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Author SHA1 Message Date
Lindsey Heagy 422ec20783 set kwargs through **kwargs 2016-04-24 13:14:05 -07:00
Lindsey Heagy d9048bc3d0 allow primary fields to be inputs for raw vec sources 2016-04-24 10:23:19 -07:00
174 changed files with 1698 additions and 8813 deletions
+1 -1
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@@ -1,4 +1,4 @@
[bumpversion]
current_version = 0.1.12
current_version = 0.1.10
files = setup.py SimPEG/__init__.py docs/conf.py
-2
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@@ -39,5 +39,3 @@ nosetests.xml
*.sublime-workspace
docs/_build/
Makefile
docs/warnings.txt
.DS_Store
+4 -26
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@@ -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
@@ -53,26 +46,11 @@ install:
# Run test
script:
# test docs
- nosetests $TEST_DIR --with-cov --cov SimPEG --cov-config .coveragerc -v -s
# Calculate coverage
after_success:
- bash <(curl -s https://codecov.io/bash)
- if [ "$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
- coveralls --config_file .coveragerc
notifications:
email:
+2 -11
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@@ -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
======
@@ -15,7 +15,7 @@ SimPEG
.. image:: https://img.shields.io/badge/license-MIT-blue.svg
:target: https://github.com/simpeg/simpeg/blob/master/LICENSE
:alt: MIT license
:alt: BSD 3 clause license.
.. image:: https://api.travis-ci.org/simpeg/simpeg.svg?branch=master
:target: https://travis-ci.org/simpeg/simpeg
@@ -25,15 +25,6 @@ SimPEG
:target: https://coveralls.io/r/simpeg/simpeg?branch=master
:alt: Coverage status
.. image:: http://img.shields.io/badge/GITTER-JOIN_CHAT-brightgreen.svg?style=flat-square
:alt: gitter chat room at https://gitter.im/simpeg/simpeg
:target: https://gitter.im/simpeg/simpeg
.. image:: https://codecov.io/gh/simpeg/simpeg/branch/master/graph/badge.svg
:target: https://codecov.io/gh/simpeg/simpeg
:alt: Coverage status
Simulation and Parameter Estimation in Geophysics - A python package for simulation and gradient based parameter estimation in the context of geophysical applications.
The vision is to create a package for finite volume simulation with applications to geophysical imaging and subsurface flow. To enable the understanding of the many different components, this package has the following features:
+2 -2
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@@ -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::
+1 -1
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@@ -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::
+215 -324
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@@ -1,16 +1,12 @@
from SimPEG import np, Utils
from SimPEG import np
import BaseDC as DC
import BaseDC as IP
import warnings
def getActiveindfromTopo(mesh, topo):
# def genActiveindfromTopo(mesh, topo):
"""
Get active indices from topography
"""
warnings.warn(
"`getActiveindfromTopo` is deprecated and will be removed in future versions. Use `SimPEG.Utils.surface2ind_topo` instead",
FutureWarning)
from scipy.interpolate import NearestNDInterpolator
if mesh.dim==3:
nCxy = mesh.nCx*mesh.nCy
@@ -32,9 +28,6 @@ def gettopoCC(mesh, airind):
"""
Get topography from active indices of mesh.
"""
warnings.warn(
"`gettopoCC` is deprecated and will be removed in future versions. Use `SimPEG.Utils.surface2ind_topo` instead",
FutureWarning)
mesh2D = Mesh.TensorMesh([mesh.hx, mesh.hy], mesh.x0[:2])
zc = mesh.gridCC[:,2]
AIRIND = airind.reshape((mesh.vnC[0]*mesh.vnC[1],mesh.vnC[2]), order='F')
@@ -125,27 +118,34 @@ def readUBC_DC3Dobstopo(filename,mesh,topo,probType="CC"):
def readUBC_DC2DModel(fileName):
"""
Read UBC GIF 2DTensor model and generate 2D Tensor model in simpeg
Read UBC GIF 2DTensor model and generate 2D Tensor model in simpeg
:param string fileName: path to the UBC GIF 2D model file
:rtype: TensorMesh
:return: SimPEG TensorMesh 2D object
Input:
:param fileName, path to the UBC GIF 2D model file
Output:
:param SimPEG TensorMesh 2D object
:return
Created on Thu Nov 12 13:14:10 2015
@author: dominiquef
"""
from SimPEG import np, mkvc
# Open fileand skip header... assume that we know the mesh already
obsfile = np.genfromtxt(fileName, delimiter=' \n', dtype=np.str, comments='!')
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
dim = np.array(obsfile[0].split(), dtype=float)
dim = np.array(obsfile[0].split(),dtype=float)
temp = np.array(obsfile[1].split(), dtype=float)
temp = np.array(obsfile[1].split(),dtype=float)
if len(temp) > 1:
model = np.zeros(dim)
for ii in range(len(obsfile)-1):
mm = np.array(obsfile[ii+1].split(), dtype=float)
mm = np.array(obsfile[ii+1].split(),dtype=float)
model[:,ii] = mm
model = model[:,::-1]
@@ -153,10 +153,10 @@ def readUBC_DC2DModel(fileName):
else:
if len(obsfile[1:])==1:
mm = np.array(obsfile[1:].split(), dtype=float)
mm = np.array(obsfile[1:].split(),dtype=float)
else:
mm = np.array(obsfile[1:], dtype=float)
mm = np.array(obsfile[1:],dtype=float)
# Permute the second dimension to flip the order
model = mm.reshape(dim[1],dim[0])
@@ -169,25 +169,32 @@ def readUBC_DC2DModel(fileName):
return model
def plot_pseudoSection(DCsurvey, axs, surveyType='dipole-dipole', unitType='volt', clim=None, cblabel=True, axlabel = True, colorbar = True, contour = None):
def plot_pseudoSection(DCsurvey, axs, stype):
"""
Read list of 2D tx-rx location and plot a speudo-section of apparent
resistivity.
Read list of 2D tx-rx location and plot a speudo-section of apparent
resistivity.
Assumes flat topo for now...
Assumes flat topo for now...
:param SurveyDC DCsurvey:
:param string surveyType: Either 'pole-dipole' | 'dipole-dipole'
:param string unitType: Either 'appResistivity' | 'appConductivity' | 'volt'
:rtype: matplotlib.plt
:return: figure scatter plot overlayed on image
Input:
:param d2D, z0
:switch stype -> Either 'pdp' (pole-dipole) | 'dpdp' (dipole-dipole)
Output:
:figure scatter plot overlayed on image
Edited Feb 17th, 2016
@author: dominiquef
"""
from SimPEG import np
from scipy.interpolate import griddata
import pylab as plt
# Set depth to 0 for now
z0 = 0.
# Pre-allocate
midx = []
midz = []
@@ -214,117 +221,69 @@ def plot_pseudoSection(DCsurvey, axs, surveyType='dipole-dipole', unitType='volt
Cmid = (Tx[0][0] + Tx[1][0])/2
Pmid = (Rx[0][:,0] + Rx[1][:,0])/2
# Change output for unitType
if unitType == 'volt':
# Compute pant leg of apparent rho
if stype == 'pdp':
leg = data * 2*np.pi * MA * ( MA + MN ) / MN
rho = np.hstack([rho,data])
leg = np.log10(abs(1/leg))
else:
elif stype == 'dpdp':
leg = data * 2*np.pi / ( 1/MA - 1/MB - 1/NB + 1/NA )
# Compute pant leg of apparent rho
if surveyType == 'pole-dipole':
leg = data * 2*np.pi * MA * ( MA + MN ) / MN
elif surveyType == 'dipole-dipole':
leg = data * 2*np.pi / ( 1/MA - 1/MB - 1/NB + 1/NA )
else:
print """unitType must be 'pole-dipole' | 'dipole-dipole' """
break
if unitType == 'appConductivity':
leg = np.log10(abs(1./leg))
rho = np.hstack([rho,leg])
elif unitType == 'appResistivity':
leg = np.log10(abs(leg))
rho = np.hstack([rho,leg])
else:
print """unitType must be 'appResistivity' | 'appConductivity' | 'volt' """
break
midx = np.hstack([midx, ( Cmid + Pmid )/2 ])
midz = np.hstack([midz, -np.abs(Cmid-Pmid)/2 + (Tx[0][2] + Tx[1][2])/2 ])
midz = np.hstack([midz, -np.abs(Cmid-Pmid)/2 + z0 ])
rho = np.hstack([rho,leg])
ax = axs
# Grid points
grid_x, grid_z = np.mgrid[np.min(midx):np.max(midx), np.min(midz):np.max(midz)]
grid_rho = griddata(np.c_[midx,midz], rho.T, (grid_x, grid_z), method='linear')
# Scale the color scheme
if clim == None:
vmin, vmax = rho.min(), rho.max()
else:
vmin, vmax = clim[0], clim[1]
# Plot data
grid_rho = np.ma.masked_where(np.isnan(grid_rho), grid_rho)
plt.imshow(grid_rho.T, extent = (np.min(midx),np.max(midx),np.min(midz),np.max(midz)), origin='lower', alpha=0.8, vmin = np.min(rho), vmax = np.max(rho))
cbar = plt.colorbar(format = '%.2f',fraction=0.04,orientation="horizontal")
cmin,cmax = cbar.get_clim()
ticks = np.linspace(cmin,cmax,3)
cbar.set_ticks(ticks)
# Plot apparent resistivity
plt.scatter(midx,midz,s=50,c=rho.T)
ph = plt.pcolormesh(grid_x[:,0],grid_z[0,:],grid_rho.T, vmin = vmin, vmax = vmax)
plt.gca().tick_params(axis='both', which='major', labelsize=8)
if contour is not None:
plt.contour(grid_x,grid_z,grid_rho,levels = contour,colors = 'r', vmin = vmin, vmax = vmax)
# Add scatter points
axs.scatter(midx,midz,s=10,c=rho.T, vmin = vmin, vmax = vmax)
if colorbar:
if unitType == 'volt':
cbar = plt.colorbar(ph, ax = axs, format="%4.1f",fraction=0.04,orientation="horizontal")
else:
cbar = plt.colorbar(ph, ax = axs, format="$10^{%.1f}$",fraction=0.04,orientation="horizontal")
cmin,cmax = cbar.get_clim()
ticks = np.linspace(cmin,cmax,3)
cbar.set_ticks(ticks)
cbar.ax.tick_params(labelsize=10)
if unitType == 'appConductivity':
cbar.set_label("App.Cond",size=12)
elif unitType == 'appResistivity':
cbar.set_label("App.Res.",size=12)
elif unitType == 'volt':
cbar.set_label("Potential (V)",size=12)
if not axlabel:
axs.set_xticklabels([])
axs.set_yticklabels([])
ax.set_xticklabels([])
ax.set_ylabel('Z')
ax.yaxis.tick_right()
ax.yaxis.set_label_position('right')
plt.gca().set_aspect('equal', adjustable='box')
return ax
return ph
def gen_DCIPsurvey(endl, mesh, surveyType, AM_sep, MN_sep, nrx):
def gen_DCIPsurvey(endl, mesh, stype, a, b, n):
"""
Load in endpoints and survey specifications to generate Tx, Rx location
stations.
Load in endpoints and survey specifications to generate Tx, Rx location
stations.
Assumes flat topo for now...
Assumes flat topo for now...
:param numpy.array endl: input endpoints [[x1, y1] , [x2, y2]]
:param Mesh mesh: SimPEG mesh object
:param string surveyType: 'dipole-dipole' | 'pole-dipole' | 'gradient'
:param float AM_sep: transmitter (A) - receiver (M) seperation
:param float b: receiver dipole seperation
:param float nrx: pole seperation, number of rx dipoles per tx
Input:
:param endl -> input endpoints [x1, y1, z1, x2, y2, z2]
:object mesh -> SimPEG mesh object
:switch stype -> "dpdp" (dipole-dipole) | "pdp" (pole-dipole) | 'gradient'
: param a, n -> pole seperation, number of rx dipoles per tx
:rtype: DC.Survey, Src, Rx
:returns: DC survey, Source
Output:
:param Tx, Rx -> List objects for each tx location
Lines: P1x, P1y, P1z, P2x, P2y, P2z
!! Require clean up to deal with DCsurvey
Created on Wed December 9th, 2015
@author: dominiquef
!! Require clean up to deal with DCsurvey
"""
from SimPEG import np
@@ -340,17 +299,17 @@ def gen_DCIPsurvey(endl, mesh, surveyType, AM_sep, MN_sep, nrx):
dl_x = ( endl[1,0] - endl[0,0] ) / dl_len
dl_y = ( endl[1,1] - endl[0,1] ) / dl_len
nstn = np.floor( dl_len / AM_sep )
nstn = np.floor( dl_len / a )
# Compute discrete pole location along line
stn_x = endl[0,0] + np.array(range(int(nstn)))*dl_x*AM_sep
stn_y = endl[0,1] + np.array(range(int(nstn)))*dl_y*AM_sep
stn_x = endl[0,0] + np.array(range(int(nstn)))*dl_x*a
stn_y = endl[0,1] + np.array(range(int(nstn)))*dl_y*a
# Create line of P1 locations
M = np.c_[stn_x, stn_y, np.ones(nstn).T*mesh.vectorNz[-1]]
# Create line of P2 locations
N = np.c_[stn_x+AM_sep*dl_x, stn_y+AM_sep*dl_y, np.ones(nstn).T*mesh.vectorNz[-1]]
N = np.c_[stn_x+a*dl_x, stn_y+a*dl_y, np.ones(nstn).T*mesh.vectorNz[-1]]
## Build list of Tx-Rx locations depending on survey type
# Dipole-dipole: Moving tx with [a] spacing -> [AB a MN1 a MN2 ... a MNn]
@@ -360,14 +319,14 @@ def gen_DCIPsurvey(endl, mesh, surveyType, AM_sep, MN_sep, nrx):
SrcList = []
if surveyType != 'gradient':
if stype != 'gradient':
for ii in range(0, int(nstn)-1):
if surveyType == 'dipole-dipole':
if stype == 'dpdp':
tx = np.c_[M[ii,:],N[ii,:]]
elif surveyType == 'pole-dipole':
elif stype == 'pdp':
tx = np.c_[M[ii,:],M[ii,:]]
# Rx.append(np.c_[M[ii+1:indx,:],N[ii+1:indx,:]])
@@ -376,33 +335,43 @@ def gen_DCIPsurvey(endl, mesh, surveyType, AM_sep, MN_sep, nrx):
AB = xy_2_r(tx[0,1],endl[1,0],tx[1,1],endl[1,1])
# Number of receivers to fit
nstn = np.min([np.floor( (AB - MN_sep) / AM_sep ) , nrx])
nstn = np.min([np.floor( (AB - b) / a ) , n])
# Check if there is enough space, else break the loop
if nstn <= 0:
continue
# Compute discrete pole location along line
stn_x = N[ii,0] + dl_x*MN_sep + np.array(range(int(nstn)))*dl_x*AM_sep
stn_y = N[ii,1] + dl_y*MN_sep + np.array(range(int(nstn)))*dl_y*AM_sep
stn_x = N[ii,0] + dl_x*b + np.array(range(int(nstn)))*dl_x*a
stn_y = N[ii,1] + dl_y*b + np.array(range(int(nstn)))*dl_y*a
# Create receiver poles
# Create line of P1 locations
P1 = np.c_[stn_x, stn_y, np.ones(nstn).T*mesh.vectorNz[-1]]
# Create line of P2 locations
P2 = np.c_[stn_x+AM_sep*dl_x, stn_y+AM_sep*dl_y, np.ones(nstn).T*mesh.vectorNz[-1]]
P2 = np.c_[stn_x+a*dl_x, stn_y+a*dl_y, np.ones(nstn).T*mesh.vectorNz[-1]]
Rx.append(np.c_[P1,P2])
rxClass = DC.RxDipole(P1, P2)
Tx.append(tx)
if surveyType == 'dipole-dipole':
if stype == 'dpdp':
srcClass = DC.SrcDipole([rxClass], M[ii,:],N[ii,:])
elif surveyType == 'pole-dipole':
elif stype == 'pdp':
srcClass = DC.SrcDipole([rxClass], M[ii,:],M[ii,:])
SrcList.append(srcClass)
elif surveyType == 'gradient':
#==============================================================================
# elif re.match(stype,'dpdp'):
#
# for ii in range(0, int(nstn)-2):
#
# indx = np.min([ii+n+1,nstn])
# Tx.append(np.c_[M[ii,:],N[ii,:]])
# Rx.append(np.c_[M[ii+2:indx,:],N[ii+2:indx,:]])
#==============================================================================
elif stype == 'gradient':
# Gradient survey only requires Tx at end of line and creates a square
# grid of receivers at in the middle at a pre-set minimum distance
@@ -410,23 +379,23 @@ def gen_DCIPsurvey(endl, mesh, surveyType, AM_sep, MN_sep, nrx):
Tx.append(np.c_[M[0,:],N[-1,:]])
# Get the edge limit of survey area
min_x = endl[0,0] + dl_x * MN_sep
min_y = endl[0,1] + dl_y * MN_sep
min_x = endl[0,0] + dl_x * b
min_y = endl[0,1] + dl_y * b
max_x = endl[1,0] - dl_x * MN_sep
max_y = endl[1,1] - dl_y * MN_sep
max_x = endl[1,0] - dl_x * b
max_y = endl[1,1] - dl_y * b
box_l = np.sqrt( (min_x - max_x)**2 + (min_y - max_y)**2 )
box_w = box_l/2.
nstn = np.floor( box_l / AM_sep )
nstn = np.floor( box_l / a )
# Compute discrete pole location along line
stn_x = min_x + np.array(range(int(nstn)))*dl_x*AM_sep
stn_y = min_y + np.array(range(int(nstn)))*dl_y*AM_sep
stn_x = min_x + np.array(range(int(nstn)))*dl_x*a
stn_y = min_y + np.array(range(int(nstn)))*dl_y*a
# Define number of cross lines
nlin = int(np.floor( box_w / AM_sep ))
nlin = int(np.floor( box_w / a ))
lind = range(-nlin,nlin+1)
ngrad = nstn * len(lind)
@@ -435,12 +404,12 @@ def gen_DCIPsurvey(endl, mesh, surveyType, AM_sep, MN_sep, nrx):
for ii in range( len(lind) ):
# Move line in perpendicular direction by dipole spacing
lxx = stn_x - lind[ii]*AM_sep*dl_y
lyy = stn_y + lind[ii]*AM_sep*dl_x
lxx = stn_x - lind[ii]*a*dl_y
lyy = stn_y + lind[ii]*a*dl_x
M = np.c_[ lxx, lyy , np.ones(nstn).T*mesh.vectorNz[-1]]
N = np.c_[ lxx+AM_sep*dl_x, lyy+AM_sep*dl_y, np.ones(nstn).T*mesh.vectorNz[-1]]
N = np.c_[ lxx+a*dl_x, lyy+a*dl_y, np.ones(nstn).T*mesh.vectorNz[-1]]
rx[(ii*nstn):((ii+1)*nstn),:] = np.c_[M,N]
@@ -449,37 +418,37 @@ def gen_DCIPsurvey(endl, mesh, surveyType, AM_sep, MN_sep, nrx):
srcClass = DC.SrcDipole([rxClass], M[0,:], N[-1,:])
SrcList.append(srcClass)
else:
print """surveyType must be either 'pole-dipole', 'dipole-dipole' or 'gradient'. """
print """stype must be either 'pdp', 'dpdp' or 'gradient'. """
survey = DC.SurveyDC(SrcList)
return survey, Tx, Rx
def writeUBC_DCobs(fileName, DCsurvey, dim, surveyType, iptype = 0):
def writeUBC_DCobs(fileName, DCsurvey, dtype, stype):
"""
Write UBC GIF DCIP 2D or 3D observation file
:param string fileName: including path where the file is written out
:param Survey DCsurvey: DC survey class object
:param string dim: either '2D' | '3D'
:param string surveyType: either 'SURFACE' | 'GENERAL'
:rtype: file
:return: UBC2D-Data file
"""
Input:
:string fileName -> including path where the file is written out
:DCsurvey -> DC survey class object
:string dtype -> either '2D' | '3D'
:string stype -> either 'SURFACE' | 'GENERAL'
Output:
:param UBC2D-Data file
:return
Last edit: February 16th, 2016
@author: dominiquef
"""
from SimPEG import mkvc
assert (dim=='2D') | (dim=='3D'), "Data must be either '2D' | '3D'"
assert (surveyType=='SURFACE') | (surveyType=='GENERAL') | (surveyType=='SIMPLE'), "Data must be either 'SURFACE' | 'GENERAL' | 'SIMPLE'"
assert (dtype=='2D') | (dtype=='3D'), "Data must be either '2D' | '3D'"
assert (stype=='SURFACE') | (stype=='GENERAL') | (stype=='SIMPLE'), "Data must be either 'SURFACE' | 'GENERAL' | 'SIMPLE'"
fid = open(fileName,'w')
fid.write('! ' + surveyType + ' FORMAT\n')
if iptype!=0:
fid.write('IPTYPE=%i\n'%iptype)
else:
fid.write('! ' + stype + ' FORMAT\n')
fid.write('! ' + stype + ' FORMAT\n')
count = 0
@@ -494,10 +463,10 @@ def writeUBC_DCobs(fileName, DCsurvey, dim, surveyType, iptype = 0):
M = rx[0]
N = rx[1]
# Adapt source-receiver location for dim and surveyType
if dim=='2D':
# Adapt source-receiver location for dtype and stype
if dtype=='2D':
if surveyType == 'SIMPLE':
if stype == 'SIMPLE':
#fid.writelines("%e " % ii for ii in mkvc(tx[0,:]))
A = np.repeat(tx[0,0],M.shape[0],axis=0)
@@ -510,60 +479,58 @@ def writeUBC_DCobs(fileName, DCsurvey, dim, surveyType, iptype = 0):
else:
if surveyType == 'SURFACE':
if stype == 'SURFACE':
fid.writelines("%f " % ii for ii in mkvc(tx[0,:]))
fid.writelines("%e " % ii for ii in mkvc(tx[0,:]))
M = M[:,0]
N = N[:,0]
if surveyType == 'GENERAL':
# Flip sign for z-elevation to depth
tx[2::2,:] = -tx[2::2,:]
if stype == 'GENERAL':
fid.writelines("%e " % ii for ii in mkvc(tx[::2,:]))
M = M[:,0::2]
N = N[:,0::2]
# Flip sign for z-elevation to depth
M[:,1::2] = -M[:,1::2]
N[:,1::2] = -N[:,1::2]
fid.write('%i\n'% nD)
np.savetxt(fid, np.c_[ M, N , DCsurvey.dobs[count:count+nD], DCsurvey.std[count:count+nD] ], fmt='%f',delimiter=' ',newline='\n')
np.savetxt(fid, np.c_[ M, N , DCsurvey.dobs[count:count+nD], DCsurvey.std[count:count+nD] ], fmt='%e',delimiter=' ',newline='\n')
if dim=='3D':
if dtype=='3D':
if surveyType == 'SURFACE':
if stype == 'SURFACE':
fid.writelines("%e " % ii for ii in mkvc(tx[0:2,:]))
M = M[:,0:2]
N = N[:,0:2]
if surveyType == 'GENERAL':
if stype == 'GENERAL':
fid.writelines("%e " % ii for ii in mkvc(tx[0:3,:]))
fid.writelines("%e " % ii for ii in mkvc(tx))
fid.write('%i\n'% nD)
np.savetxt(fid, np.c_[ M, N , DCsurvey.dobs[count:count+nD], DCsurvey.std[count:count+nD] ], fmt='%e',delimiter=' ',newline='\n')
fid.write('\n')
count += nD
fid.close()
def convertObs_DC3D_to_2D(DCsurvey, lineID, flag='local'):
def convertObs_DC3D_to_2D(DCsurvey,lineID):
"""
Read DC survey and projects the coordinate system
according to the flag = 'Xloc' | 'Yloc' | 'local' (default)
In the 'local' system, station coordinates are referenced
to distance from the first srcLoc[0].loc[0]
Read DC survey and data and change
coordinate system to distance along line assuming
all data is acquired along line.
First transmitter pole is assumed to be at the origin
The Z value is preserved, but Y coordinates zeroed.
Assumes flat topo for now...
:param DC.Survey survey3D: 3D simpeg DC survey
:rtype: DC.Survey
:return: survey2D
Input:
:param Tx, Rx
Output:
:figure Tx2d, Rx2d
Edited Feb 17th, 2016
@author: dominiquef
"""
from SimPEG import np
@@ -603,39 +570,25 @@ def convertObs_DC3D_to_2D(DCsurvey, lineID, flag='local'):
Rx = DCsurvey.srcList[indx[ii]].rxList[0].locs
nrx = Rx[0].shape[0]
if flag == 'local':
# Find A electrode along line
vec, r = r_unit(x0,Tx[ii][0,0:2])
A = stn_id(vecTx,vec,r)
# Find A electrode along line
vec, r = r_unit(x0,Tx[ii][0,0:2])
A = stn_id(vecTx,vec,r)
# Find B electrode along line
vec, r = r_unit(x0,Tx[ii][1,0:2])
B = stn_id(vecTx,vec,r)
# Find B electrode along line
vec, r = r_unit(x0,Tx[ii][1,0:2])
B = stn_id(vecTx,vec,r)
M = np.zeros(nrx)
N = np.zeros(nrx)
for kk in range(nrx):
M = np.zeros(nrx)
N = np.zeros(nrx)
for kk in range(nrx):
# Find all M electrodes along line
vec, r = r_unit(x0,Rx[0][kk,0:2])
M[kk] = stn_id(vecTx,vec,r)
# Find all M electrodes along line
vec, r = r_unit(x0,Rx[0][kk,0:2])
M[kk] = stn_id(vecTx,vec,r)
# Find all N electrodes along line
vec, r = r_unit(x0,Rx[1][kk,0:2])
N[kk] = stn_id(vecTx,vec,r)
elif flag == 'Yloc':
""" Flip the XY axis locs"""
A = Tx[ii][0,1]
B = Tx[ii][1,1]
M = Rx[0][:,1]
N = Rx[1][:,1]
elif flag == 'Xloc':
""" Copy the rx-tx locs"""
A = Tx[ii][0,0]
B = Tx[ii][1,0]
M = Rx[0][:,0]
N = Rx[1][:,0]
# Find all N electrodes along line
vec, r = r_unit(x0,Rx[1][kk,0:2])
N[kk] = stn_id(vecTx,vec,r)
Rx = DC.RxDipole(np.c_[M,np.zeros(nrx),Rx[0][:,2]],np.c_[N,np.zeros(nrx),Rx[1][:,2]])
@@ -649,53 +602,50 @@ def convertObs_DC3D_to_2D(DCsurvey, lineID, flag='local'):
return DCsurvey2D
def readUBC_DC3Dobs(fileName, rtype = 'DC'):
def readUBC_DC3Dobs(fileName):
"""
Read UBC GIF IP 3D observation file and generate survey
Read UBC GIF DCIP 3D observation file and generate arrays for tx-rx location
:param string fileName:, path to the UBC GIF 3D obs file
:rtype: Survey
:return: DCIPsurvey
Input:
:param fileName, path to the UBC GIF 3D obs file
Output:
:param rx, tx, d, wd
:return
Created on Mon December 7th, 2015
@author: dominiquef
"""
zflag = True # Flag for z value provided
# Load file
if rtype == 'IP':
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='IPTYPE')
elif rtype == 'DC':
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
else:
print "rtype must be 'DC'(default) | 'IP'"
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
# Pre-allocate
srcLists = []
Rx = []
d = []
wd = []
zflag = True # Flag for z value provided
# Countdown for number of obs/tx
count = 0
for ii in range(obsfile.shape[0]):
# Skip if blank line
if not obsfile[ii]:
continue
# First line or end of a transmitter block, read transmitter info
# First line is transmitter with number of receivers
if count==0:
# Read the line
temp = (np.fromstring(obsfile[ii], dtype=float, sep=' ').T)
temp = (np.fromstring(obsfile[ii], dtype=float,sep=' ').T)
count = int(temp[-1])
# Check if z value is provided, if False -> nan
if len(temp)==5:
tx = np.r_[temp[0:2],np.nan,temp[2:4],np.nan]
zflag = False # Pass on the flag to the receiver loc
tx = np.r_[temp[0:2],np.nan,temp[0:2],np.nan]
zflag = False
else:
tx = temp[:-1]
@@ -703,16 +653,8 @@ def readUBC_DC3Dobs(fileName, rtype = 'DC'):
rx = []
continue
temp = np.fromstring(obsfile[ii], dtype=float,sep=' ') # Get the string
temp = np.fromstring(obsfile[ii], dtype=float,sep=' ')
# Filter out negative IP
# if temp[-2] < 0:
# count = count -1
# print "Negative!"
#
# else:
# If the Z-location is provided, otherwise put nan
if zflag:
rx.append(temp[:-2])
@@ -722,7 +664,7 @@ def readUBC_DC3Dobs(fileName, rtype = 'DC'):
wd.append(temp[-1])
else:
rx.append(np.r_[temp[0:2],np.nan,temp[2:4],np.nan] )
rx.append(np.r_[temp[0:2],np.nan,temp[0:2],np.nan] )
# Check if there is data with the location
if len(temp)==6:
d.append(temp[-2])
@@ -730,7 +672,7 @@ def readUBC_DC3Dobs(fileName, rtype = 'DC'):
count = count -1
# Reach the end of transmitter block, append the src, rx and continue
# Reach the end of transmitter block
if count == 0:
rx = np.asarray(rx)
Rx = DC.RxDipole(rx[:,:3],rx[:,3:])
@@ -746,12 +688,19 @@ def readUBC_DC3Dobs(fileName, rtype = 'DC'):
def readUBC_DC2Dobs(fileName):
"""
------- NEEDS TO BE UPDATED ------
Read UBC GIF 2D observation file and generate arrays for tx-rx location
:param string fileName: path to the UBC GIF 2D model file
:rtype: (DC.Src, DC.Rx, ??, ??)
:return: source_locs, rx_locs, ??, ??
Input:
:param fileName, path to the UBC GIF 2D model file
Output:
:param rx, tx
:return
Created on Thu Nov 12 13:14:10 2015
@author: dominiquef
"""
from SimPEG import np
@@ -786,78 +735,16 @@ def readUBC_DC2Dobs(fileName):
return tx, rx, d, wd
def readUBC_DC2Dpre(fileName):
"""
Read UBC GIF DCIP 2D observation file and generate arrays for tx-rx location
Input:
:param string fileName: path to the UBC GIF 3D obs file
:rtype: DC.Survey
:return: DCsurvey
Created on Mon March 9th, 2016 << Doug's 70th Birthday !! >>
@author: dominiquef
"""
# Load file
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
# Pre-allocate
srcLists = []
Rx = []
d = []
zflag = True # Flag for z value provided
for ii in range(obsfile.shape[0]):
if not obsfile[ii]:
continue
# First line is transmitter with number of receivers
temp = (np.fromstring(obsfile[ii], dtype=float,sep=' ').T)
# Check if z value is provided, if False -> nan
if len(temp)==5:
tx = np.r_[temp[0],np.nan,np.nan,temp[1],np.nan,np.nan]
zflag = False
else:
tx = np.r_[temp[0],np.nan,temp[1],temp[2],np.nan,temp[3]]
if zflag:
rx = np.c_[temp[4],np.nan,temp[5],temp[6],np.nan,temp[7]]
else:
rx = np.c_[temp[2],np.nan,np.nan,temp[3],np.nan,np.nan]
# Check if there is data with the location
d.append(temp[-1])
Rx = DC.RxDipole(rx[:,:3],rx[:,3:])
srcLists.append( DC.SrcDipole( [Rx], tx[:3],tx[3:]) )
# Create survey class
survey = DC.SurveyDC(srcLists)
survey.dobs = np.asarray(d)
return {'DCsurvey':survey}
def readUBC_DC2DMesh(fileName):
"""
Read UBC GIF 2DTensor mesh and generate 2D Tensor mesh in simpeg
:param string fileName: path to the UBC GIF mesh file
:rtype: Mesh.TensorMesh
:return: SimPEG TensorMesh 2D object
Input:
:param fileName, path to the UBC GIF mesh file
Output:
:param SimPEG TensorMesh 2D object
:return
Created on Thu Nov 12 13:14:10 2015
@@ -923,9 +810,12 @@ def xy_2_lineID(DCsurvey):
they were collected. May need to generalize for random
point locations, but will be more expensive
:param numpy.array DCdict: Vectors of station location
:rtype: numpy.array
:return: LineID Vector of integers
Input:
:param DCdict Vectors of station location
Output:
:param LineID Vector of integers
:return
Created on Thu Feb 11, 2015
@@ -1038,6 +928,7 @@ def getSrc_locs(DCsurvey):
srcMat = np.zeros((DCsurvey.nSrc,2,3))
for ii in range(DCsurvey.nSrc):
print np.asarray(DCsurvey.srcList[ii].loc).shape
srcMat[ii,:,:] = np.asarray(DCsurvey.srcList[ii].loc)
return srcMat
+47 -214
View File
@@ -144,18 +144,12 @@ 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.
phi_d_star = None
@property
def target(self):
if getattr(self, '_target', None) is None:
if self.phi_d_star is None:
self.phi_d_star = 0.5 * self.survey.nD
self._target = self.chifact * self.phi_d_star # the factor of 0.5 is because we do phid = 0.5*|| dpred - dobs||^2
self._target = self.survey.nD*0.5
return self._target
@target.setter
def target(self, val):
@@ -167,7 +161,7 @@ class TargetMisfit(InversionDirective):
class SaveEveryIteration(InversionDirective):
class _SaveEveryIteration(InversionDirective):
@property
def name(self):
if getattr(self, '_name', None) is None:
@@ -188,7 +182,7 @@ class SaveEveryIteration(InversionDirective):
self._fileName = value
class SaveModelEveryIteration(SaveEveryIteration):
class SaveModelEveryIteration(_SaveEveryIteration):
"""SaveModelEveryIteration"""
def initialize(self):
@@ -198,7 +192,7 @@ 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 +206,7 @@ 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):
@@ -222,13 +216,13 @@ class SaveOutputDictEveryIteration(SaveEveryIteration):
# Save the data.
ms = self.reg.Ws * ( self.reg.mapping * (self.invProb.curModel - self.reg.mref) )
phi_ms = 0.5*ms.dot(ms)
if self.reg.mrefInSmooth == True:
if self.reg.smoothModel == True:
mref = self.reg.mref
else:
mref = 0
mx = self.reg.Wx * ( self.reg.mapping * (self.invProb.curModel - mref) )
phi_mx = 0.5 * mx.dot(mx)
if self.prob.mesh.dim >= 2:
if self.prob.mesh.dim==2:
my = self.reg.Wy * ( self.reg.mapping * (self.invProb.curModel - mref) )
phi_my = 0.5 * my.dot(my)
else:
@@ -243,210 +237,49 @@ 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 SaveOutputDictEveryIteration(_SaveEveryIteration):
"""SaveOutputDictEveryIteration
A directive that saves some relevant information from the inversion run to a numpy .npz dictionary file (see numpy.savez function for further info).
"""
def initialize(self):
print "SimPEG.SaveOutputDictEveryIteration will save your inversion progress as dictionary: '%s-###.npz'"%self.fileName
def endIter(self):
# Save the data.
ms = self.reg.Ws * ( self.reg.mapping * (self.invProb.curModel - self.reg.mref) )
phi_ms = 0.5*ms.dot(ms)
if self.reg.smoothModel == True:
mref = self.reg.mref
else:
mref = 0
mx = self.reg.Wx * ( self.reg.mapping * (self.invProb.curModel - mref) )
phi_mx = 0.5 * mx.dot(mx)
if self.prob.mesh.dim==2:
my = self.reg.Wy * ( self.reg.mapping * (self.invProb.curModel - mref) )
phi_my = 0.5 * my.dot(my)
else:
phi_my = 'NaN'
if self.prob.mesh.dim==3 and 'CYL' not in self.prob.mesh._meshType:
mz = self.reg.Wz * ( self.reg.mapping * (self.invProb.curModel - mref) )
phi_mz = 0.5 * mz.dot(mz)
else:
phi_mz = 'NaN'
# Save the file as a npz
np.savez('{:s}-{:03d}'.format(self.fileName,self.opt.iter), 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'
# mref = self.mref0
# self.m_prev = self.invProb.m_current
# return mref
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.]
def endIter(self):
# 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
else:
self.f_old = phim_new
# # 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
# 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
# Update the model used for the IRLS weights
self.reg.curModel = self.invProb.curModel
# Temporarely set gamma to 1. to get raw phi_m
self.reg.gamma = 1.
# 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
class Update_lin_PreCond(InversionDirective):
"""
Create a Jacobi preconditioner for the linear problem
"""
onlyOnStart=False
def initialize(self):
if getattr(self.opt, 'approxHinv', None) is None:
# Update the pre-conditioner
diagA = np.sum(self.prob.G**2.,axis=0) + self.invProb.beta*(self.reg.W.T*self.reg.W).diagonal() #* (self.reg.mapping * np.ones(self.reg.curModel.size))**2.
PC = Utils.sdiag((self.prob.mapping.deriv(None).T *diagA)**-1.)
self.opt.approxHinv = PC
def endIter(self):
# Cool the threshold parameter
if self.onlyOnStart==True:
return
if getattr(self.opt, 'approxHinv', None) is not None:
# Update the pre-conditioner
diagA = np.sum(self.prob.G**2.,axis=0) + self.invProb.beta*(self.reg.W.T*self.reg.W).diagonal() #* (self.reg.mapping * np.ones(self.reg.curModel.size))**2.
PC = Utils.sdiag((self.prob.mapping.deriv(None).T *diagA)**-1.)
self.opt.approxHinv = PC
class Update_Wj(InversionDirective):
"""
Create approx-sensitivity base weighting using the probing method
"""
k = None # Number of probing cycles
itr = None # Iteration number to update Wj, or always update if None
def endIter(self):
if self.itr is None or self.itr == self.opt.iter:
m = self.invProb.curModel
if self.k is None:
self.k = int(self.survey.nD/10)
def JtJv(v):
Jv = self.prob.Jvec(m, v)
return self.prob.Jtvec(m,Jv)
JtJdiag = Utils.diagEst(JtJv,len(m),k=self.k)
JtJdiag = JtJdiag / max(JtJdiag)
self.reg.wght = JtJdiag
-118
View File
@@ -1,118 +0,0 @@
import numpy as np
from scipy.constants import mu_0, pi
from scipy import special
def DCAnalyticHalf(txloc, rxlocs, sigma, earth_type="wholespace"):
"""
Analytic solution for electric potential from a postive pole
:param array txloc: a xyz location of A (+) electrode (np.r_[xa, ya, za])
:param list rxlocs: xyz locations of M (+) and N (-) electrodes [M, N]
e.g.
rxlocs = [M, N]
M: xyz locations of M (+) electrode (np.c_[xmlocs, ymlocs, zmlocs])
N: xyz locations of N (-) electrode (np.c_[xnlocs, ynlocs, znlocs])
:param float or complex sigma: values of conductivity
:param string earth_type: values of conductivity ("wholsespace" or "halfspace")
"""
M = rxlocs[0]
N = rxlocs[1]
rM = np.sqrt( (M[:,0]-txloc[0])**2 + (M[:,1]-txloc[1])**2 + (M[:,2]-txloc[1])**2 )
rN = np.sqrt( (N[:,0]-txloc[0])**2 + (N[:,1]-txloc[1])**2 + (N[:,2]-txloc[1])**2 )
phiM = 1./(4*np.pi*rM*sigma)
phiN = 1./(4*np.pi*rN*sigma)
phi = phiM - phiN
if earth_type == "halfspace":
phi *= 2
return phi
deg2rad = lambda deg: deg/180.*np.pi
rad2deg = lambda rad: rad*180./np.pi
def DCAnalyticSphere(txloc, rxloc, xc, radius, sigma, sigma1, \
field_type = "secondary", order=12, halfspace=False):
# def DCSpherePointCurrent(txloc, rxloc, xc, radius, rho, rho1, \
# field_type = "secondary", order=12):
"""
Parameters:
:param array txloc: A (+) current electrode location (x,y,z)
:param array xc: x center of depressed sphere
:param array rxloc: M(+) electrode locations / (Nx3 array, # of electrodes)
:param float radius: radius (float): radius of the sphere (m)
:param float rho: resistivity of the background (ohm-m)
:param float rho1: resistivity of the sphere
:param string field_type: : "secondary", "total", "primary"
(default="secondary")
"secondary": secondary potential only due to sphere
"primary": primary potential from the point source
"total": "secondary"+"primary"
:param float order: maximum order of Legendre polynomial (default=12)
Written by Seogi Kang (skang@eos.ubc.ca)
Ph.D. Candidate of University of British Columbia, Canada
"""
Pleg = []
# Compute Legendre Polynomial
for i in range(order):
Pleg.append(special.legendre(i, monic=0))
rho = 1./sigma
rho1 = 1./sigma1
# Center of the sphere should be aligned in txloc in y-direction
yc = txloc[1]
xyz = np.c_[rxloc[:,0]-xc, rxloc[:,1]-yc, rxloc[:,2]]
r = np.sqrt( (xyz**2).sum(axis=1) )
x0 = abs(txloc[0]-xc)
costheta = xyz[:,0]/r * (txloc[0]-xc)/x0
phi = np.zeros_like(r)
R = (r**2+x0**2.-2.*r*x0*costheta)**0.5
# primary potential in a whole space
prim = rho*1./(4*np.pi*R)
if field_type =="primary":
return prim
sphind = r < radius
out = np.zeros_like(r)
for n in range(order):
An, Bn = AnBnfun(n, radius, x0, rho, rho1)
dumout = An*r[~sphind]**(-n-1.)*Pleg[n](costheta[~sphind])
out[~sphind] += dumout
dumin = Bn*r[sphind]**(n)*Pleg[n](costheta[sphind])
out[sphind] += dumin
out[~sphind] += prim[~sphind]
if halfspace:
scale = 2
else:
scale = 1
if field_type == "secondary":
return scale*(out-prim)
elif field_type == "total":
return scale*out
def AnBnfun(n, radius, x0, rho, rho1, I=1.):
const = I*rho/(4*np.pi)
bunmo = n*rho + (n+1)*rho1
An = const * radius**(2*n+1) / x0 ** (n+1.) * n * \
(rho1-rho) / bunmo
Bn = const * 1. / x0 ** (n+1.) * (2*n+1) * (rho1) / bunmo
return An, Bn
-302
View File
@@ -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
View File
@@ -1,5 +1,3 @@
from TDEM import hzAnalyticDipoleT
from FDEM import hzAnalyticDipoleF
from FDEMcasing import *
from DC import DCAnalyticHalf, DCAnalyticSphere
from FDEMDipolarfields import *
+14 -37
View File
@@ -1,7 +1,6 @@
from SimPEG import Survey, Problem, Utils, Models, Maps, PropMaps, np, sp, Solver as SimpegSolver
from scipy.constants import mu_0
class EMPropMap(Maps.PropMap):
"""
Property Map for EM Problems. The electrical conductivity (\\(\\sigma\\)) is the default inversion property, and the default value of the magnetic permeability is that of free space (\\(\\mu = 4\\pi\\times 10^{-7} \\) H/m)
@@ -20,10 +19,10 @@ 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 = {}
@@ -62,15 +61,6 @@ class BaseEMProblem(Problem.BaseProblem):
self._Me = self.mesh.getEdgeInnerProduct()
return self._Me
@property
def MeI(self):
"""
Edge inner product matrix
"""
if getattr(self, '_MeI', None) is None:
self._MeI = self.mesh.getEdgeInnerProduct(invMat=True)
return self._MeI
@property
def Mf(self):
"""
@@ -80,20 +70,6 @@ class BaseEMProblem(Problem.BaseProblem):
self._Mf = self.mesh.getFaceInnerProduct()
return self._Mf
@property
def MfI(self):
"""
Face inner product matrix
"""
if getattr(self, '_MfI', None) is None:
self._MfI = self.mesh.getFaceInnerProduct(invMat=True)
return self._MfI
@property
def Vol(self):
if getattr(self, '_Vol', None) is None:
self._Vol = Utils.sdiag(self.mesh.vol)
return self._Vol
# ----- Magnetic Permeability ----- #
@property
@@ -151,6 +127,7 @@ class BaseEMProblem(Problem.BaseProblem):
"""
return self.mesh.getEdgeInnerProductDeriv(self.curModel.sigma)(u) * self.curModel.sigmaDeriv
@property
def MeSigmaI(self):
"""
@@ -169,7 +146,10 @@ class BaseEMProblem(Problem.BaseProblem):
dMeSigmaI_dI = -self.MeSigmaI**2
dMe_dsig = self.mesh.getEdgeInnerProductDeriv(self.curModel.sigma)(u)
return dMeSigmaI_dI * ( dMe_dsig * self.curModel.sigmaDeriv )
dsig_dm = self.curModel.sigmaDeriv
return dMeSigmaI_dI * ( dMe_dsig * ( dsig_dm))
# return self.mesh.getEdgeInnerProductDeriv(self.curModel.sigma, invMat=True)(u)
@property
def MfRho(self):
@@ -185,7 +165,8 @@ class BaseEMProblem(Problem.BaseProblem):
"""
Derivative of :code:`MfRho` with respect to the model.
"""
return self.mesh.getFaceInnerProductDeriv(self.curModel.rho)(u) * self.curModel.rhoDeriv
return self.mesh.getFaceInnerProductDeriv(self.curModel.rho)(u) * (-Utils.sdiag(self.curModel.rho**2) * self.curModel.sigmaDeriv)
# self.curModel.rhoDeriv
@property
def MfRhoI(self):
@@ -202,10 +183,7 @@ class BaseEMProblem(Problem.BaseProblem):
"""
Derivative of :code:`MfRhoI` with respect to the model.
"""
dMfRhoI_dI = -self.MfRhoI**2
dMf_drho = self.mesh.getFaceInnerProductDeriv(self.curModel.rho)(u)
return dMfRhoI_dI * ( dMf_drho * self.curModel.rhoDeriv )
return self.mesh.getFaceInnerProductDeriv(self.curModel.rho, invMat=True)(u) * self.curModel.rhoDeriv
class BaseEMSurvey(Survey.BaseSurvey):
@@ -214,10 +192,9 @@ class BaseEMSurvey(Survey.BaseSurvey):
self.srcList = srcList
Survey.BaseSurvey.__init__(self, **kwargs)
def eval(self, f):
def eval(self, u):
"""
Project fields to receiver locations
:param Fields u: fields object
:rtype: numpy.ndarray
:return: data
@@ -225,8 +202,8 @@ class BaseEMSurvey(Survey.BaseSurvey):
data = Survey.Data(self)
for src in self.srcList:
for rx in src.rxList:
data[src, rx] = rx.eval(src, self.mesh, f)
data[src, rx] = rx.eval(src, self.mesh, u)
return data
def evalDeriv(self, f):
def evalDeriv(self, u):
raise Exception('Use Receivers to project fields deriv.')
@@ -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, Fields_e, Fields_b, Fields_h, Fields_j
from SimPEG.EM.Base import BaseEMProblem
from SimPEG.EM.Utils import omega
@@ -17,8 +17,8 @@ class BaseFDEMProblem(BaseEMProblem):
\mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\\\
{\mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{s_e}}
if using the E-B formulation (:code:`Problem3D_e`
or :code:`Problem3D_b`). Note that in this case, :math:`\mathbf{s_e}` is an integrated quantity.
if using the E-B formulation (:code:`Problem_e`
or :code:`Problem_b`). Note that in this case, :math:`\mathbf{s_e}` is an integrated quantity.
If we write Maxwell's equations in terms of
\\\(\\\mathbf{h}\\\) and current density \\\(\\\mathbf{j}\\\)
@@ -28,14 +28,13 @@ class BaseFDEMProblem(BaseEMProblem):
\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{j} + i \omega \mathbf{M_{\mu}^e} \mathbf{h} = \mathbf{s_m} \\\\
\mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e}
if using the H-J formulation (:code:`Problem3D_j` or :code:`Problem3D_h`). Note that here, :math:`\mathbf{s_m}` is an integrated quantity.
if using the H-J formulation (:code:`Problem_j` or :code:`Problem_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,)
"""
@@ -88,7 +87,7 @@ class BaseFDEMProblem(BaseEMProblem):
du_dm_v = Ainv * ( - dA_dm_v + dRHS_dm_v )
for rx in src.rxList:
df_dmFun = getattr(f, '_{0}Deriv'.format(rx.projField), None)
df_dmFun = getattr(f, '_%sDeriv'%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)
Ainv.clean()
@@ -100,7 +99,7 @@ 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,)
"""
@@ -126,7 +125,7 @@ class BaseFDEMProblem(BaseEMProblem):
for rx in src.rxList:
PTv = rx.evalDeriv(src, self.mesh, f, v[src, rx], adjoint=True) # wrt f, need possibility wrt m
df_duTFun = getattr(f, '_{0}Deriv'.format(rx.projField), None)
df_duTFun = getattr(f, '_%sDeriv'%rx.projField, None)
df_duT, df_dmT = df_duTFun(src, None, PTv, adjoint=True)
ATinvdf_duT = ATinv * df_duT
@@ -138,9 +137,10 @@ class BaseFDEMProblem(BaseEMProblem):
df_dmT = df_dmT + du_dmT
# TODO: this should be taken care of by the reciever?
if rx.component is 'real':
real_or_imag = rx.projComp
if real_or_imag is 'real':
Jtv += np.array(df_dmT, dtype=complex).real
elif rx.component is 'imag':
elif real_or_imag is 'imag':
Jtv += - np.array(df_dmT, dtype=complex).real
else:
raise Exception('Must be real or imag')
@@ -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
@@ -178,7 +177,7 @@ class BaseFDEMProblem(BaseEMProblem):
################################ E-B Formulation #########################################
##########################################################################################
class Problem3D_e(BaseFDEMProblem):
class Problem_e(BaseFDEMProblem):
"""
By eliminating the magnetic flux density using
@@ -195,12 +194,12 @@ 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'
_formulation = 'EB'
fieldsPair = Fields3D_e
fieldsPair = Fields_e
def __init__(self, mesh, **kwargs):
BaseFDEMProblem.__init__(self, mesh, **kwargs)
@@ -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
@@ -289,7 +288,7 @@ class Problem3D_e(BaseFDEMProblem):
return C.T * (MfMui * s_mDeriv(v)) -1j * omega(freq) * s_eDeriv(v)
class Problem3D_b(BaseFDEMProblem):
class Problem_b(BaseFDEMProblem):
"""
We eliminate :math:`\mathbf{e}` using
@@ -306,12 +305,12 @@ 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'
_formulation = 'EB'
fieldsPair = Fields3D_b
fieldsPair = Fields_b
def __init__(self, mesh, **kwargs):
BaseFDEMProblem.__init__(self, mesh, **kwargs)
@@ -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
@@ -437,7 +436,7 @@ class Problem3D_b(BaseFDEMProblem):
##########################################################################################
class Problem3D_j(BaseFDEMProblem):
class Problem_j(BaseFDEMProblem):
"""
We eliminate \\\(\\\mathbf{h}\\\) using
@@ -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 ::
@@ -455,12 +453,12 @@ 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'
_formulation = 'HJ'
fieldsPair = Fields3D_j
fieldsPair = Fields_j
def __init__(self, mesh, **kwargs):
BaseFDEMProblem.__init__(self, mesh, **kwargs)
@@ -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
@@ -579,7 +577,7 @@ class Problem3D_j(BaseFDEMProblem):
class Problem3D_h(BaseFDEMProblem):
class Problem_h(BaseFDEMProblem):
"""
We eliminate \\\(\\\mathbf{j}\\\) using
@@ -593,12 +591,12 @@ 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'
_formulation = 'HJ'
fieldsPair = Fields3D_h
fieldsPair = Fields_h
def __init__(self, mesh, **kwargs):
BaseFDEMProblem.__init__(self, mesh, **kwargs)
@@ -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
+34 -22
View File
@@ -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 Fields_e(Fields):
"""
Fields object for Problem3D_e.
Fields object for Problem_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
@@ -423,12 +426,12 @@ class Fields3D_e(FieldsFDEM):
class Fields3D_b(FieldsFDEM):
class Fields_b(Fields):
"""
Fields object for Problem3D_b.
Fields object for Problem_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
@@ -687,12 +693,12 @@ class Fields3D_b(FieldsFDEM):
return Zero()
class Fields3D_j(FieldsFDEM):
class Fields_j(Fields):
"""
Fields object for Problem3D_j.
Fields object for Problem_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 Fields_h(Fields):
"""
Fields object for Problem3D_h.
Fields object for Problem_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
-126
View File
@@ -1,126 +0,0 @@
import SimPEG
from SimPEG import sp
class BaseRx(SimPEG.Survey.BaseRx):
"""
Frequency domain receiver base class
:param numpy.ndarray locs: receiver locations (ie. :code:`np.r_[x,y,z]`)
:param string orientation: receiver orientation 'x', 'y' or 'z'
:param string component: real or imaginary component 'real' or 'imag'
"""
def __init__(self, locs, orientation=None, component=None):
assert(orientation in ['x','y','z']), "Orientation %s not known. Orientation must be in 'x', 'y', 'z'. Arbitrary orientations have not yet been implemented."%orientation
assert(component in ['real', 'imag']), "'component' must be 'real' or 'imag', not %s"%component
self.projComp = orientation
self.component = component
SimPEG.Survey.BaseRx.__init__(self, locs, rxType=None) #TODO: remove rxType from baseRx
def projGLoc(self, u):
"""Grid Location projection (e.g. Ex Fy ...)"""
return u._GLoc(self.projField) + self.projComp
def eval(self, src, mesh, f):
"""
Project fields to receivers to get data.
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param BaseMesh mesh: mesh used
:param Fields f: fields object
:rtype: numpy.ndarray
:return: fields projected to recievers
"""
P = self.getP(mesh, self.projGLoc(f))
f_part_complex = f[src, self.projField]
f_part = getattr(f_part_complex, self.component) # get the real or imag component
return P*f_part
def evalDeriv(self, src, mesh, f, v, adjoint=False):
"""
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 Fields f: fields object
:param numpy.ndarray v: vector to multiply
:rtype: numpy.ndarray
:return: fields projected to recievers
"""
P = self.getP(mesh, self.projGLoc(f))
if not adjoint:
Pv_complex = P * v
Pv = getattr(Pv_complex, self.component)
elif adjoint:
Pv_real = P.T * v
if self.component == 'imag':
Pv = 1j*Pv_real
elif self.component == 'real':
Pv = Pv_real.astype(complex)
else:
raise NotImplementedError('must be real or imag')
return Pv
class Point_e(BaseRx):
"""
Electric field FDEM receiver
:param numpy.ndarray locs: receiver locations (ie. :code:`np.r_[x,y,z]`)
:param string orientation: receiver orientation 'x', 'y' or 'z'
:param string component: real or imaginary component 'real' or 'imag'
"""
def __init__(self, locs, orientation=None, component=None):
self.projField = 'e'
super(Point_e, self).__init__(locs, orientation, component)
class Point_b(BaseRx):
"""
Magnetic flux FDEM receiver
:param numpy.ndarray locs: receiver locations (ie. :code:`np.r_[x,y,z]`)
:param string orientation: receiver orientation 'x', 'y' or 'z'
:param string component: real or imaginary component 'real' or 'imag'
"""
def __init__(self, locs, orientation=None, component=None):
self.projField = 'b'
super(Point_b, self).__init__(locs, orientation, component)
class Point_h(BaseRx):
"""
Magnetic field FDEM receiver
:param numpy.ndarray locs: receiver locations (ie. :code:`np.r_[x,y,z]`)
:param string orientation: receiver orientation 'x', 'y' or 'z'
:param string component: real or imaginary component 'real' or 'imag'
"""
def __init__(self, locs, orientation=None, component=None):
self.projField = 'h'
super(Point_h, self).__init__(locs, orientation, component)
class Point_j(BaseRx):
"""
Current density FDEM receiver
:param numpy.ndarray locs: receiver locations (ie. :code:`np.r_[x,y,z]`)
:param string orientation: receiver orientation 'x', 'y' or 'z'
:param string component: real or imaginary component 'real' or 'imag'
"""
def __init__(self, locs, orientation=None, component=None):
self.projField = 'j'
super(Point_j, self).__init__(locs, orientation, component)
+50 -51
View File
@@ -10,21 +10,18 @@ class BaseSrc(Survey.BaseSrc):
freq = None
integrate = False
_ePrimary = None
_bPrimary = None
_hPrimary = None
_jPrimary = None
def __init__(self, rxList, **kwargs):
Survey.BaseSrc.__init__(self, rxList, **kwargs)
def eval(self, prob):
"""
Evaluate the source terms.
- :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 +34,10 @@ 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:
@@ -52,55 +49,56 @@ 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
"""
if self._bPrimary is None:
return Zero()
return self._bPrimary
#TODO : allow hPrimary to be provided and get bPrimary from it
if getattr(self, '_bPrimary', None) is not None:
return self._bPrimary
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
"""
if self._hPrimary is None:
return Zero()
return self._hPrimary
if getattr(self, '_hPrimary', None) is not None:
return self._hPrimary
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
"""
if self._ePrimary is None:
return Zero()
return self._ePrimary
if getattr(self, '_ePrimary', None) is not None:
return self._ePrimary
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
"""
if self._jPrimary is None:
return Zero()
return self._jPrimary
if getattr(self, '_jPrimary', None) is not None:
return self._jPrimary
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 +108,7 @@ 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 +118,7 @@ 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 +131,7 @@ 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
@@ -152,17 +150,17 @@ class RawVec_e(BaseSrc):
:param bool integrate: Integrate the source term (multiply by Me) [False]
"""
def __init__(self, rxList, freq, s_e, **kwargs):
def __init__(self, rxList, freq, s_e, **kwargs): #ePrimary=None, jPrimary=None, hPrimary=None, bPrimary=None
self._s_e = np.array(s_e, dtype=complex)
self.freq = float(freq)
BaseSrc.__init__(self, rxList, **kwargs)
[setattr(self, '_%s'%primField, kwargs[primField]) for primField in ['ePrimary', 'jPrimary', 'hPrimary', 'bPrimary'] if kwargs.get(primField) is not None]
BaseSrc.__init__(self, rxList)
def s_e(self, prob):
"""
Electric source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: electric source term on mesh
"""
@@ -181,17 +179,17 @@ class RawVec_m(BaseSrc):
:param bool integrate: Integrate the source term (multiply by Me) [False]
"""
def __init__(self, rxList, freq, s_m, **kwargs): #ePrimary=Zero(), bPrimary=Zero(), hPrimary=Zero(), jPrimary=Zero()):
def __init__(self, rxList, freq, s_m, **kwargs): #ePrimary=None, jPrimary=None, hPrimary=None, bPrimary=None):
self._s_m = np.array(s_m, dtype=complex)
self.freq = float(freq)
BaseSrc.__init__(self, rxList, **kwargs)
[setattr(self, '_%s'%primField, kwargs[primField]) for primField in ['ePrimary', 'jPrimary', 'hPrimary', 'bPrimary'] if kwargs.get(primField) is not None]
BaseSrc.__init__(self, rxList)
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
"""
@@ -210,17 +208,18 @@ class RawVec(BaseSrc):
:param numpy.array s_e: electric source term
:param bool integrate: Integrate the source term (multiply by Me) [False]
"""
def __init__(self, rxList, freq, s_m, s_e, **kwargs):
def __init__(self, rxList, freq, s_m, s_e, **kwargs): #ePrimary=None, jPrimary=None, hPrimary=None, bPrimary=None, **kwargs):
self._s_m = np.array(s_m, dtype=complex)
self._s_e = np.array(s_e, dtype=complex)
self.freq = float(freq)
[setattr(self, '_%s'%primField, kwargs[primField]) for primField in ['ePrimary', 'jPrimary', 'hPrimary', 'bPrimary'] if kwargs.get(primField) is not None]
BaseSrc.__init__(self, rxList, **kwargs)
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
"""
@@ -232,7 +231,7 @@ 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 +300,7 @@ 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 +338,7 @@ 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 +349,7 @@ 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 +363,7 @@ 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 +415,7 @@ 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 +454,7 @@ 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 +465,7 @@ 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 +478,7 @@ 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 +529,7 @@ 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
"""
@@ -567,7 +566,7 @@ 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 +577,7 @@ 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 +590,7 @@ class CircularLoop(BaseSrc):
"""
The electric source term
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
+119 -2
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@@ -4,9 +4,126 @@ from SimPEG.EM.Base import BaseEMSurvey
from scipy.constants import mu_0
from SimPEG.Utils import Zero, Identity
import SrcFDEM as Src
import RxFDEM as Rx
from SimPEG import sp
####################################################
# Receivers
####################################################
class Rx(SimPEG.Survey.BaseRx):
"""
Frequency domain receivers
:param numpy.ndarray locs: receiver locations (ie. :code:`np.r_[x,y,z]`)
:param string rxType: reciever type from knownRxTypes
"""
knownRxTypes = {
'exr':['e', 'x', 'real'],
'eyr':['e', 'y', 'real'],
'ezr':['e', 'z', 'real'],
'exi':['e', 'x', 'imag'],
'eyi':['e', 'y', 'imag'],
'ezi':['e', 'z', 'imag'],
'bxr':['b', 'x', 'real'],
'byr':['b', 'y', 'real'],
'bzr':['b', 'z', 'real'],
'bxi':['b', 'x', 'imag'],
'byi':['b', 'y', 'imag'],
'bzi':['b', 'z', 'imag'],
'jxr':['j', 'x', 'real'],
'jyr':['j', 'y', 'real'],
'jzr':['j', 'z', 'real'],
'jxi':['j', 'x', 'imag'],
'jyi':['j', 'y', 'imag'],
'jzi':['j', 'z', 'imag'],
'hxr':['h', 'x', 'real'],
'hyr':['h', 'y', 'real'],
'hzr':['h', 'z', 'real'],
'hxi':['h', 'x', 'imag'],
'hyi':['h', 'y', 'imag'],
'hzi':['h', 'z', 'imag'],
}
radius = None
def __init__(self, locs, rxType):
SimPEG.Survey.BaseRx.__init__(self, locs, rxType)
@property
def projField(self):
"""Field Type projection (e.g. e b ...)"""
return self.knownRxTypes[self.rxType][0]
@property
def projComp(self):
"""Component projection (real/imag)"""
return self.knownRxTypes[self.rxType][2]
def projGLoc(self, u):
"""Grid Location projection (e.g. Ex Fy ...)"""
return u._GLoc(self.rxType[0]) + self.knownRxTypes[self.rxType][1]
def eval(self, src, mesh, f):
"""
Project fields to recievers to get data.
:param Source src: FDEM source
:param Mesh mesh: mesh used
:param Fields f: fields object
:rtype: numpy.ndarray
:return: fields projected to recievers
"""
# projGLoc = u._GLoc(self.knownRxTypes[self.rxType][0])
# projGLoc += self.knownRxTypes[self.rxType][1]
P = self.getP(mesh, self.projGLoc(f))
f_part_complex = f[src, self.projField]
# get the real or imag component
real_or_imag = self.projComp
f_part = getattr(f_part_complex, real_or_imag)
return P*f_part
def evalDeriv(self, src, mesh, f, v, adjoint=False):
"""
Derivative of projected fields with respect to the inversion model times a vector.
: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
:return: fields projected to recievers
"""
P = self.getP(mesh, self.projGLoc(f))
if not adjoint:
Pv_complex = P * v
real_or_imag = self.projComp
Pv = getattr(Pv_complex, real_or_imag)
elif adjoint:
Pv_real = P.T * v
real_or_imag = self.projComp
if real_or_imag == 'imag':
Pv = 1j*Pv_real
elif real_or_imag == 'real':
Pv = Pv_real.astype(complex)
else:
raise NotImplementedError('must be real or imag')
return Pv
####################################################
# Survey
####################################################
class Survey(BaseEMSurvey):
"""
Frequency domain electromagnetic survey
@@ -15,7 +132,7 @@ class Survey(BaseEMSurvey):
"""
srcPair = Src.BaseSrc
rxPair = Rx.BaseRx
rxPair = Rx
def __init__(self, srcList, **kwargs):
# Sort these by frequency
+3 -5
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@@ -1,5 +1,3 @@
from SurveyFDEM import Survey
import SrcFDEM as Src
import RxFDEM as Rx
from ProblemFDEM import Problem3D_e, Problem3D_b, Problem3D_j, Problem3D_h
from FieldsFDEM import Fields3D_e, Fields3D_b, Fields3D_j, Fields3D_h
from SurveyFDEM import Rx, Src, Survey
from FDEM import BaseFDEMProblem, Problem_e, Problem_b, Problem_j, Problem_h
from FieldsFDEM import *
-160
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@@ -1,160 +0,0 @@
import numpy as np
def getxBCyBC_CC(mesh, alpha, beta, gamma):
# def getxBCyBC(mesh, alpha, beta, gamma):
"""
This is a subfunction generating mixed-boundary condition:
.. math::
\nabla \cdot \vec{j} = -\nabla \cdot \vec{j}_s = q
\rho \vec{j} = -\nabla \phi \phi
\alpha \phi + \beta \frac{\partial \phi}{\partial r} = \gamma \ at \ r = \partial \Omega
xBC = f_1(\alpha, \beta, \gamma)
yBC = f(\alpha, \beta, \gamma)
Computes xBC and yBC for cell-centered discretizations
"""
if mesh.dim == 1: #1D
if (len(alpha) != 2 or len(beta) != 2 or len(gamma) != 2):
raise Exception("Lenght of list, alpha should be 2")
fCCxm,fCCxp = mesh.cellBoundaryInd
nBC = fCCxm.sum()+fCCxp.sum()
h_xm, h_xp = mesh.gridCC[fCCxm], mesh.gridCC[fCCxp]
alpha_xm, beta_xm, gamma_xm = alpha[0], beta[0], gamma[0]
alpha_xp, beta_xp, gamma_xp = alpha[1], beta[1], gamma[1]
# h_xm, h_xp = mesh.gridCC[fCCxm], mesh.gridCC[fCCxp]
h_xm, h_xp = mesh.hx[0], mesh.hx[-1]
a_xm = gamma_xm/(0.5*alpha_xm-beta_xm/h_xm)
b_xm = (0.5*alpha_xm+beta_xm/h_xm)/(0.5*alpha_xm-beta_xm/h_xm)
a_xp = gamma_xp/(0.5*alpha_xp-beta_xp/h_xp)
b_xp = (0.5*alpha_xp+beta_xp/h_xp)/(0.5*alpha_xp-beta_xp/h_xp)
xBC_xm = 0.5*a_xm
xBC_xp = 0.5*a_xp/b_xp
yBC_xm = 0.5*(1.-b_xm)
yBC_xp = 0.5*(1.-1./b_xp)
xBC = np.r_[xBC_xm, xBC_xp]
yBC = np.r_[yBC_xm, yBC_xp]
elif mesh.dim == 2: #2D
if (len(alpha) != 4 or len(beta) != 4 or len(gamma) != 4):
raise Exception("Lenght of list, alpha should be 4")
fxm,fxp,fym,fyp = mesh.faceBoundaryInd
nBC = fxm.sum()+fxp.sum()+fxm.sum()+fxp.sum()
alpha_xm, beta_xm, gamma_xm = alpha[0], beta[0], gamma[0]
alpha_xp, beta_xp, gamma_xp = alpha[1], beta[1], gamma[1]
alpha_ym, beta_ym, gamma_ym = alpha[2], beta[2], gamma[2]
alpha_yp, beta_yp, gamma_yp = alpha[3], beta[3], gamma[3]
# h_xm, h_xp = mesh.gridCC[fCCxm,0], mesh.gridCC[fCCxp,0]
# h_ym, h_yp = mesh.gridCC[fCCym,1], mesh.gridCC[fCCyp,1]
h_xm, h_xp = mesh.hx[0]*np.ones_like(alpha_xm), mesh.hx[-1]*np.ones_like(alpha_xp)
h_ym, h_yp = mesh.hy[0]*np.ones_like(alpha_ym), mesh.hy[-1]*np.ones_like(alpha_yp)
a_xm = gamma_xm/(0.5*alpha_xm-beta_xm/h_xm)
b_xm = (0.5*alpha_xm+beta_xm/h_xm)/(0.5*alpha_xm-beta_xm/h_xm)
a_xp = gamma_xp/(0.5*alpha_xp-beta_xp/h_xp)
b_xp = (0.5*alpha_xp+beta_xp/h_xp)/(0.5*alpha_xp-beta_xp/h_xp)
a_ym = gamma_ym/(0.5*alpha_ym-beta_ym/h_ym)
b_ym = (0.5*alpha_ym+beta_ym/h_ym)/(0.5*alpha_ym-beta_ym/h_ym)
a_yp = gamma_yp/(0.5*alpha_yp-beta_yp/h_yp)
b_yp = (0.5*alpha_yp+beta_yp/h_yp)/(0.5*alpha_yp-beta_yp/h_yp)
xBC_xm = 0.5*a_xm
xBC_xp = 0.5*a_xp/b_xp
yBC_xm = 0.5*(1.-b_xm)
yBC_xp = 0.5*(1.-1./b_xp)
xBC_ym = 0.5*a_ym
xBC_yp = 0.5*a_yp/b_yp
yBC_ym = 0.5*(1.-b_ym)
yBC_yp = 0.5*(1.-1./b_yp)
sortindsfx = np.argsort(np.r_[np.arange(mesh.nFx)[fxm], np.arange(mesh.nFx)[fxp]])
sortindsfy = np.argsort(np.r_[np.arange(mesh.nFy)[fym], np.arange(mesh.nFy)[fyp]])
xBC_x = np.r_[xBC_xm, xBC_xp][sortindsfx]
xBC_y = np.r_[xBC_ym, xBC_yp][sortindsfy]
yBC_x = np.r_[yBC_xm, yBC_xp][sortindsfx]
yBC_y = np.r_[yBC_ym, yBC_yp][sortindsfy]
xBC = np.r_[xBC_x, xBC_y]
yBC = np.r_[yBC_x, yBC_y]
elif mesh.dim == 3: #3D
if (len(alpha) != 6 or len(beta) != 6 or len(gamma) != 6):
raise Exception("Lenght of list, alpha should be 6")
# fCCxm,fCCxp,fCCym,fCCyp,fCCzm,fCCzp = mesh.cellBoundaryInd
fxm,fxp,fym,fyp,fzm,fzp = mesh.faceBoundaryInd
nBC = fxm.sum()+fxp.sum()+fxm.sum()+fxp.sum()
alpha_xm, beta_xm, gamma_xm = alpha[0], beta[0], gamma[0]
alpha_xp, beta_xp, gamma_xp = alpha[1], beta[1], gamma[1]
alpha_ym, beta_ym, gamma_ym = alpha[2], beta[2], gamma[2]
alpha_yp, beta_yp, gamma_yp = alpha[3], beta[3], gamma[3]
alpha_zm, beta_zm, gamma_zm = alpha[4], beta[4], gamma[4]
alpha_zp, beta_zp, gamma_zp = alpha[5], beta[5], gamma[5]
# h_xm, h_xp = mesh.gridCC[fCCxm,0], mesh.gridCC[fCCxp,0]
# h_ym, h_yp = mesh.gridCC[fCCym,1], mesh.gridCC[fCCyp,1]
# h_zm, h_zp = mesh.gridCC[fCCzm,2], mesh.gridCC[fCCzp,2]
h_xm, h_xp = mesh.hx[0]*np.ones_like(alpha_xm), mesh.hx[-1]*np.ones_like(alpha_xp)
h_ym, h_yp = mesh.hy[0]*np.ones_like(alpha_ym), mesh.hy[-1]*np.ones_like(alpha_yp)
h_zm, h_zp = mesh.hz[0]*np.ones_like(alpha_zm), mesh.hz[-1]*np.ones_like(alpha_zp)
a_xm = gamma_xm/(0.5*alpha_xm-beta_xm/h_xm)
b_xm = (0.5*alpha_xm+beta_xm/h_xm)/(0.5*alpha_xm-beta_xm/h_xm)
a_xp = gamma_xp/(0.5*alpha_xp-beta_xp/h_xp)
b_xp = (0.5*alpha_xp+beta_xp/h_xp)/(0.5*alpha_xp-beta_xp/h_xp)
a_ym = gamma_ym/(0.5*alpha_ym-beta_ym/h_ym)
b_ym = (0.5*alpha_ym+beta_ym/h_ym)/(0.5*alpha_ym-beta_ym/h_ym)
a_yp = gamma_yp/(0.5*alpha_yp-beta_yp/h_yp)
b_yp = (0.5*alpha_yp+beta_yp/h_yp)/(0.5*alpha_yp-beta_yp/h_yp)
a_zm = gamma_zm/(0.5*alpha_zm-beta_zm/h_zm)
b_zm = (0.5*alpha_zm+beta_zm/h_zm)/(0.5*alpha_zm-beta_zm/h_zm)
a_zp = gamma_zp/(0.5*alpha_zp-beta_zp/h_zp)
b_zp = (0.5*alpha_zp+beta_zp/h_zp)/(0.5*alpha_zp-beta_zp/h_zp)
xBC_xm = 0.5*a_xm
xBC_xp = 0.5*a_xp/b_xp
yBC_xm = 0.5*(1.-b_xm)
yBC_xp = 0.5*(1.-1./b_xp)
xBC_ym = 0.5*a_ym
xBC_yp = 0.5*a_yp/b_yp
yBC_ym = 0.5*(1.-b_ym)
yBC_yp = 0.5*(1.-1./b_yp)
xBC_zm = 0.5*a_zm
xBC_zp = 0.5*a_zp/b_zp
yBC_zm = 0.5*(1.-b_zm)
yBC_zp = 0.5*(1.-1./b_zp)
sortindsfx = np.argsort(np.r_[np.arange(mesh.nFx)[fxm], np.arange(mesh.nFx)[fxp]])
sortindsfy = np.argsort(np.r_[np.arange(mesh.nFy)[fym], np.arange(mesh.nFy)[fyp]])
sortindsfz = np.argsort(np.r_[np.arange(mesh.nFz)[fzm], np.arange(mesh.nFz)[fzp]])
xBC_x = np.r_[xBC_xm, xBC_xp][sortindsfx]
xBC_y = np.r_[xBC_ym, xBC_yp][sortindsfy]
xBC_z = np.r_[xBC_zm, xBC_zp][sortindsfz]
yBC_x = np.r_[yBC_xm, yBC_xp][sortindsfx]
yBC_y = np.r_[yBC_ym, yBC_yp][sortindsfy]
yBC_z = np.r_[yBC_zm, yBC_zp][sortindsfz]
xBC = np.r_[xBC_x, xBC_y, xBC_z]
yBC = np.r_[yBC_x, yBC_y, yBC_z]
return xBC, yBC
-148
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@@ -1,148 +0,0 @@
import SimPEG
from SimPEG.Utils import Identity, Zero
import numpy as np
from scipy.constants import epsilon_0
class Fields(SimPEG.Problem.Fields):
knownFields = {}
dtype = float
def _phiDeriv(self, src, du_dm_v, v, adjoint=False):
if getattr(self, '_phiDeriv_u', None) is None or getattr(self, '_phiDeriv_m', None) is None:
raise NotImplementedError ('Getting phiDerivs from %s is not implemented' %self.knownFields.keys()[0])
if adjoint:
return self._phiDeriv_u(src, v, adjoint=adjoint), self._phiDeriv_m(src, v, adjoint=adjoint)
return np.array(self._phiDeriv_u(src, du_dm_v, adjoint) + self._phiDeriv_m(src, v, adjoint), dtype = float)
def _eDeriv(self, src, du_dm_v, v, adjoint=False):
if getattr(self, '_eDeriv_u', None) is None or getattr(self, '_eDeriv_m', None) is None:
raise NotImplementedError ('Getting eDerivs from %s is not implemented' %self.knownFields.keys()[0])
if adjoint:
return self._eDeriv_u(src, v, adjoint), self._eDeriv_m(src, v, adjoint)
return np.array(self._eDeriv_u(src, du_dm_v, adjoint) + self._eDeriv_m(src, v, adjoint), dtype = float)
def _jDeriv(self, src, du_dm_v, v, adjoint=False):
if getattr(self, '_jDeriv_u', None) is None or getattr(self, '_jDeriv_m', None) is None:
raise NotImplementedError ('Getting jDerivs from %s is not implemented' %self.knownFields.keys()[0])
if adjoint:
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 = float)
class Fields_CC(Fields):
knownFields = {'phiSolution':'CC'}
aliasFields = {
'phi': ['phiSolution','CC','_phi'],
'j' : ['phiSolution','F','_j'],
'e' : ['phiSolution','F','_e'],
'charge' : ['phiSolution','CC','_charge'],
}
# primary - secondary
# CC variables
def __init__(self, mesh, survey, **kwargs):
Fields.__init__(self, mesh, survey, **kwargs)
mesh.setCellGradBC("neumann")
cellGrad = mesh.cellGrad
def startup(self):
self.prob = self.survey.prob
def _GLoc(self, fieldType):
if fieldType == 'phi':
return 'CC'
elif fieldType == 'e' or fieldType == 'j':
return 'F'
else:
raise Exception('Field type must be phi, e, j')
def _phi(self, phiSolution, srcList):
return phiSolution
def _phiDeriv_u(self, src, v, adjoint = False):
return Identity()*v
def _phiDeriv_m(self, src, v, adjoint = False):
return Zero()
def _j(self, phiSolution, srcList):
"""
.. math::
\mathbf{j} = \mathbf{M}^{f \ -1}_{\rho} \mathbf{G} \phi
"""
return self.prob.MfRhoI*self.prob.Grad*phiSolution
def _e(self, phiSolution, srcList):
"""
In HJ formulation e is not well-defined!!
.. math::
\vec{e} = -\nabla \phi
"""
return -self.mesh.cellGrad*phiSolution
def _charge(self, phiSolution, srcList):
"""
.. math::
\int \nabla \codt \vec{e} = \int \frac{\rho_v }{\epsillon_0}
"""
return epsilon_0*self.prob.Vol*(self.mesh.faceDiv*self._e(phiSolution, srcList))
class Fields_N(Fields):
knownFields = {'phiSolution':'N'}
aliasFields = {
'phi': ['phiSolution','N','_phi'],
'j' : ['phiSolution','E','_j'],
'e' : ['phiSolution','E','_e'],
'charge' : ['phiSolution','N','_charge'],
}
# primary - secondary
# N variables
def __init__(self, mesh, survey, **kwargs):
Fields.__init__(self, mesh, survey, **kwargs)
def startup(self):
self.prob = self.survey.prob
def _GLoc(self, fieldType):
if fieldType == 'phi':
return 'N'
elif fieldType == 'e' or fieldType == 'j':
return 'E'
else:
raise Exception('Field type must be phi, e, j')
def _phi(self, phiSolution, srcList):
return phiSolution
def _phiDeriv_u(self, src, v, adjoint = False):
return Identity()*v
def _phiDeriv_m(self, src, v, adjoint = False):
return Zero()
def _j(self, phiSolution, srcList):
"""
In EB formulation j is not well-defined!!
.. math::
\mathbf{j} = - \mathbf{M}^{e}_{\sigma} \mathbf{G} \phi
"""
return self.prob.MeSigma * self._e(phiSolution, srcList)
def _e(self, phiSolution, srcList):
"""
In HJ formulation e is not well-defined!!
.. math::
\vec{e} = -\nabla \phi
"""
return -self.mesh.nodalGrad * phiSolution
def _charge(self, phiSolution, srcList):
"""
.. math::
\int \nabla \codt \vec{e} = \int \frac{\rho_v }{\epsillon_0}
"""
return - epsilon_0*(self.mesh.nodalGrad.T*self.mesh.getEdgeInnerProduct()*self._e(phiSolution, srcList))
-146
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@@ -1,146 +0,0 @@
import SimPEG
from SimPEG.Utils import Identity, Zero
import numpy as np
class Fields_ky(SimPEG.Problem.TimeFields):
"""
Fancy Field Storage for a 2.5D code.
u[:,'phi', kyInd] = phi
print u[src0,'phi']
Only one field type is stored for
each problem, the rest are computed. The fields obejct acts like an array and is indexed by
.. code-block:: python
f = problem.fields(m)
e = f[srcList,'e']
j = f[srcList,'j']
If accessing all sources for a given field, use the :code:`:`
.. code-block:: python
f = problem.fields(m)
phi = f[:,'phi']
e = f[:,'e']
b = f[:,'b']
The array returned will be size (nE or nF, nSrcs :math:`\\times` nFrequencies)
"""
knownFields = {}
dtype = float
def _phiDeriv(self,kyInd, src, du_dm_v, v, adjoint=False):
if getattr(self, '_phiDeriv_u', None) is None or getattr(self, '_phiDeriv_m', None) is None:
raise NotImplementedError ('Getting phiDerivs from %s is not implemented' %self.knownFields.keys()[0])
if adjoint:
return self._phiDeriv_u(kyInd, src, v, adjoint=adjoint), self._phiDeriv_m(kyInd, src, v, adjoint=adjoint)
return np.array(self._phiDeriv_u(kyInd, src, du_dm_v, adjoint) + self._phiDeriv_m(kyInd, src, v, adjoint), dtype = float)
def _eDeriv(self,kyInd, src, du_dm_v, v, adjoint=False):
if getattr(self, '_eDeriv_u', None) is None or getattr(self, '_eDeriv_m', None) is None:
raise NotImplementedError ('Getting eDerivs from %s is not implemented' %self.knownFields.keys()[0])
if adjoint:
return self._eDeriv_u(kyInd, src, v, adjoint), self._eDeriv_m(kyInd, src, v, adjoint)
return np.array(self._eDeriv_u(kyInd, src, du_dm_v, adjoint) + self._eDeriv_m(kyInd, src, v, adjoint), dtype = float)
def _jDeriv(self,kyInd, src, du_dm_v, v, adjoint=False):
if getattr(self, '_jDeriv_u', None) is None or getattr(self, '_jDeriv_m', None) is None:
raise NotImplementedError ('Getting jDerivs from %s is not implemented' %self.knownFields.keys()[0])
if adjoint:
return self._jDeriv_u(kyInd, src, v, adjoint), self._jDeriv_m(kyInd, src, v, adjoint)
return np.array(self._jDeriv_u(kyInd, src, du_dm_v, adjoint) + self._jDeriv_m(kyInd, src, v, adjoint), dtype = float)
# def _eDeriv(self, tInd, src, dun_dm_v, v, adjoint=False):
# if adjoint is True:
# return self._eDeriv_u(tInd, src, v, adjoint), self._eDeriv_m(tInd, src, v, adjoint)
# return self._eDeriv_u(tInd, src, dun_dm_v) + self._eDeriv_m(tInd, src, v)
# def _bDeriv(self, tInd, src, dun_dm_v, v, adjoint=False):
# if adjoint is True:
# return self._bDeriv_u(tInd, src, v, adjoint), self._bDeriv_m(tInd, src, v, adjoint)
# return self._bDeriv_u(tInd, src, dun_dm_v) + self._bDeriv_m(tInd, src, v)
class Fields_ky_CC(Fields_ky):
knownFields = {'phiSolution':'CC'}
aliasFields = {
'phi': ['phiSolution','CC','_phi'],
'j' : ['phiSolution','F','_j'],
'e' : ['phiSolution','F','_e'],
}
# primary - secondary
# CC variables
def __init__(self, mesh, survey, **kwargs):
Fields_ky.__init__(self, mesh, survey, **kwargs)
def startup(self):
self.prob = self.survey.prob
def _GLoc(self, fieldType):
if fieldType == 'phi':
return 'CC'
elif fieldType == 'e' or fieldType == 'j':
return 'F'
else:
raise Exception('Field type must be phi, e, j')
def _phi(self, phiSolution, src, kyInd):
return phiSolution
def _phiDeriv_u(self, kyInd, src, v, adjoint = False):
return Identity()*v
def _phiDeriv_m(self, kyInd, src, v, adjoint = False):
return Zero()
def _j(self, phiSolution, srcList):
raise NotImplementedError
def _e(self, phiSolution, srcList):
raise NotImplementedError
class Fields_ky_N(Fields_ky):
knownFields = {'phiSolution':'N'}
aliasFields = {
'phi': ['phiSolution','N','_phi'],
'j' : ['phiSolution','E','_j'],
'e' : ['phiSolution','E','_e'],
}
# primary - secondary
# CC variables
def __init__(self, mesh, survey, **kwargs):
Fields_ky.__init__(self, mesh, survey, **kwargs)
def startup(self):
self.prob = self.survey.prob
def _GLoc(self, fieldType):
if fieldType == 'phi':
return 'N'
elif fieldType == 'e' or fieldType == 'j':
return 'E'
else:
raise Exception('Field type must be phi, e, j')
def _phi(self, phiSolution, src, kyInd):
return phiSolution
def _phiDeriv_u(self, kyInd, src, v, adjoint = False):
return Identity()*v
def _phiDeriv_m(self, kyInd, src, v, adjoint = False):
return Zero()
def _j(self, phiSolution, srcList):
raise NotImplementedError
def _e(self, phiSolution, srcList):
raise NotImplementedError
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from SimPEG import Problem, Utils
from SimPEG.EM.Base import BaseEMProblem
from SurveyDC import Survey
from FieldsDC import Fields, Fields_CC, Fields_N
from SimPEG.Utils import sdiag
import numpy as np
from SimPEG.Utils import Zero
from BoundaryUtils import getxBCyBC_CC
class BaseDCProblem(BaseEMProblem):
surveyPair = Survey
fieldsPair = Fields
Ainv = None
def fields(self, m):
self.curModel = m
if not self.Ainv == None:
self.Ainv.clean()
f = self.fieldsPair(self.mesh, self.survey)
A = self.getA()
self.Ainv = self.Solver(A, **self.solverOpts)
RHS = self.getRHS()
u = self.Ainv * RHS
Srcs = self.survey.srcList
f[Srcs, self._solutionType] = u
return f
def Jvec(self, m, v, f=None):
if f is None:
f = self.fields(m)
self.curModel = m
Jv = self.dataPair(self.survey) #same size as the data
A = self.getA()
for src in self.survey.srcList:
u_src = f[src, self._solutionType] # solution vector
dA_dm_v = self.getADeriv(u_src, v)
dRHS_dm_v = self.getRHSDeriv(src, v)
du_dm_v = self.Ainv * ( - dA_dm_v + dRHS_dm_v )
for rx in src.rxList:
df_dmFun = getattr(f, '_%sDeriv'%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)
return Utils.mkvc(Jv)
def Jtvec(self, m, v, f=None):
if f is None:
f = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
AT = self.getA()
for src in self.survey.srcList:
u_src = f[src, self._solutionType]
for rx in src.rxList:
PTv = rx.evalDeriv(src, self.mesh, f, v[src, rx], adjoint=True) # wrt f, need possibility wrt m
df_duTFun = getattr(f, '_%sDeriv'%rx.projField, None)
df_duT, df_dmT = df_duTFun(src, None, PTv, adjoint=True)
ATinvdf_duT = self.Ainv * df_duT
dA_dmT = self.getADeriv(u_src, ATinvdf_duT, adjoint=True)
dRHS_dmT = self.getRHSDeriv(src, ATinvdf_duT, adjoint=True)
du_dmT = -dA_dmT + dRHS_dmT
Jtv += (df_dmT + du_dmT).astype(float)
return Utils.mkvc(Jtv)
def getSourceTerm(self):
"""
takes concept of source and turns it into a matrix
"""
"""
Evaluates the sources, and puts them in matrix form
:rtype: (numpy.ndarray, numpy.ndarray)
:return: q (nC or nN, nSrc)
"""
Srcs = self.survey.srcList
if self._formulation is 'EB':
n = self.mesh.nN
# return NotImplementedError
elif self._formulation is 'HJ':
n = self.mesh.nC
q = np.zeros((n, len(Srcs)))
for i, src in enumerate(Srcs):
q[:,i] = src.eval(self)
return q
class Problem3D_CC(BaseDCProblem):
_solutionType = 'phiSolution'
_formulation = 'HJ' # CC potentials means J is on faces
fieldsPair = Fields_CC
def __init__(self, mesh, **kwargs):
BaseDCProblem.__init__(self, mesh, **kwargs)
self.setBC()
def getA(self):
"""
Make the A matrix for the cell centered DC resistivity problem
A = D MfRhoI G
"""
D = self.Div
G = self.Grad
MfRhoI = self.MfRhoI
A = D * MfRhoI * G
# I think we should deprecate this for DC problem.
# if self._makeASymmetric is True:
# return V.T * A
return A
def getADeriv(self, u, v, adjoint= False):
D = self.Div
G = self.Grad
MfRhoIDeriv = self.MfRhoIDeriv
if adjoint:
return(MfRhoIDeriv( G * u ).T) * ( D.T * v)
return D * (MfRhoIDeriv( G * u ) * v)
def getRHS(self):
"""
RHS for the DC problem
q
"""
RHS = self.getSourceTerm()
return RHS
def getRHSDeriv(self, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
"""
# TODO: add qDeriv for RHS depending on m
# qDeriv = src.evalDeriv(self, adjoint=adjoint)
# return qDeriv
return Zero()
def setBC(self):
if self.mesh.dim==3:
fxm,fxp,fym,fyp,fzm,fzp = self.mesh.faceBoundaryInd
gBFxm = self.mesh.gridFx[fxm,:]
gBFxp = self.mesh.gridFx[fxp,:]
gBFym = self.mesh.gridFy[fym,:]
gBFyp = self.mesh.gridFy[fyp,:]
gBFzm = self.mesh.gridFz[fzm,:]
gBFzp = self.mesh.gridFz[fzp,:]
# Setup Mixed B.C (alpha, beta, gamma)
temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
temp_zm, temp_zp = np.ones_like(gBFzm[:,2]), np.ones_like(gBFzp[:,2])
alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.
alpha_zm, alpha_zp = temp_zm*0., temp_zp*0.
beta_xm, beta_xp = temp_xm, temp_xp
beta_ym, beta_yp = temp_ym, temp_yp
beta_zm, beta_zp = temp_zm, temp_zp
gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.
gamma_zm, gamma_zp = temp_zm*0., temp_zp*0.
alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp, alpha_zm, alpha_zp]
beta = [beta_xm, beta_xp, beta_ym, beta_yp, beta_zm, beta_zp]
gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp, gamma_zm, gamma_zp]
elif self.mesh.dim==2:
fxm,fxp,fym,fyp = self.mesh.faceBoundaryInd
gBFxm = self.mesh.gridFx[fxm,:]
gBFxp = self.mesh.gridFx[fxp,:]
gBFym = self.mesh.gridFy[fym,:]
gBFyp = self.mesh.gridFy[fyp,:]
# Setup Mixed B.C (alpha, beta, gamma)
temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.
beta_xm, beta_xp = temp_xm, temp_xp
beta_ym, beta_yp = temp_ym, temp_yp
gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.
alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp]
beta = [beta_xm, beta_xp, beta_ym, beta_yp]
gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp]
x_BC, y_BC = getxBCyBC_CC(self.mesh, alpha, beta, gamma)
V = self.Vol
self.Div = V * self.mesh.faceDiv
P_BC, B = self.mesh.getBCProjWF_simple()
M = B*self.mesh.aveCC2F
self.Grad = self.Div.T - P_BC*Utils.sdiag(y_BC)*M
class Problem3D_N(BaseDCProblem):
_solutionType = 'phiSolution'
_formulation = 'EB' # N potentials means B is on faces
fieldsPair = Fields_N
def __init__(self, mesh, **kwargs):
BaseDCProblem.__init__(self, mesh, **kwargs)
def getA(self):
"""
Make the A matrix for the cell centered DC resistivity problem
A = G.T MeSigma G
"""
MeSigma = self.MeSigma
Grad = self.mesh.nodalGrad
A = Grad.T * MeSigma * Grad
# Handling Null space of A
A[0,0] = A[0,0] + 1.
return A
def getADeriv(self, u, v, adjoint=False):
"""
Product of the derivative of our system matrix with respect to the model and a vector
"""
MeSigma = self.MeSigma
Grad = self.mesh.nodalGrad
if not adjoint:
return Grad.T*(self.MeSigmaDeriv(Grad*u)*v)
elif adjoint:
return self.MeSigmaDeriv(Grad*u).T * (Grad*v)
def getRHS(self):
"""
RHS for the DC problem
q
"""
RHS = self.getSourceTerm()
return RHS
def getRHSDeriv(self, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
"""
# TODO: add qDeriv for RHS depending on m
# qDeriv = src.evalDeriv(self, adjoint=adjoint)
# return qDeriv
return Zero()
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from SimPEG import Problem, Utils
from SimPEG.EM.Base import BaseEMProblem
from SurveyDC import Survey, Survey_ky
from FieldsDC_2D import Fields_ky, Fields_ky_CC, Fields_ky_N
from SimPEG.Utils import sdiag
import numpy as np
from SimPEG.Utils import Zero
from BoundaryUtils import getxBCyBC_CC
class BaseDCProblem_2D(BaseEMProblem):
surveyPair = Survey_ky
fieldsPair = Fields_ky
nky = 15
kys = np.logspace(-4, 1, nky)
Ainv = [None for i in range(nky)]
nT = nky # Only for using TimeFields
def fields(self, m):
self.curModel = m
if not self.Ainv[0] == None:
for i in range(self.nky):
self.Ainv[i].clean()
f = self.fieldsPair(self.mesh, self.survey)
Srcs = self.survey.srcList
for iky in range(self.nky):
ky = self.kys[iky]
A = self.getA(ky)
self.Ainv[iky] = self.Solver(A, **self.solverOpts)
RHS = self.getRHS(ky)
u = self.Ainv[iky] * RHS
f[Srcs, self._solutionType, iky] = u
return f
def Jvec(self, m, v, f=None):
if f is None:
f = self.fields(m)
self.curModel = m
Jv = self.dataPair(self.survey) #same size as the data
Jv0 = self.dataPair(self.survey)
# Assume y=0.
# This needs some thoughts to implement in general when src is dipole
dky = np.diff(self.kys)
dky = np.r_[dky[0], dky]
y = 0.
#TODO: this loop is pretty slow .. (Parellize)
for iky in range(self.nky):
ky = self.kys[iky]
A = self.getA(ky)
for src in self.survey.srcList:
u_src = f[src, self._solutionType, iky] # solution vector
dA_dm_v = self.getADeriv(ky, u_src, v)
dRHS_dm_v = self.getRHSDeriv(ky, src, v)
du_dm_v = self.Ainv[iky] * ( - dA_dm_v + dRHS_dm_v )
for rx in src.rxList:
df_dmFun = getattr(f, '_%sDeriv'%rx.projField, None)
df_dm_v = df_dmFun(iky, src, du_dm_v, v, adjoint=False)
# Trapezoidal intergration
Jv1_temp = 1./np.pi*rx.evalDeriv(ky, src, self.mesh, f, df_dm_v)
if iky==0:
#First assigment
Jv[src, rx] = Jv1_temp*dky[iky]*np.cos(ky*y)
else:
Jv[src, rx] += Jv1_temp*dky[iky] /2.*np.cos(ky*y)
Jv[src, rx] += Jv0[src, rx]*dky[iky]/2.*np.cos(ky*y)
Jv0[src, rx] = Jv1_temp.copy()
return Utils.mkvc(Jv)
def Jtvec(self, m, v, f=None):
if f is None:
f = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size, dtype=float)
# Assume y=0.
# This needs some thoughts to implement in general when src is dipole
dky = np.diff(self.kys)
dky = np.r_[dky[0], dky]
y = 0.
for src in self.survey.srcList:
for rx in src.rxList:
Jtv_temp1 = np.zeros(m.size, dtype=float)
Jtv_temp0 = np.zeros(m.size, dtype=float)
#TODO: this loop is pretty slow .. (Parellize)
for iky in range(self.nky):
u_src = f[src, self._solutionType, iky]
ky = self.kys[iky]
AT = self.getA(ky)
PTv = rx.evalDeriv(ky, src, self.mesh, f, v[src, rx], adjoint=True) # wrt f, need possibility wrt m
df_duTFun = getattr(f, '_%sDeriv'%rx.projField, None)
df_duT, df_dmT = df_duTFun(iky, src, None, PTv, adjoint=True)
ATinvdf_duT = self.Ainv[iky] * df_duT
dA_dmT = self.getADeriv(ky, u_src, ATinvdf_duT, adjoint=True)
dRHS_dmT = self.getRHSDeriv(ky, src, ATinvdf_duT, adjoint=True)
du_dmT = -dA_dmT + dRHS_dmT
Jtv_temp1 = 1./np.pi*(df_dmT + du_dmT).astype(float)
# Trapezoidal intergration
if iky==0:
#First assigment
Jtv += Jtv_temp1*dky[iky]*np.cos(ky*y)
else:
Jtv += Jtv_temp1*dky[iky]/2.*np.cos(ky*y)
Jtv += Jtv_temp0*dky[iky]/2.*np.cos(ky*y)
Jtv_temp0 = Jtv_temp1.copy()
return Utils.mkvc(Jtv)
def getSourceTerm(self, ky):
"""
takes concept of source and turns it into a matrix
"""
"""
Evaluates the sources, and puts them in matrix form
:rtype: (numpy.ndarray, numpy.ndarray)
:return: q (nC or nN, nSrc)
"""
Srcs = self.survey.srcList
if self._formulation is 'EB':
n = self.mesh.nN
# return NotImplementedError
elif self._formulation is 'HJ':
n = self.mesh.nC
q = np.zeros((n, len(Srcs)))
for i, src in enumerate(Srcs):
q[:,i] = src.eval(self)
return q
class Problem2D_CC(BaseDCProblem_2D):
_solutionType = 'phiSolution'
_formulation = 'HJ' # CC potentials means J is on faces
fieldsPair = Fields_ky_CC
def __init__(self, mesh, **kwargs):
BaseDCProblem_2D.__init__(self, mesh, **kwargs)
self.setBC()
def getA(self, ky):
"""
Make the A matrix for the cell centered DC resistivity problem
A = D MfRhoI G
"""
D = self.Div
G = self.Grad
vol = self.mesh.vol
MfRhoI = self.MfRhoI
# Get resistivity rho
rho = self.curModel.rho
A = D * MfRhoI * G + Utils.sdiag(ky**2*vol/rho)
return A
def getADeriv(self, ky, u, v, adjoint= False):
D = self.Div
G = self.Grad
vol = self.mesh.vol
MfRhoIDeriv = self.MfRhoIDeriv
rho = self.curModel.rho
if adjoint:
return(MfRhoIDeriv( G * u ).T) * ( D.T * v) + ky**2*Utils.sdiag(u.flatten()*vol*(-1./rho**2))*v
return D * ((MfRhoIDeriv( G * u )) * v) + ky**2*Utils.sdiag(u.flatten()*vol*(-1./rho**2))*v
def getRHS(self, ky):
"""
RHS for the DC problem
q
"""
RHS = self.getSourceTerm(ky)
return RHS
def getRHSDeriv(self, ky, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
"""
# TODO: add qDeriv for RHS depending on m
# qDeriv = src.evalDeriv(self, ky, adjoint=adjoint)
# return qDeriv
return Zero()
def setBC(self):
if self.mesh.dim==3:
fxm,fxp,fym,fyp,fzm,fzp = self.mesh.faceBoundaryInd
gBFxm = self.mesh.gridFx[fxm,:]
gBFxp = self.mesh.gridFx[fxp,:]
gBFym = self.mesh.gridFy[fym,:]
gBFyp = self.mesh.gridFy[fyp,:]
gBFzm = self.mesh.gridFz[fzm,:]
gBFzp = self.mesh.gridFz[fzp,:]
# Setup Mixed B.C (alpha, beta, gamma)
temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
temp_zm, temp_zp = np.ones_like(gBFzm[:,2]), np.ones_like(gBFzp[:,2])
alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.
alpha_zm, alpha_zp = temp_zm*0., temp_zp*0.
beta_xm, beta_xp = temp_xm, temp_xp
beta_ym, beta_yp = temp_ym, temp_yp
beta_zm, beta_zp = temp_zm, temp_zp
gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.
gamma_zm, gamma_zp = temp_zm*0., temp_zp*0.
alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp, alpha_zm, alpha_zp]
beta = [beta_xm, beta_xp, beta_ym, beta_yp, beta_zm, beta_zp]
gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp, gamma_zm, gamma_zp]
elif self.mesh.dim==2:
fxm,fxp,fym,fyp = self.mesh.faceBoundaryInd
gBFxm = self.mesh.gridFx[fxm,:]
gBFxp = self.mesh.gridFx[fxp,:]
gBFym = self.mesh.gridFy[fym,:]
gBFyp = self.mesh.gridFy[fyp,:]
# Setup Mixed B.C (alpha, beta, gamma)
temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.
beta_xm, beta_xp = temp_xm, temp_xp
beta_ym, beta_yp = temp_ym, temp_yp
gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.
alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp]
beta = [beta_xm, beta_xp, beta_ym, beta_yp]
gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp]
x_BC, y_BC = getxBCyBC_CC(self.mesh, alpha, beta, gamma)
V = self.Vol
self.Div = V * self.mesh.faceDiv
P_BC, B = self.mesh.getBCProjWF_simple()
M = B*self.mesh.aveCC2F
self.Grad = self.Div.T - P_BC*Utils.sdiag(y_BC)*M
class Problem2D_N(BaseDCProblem_2D):
_solutionType = 'phiSolution'
_formulation = 'EB' # CC potentials means J is on faces
fieldsPair = Fields_ky_N
def __init__(self, mesh, **kwargs):
BaseDCProblem_2D.__init__(self, mesh, **kwargs)
# self.setBC()
@property
def MnSigma(self):
"""
Node inner product matrix for \\(\\sigma\\). Used in the E-B formulation
"""
# TODO: only works isotropic sigma
sigma = self.curModel.sigma
vol = self.mesh.vol
MnSigma = Utils.sdiag(self.mesh.aveN2CC.T*(Utils.sdiag(vol)*sigma))
return MnSigma
def MnSigmaDeriv(self, u):
"""
Derivative of MnSigma with respect to the model
"""
sigma = self.curModel.sigma
sigmaderiv = self.curModel.sigmaDeriv
vol = self.mesh.vol
return Utils.sdiag(u)*self.mesh.aveN2CC.T*Utils.sdiag(vol) * self.curModel.sigmaDeriv
def getA(self, ky):
"""
Make the A matrix for the cell centered DC resistivity problem
A = D MfRhoI G
"""
MeSigma = self.MeSigma
MnSigma = self.MnSigma
Grad = self.mesh.nodalGrad
# Get conductivity sigma
sigma = self.curModel.sigma
A = Grad.T * MeSigma * Grad + ky**2*MnSigma
# Handling Null space of A
A[0,0] = A[0,0] + 1.
return A
def getADeriv(self, ky, u, v, adjoint= False):
MeSigma = self.MeSigma
Grad = self.mesh.nodalGrad
sigma = self.curModel.sigma
vol = self.mesh.vol
if adjoint:
return self.MeSigmaDeriv(Grad*u).T * (Grad*v) + ky**2*self.MnSigmaDeriv(u).T*v
return Grad.T*(self.MeSigmaDeriv(Grad*u)*v) + ky**2*self.MnSigmaDeriv(u)*v
def getRHS(self, ky):
"""
RHS for the DC problem
q
"""
RHS = self.getSourceTerm(ky)
return RHS
def getRHSDeriv(self, ky, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
"""
# TODO: add qDeriv for RHS depending on m
# qDeriv = src.evalDeriv(self, ky, adjoint=adjoint)
# return qDeriv
return Zero()
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import SimPEG
import numpy as np
from SimPEG.Utils import Zero, closestPoints
class BaseRx(SimPEG.Survey.BaseRx):
locs = None
rxType = None
knownRxTypes = {
'phi':['phi',None],
'ex':['e','x'],
'ey':['e','y'],
'ez':['e','z'],
'jx':['j','x'],
'jy':['j','y'],
'jz':['j','z'],
}
def __init__(self, locs, rxType, **kwargs):
SimPEG.Survey.BaseRx.__init__(self, locs, rxType, **kwargs)
@property
def projField(self):
"""Field Type projection (e.g. e b ...)"""
return self.knownRxTypes[self.rxType][0]
def projGLoc(self, f):
"""Grid Location projection (e.g. Ex Fy ...)"""
comp = self.knownRxTypes[self.rxType][1]
if comp is not None:
return f._GLoc(self.rxType) + comp
return f._GLoc(self.rxType)
def eval(self, src, mesh, f):
P = self.getP(mesh, self.projGLoc(f))
return P*f[src, self.projField]
def evalDeriv(self, src, mesh, f, v, adjoint=False):
P = self.getP(mesh, self.projGLoc(f))
if not adjoint:
return P*v
elif adjoint:
return P.T*v
# DC.Rx.Dipole(locs)
class Dipole(BaseRx):
def __init__(self, locsM, locsN, rxType = 'phi', **kwargs):
assert locsM.shape == locsN.shape, 'locsM and locsN need to be the same size'
locs = [locsM, locsN]
# We may not need this ...
BaseRx.__init__(self, locs, rxType)
@property
def nD(self):
"""Number of data in the receiver."""
return self.locs[0].shape[0]
# Not sure why ...
# return int(self.locs[0].size / 2)
def getP(self, mesh, Gloc):
if mesh in self._Ps:
return self._Ps[mesh]
P0 = mesh.getInterpolationMat(self.locs[0], Gloc)
P1 = mesh.getInterpolationMat(self.locs[1], Gloc)
P = P0 - P1
if self.storeProjections:
self._Ps[mesh] = P
return P
class Dipole_ky(BaseRx):
def __init__(self, locsM, locsN, rxType = 'phi', **kwargs):
assert locsM.shape == locsN.shape, 'locsM and locsN need to be the same size'
locs = [locsM, locsN]
# We may not need this ...
BaseRx.__init__(self, locs, rxType)
@property
def nD(self):
"""Number of data in the receiver."""
return self.locs[0].shape[0]
# Not sure why ...
# return int(self.locs[0].size / 2)
def getP(self, mesh, Gloc):
if mesh in self._Ps:
return self._Ps[mesh]
P0 = mesh.getInterpolationMat(self.locs[0], Gloc)
P1 = mesh.getInterpolationMat(self.locs[1], Gloc)
P = P0 - P1
if self.storeProjections:
self._Ps[mesh] = P
return P
def eval(self, kys, src, mesh, f):
P = self.getP(mesh, self.projGLoc(f))
Pf = P*f[src, self.projField,:]
return self.IntTrapezoidal(kys, Pf, y=0.)
def evalDeriv(self, ky, src, mesh, f, v, adjoint=False):
P = self.getP(mesh, self.projGLoc(f))
if not adjoint:
return P*v
elif adjoint:
return P.T*v
def IntTrapezoidal(self, kys, Pf, y=0.):
phi = np.zeros(Pf.shape[0])
nky = kys.size
dky = np.diff(kys)
dky = np.r_[dky[0], dky]
phi0 = 1./np.pi*Pf[:,0]
for iky in range(nky):
phi1 = 1./np.pi*Pf[:,iky]
phi += phi1*dky[iky]/2.*np.cos(kys[iky]*y)
phi += phi0*dky[iky]/2.*np.cos(kys[iky]*y)
phi0 = phi1.copy()
return phi
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import SimPEG
# from SimPEG.EM.Base import BaseEMSurvey
from SimPEG.Utils import Zero, closestPoints, mkvc
import numpy as np
class BaseSrc(SimPEG.Survey.BaseSrc):
current = 1.0
loc = None
def __init__(self, rxList, **kwargs):
SimPEG.Survey.BaseSrc.__init__(self, rxList, **kwargs)
def eval(self, prob):
raise NotImplementedError
def evalDeriv(self, prob):
return Zero()
class Dipole(BaseSrc):
def __init__(self, rxList, locA, locB, **kwargs):
assert locA.shape == locB.shape, 'Shape of locA and locB should be the same'
self.loc = [locA, locB]
BaseSrc.__init__(self, rxList, **kwargs)
def eval(self, prob):
if prob._formulation == 'HJ':
inds = closestPoints(prob.mesh, self.loc, gridLoc='CC')
q = np.zeros(prob.mesh.nC)
q[inds] = self.current * np.r_[1., -1.]
elif prob._formulation == 'EB':
qa = prob.mesh.getInterpolationMat(self.loc[0], locType='N').todense()
qb = -prob.mesh.getInterpolationMat(self.loc[1], locType='N').todense()
q = self.current * mkvc(qa+qb)
return q
class Pole(BaseSrc):
def __init__(self, rxList, loc, **kwargs):
BaseSrc.__init__(self, rxList, loc=loc, **kwargs)
def eval(self, prob):
if prob._formulation == 'HJ':
inds = closestPoints(prob.mesh, self.loc)
q = np.zeros(prob.mesh.nC)
q[inds] = self.current * np.r_[1.]
elif prob._formulation == 'EB':
q = prob.mesh.getInterpolationMat(self.loc, locType='N').todense()
q = self.current * mkvc(q)
return q
# class Dipole_ky(BaseSrc):
# def __init__(self, rxList, locA, locB, **kwargs):
# assert locA.shape == locB.shape, 'Shape of locA and locB should be the same'
# self.loc = [locA[[0,2]], locB[[0,2]]]
# BaseSrc.__init__(self, rxList, **kwargs)
# def eval(self, prob):
# if prob._formulation == 'HJ':
# inds = closestPoints(prob.mesh, self.loc, gridLoc='CC')
# q = np.zeros(prob.mesh.nC)
# q[inds] = self.current * np.r_[1., -1.]
# elif prob._formulation == 'EB':
# qa = prob.mesh.getInterpolationMat(self.loc[0], locType='N').todense()
# qb = -prob.mesh.getInterpolationMat(self.loc[1], locType='N').todense()
# q = self.current * mkvc(qa+qb)
# return q
# class Pole_ky(BaseSrc):
# def __init__(self, rxList, loc, **kwargs):
# BaseSrc.__init__(self, rxList, loc=loc, **kwargs)
# def eval(self, prob):
# if prob._formulation == 'HJ':
# inds = closestPoints(prob.mesh, self.loc[[0,2]])
# q = np.zeros(prob.mesh.nC)
# q[inds] = self.current * np.r_[1.]
# elif prob._formulation == 'EB':
# q = prob.mesh.getInterpolationMat(self.loc[[0,2]], locType='N').todense()
# q = self.current * mkvc(q)
# return q
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import SimPEG
from SimPEG.EM.Base import BaseEMSurvey
from SimPEG import sp, Survey
from SimPEG.Utils import Zero, Identity
from RxDC import BaseRx
from SrcDC import BaseSrc
class Survey(BaseEMSurvey):
rxPair = BaseRx
srcPair = BaseSrc
def __init__(self, srcList, **kwargs):
self.srcList = srcList
BaseEMSurvey.__init__(self, srcList, **kwargs)
class Survey_ky(BaseEMSurvey):
rxPair = BaseRx
srcPair = BaseSrc
def __init__(self, srcList, **kwargs):
self.srcList = srcList
BaseEMSurvey.__init__(self, srcList, **kwargs)
def eval(self, f):
"""
Project fields to receiver locations
:param Fields u: fields object
:rtype: numpy.ndarray
:return: data
"""
data = SimPEG.Survey.Data(self)
kys = self.prob.kys
for src in self.srcList:
for rx in src.rxList:
data[src, rx] = rx.eval(kys, src, self.mesh, f)
return data
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import numpy as np
def WennerSrcList(nElecs, aSpacing, in2D=False, plotIt=False):
import SimPEG.EM.Static.DC as DC
elocs = np.arange(0,aSpacing*nElecs,aSpacing)
elocs -= (nElecs*aSpacing - aSpacing)/2
space = 1
WENNER = np.zeros((0,),dtype=int)
for ii in range(nElecs):
for jj in range(nElecs):
test = np.r_[jj,jj+space,jj+space*2,jj+space*3]
if np.any(test >= nElecs):
break
WENNER = np.r_[WENNER, test]
space += 1
WENNER = WENNER.reshape((-1,4))
if plotIt:
for i, s in enumerate('rbkg'):
plt.plot(elocs[WENNER[:,i]],s+'.')
plt.show()
# Create sources and receivers
i = 0
if in2D:
getLoc = lambda ii, abmn: np.r_[elocs[WENNER[ii,abmn]],0]
else:
getLoc = lambda ii, abmn: np.r_[elocs[WENNER[ii,abmn]],0, 0]
srcList = []
for i in range(WENNER.shape[0]):
rx = DC.Rx.Dipole(getLoc(i,1).reshape([1,-1]),getLoc(i,2).reshape([1,-1]))
src = DC.Src.Dipole([rx], getLoc(i,0),getLoc(i,3))
srcList += [src]
return srcList
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from ProblemDC import Problem3D_CC, Problem3D_N
from ProblemDC_2D import Problem2D_CC, Problem2D_N
from SurveyDC import Survey, Survey_ky
import SrcDC as Src #Pole
import RxDC as Rx
from FieldsDC import Fields_CC
from BoundaryUtils import getxBCyBC_CC
import Utils
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from SimPEG import Problem, Utils, Maps, Mesh
from SimPEG.EM.Base import BaseEMProblem
from SimPEG.EM.Static.DC.FieldsDC import Fields, Fields_CC, Fields_N
from SimPEG.Utils import sdiag
import numpy as np
from SimPEG.Utils import Zero
from SimPEG.EM.Static.DC import getxBCyBC_CC
from SurveyIP import Survey
class IPPropMap(Maps.PropMap):
"""
Property Map for IP Problems. The electrical chargeability,
(\\(\\eta\\)) is the default inversion property
"""
eta = Maps.Property("Electrical Chargeability", defaultInvProp = True)
class BaseIPProblem(BaseEMProblem):
surveyPair = Survey
fieldsPair = Fields
PropMap = IPPropMap
Ainv = None
sigma = None
rho = None
f = None
Ainv = None
def fields(self, m):
self.curModel = m
if self.f is None:
self.f = self.fieldsPair(self.mesh, self.survey)
if self.Ainv == None:
A = self.getA()
self.Ainv = self.Solver(A, **self.solverOpts)
RHS = self.getRHS()
u = self.Ainv * RHS
Srcs = self.survey.srcList
self.f[Srcs, self._solutionType] = u
return self.f
def Jvec(self, m, v, f=None):
if f is None:
f = self.fields(m)
self.curModel = m
Jv = self.dataPair(self.survey) #same size as the data
A = self.getA()
for src in self.survey.srcList:
u_src = f[src, self._solutionType] # solution vector
dA_dm_v = self.getADeriv(u_src, v)
dRHS_dm_v = self.getRHSDeriv(src, v)
du_dm_v = self.Ainv * ( - dA_dm_v + dRHS_dm_v )
for rx in src.rxList:
df_dmFun = getattr(f, '_%sDeriv'%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)
# Conductivity (d u / d log sigma)
if self._formulation is 'EB':
return -Utils.mkvc(Jv)
# Conductivity (d u / d log rho)
if self._formulation is 'HJ':
return Utils.mkvc(Jv)
def Jtvec(self, m, v, f=None):
if f is None:
f = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
AT = self.getA()
for src in self.survey.srcList:
u_src = f[src, self._solutionType]
for rx in src.rxList:
PTv = rx.evalDeriv(src, self.mesh, f, v[src, rx], adjoint=True) # wrt f, need possibility wrt m
df_duTFun = getattr(f, '_%sDeriv'%rx.projField, None)
df_duT, df_dmT = df_duTFun(src, None, PTv, adjoint=True)
ATinvdf_duT = self.Ainv * df_duT
dA_dmT = self.getADeriv(u_src, ATinvdf_duT, adjoint=True)
dRHS_dmT = self.getRHSDeriv(src, ATinvdf_duT, adjoint=True)
du_dmT = -dA_dmT + dRHS_dmT
Jtv += (df_dmT + du_dmT).astype(float)
# Conductivity ((d u / d log sigma).T)
if self._formulation is 'EB':
return -Utils.mkvc(Jtv)
# Conductivity ((d u / d log rho).T)
if self._formulation is 'HJ':
return Utils.mkvc(Jtv)
def getSourceTerm(self):
"""
takes concept of source and turns it into a matrix
"""
"""
Evaluates the sources, and puts them in matrix form
:rtype: (numpy.ndarray, numpy.ndarray)
:return: q (nC or nN, nSrc)
"""
Srcs = self.survey.srcList
if self._formulation is 'EB':
n = self.mesh.nN
# return NotImplementedError
elif self._formulation is 'HJ':
n = self.mesh.nC
q = np.zeros((n, len(Srcs)))
for i, src in enumerate(Srcs):
q[:,i] = src.eval(self)
return q
@property
def deleteTheseOnModelUpdate(self):
toDelete = []
return toDelete
# assume log rho or log cond
@property
def MeSigma(self):
"""
Edge inner product matrix for \\(\\sigma\\). Used in the E-B formulation
"""
if getattr(self, '_MeSigma', None) is None:
self._MeSigma = self.mesh.getEdgeInnerProduct(self.sigma)
return self._MeSigma
@property
def MfRhoI(self):
"""
Inverse of :code:`MfRho`
"""
if getattr(self, '_MfRhoI', None) is None:
self._MfRhoI = self.mesh.getFaceInnerProduct(self.rho, invMat=True)
return self._MfRhoI
def MfRhoIDeriv(self,u):
"""
Derivative of :code:`MfRhoI` with respect to the model.
"""
dMfRhoI_dI = -self.MfRhoI**2
dMf_drho = self.mesh.getFaceInnerProductDeriv(self.rho)(u)
drho_dlogrho = Utils.sdiag(self.rho)*self.curModel.etaDeriv
return dMfRhoI_dI * ( dMf_drho * ( drho_dlogrho))
# TODO: This should take a vector
def MeSigmaDeriv(self, u):
"""
Derivative of MeSigma with respect to the model
"""
dsigma_dlogsigma = Utils.sdiag(self.sigma)*self.curModel.etaDeriv
return self.mesh.getEdgeInnerProductDeriv(self.sigma)(u) * dsigma_dlogsigma
class Problem3D_CC(BaseIPProblem):
_solutionType = 'phiSolution'
_formulation = 'HJ' # CC potentials means J is on faces
fieldsPair = Fields_CC
def __init__(self, mesh, **kwargs):
BaseIPProblem.__init__(self, mesh, **kwargs)
self.setBC()
def getA(self):
"""
Make the A matrix for the cell centered DC resistivity problem
A = D MfRhoI G
"""
D = self.Div
G = self.Grad
MfRhoI = self.MfRhoI
A = D * MfRhoI * G
# I think we should deprecate this for DC problem.
# if self._makeASymmetric is True:
# return V.T * A
return A
def getADeriv(self, u, v, adjoint= False):
D = self.Div
G = self.Grad
MfRhoIDeriv = self.MfRhoIDeriv
if adjoint:
# if self._makeASymmetric is True:
# v = V * v
return(MfRhoIDeriv( G * u ).T) * ( D.T * v)
# I think we should deprecate this for DC problem.
# if self._makeASymmetric is True:
# return V.T * ( D * ( MfRhoIDeriv( D.T * ( V * u ) ) * v ) )
return D * (MfRhoIDeriv( G * u ) * v)
def getRHS(self):
"""
RHS for the DC problem
q
"""
RHS = self.getSourceTerm()
# I think we should deprecate this for DC problem.
# if self._makeASymmetric is True:
# return self.Vol.T * RHS
return RHS
def getRHSDeriv(self, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
"""
# TODO: add qDeriv for RHS depending on m
# qDeriv = src.evalDeriv(self, adjoint=adjoint)
# return qDeriv
return Zero()
def setBC(self):
if self.mesh.dim==3:
fxm,fxp,fym,fyp,fzm,fzp = self.mesh.faceBoundaryInd
gBFxm = self.mesh.gridFx[fxm,:]
gBFxp = self.mesh.gridFx[fxp,:]
gBFym = self.mesh.gridFy[fym,:]
gBFyp = self.mesh.gridFy[fyp,:]
gBFzm = self.mesh.gridFz[fzm,:]
gBFzp = self.mesh.gridFz[fzp,:]
# Setup Mixed B.C (alpha, beta, gamma)
temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
temp_zm, temp_zp = np.ones_like(gBFzm[:,2]), np.ones_like(gBFzp[:,2])
alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.
alpha_zm, alpha_zp = temp_zm*0., temp_zp*0.
beta_xm, beta_xp = temp_xm, temp_xp
beta_ym, beta_yp = temp_ym, temp_yp
beta_zm, beta_zp = temp_zm, temp_zp
gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.
gamma_zm, gamma_zp = temp_zm*0., temp_zp*0.
alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp, alpha_zm, alpha_zp]
beta = [beta_xm, beta_xp, beta_ym, beta_yp, beta_zm, beta_zp]
gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp, gamma_zm, gamma_zp]
elif self.mesh.dim==2:
fxm,fxp,fym,fyp = self.mesh.faceBoundaryInd
gBFxm = self.mesh.gridFx[fxm,:]
gBFxp = self.mesh.gridFx[fxp,:]
gBFym = self.mesh.gridFy[fym,:]
gBFyp = self.mesh.gridFy[fyp,:]
# Setup Mixed B.C (alpha, beta, gamma)
temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.
beta_xm, beta_xp = temp_xm, temp_xp
beta_ym, beta_yp = temp_ym, temp_yp
gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.
alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp]
beta = [beta_xm, beta_xp, beta_ym, beta_yp]
gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp]
x_BC, y_BC = getxBCyBC_CC(self.mesh, alpha, beta, gamma)
V = self.Vol
self.Div = V * self.mesh.faceDiv
P_BC, B = self.mesh.getBCProjWF_simple()
M = B*self.mesh.aveCC2F
self.Grad = self.Div.T - P_BC*Utils.sdiag(y_BC)*M
class Problem3D_N(BaseIPProblem):
_solutionType = 'phiSolution'
_formulation = 'EB' # N potentials means B is on faces
fieldsPair = Fields_N
def __init__(self, mesh, **kwargs):
BaseIPProblem.__init__(self, mesh, **kwargs)
def getA(self):
"""
Make the A matrix for the cell centered DC resistivity problem
A = G.T MeSigma G
"""
MeSigma = self.MeSigma
Grad = self.mesh.nodalGrad
A = Grad.T * MeSigma * Grad
# Handling Null space of A
A[0,0] = A[0,0] + 1.
return A
def getADeriv(self, u, v, adjoint=False):
"""
Product of the derivative of our system matrix with respect to the model and a vector
"""
MeSigma = self.MeSigma
Grad = self.mesh.nodalGrad
if not adjoint:
return Grad.T*(self.MeSigmaDeriv(Grad*u)*v)
elif adjoint:
return self.MeSigmaDeriv(Grad*u).T * (Grad*v)
def getRHS(self):
"""
RHS for the DC problem
q
"""
RHS = self.getSourceTerm()
return RHS
def getRHSDeriv(self, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
"""
# TODO: add qDeriv for RHS depending on m
# qDeriv = src.evalDeriv(self, adjoint=adjoint)
# return qDeriv
return Zero()
if __name__ == '__main__':
cs = 12.5
hx = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
hy = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
hz = [(cs,7, -1.3),(cs,20)]
mesh = Mesh.TensorMesh([hx, hy, hz],x0="CCN")
sigma = np.ones(mesh.nC)
prob = BaseIPProblem(mesh, sigma=sigma)
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import SimPEG
from SimPEG.EM.Base import BaseEMSurvey
from SimPEG import sp, Survey
from SimPEG.Utils import Zero, Identity
from SimPEG.EM.Static.DC.SrcDC import BaseSrc
from SimPEG.EM.Static.DC.RxDC import BaseRx
class Survey(BaseEMSurvey):
rxPair = BaseRx
srcPair = BaseSrc
def __init__(self, srcList, **kwargs):
self.srcList = srcList
BaseEMSurvey.__init__(self, srcList, **kwargs)
def dpred(self, m, f=None):
"""
Predicted data.
.. math::
d_\\text{pred} = Pf(m)
"""
return self.prob.Jvec(m, m, f=f)
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from ProblemIP import Problem3D_CC, Problem3D_N
from SurveyIP import Survey
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from SimPEG import Problem, Utils, Maps, Mesh
from SimPEG.EM.Base import BaseEMProblem
from SimPEG.EM.Static.DC.FieldsDC import Fields, Fields_CC, Fields_N
from SimPEG.Utils import sdiag
import numpy as np
from SimPEG.Utils import Zero
from SimPEG.EM.Static.DC import getxBCyBC_CC
from SurveySIP import Survey, Data
class ColeColePropMap(Maps.PropMap):
"""
Property Map for EM Problems. The electrical conductivity (\\(\\sigma\\)) is the default inversion property, and the default value of the magnetic permeability is that of free space (\\(\\mu = 4\\pi\\times 10^{-7} \\) H/m)
"""
eta = Maps.Property("Electrical Conductivity", defaultInvProp=True)
tau = Maps.Property("Electrical Conductivity", defaultVal=0.1, propertyLink=('taui', Maps.ReciprocalMap))
taui = Maps.Property("Electrical Conductivity", defaultVal=1., propertyLink=('tau', Maps.ReciprocalMap))
c = Maps.Property("Electrical Conductivity", defaultVal=1.)
class BaseSIPProblem(BaseEMProblem):
surveyPair = Survey
fieldsPair = Fields
dataPair = Data
PropMap = ColeColePropMap
Ainv = None
sigma = None
rho = None
f = None
Ainv = None
def DebyeTime(self, t):
peta = self.curModel.eta*np.exp(-self.curModel.taui*t)
return peta
def EtaDeriv(self, t, v, adjoint=False):
v = np.array(v, dtype=float)
if adjoint:
return self.curModel.etaDeriv.T * (np.exp(-self.curModel.taui*t)*v)
else:
return np.exp(-self.curModel.taui*t) * (self.curModel.etaDeriv*v)
def TauiDeriv(self, t, v, adjoint=False):
v = np.array(v, dtype=float)
if adjoint:
return -self.curModel.tauiDeriv.T * (self.curModel.eta*t*np.exp(-self.curModel.taui*t)*v)
else:
return -self.curModel.eta*t*np.exp(-self.curModel.taui*t) * (self.curModel.tauiDeriv*v)
def fields(self, m):
self.curModel = m
if self.f is None:
self.f = self.fieldsPair(self.mesh, self.survey)
if self.Ainv == None:
A = self.getA()
self.Ainv = self.Solver(A, **self.solverOpts)
RHS = self.getRHS()
u = self.Ainv * RHS
Srcs = self.survey.srcList
self.f[Srcs, self._solutionType] = u
return self.f
def forward(self, m, f=None):
if f is None:
f = self.fields(m)
self.curModel = m
Jv = self.dataPair(self.survey) #same size as the data
# A = self.getA()
JvAll = []
for tind in range(len(self.survey.times)):
#Pseudo-chareability
t = self.survey.times[tind]
v = self.DebyeTime(t)
for src in self.survey.srcList:
u_src = f[src, self._solutionType] # solution vector
dA_dm_v = self.getADeriv(u_src, v)
dRHS_dm_v = self.getRHSDeriv(src, v)
du_dm_v = self.Ainv * ( - dA_dm_v + dRHS_dm_v )
for rx in src.rxList:
timeindex = rx.getTimeP(self.survey.times)
if timeindex[tind]:
df_dmFun = getattr(f, '_%sDeriv'%rx.projField, None)
df_dm_v = df_dmFun(src, du_dm_v, v, adjoint=False)
Jv[src, rx, t] = rx.evalDeriv(src, self.mesh, f, df_dm_v)
# Conductivity (d u / d log sigma)
if self._formulation is 'EB':
return -Utils.mkvc(Jv)
# Resistivity (d u / d log rho)
if self._formulation is 'HJ':
return Utils.mkvc(Jv)
def Jvec(self, m, v, f=None):
if f is None:
f = self.fields(m)
self.curModel = m
Jv = self.dataPair(self.survey) #same size as the data
# A = self.getA()
JvAll = []
#Assume only eta and tau (eta first then tau)
# v = [2*Mx1]
v = v.reshape((int(v.size/2), 2), order='F')
for tind in range(len(self.survey.times)):
t = self.survey.times[tind]
v0 = self.EtaDeriv(t, v[:,0])
v1 = self.TauiDeriv(t, v[:,1])
for src in self.survey.srcList:
u_src = f[src, self._solutionType] # solution vector
dA_dm_v0 = self.getADeriv(u_src, v0)
dRHS_dm_v0 = self.getRHSDeriv(src, v0)
du_dm_v0 = self.Ainv * ( - dA_dm_v0 + dRHS_dm_v0 )
dA_dm_v1 = self.getADeriv(u_src, v1)
dRHS_dm_v1 = self.getRHSDeriv(src, v1)
du_dm_v1 = self.Ainv * ( - dA_dm_v1 + dRHS_dm_v1 )
for rx in src.rxList:
timeindex = rx.getTimeP(self.survey.times)
if timeindex[tind]:
df_dmFun = getattr(f, '_%sDeriv'%rx.projField, None)
df_dm_v0 = df_dmFun(src, du_dm_v0, v0, adjoint=False)
df_dm_v1 = df_dmFun(src, du_dm_v1, v1, adjoint=False)
Jv[src, rx, t] = rx.evalDeriv(src, self.mesh, f, df_dm_v0)
Jv[src, rx, t] += rx.evalDeriv(src, self.mesh, f, df_dm_v1)
# Conductivity (d u / d log sigma)
if self._formulation is 'EB':
return -Jv.tovec()
# Resistivity (d u / d log rho)
if self._formulation is 'HJ':
return Jv.tovec()
def Jtvec(self, m, v, f=None):
if f is None:
f = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv= np.zeros(m.size)
for tind in range(len(self.survey.times)):
t = self.survey.times[tind]
for src in self.survey.srcList:
u_src = f[src, self._solutionType]
for rx in src.rxList:
timeindex = rx.getTimeP(self.survey.times)
if timeindex[tind]:
PTv = rx.evalDeriv(src, self.mesh, f, v[src, rx, t], adjoint=True) # wrt f, need possibility wrt m
df_duTFun = getattr(f, '_%sDeriv'%rx.projField, None)
df_duT, df_dmT = df_duTFun(src, None, PTv, adjoint=True)
ATinvdf_duT = self.Ainv * df_duT
dA_dmT = self.getADeriv(u_src, ATinvdf_duT, adjoint=True)
dRHS_dmT = self.getRHSDeriv(src, ATinvdf_duT, adjoint=True)
du_dmT = -dA_dmT + dRHS_dmT
Jtv += np.r_[self.EtaDeriv(self.survey.times[tind], du_dmT, adjoint=True), self.TauiDeriv(self.survey.times[tind], du_dmT, adjoint=True)]
# Conductivity ((d u / d log sigma).T)
if self._formulation is 'EB':
return -Jtv
# Conductivity ((d u / d log rho).T)
if self._formulation is 'HJ':
return Jtv
def getSourceTerm(self):
"""
takes concept of source and turns it into a matrix
"""
"""
Evaluates the sources, and puts them in matrix form
:rtype: (numpy.ndarray, numpy.ndarray)
:return: q (nC or nN, nSrc)
"""
Srcs = self.survey.srcList
if self._formulation is 'EB':
n = self.mesh.nN
# return NotImplementedError
elif self._formulation is 'HJ':
n = self.mesh.nC
q = np.zeros((n, len(Srcs)))
for i, src in enumerate(Srcs):
q[:,i] = src.eval(self)
return q
@property
def deleteTheseOnModelUpdate(self):
toDelete = []
return toDelete
# assume log rho or log cond
@property
def MeSigma(self):
"""
Edge inner product matrix for \\(\\sigma\\). Used in the E-B formulation
"""
if getattr(self, '_MeSigma', None) is None:
self._MeSigma = self.mesh.getEdgeInnerProduct(self.sigma)
return self._MeSigma
@property
def MfRhoI(self):
"""
Inverse of :code:`MfRho`
"""
if getattr(self, '_MfRhoI', None) is None:
self._MfRhoI = self.mesh.getFaceInnerProduct(self.rho, invMat=True)
return self._MfRhoI
def MfRhoIDeriv(self,u):
"""
Derivative of :code:`MfRhoI` with respect to the model.
"""
dMfRhoI_dI = -self.MfRhoI**2
dMf_drho = self.mesh.getFaceInnerProductDeriv(self.rho)(u)
drho_dlogrho = Utils.sdiag(self.rho)
return dMfRhoI_dI * ( dMf_drho * ( drho_dlogrho))
# TODO: This should take a vector
def MeSigmaDeriv(self, u):
"""
Derivative of MeSigma with respect to the model
"""
dsigma_dlogsigma = Utils.sdiag(self.sigma)
return self.mesh.getEdgeInnerProductDeriv(self.sigma)(u) * dsigma_dlogsigma
class Problem3D_CC(BaseSIPProblem):
_solutionType = 'phiSolution'
_formulation = 'HJ' # CC potentials means J is on faces
fieldsPair = Fields_CC
def __init__(self, mesh, **kwargs):
BaseSIPProblem.__init__(self, mesh, **kwargs)
self.setBC()
def getA(self):
"""
Make the A matrix for the cell centered DC resistivity problem
A = D MfRhoI G
"""
D = self.Div
G = self.Grad
# TODO: this won't work for full anisotropy
MfRhoI = self.MfRhoI
A = D * MfRhoI * G
# I think we should deprecate this for DC problem.
# if self._makeASymmetric is True:
# return V.T * A
return A
def getADeriv(self, u, v, adjoint= False):
D = self.Div
G = self.Grad
MfRhoIDeriv = self.MfRhoIDeriv
if adjoint:
# if self._makeASymmetric is True:
# v = V * v
return(MfRhoIDeriv( G * u ).T) * ( D.T * v)
# I think we should deprecate this for DC problem.
# if self._makeASymmetric is True:
# return V.T * ( D * ( MfRhoIDeriv( D.T * ( V * u ) ) * v ) )
return D * (MfRhoIDeriv( G * u ) * v)
def getRHS(self):
"""
RHS for the DC problem
q
"""
RHS = self.getSourceTerm()
# I think we should deprecate this for DC problem.
# if self._makeASymmetric is True:
# return self.Vol.T * RHS
return RHS
def getRHSDeriv(self, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
"""
# TODO: add qDeriv for RHS depending on m
# qDeriv = src.evalDeriv(self, adjoint=adjoint)
# return qDeriv
return Zero()
def setBC(self):
if self.mesh.dim==3:
fxm,fxp,fym,fyp,fzm,fzp = self.mesh.faceBoundaryInd
gBFxm = self.mesh.gridFx[fxm,:]
gBFxp = self.mesh.gridFx[fxp,:]
gBFym = self.mesh.gridFy[fym,:]
gBFyp = self.mesh.gridFy[fyp,:]
gBFzm = self.mesh.gridFz[fzm,:]
gBFzp = self.mesh.gridFz[fzp,:]
# Setup Mixed B.C (alpha, beta, gamma)
temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
temp_zm, temp_zp = np.ones_like(gBFzm[:,2]), np.ones_like(gBFzp[:,2])
alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.
alpha_zm, alpha_zp = temp_zm*0., temp_zp*0.
beta_xm, beta_xp = temp_xm, temp_xp
beta_ym, beta_yp = temp_ym, temp_yp
beta_zm, beta_zp = temp_zm, temp_zp
gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.
gamma_zm, gamma_zp = temp_zm*0., temp_zp*0.
alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp, alpha_zm, alpha_zp]
beta = [beta_xm, beta_xp, beta_ym, beta_yp, beta_zm, beta_zp]
gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp, gamma_zm, gamma_zp]
elif self.mesh.dim==2:
fxm,fxp,fym,fyp = self.mesh.faceBoundaryInd
gBFxm = self.mesh.gridFx[fxm,:]
gBFxp = self.mesh.gridFx[fxp,:]
gBFym = self.mesh.gridFy[fym,:]
gBFyp = self.mesh.gridFy[fyp,:]
# Setup Mixed B.C (alpha, beta, gamma)
temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.
beta_xm, beta_xp = temp_xm, temp_xp
beta_ym, beta_yp = temp_ym, temp_yp
gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.
alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp]
beta = [beta_xm, beta_xp, beta_ym, beta_yp]
gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp]
x_BC, y_BC = getxBCyBC_CC(self.mesh, alpha, beta, gamma)
V = self.Vol
self.Div = V * self.mesh.faceDiv
P_BC, B = self.mesh.getBCProjWF_simple()
M = B*self.mesh.aveCC2F
self.Grad = self.Div.T - P_BC*Utils.sdiag(y_BC)*M
class Problem3D_N(BaseSIPProblem):
_solutionType = 'phiSolution'
_formulation = 'EB' # N potentials means B is on faces
fieldsPair = Fields_N
def __init__(self, mesh, **kwargs):
BaseSIPProblem.__init__(self, mesh, **kwargs)
def getA(self):
"""
Make the A matrix for the cell centered DC resistivity problem
A = G.T MeSigma G
"""
# TODO: this won't work for full anisotropy
MeSigma = self.MeSigma
Grad = self.mesh.nodalGrad
A = Grad.T * MeSigma * Grad
# Handling Null space of A
A[0,0] = A[0,0] + 1.
return A
def getADeriv(self, u, v, adjoint=False):
"""
Product of the derivative of our system matrix with respect to the model and a vector
"""
MeSigma = self.MeSigma
Grad = self.mesh.nodalGrad
if not adjoint:
return Grad.T*(self.MeSigmaDeriv(Grad*u)*v)
elif adjoint:
return self.MeSigmaDeriv(Grad*u).T * (Grad*v)
def getRHS(self):
"""
RHS for the DC problem
q
"""
RHS = self.getSourceTerm()
return RHS
def getRHSDeriv(self, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
"""
# TODO: add qDeriv for RHS depending on m
# qDeriv = src.evalDeriv(self, adjoint=adjoint)
# return qDeriv
return Zero()
if __name__ == '__main__':
cs = 12.5
hx = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
hy = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
hz = [(cs,7, -1.3),(cs,20)]
mesh = Mesh.TensorMesh([hx, hy, hz],x0="CCN")
sigma = np.ones(mesh.nC)
prob = BaseSIPProblem(mesh, sigma=sigma)
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from SimPEG import Utils, Maps, Mesh, sp, np
from SimPEG.Regularization import BaseRegularization, Simple
class MultiRegularization(Simple):
"""
**MultiRegularization Class**
This is used to regularize the model space
having multiple models [m1, m2, m3, ...] ::
reg = Regularization(mesh)
"""
nModels = None # Number of models
ratios = None # Ratio for different models
crossgrad = False # Use cross gradient or not
betacross = 1.
wx = []
wy = []
wz = []
def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
if self.nModels == None:
raise Exception("Put nModels as a initial input!")
if self.ratios == None:
self.ratios = [1. for imodel in range(self.nModels)]
@property
def Wsmall(self):
"""Regularization matrix Wsmall"""
if getattr(self,'_Wsmall', None) is None:
vecs = []
for imodel in range(self.nModels):
vecs.append((self.regmesh.vol*self.alpha_s*self.wght*self.ratios[imodel])**0.5)
self._Wsmall = Utils.sdiag(np.hstack(vecs))
return self._Wsmall
@property
def Wx(self):
"""Regularization matrix Wx"""
if getattr(self, '_Wx', None) is None:
mats = []
for imodel in range(self.nModels):
self.wx.append(Utils.sdiag((self.regmesh.aveCC2Fx * self.regmesh.vol*self.alpha_x*self.ratios[imodel]*(self.regmesh.aveCC2Fx*self.wght))**0.5))
mats.append(self.wx[imodel]*self.regmesh.cellDiffxStencil)
self._Wx = sp.block_diag(mats)
return self._Wx
@property
def Wy(self):
"""Regularization matrix Wy"""
if getattr(self, '_Wy', None) is None:
mats = []
for imodel in range(self.nModels):
self.wy.append(Utils.sdiag((self.regmesh.aveCC2Fy * self.regmesh.vol*self.alpha_y*self.ratios[imodel]*(self.regmesh.aveCC2Fy*self.wght))**0.5))
mats.append(self.wy[imodel]*self.regmesh.cellDiffyStencil)
self._Wy = sp.block_diag(mats)
return self._Wy
@property
def Wz(self):
"""Regularization matrix Wz"""
if getattr(self, '_Wz', None) is None:
mats = []
for imodel in range(self.nModels):
self.wz.append(Utils.sdiag((self.regmesh.aveCC2Fz * self.regmesh.vol*self.alpha_z*self.ratios[imodel]*(self.regmesh.aveCC2Fz*self.wght))**0.5))
mats.append(self.wz[imodel]*self.regmesh.cellDiffzStencil)
self._Wz = sp.block_diag(mats)
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 eval(self, m):
return self._evalSmall(m) + self._evalSmooth(m)
@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)
def cross(a,b):
ax, ay, az = a[0], a[1], a[2]
bx, by, bz = b[0], b[1], b[2]
cx = ay*bz - az*by
cy = az*bx - ax*bz
cz = ax*by - ay*bx
return [cx, cy, cz]
# TODO: Implement Cross Gradients..
@Utils.timeIt
def _evalCross(self, m):
if self.crossgrad == False:
return 0.
elif self.crossgrad == True:
M = (self.mapping * m).reshape((self.regmesh.nC, self.nModels), order="F")
ax = self.regmesh.aveFx2CC*self.regmesh.wx[0]*M[:,0]
ay = self.regmesh.aveFy2CC*self.regmesh.wy[0]*M[:,0]
az = self.regmesh.aveFz2CC*self.regmesh.wz[0]*M[:,0]
bx = self.regmesh.aveFx2CC*self.regmesh.wx[1]*M[:,1]
by = self.regmesh.aveFy2CC*self.regmesh.wy[1]*M[:,1]
bz = self.regmesh.aveFz2CC*self.regmesh.wz[1]*M[:,1]
#ab
out_ab = cross([ax, ay, az], [bx, by, bz])
r = np.r_[out_ab[0], out_ab[1], out_ab[2]]*np.sqrt(self.betacross)
if self.nModels == 3:
cx = self.regmesh.aveFx2CC*self.regmesh.wx[1]*M[:,1]
cy = self.regmesh.aveFy2CC*self.regmesh.wy[1]*M[:,1]
cz = self.regmesh.aveFz2CC*self.regmesh.wz[1]*M[:,1]
#ac
out_ac = cross([ax, ay, az], [cx, cy, cz])
#bc
out_bc = cross([bx, by, bz], [cx, cy, cz])
r = np.r_[r, np.hstack(out_ac)*np.sqrt(self.betacross), np.hstack(out_bc)*np.sqrt(self.betacross)]
return 0.5 * r.dot(r)
@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})}
"""
deriv = self._evalSmallDeriv(m) + self._evalSmoothDeriv(m)
if self.crossgrad==True:
deriv += self._evalCrossDeriv(m)
return deriv
@Utils.timeIt
def _evalCrossDeriv(self,m):
r = self.Wsmall * ( self.mapping * (m - self.mref) )
return r.T * ( self.Wsmall * self.mapping.deriv(m - self.mref) )
@Utils.timeIt
def eval2Deriv(self, m, v=None):
"""
Second derivative
:param numpy.array m: geophysical model
:param numpy.array v: vector to multiply
:rtype: scipy.sparse.csr_matrix or numpy.ndarray
:return: WtW or WtW*v
The regularization is:
.. math::
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top W(m-m_\\text{ref})}
So the second derivative is straight forward:
.. math::
R(m) = \mathbf{W^\\top W}
"""
mD = self.mapping.deriv(m - self.mref)
if v is None:
return mD.T * self.W.T * self.W * mD
return mD.T * ( self.W.T * ( self.W * ( mD * v) ) )
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import SimPEG
import numpy as np
from SimPEG.Utils import Zero, closestPoints
class BaseRx(SimPEG.Survey.BaseTimeRx):
locs = None
rxType = None
knownRxTypes = {
'phi':['phi',None],
'ex':['e','x'],
'ey':['e','y'],
'ez':['e','z'],
'jx':['j','x'],
'jy':['j','y'],
'jz':['j','z'],
}
def __init__(self, locs, times, rxType, **kwargs):
SimPEG.Survey.BaseTimeRx.__init__(self, locs, times, rxType, **kwargs)
@property
def projField(self):
"""Field Type projection (e.g. e b ...)"""
return self.knownRxTypes[self.rxType][0]
def projGLoc(self, f):
"""Grid Location projection (e.g. Ex Fy ...)"""
comp = self.knownRxTypes[self.rxType][1]
if comp is not None:
return f._GLoc(self.rxType) + comp
return f._GLoc(self.rxType)
def getTimeP(self, timesall):
"""
Returns the time projection matrix.
.. note::
This is not stored in memory, but is created on demand.
"""
time_inds = np.in1d(timesall, self.times)
return time_inds
def evalDeriv(self, src, mesh, f, v, adjoint=False):
P = self.getP(mesh, self.projGLoc(f))
if not adjoint:
return P*v
elif adjoint:
return P.T*v
# DC.Rx.Dipole(locs)
class Dipole(BaseRx):
def __init__(self, locsM, locsN, times, rxType = 'phi', **kwargs):
assert locsM.shape == locsN.shape, 'locsM and locsN need to be the same size'
locs = [locsM, locsN]
# We may not need this ...
BaseRx.__init__(self, locs, times, rxType)
@property
def nD(self):
"""Number of data in the receiver."""
# return self.locs[0].shape[0] * len(self.times)
return self.locs[0].shape[0]
@property
def nRx(self):
"""Number of data in the receiver."""
return self.locs[0].shape[0]
# Not sure why ...
# return int(self.locs[0].size / 2)
def getP(self, mesh, Gloc):
if mesh in self._Ps:
return self._Ps[mesh]
P0 = mesh.getInterpolationMat(self.locs[0], Gloc)
P1 = mesh.getInterpolationMat(self.locs[1], Gloc)
P = P0 - P1
if self.storeProjections:
self._Ps[mesh] = P
return P
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import SimPEG
# from SimPEG.EM.Base import BaseEMSurvey
from SimPEG.Utils import Zero, closestPoints, mkvc
import numpy as np
class BaseSrc(SimPEG.Survey.BaseSrc):
current = 1.0
loc = None
def __init__(self, rxList, **kwargs):
SimPEG.Survey.BaseSrc.__init__(self, rxList, **kwargs)
def eval(self, prob):
raise NotImplementedError
def evalDeriv(self, prob):
return Zero()
@property
def nD(self):
"""Number of data"""
return self.vnD.sum()
@property
def vnD(self):
"""Vector number of data"""
return np.array([rx.nD*len(rx.times) for rx in self.rxList])
class Dipole(BaseSrc):
def __init__(self, rxList, locA, locB, **kwargs):
assert locA.shape == locB.shape, 'Shape of locA and locB should be the same'
self.loc = [locA, locB]
BaseSrc.__init__(self, rxList, **kwargs)
def eval(self, prob):
if prob._formulation == 'HJ':
inds = closestPoints(prob.mesh, self.loc, gridLoc='CC')
q = np.zeros(prob.mesh.nC)
q[inds] = self.current * np.r_[1., -1.]
elif prob._formulation == 'EB':
qa = prob.mesh.getInterpolationMat(self.loc[0], locType='N').todense()
qb = -prob.mesh.getInterpolationMat(self.loc[1], locType='N').todense()
q = self.current * mkvc(qa+qb)
return q
class Pole(BaseSrc):
def __init__(self, rxList, loc, **kwargs):
BaseSrc.__init__(self, rxList, loc=loc, **kwargs)
def eval(self, prob):
if prob._formulation == 'HJ':
inds = closestPoints(prob.mesh, self.loc)
q = np.zeros(prob.mesh.nC)
q[inds] = self.current * np.r_[1.]
elif prob._formulation == 'EB':
q = prob.mesh.getInterpolationMat(self.loc, locType='N').todense()
q = self.current * mkvc(q)
return q
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import SimPEG
from SimPEG.EM.Base import BaseEMSurvey
from SimPEG import np, sp, Survey, Utils
from SimPEG.Utils import Zero, Identity
from SimPEG.EM.Static.SIP.SrcSIP import BaseSrc
from SimPEG.EM.Static.SIP.RxSIP import BaseRx
import uuid
class Survey(BaseEMSurvey):
rxPair = BaseRx
srcPair = BaseSrc
times = None
def __init__(self, srcList, **kwargs):
self.srcList = srcList
BaseEMSurvey.__init__(self, srcList, **kwargs)
self.getUniqueTimes()
def getUniqueTimes(self):
time_rx = []
for src in self.srcList:
for rx in src.rxList:
time_rx.append(rx.times)
self.times = np.unique(np.hstack(time_rx))
def dpred(self, m, f=None):
"""
Predicted data.
.. math::
d_\\text{pred} = Pf(m)
"""
return self.prob.forward(m, f=f)
class Data(SimPEG.Survey.Data):
"""Fancy data storage by Src and Rx"""
def __init__(self, survey, v=None):
self.uid = str(uuid.uuid4())
self.survey = survey
self._dataDict = {}
for src in self.survey.srcList:
self._dataDict[src] = {}
for rx in src.rxList:
self._dataDict[src][rx] = {}
if v is not None:
self.fromvec(v)
def _ensureCorrectKey(self, key):
if type(key) is tuple:
if len(key) is not 3:
raise KeyError('Key must be [Src, Rx, tInd]')
if key[0] not in self.survey.srcList:
raise KeyError('Src Key must be a source in the survey.')
if key[1] not in key[0].rxList:
raise KeyError('Rx Key must be a receiver for the source.')
return key
elif isinstance(key, self.survey.srcPair):
if key not in self.survey.srcList:
raise KeyError('Key must be a source in the survey.')
return key, None, None
else:
raise KeyError('Key must be [Src] or [Src,Rx] or [Src, Rx, tInd]')
def __setitem__(self, key, value):
src, rx, t = self._ensureCorrectKey(key)
assert rx is not None, 'set data using [Src, Rx]'
assert isinstance(value, np.ndarray), 'value must by ndarray'
assert value.size == rx.nD, "value must have the same number of data as the source."
self._dataDict[src][rx][t] = Utils.mkvc(value)
def __getitem__(self, key):
src, rx, t = self._ensureCorrectKey(key)
if rx is not None:
if rx not in self._dataDict[src]:
raise Exception('Data for receiver has not yet been set.')
return self._dataDict[src][rx][t]
return np.concatenate([self[src,rx, t] for rx in src.rxList])
def tovec(self):
val = []
for src in self.survey.srcList:
for rx in src.rxList:
for t in rx.times:
val.append(self[src, rx, t])
return np.concatenate(val)
def fromvec(self, v):
v = Utils.mkvc(v)
assert v.size == self.survey.nD, 'v must have the correct number of data.'
indBot, indTop = 0, 0
for src in self.survey.srcList:
for rx in src.rxList:
for t in rx.times:
indTop += rx.nRx
self[src, rx, t] = v[indBot:indTop]
indBot += rx.nRx
-5
View File
@@ -1,5 +0,0 @@
from ProblemSIP import Problem3D_CC, Problem3D_N
from SurveySIP import Survey, Data
import SrcSIP as Src #Pole
import RxSIP as Rx
from Regularization import MultiRegularization
-317
View File
@@ -1,317 +0,0 @@
from SimPEG import np
from SimPEG.EM.Static import DC, IP
def plot_pseudoSection(DCsurvey, axs, stype='dpdp', dtype="appc", clim=None):
"""
Read list of 2D tx-rx location and plot a speudo-section of apparent
resistivity.
Assumes flat topo for now...
Input:
:param d2D, z0
:switch stype -> Either 'pdp' (pole-dipole) | 'dpdp' (dipole-dipole)
:switch dtype=-> Either 'appr' (app. res) | 'appc' (app. con) | 'volt' (potential)
Output:
:figure scatter plot overlayed on image
Edited Feb 17th, 2016
@author: dominiquef
"""
from SimPEG import np
from scipy.interpolate import griddata
import pylab as plt
# Set depth to 0 for now
z0 = 0.
# Pre-allocate
midx = []
midz = []
rho = []
LEG = []
count = 0 # Counter for data
for ii in range(DCsurvey.nSrc):
Tx = DCsurvey.srcList[ii].loc
Rx = DCsurvey.srcList[ii].rxList[0].locs
nD = DCsurvey.srcList[ii].rxList[0].nD
data = DCsurvey.dobs[count:count+nD]
count += nD
# Get distances between each poles A-B-M-N
if stype == 'pdp':
MA = np.abs(Tx[0] - Rx[0][:,0])
NA = np.abs(Tx[0] - Rx[1][:,0])
MN = np.abs(Rx[1][:,0] - Rx[0][:,0])
# Create mid-point location
Cmid = Tx[0]
Pmid = (Rx[0][:,0] + Rx[1][:,0])/2
if DCsurvey.mesh.dim == 2:
zsrc = Tx[1]
elif DCsurvey.mesh.dim ==3:
zsrc = Tx[2]
elif stype == 'dpdp':
MA = np.abs(Tx[0][0] - Rx[0][:,0])
MB = np.abs(Tx[1][0] - Rx[0][:,0])
NA = np.abs(Tx[0][0] - Rx[1][:,0])
NB = np.abs(Tx[1][0] - Rx[1][:,0])
# Create mid-point location
Cmid = (Tx[0][0] + Tx[1][0])/2
Pmid = (Rx[0][:,0] + Rx[1][:,0])/2
if DCsurvey.mesh.dim == 2:
zsrc = (Tx[0][1] + Tx[1][1])/2
elif DCsurvey.mesh.dim ==3:
zsrc = (Tx[0][2] + Tx[1][2])/2
# Change output for dtype
if dtype == 'volt':
rho = np.hstack([rho,data])
else:
# Compute pant leg of apparent rho
if stype == 'pdp':
leg = data * 2*np.pi * MA * ( MA + MN ) / MN
elif stype == 'dpdp':
leg = data * 2*np.pi / ( 1/MA - 1/MB + 1/NB - 1/NA )
LEG.append(1./(2*np.pi) *( 1/MA - 1/MB + 1/NB - 1/NA ))
else:
print """dtype must be 'pdp'(pole-dipole) | 'dpdp' (dipole-dipole) """
break
if dtype == 'appc':
leg = np.log10(abs(1./leg))
rho = np.hstack([rho,leg])
elif dtype == 'appr':
leg = np.log10(abs(leg))
rho = np.hstack([rho,leg])
else:
print """dtype must be 'appr' | 'appc' | 'volt' """
break
midx = np.hstack([midx, ( Cmid + Pmid )/2 ])
if DCsurvey.mesh.dim==3:
midz = np.hstack([midz, -np.abs(Cmid-Pmid)/2 + zsrc ])
elif DCsurvey.mesh.dim==2:
midz = np.hstack([midz, -np.abs(Cmid-Pmid)/2 + zsrc ])
ax = axs
# Grid points
grid_x, grid_z = np.mgrid[np.min(midx):np.max(midx), np.min(midz):np.max(midz)]
grid_rho = griddata(np.c_[midx,midz], rho.T, (grid_x, grid_z), method='linear')
if clim == None:
vmin, vmax = rho.min(), rho.max()
else:
vmin, vmax = clim[0], clim[1]
grid_rho = np.ma.masked_where(np.isnan(grid_rho), grid_rho)
ph = plt.pcolormesh(grid_x[:,0],grid_z[0,:],grid_rho.T, clim=(vmin, vmax), vmin=vmin, vmax=vmax)
cbar = plt.colorbar(format="$10^{%.1f}$",fraction=0.04,orientation="horizontal")
cmin,cmax = cbar.get_clim()
ticks = np.linspace(cmin,cmax,3)
cbar.set_ticks(ticks)
cbar.ax.tick_params(labelsize=10)
if dtype == 'appc':
cbar.set_label("App.Cond",size=12)
elif dtype == 'appr':
cbar.set_label("App.Res.",size=12)
elif dtype == 'volt':
cbar.set_label("Potential (V)",size=12)
# Plot apparent resistivity
ax.scatter(midx,midz,s=10,c=rho.T, vmin =vmin, vmax = vmax, clim=(vmin, vmax))
#ax.set_xticklabels([])
#ax.set_yticklabels([])
plt.gca().set_aspect('equal', adjustable='box')
return ph, LEG
def gen_DCIPsurvey(endl, mesh, stype, a, b, n):
"""
Load in endpoints and survey specifications to generate Tx, Rx location
stations.
Assumes flat topo for now...
Input:
:param endl -> input endpoints [x1, y1, z1, x2, y2, z2]
:object mesh -> SimPEG mesh object
:switch stype -> "dpdp" (dipole-dipole) | "pdp" (pole-dipole) | 'gradient'
: param a, n -> pole seperation, number of rx dipoles per tx
Output:
:param Tx, Rx -> List objects for each tx location
Lines: P1x, P1y, P1z, P2x, P2y, P2z
Created on Wed December 9th, 2015
@author: dominiquef
!! Require clean up to deal with DCsurvey
"""
from SimPEG import np
def xy_2_r(x1,x2,y1,y2):
r = np.sqrt( np.sum((x2 - x1)**2 + (y2 - y1)**2) )
return r
## Evenly distribute electrodes and put on surface
# Mesure survey length and direction
dl_len = xy_2_r(endl[0,0],endl[1,0],endl[0,1],endl[1,1])
dl_x = ( endl[1,0] - endl[0,0] ) / dl_len
dl_y = ( endl[1,1] - endl[0,1] ) / dl_len
nstn = np.floor( dl_len / a )
# Compute discrete pole location along line
stn_x = endl[0,0] + np.array(range(int(nstn)))*dl_x*a
stn_y = endl[0,1] + np.array(range(int(nstn)))*dl_y*a
if mesh.dim==2:
ztop = mesh.vectorNy[-1]
# Create line of P1 locations
M = np.c_[stn_x, np.ones(nstn).T*ztop]
# Create line of P2 locations
N = np.c_[stn_x+a*dl_x, np.ones(nstn).T*ztop]
elif mesh.dim==3:
ztop = mesh.vectorNz[-1]
# Create line of P1 locations
M = np.c_[stn_x, stn_y, np.ones(nstn).T*ztop]
# Create line of P2 locations
N = np.c_[stn_x+a*dl_x, stn_y+a*dl_y, np.ones(nstn).T*ztop]
## Build list of Tx-Rx locations depending on survey type
# Dipole-dipole: Moving tx with [a] spacing -> [AB a MN1 a MN2 ... a MNn]
# Pole-dipole: Moving pole on one end -> [A a MN1 a MN2 ... MNn a B]
SrcList = []
if stype != 'gradient':
for ii in range(0, int(nstn)-1):
if stype == 'dpdp':
tx = np.c_[M[ii,:],N[ii,:]]
elif stype == 'pdp':
tx = np.c_[M[ii,:],M[ii,:]]
# Rx.append(np.c_[M[ii+1:indx,:],N[ii+1:indx,:]])
# Current elctrode seperation
AB = xy_2_r(tx[0,1],endl[1,0],tx[1,1],endl[1,1])
# Number of receivers to fit
nstn = np.min([np.floor( (AB - b) / a ) , n])
# Check if there is enough space, else break the loop
if nstn <= 0:
continue
# Compute discrete pole location along line
stn_x = N[ii,0] + dl_x*b + np.array(range(int(nstn)))*dl_x*a
stn_y = N[ii,1] + dl_y*b + np.array(range(int(nstn)))*dl_y*a
# Create receiver poles
if mesh.dim==3:
# Create line of P1 locations
P1 = np.c_[stn_x, stn_y, np.ones(nstn).T*ztop]
# Create line of P2 locations
P2 = np.c_[stn_x+a*dl_x, stn_y+a*dl_y, np.ones(nstn).T*ztop]
rxClass = DC.Rx.Dipole(P1, P2)
elif mesh.dim==2:
# Create line of P1 locations
P1 = np.c_[stn_x, np.ones(nstn).T*ztop]
# Create line of P2 locations
P2 = np.c_[stn_x+a*dl_x, np.ones(nstn).T*ztop]
rxClass = DC.Rx.Dipole_ky(P1, P2)
if stype == 'dpdp':
srcClass = DC.Src.Dipole([rxClass], M[ii,:],N[ii,:])
elif stype == 'pdp':
srcClass = DC.Src.Pole([rxClass], M[ii,:])
SrcList.append(srcClass)
elif stype == 'gradient':
# Gradient survey only requires Tx at end of line and creates a square
# grid of receivers at in the middle at a pre-set minimum distance
# Get the edge limit of survey area
min_x = endl[0,0] + dl_x * b
min_y = endl[0,1] + dl_y * b
max_x = endl[1,0] - dl_x * b
max_y = endl[1,1] - dl_y * b
box_l = np.sqrt( (min_x - max_x)**2 + (min_y - max_y)**2 )
box_w = box_l/2.
nstn = np.floor( box_l / a )
# Compute discrete pole location along line
stn_x = min_x + np.array(range(int(nstn)))*dl_x*a
stn_y = min_y + np.array(range(int(nstn)))*dl_y*a
# Define number of cross lines
nlin = int(np.floor( box_w / a ))
lind = range(-nlin,nlin+1)
ngrad = nstn * len(lind)
rx = np.zeros([ngrad,6])
for ii in range( len(lind) ):
# Move line in perpendicular direction by dipole spacing
lxx = stn_x - lind[ii]*a*dl_y
lyy = stn_y + lind[ii]*a*dl_x
M = np.c_[ lxx, lyy , np.ones(nstn).T*ztop]
N = np.c_[ lxx+a*dl_x, lyy+a*dl_y, np.ones(nstn).T*ztop]
rx[(ii*nstn):((ii+1)*nstn),:] = np.c_[M,N]
if mesh.dim==3:
rxClass = DC.Rx.Dipole(rx[:,:3], rx[:,3:])
elif mesh.dim==2:
M = M[:,[0,2]]
N = N[:,[0,2]]
rxClass = DC.Rx.Dipole_ky(rx[:,[0,2]], rx[:,[3,5]])
srcClass = DC.Src.Dipole([rxClass], M[0,:], N[-1,:])
SrcList.append(srcClass)
else:
print """stype must be either 'pdp', 'dpdp' or 'gradient'. """
return SrcList
-1
View File
@@ -1 +0,0 @@
from StaticUtils import *
-3
View File
@@ -1,3 +0,0 @@
import DC
import IP
import SIP
+3 -3
View File
@@ -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)
+6 -6
View File
@@ -87,7 +87,7 @@ class SrcTDEM_VMD_MVP(SrcTDEM):
def getInitialFields(self, mesh):
"""Vertical magnetic dipole, magnetic vector potential"""
if self.waveformType == "STEPOFF":
print ">> Step waveform: Non-zero initial condition"
print ">> Step waveform: Non-zero initial condition"
if mesh._meshType is 'CYL':
if mesh.isSymmetric:
MVP = MagneticDipoleVectorPotential(self.loc, mesh, 'Ey')
@@ -96,8 +96,8 @@ class SrcTDEM_VMD_MVP(SrcTDEM):
elif mesh._meshType is 'TENSOR':
MVP = MagneticDipoleVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'])
else:
raise Exception('Unknown mesh for VMD')
return {"b": mesh.edgeCurl*MVP}
raise Exception('Unknown mesh for VMD')
return {"b": mesh.edgeCurl*MVP}
elif self.waveformType == "GENERAL":
print ">> General waveform: Zero initial condition"
return {"b": np.zeros(mesh.nF)}
@@ -113,7 +113,7 @@ class SrcTDEM_VMD_MVP(SrcTDEM):
elif mesh._meshType is 'TENSOR':
MVP = MagneticDipoleVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'])
else:
raise Exception('Unknown mesh for VMD')
raise Exception('Unknown mesh for VMD')
return mesh.edgeCurl.T*MfMui*mesh.edgeCurl*MVP
@@ -122,7 +122,7 @@ class SrcTDEM_CircularLoop_MVP(SrcTDEM):
self.loc = loc
self.radius = radius
self.waveformType = waveformType
SrcTDEM.__init__(self,rxList)
SrcTDEM.__init__(self,rxList)
def getInitialFields(self, mesh):
"""Circular Loop, magnetic vector potential"""
@@ -153,7 +153,7 @@ class SrcTDEM_CircularLoop_MVP(SrcTDEM):
elif mesh._meshType is 'TENSOR':
MVP = MagneticLoopVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'], self.radius)
else:
raise Exception('Unknown mesh for CircularLoop')
raise Exception('Unknown mesh for CircularLoop')
return mesh.edgeCurl.T*MfMui*mesh.edgeCurl*MVP
+13 -13
View File
@@ -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
+10 -15
View File
@@ -26,55 +26,50 @@ def getFDEMProblem(fdemType, comp, SrcList, freq, useMu=False, verbose=False):
x = np.array([np.linspace(-5.*cs,-2.*cs,3),np.linspace(5.*cs,2.*cs,3)]) + cs/4. #don't sample right by the source, slightly off alignment from either staggered grid
XYZ = Utils.ndgrid(x,x,np.linspace(-2.*cs,2.*cs,5))
Rx0 = getattr(EM.FDEM.Rx, 'Point_' + comp[0])
if comp[2] == 'r':
real_or_imag = 'real'
elif comp[2] == 'i':
real_or_imag = 'imag'
rx0 = Rx0(XYZ, comp[1], 'imag')
Rx0 = EM.FDEM.Rx(XYZ, comp)
Src = []
for SrcType in SrcList:
if SrcType is 'MagDipole':
Src.append(EM.FDEM.Src.MagDipole([rx0], freq=freq, loc=np.r_[0.,0.,0.]))
Src.append(EM.FDEM.Src.MagDipole([Rx0], freq=freq, loc=np.r_[0.,0.,0.]))
elif SrcType is 'MagDipole_Bfield':
Src.append(EM.FDEM.Src.MagDipole_Bfield([rx0], freq=freq, loc=np.r_[0.,0.,0.]))
Src.append(EM.FDEM.Src.MagDipole_Bfield([Rx0], freq=freq, loc=np.r_[0.,0.,0.]))
elif SrcType is 'CircularLoop':
Src.append(EM.FDEM.Src.CircularLoop([rx0], freq=freq, loc=np.r_[0.,0.,0.]))
Src.append(EM.FDEM.Src.CircularLoop([Rx0], freq=freq, loc=np.r_[0.,0.,0.]))
elif SrcType is 'RawVec':
if fdemType is 'e' or fdemType is 'b':
S_m = np.zeros(mesh.nF)
S_e = np.zeros(mesh.nE)
S_m[Utils.closestPoints(mesh,[0.,0.,0.],'Fz') + np.sum(mesh.vnF[:1])] = 1e-3
S_e[Utils.closestPoints(mesh,[0.,0.,0.],'Ez') + np.sum(mesh.vnE[:1])] = 1e-3
Src.append(EM.FDEM.Src.RawVec([rx0], freq, S_m, mesh.getEdgeInnerProduct()*S_e))
Src.append(EM.FDEM.Src.RawVec([Rx0], freq, S_m, mesh.getEdgeInnerProduct()*S_e))
elif fdemType is 'h' or fdemType is 'j':
S_m = np.zeros(mesh.nE)
S_e = np.zeros(mesh.nF)
S_m[Utils.closestPoints(mesh,[0.,0.,0.],'Ez') + np.sum(mesh.vnE[:1])] = 1e-3
S_e[Utils.closestPoints(mesh,[0.,0.,0.],'Fz') + np.sum(mesh.vnF[:1])] = 1e-3
Src.append(EM.FDEM.Src.RawVec([rx0], freq, mesh.getEdgeInnerProduct()*S_m, S_e))
Src.append(EM.FDEM.Src.RawVec([Rx0], freq, mesh.getEdgeInnerProduct()*S_m, S_e))
if verbose:
print ' Fetching %s problem' % (fdemType)
if fdemType == 'e':
survey = EM.FDEM.Survey(Src)
prb = EM.FDEM.Problem3D_e(mesh, mapping=mapping)
prb = EM.FDEM.Problem_e(mesh, mapping=mapping)
elif fdemType == 'b':
survey = EM.FDEM.Survey(Src)
prb = EM.FDEM.Problem3D_b(mesh, mapping=mapping)
prb = EM.FDEM.Problem_b(mesh, mapping=mapping)
elif fdemType == 'j':
survey = EM.FDEM.Survey(Src)
prb = EM.FDEM.Problem3D_j(mesh, mapping=mapping)
prb = EM.FDEM.Problem_j(mesh, mapping=mapping)
elif fdemType == 'h':
survey = EM.FDEM.Survey(Src)
prb = EM.FDEM.Problem3D_h(mesh, mapping=mapping)
prb = EM.FDEM.Problem_h(mesh, mapping=mapping)
else:
raise NotImplementedError()
-1
View File
@@ -1,6 +1,5 @@
import TDEM
import FDEM
import Static
import Base
import Analytics
import Utils
+7 -7
View File
@@ -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)
+32 -53
View File
@@ -2,27 +2,19 @@ from SimPEG import Mesh, Utils, np, sp
import SimPEG.DCIP as DC
import time
def run(loc=None, sig=None, radi=None, param=None, surveyType='dipole-dipole', unitType='appConductivity', plotIt=True):
def run(loc=None, sig=None, radi=None, param=None, stype='dpdp', plotIt=True):
"""
DC Forward Simulation
=====================
Forward model two conductive spheres in a half-space and plot a
pseudo-section. Assumes an infinite line source and measures along the
center of the spheres.
Forward model conductive spheres in a half-space and plot a pseudo-section
INPUT:
loc = Location of spheres [[x1,y1,z1],[x2,y2,z2]]
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
Created by @fourndo on Mon Feb 01 19:28:06 2016
"""
assert surveyType in ['pole-dipole', 'dipole-dipole'], "Source type (surveyType) must be pdp or dpdp (pole dipole or dipole dipole)"
assert unitType in ['appResistivity', 'appConductivity', 'volt'], "Unit type (unitType) must be appResistivity or appConductivity or volt (potential)"
assert stype in ['pdp', 'dpdp'], "Source type (stype) must be pdp or dpdp (pole dipole or dipole dipole)"
if loc is None:
loc = np.c_[[-50.,0.,-50.],[50.,0.,-50.]]
@@ -35,6 +27,7 @@ def run(loc=None, sig=None, radi=None, param=None, surveyType='dipole-dipole', u
# First we need to create a mesh and a model.
# This is our mesh
dx = 5.
@@ -59,10 +52,14 @@ def run(loc=None, sig=None, radi=None, param=None, surveyType='dipole-dipole', u
# Get index of the center
indy = int(mesh.nCy/2)
# Plot the model for reference
# Define core mesh extent
xlim = 200
zlim = 100
zlim = 125
# Specify the survey type: "pdp" | "dpdp"
# Then specify the end points of the survey. Let's keep it simple for now and survey above the anomalies, top of the mesh
ends = [(-175,0),(175,0)]
@@ -73,20 +70,19 @@ def run(loc=None, sig=None, radi=None, param=None, surveyType='dipole-dipole', u
locs = np.c_[mesh.gridCC[indx,0],mesh.gridCC[indx,1],np.ones(2).T*mesh.vectorNz[-1]]
# We will handle the geometry of the survey for you and create all the combination of tx-rx along line
# [Tx, Rx] = DC.gen_DCIPsurvey(locs, mesh, surveyType, param[0], param[1], param[2])
survey, Tx, Rx = DC.gen_DCIPsurvey(locs, mesh, surveyType, param[0], param[1], param[2])
# [Tx, Rx] = DC.gen_DCIPsurvey(locs, mesh, stype, param[0], param[1], param[2])
survey, Tx, Rx = DC.gen_DCIPsurvey(locs, mesh, stype, param[0], param[1], param[2])
# Define some global geometry
dl_len = np.sqrt( np.sum((locs[0,:] - locs[1,:])**2) )
dl_x = ( Tx[-1][0,1] - Tx[0][0,0] ) / dl_len
dl_y = ( Tx[-1][1,1] - Tx[0][1,0] ) / dl_len
#azm = np.arctan(dl_y/dl_x)
azm = np.arctan(dl_y/dl_x)
#Set boundary conditions
mesh.setCellGradBC('neumann')
# Define the linear system needed for the DC problem. We assume an infitite
# line source for simplicity.
# Define the differential operators needed for the DC problem
Div = mesh.faceDiv
Grad = mesh.cellGrad
Msig = Utils.sdiag(1./(mesh.aveF2CC.T*(1./model)))
@@ -118,8 +114,8 @@ def run(loc=None, sig=None, radi=None, param=None, surveyType='dipole-dipole', u
rxloc_N = np.asarray(Rx[ii][:,3:])
# For usual cases 'dipole-dipole' or "gradient"
if surveyType == 'pole-dipole':
# For usual cases "dpdp" or "gradient"
if stype == 'pdp':
# Create an "inifinity" pole
tx = np.squeeze(Tx[ii][:,0:1])
tinf = tx + np.array([dl_x,dl_y,0])*dl_len*2
@@ -149,23 +145,16 @@ def run(loc=None, sig=None, radi=None, param=None, surveyType='dipole-dipole', u
print 'Forward completed'
# Let's just convert the 3D format into 2D (distance along line) and plot
survey2D = DC.convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc) , 'Xloc')
# [Tx2d, Rx2d] = DC.convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc))
survey2D = DC.convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc))
survey2D.dobs =np.hstack(data)
# Here is an example for the first tx-rx array
if plotIt:
import matplotlib.pyplot as plt
fig = plt.figure(figsize=(7,7))
fig = plt.figure()
ax = plt.subplot(2,1,1, aspect='equal')
# Plot the location of the spheres for reference
circle1=plt.Circle((loc[0,0], loc[2,0]), radi[0], color='w', fill=False, lw=3)
circle2=plt.Circle((loc[0,1], loc[2,1]), radi[1], color='k', fill=False, lw=3)
ax.add_artist(circle1)
ax.add_artist(circle2)
dat = mesh.plotSlice(np.log10(model), ax = ax, normal = 'Y',
ind = indy,grid=True, clim = np.log10([sig.min(),sig.max()]))
ax.set_title('3-D model')
mesh.plotSlice(np.log10(model), ax =ax, normal = 'Y', ind = indy,grid=True)
ax.set_title('E-W section at '+str(mesh.vectorCCy[indy])+' m')
plt.gca().set_aspect('equal', adjustable='box')
plt.scatter(Tx[0][0,:],Tx[0][2,:],s=40,c='g', marker='v')
@@ -174,32 +163,22 @@ def run(loc=None, sig=None, radi=None, param=None, surveyType='dipole-dipole', u
plt.ylim([-zlim,mesh.vectorNz[-1]+dx])
pos = ax.get_position()
ax.set_position([pos.x0 , pos.y0 + 0.025 , pos.width, pos.height])
pos = ax.get_position()
cbarax = fig.add_axes([pos.x0 , pos.y0 + 0.025 , pos.width, pos.height * 0.04]) ## the parameters are the specified position you set
cb = fig.colorbar(dat[0],cax=cbarax, orientation="horizontal",
ax = ax, ticks=np.linspace(np.log10(sig.min()),
np.log10(sig.max()), 3), format="$10^{%.1f}$")
cb.set_label("Conductivity (S/m)",size=12)
cb.ax.tick_params(labelsize=12)
# Second plot for the predicted apparent resistivity data
ax2 = plt.subplot(2,1,2, aspect='equal')
ax = plt.subplot(2,1,2, aspect='equal')
# Plot the location of the spheres for reference
circle1=plt.Circle((loc[0,0], loc[2,0]), radi[0], color='w', fill=False, lw=3)
circle2=plt.Circle((loc[0,1], loc[2,1]), radi[1], color='k', fill=False, lw=3)
ax2.add_artist(circle1)
ax2.add_artist(circle2)
circle1=plt.Circle((loc[0,0]-Tx[0][0,0],loc[2,0]),radi[0],color='w',fill=False, lw=3)
circle2=plt.Circle((loc[0,1]-Tx[0][0,0],loc[2,1]),radi[1],color='k',fill=False, lw=3)
ax.add_artist(circle1)
ax.add_artist(circle2)
# Add the speudo section
dat = DC.plot_pseudoSection(survey2D, ax2, surveyType=surveyType, unitType=unitType) # plt.scatter(Tx2d[0][:],Tx[0][2,:],s=40,c='g', marker='v')
DC.plot_pseudoSection(survey2D,ax,stype)
# plt.scatter(Tx2d[0][:],Tx[0][2,:],s=40,c='g', marker='v')
# plt.scatter(Rx2d[0][:],Rx[0][:,2::3],s=40,c='y')
# plt.plot(np.r_[Tx2d[0][0],Rx2d[-1][-1,-1]],np.ones(2)*mesh.vectorNz[-1], color='k')
ax2.set_title('Apparent Conductivity data')
plt.ylim([-zlim,mesh.vectorNz[-1]+dx])
plt.show()
return fig, ax
+5 -4
View File
@@ -42,16 +42,17 @@ def run(plotIt=True):
ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5)
rxOffset=10.
bzi = EM.FDEM.Rx.Point_b(np.array([[rxOffset, 0., 1e-3]]), orientation='z', component='imag')
rxOffset=10.
bzi = EM.FDEM.Rx(np.array([[rxOffset, 0., 1e-3]]), 'bzi')
freqs = np.logspace(1,3,10)
srcLoc = np.array([0., 0., 10.])
srcList = [EM.FDEM.Src.MagDipole([bzi],freq, srcLoc,orientation='Z') for freq in freqs]
srcList = []
[srcList.append(EM.FDEM.Src.MagDipole([bzi],freq, srcLoc,orientation='Z')) for freq in freqs]
survey = EM.FDEM.Survey(srcList)
prb = EM.FDEM.Problem3D_b(mesh, mapping=mapping)
prb = EM.FDEM.Problem_b(mesh, mapping=mapping)
try:
from pymatsolver import MumpsSolver
@@ -1,278 +0,0 @@
from SimPEG import *
from SimPEG.EM import FDEM, Analytics, mu_0
import time
try:
from pymatsolver import MumpsSolver
solver = MumpsSolver
except Exception:
solver = SolverLU
pass
def run(plotIt=True):
"""
EM: Schenkel and Morrison Casing Model
======================================
Here we create and run a FDEM forward simulation to calculate the vertical
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.
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
- 300m long
- radius of 0.1m
- thickness of 6e-3m
Inside the casing, we take the same conductivity as the background.
We are using an EM code to simulate DC, so we use frequency low enough
that the skin depth inside the casing is longer than the casing length (f
= 1e-6 Hz). The plot produced is of the current inside the casing.
These results are shown in the SEG abstract by Yang et al., 2016: 3D DC
resistivity modeling of steel casing for reservoir monitoring using
equivalent resistor network. The solver used to produce these results and
achieve the CPU time of ~30s is Mumps, which was installed using pymatsolver_
.. _pymatsolver: https://github.com/rowanc1/pymatsolver
This example is on figshare: https://dx.doi.org/10.6084/m9.figshare.3126961.v1
If you would use this example for a code comparison, or build upon it, a
citation would be much appreciated!
"""
if plotIt:
import matplotlib.pylab as plt
# ------------------ MODEL ------------------
sigmaair = 1e-8 # air
sigmaback = 1e-2 # background
sigmacasing = 1e6 # casing
sigmainside = sigmaback # inside the casing
casing_t = 0.006 # 1cm thickness
casing_l = 300 # length of the casing
casing_r = 0.1
casing_a = casing_r - casing_t/2. # inner radius
casing_b = casing_r + casing_t/2. # outer radius
casing_z = np.r_[-casing_l,0.]
# ------------------ SURVEY PARAMETERS ------------------
freqs = np.r_[1e-6] #[1e-1, 1, 5] # frequencies
dsz = -300 # down-hole z source location
src_loc = np.r_[0.,0.,dsz]
inf_loc = np.r_[0.,0.,1e4]
print 'Skin Depth: ', [(500./np.sqrt(sigmaback*_)) for _ in freqs]
# ------------------ MESH ------------------
# fine cells near well bore
csx1, csx2 = 2e-3, 60.
pfx1, pfx2 = 1.3, 1.3
ncx1 = np.ceil(casing_b/csx1+2)
# pad nicely to second cell size
npadx1 = np.floor(np.log(csx2/csx1) / np.log(pfx1))
hx1a,hx1b = Utils.meshTensor([(csx1,ncx1)]),Utils.meshTensor([(csx1,npadx1,pfx1)])
dx1 = sum(hx1a)+sum(hx1b)
dx1 = np.floor(dx1/csx2)
hx1b *= (dx1*csx2 - sum(hx1a))/sum(hx1b)
# second chunk of mesh
dx2 = 300. # uniform mesh out to here
ncx2 = np.ceil((dx2 - dx1)/csx2)
npadx2 = 45
hx2a, hx2b = Utils.meshTensor([(csx2,ncx2)]), Utils.meshTensor([(csx2,npadx2,pfx2)])
hx = np.hstack([hx1a,hx1b,hx2a,hx2b])
# z-direction
csz = 0.05
nza = 10
ncz, npadzu, npadzd = np.int(np.ceil(np.diff(casing_z)[0]/csz))+10, 68, 68 # cell size, number of core cells, number of padding cells in the x- direction
hz = Utils.meshTensor([(csz,npadzd,-1.3), (csz,ncz), (csz,npadzu,1.3)]) # vector of cell widths in the z-direction
# Mesh
mesh = Mesh.CylMesh([hx,1.,hz], [0.,0.,-np.sum(hz[:npadzu+ncz-nza])])
print 'Mesh Extent xmax: %f,: zmin: %f, zmax: %f'%(mesh.vectorCCx.max(), mesh.vectorCCz.min(), mesh.vectorCCz.max())
print 'Number of cells', mesh.nC
if plotIt is True:
fig, ax = plt.subplots(1, 1, figsize=(6, 4))
ax.set_title('Simulation Mesh')
mesh.plotGrid(ax=ax)
plt.show()
# Put the model on the mesh
sigWholespace = sigmaback*np.ones((mesh.nC))
sigBack = sigWholespace.copy()
sigBack[mesh.gridCC[:,2] > 0.] = sigmaair
sigCasing = sigBack.copy()
iCasingZ = (mesh.gridCC[:,2] <= casing_z[1]) & (mesh.gridCC[:,2] >= casing_z[0])
iCasingX = (mesh.gridCC[:,0] >= casing_a) & (mesh.gridCC[:,0] <= casing_b)
iCasing = iCasingX & iCasingZ
sigCasing[iCasing] = sigmacasing
if plotIt is True:
# plotting parameters
xlim = np.r_[0., 0.2]
zlim = np.r_[-350., 10.]
clim_sig = np.r_[-8,6]
# plot models
fig, ax = plt.subplots(1,1,figsize=(4,4))
f = plt.colorbar(mesh.plotImage(np.log10(sigCasing),ax=ax)[0], ax=ax)
ax.grid(which='both')
ax.set_title('Log_10 (Sigma)')
ax.set_xlim(xlim)
ax.set_ylim(zlim)
f.set_clim(clim_sig)
plt.show()
# -------------- Sources --------------------
# Define Custom Current Sources
# surface source
sg_x = np.zeros(mesh.vnF[0],dtype=complex)
sg_y = np.zeros(mesh.vnF[1],dtype=complex)
sg_z = np.zeros(mesh.vnF[2],dtype=complex)
nza = 2 # put the wire two cells above the surface
ncin = 2
# vertically directed wire
sgv_indx = (mesh.gridFz[:,0] > casing_a) & (mesh.gridFz[:,0] < casing_a + csx1) # hook it up to casing at the surface
sgv_indz = (mesh.gridFz[:,2] <= +csz*nza) & (mesh.gridFz[:,2] >= -csz*2)
sgv_ind = sgv_indx & sgv_indz
sg_z[sgv_ind] = -1.
# horizontally directed wire
sgh_indx = (mesh.gridFx[:,0] > casing_a) & (mesh.gridFx[:,0] <= inf_loc[2])
sgh_indz = (mesh.gridFx[:,2] > csz*(nza-0.5)) & (mesh.gridFx[:,2] < csz*(nza+0.5))
sgh_ind = sgh_indx & sgh_indz
sg_x[sgh_ind] = -1.
sgv2_indx = (mesh.gridFz[:,0] >= mesh.gridFx[sgh_ind,0].max()) & (mesh.gridFz[:,0] <= inf_loc[2]*1.2) # hook it up to casing at the surface
sgv2_indz = (mesh.gridFz[:,2] <= +csz*nza) & (mesh.gridFz[:,2] >= -csz*2)
sgv2_ind = sgv2_indx & sgv2_indz
sg_z[sgv2_ind] = 1.
# assemble the source
sg = np.hstack([sg_x,sg_y,sg_z])
sg_p = [FDEM.Src.RawVec_e([],_,sg/mesh.area) for _ in freqs]
# downhole source
dg_x = np.zeros(mesh.vnF[0],dtype=complex)
dg_y = np.zeros(mesh.vnF[1],dtype=complex)
dg_z = np.zeros(mesh.vnF[2],dtype=complex)
# vertically directed wire
dgv_indx = (mesh.gridFz[:,0] < csx1) # go through the center of the well
dgv_indz = (mesh.gridFz[:,2] <= +csz*nza) & (mesh.gridFz[:,2] > dsz + csz/2.)
dgv_ind = dgv_indx & dgv_indz
dg_z[dgv_ind] = -1.
# couple to the casing downhole
dgh_indx = mesh.gridFx[:,0] < casing_a + csx1
dgh_indz = (mesh.gridFx[:,2] < dsz + csz) & (mesh.gridFx[:,2] >= dsz)
dgh_ind = dgh_indx & dgh_indz
dg_x[dgh_ind] = 1.
# horizontal part at surface
dgh2_indx = mesh.gridFx[:,0] <= inf_loc[2]*1.2
dgh2_indz = sgh_indz.copy()
dgh2_ind = dgh2_indx & dgh2_indz
dg_x[dgh2_ind] = -1.
# vertical part at surface
dgv2_ind = sgv2_ind.copy()
dg_z[dgv2_ind] = 1.
# assemble the source
dg = np.hstack([dg_x,dg_y,dg_z])
dg_p = [FDEM.Src.RawVec_e([],_,dg/mesh.area) for _ in freqs]
# ------------ 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.pair(survey)
# ------------- Solve ---------------------------
t0 = time.time()
fieldsCasing = problem.fields(sigCasing)
print 'Time to solve 2 sources', time.time() - t0
# Plot current
# current density
jn0 = fieldsCasing[dg_p,'j']
jn1 = fieldsCasing[sg_p,'j']
# current
in0 = [mesh.area*fieldsCasing[dg_p,'j'][:,i] for i in range(len(freqs))]
in1 = [mesh.area*fieldsCasing[sg_p,'j'][:,i] for i in range(len(freqs))]
in0 = np.vstack(in0).T
in1 = np.vstack(in1).T
# integrate to get z-current inside casing
inds_inx = (mesh.gridFz[:,0] >= casing_a) & (mesh.gridFz[:,0] <= casing_b)
inds_inz = (mesh.gridFz[:,2] >= dsz ) & (mesh.gridFz[:,2] <= 0)
inds_fz = inds_inx & inds_inz
indsx = [False]*mesh.nFx
inds = list(indsx) + list(inds_fz)
in0_in = in0[np.r_[inds]]
in1_in = in1[np.r_[inds]]
z_in = mesh.gridFz[inds_fz,2]
in0_in = in0_in.reshape([in0_in.shape[0]/3,3])
in1_in = in1_in.reshape([in1_in.shape[0]/3,3])
z_in = z_in.reshape([z_in.shape[0]/3,3])
I0 = in0_in.sum(1).real
I1 = in1_in.sum(1).real
z_in = z_in[:,0]
if plotIt is True:
fig, ax = plt.subplots(1,2,figsize=(12,4))
ax[0].plot(z_in,np.absolute(I0), z_in,np.absolute(I1))
ax[0].legend(['top casing', 'bottom casing'],loc='best')
ax[0].set_title('Magnitude of Vertical Current in Casing')
ax[1].semilogy(z_in,np.absolute(I0), z_in,np.absolute(I1))
ax[1].legend(['top casing', 'bottom casing'],loc='best')
ax[1].set_title('Magnitude of Vertical Current in Casing')
ax[1].set_ylim([1e-2, 1.])
plt.show()
if __name__ == '__main__':
run()
@@ -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()
-102
View File
@@ -1,102 +0,0 @@
from SimPEG import *
def run(N=100, plotIt=True):
"""
Inversion: Linear Problem
=========================
Here we go over the basics of creating a linear problem and inversion.
"""
np.random.seed(1)
std_noise = 1e-2
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.
q = 1.
g = lambda k: np.exp(p*jk[k]*mesh.vectorCCx)*np.cos(np.pi*q*jk[k]*mesh.vectorCCx)
G = np.empty((nk, mesh.nC))
for i in range(nk):
G[i,:] = g(i)
mtrue = np.zeros(mesh.nC)
mtrue[mesh.vectorCCx > 0.3] = 1.
mtrue[mesh.vectorCCx > 0.45] = -0.5
mtrue[mesh.vectorCCx > 0.6] = 0
prob = Problem.LinearProblem(mesh, G)
survey = Survey.LinearSurvey()
survey.pair(prob)
survey.dobs = prob.fields(mtrue) + std_noise * np.random.randn(nk)
wd = np.ones(nk) * std_noise
# Distance weighting
wr = np.sum(prob.G**2.,axis=0)**0.5
wr = ( wr/np.max(wr) )
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = 1./wd
betaest = Directives.BetaEstimate_ByEig()
reg = Regularization.Sparse(mesh)
reg.mref = mref
reg.cell_weights = wr
reg.mref = np.zeros(mesh.nC)
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)
inv = Inversion.BaseInversion(invProb, directiveList=[IRLS,betaest,update_Jacobi])
# Run inversion
mrec = inv.run(m0)
print "Final misfit:" + str(invProb.dmisfit.eval(mrec))
if plotIt:
import matplotlib.pyplot as plt
fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
for i in range(prob.G.shape[0]):
axes[0].plot(prob.G[i,:])
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].legend(('True Model', 'Recovered Model'))
axes[1].set_ylim(-1.0,1.25)
axes[1].plot(mesh.vectorCCx, mrec, 'k-',lw = 2)
axes[1].legend(('True Model', 'Smooth l2-l2',
'Sparse lp:' + str(reg.norms[0]) + ', lqx:' + str(reg.norms[1]) ), fontsize = 12)
plt.show()
return prob, survey, mesh, mrec
if __name__ == '__main__':
run()
+4 -4
View File
@@ -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')
@@ -100,7 +100,7 @@ def run(plotIt=True):
# Regularization - with a regularization mesh
regMesh = simpeg.Mesh.TensorMesh([m1d.hx[problem.mapping.sigmaMap.maps[-1].indActive]],m1d.x0)
reg = simpeg.Regularization.Tikhonov(regMesh)
reg.mrefInSmooth = True
reg.smoothModel = True
reg.alpha_s = 1e-7
reg.alpha_x = 1.
# Inversion problem
+4 -3
View File
@@ -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
-62
View File
@@ -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()
-41
View File
@@ -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()
-43
View File
@@ -1,43 +0,0 @@
from SimPEG import *
from SimPEG.Utils import surface2ind_topo
def run(plotIt=True, nx=5, ny=5):
"""
Utils: surface2ind_topo
=======================
Here we show how to use :code:`Utils.surface2ind_topo` to identify cells below
a topographic surface.
"""
mesh = Mesh.TensorMesh([nx,ny], x0='CC') # 2D mesh
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
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))
mesh.plotGrid(ax=ax, nodes=True, centers=True)
ax.plot(xtopo,topo,'k',linewidth=1)
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)
plt.show()
if __name__ == '__main__':
run(plotIt=True)
+5 -10
View File
@@ -5,14 +5,10 @@ import DC_Analytic_Dipole
import DC_Forward_PseudoSection
import EM_FDEM_1D_Inversion
import EM_FDEM_Analytic_MagDipoleWholespace
import EM_Schenkel_Morrison_Casing
import EM_TDEM_1D_Inversion
import FLOW_Richards_1D_Celia1990
import Inversion_IRLS
import Forward_BasicDirectCurrent
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
@@ -22,9 +18,8 @@ import Mesh_QuadTree_HangingNodes
import Mesh_Tensor_Creation
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_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Forward_BasicDirectCurrent", "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"]
##### AUTOIMPORTS #####
@@ -40,7 +35,7 @@ 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 +92,12 @@ 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')
+2 -2
View File
@@ -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.
+1 -3
View File
@@ -33,9 +33,7 @@ class BaseInversion(object):
self._directiveList = value
self._directiveList.inversion = self
def __init__(self, invProb, directiveList=None, **kwargs):
if directiveList is None:
directiveList = []
def __init__(self, invProb, directiveList=[], **kwargs):
self.directiveList = directiveList
Utils.setKwargs(self, **kwargs)
+1 -1
View File
@@ -1,5 +1,5 @@
from SimPEG import SolverLU as SimpegSolver, PropMaps, Utils, mkvc, sp, np
from SimPEG.EM.FDEM.ProblemFDEM import BaseFDEMProblem
from SimPEG.EM.FDEM.FDEM import BaseFDEMProblem
from SurveyMT import Survey, Data
from FieldsMT import BaseMTFields
+2 -2
View File
@@ -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)
+6 -6
View File
@@ -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
+7 -12
View File
@@ -7,16 +7,17 @@ from SimPEG.MT.Utils.dataUtils import rec2ndarr
# Import modules
import numpy as np
import os, sys, re
try:
import osr
except ImportError as e:
print 'Could not import osr, missing the gdal package'
pass
class EDIimporter:
"""
A class to import EDIfiles.
"""
# Define data converters
_impUnitEDI2SI = 4*np.pi*1e-4 # Convert Z[mV/km/nT] (as in EDI)to Z[V/A] SI unit
_impUnitSI2EDI = 1./_impUnitEDI2SI # ConvertZ[V/A] SI unit to Z[mV/km/nT] (as in EDI)
@@ -25,8 +26,8 @@ class EDIimporter:
comps = None
# Hidden properties
_outEPSG = None # Project info
_2out = None # The projection operator
_outEPSG = None
_2out = None
def __init__(self, EDIfilesList, compList=None, outEPSG=None):
@@ -112,12 +113,6 @@ class EDIimporter:
# nOutData=length(obj.data);
# obj.data(nOutData+1:nOutData+length(TEMP.data),:) = TEMP.data;
def _transfromPoints(self,longD,latD):
# Import the coordinate projections
try:
import osr
except ImportError as e:
print 'Could not import osr, missing the gdal package\nCan not project coordinates'
raise e
# Coordinates convertor
if self._2out is None:
src = osr.SpatialReference()
+95 -35
View File
@@ -41,8 +41,8 @@ class IdentityMap(object):
If this is a meshless mapping (i.e. nP is defined independently)
the shape will be the the shape (nP,nP).
:rtype: tuple
:return: shape of the operator as a tuple (int,int)
:rtype: (int,int)
:return: shape of the operator as a tuple
"""
if self._nP is not None:
return (self.nP, self.nP)
@@ -86,7 +86,7 @@ class IdentityMap(object):
The derivative of the transformation.
:param numpy.array m: model
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: derivative of transformed model
"""
@@ -216,7 +216,7 @@ class ExpMap(IdentityMap):
def deriv(self, m):
"""
: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.
@@ -366,7 +366,7 @@ class SurjectVertical1D(IdentityMap):
def deriv(self, m):
"""
:param numpy.array m: model
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: derivative of transformed model
"""
repNum = self.mesh.vnC[:self.mesh.dim-1].prod()
@@ -427,7 +427,7 @@ class Surject2Dto3D(IdentityMap):
def deriv(self, m):
"""
:param numpy.array m: model
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: derivative of transformed model
"""
inds = self * np.arange(self.nP)
@@ -502,9 +502,7 @@ class InjectActiveCells(IdentityMap):
if Utils.isScalar(valInactive):
self.valInactive = np.ones(self.nC)*float(valInactive)
else:
self.valInactive = np.ones(self.nC)
self.valInactive[self.indInactive] = valInactive.copy()
self.valInactive = valInactive.copy()
self.valInactive[self.indActive] = 0
inds = np.nonzero(self.indActive)[0]
@@ -535,6 +533,83 @@ class ActiveCells(InjectActiveCells):
FutureWarning)
InjectActiveCells.__init__(self, mesh, indActive, valInactive, nC)
class InjectActiveCellsTopo(IdentityMap):
"""
Active model parameters. Extend for cells on topography to air cell (only works for tensor mesh)
"""
indActive = None #: Active Cells
valInactive = None #: Values of inactive Cells
nC = None #: Number of cells in the full model
def __init__(self, mesh, indActive, nC=None):
self.mesh = mesh
self.nC = nC or mesh.nC
if indActive.dtype is not bool:
z = np.zeros(self.nC,dtype=bool)
z[indActive] = True
indActive = z
self.indActive = indActive
self.indInactive = np.logical_not(indActive)
inds = np.nonzero(self.indActive)[0]
self.P = sp.csr_matrix((np.ones(inds.size),(inds, range(inds.size))), shape=(self.nC, self.nP))
@property
def shape(self):
return (self.nC, self.nP)
@property
def nP(self):
"""Number of parameters in the model."""
return self.indActive.sum()
def _transform(self, m):
val_temp = np.zeros(self.mesh.nC)
val_temp[self.indActive] = m
valInactive = np.zeros(self.mesh.nC)
#1D
if self.mesh.dim == 1:
z_temp = self.mesh.gridCC
val_temp[~self.indActive] = val_temp[np.argmax(z_temp[self.indActive])]
#2D
elif self.mesh.dim == 2:
act_temp = self.indActive.reshape((self.mesh.nCx, self.mesh.nCy), order = 'F')
val_temp = val_temp.reshape((self.mesh.nCx, self.mesh.nCy), order = 'F')
y_temp = self.mesh.gridCC[:,1].reshape((self.mesh.nCx, self.mesh.nCy), order = 'F')
for i in range(self.mesh.nCx):
act_tempx = act_temp[i,:] == 1
val_temp[i,~act_tempx] = val_temp[i,np.argmax(y_temp[i,act_tempx])]
valInactive[~self.indActive] = Utils.mkvc(val_temp)[~self.indActive]
#3D
elif self.mesh.dim == 3:
act_temp = self.indActive.reshape((self.mesh.nCx*self.mesh.nCy, self.mesh.nCz), order = 'F')
val_temp = val_temp.reshape((self.mesh.nCx*self.mesh.nCy, self.mesh.nCz), order = 'F')
z_temp = self.mesh.gridCC[:,2].reshape((self.mesh.nCx*self.mesh.nCy, self.mesh.nCz), order = 'F')
for i in range(self.mesh.nCx*self.mesh.nCy):
act_tempxy = act_temp[i,:] == 1
val_temp[i,~act_tempxy] = val_temp[i,np.argmax(z_temp[i,act_tempxy])]
valInactive[~self.indActive] = Utils.mkvc(val_temp)[~self.indActive]
self.valInactive = valInactive
return self.P*m + self.valInactive
def inverse(self, D):
return self.P.T*D
def deriv(self, m):
return self.P
class ActiveCellsTopo(InjectActiveCellsTopo):
def __init__(self, mesh, indActive, valInactive, nC=None):
warnings.warn(
"`ActiveCellsTopo` is deprecated and will be removed in future versions. Use `InjectActiveCellsTopo` instead",
FutureWarning)
InjectActiveCellsTopo.__init__(self, mesh, indActive, valInactive, nC)
class Weighting(IdentityMap):
"""
@@ -684,29 +759,15 @@ class PolyMap(IdentityMap):
m = [\sigma_1, \sigma_2, c]
Can take in an actInd vector to account for topography.
"""
def __init__(self, mesh, order, logSigma=True, normal='X', actInd = None):
def __init__(self, mesh, order, logSigma=True, normal='X'):
IdentityMap.__init__(self, mesh)
self.logSigma = logSigma
self.order = order
self.normal = normal
self.actInd = actInd
if getattr(self, 'actInd', None) is None:
self.actInd = range(self.mesh.nC)
self.nC = self.mesh.nC
else:
self.nC = len(self.actInd)
slope = 1e4
@property
def shape(self):
return (self.nC, self.nP)
@property
def nP(self):
if np.isscalar(self.order):
@@ -724,8 +785,8 @@ class PolyMap(IdentityMap):
sig1, sig2 = np.exp(sig1), np.exp(sig2)
#2D
if self.mesh.dim == 2:
X = self.mesh.gridCC[self.actInd,0]
Y = self.mesh.gridCC[self.actInd,1]
X = self.mesh.gridCC[:,0]
Y = self.mesh.gridCC[:,1]
if self.normal =='X':
f = polynomial.polyval(Y, c) - X
elif self.normal =='Y':
@@ -734,9 +795,9 @@ class PolyMap(IdentityMap):
raise(Exception("Input for normal = X or Y or Z"))
#3D
elif self.mesh.dim == 3:
X = self.mesh.gridCC[self.actInd,0]
Y = self.mesh.gridCC[self.actInd,1]
Z = self.mesh.gridCC[self.actInd,2]
X = self.mesh.gridCC[:,0]
Y = self.mesh.gridCC[:,1]
Z = self.mesh.gridCC[:,2]
if self.normal =='X':
f = polynomial.polyval2d(Y, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - X
elif self.normal =='Y':
@@ -745,7 +806,6 @@ class PolyMap(IdentityMap):
f = polynomial.polyval2d(X, Y, c.reshape((self.order[0]+1,self.order[1]+1))) - Z
else:
raise(Exception("Input for normal = X or Y or Z"))
else:
raise(Exception("Only supports 2D"))
@@ -759,8 +819,8 @@ class PolyMap(IdentityMap):
sig1, sig2 = np.exp(sig1), np.exp(sig2)
#2D
if self.mesh.dim == 2:
X = self.mesh.gridCC[self.actInd,0]
Y = self.mesh.gridCC[self.actInd,1]
X = self.mesh.gridCC[:,0]
Y = self.mesh.gridCC[:,1]
if self.normal =='X':
f = polynomial.polyval(Y, c) - X
@@ -772,9 +832,9 @@ class PolyMap(IdentityMap):
raise(Exception("Input for normal = X or Y or Z"))
#3D
elif self.mesh.dim == 3:
X = self.mesh.gridCC[self.actInd,0]
Y = self.mesh.gridCC[self.actInd,1]
Z = self.mesh.gridCC[self.actInd,2]
X = self.mesh.gridCC[:,0]
Y = self.mesh.gridCC[:,1]
Z = self.mesh.gridCC[:,2]
if self.normal =='X':
f = polynomial.polyval2d(Y, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - X
+24 -26
View File
@@ -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])
+97 -2
View File
@@ -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)])
+15 -18
View File
@@ -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]
@@ -330,7 +330,7 @@ class CylMesh(BaseTensorMesh, BaseRectangularMesh, InnerProducts, CylView):
raise NotImplementedError('wrapping in the averaging is not yet implemented')
return self._aveF2CCV
def getInterpolationMatCartMesh(self, Mrect, locType='CC', locTypeTo=None):
def getInterpolationMatCartMesh(self, Mrect, locType='CC'):
"""
Takes a cartesian mesh and returns a projection to translate onto the cartesian grid.
"""
@@ -338,22 +338,19 @@ class CylMesh(BaseTensorMesh, BaseRectangularMesh, InnerProducts, CylView):
assert self.isSymmetric, "Currently we have not taken into account other projections for more complicated CylMeshes"
if locTypeTo is None:
locTypeTo = locType
if locType == 'F':
# do this three times for each component
X = self.getInterpolationMatCartMesh(Mrect, locType='Fx', locTypeTo=locTypeTo+'x')
Y = self.getInterpolationMatCartMesh(Mrect, locType='Fy', locTypeTo=locTypeTo+'y')
Z = self.getInterpolationMatCartMesh(Mrect, locType='Fz', locTypeTo=locTypeTo+'z')
X = self.getInterpolationMatCartMesh(Mrect, locType='Fx')
Y = self.getInterpolationMatCartMesh(Mrect, locType='Fy')
Z = self.getInterpolationMatCartMesh(Mrect, locType='Fz')
return sp.vstack((X,Y,Z))
if locType == 'E':
X = self.getInterpolationMatCartMesh(Mrect, locType='Ex', locTypeTo=locTypeTo+'x')
Y = self.getInterpolationMatCartMesh(Mrect, locType='Ey', locTypeTo=locTypeTo+'y')
Z = spzeros(getattr(Mrect, 'n' + locTypeTo + 'z'), self.nE)
X = self.getInterpolationMatCartMesh(Mrect, locType='Ex')
Y = self.getInterpolationMatCartMesh(Mrect, locType='Ey')
Z = spzeros(Mrect.nEz, self.nE)
return sp.vstack((X,Y,Z))
grid = getattr(Mrect, 'grid' + locTypeTo)
grid = getattr(Mrect, 'grid' + locType)
# This is unit circle stuff, 0 to 2*pi, starting at x-axis, rotating counter clockwise in an x-y slice
theta = - np.arctan2(grid[:,0] - self.cartesianOrigin[0], grid[:,1] - self.cartesianOrigin[1]) + np.pi/2
theta[theta < 0] += np.pi*2.0
@@ -369,7 +366,7 @@ class CylMesh(BaseTensorMesh, BaseRectangularMesh, InnerProducts, CylView):
'Ex': Mrect.tangents[:Mrect.nEx,:],
'Ey': Mrect.tangents[Mrect.nEx:(Mrect.nEx+Mrect.nEy),:],
'Ez': Mrect.tangents[-Mrect.nEz:,:],
}[locTypeTo]
}[locType]
if 'F' in locType:
normals = np.c_[np.cos(theta), np.sin(theta), np.zeros(theta.size)]
proj = ( normals * dotMe ).sum(axis=1)
+30 -109
View File
@@ -307,28 +307,24 @@ class DiffOperators(object):
return BC
_cellGradBC_list = 'neumann'
def _cellGradStencil(self):
BC = self.setCellGradBC(self._cellGradBC_list)
n = self.vnC
if(self.dim == 1):
G = ddxCellGrad(n[0], BC[0])
elif(self.dim == 2):
G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC[0]))
G2 = sp.kron(ddxCellGrad(n[1], BC[1]), speye(n[0]))
G = sp.vstack((G1, G2), format="csr")
elif(self.dim == 3):
G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC[0]))
G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC[1]), speye(n[0]))
G3 = kron3(ddxCellGrad(n[2], BC[2]), speye(n[1]), speye(n[0]))
G = sp.vstack((G1, G2, G3), format="csr")
return G
def cellGrad():
doc = "The cell centered Gradient, takes you to cell faces."
def fget(self):
if(self._cellGrad is None):
G = self._cellGradStencil()
BC = self.setCellGradBC(self._cellGradBC_list)
n = self.vnC
if(self.dim == 1):
G = ddxCellGrad(n[0], BC[0])
elif(self.dim == 2):
G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC[0]))
G2 = sp.kron(ddxCellGrad(n[1], BC[1]), speye(n[0]))
G = sp.vstack((G1, G2), format="csr")
elif(self.dim == 3):
G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC[0]))
G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC[1]), speye(n[0]))
G3 = kron3(ddxCellGrad(n[2], BC[2]), speye(n[1]), speye(n[0]))
G = sp.vstack((G1, G2, G3), format="csr")
# Compute areas of cell faces & volumes
S = self.area
V = self.aveCC2F*self.vol # Average volume between adjacent cells
@@ -365,24 +361,19 @@ class DiffOperators(object):
_cellGradBC = None
cellGradBC = property(**cellGradBC())
def _cellGradxStencil(self):
BC = ['neumann', 'neumann']
n = self.vnC
if(self.dim == 1):
G1 = ddxCellGrad(n[0], BC)
elif(self.dim == 2):
G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC))
elif(self.dim == 3):
G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC))
return G1
def cellGradx():
doc = "Cell centered Gradient in the x dimension. Has neumann boundary conditions."
def fget(self):
if getattr(self, '_cellGradx', None) is None:
G1 = self._cellGradxStencil()
BC = ['neumann', 'neumann']
n = self.vnC
if(self.dim == 1):
G1 = ddxCellGrad(n[0], BC)
elif(self.dim == 2):
G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC))
elif(self.dim == 3):
G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC))
# Compute areas of cell faces & volumes
V = self.aveCC2F*self.vol
L = self.r(self.area/V, 'F','Fx', 'V')
@@ -391,22 +382,17 @@ class DiffOperators(object):
return locals()
cellGradx = property(**cellGradx())
def _cellGradyStencil(self):
if self.dim < 2: return None
BC = ['neumann', 'neumann']
n = self.vnC
if(self.dim == 2):
G2 = sp.kron(ddxCellGrad(n[1], BC), speye(n[0]))
elif(self.dim == 3):
G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC), speye(n[0]))
return G2
def cellGrady():
doc = "Cell centered Gradient in the x dimension. Has neumann boundary conditions."
def fget(self):
if self.dim < 2: return None
if getattr(self, '_cellGrady', None) is None:
G2 = self._cellGradyStencil()
BC = ['neumann', 'neumann']
n = self.vnC
if(self.dim == 2):
G2 = sp.kron(ddxCellGrad(n[1], BC), speye(n[0]))
elif(self.dim == 3):
G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC), speye(n[0]))
# Compute areas of cell faces & volumes
V = self.aveCC2F*self.vol
L = self.r(self.area/V, 'F','Fy', 'V')
@@ -415,19 +401,14 @@ class DiffOperators(object):
return locals()
cellGrady = property(**cellGrady())
def _cellGradzStencil(self):
if self.dim < 3: return None
BC = ['neumann', 'neumann']
n = self.vnC
G3 = kron3(ddxCellGrad(n[2], BC), speye(n[1]), speye(n[0]))
return G3
def cellGradz():
doc = "Cell centered Gradient in the x dimension. Has neumann boundary conditions."
def fget(self):
if self.dim < 3: return None
if getattr(self, '_cellGradz', None) is None:
G3 = self._cellGradzStencil()
BC = ['neumann', 'neumann']
n = self.vnC
G3 = kron3(ddxCellGrad(n[2], BC), speye(n[1]), speye(n[0]))
# Compute areas of cell faces & volumes
V = self.aveCC2F*self.vol
L = self.r(self.area/V, 'F','Fz', 'V')
@@ -584,67 +565,7 @@ class DiffOperators(object):
return Pbc, Pin, Pout
def getBCProjWF_simple(self, discretization='CC'):
"""
The weak form boundary condition projection matrices
when mixed boundary condition is used
"""
if discretization is not 'CC':
raise NotImplementedError('Boundary conditions only implemented for CC discretization.')
def projBC(n):
ij = ([0,n], [0,1])
vals = [0,0]
vals[0] = 1
vals[1] = 1
return sp.csr_matrix((vals, ij), shape=(n+1,2))
def projDirichlet(n, bc):
bc = checkBC(bc)
ij = ([0,n], [0,1])
vals = [0,0]
if(bc[0] == 'dirichlet'):
vals[0] = -1
if(bc[1] == 'dirichlet'):
vals[1] = 1
return sp.csr_matrix((vals, ij), shape=(n+1,2))
BC = [['dirichlet','dirichlet'],['dirichlet','dirichlet'],['dirichlet','dirichlet']]
n = self.vnC
indF = self.faceBoundaryInd
if(self.dim == 1):
Pbc = projDirichlet(n[0], BC[0])
B = projBC(n[0])
indF = indF[0] | indF[1]
Pbc = Pbc*sdiag(self.area[indF])
elif(self.dim == 2):
Pbc1 = sp.kron(speye(n[1]), projDirichlet(n[0], BC[0]))
Pbc2 = sp.kron(projDirichlet(n[1], BC[1]), speye(n[0]))
Pbc = sp.block_diag((Pbc1, Pbc2), format="csr")
B1 = sp.kron(speye(n[1]), projBC(n[0]))
B2 = sp.kron(projBC(n[1]), speye(n[0]))
B = sp.block_diag((B1, B2), format="csr")
indF = np.r_[(indF[0] | indF[1]), (indF[2] | indF[3])]
Pbc = Pbc*sdiag(self.area[indF])
elif(self.dim == 3):
Pbc1 = kron3(speye(n[2]), speye(n[1]), projDirichlet(n[0], BC[0]))
Pbc2 = kron3(speye(n[2]), projDirichlet(n[1], BC[1]), speye(n[0]))
Pbc3 = kron3(projDirichlet(n[2], BC[2]), speye(n[1]), speye(n[0]))
Pbc = sp.block_diag((Pbc1, Pbc2, Pbc3), format="csr")
B1 = kron3(speye(n[2]), speye(n[1]), projBC(n[0]))
B2 = kron3(speye(n[2]), projBC(n[1]), speye(n[0]))
B3 = kron3(projBC(n[2]), speye(n[1]), speye(n[0]))
B = sp.block_diag((B1, B2, B3), format="csr")
indF = np.r_[(indF[0] | indF[1]), (indF[2] | indF[3]), (indF[4] | indF[5])]
Pbc = Pbc*sdiag(self.area[indF])
return Pbc, B.T
# --------------- Averaging ---------------------
@property
+9 -8
View File
@@ -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"
+37 -23
View File
@@ -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.
@@ -19,9 +21,10 @@ class TensorMeshIO(object):
if '*' in seg:
st = seg
sp = seg.split('*')
re = int(sp[0])*(' ' + sp[1])
re = np.array(sp[0],dtype=int)*(' ' + sp[1])
line = line.replace(st,re.strip())
return np.array(line.split(),dtype=float)
# Read the file as line strings, remove lines with comment = !
msh = np.genfromtxt(fileName,delimiter='\n',dtype=np.str,comments='!')
@@ -46,9 +49,11 @@ 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 +103,9 @@ 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 +163,12 @@ 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 +184,8 @@ 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 +202,8 @@ 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 +232,9 @@ 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 +287,10 @@ 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 +336,11 @@ 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:
+4 -4
View File
@@ -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"
+4 -10
View File
@@ -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::
@@ -2131,16 +2131,10 @@ class TreeMesh(BaseTensorMesh, InnerProducts, TreeMeshIO):
def plotSlice(self, v, vType='CC',
normal='Z', ind=None, grid=True, view='real',
ax=None, clim=None, showIt=False,
pcolorOpts=None,
streamOpts=None,
gridOpts=None):
pcolorOpts={},
streamOpts={'color':'k'},
gridOpts={'color':'k', 'alpha':0.5}):
if pcolorOpts is None:
pcolorOpts = {}
if streamOpts is None:
streamOpts = {'color':'k'}
if gridOpts is None:
gridOpts = {'color':'k', 'alpha':0.5}
assert vType in ['CC','F','E']
assert self.dim == 3
+50 -106
View File
@@ -42,9 +42,9 @@ class TensorView(object):
def plotImage(self, v, vType='CC', grid=False, view='real',
ax=None, clim=None, showIt=False,
pcolorOpts=None,
streamOpts=None,
gridOpts=None,
pcolorOpts={},
streamOpts={'color':'k'},
gridOpts={'color':'k'},
numbering=True, annotationColor='w'
):
"""
@@ -84,12 +84,6 @@ class TensorView(object):
M.plotImage(v, annotationColor='k', showIt=True)
"""
if pcolorOpts is None:
pcolorOpts = {}
if streamOpts is None:
streamOpts = {'color':'k'}
if gridOpts is None:
gridOpts = {'color':'k'}
if ax is None:
fig = plt.figure()
@@ -180,9 +174,9 @@ class TensorView(object):
def plotSlice(self, v, vType='CC',
normal='Z', ind=None, grid=False, view='real',
ax=None, clim=None, showIt=False,
pcolorOpts=None,
streamOpts=None,
gridOpts=None
pcolorOpts={},
streamOpts={'color':'k'},
gridOpts={'color':'k', 'alpha':0.5}
):
"""
@@ -203,12 +197,6 @@ class TensorView(object):
M.plotSlice(M.cellGrad*b, 'F', view='vec', grid=True, showIt=True, pcolorOpts={'alpha':0.8})
"""
if pcolorOpts is None:
pcolorOpts = {}
if streamOpts is None:
streamOpts = {'color':'k'}
if gridOpts is None:
gridOpts = {'color':'k', 'alpha':0.5}
if type(vType) in [list, tuple]:
assert ax is None, "cannot specify an axis to plot on with this function."
fig, axs = plt.subplots(1,len(vType))
@@ -218,7 +206,7 @@ class TensorView(object):
return out
viewOpts = ['real','imag','abs','vec']
normalOpts = ['X', 'Y', 'Z']
vTypeOpts = ['CC', 'CCv','N','F','E','Fx','Fy','Fz','E','Ex','Ey','Ez']
vTypeOpts = ['CC', 'CCv','F','E','Fx','Fy','Fz','E','Ex','Ey','Ez']
# Some user error checking
assert vType in vTypeOpts, "vType must be in ['%s']" % "','".join(vTypeOpts)
@@ -301,17 +289,11 @@ class TensorView(object):
def _plotImage2D(self, v, vType='CC', grid=False, view='real',
ax=None, clim=None, showIt=False,
pcolorOpts=None,
streamOpts=None,
gridOpts=None
pcolorOpts={},
streamOpts={'color':'k'},
gridOpts={'color':'k'}
):
if pcolorOpts is None:
pcolorOpts = {}
if streamOpts is None:
streamOpts = {'color':'k'}
if gridOpts is None:
gridOpts = {'color':'k'}
vTypeOptsCC = ['N','CC','Fx','Fy','Ex','Ey']
vTypeOptsV = ['CCv','F','E']
vTypeOpts = vTypeOptsCC + vTypeOptsV
@@ -552,8 +534,7 @@ 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 +542,60 @@ 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 +612,16 @@ 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 *
+6 -24
View File
@@ -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.'
@@ -888,8 +888,6 @@ class ProjectedGNCG(BFGS, Minimize, Remember):
maxIterCG = 5
tolCG = 1e-1
stepOffBoundsFact = 0.1 # perturbation of the inactive set off the bounds
lower = -np.inf
upper = np.inf
@@ -992,20 +990,4 @@ class ProjectedGNCG(BFGS, Minimize, Remember):
cgFlag = 1
# End CG Iterations
# Take a gradient step on the active cells if exist
if temp != self.xc.size:
rhs_a = (Active) * -self.g
dm_i = max( abs( delx ) )
dm_a = max( abs(rhs_a) )
# perturb inactive set off of bounds so that they are included in the step
delx = delx + self.stepOffBoundsFact * (rhs_a * dm_i / dm_a)
# Only keep gradients going in the right direction on the active set
indx = ((self.xc<=self.lower) & (delx < 0)) | ((self.xc>=self.upper) & (delx > 0))
delx[indx] = 0.
return delx
return delx
+3 -3
View File
@@ -74,7 +74,7 @@ class Property(object):
if linkedMap is None:
return None
linkMap = linkMapClass(None) * linkedMap
m = getattr(self, '%sModel'%linkName)
m = getattr(self, '%s'%linkName)
return linkMap.deriv( m )
m = getattr(self, '%sModel'%prop.name)
@@ -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):
@@ -239,7 +239,7 @@ class PropMap(object):
setattr(self, '%sMap'%name, mapping)
setattr(self, '%sIndex'%name, slices.get(name, slice(nP, nP + mapping.nP)))
nP += mapping.nP
self.nP = nP
self.nP = nP
@property
def defaultInvProp(self):
+321 -799
View File
File diff suppressed because it is too large Load Diff
+3 -2
View File
@@ -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
View File
@@ -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
+17 -27
View File
@@ -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
"""
@@ -88,14 +88,12 @@ def getIndicesBlock(p0,p1,ccMesh):
# Return a tuple
return ind
def defineBlock(ccMesh,p0,p1,vals=None):
def defineBlock(ccMesh,p0,p1,vals=[0,1]):
"""
Build a block with the conductivity specified by condVal. Returns an array.
vals[0] conductivity of the block
vals[1] conductivity of the ground
"""
if vals is None:
vals = [0,1]
sigma = np.zeros(ccMesh.shape[0]) + vals[1]
ind = getIndicesBlock(p0,p1,ccMesh)
@@ -103,11 +101,7 @@ def defineBlock(ccMesh,p0,p1,vals=None):
return mkvc(sigma)
def defineElipse(ccMesh, center=None, anisotropy=None, slope=10., theta=0.):
if center is None:
center = [0,0,0]
if anisotropy is None:
anisotropy = [1,1,1]
def defineElipse(ccMesh, center=[0,0,0], anisotropy=[1,1,1], slope=10., theta=0.):
G = ccMesh.copy()
dim = ccMesh.shape[1]
for i in range(dim):
@@ -147,7 +141,7 @@ def getIndicesSphere(center,radius,ccMesh):
if dimMesh == 1:
# Define the reference points
ind = np.abs(center[0] - ccMesh[:,0]) < radius
elif dimMesh == 2:
@@ -162,7 +156,7 @@ def getIndicesSphere(center,radius,ccMesh):
# Return a tuple
return ind
def defineTwoLayers(ccMesh,depth,vals=None):
def defineTwoLayers(ccMesh,depth,vals=[0,1]):
"""
Define a two layered model. Depth of the first layer must be specified.
CondVals vector with the conductivity values of the layers. Eg:
@@ -173,8 +167,6 @@ def defineTwoLayers(ccMesh,depth,vals=None):
0 depth zf
1st layer 2nd layer
"""
if vals is None:
vals = [0,1]
sigma = np.zeros(ccMesh.shape[0]) + vals[1]
dim = np.size(ccMesh[0,:])
@@ -222,14 +214,14 @@ 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
@@ -253,21 +245,21 @@ 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
def randomModel(shape, seed=None, anisotropy=None, its=100, bounds=None):
def randomModel(shape, seed=None, anisotropy=None, its=100, bounds=[0,1]):
"""
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
@@ -284,8 +276,6 @@ def randomModel(shape, seed=None, anisotropy=None, its=100, bounds=None):
"""
if bounds is None:
bounds = [0,1]
if seed is None:
seed = np.random.randint(1e3)
+7 -7
View File
@@ -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):
-1
View File
@@ -7,4 +7,3 @@ from CounterUtils import *
import ModelBuilder
import SolverUtils
from coordutils import *
from modelutils import *
+1 -3
View File
@@ -55,10 +55,8 @@ def hook(obj, method, name=None, overwrite=False, silent=False):
print 'Method '+name+' was not overwritten.'
def setKwargs(obj, ignore=None, **kwargs):
def setKwargs(obj, ignore=[], **kwargs):
"""Sets key word arguments (kwargs) that are present in the object, throw an error if they don't exist."""
if ignore is None:
ignore = []
for attr in kwargs:
if attr in ignore:
continue
+1 -1
View File
@@ -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::
-137
View File
@@ -1,137 +0,0 @@
from SimPEG import np, Mesh
import time as tm
import vtk, vtk.util.numpy_support as npsup
import re
def read_GOCAD_ts(tsfile):
"""
Read GOCAD triangulated surface (*.ts) file
INPUT:
tsfile: Triangulated surface
OUTPUT:
vrts : Array of vertices in XYZ coordinates [n x 3]
trgl : Array of index for triangles [m x 3]. The order of the vertices
is important and describes the normal
n = cross( (P2 - P1 ) , (P3 - P1) )
Author: @fourndo
.. note::
Remove all attributes from the GoCAD surface before exporting it!
"""
fid = open(tsfile,'r')
line = fid.readline()
# Skip all the lines until the vertices
while re.match('TFACE',line)==None:
line = fid.readline()
line = fid.readline()
vrtx = []
# Run down all the vertices and save in array
while re.match('VRTX',line):
l_input = re.split('[\s*]',line)
temp = np.array(l_input[2:5])
vrtx.append(temp.astype(np.float))
# Read next line
line = fid.readline()
vrtx = np.asarray(vrtx)
# Skip lines to the triangles
while re.match('TRGL',line)==None:
line = fid.readline()
# Run down the list of triangles
trgl = []
# Run down all the vertices and save in array
while re.match('TRGL',line):
l_input = re.split('[\s*]',line)
temp = np.array(l_input[1:4])
trgl.append(temp.astype(np.int))
# Read next line
line = fid.readline()
trgl = np.asarray(trgl)
return vrtx, trgl
def surface2inds(vrtx, trgl, mesh, boundaries=True, internal=True):
""""
Function to read gocad polystructure file and output indexes of mesh with in the structure.
"""
# Adjust the index
trgl = trgl - 1
# Make vtk pts
ptsvtk = vtk.vtkPoints()
ptsvtk.SetData(npsup.numpy_to_vtk(vrtx,deep=1))
# Make the polygon connection
polys = vtk.vtkCellArray()
for face in trgl:
poly = vtk.vtkPolygon()
poly.GetPointIds().SetNumberOfIds(len(face))
for nrv, vert in enumerate(face):
poly.GetPointIds().SetId(nrv,vert)
polys.InsertNextCell(poly)
# Make the polydata, structure of connections and vrtx
polyData = vtk.vtkPolyData()
polyData.SetPoints(ptsvtk)
polyData.SetPolys(polys)
# Make implicit func
ImpDistFunc = vtk.vtkImplicitPolyDataDistance()
ImpDistFunc.SetInput(polyData)
# Convert the mesh
vtkMesh = vtk.vtkRectilinearGrid()
vtkMesh.SetDimensions(mesh.nNx,mesh.nNy,mesh.nNz)
vtkMesh.SetXCoordinates(npsup.numpy_to_vtk(mesh.vectorNx, deep=1))
vtkMesh.SetYCoordinates(npsup.numpy_to_vtk(mesh.vectorNy, deep=1))
vtkMesh.SetZCoordinates(npsup.numpy_to_vtk(mesh.vectorNz, deep=1))
# Add indexes
vtkInd = npsup.numpy_to_vtk(np.arange(mesh.nC), deep=1)
vtkInd.SetName('Index')
vtkMesh.GetCellData().AddArray(vtkInd)
extractImpDistRectGridFilt = vtk.vtkExtractGeometry() # Object constructor
extractImpDistRectGridFilt.SetImplicitFunction(ImpDistFunc) #
extractImpDistRectGridFilt.SetInputData(vtkMesh)
if boundaries is True:
extractImpDistRectGridFilt.ExtractBoundaryCellsOn()
else:
extractImpDistRectGridFilt.ExtractBoundaryCellsOff()
if internal is True:
extractImpDistRectGridFilt.ExtractInsideOn()
else:
extractImpDistRectGridFilt.ExtractInsideOff()
print "Extracting indices from grid..."
# Executing the pipe
extractImpDistRectGridFilt.Update()
# Get index inside
insideGrid = extractImpDistRectGridFilt.GetOutput()
insideGrid = npsup.vtk_to_numpy(insideGrid.GetCellData().GetArray('Index'))
# Return the indexes inside
return insideGrid
+6 -6
View File
@@ -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
View File
@@ -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) \
-63
View File
@@ -1,63 +0,0 @@
from matutils import mkvc, ndgrid
import numpy as np
def surface2ind_topo(mesh, topo, gridLoc='CC'):
# def genActiveindfromTopo(mesh, topo):
"""
Get active indices from topography
"""
if mesh.dim == 3:
from scipy.interpolate import NearestNDInterpolator
Ftopo = NearestNDInterpolator(topo[:,:2], topo[:,2])
if gridLoc == 'CC':
XY = ndgrid(mesh.vectorCCx, mesh.vectorCCy)
Zcc = mesh.gridCC[:,2].reshape((np.prod(mesh.vnC[:2]), mesh.nCz), order='F')
gridTopo = Ftopo(XY)
actind = [gridTopo[ixy] <= Zcc[ixy,:] for ixy in range(np.prod(mesh.vnC[0]))]
actind = np.hstack(actind)
elif gridLoc == 'N':
XY = ndgrid(mesh.vectorNx, mesh.vectorNy)
gridTopo = Ftopo(XY).reshape(mesh.vnN[:2], order='F')
if mesh._meshType not in ['TENSOR', 'CYL', 'BASETENSOR']:
raise NotImplementedError('Nodal surface2ind_topo not implemented for %s mesh'%mesh._meshType)
Nz = mesh.vectorNz[1:] # TODO: this will only work for tensor meshes
actind = np.array([False]*mesh.nC).reshape(mesh.vnC, order='F')
for ii in range(mesh.nCx):
for jj in range(mesh.nCy):
actind[ii,jj,:] = [np.all(gridTopo[ii:ii+2, jj:jj+2] >= Nz[kk]) for kk in range(len(Nz)) ]
elif mesh.dim == 2:
from scipy.interpolate import interp1d
Ftopo = interp1d(topo[:,0], topo[:,1])
if gridLoc == 'CC':
gridTopo = Ftopo(mesh.gridCC[:,0])
actind = mesh.gridCC[:,1] <= gridTopo
elif gridLoc == 'N':
gridTopo = Ftopo(mesh.vectorNx)
if mesh._meshType not in ['TENSOR', 'CYL', 'BASETENSOR']:
raise NotImplementedError('Nodal surface2ind_topo not implemented for %s mesh'%mesh._meshType)
Ny = mesh.vectorNy[1:] # TODO: this will only work for tensor meshes
actind = np.array([False]*mesh.nC).reshape(mesh.vnC, order='F')
for ii in range(mesh.nCx):
actind[ii,:] = [np.all(gridTopo[ii:ii+2] > Ny[kk]) for kk in range(len(Ny)) ]
else:
raise NotImplementedError('surface2ind_topo not implemented for 1D mesh')
return mkvc(actind)
+1 -1
View File
@@ -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'

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+1 -1
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@@ -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

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-22
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@@ -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 %}
+9 -16
View File
@@ -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
+19
View File
@@ -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:

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