
a[a > 0] = 1.
|
||||
a[a < 0.25] = np.nan
|
||||
a = a.reshape(mesh.vnN, order='F')
|
||||
masked_array = np.ma.array(a, mask=np.isnan(a))
|
||||
ax.pcolor(mesh.vectorNx,mesh.vectorNy,masked_array.T, cmap=plt.cm.gray, alpha=0.2)
|
||||
ax.pcolor(mesh.vectorNx,mesh.vectorNy,masked_array.T, cmap = plt.cm.gray,alpha=0.2)
|
||||
plt.show()
|
||||
|
||||
|
||||
|
||||
@@ -8,11 +8,9 @@ import EM_FDEM_Analytic_MagDipoleWholespace
|
||||
import EM_Schenkel_Morrison_Casing
|
||||
import EM_TDEM_1D_Inversion
|
||||
import FLOW_Richards_1D_Celia1990
|
||||
import Forward_BasicDirectCurrent
|
||||
import Inversion_IRLS
|
||||
import Inversion_Linear
|
||||
import Maps_ComboMaps
|
||||
import Maps_Mesh2Mesh
|
||||
import Mesh_Basic_ForwardDC
|
||||
import Mesh_Basic_PlotImage
|
||||
import Mesh_Basic_Types
|
||||
import Mesh_Operators_CahnHilliard
|
||||
@@ -24,7 +22,7 @@ import MT_1D_ForwardAndInversion
|
||||
import MT_3D_Foward
|
||||
import Utils_surface2ind_topo
|
||||
|
||||
__examples__ = ["DC_Analytic_Dipole", "DC_Forward_PseudoSection", "EM_FDEM_1D_Inversion", "EM_FDEM_Analytic_MagDipoleWholespace", "EM_Schenkel_Morrison_Casing", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Inversion_IRLS", "Inversion_Linear", "Maps_ComboMaps", "Maps_Mesh2Mesh", "Mesh_Basic_ForwardDC", "Mesh_Basic_PlotImage", "Mesh_Basic_Types", "Mesh_Operators_CahnHilliard", "Mesh_QuadTree_Creation", "Mesh_QuadTree_FaceDiv", "Mesh_QuadTree_HangingNodes", "Mesh_Tensor_Creation", "MT_1D_ForwardAndInversion", "MT_3D_Foward", "Utils_surface2ind_topo"]
|
||||
__examples__ = ["DC_Analytic_Dipole", "DC_Forward_PseudoSection", "EM_FDEM_1D_Inversion", "EM_FDEM_Analytic_MagDipoleWholespace", "EM_Schenkel_Morrison_Casing", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Forward_BasicDirectCurrent", "Inversion_IRLS", "Inversion_Linear", "Mesh_Basic_PlotImage", "Mesh_Basic_Types", "Mesh_Operators_CahnHilliard", "Mesh_QuadTree_Creation", "Mesh_QuadTree_FaceDiv", "Mesh_QuadTree_HangingNodes", "Mesh_Tensor_Creation", "MT_1D_ForwardAndInversion", "MT_3D_Foward", "Utils_surface2ind_topo"]
|
||||
|
||||
##### AUTOIMPORTS #####
|
||||
|
||||
@@ -40,7 +38,7 @@ if __name__ == '__main__':
|
||||
|
||||
# Create the examples dir in the docs folder.
|
||||
fName = os.path.realpath(__file__)
|
||||
docExamplesDir = os.path.sep.join(fName.split(os.path.sep)[:-3] + ['docs', 'content', 'examples'])
|
||||
docExamplesDir = os.path.sep.join(fName.split(os.path.sep)[:-3] + ['docs', 'examples'])
|
||||
shutil.rmtree(docExamplesDir)
|
||||
os.makedirs(docExamplesDir)
|
||||
|
||||
@@ -97,12 +95,12 @@ if __name__ == '__main__':
|
||||
from SimPEG import Examples
|
||||
Examples.%s.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/%s.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/%s.py
|
||||
:language: python
|
||||
:linenos:
|
||||
"""%(name,doc,name,name)
|
||||
|
||||
rst = os.path.sep.join((filePath.split(os.path.sep)[:-3] + ['docs', 'content', 'examples', name + '.rst']))
|
||||
rst = os.path.sep.join((filePath.split(os.path.sep)[:-3] + ['docs', 'examples', name + '.rst']))
|
||||
|
||||
print 'Creating: %s.rst'%name
|
||||
f = open(rst, 'w')
|
||||
|
||||
@@ -31,7 +31,7 @@ class NonLinearMap(object):
|
||||
"""
|
||||
:param numpy.array u: fields
|
||||
:param numpy.array m: model
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.csr_matrix
|
||||
:return: derivative of transformed model
|
||||
|
||||
The *transform* changes the model into the physical property.
|
||||
@@ -44,7 +44,7 @@ class NonLinearMap(object):
|
||||
"""
|
||||
:param numpy.array u: fields
|
||||
:param numpy.array m: model
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.csr_matrix
|
||||
:return: derivative of transformed model
|
||||
|
||||
The *transform* changes the model into the physical property.
|
||||
|
||||
+2
-2
@@ -86,7 +86,7 @@ class polxy_1Dprimary(BaseMTSrc):
|
||||
Get the electrical field source
|
||||
"""
|
||||
e_p = self.ePrimary(problem)
|
||||
Map_sigma_p = Maps.SurjectVertical1D(problem.mesh)
|
||||
Map_sigma_p = Maps.Vertical1DMap(problem.mesh)
|
||||
sigma_p = Map_sigma_p._transform(self.sigma1d)
|
||||
# Make mass matrix
|
||||
# Note: M(sig) - M(sig_p) = M(sig - sig_p)
|
||||
@@ -163,7 +163,7 @@ class polxy_3Dprimary(BaseMTSrc):
|
||||
Get the electrical field source
|
||||
"""
|
||||
e_p = self.ePrimary(problem)
|
||||
Map_sigma_p = Maps.SurjectVertical1D(problem.mesh)
|
||||
Map_sigma_p = Maps.Vertical1DMap(problem.mesh)
|
||||
sigma_p = Map_sigma_p._transform(self.sigma1d)
|
||||
# Make mass matrix
|
||||
# Note: M(sig) - M(sig_p) = M(sig - sig_p)
|
||||
|
||||
@@ -19,7 +19,7 @@ def getAppRes(MTdata):
|
||||
zList.append(zc)
|
||||
return [appResPhs(zList[i][0],np.sum(zList[i][1:3])) for i in np.arange(len(zList))]
|
||||
|
||||
def rotateData(MTdata, rotAngle):
|
||||
def rotateData(MTdata,rotAngle):
|
||||
'''
|
||||
Function that rotates clockwist by rotAngle (- negative for a counter-clockwise rotation)
|
||||
'''
|
||||
@@ -44,19 +44,19 @@ def rotateData(MTdata, rotAngle):
|
||||
return MT.Data.fromRecArray(outRec)
|
||||
|
||||
|
||||
def appResPhs(freq, z):
|
||||
def appResPhs(freq,z):
|
||||
app_res = ((1./(8e-7*np.pi**2))/freq)*np.abs(z)**2
|
||||
app_phs = np.arctan2(z.imag,z.real)*(180/np.pi)
|
||||
return app_res, app_phs
|
||||
|
||||
def skindepth(rho, freq):
|
||||
def skindepth(rho,freq):
|
||||
''' Function to calculate the skindepth of EM waves'''
|
||||
return np.sqrt( (rho*((1/(freq * mu_0 * np.pi )))))
|
||||
|
||||
def rec2ndarr(x, dt=float):
|
||||
def rec2ndarr(x,dt=float):
|
||||
return x.view((dt, len(x.dtype.names)))
|
||||
|
||||
def makeAnalyticSolution(mesh, model, elev, freqs):
|
||||
def makeAnalyticSolution(mesh,model,elev,freqs):
|
||||
from SimPEG import MT
|
||||
data1D = []
|
||||
for freq in freqs:
|
||||
@@ -70,7 +70,7 @@ def makeAnalyticSolution(mesh, model, elev, freqs):
|
||||
dataRec = np.array(data1D,dtype=[('freq',float),('x',float),('y',float),('z',float),('zyx',complex)])
|
||||
return dataRec
|
||||
|
||||
def plotMT1DModelData(problem, models, symList=None):
|
||||
def plotMT1DModelData(problem,models,symList=None):
|
||||
from SimPEG import MT
|
||||
# Setup the figure
|
||||
fontSize = 15
|
||||
|
||||
+942
-317
File diff suppressed because it is too large
Load Diff
+24
-26
@@ -7,8 +7,8 @@ class BaseMesh(object):
|
||||
BaseMesh does all the counting you don't want to do.
|
||||
BaseMesh should be inherited by meshes with a regular structure.
|
||||
|
||||
:param numpy.array n: (or list) number of cells in each direction (dim, )
|
||||
:param numpy.array x0: (or list) Origin of the mesh (dim, )
|
||||
:param numpy.array,list n: number of cells in each direction (dim, )
|
||||
:param numpy.array,list x0: Origin of the mesh (dim, )
|
||||
|
||||
"""
|
||||
|
||||
@@ -34,8 +34,8 @@ class BaseMesh(object):
|
||||
"""
|
||||
Origin of the mesh
|
||||
|
||||
:rtype: numpy.array
|
||||
:return: x0, (dim, )
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: x0
|
||||
"""
|
||||
return self._x0
|
||||
|
||||
@@ -116,8 +116,8 @@ class BaseMesh(object):
|
||||
"""
|
||||
Total number of edges in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:return: [nEx, nEy, nEz], (dim, )
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: [nEx, nEy, nEz]
|
||||
|
||||
.. plot::
|
||||
:include-source:
|
||||
@@ -173,8 +173,8 @@ class BaseMesh(object):
|
||||
"""
|
||||
Total number of faces in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:return: [nFx, nFy, nFz], (dim, )
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: [nFx, nFy, nFz]
|
||||
|
||||
.. plot::
|
||||
:include-source:
|
||||
@@ -200,8 +200,8 @@ class BaseMesh(object):
|
||||
"""
|
||||
Face Normals
|
||||
|
||||
:rtype: numpy.array
|
||||
:return: normals, (sum(nF), dim)
|
||||
:rtype: numpy.array (sum(nF), dim)
|
||||
:return: normals
|
||||
"""
|
||||
if self.dim == 2:
|
||||
nX = np.c_[np.ones(self.nFx), np.zeros(self.nFx)]
|
||||
@@ -218,8 +218,8 @@ class BaseMesh(object):
|
||||
"""
|
||||
Edge Tangents
|
||||
|
||||
:rtype: numpy.array
|
||||
:return: normals, (sum(nE), dim)
|
||||
:rtype: numpy.array (sum(nE), dim)
|
||||
:return: normals
|
||||
"""
|
||||
if self.dim == 2:
|
||||
tX = np.c_[np.ones(self.nEx), np.zeros(self.nEx)]
|
||||
@@ -236,9 +236,8 @@ class BaseMesh(object):
|
||||
Given a vector, fV, in cartesian coordinates, this will project it onto the mesh using the normals
|
||||
|
||||
:param numpy.array fV: face vector with shape (nF, dim)
|
||||
:rtype: numpy.array
|
||||
:return: projected face vector, (nF, )
|
||||
|
||||
:rtype: numpy.array with shape (nF, )
|
||||
:return: projected face vector
|
||||
"""
|
||||
assert isinstance(fV, np.ndarray), 'fV must be an ndarray'
|
||||
assert len(fV.shape) == 2 and fV.shape[0] == self.nF and fV.shape[1] == self.dim, 'fV must be an ndarray of shape (nF x dim)'
|
||||
@@ -249,9 +248,8 @@ class BaseMesh(object):
|
||||
Given a vector, eV, in cartesian coordinates, this will project it onto the mesh using the tangents
|
||||
|
||||
:param numpy.array eV: edge vector with shape (nE, dim)
|
||||
:rtype: numpy.array
|
||||
:return: projected edge vector, (nE, )
|
||||
|
||||
:rtype: numpy.array with shape (nE, )
|
||||
:return: projected edge vector
|
||||
"""
|
||||
assert isinstance(eV, np.ndarray), 'eV must be an ndarray'
|
||||
assert len(eV.shape) == 2 and eV.shape[0] == self.nE and eV.shape[1] == self.dim, 'eV must be an ndarray of shape (nE x dim)'
|
||||
@@ -297,7 +295,7 @@ class BaseRectangularMesh(BaseMesh):
|
||||
"""
|
||||
Total number of cells in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: [nCx, nCy, nCz]
|
||||
"""
|
||||
return np.array([x for x in [self.nCx, self.nCy, self.nCz] if not x is None])
|
||||
@@ -337,7 +335,7 @@ class BaseRectangularMesh(BaseMesh):
|
||||
"""
|
||||
Total number of nodes in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: [nNx, nNy, nNz]
|
||||
"""
|
||||
return np.array([x for x in [self.nNx, self.nNy, self.nNz] if not x is None])
|
||||
@@ -347,7 +345,7 @@ class BaseRectangularMesh(BaseMesh):
|
||||
"""
|
||||
Number of x-edges in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: vnEx
|
||||
"""
|
||||
return np.array([x for x in [self.nCx, self.nNy, self.nNz] if not x is None])
|
||||
@@ -357,7 +355,7 @@ class BaseRectangularMesh(BaseMesh):
|
||||
"""
|
||||
Number of y-edges in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: vnEy or None if dim < 2
|
||||
"""
|
||||
return None if self.dim < 2 else np.array([x for x in [self.nNx, self.nCy, self.nNz] if not x is None])
|
||||
@@ -367,7 +365,7 @@ class BaseRectangularMesh(BaseMesh):
|
||||
"""
|
||||
Number of z-edges in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: vnEz or None if dim < 3
|
||||
"""
|
||||
return None if self.dim < 3 else np.array([x for x in [self.nNx, self.nNy, self.nCz] if not x is None])
|
||||
@@ -377,7 +375,7 @@ class BaseRectangularMesh(BaseMesh):
|
||||
"""
|
||||
Number of x-faces in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: vnFx
|
||||
"""
|
||||
return np.array([x for x in [self.nNx, self.nCy, self.nCz] if not x is None])
|
||||
@@ -387,7 +385,7 @@ class BaseRectangularMesh(BaseMesh):
|
||||
"""
|
||||
Number of y-faces in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: vnFy or None if dim < 2
|
||||
"""
|
||||
return None if self.dim < 2 else np.array([x for x in [self.nCx, self.nNy, self.nCz] if not x is None])
|
||||
@@ -397,7 +395,7 @@ class BaseRectangularMesh(BaseMesh):
|
||||
"""
|
||||
Number of z-faces in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: vnFz or None if dim < 3
|
||||
"""
|
||||
return None if self.dim < 3 else np.array([x for x in [self.nCx, self.nCy, self.nNz] if not x is None])
|
||||
|
||||
@@ -2,7 +2,6 @@ from SimPEG import Utils, np
|
||||
from BaseMesh import BaseRectangularMesh
|
||||
from DiffOperators import DiffOperators
|
||||
from InnerProducts import InnerProducts
|
||||
from View import CurvView
|
||||
|
||||
# Some helper functions.
|
||||
length2D = lambda x: (x[:, 0]**2 + x[:, 1]**2)**0.5
|
||||
@@ -11,7 +10,7 @@ normalize2D = lambda x: x/np.kron(np.ones((1, 2)), Utils.mkvc(length2D(x), 2))
|
||||
normalize3D = lambda x: x/np.kron(np.ones((1, 3)), Utils.mkvc(length3D(x), 2))
|
||||
|
||||
|
||||
class CurvilinearMesh(BaseRectangularMesh, DiffOperators, InnerProducts, CurvView):
|
||||
class CurvilinearMesh(BaseRectangularMesh, DiffOperators, InnerProducts):
|
||||
"""
|
||||
CurvilinearMesh is a mesh class that deals with curvilinear meshes.
|
||||
|
||||
@@ -331,6 +330,102 @@ class CurvilinearMesh(BaseRectangularMesh, DiffOperators, InnerProducts, CurvVie
|
||||
|
||||
|
||||
|
||||
#############################################
|
||||
# Plotting Functions #
|
||||
#############################################
|
||||
|
||||
def plotGrid(self, ax=None, nodes=False, faces=False, centers=False, edges=False, lines=True, showIt=False):
|
||||
"""Plot the nodal, cell-centered and staggered grids for 1,2 and 3 dimensions.
|
||||
|
||||
|
||||
.. plot::
|
||||
:include-source:
|
||||
|
||||
from SimPEG import Mesh, Utils
|
||||
X, Y = Utils.exampleLrmGrid([3,3],'rotate')
|
||||
M = Mesh.CurvilinearMesh([X, Y])
|
||||
M.plotGrid(showIt=True)
|
||||
|
||||
"""
|
||||
import matplotlib.pyplot as plt
|
||||
import matplotlib
|
||||
from mpl_toolkits.mplot3d import Axes3D
|
||||
mkvc = Utils.mkvc
|
||||
|
||||
axOpts = {'projection':'3d'} if self.dim == 3 else {}
|
||||
if ax is None: ax = plt.subplot(111, **axOpts)
|
||||
|
||||
NN = self.r(self.gridN, 'N', 'N', 'M')
|
||||
if self.dim == 2:
|
||||
|
||||
if lines:
|
||||
X1 = np.c_[mkvc(NN[0][:-1, :]), mkvc(NN[0][1:, :]), mkvc(NN[0][:-1, :])*np.nan].flatten()
|
||||
Y1 = np.c_[mkvc(NN[1][:-1, :]), mkvc(NN[1][1:, :]), mkvc(NN[1][:-1, :])*np.nan].flatten()
|
||||
|
||||
X2 = np.c_[mkvc(NN[0][:, :-1]), mkvc(NN[0][:, 1:]), mkvc(NN[0][:, :-1])*np.nan].flatten()
|
||||
Y2 = np.c_[mkvc(NN[1][:, :-1]), mkvc(NN[1][:, 1:]), mkvc(NN[1][:, :-1])*np.nan].flatten()
|
||||
|
||||
X = np.r_[X1, X2]
|
||||
Y = np.r_[Y1, Y2]
|
||||
|
||||
ax.plot(X, Y, 'b-')
|
||||
if centers:
|
||||
ax.plot(self.gridCC[:,0],self.gridCC[:,1],'ro')
|
||||
|
||||
# Nx = self.r(self.normals, 'F', 'Fx', 'V')
|
||||
# Ny = self.r(self.normals, 'F', 'Fy', 'V')
|
||||
# Tx = self.r(self.tangents, 'E', 'Ex', 'V')
|
||||
# Ty = self.r(self.tangents, 'E', 'Ey', 'V')
|
||||
|
||||
# ax.plot(self.gridN[:, 0], self.gridN[:, 1], 'bo')
|
||||
|
||||
# nX = np.c_[self.gridFx[:, 0], self.gridFx[:, 0] + Nx[0]*length, self.gridFx[:, 0]*np.nan].flatten()
|
||||
# nY = np.c_[self.gridFx[:, 1], self.gridFx[:, 1] + Nx[1]*length, self.gridFx[:, 1]*np.nan].flatten()
|
||||
# ax.plot(self.gridFx[:, 0], self.gridFx[:, 1], 'rs')
|
||||
# ax.plot(nX, nY, 'r-')
|
||||
|
||||
# nX = np.c_[self.gridFy[:, 0], self.gridFy[:, 0] + Ny[0]*length, self.gridFy[:, 0]*np.nan].flatten()
|
||||
# nY = np.c_[self.gridFy[:, 1], self.gridFy[:, 1] + Ny[1]*length, self.gridFy[:, 1]*np.nan].flatten()
|
||||
# #ax.plot(self.gridFy[:, 0], self.gridFy[:, 1], 'gs')
|
||||
# ax.plot(nX, nY, 'g-')
|
||||
|
||||
# tX = np.c_[self.gridEx[:, 0], self.gridEx[:, 0] + Tx[0]*length, self.gridEx[:, 0]*np.nan].flatten()
|
||||
# tY = np.c_[self.gridEx[:, 1], self.gridEx[:, 1] + Tx[1]*length, self.gridEx[:, 1]*np.nan].flatten()
|
||||
# ax.plot(self.gridEx[:, 0], self.gridEx[:, 1], 'r^')
|
||||
# ax.plot(tX, tY, 'r-')
|
||||
|
||||
# nX = np.c_[self.gridEy[:, 0], self.gridEy[:, 0] + Ty[0]*length, self.gridEy[:, 0]*np.nan].flatten()
|
||||
# nY = np.c_[self.gridEy[:, 1], self.gridEy[:, 1] + Ty[1]*length, self.gridEy[:, 1]*np.nan].flatten()
|
||||
# #ax.plot(self.gridEy[:, 0], self.gridEy[:, 1], 'g^')
|
||||
# ax.plot(nX, nY, 'g-')
|
||||
|
||||
elif self.dim == 3:
|
||||
X1 = np.c_[mkvc(NN[0][:-1, :, :]), mkvc(NN[0][1:, :, :]), mkvc(NN[0][:-1, :, :])*np.nan].flatten()
|
||||
Y1 = np.c_[mkvc(NN[1][:-1, :, :]), mkvc(NN[1][1:, :, :]), mkvc(NN[1][:-1, :, :])*np.nan].flatten()
|
||||
Z1 = np.c_[mkvc(NN[2][:-1, :, :]), mkvc(NN[2][1:, :, :]), mkvc(NN[2][:-1, :, :])*np.nan].flatten()
|
||||
|
||||
X2 = np.c_[mkvc(NN[0][:, :-1, :]), mkvc(NN[0][:, 1:, :]), mkvc(NN[0][:, :-1, :])*np.nan].flatten()
|
||||
Y2 = np.c_[mkvc(NN[1][:, :-1, :]), mkvc(NN[1][:, 1:, :]), mkvc(NN[1][:, :-1, :])*np.nan].flatten()
|
||||
Z2 = np.c_[mkvc(NN[2][:, :-1, :]), mkvc(NN[2][:, 1:, :]), mkvc(NN[2][:, :-1, :])*np.nan].flatten()
|
||||
|
||||
X3 = np.c_[mkvc(NN[0][:, :, :-1]), mkvc(NN[0][:, :, 1:]), mkvc(NN[0][:, :, :-1])*np.nan].flatten()
|
||||
Y3 = np.c_[mkvc(NN[1][:, :, :-1]), mkvc(NN[1][:, :, 1:]), mkvc(NN[1][:, :, :-1])*np.nan].flatten()
|
||||
Z3 = np.c_[mkvc(NN[2][:, :, :-1]), mkvc(NN[2][:, :, 1:]), mkvc(NN[2][:, :, :-1])*np.nan].flatten()
|
||||
|
||||
X = np.r_[X1, X2, X3]
|
||||
Y = np.r_[Y1, Y2, Y3]
|
||||
Z = np.r_[Z1, Z2, Z3]
|
||||
|
||||
ax.plot(X, Y, 'b', zs=Z)
|
||||
ax.set_zlabel('x3')
|
||||
|
||||
ax.grid(True)
|
||||
ax.set_xlabel('x1')
|
||||
ax.set_ylabel('x2')
|
||||
|
||||
if showIt: plt.show()
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
nc = 5
|
||||
h1 = np.cumsum(np.r_[0, np.ones(nc)/(nc)])
|
||||
|
||||
@@ -68,8 +68,8 @@ class CylMesh(BaseTensorMesh, BaseRectangularMesh, InnerProducts, CylView):
|
||||
"""
|
||||
Number of x-faces in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:return: vnFx, (dim, )
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: vnFx
|
||||
"""
|
||||
return self.vnC
|
||||
|
||||
@@ -78,8 +78,8 @@ class CylMesh(BaseTensorMesh, BaseRectangularMesh, InnerProducts, CylView):
|
||||
"""
|
||||
Number of y-edges in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:return: vnEy or None if dim < 2, (dim, )
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: vnEy or None if dim < 2
|
||||
"""
|
||||
nNx = self.nNx if self.isSymmetric else self.nNx - 1
|
||||
return np.r_[nNx, self.nCy, self.nNz]
|
||||
@@ -89,8 +89,8 @@ class CylMesh(BaseTensorMesh, BaseRectangularMesh, InnerProducts, CylView):
|
||||
"""
|
||||
Number of z-edges in each direction
|
||||
|
||||
:rtype: numpy.array
|
||||
:return: vnEz or None if nCy > 1, (dim, )
|
||||
:rtype: numpy.array (dim, )
|
||||
:return: vnEz or None if nCy > 1
|
||||
"""
|
||||
if self.isSymmetric:
|
||||
return np.r_[self.nNx, self.nNy, self.nCz]
|
||||
|
||||
@@ -16,7 +16,7 @@ class InnerProducts(object):
|
||||
:param bool invProp: inverts the material property
|
||||
:param bool invMat: inverts the matrix
|
||||
:param bool doFast: do a faster implementation if available.
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.csr_matrix
|
||||
:return: M, the inner product matrix (nF, nF)
|
||||
"""
|
||||
return self._getInnerProduct('F', prop=prop, invProp=invProp, invMat=invMat, doFast=doFast)
|
||||
@@ -27,7 +27,7 @@ class InnerProducts(object):
|
||||
:param bool invProp: inverts the material property
|
||||
:param bool invMat: inverts the matrix
|
||||
:param bool doFast: do a faster implementation if available.
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.csr_matrix
|
||||
:return: M, the inner product matrix (nE, nE)
|
||||
"""
|
||||
return self._getInnerProduct('E', prop=prop, invProp=invProp, invMat=invMat, doFast=doFast)
|
||||
@@ -39,7 +39,7 @@ class InnerProducts(object):
|
||||
:param bool invProp: inverts the material property
|
||||
:param bool invMat: inverts the matrix
|
||||
:param bool doFast: do a faster implementation if available.
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.csr_matrix
|
||||
:return: M, the inner product matrix (nE, nE)
|
||||
"""
|
||||
assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
|
||||
@@ -115,12 +115,13 @@ class InnerProducts(object):
|
||||
:param bool doFast: do a faster implementation if available.
|
||||
:param bool invProp: inverts the material property
|
||||
:param bool invMat: inverts the matrix
|
||||
:rtype: function
|
||||
:return: dMdmu(u), the derivative of the inner product matrix (u)
|
||||
|
||||
Given u, dMdmu returns (nF, nC*nA)
|
||||
|
||||
:param numpy.ndarray u: vector that multiplies dMdmu
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:param np.ndarray u: vector that multiplies dMdmu
|
||||
:rtype: scipy.csr_matrix
|
||||
:return: dMdmu, the derivative of the inner product matrix for a certain u
|
||||
"""
|
||||
return self._getInnerProductDeriv(prop, 'F', doFast=doFast, invProp=invProp, invMat=invMat)
|
||||
@@ -132,7 +133,7 @@ class InnerProducts(object):
|
||||
:param bool doFast: do a faster implementation if available.
|
||||
:param bool invProp: inverts the material property
|
||||
:param bool invMat: inverts the matrix
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.csr_matrix
|
||||
:return: dMdm, the derivative of the inner product matrix (nE, nC*nA)
|
||||
"""
|
||||
return self._getInnerProductDeriv(prop, 'E', doFast=doFast, invProp=invProp, invMat=invMat)
|
||||
@@ -144,7 +145,7 @@ class InnerProducts(object):
|
||||
:param bool doFast: do a faster implementation if available.
|
||||
:param bool invProp: inverts the material property
|
||||
:param bool invMat: inverts the matrix
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.csr_matrix
|
||||
:return: dMdm, the derivative of the inner product matrix (nE, nC*nA)
|
||||
"""
|
||||
fast = None
|
||||
@@ -168,7 +169,7 @@ class InnerProducts(object):
|
||||
:param numpy.array v: vector to multiply (required in the general implementation)
|
||||
:param list P: list of projection matrices
|
||||
:param str projType: 'F' for faces 'E' for edges
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.csr_matrix
|
||||
:return: dMdm, the derivative of the inner product matrix (n, nC*nA)
|
||||
"""
|
||||
assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
|
||||
|
||||
+35
-22
@@ -6,11 +6,13 @@ class TensorMeshIO(object):
|
||||
@classmethod
|
||||
def readUBC(TensorMesh, fileName):
|
||||
"""
|
||||
Read UBC GIF 3D tensor mesh and generate 3D TensorMesh in SimPEG.
|
||||
Read UBC GIF 3DTensor mesh and generate 3D Tensor mesh in simpegTD
|
||||
|
||||
:param string fileName: path to the UBC GIF mesh file
|
||||
:rtype: TensorMesh
|
||||
:return: The tensor mesh for the fileName.
|
||||
Input:
|
||||
:param fileName, path to the UBC GIF mesh file
|
||||
|
||||
Output:
|
||||
:param SimPEG TensorMesh object
|
||||
"""
|
||||
|
||||
# Interal function to read cell size lines for the UBC mesh files.
|
||||
@@ -46,9 +48,11 @@ class TensorMeshIO(object):
|
||||
Read VTK Rectilinear (vtr xml file) and return SimPEG Tensor mesh and model
|
||||
|
||||
Input:
|
||||
:param string fileName: path to the vtr model file to read
|
||||
:rtype: tuple
|
||||
:return: (TensorMesh, modelDictionary)
|
||||
:param vtrFileName, path to the vtr model file to write to
|
||||
|
||||
Output:
|
||||
:return SimPEG TensorMesh object
|
||||
:return SimPEG model dictionary
|
||||
|
||||
"""
|
||||
# Import
|
||||
@@ -98,8 +102,9 @@ class TensorMeshIO(object):
|
||||
Makes and saves a VTK rectilinear file (vtr) for a simpeg Tensor mesh and model.
|
||||
|
||||
Input:
|
||||
:param string fileName: path to the output vtk file
|
||||
:param dict models: dictionary of numpy.array - Name('s) and array('s). Match number of cells
|
||||
:param str, path to the output vtk file
|
||||
:param mesh, SimPEG TensorMesh object - mesh to be transfer to VTK
|
||||
:param models, dictionary of numpy.array - Name('s) and array('s). Match number of cells
|
||||
|
||||
"""
|
||||
# Import
|
||||
@@ -157,9 +162,12 @@ class TensorMeshIO(object):
|
||||
"""
|
||||
Read UBC 3DTensor mesh model and generate 3D Tensor mesh model in simpeg
|
||||
|
||||
:param string fileName: path to the UBC GIF mesh file to read
|
||||
:rtype: numpy.ndarray
|
||||
:return: model with TensorMesh ordered
|
||||
Input:
|
||||
:param fileName, path to the UBC GIF mesh file to read
|
||||
:param mesh, TensorMesh object, mesh that coresponds to the model
|
||||
|
||||
Output:
|
||||
:return numpy array, model with TensorMesh ordered
|
||||
"""
|
||||
f = open(fileName, 'r')
|
||||
model = np.array(map(float, f.readlines()))
|
||||
@@ -175,7 +183,8 @@ class TensorMeshIO(object):
|
||||
Writes a model associated with a SimPEG TensorMesh
|
||||
to a UBC-GIF format model file.
|
||||
|
||||
:param string fileName: File to write to
|
||||
:param str fileName: File to write to
|
||||
:param simpeg.Mesh.TensorMesh mesh: The mesh
|
||||
:param numpy.ndarray model: The model
|
||||
"""
|
||||
|
||||
@@ -192,8 +201,8 @@ class TensorMeshIO(object):
|
||||
"""
|
||||
Writes a SimPEG TensorMesh to a UBC-GIF format mesh file.
|
||||
|
||||
:param string fileName: File to write to
|
||||
:param dict models: A dictionary of the models
|
||||
:param str fileName: File to write to
|
||||
:param simpeg.Mesh.TensorMesh mesh: The mesh
|
||||
|
||||
"""
|
||||
assert mesh.dim == 3
|
||||
@@ -222,8 +231,9 @@ class TreeMeshIO(object):
|
||||
"""
|
||||
Write UBC ocTree mesh and model files from a simpeg ocTree mesh and model.
|
||||
|
||||
:param string fileName: File to write to
|
||||
:param dict models: The models in a dictionary, where the keys is the name of the of the model file
|
||||
:param str fileName: File to write to
|
||||
:param simpeg.Mesh.TreeMesh mesh: The mesh
|
||||
:param dictionary models: The models in a dictionary, where the keys is the name of the of the model file
|
||||
"""
|
||||
|
||||
# Calculate information to write in the file.
|
||||
@@ -276,9 +286,10 @@ class TreeMeshIO(object):
|
||||
|
||||
Input:
|
||||
:param str meshFile: path to the UBC GIF OcTree mesh file to read
|
||||
:rtype: SimPEG.Mesh.TreeMesh
|
||||
:return: The octree mesh
|
||||
|
||||
Output:
|
||||
:return SimPEG.Mesh.TreeMesh mesh: The octree mesh
|
||||
:return list of ndarray's: models as a list of numpy array's
|
||||
"""
|
||||
|
||||
## Read the file lines
|
||||
@@ -324,9 +335,11 @@ class TreeMeshIO(object):
|
||||
"""
|
||||
Read UBC OcTree model and get vector
|
||||
|
||||
:param string fileName: path to the UBC GIF model file to read
|
||||
:rtype: numpy.ndarray
|
||||
:return: OcTree model
|
||||
Input:
|
||||
:param fileName, path to the UBC GIF model file to read
|
||||
|
||||
Output:
|
||||
:return numpy array, OcTree model
|
||||
"""
|
||||
|
||||
if type(fileName) is list:
|
||||
|
||||
@@ -198,8 +198,8 @@ class BaseTensorMesh(BaseMesh):
|
||||
Determines if a set of points are inside a mesh.
|
||||
|
||||
:param numpy.ndarray pts: Location of points to test
|
||||
:rtype numpy.ndarray:
|
||||
:return: inside, numpy array of booleans
|
||||
:rtype numpy.ndarray
|
||||
:return inside, numpy array of booleans
|
||||
"""
|
||||
pts = Utils.asArray_N_x_Dim(pts, self.dim)
|
||||
|
||||
@@ -221,7 +221,7 @@ class BaseTensorMesh(BaseMesh):
|
||||
|
||||
:param numpy.ndarray loc: Location of points to interpolate to
|
||||
:param str locType: What to interpolate (see below)
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.sparse.csr.csr_matrix
|
||||
:return: M, the interpolation matrix
|
||||
|
||||
locType can be::
|
||||
@@ -289,7 +289,7 @@ class BaseTensorMesh(BaseMesh):
|
||||
:param bool returnP: returns the projection matrices
|
||||
:param bool invProp: inverts the material property
|
||||
:param bool invMat: inverts the matrix
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.csr_matrix
|
||||
:return: M, the inner product matrix (nF, nF)
|
||||
"""
|
||||
assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
|
||||
|
||||
@@ -1875,7 +1875,7 @@ class TreeMesh(BaseTensorMesh, InnerProducts, TreeMeshIO):
|
||||
|
||||
:param numpy.ndarray locs: Location of points to interpolate to
|
||||
:param str locType: What to interpolate (see below)
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.sparse.csr.csr_matrix
|
||||
:return: M, the interpolation matrix
|
||||
|
||||
locType can be::
|
||||
|
||||
+40
-78
@@ -552,8 +552,7 @@ class CurvView(object):
|
||||
def __init__(self):
|
||||
pass
|
||||
|
||||
|
||||
def plotGrid(self, ax=None, nodes=False, faces=False, centers=False, edges=False, lines=True, showIt=False):
|
||||
def plotGrid(self, length=0.05, showIt=False):
|
||||
"""Plot the nodal, cell-centered and staggered grids for 1,2 and 3 dimensions.
|
||||
|
||||
|
||||
@@ -561,63 +560,60 @@ class CurvView(object):
|
||||
:include-source:
|
||||
|
||||
from SimPEG import Mesh, Utils
|
||||
X, Y = Utils.exampleLrmGrid([3,3],'rotate')
|
||||
X, Y = Utils.exampleCurvGird([3,3],'rotate')
|
||||
M = Mesh.CurvilinearMesh([X, Y])
|
||||
M.plotGrid(showIt=True)
|
||||
|
||||
"""
|
||||
import matplotlib.pyplot as plt
|
||||
import matplotlib
|
||||
from mpl_toolkits.mplot3d import Axes3D
|
||||
|
||||
axOpts = {'projection':'3d'} if self.dim == 3 else {}
|
||||
if ax is None: ax = plt.subplot(111, **axOpts)
|
||||
|
||||
NN = self.r(self.gridN, 'N', 'N', 'M')
|
||||
if self.dim == 2:
|
||||
fig = plt.figure(2)
|
||||
fig.clf()
|
||||
ax = plt.subplot(111)
|
||||
X1 = np.c_[mkvc(NN[0][:-1, :]), mkvc(NN[0][1:, :]), mkvc(NN[0][:-1, :])*np.nan].flatten()
|
||||
Y1 = np.c_[mkvc(NN[1][:-1, :]), mkvc(NN[1][1:, :]), mkvc(NN[1][:-1, :])*np.nan].flatten()
|
||||
|
||||
if lines:
|
||||
X1 = np.c_[mkvc(NN[0][:-1, :]), mkvc(NN[0][1:, :]), mkvc(NN[0][:-1, :])*np.nan].flatten()
|
||||
Y1 = np.c_[mkvc(NN[1][:-1, :]), mkvc(NN[1][1:, :]), mkvc(NN[1][:-1, :])*np.nan].flatten()
|
||||
X2 = np.c_[mkvc(NN[0][:, :-1]), mkvc(NN[0][:, 1:]), mkvc(NN[0][:, :-1])*np.nan].flatten()
|
||||
Y2 = np.c_[mkvc(NN[1][:, :-1]), mkvc(NN[1][:, 1:]), mkvc(NN[1][:, :-1])*np.nan].flatten()
|
||||
|
||||
X2 = np.c_[mkvc(NN[0][:, :-1]), mkvc(NN[0][:, 1:]), mkvc(NN[0][:, :-1])*np.nan].flatten()
|
||||
Y2 = np.c_[mkvc(NN[1][:, :-1]), mkvc(NN[1][:, 1:]), mkvc(NN[1][:, :-1])*np.nan].flatten()
|
||||
X = np.r_[X1, X2]
|
||||
Y = np.r_[Y1, Y2]
|
||||
|
||||
X = np.r_[X1, X2]
|
||||
Y = np.r_[Y1, Y2]
|
||||
plt.plot(X, Y)
|
||||
|
||||
ax.plot(X, Y, 'b-')
|
||||
if centers:
|
||||
ax.plot(self.gridCC[:,0],self.gridCC[:,1],'ro')
|
||||
plt.hold(True)
|
||||
Nx = self.r(self.normals, 'F', 'Fx', 'V')
|
||||
Ny = self.r(self.normals, 'F', 'Fy', 'V')
|
||||
Tx = self.r(self.tangents, 'E', 'Ex', 'V')
|
||||
Ty = self.r(self.tangents, 'E', 'Ey', 'V')
|
||||
|
||||
# Nx = self.r(self.normals, 'F', 'Fx', 'V')
|
||||
# Ny = self.r(self.normals, 'F', 'Fy', 'V')
|
||||
# Tx = self.r(self.tangents, 'E', 'Ex', 'V')
|
||||
# Ty = self.r(self.tangents, 'E', 'Ey', 'V')
|
||||
plt.plot(self.gridN[:, 0], self.gridN[:, 1], 'bo')
|
||||
|
||||
# ax.plot(self.gridN[:, 0], self.gridN[:, 1], 'bo')
|
||||
nX = np.c_[self.gridFx[:, 0], self.gridFx[:, 0] + Nx[0]*length, self.gridFx[:, 0]*np.nan].flatten()
|
||||
nY = np.c_[self.gridFx[:, 1], self.gridFx[:, 1] + Nx[1]*length, self.gridFx[:, 1]*np.nan].flatten()
|
||||
plt.plot(self.gridFx[:, 0], self.gridFx[:, 1], 'rs')
|
||||
plt.plot(nX, nY, 'r-')
|
||||
|
||||
# nX = np.c_[self.gridFx[:, 0], self.gridFx[:, 0] + Nx[0]*length, self.gridFx[:, 0]*np.nan].flatten()
|
||||
# nY = np.c_[self.gridFx[:, 1], self.gridFx[:, 1] + Nx[1]*length, self.gridFx[:, 1]*np.nan].flatten()
|
||||
# ax.plot(self.gridFx[:, 0], self.gridFx[:, 1], 'rs')
|
||||
# ax.plot(nX, nY, 'r-')
|
||||
nX = np.c_[self.gridFy[:, 0], self.gridFy[:, 0] + Ny[0]*length, self.gridFy[:, 0]*np.nan].flatten()
|
||||
nY = np.c_[self.gridFy[:, 1], self.gridFy[:, 1] + Ny[1]*length, self.gridFy[:, 1]*np.nan].flatten()
|
||||
#plt.plot(self.gridFy[:, 0], self.gridFy[:, 1], 'gs')
|
||||
plt.plot(nX, nY, 'g-')
|
||||
|
||||
# nX = np.c_[self.gridFy[:, 0], self.gridFy[:, 0] + Ny[0]*length, self.gridFy[:, 0]*np.nan].flatten()
|
||||
# nY = np.c_[self.gridFy[:, 1], self.gridFy[:, 1] + Ny[1]*length, self.gridFy[:, 1]*np.nan].flatten()
|
||||
# #ax.plot(self.gridFy[:, 0], self.gridFy[:, 1], 'gs')
|
||||
# ax.plot(nX, nY, 'g-')
|
||||
tX = np.c_[self.gridEx[:, 0], self.gridEx[:, 0] + Tx[0]*length, self.gridEx[:, 0]*np.nan].flatten()
|
||||
tY = np.c_[self.gridEx[:, 1], self.gridEx[:, 1] + Tx[1]*length, self.gridEx[:, 1]*np.nan].flatten()
|
||||
plt.plot(self.gridEx[:, 0], self.gridEx[:, 1], 'r^')
|
||||
plt.plot(tX, tY, 'r-')
|
||||
|
||||
# tX = np.c_[self.gridEx[:, 0], self.gridEx[:, 0] + Tx[0]*length, self.gridEx[:, 0]*np.nan].flatten()
|
||||
# tY = np.c_[self.gridEx[:, 1], self.gridEx[:, 1] + Tx[1]*length, self.gridEx[:, 1]*np.nan].flatten()
|
||||
# ax.plot(self.gridEx[:, 0], self.gridEx[:, 1], 'r^')
|
||||
# ax.plot(tX, tY, 'r-')
|
||||
|
||||
# nX = np.c_[self.gridEy[:, 0], self.gridEy[:, 0] + Ty[0]*length, self.gridEy[:, 0]*np.nan].flatten()
|
||||
# nY = np.c_[self.gridEy[:, 1], self.gridEy[:, 1] + Ty[1]*length, self.gridEy[:, 1]*np.nan].flatten()
|
||||
# #ax.plot(self.gridEy[:, 0], self.gridEy[:, 1], 'g^')
|
||||
# ax.plot(nX, nY, 'g-')
|
||||
nX = np.c_[self.gridEy[:, 0], self.gridEy[:, 0] + Ty[0]*length, self.gridEy[:, 0]*np.nan].flatten()
|
||||
nY = np.c_[self.gridEy[:, 1], self.gridEy[:, 1] + Ty[1]*length, self.gridEy[:, 1]*np.nan].flatten()
|
||||
#plt.plot(self.gridEy[:, 0], self.gridEy[:, 1], 'g^')
|
||||
plt.plot(nX, nY, 'g-')
|
||||
plt.axis('equal')
|
||||
|
||||
elif self.dim == 3:
|
||||
fig = plt.figure(3)
|
||||
fig.clf()
|
||||
ax = fig.add_subplot(111, projection='3d')
|
||||
X1 = np.c_[mkvc(NN[0][:-1, :, :]), mkvc(NN[0][1:, :, :]), mkvc(NN[0][:-1, :, :])*np.nan].flatten()
|
||||
Y1 = np.c_[mkvc(NN[1][:-1, :, :]), mkvc(NN[1][1:, :, :]), mkvc(NN[1][:-1, :, :])*np.nan].flatten()
|
||||
Z1 = np.c_[mkvc(NN[2][:-1, :, :]), mkvc(NN[2][1:, :, :]), mkvc(NN[2][:-1, :, :])*np.nan].flatten()
|
||||
@@ -634,50 +630,16 @@ class CurvView(object):
|
||||
Y = np.r_[Y1, Y2, Y3]
|
||||
Z = np.r_[Z1, Z2, Z3]
|
||||
|
||||
ax.plot(X, Y, 'b', zs=Z)
|
||||
plt.plot(X, Y, 'b', zs=Z)
|
||||
ax.set_zlabel('x3')
|
||||
|
||||
ax.grid(True)
|
||||
ax.hold(False)
|
||||
ax.set_xlabel('x1')
|
||||
ax.set_ylabel('x2')
|
||||
|
||||
if showIt: plt.show()
|
||||
|
||||
def plotImage(self, I, ax=None, showIt=False, grid=False, clim=None):
|
||||
if self.dim == 3: raise NotImplementedError('This is not yet done!')
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
import matplotlib
|
||||
from mpl_toolkits.mplot3d import Axes3D
|
||||
import matplotlib.colors as colors
|
||||
import matplotlib.cm as cmx
|
||||
|
||||
if ax is None: ax = plt.subplot(111)
|
||||
jet = cm = plt.get_cmap('jet')
|
||||
cNorm = colors.Normalize(
|
||||
vmin=I.min() if clim is None else clim[0],
|
||||
vmax=I.max() if clim is None else clim[1])
|
||||
|
||||
scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=jet)
|
||||
# ax.set_xlim((self.x0[0], self.h[0].sum()))
|
||||
# ax.set_ylim((self.x0[1], self.h[1].sum()))
|
||||
|
||||
Nx = self.r(self.gridN[:,0],'N','N','M')
|
||||
Ny = self.r(self.gridN[:,1],'N','N','M')
|
||||
cell = self.r(I,'CC','CC','M')
|
||||
|
||||
for ii in range(self.nCx):
|
||||
for jj in range(self.nCy):
|
||||
I = [ii,ii+1,ii+1,ii]
|
||||
J = [jj,jj,jj+1,jj+1]
|
||||
ax.add_patch(plt.Polygon(np.c_[Nx[I,J],Ny[I,J]], facecolor=scalarMap.to_rgba(cell[ii,jj]), edgecolor='k' if grid else 'none'))
|
||||
|
||||
scalarMap._A = [] # http://stackoverflow.com/questions/8342549/matplotlib-add-colorbar-to-a-sequence-of-line-plots
|
||||
ax.set_xlabel('x')
|
||||
ax.set_ylabel('y')
|
||||
if showIt: plt.show()
|
||||
return [scalarMap]
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
from SimPEG import *
|
||||
|
||||
@@ -131,7 +131,7 @@ class Minimize(object):
|
||||
|
||||
Minimizes the function (evalFunction) starting at the location x0.
|
||||
|
||||
:param callable evalFunction: function handle that evaluates: f, g, H = F(x)
|
||||
:param def evalFunction: function handle that evaluates: f, g, H = F(x)
|
||||
:param numpy.ndarray x0: starting location
|
||||
:rtype: numpy.ndarray
|
||||
:return: x, the last iterate of the optimization algorithm
|
||||
@@ -372,8 +372,8 @@ class Minimize(object):
|
||||
Else, a modifySearchDirectionBreak call is preformed.
|
||||
|
||||
:param numpy.ndarray p: searchDirection
|
||||
:rtype: tuple
|
||||
:return: (xt, passLS) numpy.ndarray, bool
|
||||
:rtype: numpy.ndarray,bool
|
||||
:return: (xt, passLS)
|
||||
"""
|
||||
# Projected Armijo linesearch
|
||||
self._LS_t = 1
|
||||
@@ -408,8 +408,8 @@ class Minimize(object):
|
||||
evalFunction returns a False indicating the break was not caught.
|
||||
|
||||
:param numpy.ndarray p: searchDirection
|
||||
:rtype: tuple
|
||||
:return: (xt, breakCaught) numpy.ndarray, bool
|
||||
:rtype: numpy.ndarray,bool
|
||||
:return: (xt, breakCaught)
|
||||
"""
|
||||
self.printDone(inLS=True)
|
||||
print 'The linesearch got broken. Boo.'
|
||||
@@ -1008,4 +1008,4 @@ class ProjectedGNCG(BFGS, Minimize, Remember):
|
||||
indx = ((self.xc<=self.lower) & (delx < 0)) | ((self.xc>=self.upper) & (delx > 0))
|
||||
delx[indx] = 0.
|
||||
|
||||
return delx
|
||||
return delx
|
||||
|
||||
+1
-1
@@ -187,7 +187,7 @@ class _PropMapMetaClass(type):
|
||||
attrs[attr + 'Model'] = prop._getModelProperty()
|
||||
attrs[attr + 'Deriv'] = prop._getModelDerivProperty()
|
||||
|
||||
return type('PropModel', (PropModel, ), attrs)
|
||||
return type(name.replace('PropMap', 'PropModel'), (PropModel, ), attrs)
|
||||
|
||||
|
||||
class PropMap(object):
|
||||
|
||||
+200
-450
@@ -1,6 +1,4 @@
|
||||
import Utils, Maps, Mesh
|
||||
import numpy as np
|
||||
import scipy.sparse as sp
|
||||
import Utils, Maps, Mesh, numpy as np, scipy.sparse as sp
|
||||
|
||||
class RegularizationMesh(object):
|
||||
"""
|
||||
@@ -10,7 +8,7 @@ class RegularizationMesh(object):
|
||||
are not necessarily true differential operators, but are constructed from
|
||||
a SimPEG Mesh.
|
||||
|
||||
:param BaseMesh mesh: problem mesh
|
||||
:param Mesh mesh: problem mesh
|
||||
:param numpy.array indActive: bool array, size nC, that is True where we have active cells. Used to reduce the operators so we regularize only on active cells
|
||||
"""
|
||||
|
||||
@@ -41,7 +39,7 @@ class RegularizationMesh(object):
|
||||
if self.indActive is None:
|
||||
self._nC = self.mesh.nC
|
||||
else:
|
||||
self._nC = sum(self.indActive)
|
||||
self._nC = int(sum(self.indActive))
|
||||
return self._nC
|
||||
|
||||
@property
|
||||
@@ -306,7 +304,7 @@ class BaseRegularization(object):
|
||||
mesh = None #: A SimPEG.Mesh instance.
|
||||
mref = None #: Reference model.
|
||||
|
||||
def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
|
||||
def __init__(self, mesh=None, nP=None, mapping=None, indActive=None, **kwargs):
|
||||
Utils.setKwargs(self, **kwargs)
|
||||
assert isinstance(mesh, Mesh.BaseMesh), "mesh must be a SimPEG.Mesh object."
|
||||
if indActive is not None and indActive.dtype != 'bool':
|
||||
@@ -316,11 +314,19 @@ class BaseRegularization(object):
|
||||
if indActive is not None and mapping is None:
|
||||
mapping = Maps.IdentityMap(nP=indActive.nonzero()[0].size)
|
||||
|
||||
if mesh is None and nP is None:
|
||||
raise Exception, 'either Mesh or number of parameters must be provided to the BaseRegularization'
|
||||
|
||||
self.regmesh = RegularizationMesh(mesh,indActive)
|
||||
self.mapping = mapping or self.mapPair(mesh)
|
||||
self.mapping._assertMatchesPair(self.mapPair)
|
||||
self.indActive = indActive
|
||||
|
||||
if mesh is not None and nP is None:
|
||||
nP = self.regmesh.nC
|
||||
self.nP = nP
|
||||
|
||||
self.mapping = mapping or self.mapPair(nP=self.nP)
|
||||
self.mapping._assertMatchesPair(self.mapPair)
|
||||
|
||||
@property
|
||||
def parent(self):
|
||||
"""This is the parent of the regularization."""
|
||||
@@ -348,7 +354,7 @@ class BaseRegularization(object):
|
||||
@property
|
||||
def W(self):
|
||||
"""Full regularization weighting matrix W."""
|
||||
return sp.identity(self.regmesh.nC)
|
||||
return sp.identity(self.nP)
|
||||
|
||||
@Utils.timeIt
|
||||
def eval(self, m):
|
||||
@@ -383,8 +389,8 @@ class BaseRegularization(object):
|
||||
|
||||
:param numpy.array m: geophysical model
|
||||
:param numpy.array v: vector to multiply
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:return: WtW, or if v is supplied WtW*v (numpy.ndarray)
|
||||
:rtype: scipy.sparse.csr_matrix or numpy.ndarray
|
||||
:return: WtW or WtW*v
|
||||
|
||||
The regularization is:
|
||||
|
||||
@@ -405,238 +411,7 @@ class BaseRegularization(object):
|
||||
|
||||
return mD.T * ( self.W.T * ( self.W * ( mD * v) ) )
|
||||
|
||||
class Simple(BaseRegularization):
|
||||
"""
|
||||
Simple regularization that does not include length scales in the derivatives.
|
||||
"""
|
||||
|
||||
mrefInSmooth = False #: include mref in the smoothness?
|
||||
alpha_s = Utils.dependentProperty('_alpha_s', 1.0, ['_W', '_Wsmall'], "Smallness weight")
|
||||
alpha_x = Utils.dependentProperty('_alpha_x', 1.0, ['_W', '_Wx'], "Weight for the first derivative in the x direction")
|
||||
alpha_y = Utils.dependentProperty('_alpha_y', 1.0, ['_W', '_Wy'], "Weight for the first derivative in the y direction")
|
||||
alpha_z = Utils.dependentProperty('_alpha_z', 1.0, ['_W', '_Wz'], "Weight for the first derivative in the z direction")
|
||||
cell_weights = 1.
|
||||
|
||||
def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
|
||||
BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
|
||||
|
||||
if isinstance(self.cell_weights,float):
|
||||
self.cell_weights = np.ones(self.regmesh.nC) * self.cell_weights
|
||||
|
||||
@property
|
||||
def Wsmall(self):
|
||||
"""Regularization matrix Wsmall"""
|
||||
if getattr(self,'_Wsmall', None) is None:
|
||||
self._Wsmall = Utils.sdiag((self.alpha_s*self.cell_weights)**0.5)
|
||||
return self._Wsmall
|
||||
|
||||
@property
|
||||
def Wx(self):
|
||||
"""Regularization matrix Wx"""
|
||||
if getattr(self, '_Wx', None) is None:
|
||||
self._Wx = Utils.sdiag((self.alpha_x * (self.regmesh.aveCC2Fx*self.cell_weights))**0.5)*self.regmesh.cellDiffxStencil
|
||||
return self._Wx
|
||||
|
||||
@property
|
||||
def Wy(self):
|
||||
"""Regularization matrix Wy"""
|
||||
if getattr(self, '_Wy', None) is None:
|
||||
self._Wy = Utils.sdiag((self.alpha_y * (self.regmesh.aveCC2Fy*self.cell_weights))**0.5)*self.regmesh.cellDiffyStencil
|
||||
return self._Wy
|
||||
|
||||
@property
|
||||
def Wz(self):
|
||||
"""Regularization matrix Wz"""
|
||||
if getattr(self, '_Wz', None) is None:
|
||||
self._Wz = Utils.sdiag((self.alpha_z * (self.regmesh.aveCC2Fz*self.cell_weights))**0.5)*self.regmesh.cellDiffzStencil
|
||||
return self._Wz
|
||||
|
||||
# @property
|
||||
# def Wsmooth(self):
|
||||
# """Full smoothness regularization matrix W"""
|
||||
# print 'wtf why are we using Wsmooth'
|
||||
# raise NotImplementedError
|
||||
# if getattr(self, '_Wsmooth', None) is None:
|
||||
# wlist = (self.Wx,)
|
||||
# if self.regmesh.dim > 1:
|
||||
# wlist += (self.Wy,)
|
||||
# if self.regmesh.dim > 2:
|
||||
# wlist += (self.Wz,)
|
||||
# self._Wsmooth = sp.vstack(wlist)
|
||||
# return self._Wsmooth
|
||||
#
|
||||
# @property
|
||||
# def W(self):
|
||||
# """Full regularization matrix W"""
|
||||
# print 'wtf why are we using W'
|
||||
# if getattr(self, '_W', None) is None:
|
||||
# wlist = (self.Wsmall, self.Wx)
|
||||
# if self.regmesh.dim > 1:
|
||||
# wlist += (self.Wy,)
|
||||
# if self.regmesh.dim > 2:
|
||||
# wlist += (self.Wz,)
|
||||
# self._W = sp.vstack(wlist)
|
||||
# return self._W
|
||||
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmall(self, m):
|
||||
r = self.Wsmall * ( self.mapping * (m - self.mref) )
|
||||
return 0.5 * r.dot(r)
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmallDeriv(self, m):
|
||||
r = self.Wsmall * ( self.mapping * (m - self.mref) )
|
||||
return r.T * ( self.Wsmall * self.mapping.deriv(m - self.mref) )
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmall2Deriv(self, m, v = None):
|
||||
rDeriv = self.Wsmall * ( self.mapping.deriv(m - self.mref) )
|
||||
if v is not None:
|
||||
return rDeriv.T * (rDeriv * v)
|
||||
return rDeriv.T * rDeriv
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothx(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wx * ( self.mapping * (m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wx * ( self.mapping * (m) )
|
||||
return 0.5 * r.dot(r)
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothy(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wy * ( self.mapping * (m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wy * ( self.mapping * (m) )
|
||||
return 0.5 * r.dot(r)
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothz(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wz * ( self.mapping * (m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wz * ( self.mapping * (m) )
|
||||
return 0.5 * r.dot(r)
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmooth(self, m):
|
||||
phiSmooth = self._evalSmoothx(m)
|
||||
if self.regmesh.dim > 1:
|
||||
phiSmooth += self._evalSmoothy(m)
|
||||
if self.regmesh.dim > 2:
|
||||
phiSmooth += self._evalSmoothz(m)
|
||||
return phiSmooth
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothxDeriv(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wx * ( self.mapping * ( m - self.mref ) )
|
||||
return r.T * ( self.Wx * self.mapping.deriv(m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wx * ( self.mapping * m )
|
||||
return r.T * ( self.Wx * self.mapping.deriv(m) )
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothx2Deriv(self, m, v=None):
|
||||
if self.mrefInSmooth == True:
|
||||
rDeriv = self.Wx * ( self.mapping.deriv( m - self.mref ) )
|
||||
elif self.mrefInSmooth == False:
|
||||
rDeriv = self.Wx * ( self.mapping.deriv(m) )
|
||||
|
||||
if v is not None:
|
||||
return rDeriv.T * ( rDeriv * v )
|
||||
return rDeriv.T * rDeriv
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothyDeriv(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wy * ( self.mapping * ( m - self.mref ) )
|
||||
return r.T * ( self.Wy * self.mapping.deriv(m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wy * ( self.mapping * m )
|
||||
return r.T * ( self.Wy * self.mapping.deriv(m) )
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothy2Deriv(self, m, v=None):
|
||||
if self.mrefInSmooth == True:
|
||||
rDeriv = self.Wy * ( self.mapping.deriv( m - self.mref ) )
|
||||
elif self.mrefInSmooth == False:
|
||||
rDeriv = self.Wy * ( self.mapping.deriv(m) )
|
||||
|
||||
if v is not None:
|
||||
return rDeriv.T * ( rDeriv * v )
|
||||
return rDeriv.T * rDeriv
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothzDeriv(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wz * ( self.mapping * ( m - self.mref ) )
|
||||
return r.T * ( self.Wz * self.mapping.deriv(m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wz * ( self.mapping * m )
|
||||
return r.T * ( self.Wz * self.mapping.deriv(m) )
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothz2Deriv(self, m, v=None):
|
||||
if self.mrefInSmooth == True:
|
||||
rDeriv = self.Wz * ( self.mapping.deriv( m - self.mref ) )
|
||||
elif self.mrefInSmooth == False:
|
||||
rDeriv = self.Wz * ( self.mapping.deriv(m) )
|
||||
|
||||
if v is not None:
|
||||
return rDeriv.T * ( rDeriv * v )
|
||||
return rDeriv.T * rDeriv
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothDeriv(self, m):
|
||||
deriv = self._evalSmoothxDeriv(m)
|
||||
if self.regmesh.dim > 1:
|
||||
deriv += self._evalSmoothyDeriv(m)
|
||||
if self.regmesh.dim > 2:
|
||||
deriv += self._evalSmoothzDeriv(m)
|
||||
return deriv
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmooth2Deriv(self, m, v=None):
|
||||
deriv = self._evalSmoothx2Deriv(m, v)
|
||||
if self.regmesh.dim > 1:
|
||||
deriv += self._evalSmoothy2Deriv(m, v)
|
||||
if self.regmesh.dim > 2:
|
||||
deriv += self._evalSmoothz2Deriv(m, v)
|
||||
return deriv
|
||||
|
||||
|
||||
@Utils.timeIt
|
||||
def eval(self, m):
|
||||
return self._evalSmall(m) + self._evalSmooth(m)
|
||||
|
||||
@Utils.timeIt
|
||||
def evalDeriv(self, m):
|
||||
"""
|
||||
The regularization is:
|
||||
|
||||
.. math::
|
||||
|
||||
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top W(m-m_\\text{ref})}
|
||||
|
||||
So the derivative is straight forward:
|
||||
|
||||
.. math::
|
||||
|
||||
R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
|
||||
|
||||
"""
|
||||
return self._evalSmallDeriv(m) + self._evalSmoothDeriv(m)
|
||||
|
||||
@Utils.timeIt
|
||||
def eval2Deriv(self, m, v=None):
|
||||
return self._evalSmall2Deriv(m, v) + self._evalSmooth2Deriv(m, v)
|
||||
|
||||
|
||||
|
||||
class Tikhonov(Simple):
|
||||
class Tikhonov(BaseRegularization):
|
||||
"""
|
||||
L2 Tikhonov regularization with both smallness and smoothness (first order
|
||||
derivative) contributions.
|
||||
@@ -650,8 +425,8 @@ class Tikhonov(Simple):
|
||||
Note if the key word argument `mrefInSmooth` is False, then mref is not
|
||||
included in the smoothness contribution.
|
||||
|
||||
:param BaseMesh mesh: SimPEG mesh
|
||||
:param IdentityMap mapping: regularization mapping, takes the model from model space to the thing you want to regularize
|
||||
:param Mesh mesh: SimPEG mesh
|
||||
:param Maps mapping: regularization mapping, takes the model from model space to the thing you want to regularize
|
||||
:param numpy.ndarray indActive: active cell indices for reducing the size of differential operators in the definition of a regularization mesh
|
||||
:param bool mrefInSmooth: (default = False) put mref in the smoothness component?
|
||||
:param float alpha_s: (default 1e-6) smallness weight
|
||||
@@ -671,7 +446,7 @@ class Tikhonov(Simple):
|
||||
alpha_yy = Utils.dependentProperty('_alpha_yy', 0.0, ['_W', '_Wyy'], "Weight for the second derivative in the y direction")
|
||||
alpha_zz = Utils.dependentProperty('_alpha_zz', 0.0, ['_W', '_Wzz'], "Weight for the second derivative in the z direction")
|
||||
|
||||
def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
|
||||
def __init__(self, mesh, mapping=None, indActive = None, **kwargs):
|
||||
BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
|
||||
|
||||
@property
|
||||
@@ -726,131 +501,56 @@ class Tikhonov(Simple):
|
||||
self._Wzz = Utils.sdiag((self.regmesh.vol*self.alpha_zz)**0.5)*self.regmesh.faceDiffz*self.regmesh.cellDiffz
|
||||
return self._Wzz
|
||||
|
||||
|
||||
@property
|
||||
def Wsmooth2(self):
|
||||
def Wsmooth(self):
|
||||
"""Full smoothness regularization matrix W"""
|
||||
if getattr(self, '_Wsmooth', None) is None:
|
||||
wlist = (self.Wxx)
|
||||
wlist = (self.Wx, self.Wxx)
|
||||
if self.regmesh.dim > 1:
|
||||
wlist += (self.Wyy)
|
||||
wlist += (self.Wy, self.Wyy)
|
||||
if self.regmesh.dim > 2:
|
||||
wlist += (self.Wzz)
|
||||
wlist += (self.Wz, self.Wzz)
|
||||
self._Wsmooth = sp.vstack(wlist)
|
||||
return self._Wsmooth
|
||||
|
||||
@property
|
||||
def W(self):
|
||||
"""Full regularization matrix W"""
|
||||
if getattr(self, '_W', None) is None:
|
||||
wlist = (self.Wsmall, self.Wsmooth)
|
||||
self._W = sp.vstack(wlist)
|
||||
return self._W
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothxx(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wxx * ( self.mapping * (m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wxx * ( self.mapping * (m) )
|
||||
def _evalSmall(self, m):
|
||||
r = self.Wsmall * ( self.mapping * (m - self.mref) )
|
||||
return 0.5 * r.dot(r)
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothyy(self, m):
|
||||
def _evalSmooth(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wyy * ( self.mapping * (m - self.mref) )
|
||||
r = self.Wsmooth * ( self.mapping * (m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wyy * ( self.mapping * (m) )
|
||||
r = self.Wsmooth * ( self.mapping * (m) )
|
||||
return 0.5 * r.dot(r)
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothzz(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wzz * ( self.mapping * (m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wzz * ( self.mapping * (m) )
|
||||
return 0.5 * r.dot(r)
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmooth2(self, m):
|
||||
phiSmooth2 = self._evalSmoothxx(m)
|
||||
if self.regmesh.dim > 1:
|
||||
phiSmooth2 += self._evalSmoothyy(m)
|
||||
if self.regmesh.dim > 2:
|
||||
phiSmooth2 += self._evalSmoothzz(m)
|
||||
return phiSmooth2
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothxxDeriv(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wxx * ( self.mapping * ( m - self.mref ) )
|
||||
return r.T * ( self.Wxx * self.mapping.deriv(m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wxx * ( self.mapping * m )
|
||||
return r.T * ( self.Wxx * self.mapping.deriv(m) )
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothyyDeriv(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wyy * ( self.mapping * ( m - self.mref ) )
|
||||
return r.T * ( self.Wyy * self.mapping.deriv(m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wyy * ( self.mapping * m )
|
||||
return r.T * ( self.Wyy * self.mapping.deriv(m) )
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothzzDeriv(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wzz * ( self.mapping * ( m - self.mref ) )
|
||||
return r.T * ( self.Wzz * self.mapping.deriv(m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wzz * ( self.mapping * m )
|
||||
return r.T * ( self.Wzz * self.mapping.deriv(m) )
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothxx2Deriv(self, m, v=None):
|
||||
if self.mrefInSmooth == True:
|
||||
rDeriv = self.Wxx * ( self.mapping.deriv( m - self.mref ) )
|
||||
elif self.mrefInSmooth == False:
|
||||
rDeriv = self.Wxx * self.mapping.deriv(m)
|
||||
if v is not None:
|
||||
return rDeriv.T * (rDeriv * v)
|
||||
return rDeriv.T * rDeriv
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothyy2Deriv(self, m, v=None):
|
||||
if self.mrefInSmooth == True:
|
||||
rDeriv = self.Wyy * ( self.mapping.deriv( m - self.mref ) )
|
||||
elif self.mrefInSmooth == False:
|
||||
rDeriv = self.Wyy * self.mapping.deriv(m)
|
||||
if v is not None:
|
||||
return rDeriv.T * (rDeriv * v)
|
||||
return rDeriv.T * rDeriv
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothzz2Deriv(self, m, v=None):
|
||||
if self.mrefInSmooth == True:
|
||||
rDeriv = self.Wzz * ( self.mapping.deriv( m - self.mref ) )
|
||||
elif self.mrefInSmooth == False:
|
||||
rDeriv = self.Wzz * self.mapping.deriv(m)
|
||||
if v is not None:
|
||||
return rDeriv.T * (rDeriv * v)
|
||||
return rDeriv.T * rDeriv
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothDeriv2(self, m):
|
||||
deriv = self._evalSmoothxxDeriv(m)
|
||||
if self.regmesh.dim > 1:
|
||||
deriv += self._evalSmoothyyDeriv(m)
|
||||
if self.regmesh.dim > 2:
|
||||
deriv += self._evalSmoothzzDeriv(m)
|
||||
return deriv
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmooth2Deriv2(self, m, v=None):
|
||||
deriv = self._evalSmoothxx2Deriv(m, v)
|
||||
if self.regmesh.dim > 1:
|
||||
deriv += self._evalSmoothyy2Deriv(m, v)
|
||||
if self.regmesh.dim > 2:
|
||||
deriv += self._evalSmoothzz2Deriv(m, v)
|
||||
return deriv
|
||||
|
||||
|
||||
@Utils.timeIt
|
||||
def eval(self, m):
|
||||
return self._evalSmall(m) + self._evalSmooth(m) + self._evalSmooth2(m)
|
||||
return self._evalSmall(m) + self._evalSmooth(m)
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmallDeriv(self,m):
|
||||
r = self.Wsmall * ( self.mapping * (m - self.mref) )
|
||||
return r.T * ( self.Wsmall * self.mapping.deriv(m - self.mref) )
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmoothDeriv(self,m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wsmooth * ( self.mapping * ( m - self.mref ) )
|
||||
return r.T * ( self.Wsmooth * self.mapping.deriv(m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wsmooth * ( self.mapping * m )
|
||||
return r.T * ( self.Wsmooth * self.mapping.deriv(m) )
|
||||
|
||||
@Utils.timeIt
|
||||
def evalDeriv(self, m):
|
||||
@@ -868,134 +568,184 @@ class Tikhonov(Simple):
|
||||
R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
|
||||
|
||||
"""
|
||||
return self._evalSmallDeriv(m) + self._evalSmoothDeriv(m) + self._evalSmoothDeriv2(m)
|
||||
|
||||
def eval2Deriv(self, m, v=None):
|
||||
"""
|
||||
The regularization is:
|
||||
|
||||
.. math::
|
||||
|
||||
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top W(m-m_\\text{ref})}
|
||||
|
||||
So the derivative is straight forward:
|
||||
|
||||
.. math::
|
||||
|
||||
R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
|
||||
|
||||
"""
|
||||
return self._evalSmall2Deriv(m, v) + self._evalSmooth2Deriv(m, v) + self._evalSmooth2Deriv2(m, v)
|
||||
return self._evalSmallDeriv(m) + self._evalSmoothDeriv(m)
|
||||
|
||||
|
||||
|
||||
class Sparse(Simple):
|
||||
class Simple(Tikhonov):
|
||||
"""
|
||||
The regularization is:
|
||||
|
||||
.. math::
|
||||
|
||||
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top R^\\top R W(m-m_\\text{ref})}
|
||||
|
||||
where the IRLS weight
|
||||
|
||||
.. math::
|
||||
|
||||
R = \eta TO FINISH LATER!!!
|
||||
|
||||
So the derivative is straight forward:
|
||||
|
||||
.. math::
|
||||
|
||||
R(m) = \mathbf{W^\\top R^\\top R W (m-m_\\text{ref})}
|
||||
|
||||
The IRLS weights are recomputed after each beta solves.
|
||||
It is strongly recommended to do a few Gauss-Newton iterations
|
||||
before updating.
|
||||
Simple regularization that does not include length scales in the derivatives.
|
||||
"""
|
||||
|
||||
# set default values
|
||||
eps_p = 1e-1 # Threshold value for the model norm
|
||||
eps_q = 1e-1 # Threshold value for the model gradient norm
|
||||
curModel = None # Requires model to compute the weights
|
||||
l2model = None
|
||||
gamma = 1. # Model norm scaling to smooth out convergence
|
||||
norms = [0., 2., 2., 2.] # Values for norm on (m, dmdx, dmdy, dmdz)
|
||||
cell_weights = 1. # Consider overwriting with sensitivity weights
|
||||
|
||||
mrefInSmooth = False #: SMOOTH and SMOOTH_MOD_DIF options
|
||||
alpha_s = Utils.dependentProperty('_alpha_s', 1.0, ['_W', '_Wsmall'], "Smallness weight")
|
||||
alpha_x = Utils.dependentProperty('_alpha_x', 1.0, ['_W', '_Wx'], "Weight for the first derivative in the x direction")
|
||||
alpha_y = Utils.dependentProperty('_alpha_y', 1.0, ['_W', '_Wy'], "Weight for the first derivative in the y direction")
|
||||
alpha_z = Utils.dependentProperty('_alpha_z', 1.0, ['_W', '_Wz'], "Weight for the first derivative in the z direction")
|
||||
wght = 1.
|
||||
|
||||
def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
|
||||
Simple.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
|
||||
BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
|
||||
|
||||
if isinstance(self.cell_weights,float):
|
||||
self.cell_weights = np.ones(self.regmesh.nC) * self.cell_weights
|
||||
if isinstance(self.wght,float):
|
||||
self.wght = np.ones(self.regmesh.nC) * self.wght
|
||||
|
||||
@property
|
||||
def Wsmall(self):
|
||||
"""Regularization matrix Wsmall"""
|
||||
if getattr(self,'_Wsmall', None) is None:
|
||||
if getattr(self, 'curModel', None) is None:
|
||||
self.Rs = Utils.speye(self.regmesh.nC)
|
||||
|
||||
else:
|
||||
f_m = self.mapping * (self.curModel - self.reg.mref)
|
||||
self.rs = self.R(f_m , self.eps_p, self.norms[0])
|
||||
self.Rs = Utils.sdiag( self.rs )
|
||||
|
||||
self._Wsmall = Utils.sdiag((self.alpha_s*self.gamma*self.cell_weights)**0.5)*self.Rs
|
||||
|
||||
self._Wsmall = Utils.sdiag((self.regmesh.vol*self.alpha_s*self.wght)**0.5)
|
||||
return self._Wsmall
|
||||
|
||||
@property
|
||||
def Wx(self):
|
||||
"""Regularization matrix Wx"""
|
||||
if getattr(self,'_Wx', None) is None:
|
||||
if getattr(self, 'curModel', None) is None:
|
||||
self.Rx = Utils.speye(self.regmesh.cellDiffxStencil.shape[0])
|
||||
|
||||
else:
|
||||
f_m = self.regmesh.cellDiffxStencil * (self.mapping * self.curModel)
|
||||
self.rx = self.R( f_m , self.eps_q, self.norms[1])
|
||||
self.Rx = Utils.sdiag( self.rx )
|
||||
|
||||
self._Wx = Utils.sdiag(( self.alpha_x*self.gamma*(self.regmesh.aveCC2Fx*self.cell_weights))**0.5)*self.Rx*self.regmesh.cellDiffxStencil
|
||||
|
||||
if getattr(self, '_Wx', None) is None:
|
||||
self._Wx = Utils.sdiag((self.regmesh.aveCC2Fx * self.regmesh.vol*self.alpha_x*(self.regmesh.aveCC2Fx*self.wght))**0.5)*self.regmesh.cellDiffxStencil
|
||||
return self._Wx
|
||||
|
||||
@property
|
||||
def Wy(self):
|
||||
"""Regularization matrix Wy"""
|
||||
if getattr(self,'_Wy', None) is None:
|
||||
if getattr(self, 'curModel', None) is None:
|
||||
self.Ry = Utils.speye(self.regmesh.cellDiffyStencil.shape[0])
|
||||
|
||||
else:
|
||||
f_m = self.regmesh.cellDiffyStencil * (self.mapping * self.curModel)
|
||||
self.ry = self.R( f_m , self.eps_q, self.norms[2])
|
||||
self.Ry = Utils.sdiag( self.ry )
|
||||
|
||||
self._Wy = Utils.sdiag((self.alpha_y*self.gamma*(self.regmesh.aveCC2Fy*self.cell_weights))**0.5)*self.Ry*self.regmesh.cellDiffyStencil
|
||||
|
||||
if getattr(self, '_Wy', None) is None:
|
||||
self._Wy = Utils.sdiag((self.regmesh.aveCC2Fy * self.regmesh.vol * self.alpha_y*(self.regmesh.aveCC2Fy*self.wght))**0.5)*self.regmesh.cellDiffyStencil
|
||||
return self._Wy
|
||||
|
||||
@property
|
||||
def Wz(self):
|
||||
"""Regularization matrix Wz"""
|
||||
if getattr(self,'_Wz', None) is None:
|
||||
if getattr(self, 'curModel', None) is None:
|
||||
self.Rz = Utils.speye(self.regmesh.cellDiffzStencil.shape[0])
|
||||
|
||||
else:
|
||||
f_m = self.regmesh.cellDiffzStencil * (self.mapping * self.curModel)
|
||||
self.rz = self.R( f_m , self.eps_q, self.norms[3])
|
||||
self.Rz = Utils.sdiag( self.rz )
|
||||
|
||||
self._Wz = Utils.sdiag((self.alpha_z*self.gamma*(self.regmesh.aveCC2Fz*self.cell_weights))**0.5)*self.Rz*self.regmesh.cellDiffzStencil
|
||||
|
||||
if getattr(self, '_Wz', None) is None:
|
||||
self._Wz = Utils.sdiag((self.regmesh.aveCC2Fz * self.regmesh.vol*self.alpha_z*(self.regmesh.aveCC2Fz*self.wght))**0.5)*self.regmesh.cellDiffzStencil
|
||||
return self._Wz
|
||||
|
||||
@property
|
||||
def Wsmooth(self):
|
||||
"""Full smoothness regularization matrix W"""
|
||||
if getattr(self, '_Wsmooth', None) is None:
|
||||
wlist = (self.Wx,)
|
||||
if self.regmesh.dim > 1:
|
||||
wlist += (self.Wy,)
|
||||
if self.regmesh.dim > 2:
|
||||
wlist += (self.Wz,)
|
||||
self._Wsmooth = sp.vstack(wlist)
|
||||
return self._Wsmooth
|
||||
|
||||
@property
|
||||
def W(self):
|
||||
"""Full regularization matrix W"""
|
||||
if getattr(self, '_W', None) is None:
|
||||
wlist = (self.Wsmall, self.Wsmooth)
|
||||
self._W = sp.vstack(wlist)
|
||||
return self._W
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmall(self, m):
|
||||
r = self.Wsmall * ( self.mapping * (m - self.mref) )
|
||||
return 0.5 * r.dot(r)
|
||||
|
||||
@Utils.timeIt
|
||||
def _evalSmooth(self, m):
|
||||
if self.mrefInSmooth == True:
|
||||
r = self.Wsmooth * ( self.mapping * (m - self.mref) )
|
||||
elif self.mrefInSmooth == False:
|
||||
r = self.Wsmooth * ( self.mapping * m)
|
||||
return 0.5 * r.dot(r)
|
||||
|
||||
|
||||
class Sparse(Simple):
|
||||
|
||||
# set default values
|
||||
eps_p = 1e-1
|
||||
eps_q = 1e-1
|
||||
curModel = None # use a model to compute the weights
|
||||
gamma = 1.
|
||||
norms = [0., 2., 2., 2.]
|
||||
wght = 1.
|
||||
|
||||
def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
|
||||
Simple.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
|
||||
|
||||
if isinstance(self.wght,float):
|
||||
self.wght = np.ones(self.regmesh.nC) * self.wght
|
||||
|
||||
@property
|
||||
def Wsmall(self):
|
||||
"""Regularization matrix Wsmall"""
|
||||
if getattr(self, 'curModel', None) is None:
|
||||
self.Rs = Utils.speye(self.regmesh.nC)
|
||||
|
||||
else:
|
||||
f_m = self.curModel - self.reg.mref
|
||||
self.rs = self.R(f_m , self.eps_p, self.norms[0])
|
||||
#print "Min rs: " + str(np.max(self.rs)) + "Max rs: " + str(np.min(self.rs))
|
||||
self.Rs = Utils.sdiag( self.rs )
|
||||
|
||||
return Utils.sdiag((self.regmesh.vol*self.alpha_s*self.gamma*self.wght)**0.5)*self.Rs
|
||||
|
||||
|
||||
@property
|
||||
def Wx(self):
|
||||
"""Regularization matrix Wx"""
|
||||
|
||||
if getattr(self, 'curModel', None) is None:
|
||||
self.Rx = Utils.speye(self.regmesh.cellDiffxStencil.shape[0])
|
||||
|
||||
else:
|
||||
f_m = self.regmesh.cellDiffxStencil * self.curModel
|
||||
self.rx = self.R( f_m , self.eps_q, self.norms[1])
|
||||
self.Rx = Utils.sdiag( self.rx )
|
||||
|
||||
return Utils.sdiag(( (self.regmesh.aveCC2Fx * self.regmesh.vol) *self.alpha_x*self.gamma*(self.regmesh.aveCC2Fx*self.wght))**0.5)*self.Rx*self.regmesh.cellDiffxStencil
|
||||
|
||||
@property
|
||||
def Wy(self):
|
||||
"""Regularization matrix Wy"""
|
||||
|
||||
if getattr(self, 'curModel', None) is None:
|
||||
self.Ry = Utils.speye(self.regmesh.cellDiffyStencil.shape[0])
|
||||
|
||||
else:
|
||||
f_m = self.regmesh.cellDiffyStencil * self.curModel
|
||||
self.ry = self.R( f_m , self.eps_q, self.norms[2])
|
||||
self.Ry = Utils.sdiag( self.ry )
|
||||
|
||||
return Utils.sdiag(((self.regmesh.aveCC2Fy * self.regmesh.vol)*self.alpha_y*self.gamma*(self.regmesh.aveCC2Fy*self.wght))**0.5)*self.Ry*self.regmesh.cellDiffyStencil
|
||||
|
||||
@property
|
||||
def Wz(self):
|
||||
"""Regularization matrix Wz"""
|
||||
|
||||
if getattr(self, 'curModel', None) is None:
|
||||
self.Rz = Utils.speye(self.regmesh.cellDiffzStencil.shape[0])
|
||||
|
||||
else:
|
||||
f_m = self.regmesh.cellDiffzStencil * self.curModel
|
||||
self.rz = self.R( f_m , self.eps_q, self.norms[3])
|
||||
self.Rz = Utils.sdiag( self.rz )
|
||||
|
||||
return Utils.sdiag(((self.regmesh.aveCC2Fz * self.regmesh.vol)*self.alpha_z*self.gamma*(self.regmesh.aveCC2Fz*self.wght))**0.5)*self.Rz*self.regmesh.cellDiffzStencil
|
||||
|
||||
@property
|
||||
def Wsmooth(self):
|
||||
"""Full smoothness regularization matrix W"""
|
||||
#if getattr(self, '_Wsmooth', None) is None:
|
||||
wlist = (self.Wx,)
|
||||
if self.regmesh.dim > 1:
|
||||
wlist += (self.Wy,)
|
||||
if self.regmesh.dim > 2:
|
||||
wlist += (self.Wz,)
|
||||
#self._Wsmooth = sp.vstack(wlist)
|
||||
return sp.vstack(wlist)
|
||||
|
||||
@property
|
||||
def W(self):
|
||||
"""Full regularization matrix W"""
|
||||
if getattr(self, '_W', None) is None:
|
||||
wlist = (self.Wsmall, self.Wsmooth)
|
||||
self._W = sp.vstack(wlist)
|
||||
return self._W
|
||||
|
||||
def R(self, f_m , eps, exponent):
|
||||
|
||||
# Eta scaling is important for mix-norms...do not mess with it
|
||||
eta = (eps**(1.-exponent/2.))**0.5
|
||||
r = eta / (f_m**2.+ eps**2.)**((1.-exponent/2.)/2.)
|
||||
|
||||
|
||||
+3
-2
@@ -311,6 +311,7 @@ class BaseSurvey(object):
|
||||
if f is None: f = self.prob.fields(m)
|
||||
return Utils.mkvc(self.eval(f))
|
||||
|
||||
|
||||
@Utils.count
|
||||
def eval(self, f):
|
||||
"""eval(f)
|
||||
@@ -321,7 +322,7 @@ class BaseSurvey(object):
|
||||
|
||||
d_\\text{pred} = \mathbf{P} f(m)
|
||||
"""
|
||||
raise NotImplementedError('eval is not yet implemented.')
|
||||
raise NotImplemented('eval is not yet implemented.')
|
||||
|
||||
@Utils.count
|
||||
def evalDeriv(self, f):
|
||||
@@ -333,7 +334,7 @@ class BaseSurvey(object):
|
||||
|
||||
\\frac{\partial d_\\text{pred}}{\partial u} = \mathbf{P}
|
||||
"""
|
||||
raise NotImplementedError('eval is not yet implemented.')
|
||||
raise NotImplemented('eval is not yet implemented.')
|
||||
|
||||
@Utils.count
|
||||
def residual(self, m, f=None):
|
||||
|
||||
+1
-1
@@ -237,7 +237,7 @@ def checkDerivative(fctn, x0, num=7, plotIt=True, dx=None, expectedOrder=2, tole
|
||||
Compares error decay of 0th and 1st order Taylor approximation at point
|
||||
x0 for a randomized search direction.
|
||||
|
||||
:param callable fctn: function handle
|
||||
:param lambda fctn: function handle
|
||||
:param numpy.array x0: point at which to check derivative
|
||||
:param int num: number of times to reduce step length, h
|
||||
:param bool plotIt: if you would like to plot
|
||||
|
||||
@@ -7,11 +7,11 @@ def addBlock(gridCC, modelCC, p0, p1, blockProp):
|
||||
"""
|
||||
Add a block to an exsisting cell centered model, modelCC
|
||||
|
||||
:param numpy.array gridCC: mesh.gridCC is the cell centered grid
|
||||
:param numpy.array modelCC: cell centered model
|
||||
:param numpy.array p0: bottom, southwest corner of block
|
||||
:param numpy.array p1: top, northeast corner of block
|
||||
:blockProp float blockProp: property to assign to the model
|
||||
:param numpy.array, gridCC: mesh.gridCC is the cell centered grid
|
||||
:param numpy.array, modelCC: cell centered model
|
||||
:param numpy.array, p0: bottom, southwest corner of block
|
||||
:param numpy.array, p1: top, northeast corner of block
|
||||
:blockProp float, blockProp: property to assign to the model
|
||||
|
||||
:return numpy.array, modelBlock: model with block
|
||||
"""
|
||||
@@ -147,7 +147,7 @@ def getIndicesSphere(center,radius,ccMesh):
|
||||
|
||||
if dimMesh == 1:
|
||||
# Define the reference points
|
||||
|
||||
|
||||
ind = np.abs(center[0] - ccMesh[:,0]) < radius
|
||||
|
||||
elif dimMesh == 2:
|
||||
@@ -222,14 +222,14 @@ def layeredModel(ccMesh, layerTops, layerValues):
|
||||
|
||||
:param numpy.array ccMesh: cell-centered mesh
|
||||
:param numpy.array layerTops: z-locations of the tops of each layer
|
||||
:param numpy.array layerValue: values of the property to assign for each layer (starting at the top)
|
||||
:param numpy.array layerValue: values of the property to assign for each layer (starting at the top)
|
||||
:rtype: numpy.array
|
||||
:return: M, layered model on the mesh
|
||||
:return: M, layered model on the mesh
|
||||
"""
|
||||
|
||||
descending = np.linalg.norm(sorted(layerTops, reverse=True) - layerTops) < 1e-20
|
||||
|
||||
# TODO: put an error check to make sure that there is an ordering... needs to work with inf elts
|
||||
# TODO: put an error check to make sure that there is an ordering... needs to work with inf elts
|
||||
# assert ascending or descending, "Layers must be listed in either ascending or descending order"
|
||||
|
||||
# start from bottom up
|
||||
@@ -253,10 +253,10 @@ def layeredModel(ccMesh, layerTops, layerValues):
|
||||
model = np.zeros(ccMesh.shape[0])
|
||||
|
||||
for i, top in enumerate(layerTops):
|
||||
zind = z <= top
|
||||
zind = z <= top
|
||||
model[zind] = layerValues[i]
|
||||
|
||||
return model
|
||||
return model
|
||||
|
||||
|
||||
|
||||
@@ -265,9 +265,9 @@ def randomModel(shape, seed=None, anisotropy=None, its=100, bounds=None):
|
||||
Create a random model by convolving a kernel with a
|
||||
uniformly distributed model.
|
||||
|
||||
:param tuple shape: shape of the model.
|
||||
:param int,tuple shape: shape of the model.
|
||||
:param int seed: pick which model to produce, prints the seed if you don't choose.
|
||||
:param numpy.ndarray anisotropy: this is the (3 x n) blurring kernel that is used.
|
||||
:param numpy.ndarray,list anisotropy: this is the (3 x n) blurring kernel that is used.
|
||||
:param int its: number of smoothing iterations
|
||||
:param list bounds: bounds on the model, len(list) == 2
|
||||
:rtype: numpy.ndarray
|
||||
|
||||
@@ -13,7 +13,7 @@ def _checkAccuracy(A, b, X, accuracyTol):
|
||||
warnings.warn(msg, RuntimeWarning)
|
||||
|
||||
|
||||
def SolverWrapD(fun, factorize=True, checkAccuracy=True, accuracyTol=1e-6, name=None):
|
||||
def SolverWrapD(fun, factorize=True, checkAccuracy=True, accuracyTol=1e-6):
|
||||
"""
|
||||
Wraps a direct Solver.
|
||||
|
||||
@@ -72,11 +72,11 @@ def SolverWrapD(fun, factorize=True, checkAccuracy=True, accuracyTol=1e-6, name=
|
||||
if factorize and hasattr(self.solver, 'clean'):
|
||||
return self.solver.clean()
|
||||
|
||||
return type(name if name is not None else fun.__name__, (object,), {"__init__": __init__, "clean": clean, "__mul__": __mul__})
|
||||
return type(fun.__name__+'_Wrapped', (object,), {"__init__": __init__, "clean": clean, "__mul__": __mul__})
|
||||
|
||||
|
||||
|
||||
def SolverWrapI(fun, checkAccuracy=True, accuracyTol=1e-5, name=None):
|
||||
def SolverWrapI(fun, checkAccuracy=True, accuracyTol=1e-5):
|
||||
"""
|
||||
Wraps an iterative Solver.
|
||||
|
||||
@@ -128,13 +128,13 @@ def SolverWrapI(fun, checkAccuracy=True, accuracyTol=1e-5, name=None):
|
||||
def clean(self):
|
||||
pass
|
||||
|
||||
return type(name if name is not None else fun.__name__, (object,), {"__init__": __init__, "clean": clean, "__mul__": __mul__})
|
||||
return type(fun.__name__+'_Wrapped', (object,), {"__init__": __init__, "clean": clean, "__mul__": __mul__})
|
||||
|
||||
|
||||
from scipy.sparse import linalg
|
||||
Solver = SolverWrapD(linalg.spsolve, factorize=False, name="Solver")
|
||||
SolverLU = SolverWrapD(linalg.splu, factorize=True, name="SolverLU")
|
||||
SolverCG = SolverWrapI(linalg.cg, name="SolverCG")
|
||||
Solver = SolverWrapD(linalg.spsolve, factorize=False)
|
||||
SolverLU = SolverWrapD(linalg.splu, factorize=True)
|
||||
SolverCG = SolverWrapI(linalg.cg)
|
||||
|
||||
|
||||
class SolverDiag(object):
|
||||
|
||||
@@ -25,7 +25,7 @@ def interpmat(locs, x, y=None, z=None):
|
||||
:param numpy.ndarray x: Tensor vector of 1st dimension of grid.
|
||||
:param numpy.ndarray y: Tensor vector of 2nd dimension of grid. None by default.
|
||||
:param numpy.ndarray z: Tensor vector of 3rd dimension of grid. None by default.
|
||||
:rtype: scipy.sparse.csr_matrix
|
||||
:rtype: scipy.sparse.csr.csr_matrix
|
||||
:return: Interpolation matrix
|
||||
|
||||
.. plot::
|
||||
|
||||
@@ -27,7 +27,7 @@ def mkvc(x, numDims=1):
|
||||
|
||||
if isinstance(x, Zero):
|
||||
return x
|
||||
|
||||
|
||||
assert isinstance(x, np.ndarray), "Vector must be a numpy array"
|
||||
|
||||
if numDims == 1:
|
||||
@@ -355,9 +355,9 @@ def diagEst(matFun, n, k=None, approach='Probing'):
|
||||
2. Ones : random +/- 1 entries
|
||||
3. Random : random vectors
|
||||
|
||||
:param callable matFun: takes a (numpy.array) and multiplies it by a matrix to estimate the diagonal
|
||||
:param int n: size of the vector that should be used to compute matFun(v)
|
||||
:param int k: number of vectors to be used to estimate the diagonal
|
||||
:param lambda (numpy.array) matFun: matrix to estimate the diagonal of
|
||||
:param int64 n: size of the vector that should be used to compute matFun(v)
|
||||
:param int64 k: number of vectors to be used to estimate the diagonal
|
||||
:param str approach: approach to be used for getting vectors
|
||||
:rtype: numpy.array
|
||||
:return: est_diag(A)
|
||||
@@ -422,9 +422,9 @@ class Zero(object):
|
||||
def __ge__(self, v):return 0 >= v
|
||||
def __gt__(self, v):return 0 > v
|
||||
|
||||
@property
|
||||
@property
|
||||
def transpose(self): return Zero()
|
||||
|
||||
|
||||
@property
|
||||
def T(self): return Zero()
|
||||
|
||||
|
||||
+14
-18
@@ -83,7 +83,7 @@ def closestPoints(mesh, pts, gridLoc='CC'):
|
||||
"""
|
||||
Move a list of points to the closest points on a grid.
|
||||
|
||||
:param BaseMesh mesh: The mesh
|
||||
:param simpeg.Mesh.BaseMesh mesh: The mesh
|
||||
:param numpy.ndarray pts: Points to move
|
||||
:param string gridLoc: ['CC', 'N', 'Fx', 'Fy', 'Fz', 'Ex', 'Ex', 'Ey', 'Ez']
|
||||
:rtype: numpy.ndarray
|
||||
@@ -104,20 +104,16 @@ def closestPoints(mesh, pts, gridLoc='CC'):
|
||||
|
||||
def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
|
||||
"""
|
||||
Extracts Core Mesh from Global mesh
|
||||
|
||||
:param numpy.ndarray xyzlim: 2D array [ndim x 2]
|
||||
:param BaseMesh mesh: The mesh
|
||||
|
||||
This function ouputs::
|
||||
|
||||
- actind: corresponding boolean index from global to core
|
||||
- meshcore: core SimPEG mesh
|
||||
|
||||
Warning: 1D and 2D has not been tested
|
||||
Extracts Core Mesh from Global mesh
|
||||
xyzlim: 2D array [ndim x 2]
|
||||
mesh: SimPEG mesh
|
||||
This function ouputs:
|
||||
- actind: corresponding boolean index from global to core
|
||||
- meshcore: core SimPEG mesh
|
||||
Warning: 1D and 2D has not been tested
|
||||
"""
|
||||
from SimPEG import Mesh
|
||||
if mesh.dim == 1:
|
||||
if mesh.dim ==1:
|
||||
xyzlim = xyzlim.flatten()
|
||||
xmin, xmax = xyzlim[0], xyzlim[1]
|
||||
|
||||
@@ -129,11 +125,11 @@ def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
|
||||
|
||||
x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5]
|
||||
|
||||
meshCore = Mesh.TensorMesh([hx, hy], x0=x0)
|
||||
meshCore = Mesh.TensorMesh([hx, hy] ,x0=x0)
|
||||
|
||||
actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax)
|
||||
|
||||
elif mesh.dim == 2:
|
||||
elif mesh.dim ==2:
|
||||
xmin, xmax = xyzlim[0,0], xyzlim[0,1]
|
||||
ymin, ymax = xyzlim[1,0], xyzlim[1,1]
|
||||
|
||||
@@ -148,12 +144,12 @@ def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
|
||||
|
||||
x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5]
|
||||
|
||||
meshCore = Mesh.TensorMesh([hx, hy], x0=x0)
|
||||
meshCore = Mesh.TensorMesh([hx, hy] ,x0=x0)
|
||||
|
||||
actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax) \
|
||||
& (mesh.gridCC[:,1]>ymin) & (mesh.gridCC[:,1]<ymax) \
|
||||
|
||||
elif mesh.dim == 3:
|
||||
elif mesh.dim==3:
|
||||
xmin, xmax = xyzlim[0,0], xyzlim[0,1]
|
||||
ymin, ymax = xyzlim[1,0], xyzlim[1,1]
|
||||
zmin, zmax = xyzlim[2,0], xyzlim[2,1]
|
||||
@@ -172,7 +168,7 @@ def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
|
||||
|
||||
x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5, zc[0]-hz[0]*0.5]
|
||||
|
||||
meshCore = Mesh.TensorMesh([hx, hy, hz], x0=x0)
|
||||
meshCore = Mesh.TensorMesh([hx, hy, hz] ,x0=x0)
|
||||
|
||||
actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax) \
|
||||
& (mesh.gridCC[:,1]>ymin) & (mesh.gridCC[:,1]<ymax) \
|
||||
|
||||
+1
-1
@@ -15,7 +15,7 @@ import Directives
|
||||
import Inversion
|
||||
import Tests
|
||||
|
||||
__version__ = '0.1.12'
|
||||
__version__ = '0.1.10'
|
||||
__author__ = 'Rowan Cockett'
|
||||
__license__ = 'MIT'
|
||||
__copyright__ = 'Copyright 2014 Rowan Cockett'
|
||||
|
||||
|
Before Width: | Height: | Size: 49 KiB After Width: | Height: | Size: 49 KiB |
|
Before Width: | Height: | Size: 58 KiB After Width: | Height: | Size: 58 KiB |
+1
-1
@@ -2,7 +2,7 @@
|
||||
#
|
||||
|
||||
# You can set these variables from the command line.
|
||||
SPHINXOPTS = -n -w warnings.txt
|
||||
SPHINXOPTS =
|
||||
SPHINXBUILD = sphinx-build
|
||||
PAPER =
|
||||
BUILDDIR = _build
|
||||
|
||||
|
Before Width: | Height: | Size: 30 KiB After Width: | Height: | Size: 30 KiB |
Vendored
-22
@@ -1,22 +0,0 @@
|
||||
{# Import the theme's layout. #}
|
||||
{% extends "!layout.html" %}
|
||||
|
||||
{% block extrahead %}
|
||||
{{ super() }}
|
||||
|
||||
<meta name="description" content="Simulation and Parameter Estimation in Geophysics">
|
||||
<meta name="author" content="SimPEG Developers">
|
||||
<meta name="keywords" content="python, geophysics, inversion, electromagnetics, magnetotellurics, magnetics, gravity, DC, flow inverse problems, open source, finite volume">
|
||||
|
||||
|
||||
<script>
|
||||
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
|
||||
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
|
||||
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
|
||||
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
|
||||
|
||||
ga('create', 'UA-45185336-1', 'auto');
|
||||
ga('send', 'pageview');
|
||||
|
||||
</script>
|
||||
{% endblock %}
|
||||
@@ -1,3 +1,5 @@
|
||||
.. _api_DC:
|
||||
|
||||
.. math::
|
||||
|
||||
\renewcommand{\div}{\nabla\cdot\,}
|
||||
@@ -36,16 +38,8 @@
|
||||
\renewcommand {\u} { {\vec u} }
|
||||
\newcommand{\I}{\vec{I}}
|
||||
|
||||
|
||||
Direct Current Resistivity
|
||||
**************************
|
||||
|
||||
`SimPEG.DCIP` uses SimPEG as the framework for the forward and inverse
|
||||
direct current (DC) resistivity and induced polarization (IP) geophysical problems.
|
||||
|
||||
|
||||
DC resistivity survey
|
||||
=====================
|
||||
*********************
|
||||
|
||||
Electrical resistivity of subsurface materials is measured by causing an electrical current to flow in the earth between one pair of electrodes while the voltage across a second pair of electrodes is measured. The result is an "apparent" resistivity which is a value representing the weighted average resistivity over a volume of the earth. Variations in this measurement are caused by variations in the soil, rock, and pore fluid electrical resistivity. Surveys require contact with the ground, so they can be labour intensive. Results are sometimes interpreted directly, but more commonly, 1D, 2D or 3D models are estimated using inversion procedures (`GPG <http://www.eos.ubc.ca/courses/eosc350/content/>`_).
|
||||
|
||||
@@ -61,7 +55,7 @@ As direct current (DC) implies, in DC resistivity survey, we assume steady-state
|
||||
|
||||
\curl \e = 0
|
||||
|
||||
Then by taking \\(\\div\\) of the first equation, we have
|
||||
Then by taking \\(\\curl\\) for the first equation, we have
|
||||
|
||||
.. math::
|
||||
|
||||
@@ -143,14 +137,13 @@ Comparing to the analytic function:
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.DC_Analytic_Dipole.run(plotIt=True)
|
||||
import simpegDC as DC
|
||||
DC.Examples.Verification.run(plotIt=True)
|
||||
|
||||
API
|
||||
===
|
||||
|
||||
API for DC codes
|
||||
================
|
||||
|
||||
.. automodule:: SimPEG.DCIP.BaseDC
|
||||
.. automodule:: simpegDC.BaseDC
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
@@ -7,7 +7,7 @@ Examples
|
||||
:maxdepth: 1
|
||||
:glob:
|
||||
|
||||
../examples/*
|
||||
examples/*
|
||||
|
||||
|
||||
External Notebooks
|
||||
@@ -0,0 +1,19 @@
|
||||
.. _api_FiniteVolume:
|
||||
|
||||
Finite Volume
|
||||
*************
|
||||
|
||||
Any numerical implementation requires the discretization of continuous functions into discrete approximations. These approximations are typically organized in a mesh, which defines boundaries, locations, and connectivity. Of specific interest to geophysical simulations, we require that averaging, interpolation and differential operators be defined for any mesh. In SimPEG, we have implemented a staggered mimetic finite volume approach (`Hyman and Shashkov, 1999 <http://math.lanl.gov/~mac/papers/numerics/HS99B.pdf>`_). This approach requires the definitions of variables at either cell-centers, nodes, faces, or edges as seen in the figure below.
|
||||
|
||||
.. image:: images/finitevolrealestate.png
|
||||
:width: 400 px
|
||||
:alt: FiniteVolume
|
||||
:align: center
|
||||
|
||||
|
||||
.. toctree::
|
||||
:maxdepth: 2
|
||||
|
||||
api_Mesh
|
||||
api_DiffOps
|
||||
api_InnerProducts
|
||||
@@ -52,15 +52,13 @@ We can take the derivative of the PDE:
|
||||
|
||||
\nabla_m c(m, u) \partial m + \nabla_u c(m, u) \partial u = 0
|
||||
|
||||
If the forward problem is invertible, then we can rearrange for
|
||||
\\(\\frac{\\partial u}{\\partial m}\\):
|
||||
If the forward problem is invertible, then we can rearrange for \\(\\frac{\\partial u}{\\partial m}\\):
|
||||
|
||||
.. math::
|
||||
|
||||
J = - P \left( \nabla_u c(m, u) \right)^{-1} \nabla_m c(m, u)
|
||||
|
||||
This can often be computed given a vector (i.e. \\(J(v)\\)) rather than
|
||||
stored, as \\(J\\) is a large dense matrix.
|
||||
This can often be computed given a vector (i.e. \\(J(v)\\)) rather than stored, as \\(J\\) is a large dense matrix.
|
||||
|
||||
|
||||
|
||||
@@ -69,45 +67,13 @@ The API
|
||||
|
||||
Problem
|
||||
-------
|
||||
|
||||
.. autoclass:: SimPEG.Problem.BaseProblem
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
.. autoclass:: SimPEG.Problem.BaseTimeProblem
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
Fields
|
||||
------
|
||||
|
||||
.. autoclass:: SimPEG.Fields.Fields
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
.. autoclass:: SimPEG.Fields.TimeFields
|
||||
.. automodule:: SimPEG.Problem
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
Survey
|
||||
------
|
||||
|
||||
.. autoclass:: SimPEG.Survey.BaseSurvey
|
||||
.. automodule:: SimPEG.Survey
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
.. autoclass:: SimPEG.Survey.BaseSrc
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
.. autoclass:: SimPEG.Survey.BaseRx
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
.. autoclass:: SimPEG.Survey.BaseTimeRx
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
.. autoclass:: SimPEG.Survey.Data
|
||||
:members:
|
||||
:undoc-members:
|
||||
@@ -4,10 +4,7 @@
|
||||
Inner Products
|
||||
**************
|
||||
|
||||
By using the weak formulation of many of the PDEs in geophysical applications,
|
||||
we can rapidly develop discretizations. Much of this work, however, needs a
|
||||
good understanding of how to approximate inner products on our discretized
|
||||
meshes. We will define the inner product as:
|
||||
By using the weak formulation of many of the PDEs in geophysical applications, we can rapidly develop discretizations. Much of this work, however, needs a good understanding of how to approximate inner products on our discretized meshes. We will define the inner product as:
|
||||
|
||||
.. math::
|
||||
|
||||
@@ -17,15 +14,12 @@ where a and b are either scalars or vectors.
|
||||
|
||||
.. note::
|
||||
|
||||
The InnerProducts class is a base class providing inner product matrices
|
||||
for meshes and cannot run on its own.
|
||||
The InnerProducts class is a base class providing inner product matrices for meshes and cannot run on its own.
|
||||
|
||||
|
||||
Example problem for DC resistivity
|
||||
----------------------------------
|
||||
|
||||
We will start with the formulation of the Direct Current (DC) resistivity
|
||||
problem in geophysics.
|
||||
We will start with the formulation of the Direct Current (DC) resistivity problem in geophysics.
|
||||
|
||||
|
||||
.. math::
|
||||
@@ -34,13 +28,12 @@ problem in geophysics.
|
||||
|
||||
\nabla\cdot \vec{j} = q
|
||||
|
||||
In the following discretization, :math:`\sigma` and :math:`\phi`
|
||||
will be discretized on the cell-centers and the flux, :math:`\vec{j}`,
|
||||
In the following discretization, \\\( \\sigma \\\) and \\\( \\phi \\\)
|
||||
will be discretized on the cell-centers and the flux, \\\(\\vec{j}\\\),
|
||||
will be on the faces. We will use the weak formulation to discretize
|
||||
the DC resistivity equation.
|
||||
|
||||
We can define in weak form by integrating with a general face function
|
||||
:math:`\vec{f}`:
|
||||
We can define in weak form by integrating with a general face function \\\(\\vec{f}\\\):
|
||||
|
||||
.. math::
|
||||
|
||||
@@ -68,16 +61,9 @@ We can then discretize for every cell:
|
||||
|
||||
.. note::
|
||||
|
||||
We have discretized the dot product above, but remember that we do not
|
||||
really have a single vector :math:`\mathbf{J}`, but approximations of
|
||||
:math:`\vec{j}` on each face of our cell. In 2D that means 2
|
||||
approximations of :math:`\mathbf{J}_x` and 2 approximations of
|
||||
:math:`\mathbf{J}_y`. In 3D we also have 2 approximations of
|
||||
:math:`\mathbf{J}_z`.
|
||||
We have discretized the dot product above, but remember that we do not really have a single vector \\\(\\mathbf{J}\\\), but approximations of \\\(\\vec{j}\\\) on each face of our cell. In 2D that means 2 approximations of \\\(\\mathbf{J}_x\\\) and 2 approximations of \\\(\\mathbf{J}_y\\\). In 3D we also have 2 approximations of \\\(\\mathbf{J}_z\\\).
|
||||
|
||||
Regardless of how we choose to approximate this dot product, we can represent
|
||||
this in vector form (again this is for every cell), and will generalize for
|
||||
the case of anisotropic (tensor) sigma.
|
||||
Regardless of how we choose to approximate this dot product, we can represent this in vector form (again this is for every cell), and will generalize for the case of anisotropic (tensor) sigma.
|
||||
|
||||
.. math::
|
||||
|
||||
@@ -85,17 +71,14 @@ the case of anisotropic (tensor) sigma.
|
||||
-\phi^{\top} v_{\text{cell}} \mathbf{D}_{\text{cell}} \mathbf{F})
|
||||
+ \text{BC}
|
||||
|
||||
We multiply by square-root of volume on each side of the tensor conductivity
|
||||
to keep symmetry in the system. Here :math:`\mathbf{J}_c` is the Cartesian
|
||||
:math:`\mathbf{J}` (on the faces that we choose to use in our approximation)
|
||||
and must be calculated differently depending on the mesh:
|
||||
We multiply by square-root of volume on each side of the tensor conductivity to keep symmetry in the system. Here \\\(\\mathbf{J}_c\\\) is the Cartesian \\\(\\mathbf{J}\\\) (on the faces that we choose to use in our approximation) and must be calculated differently depending on the mesh:
|
||||
|
||||
.. math::
|
||||
\mathbf{J}_c = \mathbf{Q}_{(i)}\mathbf{J}_\text{TENSOR} \\
|
||||
\mathbf{J}_c = \mathbf{N}_{(i)}^{-1}\mathbf{Q}_{(i)}\mathbf{J}_\text{Curv}
|
||||
|
||||
Here the :math:`i` index refers to where we choose to approximate this integral, as discussed in the note above.
|
||||
We will approximate this integral by taking the fluxes clustered around every node of the cell, there are 8 combinations in 3D, and 4 in 2D. We will use a projection matrix :math:`\mathbf{Q}_{(i)}` to pick the appropriate fluxes. So, now that we have 8 approximations of this integral, we will just take the average. For the TensorMesh, this looks like:
|
||||
Here the \\\(i\\\) index refers to where we choose to approximate this integral, as discussed in the note above.
|
||||
We will approximate this integral by taking the fluxes clustered around every node of the cell, there are 8 combinations in 3D, and 4 in 2D. We will use a projection matrix \\\( \\mathbf{Q}_{(i)} \\\) to pick the appropriate fluxes. So, now that we have 8 approximations of this integral, we will just take the average. For the TensorMesh, this looks like:
|
||||
|
||||
.. math::
|
||||
|
||||
@@ -124,12 +107,10 @@ By defining the faceInnerProduct (8 combinations of fluxes in 3D, 4 in 2D, 2 in
|
||||
\sum_{i=1}^{2^d}
|
||||
\mathbf{P}_{(i)}^{\top} \Sigma^{-1} \mathbf{P}_{(i)}
|
||||
|
||||
Where :math:`d` is the dimension of the mesh.
|
||||
The :math:`\mathbf{M}^f` is returned when given the input of :math:`\Sigma^{-1}`.
|
||||
Where \\\(d\\\) is the dimension of the mesh.
|
||||
The \\\( \\mathbf{M}^f \\\) is returned when given the input of \\\( \\Sigma^{-1} \\\).
|
||||
|
||||
Here each :math:`\mathbf{P} ~ \in ~ \mathbb{R}^{(d*nC, nF)}` is a combination
|
||||
of the projection, volume, and any normalization to Cartesian coordinates
|
||||
(where the dot product is well defined):
|
||||
Here each \\( \\mathbf{P} \\in \\mathbb{R}^{(d*nC, nF)} \\\) is a combination of the projection, volume, and any normalization to Cartesian coordinates (where the dot product is well defined):
|
||||
|
||||
.. math::
|
||||
|
||||
@@ -148,10 +129,7 @@ If ``returnP=True`` is requested in any of these methods the projection matrices
|
||||
# In 1D
|
||||
P = [P0, P1]
|
||||
|
||||
The derivation for ``edgeInnerProducts`` is exactly the same, however, when we
|
||||
approximate the integral using the fields around each node, the projection
|
||||
matrices look a bit different because we have 12 edges in 3D instead of just 6
|
||||
faces. The interface to the code is exactly the same.
|
||||
The derivation for ``edgeInnerProducts`` is exactly the same, however, when we approximate the integral using the fields around each node, the projection matrices look a bit different because we have 12 edges in 3D instead of just 6 faces. The interface to the code is exactly the same.
|
||||
|
||||
|
||||
Defining Tensor Properties
|
||||
@@ -159,8 +137,7 @@ Defining Tensor Properties
|
||||
|
||||
**For 3D:**
|
||||
|
||||
Depending on the number of columns (either 1, 3, or 6) of mu, the material
|
||||
property is interpreted as follows:
|
||||
Depending on the number of columns (either 1, 3, or 6) of mu, the material property is interpreted as follows:
|
||||
|
||||
.. math::
|
||||
|
||||
@@ -211,16 +188,13 @@ Which is nice and easy to invert if necessary, however, in the fully anisotropic
|
||||
Taking Derivatives
|
||||
------------------
|
||||
|
||||
We will take the derivative of the fully anisotropic tensor for a 3D mesh, the
|
||||
other cases are easier and will not be discussed here. Let us start with one
|
||||
part of the sum which makes up :math:`\mathbf{M}^f_\Sigma` and take the
|
||||
derivative when this is multiplied by some vector :math:`\mathbf{v}`:
|
||||
We will take the derivative of the fully anisotropic tensor for a 3D mesh, the other cases are easier and will not be discussed here. Let us start with one part of the sum which makes up \\\(\\mathbf{M}^f_\\Sigma\\\) and take the derivative when this is multiplied by some vector \\\(\\mathbf{v}\\\):
|
||||
|
||||
.. math::
|
||||
|
||||
\mathbf{P}^\top \boldsymbol{\Sigma} \mathbf{Pv}
|
||||
|
||||
Here we will let :math:`\mathbf{Pv} = \mathbf{y}` and :math:`\mathbf{y}` will have the form:
|
||||
Here we will let \\\( \\mathbf{Pv} = \\mathbf{y} \\\) and \\\(\\mathbf{y}\\\) will have the form:
|
||||
|
||||
.. math::
|
||||
|
||||
@@ -259,9 +233,7 @@ Here we will let :math:`\mathbf{Pv} = \mathbf{y}` and :math:`\mathbf{y}` will ha
|
||||
\end{matrix}
|
||||
\right]
|
||||
|
||||
Now it is easy to take the derivative with respect to any one of the
|
||||
parameters, for example,
|
||||
:math:`\frac{\partial}{\partial\boldsymbol{\sigma}_1}`
|
||||
Now it is easy to take the derivative with respect to any one of the parameters, for example, \\\(\\frac{\\partial}{\\partial\\boldsymbol{\\sigma}_1}\\\)
|
||||
|
||||
.. math::
|
||||
\frac{\partial}{\partial \boldsymbol{\sigma}_1}\left(\mathbf{P}^\top\Sigma\mathbf{y}\right)
|
||||
@@ -275,8 +247,7 @@ parameters, for example,
|
||||
\end{matrix}
|
||||
\right]
|
||||
|
||||
Whereas :math:`\frac{\partial}{\partial\boldsymbol{\sigma}_4}`, for
|
||||
example, is:
|
||||
Whereas \\\(\\frac{\\partial}{\\partial\\boldsymbol{\\sigma}_4}\\\), for example, is:
|
||||
|
||||
.. math::
|
||||
\frac{\partial}{\partial \boldsymbol{\sigma}_4}\left(\mathbf{P}^\top\Sigma\mathbf{y}\right)
|
||||
@@ -290,12 +261,11 @@ example, is:
|
||||
\end{matrix}
|
||||
\right]
|
||||
|
||||
These are computed for each of the 8 projections, horizontally concatenated,
|
||||
and returned.
|
||||
These are computed for each of the 8 projections, horizontally concatenated, and returned.
|
||||
|
||||
The API
|
||||
-------
|
||||
|
||||
.. autoclass:: SimPEG.Mesh.InnerProducts.InnerProducts
|
||||
.. automodule:: SimPEG.Mesh.InnerProducts
|
||||
:members:
|
||||
:undoc-members:
|
||||
@@ -3,7 +3,7 @@
|
||||
InvProblem
|
||||
**********
|
||||
|
||||
.. autoclass:: SimPEG.InvProblem.BaseInvProblem
|
||||
.. automodule:: SimPEG.InvProblem
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
@@ -12,7 +12,7 @@ InvProblem
|
||||
Inversion
|
||||
*********
|
||||
|
||||
.. autoclass:: SimPEG.Inversion.BaseInversion
|
||||
.. automodule:: SimPEG.Inversion
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
@@ -27,8 +27,7 @@ back to conductivity. This is a relatively trivial example (we are just taking
|
||||
the exponential!) but by defining maps we can start to combine and manipulate
|
||||
exactly what we think about as our model, \\\(m\\\). In code, this looks like
|
||||
|
||||
.. code-block:: python
|
||||
:linenos:
|
||||
::
|
||||
|
||||
M = Mesh.TensorMesh([100]) # Create a mesh
|
||||
expMap = Maps.ExpMap(M) # Create a mapping
|
||||
@@ -47,15 +46,14 @@ We will use an example where we want a 1D layered earth as
|
||||
our model, but we want to map this to a 2D discretization to do our forward
|
||||
modeling. We will also assume that we are working in log conductivity still,
|
||||
so after the transformation we want to map to conductivity space.
|
||||
To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.SurjectVertical1D`),
|
||||
To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.Vertical1DMap`),
|
||||
which does the first part of what we just described. The second part will be
|
||||
done by the :class:`SimPEG.Maps.ExpMap` described above.
|
||||
|
||||
.. code-block:: python
|
||||
:linenos:
|
||||
::
|
||||
|
||||
M = Mesh.TensorMesh([7,5])
|
||||
v1dMap = Maps.SurjectVertical1D(M)
|
||||
v1dMap = Maps.Vertical1DMap(M)
|
||||
expMap = Maps.ExpMap(M)
|
||||
myMap = expMap * v1dMap
|
||||
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
|
||||
@@ -63,8 +61,26 @@ done by the :class:`SimPEG.Maps.ExpMap` described above.
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Maps_ComboMaps.run()
|
||||
from SimPEG import *
|
||||
import matplotlib.pyplot as plt
|
||||
M = Mesh.TensorMesh([7,5])
|
||||
v1dMap = Maps.Vertical1DMap(M)
|
||||
expMap = Maps.ExpMap(M)
|
||||
myMap = expMap * v1dMap
|
||||
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
|
||||
sig = myMap * m
|
||||
figs, axs = plt.subplots(1,2)
|
||||
axs[0].plot(m, M.vectorCCy, 'b-o')
|
||||
axs[0].set_title('Model')
|
||||
axs[0].set_ylabel('Depth, y')
|
||||
axs[0].set_xlabel('Value, $m_i$')
|
||||
axs[0].set_xlim(0,3)
|
||||
axs[0].set_ylim(0,1)
|
||||
clbar = plt.colorbar(M.plotImage(sig,ax=axs[1],grid=True,gridOpts=dict(color='grey'))[0])
|
||||
axs[1].set_title('Physical Property')
|
||||
axs[1].set_ylabel('Depth, y')
|
||||
clbar.set_label('$\sigma = \exp(\mathbf{P}m)$')
|
||||
plt.tight_layout()
|
||||
|
||||
If you noticed, it was pretty easy to combine maps. What is even cooler is
|
||||
that the derivatives also are made for you (if everything goes right).
|
||||
@@ -106,72 +122,10 @@ When these are used in the inverse problem, this is extremely important!!
|
||||
The API
|
||||
=======
|
||||
|
||||
The :code:`IdentityMap` is the base class for all mappings, and it does absolutely nothing.
|
||||
|
||||
.. autoclass:: SimPEG.Maps.IdentityMap
|
||||
.. automodule:: SimPEG.Maps
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
Common Maps
|
||||
===========
|
||||
|
||||
Exponential Map
|
||||
---------------
|
||||
|
||||
Electrical conductivity varies over many orders of magnitude, so it is a common
|
||||
technique when solving the inverse problem to parameterize and optimize in terms
|
||||
of log conductivity. This makes sense not only because it ensures all conductivities
|
||||
will be positive, but because this is fundamentally the space where conductivity
|
||||
lives (i.e. it varies logarithmically).
|
||||
|
||||
.. autoclass:: SimPEG.Maps.ExpMap
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
Vertical 1D Map
|
||||
---------------
|
||||
|
||||
.. autoclass:: SimPEG.Maps.SurjectVertical1D
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
Map 2D Cross-Section to 3D Model
|
||||
--------------------------------
|
||||
|
||||
.. autoclass:: SimPEG.Maps.Map2Dto3D
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
Mesh to Mesh Map
|
||||
----------------
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Maps_Mesh2Mesh.run()
|
||||
|
||||
|
||||
.. autoclass:: SimPEG.Maps.Mesh2Mesh
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
Under the Hood
|
||||
==============
|
||||
|
||||
Combo Map
|
||||
---------
|
||||
|
||||
The ComboMap holds the information for multiplying and combining
|
||||
maps. It also uses the chain rule to create the derivative.
|
||||
Remember, any time that you make your own combination of mappings
|
||||
be sure to test that the derivative is correct.
|
||||
|
||||
.. autoclass:: SimPEG.Maps.ComboMap
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
@@ -188,6 +188,6 @@ other types of meshes in this SimPEG framework.
|
||||
The API
|
||||
=======
|
||||
|
||||
.. autoclass:: SimPEG.Mesh.BaseMesh.BaseMesh
|
||||
.. automodule:: SimPEG.Mesh.BaseMesh
|
||||
:members:
|
||||
:undoc-members:
|
||||
@@ -0,0 +1,36 @@
|
||||
.. _api_MeshCode:
|
||||
|
||||
Tensor Mesh
|
||||
===========
|
||||
|
||||
.. automodule:: SimPEG.Mesh.TensorMesh
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
Cylindrical Mesh
|
||||
================
|
||||
|
||||
.. automodule:: SimPEG.Mesh.CylMesh
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
Tree Mesh
|
||||
=========
|
||||
|
||||
.. autoclass:: SimPEG.Mesh.TreeMesh.TreeMesh
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
Curvilinear Mesh
|
||||
================
|
||||
|
||||
.. automodule:: SimPEG.Mesh.CurvilinearMesh
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
@@ -91,21 +91,10 @@ The API
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
.. autoclass:: SimPEG.Regularization.Simple
|
||||
:show-inheritance:
|
||||
:members:
|
||||
|
||||
.. autoclass:: SimPEG.Regularization.Tikhonov
|
||||
:show-inheritance:
|
||||
:members:
|
||||
|
||||
.. autoclass:: SimPEG.Regularization.Sparse
|
||||
:show-inheritance:
|
||||
:members:
|
||||
|
||||
.. autoclass:: SimPEG.Regularization.RegularizationMesh
|
||||
:show-inheritance:
|
||||
:members:
|
||||
|
||||
|
||||
|
||||
@@ -46,8 +46,6 @@ The API
|
||||
=======
|
||||
|
||||
.. autofunction:: SimPEG.Utils.SolverUtils.SolverWrapD
|
||||
:noindex:
|
||||
|
||||
.. autofunction:: SimPEG.Utils.SolverUtils.SolverWrapI
|
||||
:noindex:
|
||||
|
||||
@@ -6,6 +6,5 @@ Utilities
|
||||
|
||||
api_Solver
|
||||
api_Maps
|
||||
api_PropMaps
|
||||
api_Utils
|
||||
api_Tests
|
||||
@@ -21,7 +21,7 @@ Solver Utilities
|
||||
:undoc-members:
|
||||
|
||||
Curv Utilities
|
||||
==============
|
||||
=============
|
||||
|
||||
.. automodule:: SimPEG.Utils.curvutils
|
||||
:members:
|
||||
@@ -51,9 +51,7 @@ Interpolation Utilities
|
||||
Counter Utilities
|
||||
=================
|
||||
|
||||
.. code-block:: python
|
||||
:linenos:
|
||||
|
||||
::
|
||||
class MyClass(object):
|
||||
def __init__(self, url):
|
||||
self.counter = Counter()
|
||||
@@ -71,9 +69,7 @@ Counter Utilities
|
||||
for i in range(300): c.MySecondMethod()
|
||||
c.counter.summary()
|
||||
|
||||
|
||||
.. code-block:: text
|
||||
:linenos:
|
||||
::
|
||||
|
||||
Counters:
|
||||
MyClass.MyMethod : 100
|
||||
@@ -81,8 +77,6 @@ Counter Utilities
|
||||
Times: mean sum
|
||||
MyClass.MySecondMethod : 1.70e-06, 5.10e-04, 300x
|
||||
|
||||
|
||||
|
||||
The API
|
||||
-------
|
||||
|
||||
@@ -35,7 +35,7 @@ The Big Picture
|
||||
Defining a well-posed inverse problem and solving it is a complex task that requires many components that must interact. It is helpful
|
||||
to view this task as a workflow in which various elements are explicitly identified and integrated. The figure below outlines the inversion components that consists of inputs, implementation, and evaluation. The inputs are composed of the geophysical data, the equations which are a mathematical description of the governing physics, and prior knowledge or assumptions about the setting. The implementation consists of two broad categories: the forward simulation and the inversion. The **forward simulation** is the means by which we solve the governing equations given a model and the **inversion components** evaluate and update this model. We are considering a gradient based approach, which updates the model through an optimization routine. The output of this implementation is a model, which, prior to interpretation, must be evaluated. This requires considering, and often re-assessing, the choices and assumptions made in both the input and implementation stages.
|
||||
|
||||
.. image:: ../../images/InversionWorkflow-PreSimPEG.png
|
||||
.. image:: InversionWorkflow-PreSimPEG.png
|
||||
:width: 400 px
|
||||
:alt: Components
|
||||
:align: center
|
||||
@@ -46,24 +46,24 @@ A Comprehensive Framework
|
||||
|
||||
There are an overwhelming amount of choices to be made as one works through the forward modeling and inversion process (see figure above). As a result, software implementations of this workflow often become complex and highly interdependent, making it difficult to interact with and to ask other scientists to pick up and change. Our approach to handling this complexity is to propose a framework, (see below), that compartmentalizes the implementation of inversions into various units. We present it in this specific modular style, as each unit contains a targeted subset of choices crucial to the inversion process.
|
||||
|
||||
.. image:: ../../images/InversionWorkflow.png
|
||||
.. image:: InversionWorkflow.png
|
||||
:width: 400 px
|
||||
:alt: Framework
|
||||
:align: center
|
||||
|
||||
The process of obtaining an acceptable model from an inversion generally requires the geophysicist to perform several iterations of the inversion workflow, rethinking and redesigning each piece of the framework to ensure it is appropriate in the current context. Inversions are experimental and empirical by nature and our software package is designed to facilitate this iterative process. To accomplish this, we have divided the inversion methodology into eight major components (See figure above). The :class:`SimPEG.Mesh.BaseMesh.BaseMesh` class handles the discretization of the earth and also provides numerical operators. The forward simulation is split into two classes, the :class:`SimPEG.Survey.BaseSurvey` and the :class:`SimPEG.Problem.BaseProblem`. The :class:`SimPEG.Survey.BaseSurvey` class handles the geometry of a geophysical problem as well as sources. The :class:`SimPEG.Problem.BaseProblem` class handles the simulation of the physics for the geophysical problem of interest. Although created independently, these two classes must be paired to form all of the components necessary for a geophysical forward simulation and calculation of the sensitivity. The :class:`SimPEG.Problem.BaseProblem` creates geophysical fields given a source from the :class:`SimPEG.Survey.BaseSurvey`. The :class:`SimPEG.Survey.BaseSurvey` interpolates these fields to the receiver locations and converts them to the appropriate data type, for example, by selecting only the measured components of the field. Each of these operations may have associated derivatives with respect to the model and the computed field; these are included in the calculation of the sensitivity. For the inversion, a :class:`SimPEG.DataMisfit.BaseDataMisfit` is chosen to capture the goodness of fit of the predicted data and a :class:`SimPEG.Regularization.BaseRegularization` is chosen to handle the non-uniqueness. These inversion elements and an Optimization routine are combined into an inverse problem class :class:`SimPEG.InvProblem.BaseInvProblem`. :class:`SimPEG.InvProblem.BaseInvProblem` is the mathematical statement that will be numerically solved by running an Inversion. The :class:`SimPEG.Inversion.BaseInversion` class handles organization and dispatch of directives between all of the various pieces of the framework.
|
||||
The process of obtaining an acceptable model from an inversion generally requires the geophysicist to perform several iterations of the inversion workflow, rethinking and redesigning each piece of the framework to ensure it is appropriate in the current context. Inversions are experimental and empirical by nature and our software package is designed to facilitate this iterative process. To accomplish this, we have divided the inversion methodology into eight major components (See figure above). The (:class:`SimPEG.Mesh.BaseMesh`) class handles the discretization of the earth and also provides numerical operators. The forward simulation is split into two classes, the (:class:`SimPEG.Survey.BaseSurvey`) and the (:class:`SimPEG.Problem.BaseProblem`). The (:class:`SimPEG.Survey.BaseSurvey`) class handles the geometry of a geophysical problem as well as sources. The (:class:`SimPEG.Problem.BaseProblem`) class handles the simulation of the physics for the geophysical problem of interest. Although created independently, these two classes must be paired to form all of the components necessary for a geophysical forward simulation and calculation of the sensitivity. The (:class:`SimPEG.Problem.BaseProblem`) creates geophysical fields given a source from the (:class:`SimPEG.Survey.BaseSurvey`). The (:class:`SimPEG.Survey.BaseSurvey`) interpolates these fields to the receiver locations and converts them to the appropriate data type, for example, by selecting only the measured components of the field. Each of these operations may have associated derivatives with respect to the model and the computed field; these are included in the calculation of the sensitivity. For the inversion, a (:class:`SimPEG.DataMisfit.BaseDataMisfit`) is chosen to capture the goodness of fit of the predicted data and a (:class:`SimPEG.Regularization.BaseRegularization`) is chosen to handle the non-uniqueness. These inversion elements and an Optimization routine are combined into an inverse problem class (:class:`SimPEG.InvProblem.BaseInvProblem`). (:class:`SimPEG.InvProblem.BaseInvProblem`) is the mathematical statement that will be numerically solved by running an Inversion. The (:class:`SimPEG.Inversion.BaseInversion`) class handles organization and dispatch of directives between all of the various pieces of the framework.
|
||||
|
||||
The arrows in the figure above indicate what each class takes as a primary argument. For example, both the :class:`SimPEG.Problem.BaseProblem` and :class:`SimPEG.Regularization.BaseRegularization` classes take a :class:`SimPEG.Mesh.BaseMesh.BaseMesh` class as an argument. The diagram does not show class inheritance, as each of the base classes outlined have many subtypes that can be interchanged. The :class:`SimPEG.Mesh.BaseMesh.BaseMesh` class, for example, could be a regular Cartesian mesh :class:`SimPEG.Mesh.TensorMesh` or a cylindrical coordinate mesh :class:`SimPEG.Mesh.CylMesh`, which have many properties in common. These common features, such as both meshes being created from tensor products, can be exploited through inheritance of base classes, and differences can be expressed through subtype polymorphism. Please look at the documentation here for more in-depth information.
|
||||
The arrows in the figure above indicate what each class takes as a primary argument. For example, both the (:class:`SimPEG.Problem.BaseProblem`) and (:class:`SimPEG.Regularization.BaseRegularization`) classes take a (:class:`SimPEG.Mesh.BaseMesh`) class as an argument. The diagram does not show class inheritance, as each of the base classes outlined have many subtypes that can be interchanged. The (:class:`SimPEG.Mesh.BaseMesh`) class, for example, could be a regular Cartesian mesh (:class:`SimPEG.Mesh.TensorMesh`) or a cylindrical coordinate mesh (:class:`SimPEG.Mesh.CylMesh`), which have many properties in common. These common features, such as both meshes being created from tensor products, can be exploited through inheritance of base classes, and differences can be expressed through subtype polymorphism. Please look at the documentation here for more in-depth information.
|
||||
|
||||
|
||||
.. include:: ../../../CITATION.rst
|
||||
.. include:: ../CITATION.rst
|
||||
|
||||
Authors
|
||||
-------
|
||||
|
||||
.. include:: ../../../AUTHORS.rst
|
||||
.. include:: ../AUTHORS.rst
|
||||
|
||||
License
|
||||
-------
|
||||
|
||||
.. include:: ../../../LICENSE
|
||||
.. include:: ../LICENSE
|
||||
@@ -1,95 +0,0 @@
|
||||
# application: simpegdocs
|
||||
# version: 1
|
||||
runtime: python27
|
||||
api_version: 1
|
||||
threadsafe: yes
|
||||
|
||||
handlers:
|
||||
|
||||
# favicon
|
||||
- url: /images/logo-block\.ico
|
||||
static_files: /images/logo-block.ico
|
||||
upload: /images/logo-block\.ico
|
||||
|
||||
# all css
|
||||
- url: /(.*\.css)
|
||||
mime_type: text/css
|
||||
static_files: _build/html/\1
|
||||
upload: _build/html/(.*\.css)
|
||||
|
||||
# webfonts
|
||||
- url: /(.*\.(eot|svg|ttf|woff|woff2|otf))
|
||||
static_files: _build/html/\1
|
||||
upload: _build/html/(.*\.(eot|svg|ttf|woff|woff2|otf))
|
||||
|
||||
# javascript
|
||||
- url: /(.*\.js)
|
||||
mime_type: text/javascript
|
||||
static_files: _build/html/\1
|
||||
upload: _build/html/(.*\.js)
|
||||
|
||||
# plain text source
|
||||
- url: /(.*\.txt)
|
||||
mime_type: text/plain
|
||||
static_files: _build/html/\1
|
||||
upload: _build/html/(.*\.txt)
|
||||
|
||||
# images
|
||||
- url: /_images/(.*\.(gif|png|jpg|ico))
|
||||
static_files: _build/html/_images/\1
|
||||
upload: _build/html/_images/(.*\.(gif|png|jpg|ico))
|
||||
|
||||
# redirect en/latest traffic
|
||||
- url: /en/latest/(.*\.html)
|
||||
script: simpegdocs.app
|
||||
|
||||
# raw html
|
||||
- url: /(.*\.html)
|
||||
mime_type: text/html
|
||||
static_files: _build/html/\1
|
||||
upload: _build/html/(.*\.html)
|
||||
|
||||
# serve index files
|
||||
- url: /(.+)/
|
||||
static_files: _build/html/\1/index.html
|
||||
upload: _build/html/(.+)/index.html
|
||||
|
||||
- url: /(.+)
|
||||
static_files: _build/html/\1/index.html
|
||||
upload: _build/html/(.+)/index.html
|
||||
|
||||
- url: /
|
||||
static_files: _build/html/index.html
|
||||
upload: _build/html/index.html
|
||||
|
||||
- url: .*
|
||||
script: simpegdocs.app
|
||||
|
||||
# Recommended file skipping declaration from the GAE tutorials
|
||||
skip_files:
|
||||
- ^(.*/)?app\.yaml
|
||||
- ^(.*/)?app\.yml
|
||||
- ^(.*/)?#.*#
|
||||
- ^(.*/)?.*~
|
||||
- ^(.*/)?.*\.py[co]
|
||||
- ^(.*/)?.*/RCS/.*
|
||||
- ^(.*/)?\..*
|
||||
- ^(.*/)?tests$
|
||||
- ^(.*/)?test$
|
||||
- ^test/(.*/)?
|
||||
- ^COPYING.LESSER
|
||||
- ^README\..*
|
||||
- \.gitignore
|
||||
- ^\.git/.*
|
||||
- \.*\.lint$
|
||||
- ^(.*/)?.*\.doctree$
|
||||
|
||||
libraries:
|
||||
- name: webapp2
|
||||
version: "2.5.2"
|
||||
- name: PIL
|
||||
version: "1.1.7"
|
||||
- name: numpy
|
||||
version: "latest"
|
||||
- name: jinja2
|
||||
version: "latest"
|
||||
+6
-45
@@ -28,7 +28,7 @@ sys.path.append('../')
|
||||
|
||||
# Add any Sphinx extension module names here, as strings. They can be extensions
|
||||
# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
|
||||
extensions = ['sphinx.ext.todo', 'sphinx.ext.mathjax', 'sphinx.ext.viewcode', 'sphinx.ext.autodoc', 'sphinx.ext.intersphinx', 'matplotlib.sphinxext.plot_directive']
|
||||
extensions = ['sphinx.ext.todo', 'sphinx.ext.mathjax', 'sphinx.ext.viewcode', 'sphinx.ext.autodoc', 'matplotlib.sphinxext.plot_directive']
|
||||
|
||||
# Add any paths that contain templates here, relative to this directory.
|
||||
templates_path = ['_templates']
|
||||
@@ -44,16 +44,16 @@ master_doc = 'index'
|
||||
|
||||
# General information about the project.
|
||||
project = u'SimPEG'
|
||||
copyright = u'2013 - 2016, SimPEG Developers'
|
||||
copyright = u'2013, SimPEG Developers'
|
||||
|
||||
# The version info for the project you're documenting, acts as replacement for
|
||||
# |version| and |release|, also used in various other places throughout the
|
||||
# built documents.
|
||||
#
|
||||
# The short X.Y version.
|
||||
version = '0.1.12'
|
||||
version = '0.1.10'
|
||||
# The full version, including alpha/beta/rc tags.
|
||||
release = '0.1.12'
|
||||
release = '0.1.10'
|
||||
|
||||
# The language for content autogenerated by Sphinx. Refer to documentation
|
||||
# for a list of supported languages.
|
||||
@@ -124,12 +124,12 @@ except Exception, e:
|
||||
# The name of an image file (within the static path) to use as favicon of the
|
||||
# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32
|
||||
# pixels large.
|
||||
html_favicon = './images/logo-block.ico'
|
||||
#html_favicon = None
|
||||
|
||||
# Add any paths that contain custom static files (such as style sheets) here,
|
||||
# relative to this directory. They are copied after the builtin static files,
|
||||
# so a file named "default.css" will overwrite the builtin "default.css".
|
||||
html_static_path = []
|
||||
html_static_path = ['_static']
|
||||
|
||||
# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
|
||||
# using the given strftime format.
|
||||
@@ -229,12 +229,6 @@ man_pages = [
|
||||
# If true, show URL addresses after external links.
|
||||
#man_show_urls = False
|
||||
|
||||
# Intersphinx
|
||||
intersphinx_mapping = {'python': ('http://docs.python.org/2', None),
|
||||
'numpy': ('http://docs.scipy.org/doc/numpy/', None),
|
||||
'scipy': ('http://docs.scipy.org/doc/scipy/reference/', None),
|
||||
'matplotlib': ('http://matplotlib.sourceforge.net/', None)}
|
||||
|
||||
|
||||
# -- Options for Texinfo output ------------------------------------------------
|
||||
|
||||
@@ -257,36 +251,3 @@ texinfo_documents = [
|
||||
#texinfo_show_urls = 'footnote'
|
||||
|
||||
autodoc_member_order = 'bysource'
|
||||
|
||||
def supress_nonlocal_image_warn():
|
||||
import sphinx.environment
|
||||
sphinx.environment.BuildEnvironment.warn_node = _supress_nonlocal_image_warn
|
||||
|
||||
def _supress_nonlocal_image_warn(self, msg, node):
|
||||
from docutils.utils import get_source_line
|
||||
|
||||
if not msg.startswith('nonlocal image URI found:'):
|
||||
self._warnfunc(msg, '%s:%s' % get_source_line(node))
|
||||
|
||||
supress_nonlocal_image_warn()
|
||||
|
||||
|
||||
nitpick_ignore = [
|
||||
('py:class', 'IdentityMap'),
|
||||
('py:class', 'BaseSurvey'),
|
||||
('py:class', 'BaseSrc'),
|
||||
('py:class', 'BaseRx'),
|
||||
('py:class', 'Survey'),
|
||||
('py:class', 'FieldsFDEM'),
|
||||
('py:class', 'Fields3D_e'),
|
||||
('py:class', 'Fields3D_b'),
|
||||
('py:class', 'Fields3D_j'),
|
||||
('py:class', 'Fields3D_h'),
|
||||
('py:class', 'SurveyTDEM'),
|
||||
('py:class', 'SrcTDEM'),
|
||||
('py:class', 'EMPropMap'),
|
||||
('py:class', 'Data'),
|
||||
('py:class', 'SurveyDC'),
|
||||
('py:class', 'BaseMTFields'),
|
||||
('py:class', 'SolverLU'),
|
||||
]
|
||||
|
||||
@@ -1,27 +0,0 @@
|
||||
.. _api_FiniteVolume:
|
||||
|
||||
Finite Volume
|
||||
*************
|
||||
|
||||
Any numerical implementation requires the discretization of continuous
|
||||
functions into discrete approximations. These approximations are typically
|
||||
organized in a mesh, which defines boundaries, locations, and connectivity. Of
|
||||
specific interest to geophysical simulations, we require that averaging,
|
||||
interpolation and differential operators be defined for any mesh. In SimPEG,
|
||||
we have implemented a staggered mimetic finite volume approach (`Hyman and
|
||||
Shashkov, 1999 <http://math.lanl.gov/~mac/papers/numerics/HS99B.pdf>`_). This
|
||||
approach requires the definitions of variables at either cell-centers, nodes,
|
||||
faces, or edges as seen in the figure below.
|
||||
|
||||
.. image:: ../../images/finitevolrealestate.png
|
||||
:width: 400 px
|
||||
:alt: FiniteVolume
|
||||
:align: center
|
||||
|
||||
|
||||
.. toctree::
|
||||
:maxdepth: 2
|
||||
|
||||
api_Mesh
|
||||
api_DiffOps
|
||||
api_InnerProducts
|
||||
@@ -1,68 +0,0 @@
|
||||
.. _api_MeshCode:
|
||||
|
||||
Tensor Mesh
|
||||
===========
|
||||
|
||||
.. autoclass:: SimPEG.Mesh.TensorMesh
|
||||
:members:
|
||||
:undoc-members:
|
||||
:show-inheritance:
|
||||
|
||||
Cylindrical Mesh
|
||||
================
|
||||
|
||||
.. autoclass:: SimPEG.Mesh.CylMesh
|
||||
:members:
|
||||
:undoc-members:
|
||||
:show-inheritance:
|
||||
|
||||
Tree Mesh
|
||||
=========
|
||||
|
||||
.. autoclass:: SimPEG.Mesh.TreeMesh
|
||||
:members:
|
||||
:undoc-members:
|
||||
:show-inheritance:
|
||||
|
||||
Curvilinear Mesh
|
||||
================
|
||||
|
||||
.. autoclass:: SimPEG.Mesh.CurvilinearMesh
|
||||
:members:
|
||||
:undoc-members:
|
||||
:show-inheritance:
|
||||
|
||||
|
||||
Base Rectangular Mesh
|
||||
=====================
|
||||
|
||||
.. autoclass:: SimPEG.Mesh.BaseMesh.BaseRectangularMesh
|
||||
:members:
|
||||
:undoc-members:
|
||||
:show-inheritance:
|
||||
|
||||
Base Tensor Mesh
|
||||
================
|
||||
|
||||
.. autoclass:: SimPEG.Mesh.TensorMesh.BaseTensorMesh
|
||||
:members:
|
||||
:undoc-members:
|
||||
:show-inheritance:
|
||||
|
||||
|
||||
Mesh IO
|
||||
=======
|
||||
|
||||
.. automodule:: SimPEG.Mesh.MeshIO
|
||||
:members:
|
||||
:undoc-members:
|
||||
:show-inheritance:
|
||||
|
||||
|
||||
Mesh Viewing
|
||||
============
|
||||
|
||||
.. automodule:: SimPEG.Mesh.View
|
||||
:members:
|
||||
:undoc-members:
|
||||
:show-inheritance:
|
||||
@@ -1,29 +0,0 @@
|
||||
SimPEG PropMaps
|
||||
***************
|
||||
|
||||
The API
|
||||
=======
|
||||
|
||||
Property
|
||||
--------
|
||||
|
||||
.. autoclass:: SimPEG.PropMaps.Property
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
PropMap
|
||||
-------
|
||||
|
||||
.. autoclass:: SimPEG.PropMaps.PropMap
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
PropModel
|
||||
---------
|
||||
|
||||
.. autoclass:: SimPEG.PropMaps.PropModel
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
@@ -1,33 +0,0 @@
|
||||
Overview of Electromagnetics in SimPEG
|
||||
**************************************
|
||||
|
||||
|
||||
The API
|
||||
=======
|
||||
|
||||
Physical Properties
|
||||
-------------------
|
||||
|
||||
.. autoclass:: SimPEG.EM.Base.EMPropMap
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
Problem
|
||||
-------
|
||||
|
||||
.. autoclass:: SimPEG.EM.Base.BaseEMProblem
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
Survey
|
||||
------
|
||||
|
||||
.. autoclass:: SimPEG.EM.Base.BaseEMSurvey
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
|
||||
@@ -1,48 +0,0 @@
|
||||
.. _examples_Maps_ComboMaps:
|
||||
|
||||
.. --------------------------------- ..
|
||||
.. ..
|
||||
.. THIS FILE IS AUTO GENEREATED ..
|
||||
.. ..
|
||||
.. SimPEG/Examples/__init__.py ..
|
||||
.. ..
|
||||
.. --------------------------------- ..
|
||||
|
||||
|
||||
|
||||
Maps: ComboMaps
|
||||
===============
|
||||
|
||||
We will use an example where we want a 1D layered earth as
|
||||
our model, but we want to map this to a 2D discretization to do our forward
|
||||
modeling. We will also assume that we are working in log conductivity still,
|
||||
so after the transformation we want to map to conductivity space.
|
||||
To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.SurjectVertical1D`),
|
||||
which does the first part of what we just described. The second part will be
|
||||
done by the :class:`SimPEG.Maps.ExpMap` described above.
|
||||
|
||||
.. code-block:: python
|
||||
:linenos:
|
||||
|
||||
M = Mesh.TensorMesh([7,5])
|
||||
v1dMap = Maps.SurjectVertical1D(M)
|
||||
expMap = Maps.ExpMap(M)
|
||||
myMap = expMap * v1dMap
|
||||
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
|
||||
sig = myMap * m
|
||||
|
||||
If you noticed, it was pretty easy to combine maps. What is even cooler is
|
||||
that the derivatives also are made for you (if everything goes right).
|
||||
Just to be sure that the derivative is correct, you should always run the test
|
||||
on the mapping that you create.
|
||||
|
||||
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Maps_ComboMaps.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/Maps_ComboMaps.py
|
||||
:language: python
|
||||
:linenos:
|
||||
@@ -1,25 +0,0 @@
|
||||
.. _examples_Mesh_Basic_ForwardDC:
|
||||
|
||||
.. --------------------------------- ..
|
||||
.. ..
|
||||
.. THIS FILE IS AUTO GENEREATED ..
|
||||
.. ..
|
||||
.. SimPEG/Examples/__init__.py ..
|
||||
.. ..
|
||||
.. --------------------------------- ..
|
||||
|
||||
|
||||
Mesh: Basic Forward 2D DC Resistivity
|
||||
=====================================
|
||||
|
||||
2D DC forward modeling example with Tensor and Curvilinear Meshes
|
||||
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Mesh_Basic_ForwardDC.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/Mesh_Basic_ForwardDC.py
|
||||
:language: python
|
||||
:linenos:
|
||||
@@ -1,14 +0,0 @@
|
||||
Induced Polarization
|
||||
********************
|
||||
|
||||
Todo: docs for IP!
|
||||
|
||||
|
||||
API for IP codes
|
||||
================
|
||||
|
||||
.. automodule:: SimPEG.DCIP.BaseIP
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
:inherited-members:
|
||||
Binary file not shown.
@@ -9,28 +9,17 @@
|
||||
Frequency Domain Electromagnetics
|
||||
*********************************
|
||||
|
||||
Electromagnetic (EM) geophysical methods are used in a variety of applications
|
||||
from resource exploration, including for hydrocarbons and minerals, to
|
||||
environmental applications, such as groundwater monitoring. The primary
|
||||
physical property of interest in EM is electrical conductivity, which
|
||||
describes the ease with which electric current flows through a material.
|
||||
Electromagnetic (EM) geophysical methods are used in a variety of applications from resource exploration, including for hydrocarbons and minerals, to environmental applications, such as groundwater monitoring. The primary physical property of interest in EM is electrical conductivity, which describes the ease with which electric current flows through a material.
|
||||
|
||||
|
||||
Background
|
||||
==========
|
||||
|
||||
Electromagnetic phenomena are governed by Maxwell's equations. They describe
|
||||
the behavior of EM fields and fluxes. Electromagnetic theory for geophysical
|
||||
applications by Ward and Hohmann (1988) is a highly recommended resource on
|
||||
this topic.
|
||||
Electromagnetic phenomena are governed by Maxwell's equations. They describe the behavior of EM fields and fluxes. Electromagnetic theory for geophysical applications by Ward and Hohmann (1988) is a highly recommended resource on this topic.
|
||||
|
||||
Fourier Transform Convention
|
||||
----------------------------
|
||||
|
||||
In order to examine Maxwell's equations in the frequency domain, we must first
|
||||
define our choice of harmonic time-dependence by choosing a Fourier transform
|
||||
convention. We use the :math:`e^{i \omega t}` convention, so we define our
|
||||
Fourier Transform pair as
|
||||
In order to examine Maxwell's equations in the frequency domain, we must first define our choice of harmonic time-dependence by choosing a Fourier transform convention. We use the :math:`e^{i \omega t}` convention, so we define our Fourier Transform pair as
|
||||
|
||||
.. math ::
|
||||
F(\omega) = \int_{-\infty}^{\infty} f(t) e^{- i \omega t} dt \\
|
||||
@@ -42,7 +31,6 @@ where :math:`\omega` is angular frequency, :math:`t` is time, :math:`F(\omega)`
|
||||
|
||||
Maxwell's Equations
|
||||
===================
|
||||
|
||||
In the frequency domain, Maxwell's equations are given by
|
||||
|
||||
.. math ::
|
||||
@@ -116,20 +104,19 @@ The H-J formulation is in terms of the current density and the magnetic field:
|
||||
|
||||
Discretizing
|
||||
------------
|
||||
|
||||
For both formulations, we use a finite volume discretization
|
||||
and discretize fields on cell edges, fluxes on cell faces and
|
||||
physical properties in cell centers. This is particularly
|
||||
important when using symmetry to reduce the dimensionality of a problem
|
||||
(for instance on a 2D CylMesh, there are :math:`r`, :math:`z` faces and :math:`\theta` edges)
|
||||
|
||||
.. figure:: ../../images/finitevolrealestate.png
|
||||
.. figure:: ../images/finitevolrealestate.png
|
||||
:align: center
|
||||
:scale: 60 %
|
||||
|
||||
For the two formulations, the discretization of the physical properties, fields and fluxes are summarized below.
|
||||
|
||||
.. figure:: ../../images/ebjhdiscretizations.png
|
||||
.. figure:: ../images/ebjhdiscretizations.png
|
||||
:align: center
|
||||
:scale: 60 %
|
||||
|
||||
@@ -163,7 +150,7 @@ API
|
||||
FDEM Problem
|
||||
------------
|
||||
|
||||
.. automodule:: SimPEG.EM.FDEM.ProblemFDEM
|
||||
.. automodule:: SimPEG.EM.FDEM.FDEM
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
@@ -182,11 +169,6 @@ FDEM Survey
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
.. automodule:: SimPEG.EM.FDEM.RxFDEM
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
|
||||
FDEM Fields
|
||||
-----------
|
||||
|
||||
@@ -359,7 +359,7 @@ TDEM - B formulation
|
||||
Field Storage
|
||||
=============
|
||||
|
||||
.. autoclass:: SimPEG.EM.TDEM.BaseTDEM.FieldsTDEM
|
||||
.. autoclass:: SimPEG.EM.TDEM.SurveyTDEM.FieldsTDEM
|
||||
:show-inheritance:
|
||||
:members:
|
||||
:undoc-members:
|
||||
@@ -3,23 +3,22 @@ Electromagnetics
|
||||
================
|
||||
|
||||
`SimPEG.EM` uses SimPEG as the framework for the forward and inverse
|
||||
electromagnetics geophysical problems.
|
||||
electromagnetics geophysical problems.
|
||||
|
||||
To solve for predicted data, we follow the framework shown below. The model is
|
||||
what we invert for. This is mapped to a physical property on the simulation
|
||||
mesh. A source which is used to excite the system is specified. Having a model
|
||||
and a source, we can solve Maxwell's equations for fields. We sample these
|
||||
fields with recievers to give us predicted data.
|
||||
fields with recievers to give us predicted data.
|
||||
|
||||
|
||||
.. image:: ../../images/simpegEM_noMath.png
|
||||
.. image:: ../images/simpegEM_noMath.png
|
||||
:scale: 50%
|
||||
|
||||
|
||||
.. toctree::
|
||||
:maxdepth: 2
|
||||
|
||||
api_basic
|
||||
api_FDEM
|
||||
api_TDEM
|
||||
api_Utils
|
||||
@@ -16,6 +16,6 @@ DC Analytic Dipole
|
||||
from SimPEG import Examples
|
||||
Examples.DC_Analytic_Dipole.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/DC_Analytic_Dipole.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/DC_Analytic_Dipole.py
|
||||
:language: python
|
||||
:linenos:
|
||||
+2
-1
@@ -22,6 +22,7 @@ radi = Radius of spheres [r1,r2]
|
||||
param = Conductivity of background and two spheres [m0,m1,m2]
|
||||
surveyType = survey type 'pole-dipole' or 'dipole-dipole'
|
||||
unitType = Data type "appResistivity" | "appConductivity" | "volt"
|
||||
|
||||
Created by @fourndo
|
||||
|
||||
|
||||
@@ -31,6 +32,6 @@ Created by @fourndo
|
||||
from SimPEG import Examples
|
||||
Examples.DC_Forward_PseudoSection.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/DC_Forward_PseudoSection.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/DC_Forward_PseudoSection.py
|
||||
:language: python
|
||||
:linenos:
|
||||
+1
-1
@@ -21,6 +21,6 @@ Here we will create and run a FDEM 1D inversion.
|
||||
from SimPEG import Examples
|
||||
Examples.EM_FDEM_1D_Inversion.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/EM_FDEM_1D_Inversion.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/EM_FDEM_1D_Inversion.py
|
||||
:language: python
|
||||
:linenos:
|
||||
+1
-1
@@ -21,6 +21,6 @@ Here we plot the magnetic flux density from a harmonic dipole in a wholespace.
|
||||
from SimPEG import Examples
|
||||
Examples.EM_FDEM_Analytic_MagDipoleWholespace.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/EM_FDEM_Analytic_MagDipoleWholespace.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/EM_FDEM_Analytic_MagDipoleWholespace.py
|
||||
:language: python
|
||||
:linenos:
|
||||
+2
-5
@@ -17,13 +17,10 @@ current inside a steel-cased. The model is based on the Schenkel and
|
||||
Morrison Casing Model, and the results are used in a 2016 SEG abstract by
|
||||
Yang et al.
|
||||
|
||||
.. code-block:: text
|
||||
|
||||
Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
|
||||
- Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
|
||||
|
||||
|
||||
The model consists of:
|
||||
|
||||
- Air: Conductivity 1e-8 S/m, above z = 0
|
||||
- Background: conductivity 1e-2 S/m, below z = 0
|
||||
- Casing: conductivity 1e6 S/m
|
||||
@@ -56,6 +53,6 @@ citation would be much appreciated!
|
||||
from SimPEG import Examples
|
||||
Examples.EM_Schenkel_Morrison_Casing.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/EM_Schenkel_Morrison_Casing.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/EM_Schenkel_Morrison_Casing.py
|
||||
:language: python
|
||||
:linenos:
|
||||
+1
-1
@@ -21,6 +21,6 @@ Here we will create and run a TDEM 1D inversion.
|
||||
from SimPEG import Examples
|
||||
Examples.EM_TDEM_1D_Inversion.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/EM_TDEM_1D_Inversion.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/EM_TDEM_1D_Inversion.py
|
||||
:language: python
|
||||
:linenos:
|
||||
+1
-1
@@ -47,6 +47,6 @@ Here we reproduce the results from Celia1990_ demonstrating the head-based formu
|
||||
from SimPEG import Examples
|
||||
Examples.FLOW_Richards_1D_Celia1990.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/FLOW_Richards_1D_Celia1990.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/FLOW_Richards_1D_Celia1990.py
|
||||
:language: python
|
||||
:linenos:
|
||||
+5
-11
@@ -1,4 +1,4 @@
|
||||
.. _examples_Maps_Mesh2Mesh:
|
||||
.. _examples_Forward_BasicDirectCurrent:
|
||||
|
||||
.. --------------------------------- ..
|
||||
.. ..
|
||||
@@ -8,20 +8,14 @@
|
||||
.. ..
|
||||
.. --------------------------------- ..
|
||||
|
||||
|
||||
|
||||
Maps: Mesh2Mesh
|
||||
===============
|
||||
|
||||
This mapping allows you to go from one mesh to another.
|
||||
|
||||
|
||||
Forward BasicDirectCurrent
|
||||
==========================
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Maps_Mesh2Mesh.run()
|
||||
Examples.Forward_BasicDirectCurrent.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/Maps_Mesh2Mesh.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/Forward_BasicDirectCurrent.py
|
||||
:language: python
|
||||
:linenos:
|
||||
@@ -21,6 +21,6 @@ Here we go over the basics of creating a linear problem and inversion.
|
||||
from SimPEG import Examples
|
||||
Examples.Inversion_IRLS.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/Inversion_IRLS.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/Inversion_IRLS.py
|
||||
:language: python
|
||||
:linenos:
|
||||
@@ -21,6 +21,6 @@ Here we go over the basics of creating a linear problem and inversion.
|
||||
from SimPEG import Examples
|
||||
Examples.Inversion_Linear.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/Inversion_Linear.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/Inversion_Linear.py
|
||||
:language: python
|
||||
:linenos:
|
||||
+2
-2
@@ -10,7 +10,7 @@
|
||||
|
||||
|
||||
MT: 1D: Inversion
|
||||
=================
|
||||
=======================
|
||||
|
||||
Forward model 1D MT data.
|
||||
Setup and run a MT 1D inversion.
|
||||
@@ -22,6 +22,6 @@ Setup and run a MT 1D inversion.
|
||||
from SimPEG import Examples
|
||||
Examples.MT_1D_ForwardAndInversion.run()
|
||||
|
||||
.. literalinclude:: ../../../SimPEG/Examples/MT_1D_ForwardAndInversion.py
|
||||
.. literalinclude:: ../../SimPEG/Examples/MT_1D_ForwardAndInversion.py
|
||||
:language: python
|
||||
:linenos:
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user