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6 Commits
153 changed files with 1410 additions and 117029 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
+3 -27
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@@ -18,32 +18,24 @@ env:
- TEST_DIR="tests/mesh tests/base tests/utils"
- TEST_DIR=tests/em/fdem/inverse/derivs
- TEST_DIR=tests/em/tdem
- TEST_DIR=tests/pf
- TEST_DIR=tests/dcip
- TEST_DIR=tests/flow
- TEST_DIR=tests/mt
- 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
@@ -54,28 +46,12 @@ install:
# Run test
script:
# test docs
- nosetests $TEST_DIR --with-cov --cov SimPEG --cov-config .coveragerc -v -s
# Calculate coverage
after_success:
- coveralls --config_file .coveragerc
- if [ "$TRAVIS_BRANCH" = "master" -a "$TRAVIS_PULL_REQUEST" = "false" ]; then
if [ ${TEST_DIR} == "tests/docs" ]; then
python scripts/fetch_gae_sdk.py $(dirname "${GAE_PYTHONPATH}");
openssl aes-256-cbc -K $encrypted_93066031461c_key -iv $encrypted_93066031461c_iv
-in docs/credentials.tar.gz.enc -out credentials.tar.gz -d ;
if [ ! -d ${HOME}/google-cloud-sdk ]; then curl https://sdk.cloud.google.com | bash; fi ;
tar -xzf credentials.tar.gz ;
gcloud auth activate-service-account --key-file client-secret.json ;
gcloud config set project simpegdocs;
gcloud -q components update gae-python;
gcloud -q preview app deploy ./docs/app.yaml --version ${TRAVIS_COMMIT} --promote;
fi;
fi
notifications:
email:
- rowanc1@gmail.com
+1 -1
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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
======
+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::
+194 -155
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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])
@@ -169,19 +169,23 @@ 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='dpdp', dtype="appc", clim=None, cblabel=True, axlabel = True, colorbar = True, contour = None):
"""
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)
: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
@@ -214,39 +218,39 @@ 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':
# Change output for dtype
if dtype == 'volt':
rho = np.hstack([rho,data])
else:
# Compute pant leg of apparent rho
if surveyType == 'pole-dipole':
if stype == 'pdp':
leg = data * 2*np.pi * MA * ( MA + MN ) / MN
elif surveyType == 'dipole-dipole':
elif stype == 'dpdp':
leg = data * 2*np.pi / ( 1/MA - 1/MB - 1/NB + 1/NA )
else:
print """unitType must be 'pole-dipole' | 'dipole-dipole' """
print """dtype must be 'pdp'(pole-dipole) | 'dpdp' (dipole-dipole) """
break
if unitType == 'appConductivity':
if dtype == 'appc':
leg = np.log10(abs(1./leg))
rho = np.hstack([rho,leg])
elif unitType == 'appResistivity':
elif dtype == 'appr':
leg = np.log10(abs(leg))
rho = np.hstack([rho,leg])
else:
print """unitType must be 'appResistivity' | 'appConductivity' | 'volt' """
print """dtype must be 'appr' | 'appc' | 'volt' """
break
midx = np.hstack([midx, ( Cmid + Pmid )/2 ])
@@ -255,7 +259,7 @@ def plot_pseudoSection(DCsurvey, axs, surveyType='dipole-dipole', unitType='volt
# 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()
@@ -264,39 +268,38 @@ def plot_pseudoSection(DCsurvey, axs, surveyType='dipole-dipole', unitType='volt
# Plot data
grid_rho = np.ma.masked_where(np.isnan(grid_rho), grid_rho)
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':
if dtype == 'volt':
cbar = plt.colorbar(ph, ax = axs, format="%4.1f",fraction=0.04,orientation="horizontal")
else:
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':
cmin,cmax = cbar.get_clim()
ticks = np.linspace(cmin,cmax,3)
cbar.set_ticks(ticks)
cbar.ax.tick_params(labelsize=10)
if cblabel:
if dtype == 'appc':
cbar.set_label("App.Cond",size=12)
elif unitType == 'appResistivity':
elif dtype == 'appr':
cbar.set_label("App.Res.",size=12)
elif unitType == 'volt':
elif dtype == 'volt':
cbar.set_label("Potential (V)",size=12)
if not axlabel:
axs.set_xticklabels([])
axs.set_yticklabels([])
@@ -307,24 +310,27 @@ def plot_pseudoSection(DCsurvey, axs, surveyType='dipole-dipole', unitType='volt
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 +346,17 @@ 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 +366,14 @@ 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 +382,33 @@ 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 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 +416,23 @@ 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 +441,12 @@ 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]
@@ -449,38 +455,44 @@ 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='3D', stype='SURFACE', iptype = 0):
"""
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')
count = 0
for ii in range(DCsurvey.nSrc):
@@ -494,33 +506,33 @@ 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)
B = np.repeat(tx[0,1],M.shape[0],axis=0)
M = M[:,0]
N = N[:,0]
np.savetxt(fid, np.c_[A, B, M, N , DCsurvey.dobs[count:count+nD], DCsurvey.std[count:count+nD] ], fmt='%e',delimiter=' ',newline='\n')
else:
if surveyType == 'SURFACE':
if stype == 'SURFACE':
fid.writelines("%f " % ii for ii in mkvc(tx[0,:]))
M = M[:,0]
N = N[:,0]
if surveyType == 'GENERAL':
if stype == 'GENERAL':
# Flip sign for z-elevation to depth
tx[2::2,:] = -tx[2::2,:]
fid.writelines("%e " % ii for ii in mkvc(tx[::2,:]))
M = M[:,0::2]
N = N[:,0::2]
@@ -528,31 +540,31 @@ def writeUBC_DCobs(fileName, DCsurvey, dim, surveyType, iptype = 0):
# 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')
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.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, flag = 'local'):
"""
Read DC survey and projects the coordinate system
according to the flag = 'Xloc' | 'Yloc' | 'local' (default)
@@ -561,9 +573,15 @@ def convertObs_DC3D_to_2D(DCsurvey, lineID, flag='local'):
The Z value is preserved, but Y coordinates zeroed.
:param DC.Survey survey3D: 3D simpeg DC survey
:rtype: DC.Survey
:return: survey2D
Input:
:param survey3D
Output:
:figure survey2D
Edited April 6th, 2016
@author: dominiquef
"""
from SimPEG import np
@@ -648,34 +666,39 @@ def convertObs_DC3D_to_2D(DCsurvey, lineID, flag='local'):
DCsurvey2D.std = np.asarray(DCsurvey.std)
return DCsurvey2D
def readUBC_DC3Dobs(fileName, rtype = 'DC'):
def readUBC_DC3Dobs(fileName, dtype = 'DC'):
"""
Read UBC GIF IP 3D observation file and generate survey
: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 IPsurvey
:return
@author: dominiquef
"""
zflag = True # Flag for z value provided
# Load file
if rtype == 'IP':
if dtype == 'IP':
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='IPTYPE')
elif rtype == 'DC':
elif dtype == 'DC':
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
else:
print "rtype must be 'DC'(default) | 'IP'"
print "dtype must be 'DC'(default) | 'IP'"
# Pre-allocate
srcLists = []
Rx = []
d = []
wd = []
# Countdown for number of obs/tx
count = 0
@@ -694,7 +717,7 @@ def readUBC_DC3Dobs(fileName, rtype = 'DC'):
# 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
else:
@@ -706,12 +729,12 @@ def readUBC_DC3Dobs(fileName, rtype = 'DC'):
temp = np.fromstring(obsfile[ii], dtype=float,sep=' ') # Get the string
# Filter out negative IP
# if temp[-2] < 0:
# if temp[-2] < 0:
# count = count -1
# print "Negative!"
#
#
# else:
# If the Z-location is provided, otherwise put nan
if zflag:
@@ -749,9 +772,17 @@ 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
@@ -791,9 +822,11 @@ 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
:param fileName, path to the UBC GIF 3D obs file
Output:
DCsurvey
:return
Created on Mon March 9th, 2016 << Doug's 70th Birthday !! >>
@@ -855,9 +888,12 @@ 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 +959,12 @@ 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
+58 -132
View File
@@ -144,7 +144,6 @@ class BetaSchedule(InversionDirective):
if self.debug: print 'BetaSchedule is cooling Beta. Iteration: %d' % self.opt.iter
self.invProb.beta /= self.coolingFactor
class TargetMisfit(InversionDirective):
chifact = 1.
@@ -167,7 +166,7 @@ class TargetMisfit(InversionDirective):
class SaveEveryIteration(InversionDirective):
class _SaveEveryIteration(InversionDirective):
@property
def name(self):
if getattr(self, '_name', None) is None:
@@ -188,7 +187,7 @@ class SaveEveryIteration(InversionDirective):
self._fileName = value
class SaveModelEveryIteration(SaveEveryIteration):
class SaveModelEveryIteration(_SaveEveryIteration):
"""SaveModelEveryIteration"""
def initialize(self):
@@ -198,7 +197,7 @@ class SaveModelEveryIteration(SaveEveryIteration):
np.save('%03d-%s' % (self.opt.iter, self.fileName), self.opt.xc)
class SaveOutputEveryIteration(SaveEveryIteration):
class SaveOutputEveryIteration(_SaveEveryIteration):
"""SaveModelEveryIteration"""
def initialize(self):
@@ -212,7 +211,7 @@ class SaveOutputEveryIteration(SaveEveryIteration):
f.write(' %3d %1.4e %1.4e %1.4e %1.4e\n'%(self.opt.iter, self.invProb.beta, self.invProb.phi_d, self.invProb.phi_m, self.opt.f))
f.close()
class SaveOutputDictEveryIteration(SaveEveryIteration):
class SaveOutputDictEveryIteration(_SaveEveryIteration):
"""SaveOutputDictEveryIteration"""
def initialize(self):
@@ -243,6 +242,12 @@ class SaveOutputDictEveryIteration(SaveEveryIteration):
# Save the file as a npz
np.savez('{:03d}-{:s}'.format(self.opt.iter,self.fileName), iter=self.opt.iter, beta=self.invProb.beta, phi_d=self.invProb.phi_d, phi_m=self.invProb.phi_m, phi_ms=phi_ms, phi_mx=phi_mx, phi_my=phi_my, phi_mz=phi_mz,f=self.opt.f, m=self.invProb.curModel,dpred=self.invProb.dpred)
# class UpdateReferenceModel(Parameter):
# mref0 = None
# def nextIter(self):
# mref = getattr(self, 'm_prev', None)
# if mref is None:
# if self.debug: print 'UpdateReferenceModel is using mref0'
@@ -253,151 +258,56 @@ class SaveOutputDictEveryIteration(SaveEveryIteration):
class Update_IRLS(InversionDirective):
eps_min = None
eps = None
norms = [2.,2.,2.,2.]
factor = None
gamma = None
phi_m_last = None
phi_d_last = None
f_old = None
f_min_change = 1e-2
beta_tol = 5e-2
prctile = 95
# Solving parameter for IRLS (mode:2)
IRLSiter = 0
minGNiter = 5
maxIRLSiter = 10
iterStart = 0
# Beta schedule
coolingFactor = 2.
coolingRate = 1
mode = 1
@property
def target(self):
if getattr(self, '_target', None) is None:
self._target = self.survey.nD*0.5
return self._target
@target.setter
def target(self, val):
self._target = val
def initialize(self):
if self.mode == 1:
self.reg.norms = [2., 2., 2., 2.]
# Scale the regularization for changes in norm
if getattr(self, 'phi_m_last', None) is not None:
self.reg.curModel = self.invProb.curModel
self.reg.gamma = 1.
phim_new = self.reg.eval(self.invProb.curModel)
self.gamma = self.phi_m_last / phim_new
self.reg.curModel = self.invProb.curModel
self.reg.gamma = self.gamma
if getattr(self, 'phi_d_last', None) is None:
self.phi_d_last = self.invProb.phi_d
def endIter(self):
# Cool the threshold parameter if required
if getattr(self, 'factor', None) is not None:
eps = self.reg.eps / self.factor
# After reaching target misfit with l2-norm, switch to IRLS (mode:2)
if self.invProb.phi_d < self.target and self.mode == 1:
print "Convergence with smooth l2-norm regularization: Start IRLS steps..."
self.mode = 2
# Either use the supplied epsilon, or fix base on distribution of
# model values
if getattr(self, 'eps', None) is None:
self.reg.eps_p = np.percentile(np.abs(self.invProb.curModel),self.prctile)
if getattr(self, 'eps_min', None) is not None:
self.reg.eps = np.max([self.eps_min,eps])
else:
self.reg.eps_p = self.eps[0]
self.reg.eps = eps
if getattr(self, '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]
# Get phi_m at the end of current iteration
self.phi_m_last = self.invProb.phi_m_last
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
# Update the model used for the IRLS weights
self.reg.curModel = self.invProb.curModel
self.reg.l2model = self.invProb.curModel
self.reg.curModel = self.invProb.curModel
# Temporarely set gamma to 1. to get raw phi_m
self.reg.gamma = 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)
# Compute new model objective function value
phim_new = self.reg.eval(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)
# Update gamma to scale the regularization between IRLS iterations
self.reg.gamma = self.phi_m_last / phim_new
# 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
# Set the weighting matrix to None so that it is recomputed next time
# it is called in the inversion
self.reg._W = None
class Update_lin_PreCond(InversionDirective):
"""
@@ -450,3 +360,19 @@ class Update_Wj(InversionDirective):
JtJdiag = JtJdiag / max(JtJdiag)
self.reg.wght = JtJdiag
class Scale_Beta(InversionDirective):
"""
Instead of a linear cooling schedule, beta is allowed to change based
on the ratio between the target misfit and the current data misfit. The
update is done only if the misfit is outside some threshold bounds.
"""
tol = 0.05
def endIter(self):
# Check if misfit is within the tolerance, otherwise adjust beta
val = self.invProb.phi_d / (self.survey.nD*0.5)
if np.abs(1.-val) > self.tol:
self.invProb.beta = self.invProb.beta * self.survey.nD*0.5 / self.invProb.phi_d
-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
-1
View File
@@ -2,4 +2,3 @@ from TDEM import hzAnalyticDipoleT
from FDEM import hzAnalyticDipoleF
from FDEMcasing import *
from DC import DCAnalyticHalf, DCAnalyticSphere
from FDEMDipolarfields import *
+11 -7
View File
@@ -20,10 +20,10 @@ class BaseEMProblem(Problem.BaseProblem):
Problem.BaseProblem.__init__(self, mesh, **kwargs)
surveyPair = Survey.BaseSurvey #: The survey to pair with.
dataPair = Survey.Data #: The data to pair with.
surveyPair = Survey.BaseSurvey
dataPair = Survey.Data
PropMap = EMPropMap #: The property mapping
PropMap = EMPropMap
Solver = SimpegSolver
solverOpts = {}
@@ -169,7 +169,9 @@ 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 +187,8 @@ 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):
@@ -205,7 +208,9 @@ class BaseEMProblem(Problem.BaseProblem):
dMfRhoI_dI = -self.MfRhoI**2
dMf_drho = self.mesh.getFaceInnerProductDeriv(self.curModel.rho)(u)
return dMfRhoI_dI * ( dMf_drho * self.curModel.rhoDeriv )
return dMfRhoI_dI * ( dMf_drho * (-Utils.sdiag(self.curModel.rho**2) * self.curModel.sigmaDeriv) )
# return self.mesh.getFaceInnerProductDeriv(self.curModel.rho, invMat=True)(u) * self.curModel.rhoDeriv
class BaseEMSurvey(Survey.BaseSurvey):
@@ -217,7 +222,6 @@ class BaseEMSurvey(Survey.BaseSurvey):
def eval(self, f):
"""
Project fields to receiver locations
:param Fields u: fields object
:rtype: numpy.ndarray
:return: data
+30 -18
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 Fields3D_e(Fields):
"""
Fields object for Problem3D_e.
:param BaseMesh mesh: mesh
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'eSolution':'E'}
@@ -180,6 +180,9 @@ class Fields3D_e(FieldsFDEM):
'h' : ['eSolution','CCV','_h'],
}
def __init__(self, mesh, survey, **kwargs):
Fields.__init__(self, mesh, survey, **kwargs)
def startup(self):
self.prob = self.survey.prob
self._edgeCurl = self.survey.prob.mesh.edgeCurl
@@ -423,12 +426,12 @@ class Fields3D_e(FieldsFDEM):
class Fields3D_b(FieldsFDEM):
class Fields3D_b(Fields):
"""
Fields object for Problem3D_b.
:param BaseMesh mesh: mesh
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'bSolution':'F'}
@@ -443,6 +446,9 @@ class Fields3D_b(FieldsFDEM):
'h' : ['bSolution','CCV','_h'],
}
def __init__(self,mesh,survey,**kwargs):
Fields.__init__(self,mesh,survey,**kwargs)
def startup(self):
self.prob = self.survey.prob
self._edgeCurl = self.survey.prob.mesh.edgeCurl
@@ -687,12 +693,12 @@ class Fields3D_b(FieldsFDEM):
return Zero()
class Fields3D_j(FieldsFDEM):
class Fields3D_j(Fields):
"""
Fields object for Problem3D_j.
:param BaseMesh mesh: mesh
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'jSolution':'F'}
@@ -707,6 +713,9 @@ class Fields3D_j(FieldsFDEM):
'b' : ['jSolution','CCV','_b'],
}
def __init__(self,mesh,survey,**kwargs):
Fields.__init__(self,mesh,survey,**kwargs)
def startup(self):
self.prob = self.survey.prob
self._edgeCurl = self.survey.prob.mesh.edgeCurl
@@ -979,12 +988,12 @@ class Fields3D_j(FieldsFDEM):
return 1./(1j * omega(src.freq)) * VI * (self._aveE2CCV * ( s_mDeriv(v) - self._edgeCurl.T * ( self._MfRhoDeriv(jSolution) * v ) ) )
class Fields3D_h(FieldsFDEM):
class Fields3D_h(Fields):
"""
Fields object for Problem3D_h.
:param BaseMesh mesh: mesh
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'hSolution':'E'}
@@ -999,6 +1008,9 @@ class Fields3D_h(FieldsFDEM):
'b' : ['hSolution','CCV','_b'],
}
def __init__(self,mesh,survey,**kwargs):
Fields.__init__(self,mesh,survey,**kwargs)
def startup(self):
self.prob = self.survey.prob
self._edgeCurl = self.survey.prob.mesh.edgeCurl
+16 -21
View File
@@ -1,7 +1,7 @@
from SimPEG import Problem, Utils, np, sp, Solver as SimpegSolver
from scipy.constants import mu_0
from SurveyFDEM import Survey as SurveyFDEM
from FieldsFDEM import FieldsFDEM, Fields3D_e, Fields3D_b, Fields3D_h, Fields3D_j
from FieldsFDEM import Fields, Fields3D_e, Fields3D_b, Fields3D_h, Fields3D_j
from SimPEG.EM.Base import BaseEMProblem
from SimPEG.EM.Utils import omega
@@ -31,11 +31,10 @@ class BaseFDEMProblem(BaseEMProblem):
if using the H-J formulation (:code:`Problem3D_j` or :code:`Problem3D_h`). Note that here, :math:`\mathbf{s_m}` is an integrated quantity.
The problem performs the elimination so that we are solving the system for \\\(\\\mathbf{e},\\\mathbf{b},\\\mathbf{j} \\\) or \\\(\\\mathbf{h}\\\)
"""
surveyPair = SurveyFDEM
fieldsPair = FieldsFDEM
fieldsPair = Fields
def fields(self, m):
"""
@@ -65,7 +64,7 @@ class BaseFDEMProblem(BaseEMProblem):
:param numpy.array m: inversion model (nP,)
:param numpy.array v: vector which we take sensitivity product with (nP,)
:param SimPEG.EM.FDEM.FieldsFDEM.FieldsFDEM u: fields object
:param SimPEG.EM.FDEM.Fields u: fields object
:rtype numpy.array:
:return: Jv (ndata,)
"""
@@ -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,)
"""
@@ -154,8 +153,8 @@ 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':
@@ -195,7 +194,7 @@ class Problem3D_e(BaseFDEMProblem):
which we solve for :math:`\mathbf{e}`.
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
:param SimPEG.Mesh mesh: mesh
"""
_solutionType = 'eSolution'
@@ -270,7 +269,7 @@ class Problem3D_e(BaseFDEMProblem):
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -306,7 +305,7 @@ class Problem3D_b(BaseFDEMProblem):
.. note ::
The inverse problem will not work with full anisotropy
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
:param SimPEG.Mesh mesh: mesh
"""
_solutionType = 'bSolution'
@@ -401,7 +400,7 @@ class Problem3D_b(BaseFDEMProblem):
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -445,7 +444,6 @@ class Problem3D_j(BaseFDEMProblem):
\mathbf{h} = \\frac{1}{i \omega} \mathbf{M_{\mu}^e}^{-1} \\left(-\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{j} + \mathbf{M^e} \mathbf{s_m} \\right)
and solve for \\\(\\\mathbf{j}\\\) using
.. math ::
@@ -455,7 +453,7 @@ class Problem3D_j(BaseFDEMProblem):
.. note::
This implementation does not yet work with full anisotropy!!
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
:param SimPEG.Mesh mesh: mesh
"""
_solutionType = 'jSolution'
@@ -531,8 +529,8 @@ class Problem3D_j(BaseFDEMProblem):
\mathbf{RHS} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1}\mathbf{s_m} -i\omega \mathbf{s_e}
:param float freq: Frequency
:rtype: numpy.ndarray
:return: RHS (nE, nSrc)
:rtype: numpy.ndarray (nE, nSrc)
:return: RHS
"""
s_m, s_e = self.getSourceTerm(freq)
@@ -551,7 +549,7 @@ class Problem3D_j(BaseFDEMProblem):
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -593,7 +591,7 @@ class Problem3D_h(BaseFDEMProblem):
\\left(\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{s_e}
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
:param SimPEG.Mesh mesh: mesh
"""
_solutionType = 'hSolution'
@@ -610,11 +608,9 @@ class Problem3D_h(BaseFDEMProblem):
.. math::
\mathbf{A} = \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MeMu = self.MeMu
@@ -657,7 +653,6 @@ class Problem3D_h(BaseFDEMProblem):
:param float freq: Frequency
:rtype: numpy.ndarray
:return: RHS (nE, nSrc)
"""
s_m, s_e = self.getSourceTerm(freq)
@@ -671,7 +666,7 @@ class Problem3D_h(BaseFDEMProblem):
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
+5 -5
View File
@@ -25,10 +25,10 @@ class BaseRx(SimPEG.Survey.BaseRx):
def eval(self, src, mesh, f):
"""
Project fields to receivers to get data.
Project fields to recievers to get data.
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param BaseMesh mesh: mesh used
:param Source src: FDEM source
:param Mesh mesh: mesh used
:param Fields f: fields object
:rtype: numpy.ndarray
:return: fields projected to recievers
@@ -44,8 +44,8 @@ class BaseRx(SimPEG.Survey.BaseRx):
"""
Derivative of projected fields with respect to the inversion model times a vector.
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param BaseMesh mesh: mesh used
:param Source src: FDEM source
:param Mesh mesh: mesh used
:param Fields f: fields object
:param numpy.ndarray v: vector to multiply
:rtype: numpy.ndarray
+28 -28
View File
@@ -23,8 +23,8 @@ class BaseSrc(Survey.BaseSrc):
- :math:`s_m` : magnetic source term
- :math:`s_e` : electric source term
:param BaseFDEMProblem prob: FDEM Problem
:rtype: tuple
:param Problem prob: FDEM Problem
:rtype: (numpy.ndarray, numpy.ndarray)
:return: tuple with magnetic source term and electric source term
"""
s_m = self.s_m(prob)
@@ -37,10 +37,10 @@ class BaseSrc(Survey.BaseSrc):
- :code:`s_mDeriv` : derivative of the magnetic source term
- :code:`s_eDeriv` : derivative of the electric source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: tuple
:rtype: (numpy.ndarray, numpy.ndarray)
:return: tuple with magnetic source term and electric source term derivatives times a vector
"""
if v is not None:
@@ -52,7 +52,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Primary magnetic flux density
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary magnetic flux density
"""
@@ -64,7 +64,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Primary magnetic field
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -76,7 +76,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Primary electric field
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary electric field
"""
@@ -88,7 +88,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Primary current density
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary current density
"""
@@ -100,7 +100,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Magnetic source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: magnetic source term on mesh
"""
@@ -110,7 +110,7 @@ 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 +120,7 @@ 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 +133,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Derivative of electric source term with respect to the inversion model
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -162,7 +162,7 @@ class RawVec_e(BaseSrc):
"""
Electric source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: electric source term on mesh
"""
@@ -191,7 +191,7 @@ class RawVec_m(BaseSrc):
"""
Magnetic source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: magnetic source term on mesh
"""
@@ -220,7 +220,7 @@ class RawVec(BaseSrc):
"""
Magnetic source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: magnetic source term on mesh
"""
@@ -232,7 +232,7 @@ 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 +301,7 @@ 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 +339,7 @@ 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 +350,7 @@ 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 +364,7 @@ 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 +416,7 @@ 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 +455,7 @@ 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 +466,7 @@ 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 +479,7 @@ 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 +530,7 @@ 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 +567,7 @@ 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 +578,7 @@ 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 +591,7 @@ class CircularLoop(BaseSrc):
"""
The electric source term
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
+7 -5
View File
@@ -35,10 +35,11 @@ class BaseDCProblem(BaseEMProblem):
self.curModel = m
Jv = self.dataPair(self.survey) #same size as the data
# Jv = self.dataPair(self.survey) #same size as the data
A = self.getA()
Jv = []
for src in self.survey.srcList:
u_src = f[src, self._solutionType] # solution vector
dA_dm_v = self.getADeriv(u_src, v)
@@ -48,8 +49,10 @@ class BaseDCProblem(BaseEMProblem):
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)
# Jv[src, rx] = rx.evalDeriv(src, self.mesh, f, df_dm_v)
Jv.append(rx.evalDeriv(src, self.mesh, f, df_dm_v))
# return Utils.mkvc(Jv)
return np.hstack(Jv)
def Jtvec(self, m, v, f=None):
if f is None:
@@ -64,7 +67,6 @@ class BaseDCProblem(BaseEMProblem):
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:
+8 -4
View File
@@ -45,7 +45,8 @@ class BaseIPProblem(BaseEMProblem):
self.curModel = m
Jv = self.dataPair(self.survey) #same size as the data
# Jv = self.dataPair(self.survey) #same size as the data
Jv = []
A = self.getA()
@@ -58,13 +59,16 @@ class BaseIPProblem(BaseEMProblem):
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)
# Jv[src, rx] = rx.evalDeriv(src, self.mesh, f, df_dm_v)
Jv.append(rx.evalDeriv(src, self.mesh, f, df_dm_v))
# Conductivity (d u / d log sigma)
if self._formulation is 'EB':
return -Utils.mkvc(Jv)
# return -Utils.mkvc(Jv)
return -np.hstack(Jv)
# Conductivity (d u / d log rho)
if self._formulation is 'HJ':
return Utils.mkvc(Jv)
# return Utils.mkvc(Jv)
return np.hstack(Jv)
def Jtvec(self, m, v, f=None):
if f is None:
+104
View File
@@ -315,3 +315,107 @@ def gen_DCIPsurvey(endl, mesh, stype, a, b, n):
return SrcList
def writeUBC_DCobs(fileName, DCsurvey, dtype='3D', stype='SURFACE', iptype = 0):
"""
Write UBC GIF DCIP 2D or 3D observation 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 (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')
if iptype!=0:
fid.write('IPTYPE=%i\n'%iptype)
else:
fid.write('! ' + stype + ' FORMAT\n')
count = 0
for ii in range(DCsurvey.nSrc):
tx = np.c_[DCsurvey.srcList[ii].loc]
rx = DCsurvey.srcList[ii].rxList[0].locs
nD = DCsurvey.srcList[ii].nD
M = rx[0]
N = rx[1]
# Adapt source-receiver location for dtype and stype
if dtype=='2D':
if stype == 'SIMPLE':
#fid.writelines("%e " % ii for ii in mkvc(tx[0,:]))
A = np.repeat(tx[0,0],M.shape[0],axis=0)
B = np.repeat(tx[0,1],M.shape[0],axis=0)
M = M[:,0]
N = N[:,0]
np.savetxt(fid, np.c_[A, B, M, N , DCsurvey.dobs[count:count+nD], DCsurvey.std[count:count+nD] ], fmt='%e',delimiter=' ',newline='\n')
else:
if stype == 'SURFACE':
fid.writelines("%f " % ii for ii in mkvc(tx[0,:]))
M = M[:,0]
N = N[:,0]
if stype == 'GENERAL':
# Flip sign for z-elevation to depth
tx[2::2,:] = -tx[2::2,:]
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')
if dtype=='3D':
if stype == 'SURFACE':
fid.writelines("%e " % ii for ii in mkvc(tx[0:2,:]))
M = M[:,0:2]
N = N[:,0:2]
if stype == 'GENERAL':
fid.writelines("%e " % ii for ii in mkvc(tx[0:3,:]))
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()
+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)
+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
+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)
+17 -15
View File
@@ -2,7 +2,7 @@ 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', dtype='appc', plotIt=True):
"""
DC Forward Simulation
=====================
@@ -15,14 +15,14 @@ def run(loc=None, sig=None, radi=None, param=None, surveyType='dipole-dipole', u
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"
stype = survey type "pdp" (pole dipole) or "dpdp" (dipole dipole)
dtype = Data type "appr" (app res) | "appc" (app cond) | "volt" (potential)
Created by @fourndo
"""
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)"
assert dtype in ['appr', 'appc', 'volt'], "Data type (dtype) must be appr (app res) or appc (app cond) or volt (potential)"
if loc is None:
loc = np.c_[[-50.,0.,-50.],[50.,0.,-50.]]
@@ -73,8 +73,8 @@ 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) )
@@ -118,8 +118,8 @@ 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
@@ -157,12 +157,12 @@ def run(loc=None, sig=None, radi=None, param=None, surveyType='dipole-dipole', u
fig = plt.figure(figsize=(7,7))
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)
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',
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')
@@ -188,13 +188,15 @@ def run(loc=None, sig=None, radi=None, param=None, surveyType='dipole-dipole', u
ax2 = 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)
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)
# 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')
dat = DC.plot_pseudoSection(survey2D,ax2,stype=stype, dtype = dtype)
# 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')
@@ -19,13 +19,10 @@ def run(plotIt=True):
Morrison Casing Model, and the results are used in a 2016 SEG abstract by
Yang et al.
.. code-block:: text
Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
- Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
The model consists of:
- Air: Conductivity 1e-8 S/m, above z = 0
- Background: conductivity 1e-2 S/m, below z = 0
- Casing: conductivity 1e6 S/m
@@ -218,7 +215,7 @@ def run(plotIt=True):
# ------------ Problem and Survey ---------------
survey = FDEM.Survey(sg_p + dg_p)
mapping = [('sigma', Maps.IdentityMap(mesh))]
problem = FDEM.Problem3D_h(mesh, mapping=mapping, Solver=solver)
problem = FDEM.Problem3D_h(mesh, mapping=mapping)
problem.pair(survey)
# ------------- Solve ---------------------------
@@ -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()
+46 -16
View File
@@ -1,7 +1,7 @@
from SimPEG import *
def run(N=100, plotIt=True):
def run(N=200, plotIt=True):
"""
Inversion: Linear Problem
=========================
@@ -18,8 +18,6 @@ def run(N=100, plotIt=True):
mesh = Mesh.TensorMesh([N])
m0 = np.ones(mesh.nC) * 1e-4
mref = np.zeros(mesh.nC)
nk = 10
jk = np.linspace(1.,nk,nk)
p = -2.
@@ -42,35 +40,67 @@ def run(N=100, plotIt=True):
survey = Survey.LinearSurvey()
survey.pair(prob)
survey.dobs = prob.fields(mtrue) + std_noise * np.random.randn(nk)
#survey.makeSyntheticData(mtrue, std=std_noise)
wd = np.ones(nk) * std_noise
#print survey.std[0]
#M = prob.mesh
# Distance weighting
wr = np.sum(prob.G**2.,axis=0)**0.5
wr = ( wr/np.max(wr) )
reg = Regularization.Simple(mesh)
reg.wght = wr
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = 1./wd
opt = Optimization.ProjectedGNCG(maxIter=30,lower=-2.,upper=2., maxIterCG= 20, tolCG = 1e-4)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
invProb.curModel = m0
beta = Directives.BetaSchedule(coolingFactor=2, coolingRate=1)
target = Directives.TargetMisfit()
betaest = Directives.BetaEstimate_ByEig()
inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest, target])
mrec = inv.run(m0)
ml2 = mrec
print "Final misfit:" + str(invProb.dmisfit.eval(mrec))
# Switch regularization to sparse
phim = invProb.phi_m_last
phid = invProb.phi_d
reg = Regularization.Sparse(mesh)
reg.mref = mref
reg.cell_weights = wr
#==============================================================================
# fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
# dmdx = reg.mesh.cellDiffxStencil * mrec
# plt.plot(np.sort(dmdx))
#==============================================================================
#reg.recModel = mrec
reg.wght = np.ones(mesh.nC)
reg.mref = np.zeros(mesh.nC)
reg.eps_p = 5e-2
reg.eps_q = 1e-2
reg.norms = [0., 0., 2., 2.]
reg.wght = wr
opt = Optimization.ProjectedGNCG(maxIter=100 ,lower=-2.,upper=2., maxIterLS = 20, maxIterCG= 10, tolCG = 1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
update_Jacobi = Directives.Update_lin_PreCond()
# Set the IRLS directive, penalize the lowest 25 percentile of model values
# Start with an l2-l2, then switch to lp-norms
norms = [0., 0., 2., 2.]
IRLS = Directives.Update_IRLS( norms=norms, prctile = 25, maxIRLSiter = 15, minGNiter=3)
opt = Optimization.ProjectedGNCG(maxIter=10 ,lower=-2.,upper=2., maxIterLS = 20, maxIterCG= 20, tolCG = 1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta = invProb.beta*2.)
beta = Directives.BetaSchedule(coolingFactor=1, coolingRate=1)
#betaest = Directives.BetaEstimate_ByEig()
target = Directives.TargetMisfit()
IRLS =Directives.Update_IRLS( phi_m_last = phim, phi_d_last = phid )
inv = Inversion.BaseInversion(invProb, directiveList=[IRLS,betaest,update_Jacobi])
inv = Inversion.BaseInversion(invProb, directiveList=[beta,IRLS])
m0 = mrec
# Run inversion
mrec = inv.run(m0)
@@ -87,7 +117,7 @@ def run(N=100, plotIt=True):
axes[0].set_title('Columns of matrix G')
axes[1].plot(mesh.vectorCCx, mtrue, 'b-')
axes[1].plot(mesh.vectorCCx, reg.l2model, 'r-')
axes[1].plot(mesh.vectorCCx, ml2, 'r-')
#axes[1].legend(('True Model', 'Recovered Model'))
axes[1].set_ylim(-1.0,1.25)
+3 -3
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')
+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()
+4 -5
View File
@@ -1,5 +1,4 @@
from SimPEG import Mesh, Utils, np
from SimPEG import *
def run(plotIt=True):
"""
@@ -9,15 +8,15 @@ def run(plotIt=True):
Here we show SimPEG used to create three different types of meshes.
"""
sz = [16, 16]
sz = [16,16]
tM = Mesh.TensorMesh(sz)
qM = Mesh.TreeMesh(sz)
qM.refine(lambda cell: 4 if np.sqrt(((np.r_[cell.center]-0.5)**2).sum()) < 0.4 else 3)
rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz, 'rotate'))
rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz,'rotate'))
if plotIt:
import matplotlib.pyplot as plt
fig, axes = plt.subplots(1, 3, figsize=(14, 5))
fig, axes = plt.subplots(1,3,figsize=(14,5))
opts = {}
tM.plotGrid(ax=axes[0], **opts)
axes[0].set_title('TensorMesh')
-65
View File
@@ -1,65 +0,0 @@
from SimPEG import Mesh, np, PF
def run(plotIt=True):
"""
PF: Magnetics: Analytics
========================
Comparing the magnetics field in Vancouver to Seoul
"""
xr = np.linspace(-300, 300, 41)
yr = np.linspace(-300, 300, 41)
X, Y = np.meshgrid(xr, yr)
Z = np.ones((np.size(xr), np.size(yr)))*150
# Bz component in Korea
inckr = -8. + 3./60
deckr = 54. + 9./60
btotkr = 50898.6
Bokr = PF.MagAnalytics.IDTtoxyz(inckr, deckr, btotkr)
bx, by, bz = PF.MagAnalytics.MagSphereAnaFunA(
X, Y, Z, 100., 0., 0., 0., 0.01, Bokr, 'secondary'
)
Bzkr = np.reshape(bz, (np.size(xr), np.size(yr)), order='F')
# Bz component in Canada
incca = 16. + 49./60
decca = 70. + 19./60
btotca = 54692.1
Boca = PF.MagAnalytics.IDTtoxyz(incca, decca, btotca)
bx, by, bz = PF.MagAnalytics.MagSphereAnaFunA(
X, Y, Z, 100., 0., 0., 0., 0.01, Boca, 'secondary'
)
Bzca = np.reshape(bz, (np.size(xr), np.size(yr)), order='F')
if plotIt:
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable
fig = plt.figure(figsize=(14, 5))
ax1 = plt.subplot(121)
dat1 = plt.imshow(Bzkr, extent=[min(xr), max(xr), min(yr), max(yr)])
divider = make_axes_locatable(ax1)
cax1 = divider.append_axes("right", size="5%", pad=0.05)
ax1.set_xlabel('East-West (m)')
ax1.set_ylabel('South-North (m)')
plt.colorbar(dat1, cax=cax1)
ax1.set_title('$B_z$ field at Seoul, South Korea')
ax2 = plt.subplot(122)
dat2 = plt.imshow(Bzca, extent=[min(xr), max(xr), min(yr), max(yr)])
divider = make_axes_locatable(ax2)
cax2 = divider.append_axes("right", size="5%", pad=0.05)
ax2.set_xlabel('East-West (m)')
ax2.set_ylabel('South-North (m)')
plt.colorbar(dat2, cax=cax2)
ax2.set_title('$B_z$ field at Vancouver, Canada')
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 -8
View File
@@ -8,11 +8,9 @@ import EM_FDEM_Analytic_MagDipoleWholespace
import EM_Schenkel_Morrison_Casing
import EM_TDEM_1D_Inversion
import FLOW_Richards_1D_Celia1990
import Forward_BasicDirectCurrent
import Inversion_IRLS
import Inversion_Linear
import Maps_ComboMaps
import Maps_Mesh2Mesh
import Mesh_Basic_ForwardDC
import Mesh_Basic_PlotImage
import Mesh_Basic_Types
import Mesh_Operators_CahnHilliard
@@ -22,9 +20,8 @@ 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_Schenkel_Morrison_Casing", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Forward_BasicDirectCurrent", "Inversion_IRLS", "Inversion_Linear", "Mesh_Basic_PlotImage", "Mesh_Basic_Types", "Mesh_Operators_CahnHilliard", "Mesh_QuadTree_Creation", "Mesh_QuadTree_FaceDiv", "Mesh_QuadTree_HangingNodes", "Mesh_Tensor_Creation", "MT_1D_ForwardAndInversion", "MT_3D_Foward"]
##### AUTOIMPORTS #####
@@ -40,7 +37,7 @@ 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 +94,12 @@ 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.
+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
+84 -9
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):
"""
+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)])
+6 -6
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]
+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"
+58 -34
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.
@@ -46,9 +48,11 @@ class TensorMeshIO(object):
Read VTK Rectilinear (vtr xml file) and return SimPEG Tensor mesh and model
Input:
:param string fileName: path to the vtr model file to read
:rtype: tuple
:return: (TensorMesh, modelDictionary)
:param vtrFileName, path to the vtr model file to write to
Output:
:return SimPEG TensorMesh object
:return SimPEG model dictionary
"""
# Import
@@ -98,8 +102,9 @@ class TensorMeshIO(object):
Makes and saves a VTK rectilinear file (vtr) for a simpeg Tensor mesh and model.
Input:
:param string fileName: path to the output vtk file
:param dict models: dictionary of numpy.array - Name('s) and array('s). Match number of cells
:param str, path to the output vtk file
:param mesh, SimPEG TensorMesh object - mesh to be transfer to VTK
:param models, dictionary of numpy.array - Name('s) and array('s). Match number of cells
"""
# Import
@@ -157,9 +162,12 @@ class TensorMeshIO(object):
"""
Read UBC 3DTensor mesh model and generate 3D Tensor mesh model in simpeg
:param string fileName: path to the UBC GIF mesh file to read
:rtype: numpy.ndarray
:return: model with TensorMesh ordered
Input:
:param fileName, path to the UBC GIF mesh file to read
:param mesh, TensorMesh object, mesh that coresponds to the model
Output:
:return numpy array, model with TensorMesh ordered
"""
f = open(fileName, 'r')
model = np.array(map(float, f.readlines()))
@@ -175,7 +183,8 @@ class TensorMeshIO(object):
Writes a model associated with a SimPEG TensorMesh
to a UBC-GIF format model file.
:param string fileName: File to write to
:param str fileName: File to write to
:param simpeg.Mesh.TensorMesh mesh: The mesh
:param numpy.ndarray model: The model
"""
@@ -192,23 +201,34 @@ 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
s = ''
s += '%i %i %i\n' %tuple(mesh.vnC)
origin = mesh.x0 + np.array([0,0,mesh.hz.sum()]) # Have to it in the same operation or use mesh.x0.copy(), otherwise the mesh.x0 is updated.
origin.dtype = float
if mesh.dim ==3:
s = ''
s += '%i %i %i\n' %tuple(mesh.vnC)
origin = mesh.x0 + np.array([0,0,mesh.hz.sum()]) # Have to it in the same operation or use mesh.x0.copy(), otherwise the mesh.x0 is updated.
origin.dtype = float
s += '%.2f %.2f %.2f\n' %tuple(origin)
s += ('%.2f '*mesh.nCx+'\n')%tuple(mesh.hx)
s += ('%.2f '*mesh.nCy+'\n')%tuple(mesh.hy)
s += ('%.2f '*mesh.nCz+'\n')%tuple(mesh.hz[::-1])
f = open(fileName, 'w')
f.write(s)
f.close()
s += '%.2f %.2f %.2f\n' %tuple(origin)
s += ('%.2f '*mesh.nCx+'\n')%tuple(mesh.hx)
s += ('%.2f '*mesh.nCy+'\n')%tuple(mesh.hy)
s += ('%.2f '*mesh.nCz+'\n')%tuple(mesh.hz[::-1])
f = open(fileName, 'w')
f.write(s)
f.close()
elif mesh.dim==2:
fid = open(fileName,'w')
fid.write('%i\n'% mesh.nCx)
fid.write('%f %f 1\n'% (mesh.vectorNx[0],mesh.vectorNx[1]))
np.savetxt(fid, np.c_[mesh.vectorNx[2:],np.ones(mesh.nCx-1)], fmt='\t %e %i',delimiter=' ',newline='\n')
fid.write('\n')
fid.write('%i\n'% mesh.nCy)
fid.write('%f %f 1\n'%( 0,mesh.hy[-1]))
np.savetxt(fid, np.c_[np.cumsum(mesh.hy[-2::-1])+mesh.hy[-1],np.ones(mesh.nCy-1)], fmt='\t %e %i',delimiter=' ',newline='\n')
fid.close()
if models is None: return
assert type(models) is dict, 'models must be a dict'
@@ -222,8 +242,9 @@ 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 +297,10 @@ 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 +346,11 @@ 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"
+1 -1
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::
+40 -78
View File
@@ -552,8 +552,7 @@ class CurvView(object):
def __init__(self):
pass
def plotGrid(self, ax=None, nodes=False, faces=False, centers=False, edges=False, lines=True, showIt=False):
def plotGrid(self, length=0.05, showIt=False):
"""Plot the nodal, cell-centered and staggered grids for 1,2 and 3 dimensions.
@@ -561,63 +560,60 @@ class CurvView(object):
:include-source:
from SimPEG import Mesh, Utils
X, Y = Utils.exampleLrmGrid([3,3],'rotate')
X, Y = Utils.exampleCurvGird([3,3],'rotate')
M = Mesh.CurvilinearMesh([X, Y])
M.plotGrid(showIt=True)
"""
import matplotlib.pyplot as plt
import matplotlib
from mpl_toolkits.mplot3d import Axes3D
axOpts = {'projection':'3d'} if self.dim == 3 else {}
if ax is None: ax = plt.subplot(111, **axOpts)
NN = self.r(self.gridN, 'N', 'N', 'M')
if self.dim == 2:
fig = plt.figure(2)
fig.clf()
ax = plt.subplot(111)
X1 = np.c_[mkvc(NN[0][:-1, :]), mkvc(NN[0][1:, :]), mkvc(NN[0][:-1, :])*np.nan].flatten()
Y1 = np.c_[mkvc(NN[1][:-1, :]), mkvc(NN[1][1:, :]), mkvc(NN[1][:-1, :])*np.nan].flatten()
if lines:
X1 = np.c_[mkvc(NN[0][:-1, :]), mkvc(NN[0][1:, :]), mkvc(NN[0][:-1, :])*np.nan].flatten()
Y1 = np.c_[mkvc(NN[1][:-1, :]), mkvc(NN[1][1:, :]), mkvc(NN[1][:-1, :])*np.nan].flatten()
X2 = np.c_[mkvc(NN[0][:, :-1]), mkvc(NN[0][:, 1:]), mkvc(NN[0][:, :-1])*np.nan].flatten()
Y2 = np.c_[mkvc(NN[1][:, :-1]), mkvc(NN[1][:, 1:]), mkvc(NN[1][:, :-1])*np.nan].flatten()
X2 = np.c_[mkvc(NN[0][:, :-1]), mkvc(NN[0][:, 1:]), mkvc(NN[0][:, :-1])*np.nan].flatten()
Y2 = np.c_[mkvc(NN[1][:, :-1]), mkvc(NN[1][:, 1:]), mkvc(NN[1][:, :-1])*np.nan].flatten()
X = np.r_[X1, X2]
Y = np.r_[Y1, Y2]
X = np.r_[X1, X2]
Y = np.r_[Y1, Y2]
plt.plot(X, Y)
ax.plot(X, Y, 'b-')
if centers:
ax.plot(self.gridCC[:,0],self.gridCC[:,1],'ro')
plt.hold(True)
Nx = self.r(self.normals, 'F', 'Fx', 'V')
Ny = self.r(self.normals, 'F', 'Fy', 'V')
Tx = self.r(self.tangents, 'E', 'Ex', 'V')
Ty = self.r(self.tangents, 'E', 'Ey', 'V')
# Nx = self.r(self.normals, 'F', 'Fx', 'V')
# Ny = self.r(self.normals, 'F', 'Fy', 'V')
# Tx = self.r(self.tangents, 'E', 'Ex', 'V')
# Ty = self.r(self.tangents, 'E', 'Ey', 'V')
plt.plot(self.gridN[:, 0], self.gridN[:, 1], 'bo')
# ax.plot(self.gridN[:, 0], self.gridN[:, 1], 'bo')
nX = np.c_[self.gridFx[:, 0], self.gridFx[:, 0] + Nx[0]*length, self.gridFx[:, 0]*np.nan].flatten()
nY = np.c_[self.gridFx[:, 1], self.gridFx[:, 1] + Nx[1]*length, self.gridFx[:, 1]*np.nan].flatten()
plt.plot(self.gridFx[:, 0], self.gridFx[:, 1], 'rs')
plt.plot(nX, nY, 'r-')
# nX = np.c_[self.gridFx[:, 0], self.gridFx[:, 0] + Nx[0]*length, self.gridFx[:, 0]*np.nan].flatten()
# nY = np.c_[self.gridFx[:, 1], self.gridFx[:, 1] + Nx[1]*length, self.gridFx[:, 1]*np.nan].flatten()
# ax.plot(self.gridFx[:, 0], self.gridFx[:, 1], 'rs')
# ax.plot(nX, nY, 'r-')
nX = np.c_[self.gridFy[:, 0], self.gridFy[:, 0] + Ny[0]*length, self.gridFy[:, 0]*np.nan].flatten()
nY = np.c_[self.gridFy[:, 1], self.gridFy[:, 1] + Ny[1]*length, self.gridFy[:, 1]*np.nan].flatten()
#plt.plot(self.gridFy[:, 0], self.gridFy[:, 1], 'gs')
plt.plot(nX, nY, 'g-')
# nX = np.c_[self.gridFy[:, 0], self.gridFy[:, 0] + Ny[0]*length, self.gridFy[:, 0]*np.nan].flatten()
# nY = np.c_[self.gridFy[:, 1], self.gridFy[:, 1] + Ny[1]*length, self.gridFy[:, 1]*np.nan].flatten()
# #ax.plot(self.gridFy[:, 0], self.gridFy[:, 1], 'gs')
# ax.plot(nX, nY, 'g-')
tX = np.c_[self.gridEx[:, 0], self.gridEx[:, 0] + Tx[0]*length, self.gridEx[:, 0]*np.nan].flatten()
tY = np.c_[self.gridEx[:, 1], self.gridEx[:, 1] + Tx[1]*length, self.gridEx[:, 1]*np.nan].flatten()
plt.plot(self.gridEx[:, 0], self.gridEx[:, 1], 'r^')
plt.plot(tX, tY, 'r-')
# tX = np.c_[self.gridEx[:, 0], self.gridEx[:, 0] + Tx[0]*length, self.gridEx[:, 0]*np.nan].flatten()
# tY = np.c_[self.gridEx[:, 1], self.gridEx[:, 1] + Tx[1]*length, self.gridEx[:, 1]*np.nan].flatten()
# ax.plot(self.gridEx[:, 0], self.gridEx[:, 1], 'r^')
# ax.plot(tX, tY, 'r-')
# nX = np.c_[self.gridEy[:, 0], self.gridEy[:, 0] + Ty[0]*length, self.gridEy[:, 0]*np.nan].flatten()
# nY = np.c_[self.gridEy[:, 1], self.gridEy[:, 1] + Ty[1]*length, self.gridEy[:, 1]*np.nan].flatten()
# #ax.plot(self.gridEy[:, 0], self.gridEy[:, 1], 'g^')
# ax.plot(nX, nY, 'g-')
nX = np.c_[self.gridEy[:, 0], self.gridEy[:, 0] + Ty[0]*length, self.gridEy[:, 0]*np.nan].flatten()
nY = np.c_[self.gridEy[:, 1], self.gridEy[:, 1] + Ty[1]*length, self.gridEy[:, 1]*np.nan].flatten()
#plt.plot(self.gridEy[:, 0], self.gridEy[:, 1], 'g^')
plt.plot(nX, nY, 'g-')
plt.axis('equal')
elif self.dim == 3:
fig = plt.figure(3)
fig.clf()
ax = fig.add_subplot(111, projection='3d')
X1 = np.c_[mkvc(NN[0][:-1, :, :]), mkvc(NN[0][1:, :, :]), mkvc(NN[0][:-1, :, :])*np.nan].flatten()
Y1 = np.c_[mkvc(NN[1][:-1, :, :]), mkvc(NN[1][1:, :, :]), mkvc(NN[1][:-1, :, :])*np.nan].flatten()
Z1 = np.c_[mkvc(NN[2][:-1, :, :]), mkvc(NN[2][1:, :, :]), mkvc(NN[2][:-1, :, :])*np.nan].flatten()
@@ -634,50 +630,16 @@ class CurvView(object):
Y = np.r_[Y1, Y2, Y3]
Z = np.r_[Z1, Z2, Z3]
ax.plot(X, Y, 'b', zs=Z)
plt.plot(X, Y, 'b', zs=Z)
ax.set_zlabel('x3')
ax.grid(True)
ax.hold(False)
ax.set_xlabel('x1')
ax.set_ylabel('x2')
if showIt: plt.show()
def plotImage(self, I, ax=None, showIt=False, grid=False, clim=None):
if self.dim == 3: raise NotImplementedError('This is not yet done!')
import matplotlib.pyplot as plt
import matplotlib
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.colors as colors
import matplotlib.cm as cmx
if ax is None: ax = plt.subplot(111)
jet = cm = plt.get_cmap('jet')
cNorm = colors.Normalize(
vmin=I.min() if clim is None else clim[0],
vmax=I.max() if clim is None else clim[1])
scalarMap = cmx.ScalarMappable(norm=cNorm, cmap=jet)
# ax.set_xlim((self.x0[0], self.h[0].sum()))
# ax.set_ylim((self.x0[1], self.h[1].sum()))
Nx = self.r(self.gridN[:,0],'N','N','M')
Ny = self.r(self.gridN[:,1],'N','N','M')
cell = self.r(I,'CC','CC','M')
for ii in range(self.nCx):
for jj in range(self.nCy):
I = [ii,ii+1,ii+1,ii]
J = [jj,jj,jj+1,jj+1]
ax.add_patch(plt.Polygon(np.c_[Nx[I,J],Ny[I,J]], facecolor=scalarMap.to_rgba(cell[ii,jj]), edgecolor='k' if grid else 'none'))
scalarMap._A = [] # http://stackoverflow.com/questions/8342549/matplotlib-add-colorbar-to-a-sequence-of-line-plots
ax.set_xlabel('x')
ax.set_ylabel('y')
if showIt: plt.show()
return [scalarMap]
if __name__ == '__main__':
from SimPEG import *
+6 -6
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.'
@@ -1008,4 +1008,4 @@ class ProjectedGNCG(BFGS, Minimize, Remember):
indx = ((self.xc<=self.lower) & (delx < 0)) | ((self.xc>=self.upper) & (delx > 0))
delx[indx] = 0.
return delx
return delx
-53
View File
@@ -1,53 +0,0 @@
from SimPEG import Maps, Survey, Utils, np, sp
from scipy.constants import mu_0
import re
class LinearSurvey(Survey.BaseSurvey):
"""Base Magnetics Survey"""
rxLoc = None #: receiver locations
rxType = None #: receiver type
def __init__(self, srcField, **kwargs):
self.srcField = srcField
Survey.BaseSurvey.__init__(self, **kwargs)
def eval(self, u):
return u
@property
def nD(self):
return self.prob.G.shape[0]
@property
def nRx(self):
return self.srcField.rxList[0].locs.shape[0]
# def setBackgroundField(self, SrcField):
# if getattr(self, 'B0', None) is None:
# self._B0 = SrcField.param[0] * dipazm_2_xyz(SrcField.param[1],SrcField.param[2])
# return self._B0
class SrcField(Survey.BaseSrc):
""" Define the inducing field """
param = None #: Inducing field param (Amp, Incl, Decl)
def __init__(self, rxList, **kwargs):
super(SrcField, self).__init__(rxList, **kwargs)
class RxObs(Survey.BaseRx):
"""A station location must have be located in 3-D"""
def __init__(self, locsXYZ, **kwargs):
locs = locsXYZ
assert locsXYZ.shape[1] == 3, 'locs must in 3-D (x,y,z).'
super(RxObs, self).__init__(locs, 'tmi', storeProjections=False, **kwargs)
@property
def nD(self):
"""Number of data in the receiver."""
return self.locs[0].shape[0]
-194
View File
@@ -1,194 +0,0 @@
from SimPEG import Maps, Survey, Utils, np, sp
from scipy.constants import mu_0
import re
class BaseMagSurvey(Survey.BaseSurvey):
"""Base Magnetics Survey"""
rxLoc = None #: receiver locations
rxType = None #: receiver type
def __init__(self, **kwargs):
Survey.BaseSurvey.__init__(self, **kwargs)
def setBackgroundField(self, Inc, Dec, Btot):
Bx = Btot*np.cos(Inc/180.*np.pi)*np.sin(Dec/180.*np.pi)
By = Btot*np.cos(Inc/180.*np.pi)*np.cos(Dec/180.*np.pi)
Bz = -Btot*np.sin(Inc/180.*np.pi)
self.B0 = np.r_[Bx, By, Bz]
@property
def Qfx(self):
if getattr(self, '_Qfx', None) is None:
self._Qfx = self.prob.mesh.getInterpolationMat(self.rxLoc, 'Fx')
return self._Qfx
@property
def Qfy(self):
if getattr(self, '_Qfy', None) is None:
self._Qfy = self.prob.mesh.getInterpolationMat(self.rxLoc, 'Fy')
return self._Qfy
@property
def Qfz(self):
if getattr(self, '_Qfz', None) is None:
self._Qfz = self.prob.mesh.getInterpolationMat(self.rxLoc, 'Fz')
return self._Qfz
def projectFields(self, u):
"""
This function projects the fields onto the data space.
Especially, here for we use total magnetic intensity (TMI) data,
which is common in practice.
First we project our B on to data location
.. math::
\mathbf{B}_{rec} = \mathbf{P} \mathbf{B}
then we take the dot product between B and b_0
.. math ::
\\text{TMI} = \\vec{B}_s \cdot \hat{B}_0
"""
# TODO: There can be some different tyes of data like |B| or B
bfx = self.Qfx*u['B']
bfy = self.Qfy*u['B']
bfz = self.Qfz*u['B']
# Generate unit vector
B0 = self.prob.survey.B0
Bot = np.sqrt(B0[0]**2+B0[1]**2+B0[2]**2)
box = B0[0]/Bot
boy = B0[1]/Bot
boz = B0[2]/Bot
# return bfx*box + bfx*boy + bfx*boz
return bfx*box + bfy*boy + bfz*boz
@Utils.count
def projectFieldsDeriv(self, B):
"""
This function projects the fields onto the data space.
.. math::
\\frac{\partial d_\\text{pred}}{\partial \mathbf{B}} = \mathbf{P}
Especially, this function is for TMI data type
"""
# Generate unit vector
B0 = self.prob.survey.B0
Bot = np.sqrt(B0[0]**2+B0[1]**2+B0[2]**2)
box = B0[0]/Bot
boy = B0[1]/Bot
boz = B0[2]/Bot
return self.Qfx*box+self.Qfy*boy+self.Qfz*boz
def projectFieldsAsVector(self, B):
bfx = self.Qfx*B
bfy = self.Qfy*B
bfz = self.Qfz*B
return np.r_[bfx, bfy, bfz]
class LinearSurvey(Survey.BaseSurvey):
"""Base Magnetics Survey"""
rxLoc = None #: receiver locations
rxType = None #: receiver type
def __init__(self, srcField, **kwargs):
self.srcField = srcField
Survey.BaseSurvey.__init__(self, **kwargs)
def eval(self, u):
return u
@property
def nD(self):
return self.prob.G.shape[0]
@property
def nRx(self):
return self.srcField.rxList[0].locs.shape[0]
# def setBackgroundField(self, SrcField):
# if getattr(self, 'B0', None) is None:
# self._B0 = SrcField.param[0] * dipazm_2_xyz(SrcField.param[1],SrcField.param[2])
# return self._B0
class SrcField(Survey.BaseSrc):
""" Define the inducing field """
param = None #: Inducing field param (Amp, Incl, Decl)
def __init__(self, rxList, **kwargs):
super(SrcField, self).__init__(rxList, **kwargs)
class RxObs(Survey.BaseRx):
"""A station location must have be located in 3-D"""
def __init__(self, locsXYZ, **kwargs):
locs = locsXYZ
assert locsXYZ.shape[1] == 3, 'locs must in 3-D (x,y,z).'
super(RxObs, self).__init__(locs, 'tmi', storeProjections=False, **kwargs)
@property
def nD(self):
"""Number of data in the receiver."""
return self.locs[0].shape[0]
class MagSurveyBx(object):
"""docstring for MagSurveyBx"""
def __init__(self, **kwargs):
Survey.BaseData.__init__(self, **kwargs)
def projectFields(self, B):
bfx = self.Qfx*B
return bfx
class BaseMagMap(Maps.IdentityMap):
"""BaseMagMap"""
def __init__(self, mesh, **kwargs):
Maps.IdentityMap.__init__(self, mesh)
def _transform(self, m):
return mu_0*(1 + m)
def deriv(self, m):
return mu_0*sp.identity(self.nP)
class WeightMap(Maps.IdentityMap):
"""Weighted Map for distributed parameters"""
def __init__(self, nP, weight, **kwargs):
Maps.IdentityMap.__init__(self, nP)
self.mesh = None
self.weight = weight
def _transform(self, m):
return m*self.weight
def deriv(self, m):
return Utils.sdiag(self.weight)
-576
View File
@@ -1,576 +0,0 @@
from SimPEG import *
import BaseGrav as GRAV
import re
class GravityIntegral(Problem.BaseProblem):
# surveyPair = Survey.LinearSurvey
forwardOnly = False #: Determine if the forward matrix is stored (defaut:yes)
actInd = None #: Active cell indices provided
rtype = 'z'
def __init__(self, mesh, mapping=None, **kwargs):
Problem.BaseProblem.__init__(self, mesh, mapping=mapping, **kwargs)
def fwr_op(self):
# Add forward function
# kappa = self.curModel.kappa TODO
rho = self.mapping*self.curModel
if self.forwardOnly:
if getattr(self, 'actInd', None) is not None:
if self.actInd.dtype=='bool':
inds = np.asarray([inds for inds, elem in enumerate(self.actInd, 1) if elem], dtype = int) - 1
else:
inds = self.actInd
else:
inds = np.asarray(range(self.mesh.nC))
nC = len(inds)
# Create active cell projector
P = sp.csr_matrix(
(np.ones(nC), (inds, range(nC))),
shape=(self.mesh.nC, nC)
)
# Create vectors of nodal location (lower and upper corners for each cell)
xn = self.mesh.vectorNx
yn = self.mesh.vectorNy
zn = self.mesh.vectorNz
yn2, xn2, zn2 = np.meshgrid(yn[1:], xn[1:], zn[1:])
yn1, xn1, zn1 = np.meshgrid(yn[0:-1], xn[0:-1], zn[0:-1])
Yn = P.T*np.c_[mkvc(yn1), mkvc(yn2)]
Xn = P.T*np.c_[mkvc(xn1), mkvc(xn2)]
Zn = P.T*np.c_[mkvc(zn1), mkvc(zn2)]
rxLoc = self.survey.srcField.rxList[0].locs
ndata = rxLoc.shape[0]
# Pre-allocate space and create magnetization matrix if required
# Pre-allocate space
if self.rtype == 'z':
fwr_d = np.zeros(self.survey.nRx)
elif self.rtype == 'xyz':
fwr_d = np.zeros(3*self.survey.nRx)
else:
print """Flag must be either 'z' | 'xyz', please revised"""
return
# Add counter to dsiplay progress. Good for large problems
count = -1;
for ii in range(ndata):
tx, ty, tz = get_T_mat(Xn, Yn, Zn, rxLoc[ii, :])
if self.rtype =='z':
fwr_d[ii] =tz.dot(rho)
elif self.rtype =='xyz':
fwr_d[ii] = tx.dot(rho)
fwr_d[ii+ndata] = ty.dot(rho)
fwr_d[ii+2*ndata] = tz.dot(rho)
# Display progress
count = progress(ii,count,ndata)
print "Done 100% ...forward operator completed!!\n"
return fwr_d
else:
return self.G.dot(rho)
def fields(self, m):
self.curModel = m
fields = self.fwr_op()
return fields
# return self.G.dot(self.mapping*(m))
def Jvec(self, m, v, f=None):
dmudm = self.mapping.deriv(m)
return self.G.dot(dmudm*v)
def Jtvec(self, m, v, f=None):
dmudm = self.mapping.deriv(m)
return dmudm.T * (self.G.T.dot(v))
@property
def G(self):
if not self.ispaired:
raise Exception('Need to pair!')
if getattr(self, '_G', None) is None:
self._G = self.Intrgl_Fwr_Op( 'z' )
return self._G
def Intrgl_Fwr_Op(self, flag):
"""
Gravity forward operator in integral form
flag = 'z' | 'xyz'
Return
_G = Linear forward modeling operation
Created on March, 15th 2016
@author: dominiquef
"""
# Find non-zero cells
# inds = np.nonzero(actv)[0]
if getattr(self, 'actInd', None) is not None:
if self.actInd.dtype=='bool':
inds = np.asarray([inds for inds, elem in enumerate(self.actInd, 1) if elem], dtype = int) - 1
else:
inds = self.actInd
else:
inds = np.asarray(range(self.mesh.nC))
nC = len(inds)
# Create active cell projector
P = sp.csr_matrix(
(np.ones(nC), (inds, range(nC))),
shape=(self.mesh.nC, nC)
)
# Create vectors of nodal location (lower and upper corners for each cell)
xn = self.mesh.vectorNx
yn = self.mesh.vectorNy
zn = self.mesh.vectorNz
yn2, xn2, zn2 = np.meshgrid(yn[1:], xn[1:], zn[1:])
yn1, xn1, zn1 = np.meshgrid(yn[0:-1], xn[0:-1], zn[0:-1])
Yn = P.T*np.c_[mkvc(yn1), mkvc(yn2)]
Xn = P.T*np.c_[mkvc(xn1), mkvc(xn2)]
Zn = P.T*np.c_[mkvc(zn1), mkvc(zn2)]
rxLoc = self.survey.srcField.rxList[0].locs
ndata = rxLoc.shape[0]
# Pre-allocate space and create magnetization matrix if required
# Pre-allocate space
if flag == 'z':
G = np.zeros((ndata, nC))
elif flag == 'xyz':
G = np.zeros((int(3*ndata), nC))
else:
print """Flag must be either 'z' | 'xyz', please revised"""
return
# Loop through all observations and create forward operator (ndata-by-nC)
print "Begin calculation of forward operator: " + flag
# Add counter to dsiplay progress. Good for large problems
count = -1;
for ii in range(ndata):
if flag=='z':
tt = get_T_mat(Xn, Yn, Zn, rxLoc[ii, :])
G[ii, :] = tt
elif flag == 'xyz':
print "Sorry 3-component not implemented yet"
# Display progress
count = progress(ii, count, ndata)
print "Done 100% ...forward operator completed!!\n"
return G
def get_T_mat(Xn, Yn, Zn, rxLoc):
"""
Load in the active nodes of a tensor mesh and computes the gravity tensor
for a given observation location rxLoc[obsx, obsy, obsz]
INPUT:
Xn, Yn, Zn: Node location matrix for the lower and upper most corners of
all cells in the mesh shape[nC,2]
M
OUTPUT:
Tx = [Txx Txy Txz]
Ty = [Tyx Tyy Tyz]
Tz = [Tzx Tzy Tzz]
where each elements have dimension 1-by-nC.
Only the upper half 5 elements have to be computed since symetric.
Currently done as for-loops but will eventually be changed to vector
indexing, once the topography has been figured out.
"""
NewtG=6.6738e-3
eps = 1e-10 # add a small value to the locations to avoid /0
nC = Xn.shape[0]
# Pre-allocate space for 1D array
tx = np.zeros((1,nC))
ty = np.zeros((1,nC))
tz = np.zeros((1,nC))
dz = rxLoc[2] - Zn + eps
dy = Yn - rxLoc[1] + eps
dx = Xn - rxLoc[0] + eps
# Compute contribution from each corners
for aa in range(2):
for bb in range(2):
for cc in range(2):
r = (
dx[:, aa] ** 2 +
dy[:, bb] ** 2 +
dz[:, cc] ** 2
) ** (0.50)
tx = tx - NewtG * (-1) ** aa * (-1) ** bb * (-1) ** cc * (
dy[:, bb] * np.log(dz[:, cc] + r) +
dz[:, cc] * np.log(dy[:, bb] + r) -
dx[:, aa] * np.arctan(dy[:, bb] * dz[:, cc] / (dx[:, aa] * r)))
ty = ty - NewtG * (-1) ** aa * (-1) ** bb * (-1) ** cc * (
dx[:, aa] * np.log(dz[:, cc] + r) +
dz[:, cc] * np.log(dx[:, aa] + r) -
dy[:, bb] * np.arctan(dx[:, aa] * dz[:, cc] / (dy[:, bb] * r)))
tz = tz - NewtG * (-1) ** aa * (-1) ** bb * (-1) ** cc * (
dx[:, aa] * np.log(dy[:, bb] + r) +
dy[:, bb] * np.log(dx[:, aa] + r) -
dz[:, cc] * np.arctan(dx[:, aa] * dy[:, bb] / (dz[:, cc] * r)))
return tx,ty,tz
def progress(iter, prog, final):
"""
progress(iter,prog,final)
Function measuring the progress of a process and print to screen the %.
Useful to estimate the remaining runtime of a large problem.
Created on Dec, 20th 2015
@author: dominiquef
"""
arg = np.floor(float(iter)/float(final)*10.)
if arg > prog:
strg = "Done " + str(arg*10) + " %"
print strg
prog = arg
return prog
def writeUBCobs(filename, survey, d):
"""
writeUBCobs(filename,survey,d)
Function writing an observation file in UBC-GRAV3D format.
INPUT
filename : Name of out file including directory
survey
flag : dobs | dpred
OUTPUT
Obsfile
"""
rxLoc = survey.srcField.rxList[0].locs
wd = survey.std
data = np.c_[rxLoc, d, wd]
with file(filename, 'w') as fid:
fid.write('%i\n' % len(d))
np.savetxt(fid, data, fmt='%e', delimiter=' ', newline='\n')
print "Observation file saved to: " + filename
def getActiveTopo(mesh, topo, flag):
"""
getActiveTopo(mesh,topo)
Function creates an active cell model from topography
INPUT
mesh : Mesh in SimPEG format
topo : Scatter points defining topography [x,y,z]
OUTPUT
actv : Active cell model
"""
import scipy.interpolate as interpolation
if flag == 'N':
Zn = np.zeros((mesh.nNx, mesh.nNy))
# wght = np.zeros((mesh.nNx,mesh.nNy))
cx = mesh.vectorNx
cy = mesh.vectorNy
F = interpolation.NearestNDInterpolator(topo[:, 0:2], topo[:, 2])
[Y, X] = np.meshgrid(cy, cx)
Zn = F(X, Y)
actv = np.zeros((mesh.nCx, mesh.nCy, mesh.nCz))
if flag == 'N':
Nz = mesh.vectorNz[1:]
for jj in range(mesh.nCy):
for ii in range(mesh.nCx):
temp = [kk for kk in range(len(Nz)) if np.all(Zn[ii:(ii+2), jj:(jj+2)] > Nz[kk]) ]
actv[ii, jj, temp] = 1
actv = mkvc(actv == 1)
inds = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem], dtype = int) - 1
return inds
def plot_obs_2D(survey,varstr, fig = None):
""" Function plot_obs(rxLoc,d,wd)
Generate a 2d interpolated plot from scatter points of data
INPUT
rxLoc : Observation locations [x,y,z]
d : Data vector
wd : Uncertainty vector
OUTPUT
figure()
Created on Dec, 27th 2015
@author: dominiquef
"""
from scipy.interpolate import griddata
import pylab as plt
rxLoc = survey.srcField.rxList[0].locs
d = survey.dobs
wd = survey.std
# Create grid of points
x = np.linspace(rxLoc[:,0].min(), rxLoc[:,0].max(), 100)
y = np.linspace(rxLoc[:,1].min(), rxLoc[:,1].max(), 100)
X, Y = np.meshgrid(x,y)
# Interpolate
d_grid = griddata(rxLoc[:,0:2],d,(X,Y), method ='linear')
# Plot result
if fig is None:
fig = plt.figure()
ax = plt.subplot()
plt.imshow(d_grid, extent=[x.min(), x.max(), y.min(), y.max()],origin = 'lower', cmap='plasma')
plt.colorbar(fraction=0.02)
plt.contour(X,Y, d_grid,10)
plt.scatter(rxLoc[:,0],rxLoc[:,1], c=d, s=20)
plt.title(varstr)
plt.gca().set_aspect('equal', adjustable='box')
def readUBCgravObs(obs_file):
"""
Read UBC grav file format
INPUT:
:param fileName, path to the UBC obs grav file
OUTPUT:
:param survey
"""
fid = open(obs_file,'r')
# First line has the number of rows
line = fid.readline()
ndat = np.array(line.split(),dtype=int)
# Pre-allocate space for obsx, obsy, obsz, data, uncert
line = fid.readline()
temp = np.array(line.split(),dtype=float)
d = np.zeros(ndat, dtype=float)
wd = np.zeros(ndat, dtype=float)
locXYZ = np.zeros( (ndat,3), dtype=float)
for ii in range(ndat):
temp = np.array(line.split(),dtype=float)
locXYZ[ii,:] = temp[:3]
d[ii] = temp[3]
wd[ii] = temp[4]
line = fid.readline()
rxLoc = GRAV.RxObs(locXYZ)
srcField = GRAV.SrcField([rxLoc])
survey = GRAV.LinearSurvey(srcField)
survey.dobs = d
survey.std = wd
return survey
def read_GRAVinv_inp(input_file):
"""Read input files for forward modeling MAG data with integral form
INPUT:
input_file: File name containing the forward parameter
OUTPUT:
mshfile
obsfile
topofile
start model
ref model
weightfile
chi_target
as, ax ,ay, az
upper, lower bounds
lp, lqx, lqy, lqz
# All files should be in the working directory, otherwise the path must
# be specified.
Created on Dec 21th, 2015
@author: dominiquef
"""
fid = open(input_file,'r')
# Line 1
line = fid.readline()
l_input = line.split('!')
mshfile = l_input[0].rstrip()
# Line 2
line = fid.readline()
l_input = line.split('!')
obsfile = l_input[0].rstrip()
# Line 3
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input=='null':
topofile = []
else:
topofile = l_input[0].rstrip()
# Line 4
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
mstart = float(l_input[1])
else:
mstart = l_input[0].rstrip()
# Line 5
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
mref = float(l_input[1])
else:
mref = l_input[0].rstrip()
# Line 7
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='DEFAULT':
wgtfile = None
else:
wgtfile = l_input[0].rstrip()
# Line 8
line = fid.readline()
l_input = re.split('[!\s]',line)
chi = float(l_input[0])
# Line 9
line = fid.readline()
l_input = re.split('[!\s]',line)
val = np.array(l_input[0:4])
alphas = val.astype(np.float)
# Line 10
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
val = np.array(l_input[1:3])
bounds = val.astype(np.float)
else:
bounds = l_input[0].rstrip()
# Line 11
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
val = np.array(l_input[1:6])
lpnorms = val.astype(np.float)
else:
lpnorms = l_input[0].rstrip()
return mshfile, obsfile, topofile, mstart, mref, wgtfile, chi, alphas, bounds, lpnorms
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import re, os
from SimPEG import Mesh, np, Utils
import BaseGrav, Gravity
class GravityDriver_Inv(object):
"""docstring for GravityDriver_Inv"""
def __init__(self, input_file=None):
if input_file is not None:
self.basePath = os.path.sep.join(input_file.split(os.path.sep)[:-1])
if len(self.basePath) > 0:
self.basePath += os.path.sep
self.readDriverFile(input_file.split(os.path.sep)[-1])
def readDriverFile(self, input_file):
"""
Read input files for forward modeling GRAV data with integral form
INPUT:
input_file: File name containing the forward parameter
OUTPUT:
mshfile
obsfile
topofile
start model
ref model
active cells model
weightfile
chi_target
as, ax ,ay, az
upper, lower bounds
lp, lqx, lqy, lqz
eps_p, eps_q
# All files should be in the working directory, otherwise the path must
# be specified.
"""
fid = open(self.basePath + input_file, 'r')
# Line 1
line = fid.readline()
l_input = line.split('!')
mshfile = l_input[0].rstrip()
# Line 2
line = fid.readline()
l_input = line.split('!')
obsfile = l_input[0].rstrip()
# Line 3
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input=='null':
topofile = []
else:
topofile = l_input[0].rstrip()
# Line 4
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0]=='VALUE':
mstart = float(l_input[1])
else:
mstart = l_input[0].rstrip()
# Line 5
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
mref = float(l_input[1])
else:
mref = l_input[0].rstrip()
# Line 6
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0]=='VALUE':
staticInput = float(l_input[1])
elif l_input[0]=='DEFAULT':
staticInput = None
else:
staticInput = l_input[0].rstrip()
# Line 7
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input=='DEFAULT':
wgtfile = []
else:
wgtfile = l_input[0].rstrip()
# Line 8
line = fid.readline()
l_input = re.split('[!\s]', line)
chi = float(l_input[0])
# Line 9
line = fid.readline()
l_input = re.split('[!\s]', line)
val = np.array(l_input[0:4])
alphas = val.astype(np.float)
# Line 10
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0]=='VALUE':
val = np.array(l_input[1:3])
bounds = val.astype(np.float)
else:
bounds = l_input[0].rstrip()
# Line 11
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0]=='VALUE':
val = np.array(l_input[1:6])
lpnorms = val.astype(np.float)
else:
lpnorms = l_input[0].rstrip()
# Line 12
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0]=='VALUE':
val = np.array(l_input[1:3])
eps = val.astype(np.float)
else:
eps = [None, None]
self.mshfile = mshfile
self.obsfile = obsfile
self.topofile = topofile
self.mstart = mstart
self._mrefInput = mref
self._staticInput = staticInput
self.wgtfile = wgtfile
self.chi = chi
self.alphas = alphas
self.bounds = bounds
self.lpnorms = lpnorms
self.eps = eps
@property
def mesh(self):
if getattr(self, '_mesh', None) is None:
self._mesh = Mesh.TensorMesh.readUBC(self.basePath + self.mshfile)
return self._mesh
@property
def survey(self):
if getattr(self, '_survey', None) is None:
self._survey = self.readGravityObservations(self.basePath + self.obsfile)
return self._survey
@property
def activeCells(self):
if getattr(self, '_activeCells', None) is None:
if self.topofile == 'null':
self._activeCells = np.arange(mesh.nC)
else:
topo = np.genfromtxt(self.basePath + self.topofile, skip_header=1)
# Find the active cells
active = Utils.surface2ind_topo(self.mesh,topo,'N')
inds = np.asarray([inds for inds, elem in enumerate(active, 1) if elem], dtype = int) - 1
self._activeCells = inds
return self._activeCells
@property
def staticCells(self):
if getattr(self, '_staticCells', None) is None:
if getattr(self, '_staticInput', None) is None:
# All cells are dynamic: 1's
self._dynamicCells = np.arange(len(self.m0))
self._staticCells = []
# Cells with specific value are static: 0's
else:
if isinstance(self._staticInput, float):
staticCells = self.m0 == self._staticInput
else:
# Read from file active cells with 0:air, 1:dynamic, -1 static
staticCells = Mesh.TensorMesh.readModelUBC(self.mesh, self.basePath + self._staticInput)
staticCells = staticCells[self.activeCells] == -1
inds = np.asarray([inds for inds, elem in enumerate(staticCells, 1) if elem], dtype = int) - 1
self._staticCells = inds
return self._staticCells
@property
def dynamicCells(self):
if getattr(self, '_dynamicCells', None) is None:
if getattr(self, '_staticInput', None) is None:
# All cells are dynamic: 1's
self._dynamicCells = np.arange(len(self.m0))
# Cells with specific value are static: 0's
else:
if isinstance(self._staticInput, float):
dynamicCells = self.m0 != self._staticInput
else:
# Read from file active cells with 0:air, 1:dynamic, -1 static
dynamicCells = Mesh.TensorMesh.readModelUBC(self.mesh, self.basePath + self._staticInput)
dynamicCells = dynamicCells[self.activeCells] == 1
inds = np.asarray([inds for inds, elem in enumerate(dynamicCells, 1) if elem], dtype = int) - 1
self._dynamicCells = inds
return self._dynamicCells
@property
def nC(self):
if getattr(self, '_nC', None) is None:
self._nC = len(self.activeCells)
return self._nC
@property
def m0(self):
if getattr(self, '_m0', None) is None:
if isinstance(self.mstart, float):
self._m0 = np.ones(self.nC) * self.mstart
else:
self._m0 = Mesh.TensorMesh.readModelUBC(self.mesh, self.basePath + self.mstart)
self._m0 = self._m0[self.activeCells]
return self._m0
@property
def mref(self):
if getattr(self, '_mref', None) is None:
if isinstance(self._mrefInput, float):
self._mref = np.ones(self.nC) * self._mrefInput
else:
self._mref = Mesh.TensorMesh.readModelUBC(self.mesh, self.basePath + self._mrefInput)
self._mref = self._mref[self.activeCells]
return self._mref
def readGravityObservations(self, obs_file):
"""
Read UBC grav file format
INPUT:
:param fileName, path to the UBC obs grav file
OUTPUT:
:param survey
"""
fid = open(obs_file,'r')
# First line has the number of rows
line = fid.readline()
ndat = np.array(line.split(),dtype=int)
# Pre-allocate space for obsx, obsy, obsz, data, uncert
line = fid.readline()
temp = np.array(line.split(),dtype=float)
d = np.zeros(ndat, dtype=float)
wd = np.zeros(ndat, dtype=float)
locXYZ = np.zeros( (ndat,3), dtype=float)
for ii in range(ndat):
temp = np.array(line.split(),dtype=float)
locXYZ[ii,:] = temp[:3]
d[ii] = temp[3]
wd[ii] = temp[4]
line = fid.readline()
rxLoc = BaseGrav.RxObs(locXYZ)
srcField = BaseGrav.SrcField([rxLoc])
survey = BaseGrav.LinearSurvey(srcField)
survey.dobs = d
survey.std = wd
return survey
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from scipy.constants import mu_0
from SimPEG import *
from SimPEG.Utils import kron3, speye, sdiag
import matplotlib.pyplot as plt
def spheremodel(mesh, x0, y0, z0, r):
"""
Generate model indicies for sphere
- (x0, y0, z0 ): is the center location of sphere
- r: is the radius of the sphere
- it returns logical indicies of cell-center model
"""
ind = np.sqrt( (mesh.gridCC[:,0]-x0)**2+(mesh.gridCC[:,1]-y0)**2+(mesh.gridCC[:,2]-z0)**2 ) < r
return ind
def MagSphereAnaFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag='total'):
"""
test
Analytic function for Magnetics problem. The set up here is
magnetic sphere in whole-space assuming that the inducing field is oriented in the x-direction.
* (x0,y0,z0)
* (x0, y0, z0 ): is the center location of sphere
* r: is the radius of the sphere
.. math::
\mathbf{H}_0 = H_0\hat{x}
"""
if (~np.size(x)==np.size(y)==np.size(z)):
print "Specify same size of x, y, z"
return
dim = x.shape
x = Utils.mkvc(x)
y = Utils.mkvc(y)
z = Utils.mkvc(z)
ind = np.sqrt((x-x0)**2+(y-y0)**2+(z-z0)**2 ) < R
r = Utils.mkvc(np.sqrt((x-x0)**2+(y-y0)**2+(z-z0)**2 ))
Bx = np.zeros(x.size)
By = np.zeros(x.size)
Bz = np.zeros(x.size)
# Inside of the sphere
rf2 = 3*mu1/(mu2+2*mu1)
if flag is 'total' and any(ind):
Bx[ind] = mu2*H0*(rf2)
elif (flag == 'secondary'):
Bx[ind] = mu2*H0*(rf2)-mu1*H0
By[ind] = 0.
Bz[ind] = 0.
# Outside of the sphere
rf1 = (mu2-mu1)/(mu2+2*mu1)
if (flag == 'total'):
Bx[~ind] = mu1*(H0+H0/r[~ind]**5*(R**3)*rf1*(2*(x[~ind]-x0)**2-(y[~ind]-y0)**2-(z[~ind]-z0)**2))
elif (flag == 'secondary'):
Bx[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(2*(x[~ind]-x0)**2-(y[~ind]-y0)**2-(z[~ind]-z0)**2))
By[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*(x[~ind]-x0)*(y[~ind]-y0)))
Bz[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*(x[~ind]-x0)*(z[~ind]-z0)))
return np.reshape(Bx, x.shape, order='F'), np.reshape(By, x.shape, order='F'), np.reshape(Bz, x.shape, order='F')
def CongruousMagBC(mesh, Bo, chi):
"""
Computing boundary condition using Congrous sphere method.
This is designed for secondary field formulation.
>> Input
* mesh: Mesh class
* Bo: np.array([Box, Boy, Boz]): Primary magnetic flux
* chi: susceptibility at cell volume
.. math::
\\vec{B}(r) = \\frac{\mu_0}{4\pi} \\frac{m}{ \| \\vec{r} - \\vec{r}_0\|^3}[3\hat{m}\cdot\hat{r}-\hat{m}]
"""
ind = chi > 0.
V = mesh.vol[ind].sum()
gamma = 1/V*(chi*mesh.vol).sum() # like a mass!
Bot = np.sqrt(sum(Bo**2))
mx = Bo[0]/Bot
my = Bo[1]/Bot
mz = Bo[2]/Bot
mom = 1/mu_0*Bot*gamma*V/(1+gamma/3)
xc = sum(chi[ind]*mesh.gridCC[:,0][ind])/sum(chi[ind])
yc = sum(chi[ind]*mesh.gridCC[:,1][ind])/sum(chi[ind])
zc = sum(chi[ind]*mesh.gridCC[:,2][ind])/sum(chi[ind])
indxd, indxu, indyd, indyu, indzd, indzu = mesh.faceBoundaryInd
const = mu_0/(4*np.pi)*mom
rfun = lambda x: np.sqrt((x[:,0]-xc)**2 + (x[:,1]-yc)**2 + (x[:,2]-zc)**2)
mdotrx = (mx*(mesh.gridFx[(indxd|indxu),0]-xc)/rfun(mesh.gridFx[(indxd|indxu),:]) +
my*(mesh.gridFx[(indxd|indxu),1]-yc)/rfun(mesh.gridFx[(indxd|indxu),:]) +
mz*(mesh.gridFx[(indxd|indxu),2]-zc)/rfun(mesh.gridFx[(indxd|indxu),:]))
Bbcx = const/(rfun(mesh.gridFx[(indxd|indxu),:])**3)*(3*mdotrx*(mesh.gridFx[(indxd|indxu),0]-xc)/rfun(mesh.gridFx[(indxd|indxu),:])-mx)
mdotry = (mx*(mesh.gridFy[(indyd|indyu),0]-xc)/rfun(mesh.gridFy[(indyd|indyu),:]) +
my*(mesh.gridFy[(indyd|indyu),1]-yc)/rfun(mesh.gridFy[(indyd|indyu),:]) +
mz*(mesh.gridFy[(indyd|indyu),2]-zc)/rfun(mesh.gridFy[(indyd|indyu),:]))
Bbcy = const/(rfun(mesh.gridFy[(indyd|indyu),:])**3)*(3*mdotry*(mesh.gridFy[(indyd|indyu),1]-yc)/rfun(mesh.gridFy[(indyd|indyu),:])-my)
mdotrz = (mx*(mesh.gridFz[(indzd|indzu),0]-xc)/rfun(mesh.gridFz[(indzd|indzu),:]) +
my*(mesh.gridFz[(indzd|indzu),1]-yc)/rfun(mesh.gridFz[(indzd|indzu),:]) +
mz*(mesh.gridFz[(indzd|indzu),2]-zc)/rfun(mesh.gridFz[(indzd|indzu),:]))
Bbcz = const/(rfun(mesh.gridFz[(indzd|indzu),:])**3)*(3*mdotrz*(mesh.gridFz[(indzd|indzu),2]-zc)/rfun(mesh.gridFz[(indzd|indzu),:])-mz)
return np.r_[Bbcx, Bbcy, Bbcz], (1/gamma-1/(3+gamma))*1/V
def MagSphereAnaFunA(x, y, z, R, xc, yc, zc, chi, Bo, flag):
"""
Computing boundary condition using Congrous sphere method.
This is designed for secondary field formulation.
>> Input
mesh: Mesh class
Bo: np.array([Box, Boy, Boz]): Primary magnetic flux
Chi: susceptibility at cell volume
.. math::
\\vec{B}(r) = \\frac{\mu_0}{4\pi}\\frac{m}{\| \\vec{r}-\\vec{r}_0\|^3}[3\hat{m}\cdot\hat{r}-\hat{m}]
"""
if (~np.size(x)==np.size(y)==np.size(z)):
print "Specify same size of x, y, z"
return
dim = x.shape
x = Utils.mkvc(x)
y = Utils.mkvc(y)
z = Utils.mkvc(z)
Bot = np.sqrt(sum(Bo**2))
mx = Bo[0]/Bot
my = Bo[1]/Bot
mz = Bo[2]/Bot
ind = np.sqrt((x-xc)**2+(y-yc)**2+(z-zc)**2 ) < R
Bx = np.zeros(x.size)
By = np.zeros(x.size)
Bz = np.zeros(x.size)
# Inside of the sphere
rf2 = 3/(chi+3)*(1+chi)
if (flag == 'total'):
Bx[ind] = Bo[0]*(rf2)
By[ind] = Bo[1]*(rf2)
Bz[ind] = Bo[2]*(rf2)
elif (flag == 'secondary'):
Bx[ind] = Bo[0]*(rf2)-Bo[0]
By[ind] = Bo[1]*(rf2)-Bo[1]
Bz[ind] = Bo[2]*(rf2)-Bo[2]
r = Utils.mkvc(np.sqrt((x-xc)**2+(y-yc)**2+(z-zc)**2 ))
V = 4*np.pi*R**3/3
mom = Bot/mu_0*chi/(1+chi/3)*V
const = mu_0/(4*np.pi)*mom
mdotr = (mx*(x[~ind]-xc)/r[~ind] + my*(y[~ind]-yc)/r[~ind] + mz*(z[~ind]-zc)/r[~ind])
Bx[~ind] = const/(r[~ind]**3)*(3*mdotr*(x[~ind]-xc)/r[~ind]-mx)
By[~ind] = const/(r[~ind]**3)*(3*mdotr*(y[~ind]-yc)/r[~ind]-my)
Bz[~ind] = const/(r[~ind]**3)*(3*mdotr*(z[~ind]-zc)/r[~ind]-mz)
return Bx, By, Bz
def IDTtoxyz(Inc, Dec, Btot):
"""
Convert from Inclination, Declination, Total intensity of earth field to x, y, z
"""
Bx = Btot*np.cos(Inc/180.*np.pi)*np.sin(Dec/180.*np.pi)
By = Btot*np.cos(Inc/180.*np.pi)*np.cos(Dec/180.*np.pi)
Bz = -Btot*np.sin(Inc/180.*np.pi)
return np.r_[Bx, By, Bz]
def MagSphereFreeSpace(x, y, z, R, xc, yc, zc, chi, Bo):
"""
Computing boundary condition using Congrous sphere method.
This is designed for secondary field formulation.
>> Input
mesh: Mesh class
Bo: np.array([Box, Boy, Boz]): Primary magnetic flux
Chi: susceptibility at cell volume
.. math::
\\vec{B}(r) = \\frac{\mu_0}{4\pi}\\frac{m}{\| \\vec{r}-\\vec{r}_0\|^3}[3\hat{m}\cdot\hat{r}-\hat{m}]
"""
if (~np.size(x)==np.size(y)==np.size(z)):
print "Specify same size of x, y, z"
return
x = Utils.mkvc(x)
y = Utils.mkvc(y)
z = Utils.mkvc(z)
nobs = len(x)
Bot = np.sqrt(sum(Bo**2))
mx = np.ones([nobs]) * Bo[0,0] * R**3 / 3. * chi
my = np.ones([nobs]) * Bo[0,1] * R**3 / 3. * chi
mz = np.ones([nobs]) * Bo[0,2] * R**3 / 3. * chi
M = np.c_[mx, my, mz]
rx = (x - xc)
ry = (y - yc)
rz = (zc - z)
rvec = np.c_[rx, ry, rz]
r = np.sqrt((rx)**2+(ry)**2+(rz)**2 )
B = -Utils.sdiag(1./r**3)*M + Utils.sdiag((3 * np.sum(M*rvec,axis=1))/r**5)*rvec
Bx = B[:,0]
By = B[:,1]
Bz = B[:,2]
return Bx, By, Bz
if __name__ == '__main__':
hxind = [(0,25,1.3),(21, 12.5),(0,25,1.3)]
hyind = [(0,25,1.3),(21, 12.5),(0,25,1.3)]
hzind = [(0,25,1.3),(20, 12.5),(0,25,1.3)]
# hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)
M3 = Mesh.TensorMesh([hxind, hyind, hzind], "CCC")
indxd, indxu, indyd, indyu, indzd, indzu = M3.faceBoundaryInd
mu0 = 4*np.pi*1e-7
chibkg = 0.
chiblk = 0.01
chi = np.ones(M3.nC)*chibkg
sph_ind = spheremodel(M3, 0, 0, 0, 100)
chi[sph_ind] = chiblk
mu = (1.+chi)*mu0
Bbc, const = CongruousMagBC(M3, np.array([1., 0., 0.]), chi)
flag = 'secondary'
Box = 1.
H0 = Box/mu_0
Bbcxx, Bbcxy, Bbcxz = MagSphereAnaFun(M3.gridFx[(indxd|indxu),0], M3.gridFx[(indxd|indxu),1], M3.gridFx[(indxd|indxu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbcyx, Bbcyy, Bbcyz = MagSphereAnaFun(M3.gridFy[(indyd|indyu),0], M3.gridFy[(indyd|indyu),1], M3.gridFy[(indyd|indyu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbczx, Bbczy, Bbczz = MagSphereAnaFun(M3.gridFz[(indzd|indzu),0], M3.gridFz[(indzd|indzu),1], M3.gridFz[(indzd|indzu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbc_ana = np.r_[Bbcxx, Bbcyy, Bbczz]
# fig, ax = plt.subplots(1,1, figsize = (10, 10))
# ax.plot(Bbc_ana)
# ax.plot(Bbc)
# plt.show()
err = np.linalg.norm(Bbc-Bbc_ana)/np.linalg.norm(Bbc_ana)
if err < 0.1:
print 'Mag Boundary computation is valid, err = ', err
else:
print 'Mag Boundary computation is wrong!!, err = ', err
pass
File diff suppressed because it is too large Load Diff
-334
View File
@@ -1,334 +0,0 @@
import re, os
from SimPEG import Mesh, np, Utils
import BaseMag, Magnetics
class MagneticsDriver_Inv(object):
"""docstring for MagneticsDriver_Inv"""
def __init__(self, input_file=None):
if input_file is not None:
self.basePath = os.path.sep.join(input_file.split(os.path.sep)[:-1])
if len(self.basePath) > 0:
self.basePath += os.path.sep
self.readDriverFile(input_file.split(os.path.sep)[-1])
def readDriverFile(self, input_file):
"""
Read input files for forward modeling MAG data with integral form
INPUT:
input_file: File name containing the forward parameter
OUTPUT:
mshfile
obsfile
topofile
start model
ref model
mag model
weightfile
chi_target
as, ax ,ay, az
upper, lower bounds
lp, lqx, lqy, lqz
# All files should be in the working directory, otherwise the path must
# be specified.
"""
fid = open(self.basePath + input_file,'r')
# Line 1
line = fid.readline()
l_input = line.split('!')
mshfile = l_input[0].rstrip()
# Line 2
line = fid.readline()
l_input = line.split('!')
obsfile = l_input[0].rstrip()
# Line 3
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input=='null':
topofile = []
else:
topofile = l_input[0].rstrip()
# Line 4
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
mstart = float(l_input[1])
else:
mstart = l_input[0].rstrip()
# Line 5
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
mref = float(l_input[1])
else:
mref = l_input[0].rstrip()
# Line 6
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
staticInput = float(l_input[1])
elif l_input[0]=='DEFAULT':
staticInput = None
else:
staticInput = l_input[0].rstrip()
# Line 7
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input=='DEFAULT':
magfile = []
else:
magfile = l_input[0].rstrip()
# Line 8
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input=='DEFAULT':
wgtfile = []
else:
wgtfile = l_input[0].rstrip()
# Line 9
line = fid.readline()
l_input = re.split('[!\s]',line)
chi = float(l_input[0])
# Line 10
line = fid.readline()
l_input = re.split('[!\s]',line)
val = np.array(l_input[0:4])
alphas = val.astype(np.float)
# Line 11
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
val = np.array(l_input[1:3])
bounds = val.astype(np.float)
else:
bounds = l_input[0].rstrip()
# Line 12
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
val = np.array(l_input[1:6])
lpnorms = val.astype(np.float)
else:
lpnorms = l_input[0].rstrip()
# Line 13
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
val = np.array(l_input[1:3])
eps = val.astype(np.float)
else:
eps = [None,None]
self.mshfile = mshfile
self.obsfile = obsfile
self.topofile = topofile
self.mstart = mstart
self._mrefInput = mref
self._staticInput = staticInput
self.magfile = magfile
self.wgtfile = wgtfile
self.chi = chi
self.alphas = alphas
self.bounds = bounds
self.lpnorms = lpnorms
self.eps = eps
@property
def mesh(self):
if getattr(self, '_mesh', None) is None:
self._mesh = Mesh.TensorMesh.readUBC(self.basePath + self.mshfile)
return self._mesh
@property
def survey(self):
if getattr(self, '_survey', None) is None:
self._survey = self.readMagneticsObservations(self.obsfile)
return self._survey
@property
def activeCells(self):
if getattr(self, '_activeCells', None) is None:
if self.topofile == 'null':
self._activeCells = np.arange(self.mesh.nC)
else:
topo = np.genfromtxt(self.basePath + self.topofile, skip_header=1)
# Find the active cells
active = Utils.surface2ind_topo(self.mesh,topo,'N')
inds = np.asarray([inds for inds, elem in enumerate(active, 1) if elem], dtype = int) - 1
self._activeCells = inds
return self._activeCells
@property
def staticCells(self):
if getattr(self, '_staticCells', None) is None:
if getattr(self, '_staticInput', None) is None:
# All cells are dynamic: 1's
self._dynamicCells = np.arange(len(self.m0))
self._staticCells = []
# Cells with specific value are static: 0's
else:
if isinstance(self._staticInput, float):
staticCells = self.m0 == self._staticInput
else:
# Read from file active cells with 0:air, 1:dynamic, -1 static
staticCells = Mesh.TensorMesh.readModelUBC(self.mesh, self.basePath + self._staticInput)
staticCells = staticCells[self.activeCells] == -1
inds = np.asarray([inds for inds, elem in enumerate(staticCells, 1) if elem], dtype = int) - 1
self._staticCells = inds
return self._staticCells
@property
def dynamicCells(self):
if getattr(self, '_dynamicCells', None) is None:
if getattr(self, '_staticInput', None) is None:
# All cells are dynamic: 1's
self._dynamicCells = np.arange(len(self.m0))
# Cells with specific value are static: 0's
else:
if isinstance(self._staticInput, float):
dynamicCells = self.m0 != self._staticInput
else:
# Read from file active cells with 0:air, 1:dynamic, -1 static
dynamicCells = Mesh.TensorMesh.readModelUBC(self.mesh, self.basePath + self._staticInput)
dynamicCells = dynamicCells[self.activeCells] == 1
inds = np.asarray([inds for inds, elem in enumerate(dynamicCells, 1) if elem], dtype = int) - 1
self._dynamicCells = inds
return self._dynamicCells
@property
def nC(self):
if getattr(self, '_nC', None) is None:
self._nC = len(self.activeCells)
return self._nC
@property
def m0(self):
if getattr(self, '_m0', None) is None:
if isinstance(self.mstart, float):
self._m0 = np.ones(self.nC) * self.mstart
else:
self._m0 = Mesh.TensorMesh.readModelUBC(self.mesh,self.basePath + self.mstart)
self._m0 = self._m0[self.activeCells]
return self._m0
@property
def mref(self):
if getattr(self, '_mref', None) is None:
if isinstance(self._mrefInput, float):
self._mref = np.ones(self.nC) * self._mrefInput
else:
self._mref = Mesh.TensorMesh.readModelUBC(self.mesh,self.basePath + self._mrefInput)
self._mref = self._mref[self.activeCells]
return self._mref
@property
def magnetizationModel(self):
"""
magnetization vector
"""
if self.magfile == 'DEFAULT':
return Magnetics.dipazm_2_xyz(np.ones(self.nC) * self.survey.srcField.param[1], np.ones(self.nC) * self.survey.srcField.param[2])
else:
raise NotImplementedError("this will require you to read in a three column vector model")
self._mref = Utils.meshutils.readUBCTensorModel(self.basePath + self._mrefInput, self.mesh)
return np.genfromtxt(self.magfile,delimiter=' \n',dtype=np.str,comments='!')
def readMagneticsObservations(self, obs_file):
"""
Read and write UBC mag file format
INPUT:
:param fileName, path to the UBC obs mag file
OUTPUT:
:param survey
:param M, magnetization orentiaton (MI, MD)
"""
fid = open(self.basePath + obs_file,'r')
# First line has the inclination,declination and amplitude of B0
line = fid.readline()
B = np.array(line.split(),dtype=float)
# Second line has the magnetization orientation and a flag
line = fid.readline()
M = np.array(line.split(),dtype=float)
# Third line has the number of rows
line = fid.readline()
ndat = np.array(line.split(),dtype=int)
# Pre-allocate space for obsx, obsy, obsz, data, uncert
line = fid.readline()
temp = np.array(line.split(),dtype=float)
d = np.zeros(ndat, dtype=float)
wd = np.zeros(ndat, dtype=float)
locXYZ = np.zeros( (ndat,3), dtype=float)
for ii in range(ndat):
temp = np.array(line.split(),dtype=float)
locXYZ[ii,:] = temp[:3]
if len(temp) > 3:
d[ii] = temp[3]
if len(temp)==5:
wd[ii] = temp[4]
line = fid.readline()
rxLoc = BaseMag.RxObs(locXYZ)
srcField = BaseMag.SrcField([rxLoc],param=(B[2],B[0],B[1]))
survey = BaseMag.LinearSurvey(srcField)
survey.dobs = d
survey.std = wd
return survey
-7
View File
@@ -1,7 +0,0 @@
import MagAnalytics
import BaseMag
import Magnetics
import BaseGrav
import Gravity
import MagneticsDriver
import GravityDriver
+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):
+187 -445
View File
@@ -1,6 +1,4 @@
import Utils, Maps, Mesh
import numpy as np
import scipy.sparse as sp
import Utils, Maps, Mesh, numpy as np, scipy.sparse as sp
class RegularizationMesh(object):
"""
@@ -10,7 +8,7 @@ class RegularizationMesh(object):
are not necessarily true differential operators, but are constructed from
a SimPEG Mesh.
:param BaseMesh mesh: problem mesh
:param Mesh mesh: problem mesh
:param numpy.array indActive: bool array, size nC, that is True where we have active cells. Used to reduce the operators so we regularize only on active cells
"""
@@ -383,8 +381,8 @@ class BaseRegularization(object):
:param numpy.array m: geophysical model
:param numpy.array v: vector to multiply
:rtype: scipy.sparse.csr_matrix
:return: WtW, or if v is supplied WtW*v (numpy.ndarray)
:rtype: scipy.sparse.csr_matrix or numpy.ndarray
:return: WtW or WtW*v
The regularization is:
@@ -405,238 +403,7 @@ class BaseRegularization(object):
return mD.T * ( self.W.T * ( self.W * ( mD * v) ) )
class Simple(BaseRegularization):
"""
Simple regularization that does not include length scales in the derivatives.
"""
mrefInSmooth = False #: include mref in the smoothness?
alpha_s = Utils.dependentProperty('_alpha_s', 1.0, ['_W', '_Wsmall'], "Smallness weight")
alpha_x = Utils.dependentProperty('_alpha_x', 1.0, ['_W', '_Wx'], "Weight for the first derivative in the x direction")
alpha_y = Utils.dependentProperty('_alpha_y', 1.0, ['_W', '_Wy'], "Weight for the first derivative in the y direction")
alpha_z = Utils.dependentProperty('_alpha_z', 1.0, ['_W', '_Wz'], "Weight for the first derivative in the z direction")
cell_weights = 1.
def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
if isinstance(self.cell_weights,float):
self.cell_weights = np.ones(self.regmesh.nC) * self.cell_weights
@property
def Wsmall(self):
"""Regularization matrix Wsmall"""
if getattr(self,'_Wsmall', None) is None:
self._Wsmall = Utils.sdiag((self.alpha_s*self.cell_weights)**0.5)
return self._Wsmall
@property
def Wx(self):
"""Regularization matrix Wx"""
if getattr(self, '_Wx', None) is None:
self._Wx = Utils.sdiag((self.alpha_x * (self.regmesh.aveCC2Fx*self.cell_weights))**0.5)*self.regmesh.cellDiffxStencil
return self._Wx
@property
def Wy(self):
"""Regularization matrix Wy"""
if getattr(self, '_Wy', None) is None:
self._Wy = Utils.sdiag((self.alpha_y * (self.regmesh.aveCC2Fy*self.cell_weights))**0.5)*self.regmesh.cellDiffyStencil
return self._Wy
@property
def Wz(self):
"""Regularization matrix Wz"""
if getattr(self, '_Wz', None) is None:
self._Wz = Utils.sdiag((self.alpha_z * (self.regmesh.aveCC2Fz*self.cell_weights))**0.5)*self.regmesh.cellDiffzStencil
return self._Wz
# @property
# def Wsmooth(self):
# """Full smoothness regularization matrix W"""
# print 'wtf why are we using Wsmooth'
# raise NotImplementedError
# if getattr(self, '_Wsmooth', None) is None:
# wlist = (self.Wx,)
# if self.regmesh.dim > 1:
# wlist += (self.Wy,)
# if self.regmesh.dim > 2:
# wlist += (self.Wz,)
# self._Wsmooth = sp.vstack(wlist)
# return self._Wsmooth
#
# @property
# def W(self):
# """Full regularization matrix W"""
# print 'wtf why are we using W'
# if getattr(self, '_W', None) is None:
# wlist = (self.Wsmall, self.Wx)
# if self.regmesh.dim > 1:
# wlist += (self.Wy,)
# if self.regmesh.dim > 2:
# wlist += (self.Wz,)
# self._W = sp.vstack(wlist)
# return self._W
@Utils.timeIt
def _evalSmall(self, m):
r = self.Wsmall * ( self.mapping * (m - self.mref) )
return 0.5 * r.dot(r)
@Utils.timeIt
def _evalSmallDeriv(self, m):
r = self.Wsmall * ( self.mapping * (m - self.mref) )
return r.T * ( self.Wsmall * self.mapping.deriv(m - self.mref) )
@Utils.timeIt
def _evalSmall2Deriv(self, m, v = None):
rDeriv = self.Wsmall * ( self.mapping.deriv(m - self.mref) )
if v is not None:
return rDeriv.T * (rDeriv * v)
return rDeriv.T * rDeriv
@Utils.timeIt
def _evalSmoothx(self, m):
if self.mrefInSmooth == True:
r = self.Wx * ( self.mapping * (m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wx * ( self.mapping * (m) )
return 0.5 * r.dot(r)
@Utils.timeIt
def _evalSmoothy(self, m):
if self.mrefInSmooth == True:
r = self.Wy * ( self.mapping * (m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wy * ( self.mapping * (m) )
return 0.5 * r.dot(r)
@Utils.timeIt
def _evalSmoothz(self, m):
if self.mrefInSmooth == True:
r = self.Wz * ( self.mapping * (m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wz * ( self.mapping * (m) )
return 0.5 * r.dot(r)
@Utils.timeIt
def _evalSmooth(self, m):
phiSmooth = self._evalSmoothx(m)
if self.regmesh.dim > 1:
phiSmooth += self._evalSmoothy(m)
if self.regmesh.dim > 2:
phiSmooth += self._evalSmoothz(m)
return phiSmooth
@Utils.timeIt
def _evalSmoothxDeriv(self, m):
if self.mrefInSmooth == True:
r = self.Wx * ( self.mapping * ( m - self.mref ) )
return r.T * ( self.Wx * self.mapping.deriv(m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wx * ( self.mapping * m )
return r.T * ( self.Wx * self.mapping.deriv(m) )
@Utils.timeIt
def _evalSmoothx2Deriv(self, m, v=None):
if self.mrefInSmooth == True:
rDeriv = self.Wx * ( self.mapping.deriv( m - self.mref ) )
elif self.mrefInSmooth == False:
rDeriv = self.Wx * ( self.mapping.deriv(m) )
if v is not None:
return rDeriv.T * ( rDeriv * v )
return rDeriv.T * rDeriv
@Utils.timeIt
def _evalSmoothyDeriv(self, m):
if self.mrefInSmooth == True:
r = self.Wy * ( self.mapping * ( m - self.mref ) )
return r.T * ( self.Wy * self.mapping.deriv(m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wy * ( self.mapping * m )
return r.T * ( self.Wy * self.mapping.deriv(m) )
@Utils.timeIt
def _evalSmoothy2Deriv(self, m, v=None):
if self.mrefInSmooth == True:
rDeriv = self.Wy * ( self.mapping.deriv( m - self.mref ) )
elif self.mrefInSmooth == False:
rDeriv = self.Wy * ( self.mapping.deriv(m) )
if v is not None:
return rDeriv.T * ( rDeriv * v )
return rDeriv.T * rDeriv
@Utils.timeIt
def _evalSmoothzDeriv(self, m):
if self.mrefInSmooth == True:
r = self.Wz * ( self.mapping * ( m - self.mref ) )
return r.T * ( self.Wz * self.mapping.deriv(m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wz * ( self.mapping * m )
return r.T * ( self.Wz * self.mapping.deriv(m) )
@Utils.timeIt
def _evalSmoothz2Deriv(self, m, v=None):
if self.mrefInSmooth == True:
rDeriv = self.Wz * ( self.mapping.deriv( m - self.mref ) )
elif self.mrefInSmooth == False:
rDeriv = self.Wz * ( self.mapping.deriv(m) )
if v is not None:
return rDeriv.T * ( rDeriv * v )
return rDeriv.T * rDeriv
@Utils.timeIt
def _evalSmoothDeriv(self, m):
deriv = self._evalSmoothxDeriv(m)
if self.regmesh.dim > 1:
deriv += self._evalSmoothyDeriv(m)
if self.regmesh.dim > 2:
deriv += self._evalSmoothzDeriv(m)
return deriv
@Utils.timeIt
def _evalSmooth2Deriv(self, m, v=None):
deriv = self._evalSmoothx2Deriv(m, v)
if self.regmesh.dim > 1:
deriv += self._evalSmoothy2Deriv(m, v)
if self.regmesh.dim > 2:
deriv += self._evalSmoothz2Deriv(m, v)
return deriv
@Utils.timeIt
def eval(self, m):
return self._evalSmall(m) + self._evalSmooth(m)
@Utils.timeIt
def evalDeriv(self, m):
"""
The regularization is:
.. math::
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top W(m-m_\\text{ref})}
So the derivative is straight forward:
.. math::
R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
"""
return self._evalSmallDeriv(m) + self._evalSmoothDeriv(m)
@Utils.timeIt
def eval2Deriv(self, m, v=None):
return self._evalSmall2Deriv(m, v) + self._evalSmooth2Deriv(m, v)
class Tikhonov(Simple):
class Tikhonov(BaseRegularization):
"""
L2 Tikhonov regularization with both smallness and smoothness (first order
derivative) contributions.
@@ -650,8 +417,8 @@ class Tikhonov(Simple):
Note if the key word argument `mrefInSmooth` is False, then mref is not
included in the smoothness contribution.
:param BaseMesh mesh: SimPEG mesh
:param IdentityMap mapping: regularization mapping, takes the model from model space to the thing you want to regularize
:param Mesh mesh: SimPEG mesh
:param Maps mapping: regularization mapping, takes the model from model space to the thing you want to regularize
:param numpy.ndarray indActive: active cell indices for reducing the size of differential operators in the definition of a regularization mesh
:param bool mrefInSmooth: (default = False) put mref in the smoothness component?
:param float alpha_s: (default 1e-6) smallness weight
@@ -671,7 +438,7 @@ class Tikhonov(Simple):
alpha_yy = Utils.dependentProperty('_alpha_yy', 0.0, ['_W', '_Wyy'], "Weight for the second derivative in the y direction")
alpha_zz = Utils.dependentProperty('_alpha_zz', 0.0, ['_W', '_Wzz'], "Weight for the second derivative in the z direction")
def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
def __init__(self, mesh, mapping=None, indActive = None, **kwargs):
BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
@property
@@ -726,131 +493,56 @@ class Tikhonov(Simple):
self._Wzz = Utils.sdiag((self.regmesh.vol*self.alpha_zz)**0.5)*self.regmesh.faceDiffz*self.regmesh.cellDiffz
return self._Wzz
@property
def Wsmooth2(self):
def Wsmooth(self):
"""Full smoothness regularization matrix W"""
if getattr(self, '_Wsmooth', None) is None:
wlist = (self.Wxx)
wlist = (self.Wx, self.Wxx)
if self.regmesh.dim > 1:
wlist += (self.Wyy)
wlist += (self.Wy, self.Wyy)
if self.regmesh.dim > 2:
wlist += (self.Wzz)
wlist += (self.Wz, self.Wzz)
self._Wsmooth = sp.vstack(wlist)
return self._Wsmooth
@property
def W(self):
"""Full regularization matrix W"""
if getattr(self, '_W', None) is None:
wlist = (self.Wsmall, self.Wsmooth)
self._W = sp.vstack(wlist)
return self._W
@Utils.timeIt
def _evalSmoothxx(self, m):
if self.mrefInSmooth == True:
r = self.Wxx * ( self.mapping * (m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wxx * ( self.mapping * (m) )
def _evalSmall(self, m):
r = self.Wsmall * ( self.mapping * (m - self.mref) )
return 0.5 * r.dot(r)
@Utils.timeIt
def _evalSmoothyy(self, m):
def _evalSmooth(self, m):
if self.mrefInSmooth == True:
r = self.Wyy * ( self.mapping * (m - self.mref) )
r = self.Wsmooth * ( self.mapping * (m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wyy * ( self.mapping * (m) )
r = self.Wsmooth * ( self.mapping * (m) )
return 0.5 * r.dot(r)
@Utils.timeIt
def _evalSmoothzz(self, m):
if self.mrefInSmooth == True:
r = self.Wzz * ( self.mapping * (m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wzz * ( self.mapping * (m) )
return 0.5 * r.dot(r)
@Utils.timeIt
def _evalSmooth2(self, m):
phiSmooth2 = self._evalSmoothxx(m)
if self.regmesh.dim > 1:
phiSmooth2 += self._evalSmoothyy(m)
if self.regmesh.dim > 2:
phiSmooth2 += self._evalSmoothzz(m)
return phiSmooth2
@Utils.timeIt
def _evalSmoothxxDeriv(self, m):
if self.mrefInSmooth == True:
r = self.Wxx * ( self.mapping * ( m - self.mref ) )
return r.T * ( self.Wxx * self.mapping.deriv(m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wxx * ( self.mapping * m )
return r.T * ( self.Wxx * self.mapping.deriv(m) )
@Utils.timeIt
def _evalSmoothyyDeriv(self, m):
if self.mrefInSmooth == True:
r = self.Wyy * ( self.mapping * ( m - self.mref ) )
return r.T * ( self.Wyy * self.mapping.deriv(m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wyy * ( self.mapping * m )
return r.T * ( self.Wyy * self.mapping.deriv(m) )
@Utils.timeIt
def _evalSmoothzzDeriv(self, m):
if self.mrefInSmooth == True:
r = self.Wzz * ( self.mapping * ( m - self.mref ) )
return r.T * ( self.Wzz * self.mapping.deriv(m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wzz * ( self.mapping * m )
return r.T * ( self.Wzz * self.mapping.deriv(m) )
@Utils.timeIt
def _evalSmoothxx2Deriv(self, m, v=None):
if self.mrefInSmooth == True:
rDeriv = self.Wxx * ( self.mapping.deriv( m - self.mref ) )
elif self.mrefInSmooth == False:
rDeriv = self.Wxx * self.mapping.deriv(m)
if v is not None:
return rDeriv.T * (rDeriv * v)
return rDeriv.T * rDeriv
@Utils.timeIt
def _evalSmoothyy2Deriv(self, m, v=None):
if self.mrefInSmooth == True:
rDeriv = self.Wyy * ( self.mapping.deriv( m - self.mref ) )
elif self.mrefInSmooth == False:
rDeriv = self.Wyy * self.mapping.deriv(m)
if v is not None:
return rDeriv.T * (rDeriv * v)
return rDeriv.T * rDeriv
@Utils.timeIt
def _evalSmoothzz2Deriv(self, m, v=None):
if self.mrefInSmooth == True:
rDeriv = self.Wzz * ( self.mapping.deriv( m - self.mref ) )
elif self.mrefInSmooth == False:
rDeriv = self.Wzz * self.mapping.deriv(m)
if v is not None:
return rDeriv.T * (rDeriv * v)
return rDeriv.T * rDeriv
@Utils.timeIt
def _evalSmoothDeriv2(self, m):
deriv = self._evalSmoothxxDeriv(m)
if self.regmesh.dim > 1:
deriv += self._evalSmoothyyDeriv(m)
if self.regmesh.dim > 2:
deriv += self._evalSmoothzzDeriv(m)
return deriv
@Utils.timeIt
def _evalSmooth2Deriv2(self, m, v=None):
deriv = self._evalSmoothxx2Deriv(m, v)
if self.regmesh.dim > 1:
deriv += self._evalSmoothyy2Deriv(m, v)
if self.regmesh.dim > 2:
deriv += self._evalSmoothzz2Deriv(m, v)
return deriv
@Utils.timeIt
def eval(self, m):
return self._evalSmall(m) + self._evalSmooth(m) + self._evalSmooth2(m)
return self._evalSmall(m) + self._evalSmooth(m)
@Utils.timeIt
def _evalSmallDeriv(self,m):
r = self.Wsmall * ( self.mapping * (m - self.mref) )
return r.T * ( self.Wsmall * self.mapping.deriv(m - self.mref) )
@Utils.timeIt
def _evalSmoothDeriv(self,m):
if self.mrefInSmooth == True:
r = self.Wsmooth * ( self.mapping * ( m - self.mref ) )
return r.T * ( self.Wsmooth * self.mapping.deriv(m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wsmooth * ( self.mapping * m )
return r.T * ( self.Wsmooth * self.mapping.deriv(m) )
@Utils.timeIt
def evalDeriv(self, m):
@@ -868,134 +560,184 @@ class Tikhonov(Simple):
R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
"""
return self._evalSmallDeriv(m) + self._evalSmoothDeriv(m) + self._evalSmoothDeriv2(m)
def eval2Deriv(self, m, v=None):
"""
The regularization is:
.. math::
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top W(m-m_\\text{ref})}
So the derivative is straight forward:
.. math::
R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
"""
return self._evalSmall2Deriv(m, v) + self._evalSmooth2Deriv(m, v) + self._evalSmooth2Deriv2(m, v)
return self._evalSmallDeriv(m) + self._evalSmoothDeriv(m)
class Sparse(Simple):
class Simple(Tikhonov):
"""
The regularization is:
.. math::
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top R^\\top R W(m-m_\\text{ref})}
where the IRLS weight
.. math::
R = \eta TO FINISH LATER!!!
So the derivative is straight forward:
.. math::
R(m) = \mathbf{W^\\top R^\\top R W (m-m_\\text{ref})}
The IRLS weights are recomputed after each beta solves.
It is strongly recommended to do a few Gauss-Newton iterations
before updating.
Simple regularization that does not include length scales in the derivatives.
"""
# set default values
eps_p = 1e-1 # Threshold value for the model norm
eps_q = 1e-1 # Threshold value for the model gradient norm
curModel = None # Requires model to compute the weights
l2model = None
gamma = 1. # Model norm scaling to smooth out convergence
norms = [0., 2., 2., 2.] # Values for norm on (m, dmdx, dmdy, dmdz)
cell_weights = 1. # Consider overwriting with sensitivity weights
mrefInSmooth = False #: SMOOTH and SMOOTH_MOD_DIF options
alpha_s = Utils.dependentProperty('_alpha_s', 1.0, ['_W', '_Wsmall'], "Smallness weight")
alpha_x = Utils.dependentProperty('_alpha_x', 1.0, ['_W', '_Wx'], "Weight for the first derivative in the x direction")
alpha_y = Utils.dependentProperty('_alpha_y', 1.0, ['_W', '_Wy'], "Weight for the first derivative in the y direction")
alpha_z = Utils.dependentProperty('_alpha_z', 1.0, ['_W', '_Wz'], "Weight for the first derivative in the z direction")
wght = 1.
def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
Simple.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
if isinstance(self.cell_weights,float):
self.cell_weights = np.ones(self.regmesh.nC) * self.cell_weights
if isinstance(self.wght,float):
self.wght = np.ones(self.regmesh.nC) * self.wght
@property
def Wsmall(self):
"""Regularization matrix Wsmall"""
if getattr(self,'_Wsmall', None) is None:
if getattr(self, 'curModel', None) is None:
self.Rs = Utils.speye(self.regmesh.nC)
else:
f_m = self.mapping * (self.curModel - self.reg.mref)
self.rs = self.R(f_m , self.eps_p, self.norms[0])
self.Rs = Utils.sdiag( self.rs )
self._Wsmall = Utils.sdiag((self.alpha_s*self.gamma*self.cell_weights)**0.5)*self.Rs
self._Wsmall = Utils.sdiag((self.regmesh.vol*self.alpha_s*self.wght)**0.5)
return self._Wsmall
@property
def Wx(self):
"""Regularization matrix Wx"""
if getattr(self,'_Wx', None) is None:
if getattr(self, 'curModel', None) is None:
self.Rx = Utils.speye(self.regmesh.cellDiffxStencil.shape[0])
else:
f_m = self.regmesh.cellDiffxStencil * (self.mapping * self.curModel)
self.rx = self.R( f_m , self.eps_q, self.norms[1])
self.Rx = Utils.sdiag( self.rx )
self._Wx = Utils.sdiag(( self.alpha_x*self.gamma*(self.regmesh.aveCC2Fx*self.cell_weights))**0.5)*self.Rx*self.regmesh.cellDiffxStencil
if getattr(self, '_Wx', None) is None:
self._Wx = Utils.sdiag((self.regmesh.aveCC2Fx * self.regmesh.vol*self.alpha_x*(self.regmesh.aveCC2Fx*self.wght))**0.5)*self.regmesh.cellDiffxStencil
return self._Wx
@property
def Wy(self):
"""Regularization matrix Wy"""
if getattr(self,'_Wy', None) is None:
if getattr(self, 'curModel', None) is None:
self.Ry = Utils.speye(self.regmesh.cellDiffyStencil.shape[0])
else:
f_m = self.regmesh.cellDiffyStencil * (self.mapping * self.curModel)
self.ry = self.R( f_m , self.eps_q, self.norms[2])
self.Ry = Utils.sdiag( self.ry )
self._Wy = Utils.sdiag((self.alpha_y*self.gamma*(self.regmesh.aveCC2Fy*self.cell_weights))**0.5)*self.Ry*self.regmesh.cellDiffyStencil
if getattr(self, '_Wy', None) is None:
self._Wy = Utils.sdiag((self.regmesh.aveCC2Fy * self.regmesh.vol * self.alpha_y*(self.regmesh.aveCC2Fy*self.wght))**0.5)*self.regmesh.cellDiffyStencil
return self._Wy
@property
def Wz(self):
"""Regularization matrix Wz"""
if getattr(self,'_Wz', None) is None:
if getattr(self, 'curModel', None) is None:
self.Rz = Utils.speye(self.regmesh.cellDiffzStencil.shape[0])
else:
f_m = self.regmesh.cellDiffzStencil * (self.mapping * self.curModel)
self.rz = self.R( f_m , self.eps_q, self.norms[3])
self.Rz = Utils.sdiag( self.rz )
self._Wz = Utils.sdiag((self.alpha_z*self.gamma*(self.regmesh.aveCC2Fz*self.cell_weights))**0.5)*self.Rz*self.regmesh.cellDiffzStencil
if getattr(self, '_Wz', None) is None:
self._Wz = Utils.sdiag((self.regmesh.aveCC2Fz * self.regmesh.vol*self.alpha_z*(self.regmesh.aveCC2Fz*self.wght))**0.5)*self.regmesh.cellDiffzStencil
return self._Wz
@property
def Wsmooth(self):
"""Full smoothness regularization matrix W"""
if getattr(self, '_Wsmooth', None) is None:
wlist = (self.Wx,)
if self.regmesh.dim > 1:
wlist += (self.Wy,)
if self.regmesh.dim > 2:
wlist += (self.Wz,)
self._Wsmooth = sp.vstack(wlist)
return self._Wsmooth
@property
def W(self):
"""Full regularization matrix W"""
if getattr(self, '_W', None) is None:
wlist = (self.Wsmall, self.Wsmooth)
self._W = sp.vstack(wlist)
return self._W
@Utils.timeIt
def _evalSmall(self, m):
r = self.Wsmall * ( self.mapping * (m - self.mref) )
return 0.5 * r.dot(r)
@Utils.timeIt
def _evalSmooth(self, m):
if self.mrefInSmooth == True:
r = self.Wsmooth * ( self.mapping * (m - self.mref) )
elif self.mrefInSmooth == False:
r = self.Wsmooth * ( self.mapping * m)
return 0.5 * r.dot(r)
class Sparse(Simple):
# set default values
eps_p = 1e-1
eps_q = 1e-1
curModel = None # use a model to compute the weights
gamma = 1.
norms = [0., 2., 2., 2.]
wght = 1.
def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
Simple.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
if isinstance(self.wght,float):
self.wght = np.ones(self.regmesh.nC) * self.wght
@property
def Wsmall(self):
"""Regularization matrix Wsmall"""
if getattr(self, 'curModel', None) is None:
self.Rs = Utils.speye(self.regmesh.nC)
else:
f_m = self.curModel - self.reg.mref
self.rs = self.R(f_m , self.eps_p, self.norms[0])
#print "Min rs: " + str(np.max(self.rs)) + "Max rs: " + str(np.min(self.rs))
self.Rs = Utils.sdiag( self.rs )
return Utils.sdiag((self.regmesh.vol*self.alpha_s*self.gamma*self.wght)**0.5)*self.Rs
@property
def Wx(self):
"""Regularization matrix Wx"""
if getattr(self, 'curModel', None) is None:
self.Rx = Utils.speye(self.regmesh.cellDiffxStencil.shape[0])
else:
f_m = self.regmesh.cellDiffxStencil * self.curModel
self.rx = self.R( f_m , self.eps_q, self.norms[1])
self.Rx = Utils.sdiag( self.rx )
return Utils.sdiag(( (self.regmesh.aveCC2Fx * self.regmesh.vol) *self.alpha_x*self.gamma*(self.regmesh.aveCC2Fx*self.wght))**0.5)*self.Rx*self.regmesh.cellDiffxStencil
@property
def Wy(self):
"""Regularization matrix Wy"""
if getattr(self, 'curModel', None) is None:
self.Ry = Utils.speye(self.regmesh.cellDiffyStencil.shape[0])
else:
f_m = self.regmesh.cellDiffyStencil * self.curModel
self.ry = self.R( f_m , self.eps_q, self.norms[2])
self.Ry = Utils.sdiag( self.ry )
return Utils.sdiag(((self.regmesh.aveCC2Fy * self.regmesh.vol)*self.alpha_y*self.gamma*(self.regmesh.aveCC2Fy*self.wght))**0.5)*self.Ry*self.regmesh.cellDiffyStencil
@property
def Wz(self):
"""Regularization matrix Wz"""
if getattr(self, 'curModel', None) is None:
self.Rz = Utils.speye(self.regmesh.cellDiffzStencil.shape[0])
else:
f_m = self.regmesh.cellDiffzStencil * self.curModel
self.rz = self.R( f_m , self.eps_q, self.norms[3])
self.Rz = Utils.sdiag( self.rz )
return Utils.sdiag(((self.regmesh.aveCC2Fz * self.regmesh.vol)*self.alpha_z*self.gamma*(self.regmesh.aveCC2Fz*self.wght))**0.5)*self.Rz*self.regmesh.cellDiffzStencil
@property
def Wsmooth(self):
"""Full smoothness regularization matrix W"""
#if getattr(self, '_Wsmooth', None) is None:
wlist = (self.Wx,)
if self.regmesh.dim > 1:
wlist += (self.Wy,)
if self.regmesh.dim > 2:
wlist += (self.Wz,)
#self._Wsmooth = sp.vstack(wlist)
return sp.vstack(wlist)
@property
def W(self):
"""Full regularization matrix W"""
if getattr(self, '_W', None) is None:
wlist = (self.Wsmall, self.Wsmooth)
self._W = sp.vstack(wlist)
return self._W
def R(self, f_m , eps, exponent):
# Eta scaling is important for mix-norms...do not mess with it
eta = (eps**(1.-exponent/2.))**0.5
r = eta / (f_m**2.+ eps**2.)**((1.-exponent/2.)/2.)
+3 -2
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
+13 -13
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
"""
@@ -147,7 +147,7 @@ def getIndicesSphere(center,radius,ccMesh):
if dimMesh == 1:
# Define the reference points
ind = np.abs(center[0] - ccMesh[:,0]) < radius
elif dimMesh == 2:
@@ -222,14 +222,14 @@ def layeredModel(ccMesh, layerTops, layerValues):
:param numpy.array ccMesh: cell-centered mesh
:param numpy.array layerTops: z-locations of the tops of each layer
:param numpy.array layerValue: values of the property to assign for each layer (starting at the top)
:param numpy.array layerValue: values of the property to assign for each layer (starting at the top)
:rtype: numpy.array
:return: M, layered model on the mesh
:return: M, layered model on the mesh
"""
descending = np.linalg.norm(sorted(layerTops, reverse=True) - layerTops) < 1e-20
# TODO: put an error check to make sure that there is an ordering... needs to work with inf elts
# TODO: put an error check to make sure that there is an ordering... needs to work with inf elts
# assert ascending or descending, "Layers must be listed in either ascending or descending order"
# start from bottom up
@@ -253,10 +253,10 @@ def layeredModel(ccMesh, layerTops, layerValues):
model = np.zeros(ccMesh.shape[0])
for i, top in enumerate(layerTops):
zind = z <= top
zind = z <= top
model[zind] = layerValues[i]
return model
return model
@@ -265,9 +265,9 @@ def randomModel(shape, seed=None, anisotropy=None, its=100, bounds=None):
Create a random model by convolving a kernel with a
uniformly distributed model.
:param tuple shape: shape of the model.
:param int,tuple shape: shape of the model.
:param int seed: pick which model to produce, prints the seed if you don't choose.
:param numpy.ndarray anisotropy: this is the (3 x n) blurring kernel that is used.
:param numpy.ndarray,list anisotropy: this is the (3 x n) blurring kernel that is used.
:param int its: number of smoothing iterations
:param list bounds: bounds on the model, len(list) == 2
:rtype: numpy.ndarray
+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 -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::
+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
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@@ -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
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@@ -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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@@ -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
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@@ -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:
@@ -3,7 +3,7 @@
InvProblem
**********
.. autoclass:: SimPEG.InvProblem.BaseInvProblem
.. automodule:: SimPEG.InvProblem
:show-inheritance:
:members:
:undoc-members:
@@ -12,7 +12,7 @@ InvProblem
Inversion
*********
.. autoclass:: SimPEG.Inversion.BaseInversion
.. automodule:: SimPEG.Inversion
:show-inheritance:
:members:
:undoc-members:
@@ -27,8 +27,7 @@ back to conductivity. This is a relatively trivial example (we are just taking
the exponential!) but by defining maps we can start to combine and manipulate
exactly what we think about as our model, \\\(m\\\). In code, this looks like
.. code-block:: python
:linenos:
::
M = Mesh.TensorMesh([100]) # Create a mesh
expMap = Maps.ExpMap(M) # Create a mapping
@@ -47,15 +46,14 @@ We will use an example where we want a 1D layered earth as
our model, but we want to map this to a 2D discretization to do our forward
modeling. We will also assume that we are working in log conductivity still,
so after the transformation we want to map to conductivity space.
To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.SurjectVertical1D`),
To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.Vertical1DMap`),
which does the first part of what we just described. The second part will be
done by the :class:`SimPEG.Maps.ExpMap` described above.
.. code-block:: python
:linenos:
::
M = Mesh.TensorMesh([7,5])
v1dMap = Maps.SurjectVertical1D(M)
v1dMap = Maps.Vertical1DMap(M)
expMap = Maps.ExpMap(M)
myMap = expMap * v1dMap
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
@@ -63,8 +61,26 @@ done by the :class:`SimPEG.Maps.ExpMap` described above.
.. plot::
from SimPEG import Examples
Examples.Maps_ComboMaps.run()
from SimPEG import *
import matplotlib.pyplot as plt
M = Mesh.TensorMesh([7,5])
v1dMap = Maps.Vertical1DMap(M)
expMap = Maps.ExpMap(M)
myMap = expMap * v1dMap
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
sig = myMap * m
figs, axs = plt.subplots(1,2)
axs[0].plot(m, M.vectorCCy, 'b-o')
axs[0].set_title('Model')
axs[0].set_ylabel('Depth, y')
axs[0].set_xlabel('Value, $m_i$')
axs[0].set_xlim(0,3)
axs[0].set_ylim(0,1)
clbar = plt.colorbar(M.plotImage(sig,ax=axs[1],grid=True,gridOpts=dict(color='grey'))[0])
axs[1].set_title('Physical Property')
axs[1].set_ylabel('Depth, y')
clbar.set_label('$\sigma = \exp(\mathbf{P}m)$')
plt.tight_layout()
If you noticed, it was pretty easy to combine maps. What is even cooler is
that the derivatives also are made for you (if everything goes right).
@@ -106,8 +122,6 @@ When these are used in the inverse problem, this is extremely important!!
The API
=======
The :code:`IdentityMap` is the base class for all mappings, and it does absolutely nothing.
.. autoclass:: SimPEG.Maps.IdentityMap
:members:
:undoc-members:
@@ -116,6 +130,7 @@ The :code:`IdentityMap` is the base class for all mappings, and it does absolute
Common Maps
===========
Exponential Map
---------------
@@ -133,7 +148,7 @@ lives (i.e. it varies logarithmically).
Vertical 1D Map
---------------
.. autoclass:: SimPEG.Maps.SurjectVertical1D
.. autoclass:: SimPEG.Maps.Vertical1DMap
:members:
:undoc-members:
@@ -149,10 +164,31 @@ Map 2D Cross-Section to 3D Model
Mesh to Mesh Map
----------------
.. plot::
from SimPEG import Examples
Examples.Maps_Mesh2Mesh.run()
from SimPEG import *
import matplotlib.pyplot as plt
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
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()
.. autoclass:: SimPEG.Maps.Mesh2Mesh
@@ -160,8 +196,8 @@ Mesh to Mesh Map
:undoc-members:
Under the Hood
==============
Some Extras
===========
Combo Map
---------
@@ -188,6 +188,6 @@ other types of meshes in this SimPEG framework.
The API
=======
.. autoclass:: SimPEG.Mesh.BaseMesh.BaseMesh
.. automodule:: SimPEG.Mesh.BaseMesh
:members:
:undoc-members:
+36
View File
@@ -0,0 +1,36 @@
.. _api_MeshCode:
Tensor Mesh
===========
.. automodule:: SimPEG.Mesh.TensorMesh
:show-inheritance:
:members:
:undoc-members:
Cylindrical Mesh
================
.. automodule:: SimPEG.Mesh.CylMesh
:show-inheritance:
:members:
:undoc-members:
Tree Mesh
=========
.. autoclass:: SimPEG.Mesh.TreeMesh.TreeMesh
:show-inheritance:
:members:
:undoc-members:
Curvilinear Mesh
================
.. automodule:: SimPEG.Mesh.CurvilinearMesh
:show-inheritance:
:members:
:undoc-members:
@@ -91,21 +91,10 @@ The API
:members:
:undoc-members:
.. autoclass:: SimPEG.Regularization.Simple
:show-inheritance:
:members:
.. autoclass:: SimPEG.Regularization.Tikhonov
:show-inheritance:
:members:
.. autoclass:: SimPEG.Regularization.Sparse
:show-inheritance:
:members:
.. autoclass:: SimPEG.Regularization.RegularizationMesh
:show-inheritance:
:members:
@@ -46,8 +46,6 @@ The API
=======
.. autofunction:: SimPEG.Utils.SolverUtils.SolverWrapD
:noindex:
.. autofunction:: SimPEG.Utils.SolverUtils.SolverWrapI
:noindex:
@@ -6,6 +6,5 @@ Utilities
api_Solver
api_Maps
api_PropMaps
api_Utils
api_Tests
@@ -21,7 +21,7 @@ Solver Utilities
:undoc-members:
Curv Utilities
==============
=============
.. automodule:: SimPEG.Utils.curvutils
:members:
@@ -51,9 +51,7 @@ Interpolation Utilities
Counter Utilities
=================
.. code-block:: python
:linenos:
::
class MyClass(object):
def __init__(self, url):
self.counter = Counter()
@@ -71,9 +69,7 @@ Counter Utilities
for i in range(300): c.MySecondMethod()
c.counter.summary()
.. code-block:: text
:linenos:
::
Counters:
MyClass.MyMethod : 100
@@ -81,8 +77,6 @@ Counter Utilities
Times: mean sum
MyClass.MySecondMethod : 1.70e-06, 5.10e-04, 300x
The API
-------
@@ -35,7 +35,7 @@ The Big Picture
Defining a well-posed inverse problem and solving it is a complex task that requires many components that must interact. It is helpful
to view this task as a workflow in which various elements are explicitly identified and integrated. The figure below outlines the inversion components that consists of inputs, implementation, and evaluation. The inputs are composed of the geophysical data, the equations which are a mathematical description of the governing physics, and prior knowledge or assumptions about the setting. The implementation consists of two broad categories: the forward simulation and the inversion. The **forward simulation** is the means by which we solve the governing equations given a model and the **inversion components** evaluate and update this model. We are considering a gradient based approach, which updates the model through an optimization routine. The output of this implementation is a model, which, prior to interpretation, must be evaluated. This requires considering, and often re-assessing, the choices and assumptions made in both the input and implementation stages.
.. image:: ../../images/InversionWorkflow-PreSimPEG.png
.. image:: InversionWorkflow-PreSimPEG.png
:width: 400 px
:alt: Components
:align: center
@@ -46,24 +46,24 @@ A Comprehensive Framework
There are an overwhelming amount of choices to be made as one works through the forward modeling and inversion process (see figure above). As a result, software implementations of this workflow often become complex and highly interdependent, making it difficult to interact with and to ask other scientists to pick up and change. Our approach to handling this complexity is to propose a framework, (see below), that compartmentalizes the implementation of inversions into various units. We present it in this specific modular style, as each unit contains a targeted subset of choices crucial to the inversion process.
.. image:: ../../images/InversionWorkflow.png
.. image:: InversionWorkflow.png
:width: 400 px
:alt: Framework
:align: center
The process of obtaining an acceptable model from an inversion generally requires the geophysicist to perform several iterations of the inversion workflow, rethinking and redesigning each piece of the framework to ensure it is appropriate in the current context. Inversions are experimental and empirical by nature and our software package is designed to facilitate this iterative process. To accomplish this, we have divided the inversion methodology into eight major components (See figure above). The :class:`SimPEG.Mesh.BaseMesh.BaseMesh` class handles the discretization of the earth and also provides numerical operators. The forward simulation is split into two classes, the :class:`SimPEG.Survey.BaseSurvey` and the :class:`SimPEG.Problem.BaseProblem`. The :class:`SimPEG.Survey.BaseSurvey` class handles the geometry of a geophysical problem as well as sources. The :class:`SimPEG.Problem.BaseProblem` class handles the simulation of the physics for the geophysical problem of interest. Although created independently, these two classes must be paired to form all of the components necessary for a geophysical forward simulation and calculation of the sensitivity. The :class:`SimPEG.Problem.BaseProblem` creates geophysical fields given a source from the :class:`SimPEG.Survey.BaseSurvey`. The :class:`SimPEG.Survey.BaseSurvey` interpolates these fields to the receiver locations and converts them to the appropriate data type, for example, by selecting only the measured components of the field. Each of these operations may have associated derivatives with respect to the model and the computed field; these are included in the calculation of the sensitivity. For the inversion, a :class:`SimPEG.DataMisfit.BaseDataMisfit` is chosen to capture the goodness of fit of the predicted data and a :class:`SimPEG.Regularization.BaseRegularization` is chosen to handle the non-uniqueness. These inversion elements and an Optimization routine are combined into an inverse problem class :class:`SimPEG.InvProblem.BaseInvProblem`. :class:`SimPEG.InvProblem.BaseInvProblem` is the mathematical statement that will be numerically solved by running an Inversion. The :class:`SimPEG.Inversion.BaseInversion` class handles organization and dispatch of directives between all of the various pieces of the framework.
The process of obtaining an acceptable model from an inversion generally requires the geophysicist to perform several iterations of the inversion workflow, rethinking and redesigning each piece of the framework to ensure it is appropriate in the current context. Inversions are experimental and empirical by nature and our software package is designed to facilitate this iterative process. To accomplish this, we have divided the inversion methodology into eight major components (See figure above). The (:class:`SimPEG.Mesh.BaseMesh`) class handles the discretization of the earth and also provides numerical operators. The forward simulation is split into two classes, the (:class:`SimPEG.Survey.BaseSurvey`) and the (:class:`SimPEG.Problem.BaseProblem`). The (:class:`SimPEG.Survey.BaseSurvey`) class handles the geometry of a geophysical problem as well as sources. The (:class:`SimPEG.Problem.BaseProblem`) class handles the simulation of the physics for the geophysical problem of interest. Although created independently, these two classes must be paired to form all of the components necessary for a geophysical forward simulation and calculation of the sensitivity. The (:class:`SimPEG.Problem.BaseProblem`) creates geophysical fields given a source from the (:class:`SimPEG.Survey.BaseSurvey`). The (:class:`SimPEG.Survey.BaseSurvey`) interpolates these fields to the receiver locations and converts them to the appropriate data type, for example, by selecting only the measured components of the field. Each of these operations may have associated derivatives with respect to the model and the computed field; these are included in the calculation of the sensitivity. For the inversion, a (:class:`SimPEG.DataMisfit.BaseDataMisfit`) is chosen to capture the goodness of fit of the predicted data and a (:class:`SimPEG.Regularization.BaseRegularization`) is chosen to handle the non-uniqueness. These inversion elements and an Optimization routine are combined into an inverse problem class (:class:`SimPEG.InvProblem.BaseInvProblem`). (:class:`SimPEG.InvProblem.BaseInvProblem`) is the mathematical statement that will be numerically solved by running an Inversion. The (:class:`SimPEG.Inversion.BaseInversion`) class handles organization and dispatch of directives between all of the various pieces of the framework.
The arrows in the figure above indicate what each class takes as a primary argument. For example, both the :class:`SimPEG.Problem.BaseProblem` and :class:`SimPEG.Regularization.BaseRegularization` classes take a :class:`SimPEG.Mesh.BaseMesh.BaseMesh` class as an argument. The diagram does not show class inheritance, as each of the base classes outlined have many subtypes that can be interchanged. The :class:`SimPEG.Mesh.BaseMesh.BaseMesh` class, for example, could be a regular Cartesian mesh :class:`SimPEG.Mesh.TensorMesh` or a cylindrical coordinate mesh :class:`SimPEG.Mesh.CylMesh`, which have many properties in common. These common features, such as both meshes being created from tensor products, can be exploited through inheritance of base classes, and differences can be expressed through subtype polymorphism. Please look at the documentation here for more in-depth information.
The arrows in the figure above indicate what each class takes as a primary argument. For example, both the (:class:`SimPEG.Problem.BaseProblem`) and (:class:`SimPEG.Regularization.BaseRegularization`) classes take a (:class:`SimPEG.Mesh.BaseMesh`) class as an argument. The diagram does not show class inheritance, as each of the base classes outlined have many subtypes that can be interchanged. The (:class:`SimPEG.Mesh.BaseMesh`) class, for example, could be a regular Cartesian mesh (:class:`SimPEG.Mesh.TensorMesh`) or a cylindrical coordinate mesh (:class:`SimPEG.Mesh.CylMesh`), which have many properties in common. These common features, such as both meshes being created from tensor products, can be exploited through inheritance of base classes, and differences can be expressed through subtype polymorphism. Please look at the documentation here for more in-depth information.
.. include:: ../../../CITATION.rst
.. include:: ../CITATION.rst
Authors
-------
.. include:: ../../../AUTHORS.rst
.. include:: ../AUTHORS.rst
License
-------
.. include:: ../../../LICENSE
.. include:: ../LICENSE
-95
View File
@@ -1,95 +0,0 @@
# application: simpegdocs
# version: 1
runtime: python27
api_version: 1
threadsafe: yes
handlers:
# favicon
- url: /images/logo-block\.ico
static_files: /images/logo-block.ico
upload: /images/logo-block\.ico
# all css
- url: /(.*\.css)
mime_type: text/css
static_files: _build/html/\1
upload: _build/html/(.*\.css)
# webfonts
- url: /(.*\.(eot|svg|ttf|woff|woff2|otf))
static_files: _build/html/\1
upload: _build/html/(.*\.(eot|svg|ttf|woff|woff2|otf))
# javascript
- url: /(.*\.js)
mime_type: text/javascript
static_files: _build/html/\1
upload: _build/html/(.*\.js)
# plain text source
- url: /(.*\.txt)
mime_type: text/plain
static_files: _build/html/\1
upload: _build/html/(.*\.txt)
# images
- url: /_images/(.*\.(gif|png|jpg|ico))
static_files: _build/html/_images/\1
upload: _build/html/_images/(.*\.(gif|png|jpg|ico))
# redirect en/latest traffic
- url: /en/latest/(.*\.html)
script: simpegdocs.app
# raw html
- url: /(.*\.html)
mime_type: text/html
static_files: _build/html/\1
upload: _build/html/(.*\.html)
# serve index files
- url: /(.+)/
static_files: _build/html/\1/index.html
upload: _build/html/(.+)/index.html
- url: /(.+)
static_files: _build/html/\1/index.html
upload: _build/html/(.+)/index.html
- url: /
static_files: _build/html/index.html
upload: _build/html/index.html
- url: .*
script: simpegdocs.app
# Recommended file skipping declaration from the GAE tutorials
skip_files:
- ^(.*/)?app\.yaml
- ^(.*/)?app\.yml
- ^(.*/)?#.*#
- ^(.*/)?.*~
- ^(.*/)?.*\.py[co]
- ^(.*/)?.*/RCS/.*
- ^(.*/)?\..*
- ^(.*/)?tests$
- ^(.*/)?test$
- ^test/(.*/)?
- ^COPYING.LESSER
- ^README\..*
- \.gitignore
- ^\.git/.*
- \.*\.lint$
- ^(.*/)?.*\.doctree$
libraries:
- name: webapp2
version: "2.5.2"
- name: PIL
version: "1.1.7"
- name: numpy
version: "latest"
- name: jinja2
version: "latest"
+6 -47
View File
@@ -28,7 +28,7 @@ sys.path.append('../')
# Add any Sphinx extension module names here, as strings. They can be extensions
# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
extensions = ['sphinx.ext.todo', 'sphinx.ext.mathjax', 'sphinx.ext.viewcode', 'sphinx.ext.autodoc', 'sphinx.ext.intersphinx', 'matplotlib.sphinxext.plot_directive']
extensions = ['sphinx.ext.todo', 'sphinx.ext.mathjax', 'sphinx.ext.viewcode', 'sphinx.ext.autodoc', 'matplotlib.sphinxext.plot_directive']
# Add any paths that contain templates here, relative to this directory.
templates_path = ['_templates']
@@ -44,16 +44,16 @@ master_doc = 'index'
# General information about the project.
project = u'SimPEG'
copyright = u'2013 - 2016, SimPEG Developers'
copyright = u'2013, SimPEG Developers'
# The version info for the project you're documenting, acts as replacement for
# |version| and |release|, also used in various other places throughout the
# built documents.
#
# The short X.Y version.
version = '0.1.12'
version = '0.1.10'
# The full version, including alpha/beta/rc tags.
release = '0.1.12'
release = '0.1.10'
# The language for content autogenerated by Sphinx. Refer to documentation
# for a list of supported languages.
@@ -124,12 +124,12 @@ except Exception, e:
# The name of an image file (within the static path) to use as favicon of the
# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32
# pixels large.
html_favicon = './images/logo-block.ico'
#html_favicon = None
# Add any paths that contain custom static files (such as style sheets) here,
# relative to this directory. They are copied after the builtin static files,
# so a file named "default.css" will overwrite the builtin "default.css".
html_static_path = []
html_static_path = ['_static']
# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
# using the given strftime format.
@@ -229,12 +229,6 @@ man_pages = [
# If true, show URL addresses after external links.
#man_show_urls = False
# Intersphinx
intersphinx_mapping = {'python': ('http://docs.python.org/2', None),
'numpy': ('http://docs.scipy.org/doc/numpy/', None),
'scipy': ('http://docs.scipy.org/doc/scipy/reference/', None),
'matplotlib': ('http://matplotlib.sourceforge.net/', None)}
# -- Options for Texinfo output ------------------------------------------------
@@ -257,38 +251,3 @@ texinfo_documents = [
#texinfo_show_urls = 'footnote'
autodoc_member_order = 'bysource'
def supress_nonlocal_image_warn():
import sphinx.environment
sphinx.environment.BuildEnvironment.warn_node = _supress_nonlocal_image_warn
def _supress_nonlocal_image_warn(self, msg, node):
from docutils.utils import get_source_line
if not msg.startswith('nonlocal image URI found:'):
self._warnfunc(msg, '%s:%s' % get_source_line(node))
supress_nonlocal_image_warn()
nitpick_ignore = [
('py:class', 'IdentityMap'),
('py:class', 'BaseSurvey'),
('py:class', 'BaseSrc'),
('py:class', 'BaseRx'),
('py:class', 'Survey'),
('py:class', 'FieldsFDEM'),
('py:class', 'Fields3D_e'),
('py:class', 'Fields3D_b'),
('py:class', 'Fields3D_j'),
('py:class', 'Fields3D_h'),
('py:class', 'SurveyTDEM'),
('py:class', 'SrcTDEM'),
('py:class', 'EMPropMap'),
('py:class', 'Data'),
('py:class', 'SurveyDC'),
('py:class', 'BaseMTFields'),
('py:class', 'SolverLU'),
('py:class', 'BaseMagSurvey'),
('py:class', 'BaseMagMap'),
]
@@ -1,27 +0,0 @@
.. _api_FiniteVolume:
Finite Volume
*************
Any numerical implementation requires the discretization of continuous
functions into discrete approximations. These approximations are typically
organized in a mesh, which defines boundaries, locations, and connectivity. Of
specific interest to geophysical simulations, we require that averaging,
interpolation and differential operators be defined for any mesh. In SimPEG,
we have implemented a staggered mimetic finite volume approach (`Hyman and
Shashkov, 1999 <http://math.lanl.gov/~mac/papers/numerics/HS99B.pdf>`_). This
approach requires the definitions of variables at either cell-centers, nodes,
faces, or edges as seen in the figure below.
.. image:: ../../images/finitevolrealestate.png
:width: 400 px
:alt: FiniteVolume
:align: center
.. toctree::
:maxdepth: 2
api_Mesh
api_DiffOps
api_InnerProducts
-68
View File
@@ -1,68 +0,0 @@
.. _api_MeshCode:
Tensor Mesh
===========
.. autoclass:: SimPEG.Mesh.TensorMesh
:members:
:undoc-members:
:show-inheritance:
Cylindrical Mesh
================
.. autoclass:: SimPEG.Mesh.CylMesh
:members:
:undoc-members:
:show-inheritance:
Tree Mesh
=========
.. autoclass:: SimPEG.Mesh.TreeMesh
:members:
:undoc-members:
:show-inheritance:
Curvilinear Mesh
================
.. autoclass:: SimPEG.Mesh.CurvilinearMesh
:members:
:undoc-members:
:show-inheritance:
Base Rectangular Mesh
=====================
.. autoclass:: SimPEG.Mesh.BaseMesh.BaseRectangularMesh
:members:
:undoc-members:
:show-inheritance:
Base Tensor Mesh
================
.. autoclass:: SimPEG.Mesh.TensorMesh.BaseTensorMesh
:members:
:undoc-members:
:show-inheritance:
Mesh IO
=======
.. automodule:: SimPEG.Mesh.MeshIO
:members:
:undoc-members:
:show-inheritance:
Mesh Viewing
============
.. automodule:: SimPEG.Mesh.View
:members:
:undoc-members:
:show-inheritance:
-29
View File
@@ -1,29 +0,0 @@
SimPEG PropMaps
***************
The API
=======
Property
--------
.. autoclass:: SimPEG.PropMaps.Property
:members:
:undoc-members:
PropMap
-------
.. autoclass:: SimPEG.PropMaps.PropMap
:members:
:undoc-members:
PropModel
---------
.. autoclass:: SimPEG.PropMaps.PropModel
:members:
:undoc-members:
-33
View File
@@ -1,33 +0,0 @@
Overview of Electromagnetics in SimPEG
**************************************
The API
=======
Physical Properties
-------------------
.. autoclass:: SimPEG.EM.Base.EMPropMap
:show-inheritance:
:members:
:undoc-members:
Problem
-------
.. autoclass:: SimPEG.EM.Base.BaseEMProblem
:show-inheritance:
:members:
:undoc-members:
Survey
------
.. autoclass:: SimPEG.EM.Base.BaseEMSurvey
:show-inheritance:
:members:
:undoc-members:
-48
View File
@@ -1,48 +0,0 @@
.. _examples_Maps_ComboMaps:
.. --------------------------------- ..
.. ..
.. THIS FILE IS AUTO GENEREATED ..
.. ..
.. SimPEG/Examples/__init__.py ..
.. ..
.. --------------------------------- ..
Maps: ComboMaps
===============
We will use an example where we want a 1D layered earth as
our model, but we want to map this to a 2D discretization to do our forward
modeling. We will also assume that we are working in log conductivity still,
so after the transformation we want to map to conductivity space.
To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.SurjectVertical1D`),
which does the first part of what we just described. The second part will be
done by the :class:`SimPEG.Maps.ExpMap` described above.
.. code-block:: python
:linenos:
M = Mesh.TensorMesh([7,5])
v1dMap = Maps.SurjectVertical1D(M)
expMap = Maps.ExpMap(M)
myMap = expMap * v1dMap
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
sig = myMap * m
If you noticed, it was pretty easy to combine maps. What is even cooler is
that the derivatives also are made for you (if everything goes right).
Just to be sure that the derivative is correct, you should always run the test
on the mapping that you create.
.. plot::
from SimPEG import Examples
Examples.Maps_ComboMaps.run()
.. literalinclude:: ../../../SimPEG/Examples/Maps_ComboMaps.py
:language: python
:linenos:
@@ -1,25 +0,0 @@
.. _examples_Mesh_Basic_ForwardDC:
.. --------------------------------- ..
.. ..
.. THIS FILE IS AUTO GENEREATED ..
.. ..
.. SimPEG/Examples/__init__.py ..
.. ..
.. --------------------------------- ..
Mesh: Basic Forward 2D DC Resistivity
=====================================
2D DC forward modeling example with Tensor and Curvilinear Meshes
.. plot::
from SimPEG import Examples
Examples.Mesh_Basic_ForwardDC.run()
.. literalinclude:: ../../../SimPEG/Examples/Mesh_Basic_ForwardDC.py
:language: python
:linenos:
@@ -1,26 +0,0 @@
.. _examples_PF_Magnetics_Analytics:
.. --------------------------------- ..
.. ..
.. THIS FILE IS AUTO GENEREATED ..
.. ..
.. SimPEG/Examples/__init__.py ..
.. ..
.. --------------------------------- ..
PF: Magnetics: Analytics
========================
Comparing the magnetics field in Vancouver to Seoul
.. plot::
from SimPEG import Examples
Examples.PF_Magnetics_Analytics.run()
.. literalinclude:: ../../../SimPEG/Examples/PF_Magnetics_Analytics.py
:language: python
:linenos:

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