wassname/simpeg
1
0 Fork 0
mirror of https://github.com/wassname/simpeg.git synced 2026-09-30 11:42:17 +08:00
Code Issues Packages Projects Releases Wiki Activity

Merge pull request #45 from simpeg/develop

Browse Source 
Merge Develop into Master
This commit is contained in:
David Marchant committed 2014-02-05 11:46:24 -08:00
2 parents 6286581827 dc62498a78
commit b56e0a2e71
98 files changed
+2517 -10556
Download Patch File Download Diff File Expand all files Collapse all files

No files matched your search

.gitignore
-1
View File
@@ -3,4 +3,3 @@
*.sublime-project
*.sublime-workspace
docs/_build/
myNotebooks/*
GCEtools/PETScIO.py
+470
View File
@@ -0,0 +1,470 @@
#!/usr/bin/python
"""
Input and output functions.
"""
import os as _os
import errno as _errno
import sys as _sys
import numpy as _np
from petsc4py import PETSc as _PETSc
import fileinput as _fl
def vecToArray(obj):
""" Converts a PETSc vector to a numpy array, available on *all* MPI nodes.
Args:
obj (petsc4py.PETSc.Vec): input vector.
Returns:
numpy.array :
"""
# scatter vector 'obj' to all processes
comm = obj.getComm()
scatter, obj0 = _PETSc.Scatter.toAll(obj)
scatter.scatter(obj, obj0, False, _PETSc.Scatter.Mode.FORWARD)
return _np.asarray(obj0)
# deallocate
comm.barrier()
scatter.destroy()
obj0.destroy()
def vecToArray0(obj):
""" Converts a PETSc vector to a numpy array available on MPI node 0.
Args:
obj (petsc4py.PETSc.Vec): input vector.
Returns:
numpy.array :
"""
# scatter vector 'obj' to process 0
comm = obj.getComm()
rank = comm.getRank()
scatter, obj0 = _PETSc.Scatter.toZero(obj)
scatter.scatter(obj, obj0, False, _PETSc.Scatter.Mode.FORWARD)
if rank == 0: return _np.asarray(obj0)
# deallocate
comm.barrier()
scatter.destroy()
obj0.destroy()
def arrayToVec(vecArray):
""" Converts a (global) array to a PETSc vector over :attr:`petsc4py.PETSc.COMM_WORLD`.
Args:
vecArray (array or numpy.array): input vector.
Returns:
petsc4py.PETSc.Vec() :
"""
vec = _PETSc.Vec().create(comm=_PETSc.COMM_WORLD)
vec.setSizes(len(vecArray))
vec.setUp()
(Istart,Iend) = vec.getOwnershipRange()
return vec.createWithArray(vecArray[Istart:Iend],
comm=_PETSc.COMM_WORLD)
vec.destroy()
def arrayToMat(matArray):
""" Converts a (global) 2D array to a PETSc matrix over :attr:`petsc4py.PETSc.COMM_WORLD`.
Args:
matArray (array or numpy.array): input square array.
:rtype: petsc4py.PETSc.Mat()
.. important::
Requires `SciPy <http://www.scipy.org>`_.
"""
try:
import scipy.sparse as sparse
except:
print '\nERROR: loading matrices from txt files requires Scipy!'
return
matSparse =matArray
mat = _PETSc.Mat().createAIJ(size=matSparse.shape,comm=_PETSc.COMM_WORLD)
(Istart,Iend) = mat.getOwnershipRange()
ai = matSparse.indptr[Istart:Iend+1] - matSparse.indptr[Istart]
aj = matSparse.indices[matSparse.indptr[Istart]:matSparse.indptr[Iend]]
av = matSparse.data[matSparse.indptr[Istart]:matSparse.indptr[Iend]]
mat.setValuesCSR(ai,aj,av)
mat.assemble()
return mat
mat.destroy()
def matToSparse(mat):
""" Converts a PETSc matrix to a (global) sparse matrix.
Args:
mat (petsc4py.PETSc.Mat): input PETSc matrix.
:rtype: scipy.sparse.csr_matrix
.. important::
Requires `SciPy <http://www.scipy.org>`_.
"""
import scipy.sparse as sparse
data = mat.getValuesCSR()
(Istart,Iend) = mat.getOwnershipRange()
columns = mat.getSize()[0]
sparseSubMat = sparse.csr_matrix(data[::-1],shape=(Iend-Istart,columns))
comm = _PETSc.COMM_WORLD
sparseSubMat = comm.tompi4py().allgather(sparseSubMat)
return sparse.vstack(sparseSubMat)
def adjToH(adj,d=[0],amp=[0.]):
""" Creates a 1 particle PETSc-type Hamiltonian matrix from a PETSc adjacency matrix.
Args:
adj (petsc4py.PETSc.Mat): input PETSc-type adjacency matrix.
d (array of ints): an array containing *integers* indicating the nodes
where diagonal defects are to be placed (e.g. ``d=[0,1,4]``).
amp (array of floats): an array containing *floats* indicating the diagonal defect
amplitudes corresponding to each element in ``d`` (e.g. ``amp=[0.5,-1,4.2]``).
Returns:
: 1 particle Hamiltonian matrix
:rtype: petsc4py.PETSc.Mat()
Warning:
* The size of ``a`` and ``d`` must be identical
>>> amp = [0.5,-1.,4.2]
>>> len(d) == len(amp)
True
* Elements of ``d`` can range from :math:`[0,N-1]` where the adjacency matrix is :math:`N\\times N`.
"""
(Istart,Iend) = adj.getOwnershipRange()
diagSum = []
for i in range(Istart,Iend):
diagSum.append(_np.sum(adj.getRow(i)[-1]))
for j,val in enumerate(d):
if i==val: diagSum[i-Istart] += amp[j]
mat = _PETSc.Mat().create(comm=_PETSc.COMM_WORLD)
mat.setSizes(adj.getSize())
mat.setUp()
for i in range(Istart,Iend):
mat.setValue(i,i,diagSum[i-Istart])
mat.assemble()
mat.axpy(-1,adj)
return mat
mat.destroy()
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#---------------------- Vec I/O functions ---------------------------
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def exportVec(vec,filename,filetype):
""" Export a PETSc vector to a file.
Args:
vec (petsc4py.PETSc.Vec): input vector.
filename (str): path to desired output file.
filetype (str): the filetype of the exported vector.
* ``'txt'`` - a column vector in text format.
* ``'bin'`` - a PETSc binary vector.
"""
if _os.path.isabs(filename):
outDir = _os.path.dirname(filename)
else:
outDir = './'+_os.path.dirname(filename)
# create output directory if it doesn't exist
try:
_os.mkdir(outDir)
except OSError as exception:
if exception.errno != _errno.EEXIST:
raise
if filetype == 'txt':
# scatter prob to process 0
comm = vec.getComm()
rank = comm.getRank()
scatter, vec0 = _PETSc.Scatter.toZero(vec)
scatter.scatter(vec, vec0, False, _PETSc.Scatter.Mode.FORWARD)
# use process 0 to write to text file
if rank == 0:
array0 = _np.asarray(vec0)
with open(filename,'w') as f:
for i in range(len(array0)):
f.write('{0: .12e}\n'.format(array0[i]))
# deallocate
comm.barrier()
scatter.destroy()
vec0.destroy()
elif filetype == 'bin':
binSave = _PETSc.Viewer().createBinary(filename, 'w')
binSave(vec)
binSave.destroy()
vec.comm.barrier()
def loadVec(filename,filetype):
""" Import a PETSc vector from a file.
Args:
filename (str): path to input file.
filetype (str): the filetype.
* ``'txt'`` - a column vector in text format.
* ``'bin'`` - a PETSc binary vector.
"""
if filetype == 'txt':
try:
vecArray = _np.loadtxt(filename,dtype=_PETSc.ScalarType)
return arrayToVec(vecArray)
except:
print "\nERROR: input state space file " + filename\
+ " does not exist or is in an incorrect format"
_sys.exit()
elif filetype == 'bin':
binLoad = _PETSc.Viewer().createBinary(filename, 'r')
try:
return _PETSc.Vec().load(binLoad)
except:
print "\nERROR: input state space file " + filename\
+ " does not exist or is in an incorrect format"
_sys.exit()
binLoad.destroy()
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#---------------------- Mat I/O functions ---------------------------
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def exportMat(mat,filename,filetype,mattype=None):
""" Export a PETSc matrix to a file.
Args:
mat (petsc4py.PETSc.Mat): input matrix.
filename (str): path to desired output file.
filetype (str): the filetype of the exported vector.
* ``'txt'`` - a 2D matrix array in text format.
* ``'bin'`` - a PETSc binary matrix.
mattype (str): (``None``,``'adj'``) - if set to ``adj``, only
integers ``0`` and ``1`` are written. Note
that this only applied in ``txt`` mode.
"""
rank = _PETSc.Comm.Get_rank(_PETSc.COMM_WORLD)
if _os.path.isabs(filename):
outDir = _os.path.dirname(filename)
else:
outDir = './'+_os.path.dirname(filename)
# create output directory if it doesn't exist
try:
_os.mkdir(outDir)
except OSError as exception:
if exception.errno != _errno.EEXIST:
raise
if filetype == 'txt':
txtSave = _PETSc.Viewer().createASCII(filename, 'w',
format=_PETSc.Viewer.Format.ASCII_DENSE, comm=_PETSc.COMM_WORLD)
txtSave(mat)
txtSave.destroy()
if rank == 0:
for line in _fl.FileInput(filename,inplace=1):
if line[2] != 't':
if mattype == 'adj':
line = line.replace(" i","j")
line = line.replace(" -","-")
line = line.replace("+-","-")
line = line.replace("0000e+01+0.00000e+00j","")
line = line.replace(".00000e+00+0.00000e+00j","")
line = line.replace(".","")
line = line.replace(" -","\t-")
line = line.replace(" ","\t")
line = line.replace(" ","")
line = line.replace("\t"," ")
print line,
else:
line = line.replace(" i","j")
line = line.replace(" -","-")
line = line.replace("+-","-")
print line,
elif filetype == 'bin':
binSave = _PETSc.Viewer().createBinary(filename, 'w', comm=_PETSc.COMM_WORLD)
binSave(mat)
binSave.destroy()
mat.comm.barrier()
def loadMat(filename,filetype,delimiter=None):
""" Import a PETSc matrix from a file.
Args:
filename (str): path to input file.
filetype (str): the filetype.
* ``'txt'`` - a 2D matrix array in text format.
* ``'bin'`` - a PETSc matrix vector.
delimiter (str): this is passed to `numpy.genfromtxt\
<http://docs.scipy.org/doc/numpy/reference/generated/numpy.genfromtxt.html>`_
in the case of strange delimiters in an imported ``txt`` file.
"""
if filetype == 'txt':
try:
try:
if delimiter is None:
matArray = _np.genfromtxt(filename,dtype=_PETSc.ScalarType)
else:
matArray = _np.genfromtxt(filename,dtype=_PETSc.ScalarType,delimiter=delimiter)
except:
filefix = []
for line in _fl.FileInput(filename,inplace=0):
if line[2] != 't':
line = line.replace(" i","j")
line = line.replace(" -","-")
line = line.replace("+-","-")
filefix.append(line)
matArray = _np.genfromtxt(filefix,dtype=_PETSc.ScalarType)
return arrayToMat(matArray)
except:
print "\nERROR: input state space file " + filename\
+ " does not exist or is in an incorrect format"
_sys.exit()
elif filetype == 'bin':
binLoad = _PETSc.Viewer().createBinary(filename, 'r')
try:
return _PETSc.Mat().load(binLoad)
except:
print "\nERROR: input state space file " + filename\
+ " does not exist or is in an incorrect format"
_sys.exit()
binLoad.destroy()
def exportVecToMat(vec,filename,filetype):
""" Export a :math:`N^2` element PETSc vector as a :math:`N\\times N` matrix.
This is useful when wanting to view the full statespace of a 2 particle
quantum walk.
Args:
vec (petsc4py.PETSc.Vec): input :math:`N^2` element vector.
filename (str): path to desired output file.
filetype (str): the filetype of the exported vector.
* ``'txt'`` - an :math:`N\\times N` 2D matrix array in text format.
* ``'bin'`` - an :math:`N\\times N` PETSc binary matrix.
"""
rank = _PETSc.Comm.Get_rank(_PETSc.COMM_WORLD)
if _os.path.isabs(filename):
outDir = _os.path.dirname(filename)
else:
outDir = './'+_os.path.dirname(filename)
# create output directory if it doesn't exist
try:
_os.mkdir(outDir)
except OSError as exception:
if exception.errno != _errno.EEXIST:
raise
vecArray = vecToArray(vec)
matArray = vecArray.reshape([_np.sqrt(vecArray.size),_np.sqrt(vecArray.size)])
if filetype == 'txt':
#if rank == 0: _np.savetxt(filename,matArray)
txtSave = _PETSc.Viewer().createASCII(filename, 'w',
format=_PETSc.Viewer.Format.ASCII_DENSE, comm=_PETSc.COMM_WORLD)
txtSave(arrayToMat(matArray))
txtSave.destroy()
if rank == 0:
for line in _fl.FileInput(filename,inplace=1):
if line[2] != 't':
line = line.replace(" i","j")
line = line.replace(" -","-")
line = line.replace("+-","-")
print line,
elif filetype == 'bin':
binSave = _PETSc.Viewer().createBinary(filename, 'w', comm=_PETSc.COMM_WORLD)
binSave(arrayToMat(matArray))
binSave.destroy()
vec.comm.barrier()
def loadMatToVec(filename,filetype):
""" Load a :math:`N\\times N` matrix as a :math:`N^2` element PETSc vector.
This is useful when wanting to import the full statespace of a 2 particle
quantum walk to use for propagation.
Args:
filename (str): path to the input file.
filetype (str): the filetype
* ``'txt'`` - an :math:`N\\times N` 2D matrix array in text format.
* ``'bin'`` - **Not yet implemented! Please use a txt \
format for this type of import**.
"""
if filetype == 'txt':
try:
try:
matArray = _np.loadtxt(filename,dtype=_PETSc.ScalarType)
except:
filefix = []
for line in _fl.FileInput(filename,inplace=0):
if line[2] != 't':
line = line.replace(" i","j")
line = line.replace(" -","-")
line = line.replace("+-","-")
filefix.append(line)
matArray = _np.loadtxt(filefix,dtype=_PETSc.ScalarType)
vecArray = matArray.reshape(matArray.shape[0]**2)
return arrayToVec(vecArray)
except:
print "\nERROR: input state space file " + filename\
+ " does not exist or is in an incorrect format"
_sys.exit()
elif filetype == 'bin':
print '\nERROR: only works for txt storage!'
_sys.exit()
GCEtools/PetscExample.ipynb
+198
View File
@@ -0,0 +1,198 @@
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"from SimPEG import *\n",
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"M = mesh.TensorMesh([20,30]) \n",
"A = M.faceDiv*M.faceDiv.T + sp.identity(M.nC)\n",
"b = np.random.rand(M.nC)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"phi = Solver(A).solve(b)\n",
"colorbar(M.plotImage(phi))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 37,
"text": [
"<matplotlib.colorbar.Colorbar instance at 0x6c411b8>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAESCAYAAAACDEUqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x67e6050>"
]
}
],
"prompt_number": 37
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print np.linalg.norm(A*phi-b)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"1.5220841846e-13\n"
]
}
],
"prompt_number": 38
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import petsc4py\n",
"import sys\n",
"petsc4py.init(sys.argv)\n",
"from petsc4py import PETSc"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 39
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import PETScIO as IO\n",
"Apetsc = PETSc.Mat().createAIJ(size=A.shape,csr=(A.indptr, A.indices, A.data))\n",
"bpetsc = IO.arrayToVec(b)\n",
"xpetsc = IO.arrayToVec(0*b)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 40
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ksp = PETSc.KSP().create()\n",
"pc = PETSc.PC().create()\n",
"\n",
"ksp.setOperators(Apetsc)\n",
"\n",
"ksp.setType(ksp.Type.CG)\n",
"pc = ksp.getPC()\n",
"pc.setType(pc.Type.HYPRE)\n",
"ksp.view()\n",
"\n",
"ksp.solve(bpetsc, xpetsc)\n",
"print ksp.its"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"3\n"
]
}
],
"prompt_number": 76
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X = IO.vecToArray(xpetsc)\n",
"print np.linalg.norm(A*X-b)\n",
"M.plotImage(X)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0.000199616893249\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 77,
"text": [
"<matplotlib.collections.QuadMesh at 0x792ae50>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAESCAYAAAD9gqKNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x77479d0>"
]
}
],
"prompt_number": 77
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
SimPEG/GCEtools/gceStartup.txt → GCEtools/gceStartup.txt
View File
File renamed without changes.
GCEtools/petscStartup.sh
Executable
+145
View File
@@ -0,0 +1,145 @@
#! /bin/bash
locale-gen en_US en_US.UTF-8 hu_HU hu_HU.UTF-8 > output.t
dpkg-reconfigure locales >> output.t
sudo apt-get update >> output.t
echo " "
echo " "
echo " ============================================"
echo " | Installing packages form package manager |"
echo " ============================================"
echo " "
echo " "
sudo apt-get -y install aptitude >> output.t
packages=(gcc gfortran git libopenmpi-dev python-pip python-dev git flex bison cmake vim cython ipython python-scipy python-numpy python-nose python-pip python-matplotlib python-vtk python-h5py libmumps-ptscotch-4.10.0 libmumps-ptscotch-dev libblas-dev liblapack-dev )
for item in ${packages[*]}
do
printf " %-30s\n" $item
done
for item in ${packages[*]}
do
tput cuu1
done
for item in ${packages[*]}
do
sudo aptitude -y install $item >> output.t
printf " %-30s %-4s\n" $item done
done
echo " "
echo " "
echo " ====================================="
echo " | Installing extra Python libraries |"
echo " ====================================="
echo " "
echo " "
pipPackages=(mpi4py pymumps)
for item in ${pipPackages[*]}
do
printf " %-30s\n" $item
done
for item in ${pipPackages[*]}
do
tput cuu1
done
for item in ${pipPackages[*]}
do
sudo pip install $item >> output.t
printf " %-30s %-4s\n" $item done
done
Upgrade=(scipy numpy ipython)
for item in ${Upgrade[*]}
do
printf " %-8s%-7s\n" $item upgrade
done
for item in ${Upgrade[*]}
do
tput cuu1
done
for item in ${Upgrade[*]}
do
sudo pip install $item --upgrade >> output.t
printf " %-8s%-7s %-4s\n" $item upgrade done
done
echo " "
echo " "
echo " ====================="
echo " | Installing SimPEG |"
echo " ====================="
echo " "
echo " "
cd ~
git clone https://github.com/simpeg/simpeg.git >> output.t
cd simpeg/SimPEG/
python setup.py >> output.t
cd ~
mkdir petsc
cd petsc
echo " "
echo " "
echo " ===================="
echo " | Installing PETSc |"
echo " ===================="
echo " "
echo " "
wget http://ftp.mcs.anl.gov/pub/petsc/release-snapshots/petsc-3.4.3.tar.gz
tar -zxf petsc-3.4.3.tar.gz
cd petsc-3.4.3
./configure --with-debugging=no --dowload-mpich=yes --download-blacs=yes --download-f-blas-lapack=yes --download-scalapack=yes --download-mumps=yes --download-ml=yes --download-spooles=yes --download-hypre=yes --dowload-trilinos=yes --download-metis=yes --download-parmetis=yes --download-umfpack=yes --download-ptscotch=yes --download-superlu=yes --download-superlu_dist=yes --download-essl=yes --download-eucild=yes --download-spai=yes --download-mpi4py=yes --download-petsc4py=yes --download-scientificpython=yes
echo "export PETSC_DIR=/home/${USER}/petsc/petsc-3.4.3" >> ~/.bashrc
echo "export PETSC_ARCH=arch-linux2-c-opt" >> ~/.bashrc
export PETSC_DIR=/home/${USER}/petsc/petsc-3.4.3
export PETSC_ARCH=arch-linux2-c-opt
. ~/.bashrc
make PETSC_DIR=/home/${USER}/petsc/petsc-3.4.3 PETSC_ARCH=arch-linux2-c-opt all
make PETSC_DIR=/home/${USER}/petsc/petsc-3.4.3 PETSC_ARCH=arch-linux2-c-opt test
cd ~/petsc
echo " "
echo " "
echo " ======================="
echo " | Installing PETSc4PY |"
echo " ======================="
echo " "
echo " "
git clone https://bitbucket.org/petsc/petsc4py.git
cd petsc4py/
python setup.py build >> output.t
python setup.py install --prefix=~/petsc >> output.t
echo "export PYTHONPATH=~/petsc/lib/python2.7/site-packages:/home/$USER/simpeg:${PYTHONPATH}" >> ~/.bashrc
cd ~
source ~/.bashrc
SimPEG/GCEtools/startup.sh → GCEtools/startup.sh
View File
File renamed without changes.
LICENSE
+20
View File
@@ -0,0 +1,20 @@
The MIT License (MIT)
Copyright (c) 2013-2014 SimPEG Developers
Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
the Software, and to permit persons to whom the Software is furnished to do so,
subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
README.md
+17 -1
View File
@@ -1,6 +1,6 @@
![SimPEG](https://raw.github.com/simpeg/simpeg/master/docs/simpeg-logo.png)
Simulation and Parameter Estimation in Geoscience - A python package for simulation and gradient based parameter estimation in the context of geophysical applications.
Simulation and Parameter Estimation in Geophysics - A python package for simulation and gradient based parameter estimation in the context of geophysical applications.
The vision is to create a package for finite volume simulation with applications to geophysical imaging and subsurface flow. To enable the understanding of the many different components, this package has the following features:
@@ -10,4 +10,20 @@ The vision is to create a package for finite volume simulation with applications
* supports 1D, 2D and 3D problems
* designed for large-scale inversions
Documentation:
[http://simpeg.readthedocs.org/en/latest/](http://simpeg.readthedocs.org/en/latest/)
Code:
[https://github.com/simpeg/simpeg](https://github.com/simpeg/simpeg)
Tests:
[https://travis-ci.org/simpeg/simpeg](https://travis-ci.org/simpeg/simpeg)
Build Status:
[![Build Status](https://travis-ci.org/simpeg/simpeg.png)](https://travis-ci.org/simpeg/simpeg)
Bugs & Issues:
[https://github.com/simpeg/simpeg/issues](https://github.com/simpeg/simpeg/issues)
Code Snippets & Tutorials:
[http://www.row1.ca/simpeg](http://www.row1.ca/simpeg)
SimPEG/Data.py
+147
View File
@@ -0,0 +1,147 @@
import Utils, numpy as np
class BaseData(object):
"""Data holds the observed data, and the standard deviations."""
__metaclass__ = Utils.Save.Savable
std = None #: Estimated Standard Deviations
dobs = None #: Observed data
dtrue = None #: True data, if data is synthetic
mtrue = None #: True model, if data is synthetic
counter = None #: A SimPEG.Utils.Counter object
def __init__(self, **kwargs):
Utils.setKwargs(self, **kwargs)
@property
def prob(self):
"""
The geophysical problem that explains this data, use::
data.pair(prob)
"""
return getattr(self, '_prob', None)
def pair(self, p):
"""Bind a problem to this data instance using pointers"""
assert hasattr(p, 'dataPair'), "Problem must have an attribute 'dataPair'."
assert isinstance(self, p.dataPair), "Problem requires data object must be an instance of a %s class."%(p.dataPair.__name__)
if p.ispaired:
raise Exception("The problem object is already paired to a data. Use prob.unpair()")
self._prob = p
p._data = self
def unpair(self):
"""Unbind a problem from this data instance"""
if not self.ispaired: return
self.prob._data = None
self._prob = None
@property
def ispaired(self): return self.prob is not None
@Utils.count
@Utils.requires('prob')
def dpred(self, m, u=None):
"""
Create the projected data from a model.
The field, u, (if provided) will be used for the predicted data
instead of recalculating the fields (which may be expensive!).
.. math::
d_\\text{pred} = P(u(m))
Where P is a projection of the fields onto the data space.
"""
if u is None: u = self.prob.field(m)
return Utils.mkvc(self.projectField(u))
@Utils.count
def projectField(self, u):
"""
This function projects the fields onto the data space.
.. math::
d_\\text{pred} = P(u(m))
"""
return u
#TODO: def projectFieldDeriv(self, u): Does this need to be made??!
@Utils.count
def residual(self, m, u=None):
"""
:param numpy.array m: geophysical model
:param numpy.array u: fields
:rtype: float
:return: data residual
The data residual:
.. math::
\mu_\\text{data} = \mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}
"""
return Utils.mkvc(self.dpred(m, u=u) - self.dobs)
@property
def Wd(self):
"""
Data weighting matrix. This is a covariance matrix used in::
def data.residualWeighted(m,u=None):
return self.Wd*self.residual(m, u=u)
By default, this is based on the norm of the data plus a noise floor.
"""
if getattr(self,'_Wd',None) is None:
eps = np.linalg.norm(Utils.mkvc(self.dobs),2)*1e-5
self._Wd = 1/(abs(self.dobs)*self.std+eps)
return self._Wd
@Wd.setter
def Wd(self, value):
self._Wd = value
def residualWeighted(self, m, u=None):
"""
:param numpy.array m: geophysical model
:param numpy.array u: fields
:rtype: float
:return: data residual
The weighted data residual:
.. math::
\mu_\\text{data}^{\\text{weighted}} = \mathbf{W}_d(\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs})
Where W_d is a covariance matrix that weights the data residual.
"""
return Utils.mkvc(self.Wd*self.residual(m, u=u))
@property
def RHS(self):
"""
Source matrix.
"""
return getattr(self, '_RHS', None)
@RHS.setter
def RHS(self, value):
self._RHS = value
@property
def isSynthetic(self):
"Check if the data is synthetic."
return (self.mtrue is not None)
if __name__ == '__main__':
d = BaseData()
d.dpred()
SimPEG/examples/DC.py → SimPEG/Examples/DC.py
+80 -72
View File
@@ -1,27 +1,53 @@
from SimPEG.mesh import TensorMesh
from SimPEG.forward import Problem, ModelTransforms
from SimPEG.tests import checkDerivative
from SimPEG.utils import ModelBuilder, sdiag, mkvc
from SimPEG import Solver
import numpy as np
import scipy.sparse as sp
from SimPEG import *
class DCProblem(ModelTransforms.LogModel, Problem):
class DCData(Data.BaseData):
"""
**DCData**
Geophysical DC resistivity data.
"""
P = None #: projection
def __init__(self, **kwargs):
Data.BaseData.__init__(self, **kwargs)
Utils.setKwargs(self, **kwargs)
def reshapeFields(self, u):
if len(u.shape) == 1:
u = u.reshape([-1, self.RHS.shape[1]], order='F')
return u
def projectField(self, u):
"""
Predicted data.
.. math::
d_\\text{pred} = Pu(m)
"""
u = self.reshapeFields(u)
return Utils.mkvc(self.P*u)
class DCProblem(Problem.BaseProblem):
"""
**DCProblem**
Geophysical DC resistivity problem.
"""
def __init__(self, mesh):
Problem.__init__(self, mesh)
self.mesh.setCellGradBC('neumann')
def reshapeFields(self, u):
if len(u.shape) == 1:
u = u.reshape([-1, self.RHS.shape[1]], order='F')
return u
dataPair = DCData
def __init__(self, mesh, model, **kwargs):
Problem.BaseProblem.__init__(self, mesh, model)
self.mesh.setCellGradBC('neumann')
Utils.setKwargs(self, **kwargs)
def createMatrix(self, m):
"""
@@ -38,30 +64,16 @@ class DCProblem(ModelTransforms.LogModel, Problem):
"""
D = self.mesh.faceDiv
G = self.mesh.cellGrad
sigma = self.modelTransform(m)
sigma = self.model.transform(m)
Msig = self.mesh.getFaceMass(sigma)
A = D*Msig*G
return A.tocsc()
def dpred(self, m, u=None):
"""
Predicted data.
.. math::
d_\\text{pred} = Pu(m)
"""
if u is None:
u = self.field(m)
u = self.reshapeFields(u)
return mkvc(self.P*u)
def field(self, m):
A = self.createMatrix(m)
solve = Solver(A)
phi = solve.solve(self.RHS)
return mkvc(phi)
phi = solve.solve(self.data.RHS)
return Utils.mkvc(phi)
def J(self, m, v, u=None):
"""
@@ -88,24 +100,24 @@ class DCProblem(ModelTransforms.LogModel, Problem):
if u is None:
u = self.field(m)
u = self.reshapeFields(u)
u = self.data.reshapeFields(u)
P = self.P
P = self.data.P
D = self.mesh.faceDiv
G = self.mesh.cellGrad
A = self.createMatrix(m)
Av_dm = self.mesh.getFaceMassDeriv()
mT_dm = self.modelTransformDeriv(m)
mT_dm = self.model.transformDeriv(m)
dCdu = A
dCdm = np.empty_like(u)
for i, ui in enumerate(u.T): # loop over each column
dCdm[:, i] = D * ( sdiag( G * ui ) * ( Av_dm * ( mT_dm * v ) ) )
dCdm[:, i] = D * ( Utils.sdiag( G * ui ) * ( Av_dm * ( mT_dm * v ) ) )
solve = Solver(dCdu)
Jv = - P * solve.solve(dCdm)
return mkvc(Jv)
return Utils.mkvc(Jv)
def Jt(self, m, v, u=None):
"""Takes data, turns it into a model..ish"""
@@ -113,15 +125,15 @@ class DCProblem(ModelTransforms.LogModel, Problem):
if u is None:
u = self.field(m)
u = self.reshapeFields(u)
v = self.reshapeFields(v)
u = self.data.reshapeFields(u)
v = self.data.reshapeFields(v)
P = self.P
P = self.data.P
D = self.mesh.faceDiv
G = self.mesh.cellGrad
A = self.createMatrix(m)
Av_dm = self.mesh.getFaceMassDeriv()
mT_dm = self.modelTransformDeriv(m)
mT_dm = self.model.transformDeriv(m)
dCdu = A.T
solve = Solver(dCdu)
@@ -130,7 +142,7 @@ class DCProblem(ModelTransforms.LogModel, Problem):
Jtv = 0
for i, ui in enumerate(u.T): # loop over each column
Jtv += sdiag( G * ui ) * ( D.T * w[:,i] )
Jtv += Utils.sdiag( G * ui ) * ( D.T * w[:,i] )
Jtv = - mT_dm.T * ( Av_dm.T * Jtv )
return Jtv
@@ -165,16 +177,13 @@ def genTxRxmat(nelec, spacelec, surfloc, elecini, mesh):
return q, Q, rxmidLoc
if __name__ == '__main__':
from SimPEG import inverse
import matplotlib.pyplot as plt
# Create the mesh
h1 = np.ones(20)
h2 = np.ones(100)
mesh = TensorMesh([h1,h2])
M = Mesh.TensorMesh([h1,h2])
# Create some parameters for the model
sig1 = np.log(1)
@@ -184,9 +193,9 @@ if __name__ == '__main__':
p0 = [5, 10]
p1 = [15, 50]
condVals = [sig1, sig2]
mSynth = ModelBuilder.defineBlockConductivity(p0,p1,mesh.gridCC,condVals)
plt.colorbar(mesh.plotImage(mSynth))
plt.show()
mSynth = Utils.ModelBuilder.defineBlockConductivity(M.gridCC,p0,p1,condVals)
plt.colorbar(M.plotImage(mSynth))
# plt.show()
# Set up the projection
nelec = 50
@@ -196,41 +205,40 @@ if __name__ == '__main__':
elecend = 0.5+spacelec*(nelec-1)
elecLocR = np.linspace(elecini, elecend, nelec)
rxmidLoc = (elecLocR[0:nelec-1]+elecLocR[1:nelec])*0.5
q, Q, rxmidloc = genTxRxmat(nelec, spacelec, surfloc, elecini, mesh)
q, Q, rxmidloc = genTxRxmat(nelec, spacelec, surfloc, elecini, M)
P = Q.T
model = Model.LogModel(M)
prob = DCProblem(M, model)
# Create some data
problem = DCProblem(mesh)
problem.P = P
problem.RHS = q
dobs, Wd = problem.createSyntheticData(mSynth, std=0.05)
data = prob.createSyntheticData(mSynth, std=0.05, P=P, RHS=q)
u = problem.field(mSynth)
u = problem.reshapeFields(u)
mesh.plotImage(u[:,10])
# plt.show()
u = prob.field(mSynth)
u = data.reshapeFields(u)
M.plotImage(u[:,10])
plt.show()
# Now set up the problem to do some minimization
problem.dobs = dobs
problem.std = dobs*0 + 0.05
m0 = mesh.gridCC[:,0]*0+sig2
# Now set up the prob to do some minimization
# prob.dobs = dobs
# prob.std = dobs*0 + 0.05
m0 = M.gridCC[:,0]*0+sig2
opt = inverse.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6)
reg = inverse.Regularization(mesh)
inv = inverse.Inversion(problem, reg, opt, beta0=1e4)
reg = Regularization.Tikhonov(model)
objFunc = ObjFunction.BaseObjFunction(data, reg)
opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=3, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6)
inv = Inversion.BaseInversion(objFunc, opt)
# Check Derivative
derChk = lambda m: [inv.dataObj(m), inv.dataObjDeriv(m)]
checkDerivative(derChk, mSynth)
derChk = lambda m: [objFunc.dataObj(m), objFunc.dataObjDeriv(m)]
# Tests.checkDerivative(derChk, mSynth)
print inv.dataObj(m0)
print inv.dataObj(mSynth)
print objFunc.dataObj(m0)
print objFunc.dataObj(mSynth)
m = inv.run(m0)
plt.colorbar(mesh.plotImage(m))
plt.colorbar(M.plotImage(m))
print m
plt.show()
SimPEG/examples/Linear.py → SimPEG/Examples/Linear.py
+17 -13
View File
@@ -1,14 +1,15 @@
from SimPEG import mesh, forward, inverse, np
from SimPEG import *
import matplotlib.pyplot as plt
class LinearProblem(forward.Problem):
class LinearProblem(Problem.BaseProblem):
"""docstring for LinearProblem"""
def __init__(self, *args, **kwargs):
forward.Problem.__init__(self, *args, **kwargs)
def __init__(self, mesh, model, G, **kwargs):
Problem.BaseProblem.__init__(self, mesh, model, **kwargs)
self.G = G
def dpred(self, m, u=None):
def field(self, m, u=None):
return self.G.dot(m)
def J(self, m, v, u=None):
@@ -20,7 +21,7 @@ class LinearProblem(forward.Problem):
def example(N):
h = np.ones(N)/N
M = mesh.TensorMesh([h])
M = Mesh.TensorMesh([h])
nk = 20
jk = np.linspace(1.,20.,nk)
@@ -39,21 +40,24 @@ def example(N):
mtrue[M.vectorCCx > 0.45] = -0.5
mtrue[M.vectorCCx > 0.6] = 0
prob = LinearProblem(M)
prob.G = G
model = Model.BaseModel(M)
prob = LinearProblem(M, model, G)
data = prob.createSyntheticData(mtrue, std=0.01)
return prob, data
return prob, data, model
if __name__ == '__main__':
prob, data = example(100)
prob, data, model = example(100)
M = prob.mesh
reg = inverse.Regularization(M)
opt = inverse.InexactGaussNewton(maxIter=20)
inv = inverse.Inversion(prob,reg,opt,data)
reg = Regularization.Tikhonov(model)
objFunc = ObjFunction.BaseObjFunction(data, reg)
opt = Optimization.InexactGaussNewton(maxIter=20)
inv = Inversion.BaseInversion(objFunc, opt)
m0 = np.zeros_like(data.mtrue)
mrec = inv.run(m0)
SimPEG/examples/__init__.py → SimPEG/Examples/__init__.py
View File
File renamed without changes.
SimPEG/Inversion.py
+125
View File
@@ -0,0 +1,125 @@
import SimPEG
from SimPEG import Utils, sp, np
from Optimization import Remember, IterationPrinters
class BaseInversion(object):
"""BaseInversion(objFunc, opt, **kwargs)
"""
__metaclass__ = Utils.Save.Savable
name = 'BaseInversion'
debug = False #: Print debugging information
counter = None #: Set this to a SimPEG.Utils.Counter() if you want to count things
def __init__(self, objFunc, opt, **kwargs):
Utils.setKwargs(self, **kwargs)
self.objFunc = objFunc
self.objFunc.parent = self
self.opt = opt
self.opt.parent = self
self.stoppers = [StoppingCriteria.iteration]
# Check if we have inserted printers into the optimization
if IterationPrinters.phi_d not in self.opt.printers:
self.opt.printers.insert(1,IterationPrinters.beta)
self.opt.printers.insert(2,IterationPrinters.phi_d)
self.opt.printers.insert(3,IterationPrinters.phi_m)
if not hasattr(opt, '_bfgsH0') and hasattr(opt, 'bfgsH0'): # Check if it has been set by the user and the default is not being used.
#TODO: I don't think that this if statement is working...
print 'Setting bfgsH0 to the inverse of the modelObj2Deriv. Done using direct methods.'
opt.bfgsH0 = SimPEG.Solver(objFunc.reg.modelObj2Deriv())
#TODO: Move this to the data class?
@property
def phi_d_target(self):
"""
target for phi_d
By default this is the number of data.
Note that we do not set the target if it is None, but we return the default value.
"""
if getattr(self, '_phi_d_target', None) is None:
return self.data.dobs.size #
return self._phi_d_target
@phi_d_target.setter
def phi_d_target(self, value):
self._phi_d_target = value
@Utils.timeIt
def run(self, m0):
"""run(m0)
Runs the inversion!
"""
self.objFunc.startup(m0)
self.m = self.opt.minimize(self.objFunc.evalFunction, m0)
self.finish()
return self.m
@Utils.callHooks('finish')
def finish(self):
"""finish()
**finish** is called at the end of the optimization.
"""
pass
def save(self, group):
group.attrs['phi_d'] = self.phi_d
group.attrs['phi_m'] = self.phi_m
group.setArray('m', self.m)
group.setArray('dpred', self.dpred)
# class Inversion(Cooling, Remember, BaseInversion):
# maxIter = 10
# name = "SimPEG Inversion"
# def __init__(self, prob, reg, opt, data, **kwargs):
# BaseInversion.__init__(self, prob, reg, opt, data, **kwargs)
# self.stoppers.append(StoppingCriteria.phi_d_target_Inversion)
# if StoppingCriteria.phi_d_target_Minimize not in self.opt.stoppers:
# self.opt.stoppers.append(StoppingCriteria.phi_d_target_Minimize)
# class TimeSteppingInversion(Remember, BaseInversion):
# """
# A slightly different view on regularization parameters,
# let Beta be viewed as 1/dt, and timestep by updating the
# reference model every optimization iteration.
# """
# maxIter = 1
# name = "Time-Stepping SimPEG Inversion"
# def __init__(self, prob, reg, opt, data, **kwargs):
# BaseInversion.__init__(self, prob, reg, opt, data, **kwargs)
# self.stoppers.append(StoppingCriteria.phi_d_target_Inversion)
# if StoppingCriteria.phi_d_target_Minimize not in self.opt.stoppers:
# self.opt.stoppers.append(StoppingCriteria.phi_d_target_Minimize)
# def _startup_TimeSteppingInversion(self, m0):
# def _doEndIteration_updateMref(self, xt):
# if self.debug: 'Updating the reference model.'
# self.parent.reg.mref = self.xc
# self.opt.hook(_doEndIteration_updateMref, overwrite=True)
SimPEG/mesh/BaseMesh.py → SimPEG/Mesh/BaseMesh.py
+24 -34
View File
@@ -1,5 +1,5 @@
import numpy as np
from SimPEG import utils
from SimPEG import Utils
class BaseMesh(object):
@@ -78,7 +78,7 @@ class BaseMesh(object):
x_array = np.ones((x.size, len(x)))
# Unwrap it and put it in a np array
for i, xi in enumerate(x):
x_array[:, i] = utils.mkvc(xi)
x_array[:, i] = Utils.mkvc(xi)
x = x_array
assert type(x) == np.ndarray, "x must be a numpy array"
@@ -91,17 +91,17 @@ class BaseMesh(object):
if format == 'M':
return xx.reshape(nn, order='F')
elif format == 'V':
return utils.mkvc(xx)
return Utils.mkvc(xx)
def switchKernal(xx):
"""Switches over the different options."""
if xType in ['CC', 'N']:
nn = (self.n) if xType == 'CC' else (self.n+1)
nn = (self._n) if xType == 'CC' else (self._n+1)
assert xx.size == np.prod(nn), "Number of elements must not change."
return outKernal(xx, nn)
elif xType in ['F', 'E']:
# This will only deal with components of fields, not full 'F' or 'E'
xx = utils.mkvc(xx) # unwrap it in case it is a matrix
xx = Utils.mkvc(xx) # unwrap it in case it is a matrix
nn = self.nFv if xType == 'F' else self.nEv
nn = np.r_[0, nn]
@@ -147,16 +147,6 @@ class BaseMesh(object):
else:
return switchKernal(x)
def n():
doc = """
Number of Cells in each dimension (array of integers)
:rtype: numpy.array
:return: n
"""
fget = lambda self: self._n
return locals()
n = property(**n())
def dim():
doc = """
@@ -176,7 +166,7 @@ class BaseMesh(object):
:rtype: int
:return: nCx
"""
fget = lambda self: self.n[0]
fget = lambda self: self._n[0]
return locals()
nCx = property(**nCx())
@@ -190,7 +180,7 @@ class BaseMesh(object):
def fget(self):
if self.dim > 1:
return self.n[1]
return self._n[1]
else:
return None
return locals()
@@ -205,7 +195,7 @@ class BaseMesh(object):
def fget(self):
if self.dim > 2:
return self.n[2]
return self._n[2]
else:
return None
return locals()
@@ -219,12 +209,12 @@ class BaseMesh(object):
:return: nC
.. plot::
:include-source:
from SimPEG.mesh import TensorMesh
import numpy as np
TensorMesh([np.ones(n) for n in [2,3]]).plotGrid(centers=True,showIt=True)
from SimPEG import Mesh, np
Mesh.TensorMesh([np.ones(n) for n in [2,3]]).plotGrid(centers=True,showIt=True)
"""
fget = lambda self: np.prod(self.n)
fget = lambda self: np.prod(self._n)
return locals()
nC = property(**nC())
@@ -260,7 +250,7 @@ class BaseMesh(object):
def fget(self):
if self.dim > 1:
return self.n[1] + 1
return self._n[1] + 1
else:
return None
return locals()
@@ -276,7 +266,7 @@ class BaseMesh(object):
def fget(self):
if self.dim > 2:
return self.n[2] + 1
return self._n[2] + 1
else:
return None
return locals()
@@ -290,12 +280,12 @@ class BaseMesh(object):
:return: nN
.. plot::
:include-source:
from SimPEG.mesh import TensorMesh
import numpy as np
TensorMesh([np.ones(n) for n in [2,3]]).plotGrid(nodes=True,showIt=True)
from SimPEG import Mesh, np
Mesh.TensorMesh([np.ones(n) for n in [2,3]]).plotGrid(nodes=True,showIt=True)
"""
fget = lambda self: np.prod(self.n + 1)
fget = lambda self: np.prod(self.nCv + 1)
return locals()
nN = property(**nN())
@@ -361,10 +351,10 @@ class BaseMesh(object):
:return: [prod(nEx), prod(nEy), prod(nEz)]
.. plot::
:include-source:
from SimPEG.mesh import TensorMesh
import numpy as np
TensorMesh([np.ones(n) for n in [2,3]]).plotGrid(edges=True,showIt=True)
from SimPEG import Mesh, np
Mesh.TensorMesh([np.ones(n) for n in [2,3]]).plotGrid(edges=True,showIt=True)
"""
fget = lambda self: np.array([np.prod(x) for x in [self.nEx, self.nEy, self.nEz] if not x is None])
return locals()
@@ -433,10 +423,10 @@ class BaseMesh(object):
:return: [prod(nFx), prod(nFy), prod(nFz)]
.. plot::
:include-source:
from SimPEG.mesh import TensorMesh
import numpy as np
TensorMesh([np.ones(n) for n in [2,3]]).plotGrid(faces=True,showIt=True)
from SimPEG import Mesh, np
Mesh.TensorMesh([np.ones(n) for n in [2,3]]).plotGrid(faces=True,showIt=True)
"""
fget = lambda self: np.array([np.prod(x) for x in [self.nFx, self.nFy, self.nFz] if not x is None])
return locals()
SimPEG/mesh/Cyl1DMesh.py → SimPEG/Mesh/Cyl1DMesh.py
+2 -2
View File
@@ -1,7 +1,7 @@
import numpy as np
import scipy.sparse as sp
from scipy.constants import pi
from SimPEG.utils import mkvc, ndgrid, sdiag
from SimPEG.Utils import mkvc, ndgrid, sdiag
class Cyl1DMesh(object):
"""
@@ -84,7 +84,7 @@ class Cyl1DMesh(object):
doc = "Total number of cells in each direction"
fget = lambda self: np.array([self.nCx, self.nCz])
return locals()
nCv = property(**nCv())
nCv = property(**nCv())
def nNr():
doc = "Number of nodes in the radial direction"
SimPEG/mesh/DiffOperators.py → SimPEG/Mesh/DiffOperators.py
+18 -17
View File
@@ -1,6 +1,6 @@
import numpy as np
from scipy import sparse as sp
from SimPEG.utils import mkvc, sdiag, speye, kron3, spzeros, ddx, av, avExtrap
from SimPEG.Utils import mkvc, sdiag, speye, kron3, spzeros, ddx, av, avExtrap
def checkBC(bc):
@@ -129,7 +129,7 @@ class DiffOperators(object):
def fget(self):
if(self._faceDiv is None):
# The number of cell centers in each direction
n = self.n
n = self.nCv
# Compute faceDivergence operator on faces
if(self.dim == 1):
D = ddx(n[0])
@@ -158,7 +158,7 @@ class DiffOperators(object):
def fget(self):
if(self._faceDivx is None):
# The number of cell centers in each direction
n = self.n
n = self.nCv
# Compute faceDivergence operator on faces
if(self.dim == 1):
D1 = ddx(n[0])
@@ -183,7 +183,7 @@ class DiffOperators(object):
if(self.dim < 2): return None
if(self._faceDivy is None):
# The number of cell centers in each direction
n = self.n
n = self.nCv
# Compute faceDivergence operator on faces
if(self.dim == 2):
D2 = sp.kron(ddx(n[1]), speye(n[0]))
@@ -225,7 +225,7 @@ class DiffOperators(object):
def fget(self):
if(self._nodalGrad is None):
# The number of cell centers in each direction
n = self.n
n = self.nCv
# Compute divergence operator on faces
if(self.dim == 1):
G = ddx(n[0])
@@ -253,7 +253,7 @@ class DiffOperators(object):
if(self._nodalLaplacian is None):
print 'Warning: Laplacian has not been tested rigorously.'
# The number of cell centers in each direction
n = self.n
n = self.nCv
# Compute divergence operator on faces
if(self.dim == 1):
D1 = sdiag(1./self.hx) * ddx(mesh.nCx)
@@ -291,7 +291,7 @@ class DiffOperators(object):
"""
if(type(BC) is str):
BC = [BC for _ in self.n] # Repeat the str self.dim times
BC = [BC for _ in self.nCv] # Repeat the str self.dim times
elif(type(BC) is list):
assert len(BC) == self.dim, 'BC list must be the size of your mesh'
else:
@@ -313,7 +313,7 @@ class DiffOperators(object):
def fget(self):
if(self._cellGrad is None):
BC = self.setCellGradBC(self._cellGradBC_list)
n = self.n
n = self.nCv
if(self.dim == 1):
G = ddxCellGrad(n[0], BC[0])
elif(self.dim == 2):
@@ -340,7 +340,7 @@ class DiffOperators(object):
def fget(self):
if(self._cellGradBC is None):
BC = self.setCellGradBC(self._cellGradBC_list)
n = self.n
n = self.nCv
if(self.dim == 1):
G = ddxCellGradBC(n[0], BC[0])
elif(self.dim == 2):
@@ -367,7 +367,7 @@ class DiffOperators(object):
def fget(self):
if getattr(self, '_cellGradx', None) is None:
BC = ['neumann', 'neumann']
n = self.n
n = self.nCv
if(self.dim == 1):
G1 = ddxCellGrad(n[0], BC)
elif(self.dim == 2):
@@ -388,7 +388,7 @@ class DiffOperators(object):
if self.dim < 2: return None
if getattr(self, '_cellGrady', None) is None:
BC = ['neumann', 'neumann']
n = self.n
n = self.nCv
if(self.dim == 2):
G2 = sp.kron(ddxCellGrad(n[1], BC), speye(n[0]))
elif(self.dim == 3):
@@ -422,6 +422,7 @@ class DiffOperators(object):
def fget(self):
if(self._edgeCurl is None):
assert self.dim > 2, "Edge Curl only programed for 3D."
# The number of cell centers in each direction
n1 = self.nCx
n2 = self.nCy
@@ -466,7 +467,7 @@ class DiffOperators(object):
def fget(self):
if(self._aveF2CC is None):
n = self.n
n = self.nCv
if(self.dim == 1):
self._aveF2CC = av(n[0])
elif(self.dim == 2):
@@ -486,7 +487,7 @@ class DiffOperators(object):
def fget(self):
if(self._aveCC2F is None):
n = self.n
n = self.nCv
if(self.dim == 1):
self._aveCC2F = avExtrap(n[0])
elif(self.dim == 2):
@@ -507,7 +508,7 @@ class DiffOperators(object):
def fget(self):
if(self._aveE2CC is None):
# The number of cell centers in each direction
n = self.n
n = self.nCv
if(self.dim == 1):
raise Exception('Edge Averaging does not make sense in 1D: Use Identity?')
elif(self.dim == 2):
@@ -528,7 +529,7 @@ class DiffOperators(object):
def fget(self):
if(self._aveN2CC is None):
# The number of cell centers in each direction
n = self.n
n = self.nCv
if(self.dim == 1):
self._aveN2CC = av(n[0])
elif(self.dim == 2):
@@ -546,7 +547,7 @@ class DiffOperators(object):
def fget(self):
if(self._aveN2E is None):
# The number of cell centers in each direction
n = self.n
n = self.nCv
if(self.dim == 1):
self._aveN2E = av(n[0])
elif(self.dim == 2):
@@ -567,7 +568,7 @@ class DiffOperators(object):
def fget(self):
if(self._aveN2F is None):
# The number of cell centers in each direction
n = self.n
n = self.nCv
if(self.dim == 1):
self._aveN2F = av(n[0])
elif(self.dim == 2):
SimPEG/mesh/InnerProducts.py → SimPEG/Mesh/InnerProducts.py
+1 -1
View File
@@ -1,5 +1,5 @@
from scipy import sparse as sp
from SimPEG.utils import sub2ind, ndgrid, mkvc, getSubArray, sdiag, inv3X3BlockDiagonal, inv2X2BlockDiagonal
from SimPEG.Utils import sub2ind, ndgrid, mkvc, getSubArray, sdiag, inv3X3BlockDiagonal, inv2X2BlockDiagonal
import numpy as np
SimPEG/mesh/LogicallyOrthogonalMesh.py → SimPEG/Mesh/LogicallyOrthogonalMesh.py
+53 -48
View File
@@ -1,4 +1,4 @@
from SimPEG import utils, np
from SimPEG import Utils, np
from BaseMesh import BaseMesh
from DiffOperators import DiffOperators
from InnerProducts import InnerProducts
@@ -7,8 +7,8 @@ from LomView import LomView
# Some helper functions.
length2D = lambda x: (x[:, 0]**2 + x[:, 1]**2)**0.5
length3D = lambda x: (x[:, 0]**2 + x[:, 1]**2 + x[:, 2]**2)**0.5
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))
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 LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
@@ -17,11 +17,16 @@ class LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
Example of a logically orthogonal mesh:
.. plot:: examples/mesh/plot_LogicallyOrthogonalMesh.py
.. plot::
:include-source:
from SimPEG import Mesh, Utils
X, Y = Utils.exampleLomGird([3,3],'rotate')
M = Mesh.LogicallyOrthogonalMesh([X, Y])
M.plotGrid(showIt=True)
"""
__metaclass__ = utils.Save.Savable
__metaclass__ = Utils.Save.Savable
_meshType = 'LOM'
@@ -40,7 +45,7 @@ class LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
# Save nodes to private variable _gridN as vectors
self._gridN = np.ones((nodes[0].size, self.dim))
for i, node_i in enumerate(nodes):
self._gridN[:, i] = utils.mkvc(node_i.astype(float))
self._gridN[:, i] = Utils.mkvc(node_i.astype(float))
def gridCC():
doc = "Cell-centered grid."
@@ -71,10 +76,10 @@ class LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
if self._gridFx is None:
N = self.r(self.gridN, 'N', 'N', 'M')
if self.dim == 2:
XY = [utils.mkvc(0.5 * (n[:, :-1] + n[:, 1:])) for n in N]
XY = [Utils.mkvc(0.5 * (n[:, :-1] + n[:, 1:])) for n in N]
self._gridFx = np.c_[XY[0], XY[1]]
elif self.dim == 3:
XYZ = [utils.mkvc(0.25 * (n[:, :-1, :-1] + n[:, :-1, 1:] + n[:, 1:, :-1] + n[:, 1:, 1:])) for n in N]
XYZ = [Utils.mkvc(0.25 * (n[:, :-1, :-1] + n[:, :-1, 1:] + n[:, 1:, :-1] + n[:, 1:, 1:])) for n in N]
self._gridFx = np.c_[XYZ[0], XYZ[1], XYZ[2]]
return self._gridFx
return locals()
@@ -88,10 +93,10 @@ class LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
if self._gridFy is None:
N = self.r(self.gridN, 'N', 'N', 'M')
if self.dim == 2:
XY = [utils.mkvc(0.5 * (n[:-1, :] + n[1:, :])) for n in N]
XY = [Utils.mkvc(0.5 * (n[:-1, :] + n[1:, :])) for n in N]
self._gridFy = np.c_[XY[0], XY[1]]
elif self.dim == 3:
XYZ = [utils.mkvc(0.25 * (n[:-1, :, :-1] + n[:-1, :, 1:] + n[1:, :, :-1] + n[1:, :, 1:])) for n in N]
XYZ = [Utils.mkvc(0.25 * (n[:-1, :, :-1] + n[:-1, :, 1:] + n[1:, :, :-1] + n[1:, :, 1:])) for n in N]
self._gridFy = np.c_[XYZ[0], XYZ[1], XYZ[2]]
return self._gridFy
return locals()
@@ -104,7 +109,7 @@ class LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
def fget(self):
if self._gridFz is None and self.dim == 3:
N = self.r(self.gridN, 'N', 'N', 'M')
XYZ = [utils.mkvc(0.25 * (n[:-1, :-1, :] + n[:-1, 1:, :] + n[1:, :-1, :] + n[1:, 1:, :])) for n in N]
XYZ = [Utils.mkvc(0.25 * (n[:-1, :-1, :] + n[:-1, 1:, :] + n[1:, :-1, :] + n[1:, 1:, :])) for n in N]
self._gridFz = np.c_[XYZ[0], XYZ[1], XYZ[2]]
return self._gridFz
return locals()
@@ -118,10 +123,10 @@ class LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
if self._gridEx is None:
N = self.r(self.gridN, 'N', 'N', 'M')
if self.dim == 2:
XY = [utils.mkvc(0.5 * (n[:-1, :] + n[1:, :])) for n in N]
XY = [Utils.mkvc(0.5 * (n[:-1, :] + n[1:, :])) for n in N]
self._gridEx = np.c_[XY[0], XY[1]]
elif self.dim == 3:
XYZ = [utils.mkvc(0.5 * (n[:-1, :, :] + n[1:, :, :])) for n in N]
XYZ = [Utils.mkvc(0.5 * (n[:-1, :, :] + n[1:, :, :])) for n in N]
self._gridEx = np.c_[XYZ[0], XYZ[1], XYZ[2]]
return self._gridEx
return locals()
@@ -135,10 +140,10 @@ class LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
if self._gridEy is None:
N = self.r(self.gridN, 'N', 'N', 'M')
if self.dim == 2:
XY = [utils.mkvc(0.5 * (n[:, :-1] + n[:, 1:])) for n in N]
XY = [Utils.mkvc(0.5 * (n[:, :-1] + n[:, 1:])) for n in N]
self._gridEy = np.c_[XY[0], XY[1]]
elif self.dim == 3:
XYZ = [utils.mkvc(0.5 * (n[:, :-1, :] + n[:, 1:, :])) for n in N]
XYZ = [Utils.mkvc(0.5 * (n[:, :-1, :] + n[:, 1:, :])) for n in N]
self._gridEy = np.c_[XYZ[0], XYZ[1], XYZ[2]]
return self._gridEy
return locals()
@@ -151,7 +156,7 @@ class LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
def fget(self):
if self._gridEz is None and self.dim == 3:
N = self.r(self.gridN, 'N', 'N', 'M')
XYZ = [utils.mkvc(0.5 * (n[:, :, :-1] + n[:, :, 1:])) for n in N]
XYZ = [Utils.mkvc(0.5 * (n[:, :, :-1] + n[:, :, 1:])) for n in N]
self._gridEz = np.c_[XYZ[0], XYZ[1], XYZ[2]]
return self._gridEz
return locals()
@@ -194,25 +199,25 @@ class LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
def fget(self):
if(self._vol is None):
if self.dim == 2:
A, B, C, D = utils.indexCube('ABCD', self.n+1)
normal, area = utils.faceInfo(np.c_[self.gridN, np.zeros((self.nN, 1))], A, B, C, D)
A, B, C, D = Utils.indexCube('ABCD', self.nCv+1)
normal, area = Utils.faceInfo(np.c_[self.gridN, np.zeros((self.nN, 1))], A, B, C, D)
self._vol = area
elif self.dim == 3:
# Each polyhedron can be decomposed into 5 tetrahedrons
# However, this presents a choice so we may as well divide in two ways and average.
A, B, C, D, E, F, G, H = utils.indexCube('ABCDEFGH', self.n+1)
A, B, C, D, E, F, G, H = Utils.indexCube('ABCDEFGH', self.nCv+1)
vol1 = (utils.volTetra(self.gridN, A, B, D, E) + # cutted edge top
utils.volTetra(self.gridN, B, E, F, G) + # cutted edge top
utils.volTetra(self.gridN, B, D, E, G) + # middle
utils.volTetra(self.gridN, B, C, D, G) + # cutted edge bottom
utils.volTetra(self.gridN, D, E, G, H)) # cutted edge bottom
vol1 = (Utils.volTetra(self.gridN, A, B, D, E) + # cutted edge top
Utils.volTetra(self.gridN, B, E, F, G) + # cutted edge top
Utils.volTetra(self.gridN, B, D, E, G) + # middle
Utils.volTetra(self.gridN, B, C, D, G) + # cutted edge bottom
Utils.volTetra(self.gridN, D, E, G, H)) # cutted edge bottom
vol2 = (utils.volTetra(self.gridN, A, F, B, C) + # cutted edge top
utils.volTetra(self.gridN, A, E, F, H) + # cutted edge top
utils.volTetra(self.gridN, A, H, F, C) + # middle
utils.volTetra(self.gridN, C, H, D, A) + # cutted edge bottom
utils.volTetra(self.gridN, C, G, H, F)) # cutted edge bottom
vol2 = (Utils.volTetra(self.gridN, A, F, B, C) + # cutted edge top
Utils.volTetra(self.gridN, A, E, F, H) + # cutted edge top
Utils.volTetra(self.gridN, A, H, F, C) + # middle
Utils.volTetra(self.gridN, C, H, D, A) + # cutted edge bottom
Utils.volTetra(self.gridN, C, G, H, F)) # cutted edge bottom
self._vol = (vol1 + vol2)/2
return self._vol
@@ -228,30 +233,30 @@ class LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
# Compute areas of cell faces
if(self.dim == 2):
xy = self.gridN
A, B = utils.indexCube('AB', self.n+1, np.array([self.nNx, self.nCy]))
A, B = Utils.indexCube('AB', self.nCv+1, np.array([self.nNx, self.nCy]))
edge1 = xy[B, :] - xy[A, :]
normal1 = np.c_[edge1[:, 1], -edge1[:, 0]]
area1 = length2D(edge1)
A, D = utils.indexCube('AD', self.n+1, np.array([self.nCx, self.nNy]))
A, D = Utils.indexCube('AD', self.nCv+1, np.array([self.nCx, self.nNy]))
# Note that we are doing A-D to make sure the normal points the right way.
# Think about it. Look at the picture. Normal points towards C iff you do this.
edge2 = xy[A, :] - xy[D, :]
normal2 = np.c_[edge2[:, 1], -edge2[:, 0]]
area2 = length2D(edge2)
self._area = np.r_[utils.mkvc(area1), utils.mkvc(area2)]
self._area = np.r_[Utils.mkvc(area1), Utils.mkvc(area2)]
self._normals = [normalize2D(normal1), normalize2D(normal2)]
elif(self.dim == 3):
A, E, F, B = utils.indexCube('AEFB', self.n+1, np.array([self.nNx, self.nCy, self.nCz]))
normal1, area1 = utils.faceInfo(self.gridN, A, E, F, B, average=False, normalizeNormals=False)
A, E, F, B = Utils.indexCube('AEFB', self.nCv+1, np.array([self.nNx, self.nCy, self.nCz]))
normal1, area1 = Utils.faceInfo(self.gridN, A, E, F, B, average=False, normalizeNormals=False)
A, D, H, E = utils.indexCube('ADHE', self.n+1, np.array([self.nCx, self.nNy, self.nCz]))
normal2, area2 = utils.faceInfo(self.gridN, A, D, H, E, average=False, normalizeNormals=False)
A, D, H, E = Utils.indexCube('ADHE', self.nCv+1, np.array([self.nCx, self.nNy, self.nCz]))
normal2, area2 = Utils.faceInfo(self.gridN, A, D, H, E, average=False, normalizeNormals=False)
A, B, C, D = utils.indexCube('ABCD', self.n+1, np.array([self.nCx, self.nCy, self.nNz]))
normal3, area3 = utils.faceInfo(self.gridN, A, B, C, D, average=False, normalizeNormals=False)
A, B, C, D = Utils.indexCube('ABCD', self.nCv+1, np.array([self.nCx, self.nCy, self.nNz]))
normal3, area3 = Utils.faceInfo(self.gridN, A, B, C, D, average=False, normalizeNormals=False)
self._area = np.r_[utils.mkvc(area1), utils.mkvc(area2), utils.mkvc(area3)]
self._area = np.r_[Utils.mkvc(area1), Utils.mkvc(area2), Utils.mkvc(area3)]
self._normals = [normal1, normal2, normal3]
return self._area
return locals()
@@ -291,21 +296,21 @@ class LogicallyOrthogonalMesh(BaseMesh, DiffOperators, InnerProducts, LomView):
if(self._edge is None or self._tangents is None):
if(self.dim == 2):
xy = self.gridN
A, D = utils.indexCube('AD', self.n+1, np.array([self.nCx, self.nNy]))
A, D = Utils.indexCube('AD', self.nCv+1, np.array([self.nCx, self.nNy]))
edge1 = xy[D, :] - xy[A, :]
A, B = utils.indexCube('AB', self.n+1, np.array([self.nNx, self.nCy]))
A, B = Utils.indexCube('AB', self.nCv+1, np.array([self.nNx, self.nCy]))
edge2 = xy[B, :] - xy[A, :]
self._edge = np.r_[utils.mkvc(length2D(edge1)), utils.mkvc(length2D(edge2))]
self._edge = np.r_[Utils.mkvc(length2D(edge1)), Utils.mkvc(length2D(edge2))]
self._tangents = np.r_[edge1, edge2]/np.c_[self._edge, self._edge]
elif(self.dim == 3):
xyz = self.gridN
A, D = utils.indexCube('AD', self.n+1, np.array([self.nCx, self.nNy, self.nNz]))
A, D = Utils.indexCube('AD', self.nCv+1, np.array([self.nCx, self.nNy, self.nNz]))
edge1 = xyz[D, :] - xyz[A, :]
A, B = utils.indexCube('AB', self.n+1, np.array([self.nNx, self.nCy, self.nNz]))
A, B = Utils.indexCube('AB', self.nCv+1, np.array([self.nNx, self.nCy, self.nNz]))
edge2 = xyz[B, :] - xyz[A, :]
A, E = utils.indexCube('AE', self.n+1, np.array([self.nNx, self.nNy, self.nCz]))
A, E = Utils.indexCube('AE', self.nCv+1, np.array([self.nNx, self.nNy, self.nCz]))
edge3 = xyz[E, :] - xyz[A, :]
self._edge = np.r_[utils.mkvc(length3D(edge1)), utils.mkvc(length3D(edge2)), utils.mkvc(length3D(edge3))]
self._edge = np.r_[Utils.mkvc(length3D(edge1)), Utils.mkvc(length3D(edge2)), Utils.mkvc(length3D(edge3))]
self._tangents = np.r_[edge1, edge2, edge3]/np.c_[self._edge, self._edge, self._edge]
return self._edge
return locals()
@@ -331,10 +336,10 @@ if __name__ == '__main__':
h3 = np.cumsum(np.r_[0, np.ones(nc)/(nc)])
dee3 = True
if dee3:
X, Y, Z = utils.ndgrid(h1, h2, h3, vector=False)
X, Y, Z = Utils.ndgrid(h1, h2, h3, vector=False)
M = LogicallyOrthogonalMesh([X, Y, Z])
else:
X, Y = utils.ndgrid(h1, h2, vector=False)
X, Y = Utils.ndgrid(h1, h2, vector=False)
M = LogicallyOrthogonalMesh([X, Y])
print M.r(M.normals, 'F', 'Fx', 'V')
SimPEG/mesh/LomView.py → SimPEG/Mesh/LomView.py
+13 -4
View File
@@ -2,7 +2,7 @@ import numpy as np
import matplotlib.pyplot as plt
import matplotlib
from mpl_toolkits.mplot3d import Axes3D
from SimPEG.utils import mkvc
from SimPEG.Utils import mkvc
class LomView(object):
@@ -15,10 +15,18 @@ class LomView(object):
def __init__(self):
pass
def plotGrid(self, length=0.05):
def plotGrid(self, length=0.05, showIt=False):
"""Plot the nodal, cell-centered and staggered grids for 1,2 and 3 dimensions.
.. plot:: examples/mesh/plot_LogicallyOrthogonalMesh.py
.. plot::
:include-source:
from SimPEG import Mesh, Utils
X, Y = Utils.exampleLomGird([3,3],'rotate')
M = Mesh.LogicallyOrthogonalMesh([X, Y])
M.plotGrid(showIt=True)
"""
NN = self.r(self.gridN, 'N', 'N', 'M')
if self.dim == 2:
@@ -92,4 +100,5 @@ class LomView(object):
ax.hold(False)
ax.set_xlabel('x1')
ax.set_ylabel('x2')
fig.show()
if showIt: plt.show()
SimPEG/mesh/TensorMesh.py → SimPEG/Mesh/TensorMesh.py
+34 -34
View File
@@ -1,4 +1,4 @@
from SimPEG import utils, np, sp
from SimPEG import Utils, np, sp
from BaseMesh import BaseMesh
from TensorView import TensorView
from DiffOperators import DiffOperators
@@ -17,23 +17,23 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
hy = np.array([1,2])
hz = np.array([1,1,1,1])
mesh = TensorMesh([hx, hy, hz])
mesh = Mesh.TensorMesh([hx, hy, hz])
Example of a padded tensor mesh:
.. plot::
from SimPEG import mesh, utils
M = mesh.TensorMesh(utils.meshTensors(((10,10),(40,10),(10,10)), ((10,10),(20,10),(0,0))))
from SimPEG import Mesh, Utils
M = Mesh.TensorMesh(Utils.meshTensors(((10,10),(40,10),(10,10)), ((10,10),(20,10),(0,0))))
M.plotGrid()
For a quick tensor mesh on a (10x12x15) unit cube::
mesh = TensorMesh([10, 12, 15])
mesh = Mesh.TensorMesh([10, 12, 15])
"""
__metaclass__ = utils.Save.Savable
__metaclass__ = Utils.Save.Savable
_meshType = 'TENSOR'
@@ -52,7 +52,7 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
assert len(h) == len(self.x0), "Dimension mismatch. x0 != len(h)"
# Ensure h contains 1D vectors
self._h = [utils.mkvc(x.astype(float)) for x in h]
self._h = [Utils.mkvc(x.astype(float)) for x in h]
def __str__(self):
outStr = ' ---- {0:d}-D TensorMesh ---- '.format(self.dim)
@@ -170,7 +170,7 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
def fget(self):
if self._gridCC is None:
self._gridCC = utils.ndgrid(self.getTensor('CC'))
self._gridCC = Utils.ndgrid(self.getTensor('CC'))
return self._gridCC
return locals()
_gridCC = None # Store grid by default
@@ -181,7 +181,7 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
def fget(self):
if self._gridN is None:
self._gridN = utils.ndgrid(self.getTensor('N'))
self._gridN = Utils.ndgrid(self.getTensor('N'))
return self._gridN
return locals()
_gridN = None # Store grid by default
@@ -192,7 +192,7 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
def fget(self):
if self._gridFx is None:
self._gridFx = utils.ndgrid(self.getTensor('Fx'))
self._gridFx = Utils.ndgrid(self.getTensor('Fx'))
return self._gridFx
return locals()
_gridFx = None # Store grid by default
@@ -203,7 +203,7 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
def fget(self):
if self._gridFy is None and self.dim > 1:
self._gridFy = utils.ndgrid(self.getTensor('Fy'))
self._gridFy = Utils.ndgrid(self.getTensor('Fy'))
return self._gridFy
return locals()
_gridFy = None # Store grid by default
@@ -214,7 +214,7 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
def fget(self):
if self._gridFz is None and self.dim > 2:
self._gridFz = utils.ndgrid(self.getTensor('Fz'))
self._gridFz = Utils.ndgrid(self.getTensor('Fz'))
return self._gridFz
return locals()
_gridFz = None # Store grid by default
@@ -225,7 +225,7 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
def fget(self):
if self._gridEx is None:
self._gridEx = utils.ndgrid(self.getTensor('Ex'))
self._gridEx = Utils.ndgrid(self.getTensor('Ex'))
return self._gridEx
return locals()
_gridEx = None # Store grid by default
@@ -236,7 +236,7 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
def fget(self):
if self._gridEy is None and self.dim > 1:
self._gridEy = utils.ndgrid(self.getTensor('Ey'))
self._gridEy = Utils.ndgrid(self.getTensor('Ey'))
return self._gridEy
return locals()
_gridEy = None # Store grid by default
@@ -247,7 +247,7 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
def fget(self):
if self._gridEz is None and self.dim > 2:
self._gridEz = utils.ndgrid(self.getTensor('Ez'))
self._gridEz = Utils.ndgrid(self.getTensor('Ez'))
return self._gridEz
return locals()
_gridEz = None # Store grid by default
@@ -262,13 +262,13 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
vh = self.h
# Compute cell volumes
if(self.dim == 1):
self._vol = utils.mkvc(vh[0])
self._vol = Utils.mkvc(vh[0])
elif(self.dim == 2):
# Cell sizes in each direction
self._vol = utils.mkvc(np.outer(vh[0], vh[1]))
self._vol = Utils.mkvc(np.outer(vh[0], vh[1]))
elif(self.dim == 3):
# Cell sizes in each direction
self._vol = utils.mkvc(np.outer(utils.mkvc(np.outer(vh[0], vh[1])), vh[2]))
self._vol = Utils.mkvc(np.outer(Utils.mkvc(np.outer(vh[0], vh[1])), vh[2]))
return self._vol
return locals()
_vol = None
@@ -282,19 +282,19 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
# Ensure that we are working with column vectors
vh = self.h
# The number of cell centers in each direction
n = self.n
n = self.nCv
# Compute areas of cell faces
if(self.dim == 1):
self._area = np.ones(n[0]+1)
elif(self.dim == 2):
area1 = np.outer(np.ones(n[0]+1), vh[1])
area2 = np.outer(vh[0], np.ones(n[1]+1))
self._area = np.r_[utils.mkvc(area1), utils.mkvc(area2)]
self._area = np.r_[Utils.mkvc(area1), Utils.mkvc(area2)]
elif(self.dim == 3):
area1 = np.outer(np.ones(n[0]+1), utils.mkvc(np.outer(vh[1], vh[2])))
area2 = np.outer(vh[0], utils.mkvc(np.outer(np.ones(n[1]+1), vh[2])))
area3 = np.outer(vh[0], utils.mkvc(np.outer(vh[1], np.ones(n[2]+1))))
self._area = np.r_[utils.mkvc(area1), utils.mkvc(area2), utils.mkvc(area3)]
area1 = np.outer(np.ones(n[0]+1), Utils.mkvc(np.outer(vh[1], vh[2])))
area2 = np.outer(vh[0], Utils.mkvc(np.outer(np.ones(n[1]+1), vh[2])))
area3 = np.outer(vh[0], Utils.mkvc(np.outer(vh[1], np.ones(n[2]+1))))
self._area = np.r_[Utils.mkvc(area1), Utils.mkvc(area2), Utils.mkvc(area3)]
return self._area
return locals()
_area = None
@@ -308,19 +308,19 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
# Ensure that we are working with column vectors
vh = self.h
# The number of cell centers in each direction
n = self.n
n = self.nCv
# Compute edge lengths
if(self.dim == 1):
self._edge = utils.mkvc(vh[0])
self._edge = Utils.mkvc(vh[0])
elif(self.dim == 2):
l1 = np.outer(vh[0], np.ones(n[1]+1))
l2 = np.outer(np.ones(n[0]+1), vh[1])
self._edge = np.r_[utils.mkvc(l1), utils.mkvc(l2)]
self._edge = np.r_[Utils.mkvc(l1), Utils.mkvc(l2)]
elif(self.dim == 3):
l1 = np.outer(vh[0], utils.mkvc(np.outer(np.ones(n[1]+1), np.ones(n[2]+1))))
l2 = np.outer(np.ones(n[0]+1), utils.mkvc(np.outer(vh[1], np.ones(n[2]+1))))
l3 = np.outer(np.ones(n[0]+1), utils.mkvc(np.outer(np.ones(n[1]+1), vh[2])))
self._edge = np.r_[utils.mkvc(l1), utils.mkvc(l2), utils.mkvc(l3)]
l1 = np.outer(vh[0], Utils.mkvc(np.outer(np.ones(n[1]+1), np.ones(n[2]+1))))
l2 = np.outer(np.ones(n[0]+1), Utils.mkvc(np.outer(vh[1], np.ones(n[2]+1))))
l3 = np.outer(np.ones(n[0]+1), Utils.mkvc(np.outer(np.ones(n[1]+1), vh[2])))
self._edge = np.r_[Utils.mkvc(l1), Utils.mkvc(l2), Utils.mkvc(l3)]
return self._edge
return locals()
_edge = None
@@ -410,11 +410,11 @@ class TensorMesh(BaseMesh, TensorView, DiffOperators, InnerProducts):
ind = 0 if 'x' in locType else 1 if 'y' in locType else 2 if 'z' in locType else -1
if locType in ['Fx','Fy','Fz','Ex','Ey','Ez'] and self.dim >= ind:
nF_nE = self.nFv if 'F' in locType else self.nEv
components = [utils.spzeros(loc.shape[0], n) for n in nF_nE]
components[ind] = utils.interpmat(loc, *self.getTensor(locType))
components = [Utils.spzeros(loc.shape[0], n) for n in nF_nE]
components[ind] = Utils.interpmat(loc, *self.getTensor(locType))
Q = sp.hstack(components)
elif locType in ['CC', 'N']:
Q = utils.interpmat(loc, *self.getTensor(locType))
Q = Utils.interpmat(loc, *self.getTensor(locType))
else:
raise NotImplementedError('getInterpolationMat: locType=='+locType+' and mesh.dim=='+str(self.dim))
return Q
SimPEG/mesh/TensorView.py → SimPEG/Mesh/TensorView.py
+36 -11
View File
@@ -2,7 +2,7 @@ import numpy as np
import matplotlib.pyplot as plt
import matplotlib
from mpl_toolkits.mplot3d import Axes3D
from SimPEG.utils import mkvc, animate
from SimPEG.Utils import mkvc, animate
class TensorView(object):
@@ -34,11 +34,22 @@ class TensorView(object):
:param str annotationColor: color of annotation, e.g. 'w', 'k', 'b'
:param bool showIt: call plt.show()
.. plot:: examples/mesh/plot_image_2D.py
:include-source:
.. plot::
:include-source:
from SimPEG import Mesh, np
M = Mesh.TensorMesh([20, 20])
I = np.sin(M.gridCC[:,0]*2*np.pi)*np.sin(M.gridCC[:,1]*2*np.pi)
M.plotImage(I, showIt=True)
.. plot::
:include-source:
from SimPEG import Mesh, np
M = Mesh.TensorMesh([20,20,20])
I = np.sin(M.gridCC[:,0]*2*np.pi)*np.sin(M.gridCC[:,1]*2*np.pi)*np.sin(M.gridCC[:,2]*2*np.pi)
M.plotImage(I, annotationColor='k', showIt=True)
.. plot:: examples/mesh/plot_image_3D.py
:include-source:
"""
assert type(I) == np.ndarray, "I must be a numpy array"
assert type(numbering) == bool, "numbering must be a bool"
@@ -124,9 +135,9 @@ class TensorView(object):
ax.axis('tight')
elif self.dim == 2:
if imageType == 'CC':
C = I[:].reshape(self.n, order='F')
C = I[:].reshape(self.nCv, order='F')
elif imageType == 'N':
C = I[:].reshape(self.n+1, order='F')
C = I[:].reshape(self.nNv, order='F')
C = 0.25*(C[:-1, :-1] + C[1:, :-1] + C[:-1, 1:] + C[1:, 1:])
elif imageType == 'Fx':
C = I[:].reshape(self.nFx, order='F')
@@ -153,9 +164,9 @@ class TensorView(object):
# get copy of image and average to cell-centres is necessary
if imageType == 'CC':
Ic = I[:].reshape(self.n, order='F')
Ic = I[:].reshape(self.nCv, order='F')
elif imageType == 'N':
Ic = I[:].reshape(self.n+1, order='F')
Ic = I[:].reshape(self.nNv, order='F')
Ic = .125*(Ic[:-1,:-1,:-1]+Ic[1:,:-1,:-1] + Ic[:-1,1:,:-1]+ Ic[1:,1:,:-1]+ Ic[:-1,:-1,1:]+Ic[1:,:-1,1:] + Ic[:-1,1:,1:]+ Ic[1:,1:,1:] )
elif imageType == 'Fx':
Ic = I[:].reshape(self.nFx, order='F')
@@ -237,11 +248,25 @@ class TensorView(object):
:param bool lines: plot lines connecting nodes
:param bool showIt: call plt.show()
.. plot:: examples/mesh/plot_grid_2D.py
.. plot::
:include-source:
.. plot:: examples/mesh/plot_grid_3D.py
from SimPEG import Mesh, np
h1 = np.linspace(.1,.5,3)
h2 = np.linspace(.1,.5,5)
mesh = Mesh.TensorMesh([h1, h2])
mesh.plotGrid(nodes=True, faces=True, centers=True, lines=True, showIt=True)
.. plot::
:include-source:
from SimPEG import Mesh, np
h1 = np.linspace(.1,.5,3)
h2 = np.linspace(.1,.5,5)
h3 = np.linspace(.1,.5,3)
mesh = Mesh.TensorMesh([h1,h2,h3])
mesh.plotGrid(nodes=True, faces=True, centers=True, lines=True, showIt=True)
"""
if self.dim == 1:
fig = plt.figure(1)
SimPEG/mesh/__init__.py → SimPEG/Mesh/__init__.py
View File
File renamed without changes.
SimPEG/Model.py
+129
View File
@@ -0,0 +1,129 @@
import Utils, Parameters, numpy as np, scipy.sparse as sp
class BaseModel(object):
"""
SimPEG Model
"""
__metaclass__ = Utils.Save.Savable
counter = None #: A SimPEG.Utils.Counter object
mesh = None #: A SimPEG Mesh
def __init__(self, mesh):
self.mesh = mesh
def transform(self, m):
"""
:param numpy.array m: model
:rtype: numpy.array
:return: transformed model
The *transform* changes the model into the physical property.
"""
return m
def transformInverse(self, D):
"""
:param numpy.array D: physical property
:rtype: numpy.array
:return: model
The *transformInverse* changes the physical property into the model.
.. note:: The *transformInverse* may not be easy to create in general.
"""
raise NotImplementedError('The transformInverse is not implemented.')
def transformDeriv(self, m):
"""
:param numpy.array m: model
:rtype: scipy.csr_matrix
:return: derivative of transformed model
The *transform* changes the model into the physical property.
The *transformDeriv* provides the derivative of the *transform*.
"""
return sp.identity(m.size)
@property
def nP(self):
"""Number of parameters in the model."""
return self.mesh.nC
def example(self, modelType=None):
return np.random.rand(self.mesh.nC)
class LogModel(BaseModel):
"""SimPEG LogModel"""
def __init__(self, mesh, **kwargs):
BaseModel.__init__(self, mesh, **kwargs)
def transform(self, m):
"""
:param numpy.array m: model
:rtype: numpy.array
:return: transformed model
The *transform* changes the model into the physical property.
A common example of this is to invert for electrical conductivity
in log space. In this case, your model will be log(sigma) and to
get back to sigma, you can take the exponential:
.. math::
m = \log{\sigma}
\exp{m} = \exp{\log{\sigma}} = \sigma
"""
return np.exp(Utils.mkvc(m))
def transformInverse(self, D):
"""
:param numpy.array D: physical property
:rtype: numpy.array
:return: model
The *transformInverse* changes the physical property into the model.
.. math::
m = \log{\sigma}
"""
return np.log(Utils.mkvc(D))
def transformDeriv(self, m):
"""
:param numpy.array m: model
:rtype: scipy.csr_matrix
:return: derivative of transformed model
The *transform* changes the model into the physical property.
The *transformDeriv* provides the derivative of the *transform*.
If the model *transform* is:
.. math::
m = \log{\sigma}
\exp{m} = \exp{\log{\sigma}} = \sigma
Then the derivative is:
.. math::
\\frac{\partial \exp{m}}{\partial m} = \\text{sdiag}(\exp{m})
"""
return Utils.sdiag(np.exp(Utils.mkvc(m)))
SimPEG/ObjFunction.py
+215
View File
@@ -0,0 +1,215 @@
import Utils, Parameters, numpy as np, scipy.sparse as sp
class BaseObjFunction(object):
"""BaseObjFunction(data, reg, **kwargs)"""
__metaclass__ = Utils.Save.Savable
beta = Parameters.ParameterProperty('beta', default=1, doc='Regularization trade-off parameter')
debug = False #: Print debugging information
counter = None #: Set this to a SimPEG.Utils.Counter() if you want to count things
name = 'Base Objective Function' #: Name of the objective function
u_current = None #: The most current evaluated field
m_current = None #: The most current model
@property
def parent(self):
"""This is the parent of the objective function."""
return getattr(self,'_parent',None)
@parent.setter
def parent(self, p):
if getattr(self,'_parent',None) is not None:
print 'Objective function has switched to a new parent!'
self._parent = p
@property
def inv(self): return self.parent
@property
def objFunc(self): return self
@property
def opt(self): return getattr(self.parent,'opt',None)
@property
def prob(self): return self.data.prob
@property
def mesh(self): return self.data.prob.mesh
@property
def model(self): return self.data.prob.model
def __init__(self, data, reg, **kwargs):
Utils.setKwargs(self, **kwargs)
self.data = data
self.reg = reg
self.reg.parent = self
@Utils.callHooks('startup')
def startup(self, m0):
"""startup(m0)
Called when inversion is first starting.
"""
if self.debug: print 'Calling ObjFunction.startup'
if self.reg.mref is None:
print 'Regularization has not set mref. SimPEG will set it to m0.'
self.reg.mref = m0
self.phi_d = np.nan
self.phi_m = np.nan
self.m_current = m0
@Utils.timeIt
def evalFunction(self, m, return_g=True, return_H=True):
"""evalFunction(m, return_g=True, return_H=True)
"""
self.u_current = None
self.m_current = m
u = self.data.prob.field(m)
self.u_current = u
phi_d = self.dataObj(m, u=u)
phi_m = self.reg.modelObj(m)
self.dpred = self.data.dpred(m, u=u) # This is a cheap matrix vector calculation.
self.phi_d, self.phi_d_last = phi_d, self.phi_d
self.phi_m, self.phi_m_last = phi_m, self.phi_m
f = phi_d + self.beta * phi_m
out = (f,)
if return_g:
phi_dDeriv = self.dataObjDeriv(m, u=u)
phi_mDeriv = self.reg.modelObjDeriv(m)
g = phi_dDeriv + self.beta * phi_mDeriv
out += (g,)
if return_H:
def H_fun(v):
phi_d2Deriv = self.dataObj2Deriv(m, v, u=u)
phi_m2Deriv = self.reg.modelObj2Deriv()*v
return phi_d2Deriv + self.beta * phi_m2Deriv
operator = sp.linalg.LinearOperator( (m.size, m.size), H_fun, dtype=m.dtype )
out += (operator,)
return out if len(out) > 1 else out[0]
@Utils.timeIt
def dataObj(self, m, u=None):
"""dataObj(m, u=None)
:param numpy.array m: geophysical model
:param numpy.array u: fields
:rtype: float
:return: data misfit
The data misfit using an l_2 norm is:
.. math::
\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
"""
# TODO: ensure that this is a data is vector and Wd is a matrix.
R = self.data.residualWeighted(m, u=u)
return 0.5*np.vdot(R, R)
@Utils.timeIt
def dataObjDeriv(self, m, u=None):
"""dataObjDeriv(m, u=None)
:param numpy.array m: geophysical model
:param numpy.array u: fields
:rtype: numpy.array
:return: data misfit derivative
The data misfit using an l_2 norm is:
.. math::
\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
If the field, u, is provided, the calculation of the data is fast:
.. math::
\mathbf{d}_\\text{pred} = \mathbf{Pu(m)}
\mathbf{R} = \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs})
Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
The derivative of this, with respect to the model, is:
.. math::
\\frac{\partial \mu_\\text{data}}{\partial \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ R}
"""
if u is None: u = self.data.prob.field(m)
R = self.data.residualWeighted(m, u=u)
dmisfit = self.data.prob.Jt(m, self.data.Wd * R, u=u)
return dmisfit
@Utils.timeIt
def dataObj2Deriv(self, m, v, u=None):
"""dataObj2Deriv(m, v, u=None)
:param numpy.array m: geophysical model
:param numpy.array v: vector to multiply
:param numpy.array u: fields
:rtype: numpy.array
:return: data misfit derivative
The data misfit using an l_2 norm is:
.. math::
\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
If the field, u, is provided, the calculation of the data is fast:
.. math::
\mathbf{d}_\\text{pred} = \mathbf{Pu(m)}
\mathbf{R} = \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs})
Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
The derivative of this, with respect to the model, is:
.. math::
\\frac{\partial \mu_\\text{data}}{\partial \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ R}
\\frac{\partial^2 \mu_\\text{data}}{\partial^2 \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ W J}
"""
if u is None: u = self.data.prob.field(m)
R = self.data.residualWeighted(m, u=u)
# TODO: abstract to different norms a little cleaner.
# \/ it goes here. in l2 it is the identity.
dmisfit = self.data.prob.Jt_approx(m, self.data.Wd * self.data.Wd * self.data.prob.J_approx(m, v, u=u), u=u)
return dmisfit
SimPEG/inverse/Optimize.py → SimPEG/Optimization.py
+62 -71
View File
@@ -1,5 +1,5 @@
from SimPEG import Solver, utils, sp, np
import matplotlib.pyplot as plt
import Utils, numpy as np, scipy.sparse as sp
from Solver import Solver
norm = np.linalg.norm
@@ -10,11 +10,11 @@ class StoppingCriteria(object):
"""docstring for StoppingCriteria"""
iteration = { "str": "%d : maxIter = %3d <= iter = %3d",
"left": lambda M: M.maxIter, "right": lambda M: M._iter,
"left": lambda M: M.maxIter, "right": lambda M: M.iter,
"stopType": "critical"}
iterationLS = { "str": "%d : maxIterLS = %3d <= iterLS = %3d",
"left": lambda M: M.maxIterLS, "right": lambda M: M._iterLS,
"left": lambda M: M.maxIterLS, "right": lambda M: M.iterLS,
"stopType": "critical"}
armijoGoldstein = { "str": "%d : ft = %1.4e <= alp*descent = %1.4e",
@@ -22,11 +22,11 @@ class StoppingCriteria(object):
"stopType": "optimal"}
tolerance_f = { "str": "%d : |fc-fOld| = %1.4e <= tolF*(1+|f0|) = %1.4e",
"left": lambda M: 1 if M._iter==0 else abs(M.f-M.f_last), "right": lambda M: 0 if M._iter==0 else M.tolF*(1+abs(M.f0)),
"left": lambda M: 1 if M.iter==0 else abs(M.f-M.f_last), "right": lambda M: 0 if M.iter==0 else M.tolF*(1+abs(M.f0)),
"stopType": "optimal"}
moving_x = { "str": "%d : |xc-x_last| = %1.4e <= tolX*(1+|x0|) = %1.4e",
"left": lambda M: 1 if M._iter==0 else norm(M.xc-M.x_last), "right": lambda M: 0 if M._iter==0 else M.tolX*(1+norm(M.x0)),
"left": lambda M: 1 if M.iter==0 else norm(M.xc-M.x_last), "right": lambda M: 0 if M.iter==0 else M.tolX*(1+norm(M.x0)),
"stopType": "optimal"}
tolerance_g = { "str": "%d : |proj(x-g)-x| = %1.4e <= tolG = %1.4e",
@@ -57,12 +57,12 @@ class StoppingCriteria(object):
class IterationPrinters(object):
"""docstring for IterationPrinters"""
iteration = {"title": "#", "value": lambda M: M._iter, "width": 5, "format": "%3d"}
iteration = {"title": "#", "value": lambda M: M.iter, "width": 5, "format": "%3d"}
f = {"title": "f", "value": lambda M: M.f, "width": 10, "format": "%1.2e"}
norm_g = {"title": "|proj(x-g)-x|", "value": lambda M: norm(M.projection(M.xc - M.g) - M.xc), "width": 15, "format": "%1.2e"}
totalLS = {"title": "LS", "value": lambda M: M._iterLS, "width": 5, "format": "%d"}
totalLS = {"title": "LS", "value": lambda M: M.iterLS, "width": 5, "format": "%d"}
iterationLS = {"title": "#", "value": lambda M: (M._iter, M._iterLS), "width": 5, "format": "%3d.%d"}
iterationLS = {"title": "#", "value": lambda M: (M.iter, M.iterLS), "width": 5, "format": "%3d.%d"}
LS_ft = {"title": "ft", "value": lambda M: M._LS_ft, "width": 10, "format": "%1.2e"}
LS_t = {"title": "t", "value": lambda M: M._LS_t, "width": 10, "format": "%0.5f"}
LS_armijoGoldstein = {"title": "f + alp*g.T*p", "value": lambda M: M.f + M.LSreduction*M._LS_descent, "width": 16, "format": "%1.2e"}
@@ -72,9 +72,9 @@ class IterationPrinters(object):
bSet = {"title": "bSet", "value": lambda M: np.sum(M.bindingSet(M.xc)), "width": 8, "format": "%d"}
comment = {"title": "Comment", "value": lambda M: M.comment, "width": 12, "format": "%s"}
beta = {"title": "beta", "value": lambda M: M.parent._beta, "width": 10, "format": "%1.2e"}
phi_d = {"title": "phi_d", "value": lambda M: M.parent.phi_d, "width": 10, "format": "%1.2e"}
phi_m = {"title": "phi_m", "value": lambda M: M.parent.phi_m, "width": 10, "format": "%1.2e"}
beta = {"title": "beta", "value": lambda M: M.parent.objFunc.beta, "width": 10, "format": "%1.2e"}
phi_d = {"title": "phi_d", "value": lambda M: M.parent.objFunc.phi_d, "width": 10, "format": "%1.2e"}
phi_m = {"title": "phi_m", "value": lambda M: M.parent.objFunc.phi_m, "width": 10, "format": "%1.2e"}
class Minimize(object):
@@ -82,7 +82,7 @@ class Minimize(object):
Minimize is a general class for derivative based optimization.
"""
__metaclass__ = utils.Save.Savable
__metaclass__ = Utils.Save.Savable
name = "General Optimization Algorithm" #: The name of the optimization algorithm
@@ -100,7 +100,8 @@ class Minimize(object):
debugLS = False #: Print debugging information for the line-search
comment = '' #: Used by some functions to indicate what is going on in the algorithm
counter = None #: Set this to a SimPEG.utils.Counter() if you want to count things
counter = None #: Set this to a SimPEG.Utils.Counter() if you want to count things
parent = None #: This is the parent of the optimization routine.
def __init__(self, **kwargs):
self.stoppers = [StoppingCriteria.tolerance_f, StoppingCriteria.moving_x, StoppingCriteria.tolerance_g, StoppingCriteria.norm_g, StoppingCriteria.iteration]
@@ -109,9 +110,9 @@ class Minimize(object):
self.printers = [IterationPrinters.iteration, IterationPrinters.f, IterationPrinters.norm_g, IterationPrinters.totalLS]
self.printersLS = [IterationPrinters.iterationLS, IterationPrinters.LS_ft, IterationPrinters.LS_t, IterationPrinters.LS_armijoGoldstein]
utils.setKwargs(self, **kwargs)
Utils.setKwargs(self, **kwargs)
@utils.timeIt
@Utils.timeIt
def minimize(self, evalFunction, x0):
"""minimize(evalFunction, x0)
@@ -179,17 +180,7 @@ class Minimize(object):
return self.xc
@property
def parent(self):
"""
This is the parent of the optimization routine.
"""
return getattr(self, '_parent', None)
@parent.setter
def parent(self, value):
self._parent = value
@utils.callHooks('startup')
@Utils.callHooks('startup')
def startup(self, x0):
"""
**startup** is called at the start of any new minimize call.
@@ -198,15 +189,15 @@ class Minimize(object):
x0 = x0
xc = x0
_iter = _iterLS = 0
iter = iterLS = 0
:param numpy.ndarray x0: initial x
:rtype: None
:return: None
"""
self._iter = 0
self._iterLS = 0
self.iter = 0
self.iterLS = 0
x0 = self.projection(x0) # ensure that we start of feasible.
self.x0 = x0
@@ -214,8 +205,8 @@ class Minimize(object):
self.f_last = np.nan
self.x_last = x0
@utils.count
@utils.callHooks('doStartIteration')
@Utils.count
@Utils.callHooks('doStartIteration')
def doStartIteration(self):
"""doStartIteration()
@@ -237,9 +228,9 @@ class Minimize(object):
"""
pad = ' '*10 if inLS else ''
name = self.name if not inLS else self.nameLS
utils.printTitles(self, self.printers if not inLS else self.printersLS, name, pad)
Utils.printTitles(self, self.printers if not inLS else self.printersLS, name, pad)
@utils.callHooks('printIter')
@Utils.callHooks('printIter')
def printIter(self, inLS=False):
"""
**printIter** is called directly after function evaluations.
@@ -249,7 +240,7 @@ class Minimize(object):
"""
pad = ' '*10 if inLS else ''
utils.printLine(self, self.printers if not inLS else self.printersLS, pad=pad)
Utils.printLine(self, self.printers if not inLS else self.printersLS, pad=pad)
def printDone(self, inLS=False):
"""
@@ -262,10 +253,10 @@ class Minimize(object):
pad = ' '*10 if inLS else ''
stop, done = (' STOP! ', ' DONE! ') if not inLS else ('----------------', ' End Linesearch ')
stoppers = self.stoppers if not inLS else self.stoppersLS
utils.printStoppers(self, stoppers, pad='', stop=stop, done=done)
Utils.printStoppers(self, stoppers, pad='', stop=stop, done=done)
@utils.callHooks('finish')
@Utils.callHooks('finish')
def finish(self):
"""finish()
@@ -278,13 +269,13 @@ class Minimize(object):
pass
def stoppingCriteria(self, inLS=False):
if self._iter == 0:
if self.iter == 0:
self.f0 = self.f
self.g0 = self.g
return utils.checkStoppers(self, self.stoppers if not inLS else self.stoppersLS)
return Utils.checkStoppers(self, self.stoppers if not inLS else self.stoppersLS)
@utils.timeIt
@utils.callHooks('projection')
@Utils.timeIt
@Utils.callHooks('projection')
def projection(self, p):
"""projection(p)
@@ -298,7 +289,7 @@ class Minimize(object):
"""
return p
@utils.timeIt
@Utils.timeIt
def findSearchDirection(self):
"""findSearchDirection()
@@ -329,7 +320,7 @@ class Minimize(object):
"""
return -self.g
@utils.count
@Utils.count
def scaleSearchDirection(self, p):
"""scaleSearchDirection(p)
@@ -348,7 +339,7 @@ class Minimize(object):
nameLS = "Armijo linesearch" #: The line-search name
@utils.timeIt
@Utils.timeIt
def modifySearchDirection(self, p):
"""modifySearchDirection(p)
@@ -370,23 +361,23 @@ class Minimize(object):
"""
# Projected Armijo linesearch
self._LS_t = 1
self._iterLS = 0
while self._iterLS < self.maxIterLS:
self.iterLS = 0
while self.iterLS < self.maxIterLS:
self._LS_xt = self.projection(self.xc + self._LS_t*p)
self._LS_ft = self.evalFunction(self._LS_xt, return_g=False, return_H=False)
self._LS_descent = np.inner(self.g, self._LS_xt - self.xc) # this takes into account multiplying by t, but is important for projection.
if self.stoppingCriteria(inLS=True): break
self._iterLS += 1
self.iterLS += 1
self._LS_t = self.LSshorten*self._LS_t
if self.debugLS:
if self._iterLS == 1: self.printInit(inLS=True)
if self.iterLS == 1: self.printInit(inLS=True)
self.printIter(inLS=True)
if self.debugLS and self._iterLS > 0: self.printDone(inLS=True)
if self.debugLS and self.iterLS > 0: self.printDone(inLS=True)
return self._LS_xt, self._iterLS < self.maxIterLS
return self._LS_xt, self.iterLS < self.maxIterLS
@utils.count
@Utils.count
def modifySearchDirectionBreak(self, p):
"""modifySearchDirectionBreak(p)
@@ -408,8 +399,8 @@ class Minimize(object):
print 'The linesearch got broken. Boo.'
return p, False
@utils.count
@utils.callHooks('doEndIteration')
@Utils.count
@Utils.callHooks('doEndIteration')
def doEndIteration(self, xt):
"""doEndIteration(xt)
@@ -426,7 +417,7 @@ class Minimize(object):
# store old values
self.f_last = self.f
self.x_last, self.xc = self.xc, xt
self._iter += 1
self.iter += 1
if self.debug: self.printDone()
@@ -527,7 +518,7 @@ class ProjectedGradient(Minimize, Remember):
self.aSet_prev = self.activeSet(x0)
@utils.count
@Utils.count
def projection(self, x):
"""projection(x)
@@ -536,7 +527,7 @@ class ProjectedGradient(Minimize, Remember):
"""
return np.median(np.c_[self.lower,x,self.upper],axis=1)
@utils.count
@Utils.count
def activeSet(self, x):
"""activeSet(x)
@@ -545,7 +536,7 @@ class ProjectedGradient(Minimize, Remember):
"""
return np.logical_or(x == self.lower, x == self.upper)
@utils.count
@Utils.count
def inactiveSet(self, x):
"""inactiveSet(x)
@@ -554,7 +545,7 @@ class ProjectedGradient(Minimize, Remember):
"""
return np.logical_not(self.activeSet(x))
@utils.count
@Utils.count
def bindingSet(self, x):
"""bindingSet(x)
@@ -567,7 +558,7 @@ class ProjectedGradient(Minimize, Remember):
bind_low = np.logical_and(x == self.upper, self.g <= 0)
return np.logical_or(bind_up, bind_low)
@utils.timeIt
@Utils.timeIt
def findSearchDirection(self):
"""findSearchDirection()
@@ -612,7 +603,7 @@ class ProjectedGradient(Minimize, Remember):
# aSet_after = self.activeSet(self.xc+p)
return p
@utils.timeIt
@Utils.timeIt
def _doEndIteration_ProjectedGradient(self, xt):
"""_doEndIteration_ProjectedGradient(xt)"""
aSet = self.activeSet(xt)
@@ -623,7 +614,7 @@ class ProjectedGradient(Minimize, Remember):
f_current_decrease = self.f_last - self.f
self.comment = ''
if self._iter < 1:
if self.iter < 1:
# Note that this is reset on every CG iteration.
self.f_decrease_max = -np.inf
else:
@@ -694,7 +685,7 @@ class BFGS(Minimize, Remember):
return self.bfgs(-self.g)
def _doEndIteration_BFGS(self, xt):
if self._iter is 0:
if self.iter is 0:
self.g_last = self.g
return
@@ -718,7 +709,7 @@ class GaussNewton(Minimize, Remember):
def __init__(self, **kwargs):
Minimize.__init__(self, **kwargs)
@utils.timeIt
@Utils.timeIt
def findSearchDirection(self):
return Solver(self.H).solve(-self.g)
@@ -765,7 +756,7 @@ class InexactGaussNewton(BFGS, Minimize, Remember):
def approxHinv(self, value):
self._approxHinv = value
@utils.timeIt
@Utils.timeIt
def findSearchDirection(self):
Hinv = Solver(self.H, doDirect=False, options={'iterSolver': 'CG', 'M': self.approxHinv, 'tol': self.tolCG, 'maxIter': self.maxIterCG})
p = Hinv.solve(-self.g)
@@ -778,7 +769,7 @@ class SteepestDescent(Minimize, Remember):
def __init__(self, **kwargs):
Minimize.__init__(self, **kwargs)
@utils.timeIt
@Utils.timeIt
def findSearchDirection(self):
return -self.g
@@ -811,7 +802,7 @@ class NewtonRoot(object):
doLS = True
def __init__(self, **kwargs):
utils.setKwargs(self, **kwargs)
Utils.setKwargs(self, **kwargs)
def root(self, fun, x):
"""root(fun, x)
@@ -827,7 +818,7 @@ class NewtonRoot(object):
"""
if self.comments: print 'Newton Method:\n'
self._iter = 0
self.iter = 0
while True:
r, J = fun(x, return_g=True)
@@ -861,10 +852,10 @@ class NewtonRoot(object):
rt = fun(xt, return_g=False)
x = xt
self._iter += 1
self.iter += 1
if norm(rt) < self.tol:
break
if self._iter > self.maxIter:
if self.iter > self.maxIter:
print 'NewtonRoot stopped by maxIters. norm: %4.4e' % norm(rt)
break
@@ -873,7 +864,7 @@ class NewtonRoot(object):
if __name__ == '__main__':
from SimPEG.tests import Rosenbrock, checkDerivative
from SimPEG.Tests import Rosenbrock, checkDerivative
import matplotlib.pyplot as plt
x0 = np.array([2.6, 3.7])
checkDerivative(Rosenbrock, x0, plotIt=False)
@@ -885,7 +876,7 @@ if __name__ == '__main__':
print 'test the newtonRoot finding.'
fun = lambda x, return_g=True: np.sin(x) if not return_g else ( np.sin(x), utils.sdiag( np.cos(x) ) )
fun = lambda x, return_g=True: np.sin(x) if not return_g else ( np.sin(x), Utils.sdiag( np.cos(x) ) )
x = np.array([np.pi-0.3, np.pi+0.1, 0])
pnt = NewtonRoot(comments=True).root(fun,x)
print pnt
SimPEG/Parameters.py
+164
View File
@@ -0,0 +1,164 @@
import Utils, numpy as np
class Parameter(object):
"""Parameter"""
debug = False #: Print debugging information
current = None #: This hold
currentIter = 0
def __init__(self, **kwargs):
Utils.setKwargs(self, **kwargs)
@property
def parent(self):
"""This is the parent of the Parameter instance."""
return getattr(self,'_parent',None)
@parent.setter
def parent(self, p):
startupName = '_startup_paramProperty_'+self._propertyName
if getattr(self,'_parent',None) is not None:
delattr(self._parent,startupName)
print 'Warning: Parameter %s has switched to a new parent.' % self._propertyName
if self.debug: print '%s function has been deleted' % startupName
self._parent = p
prop = self
def _startup_paramProperty(self, *args):
if prop.debug: print 'initializing %s' % prop._propertyName
prop.initialize()
Utils.hook(self._parent, _startup_paramProperty, name=startupName, overwrite=True)
@property
def inv(self): return self.parent.inv
@property
def objFunc(self): return self.parent.objFunc
@property
def opt(self): return self.parent.opt
@property
def reg(self): return self.parent.reg
@property
def data(self): return self.parent.data
@property
def prob(self): return self.parent.prob
@property
def model(self): return self.parent.model
@property
def mesh(self): return self.parent.mesh
def initialize(self):
pass
def get(self):
if (self.current is None or
not self.opt.iter == self.currentIter):
self.current = self.nextIter()
self.currentIter = self.opt.iter
return self.current
def nextIter(self):
raise NotImplementedError('Getting the Parameter is not yet implemented.')
def ParameterProperty(name, default=None, doc=""):
def getter(self):
out = getattr(self,'_'+name,default)
if isinstance(out, Parameter):
out = out.get()
return out
def setter(self, value):
if isinstance(value, Parameter):
value._propertyName = name
value.parent = self
setattr(self, '_'+name, value)
return property(fget=getter, fset=setter, doc=doc)
class BetaEstimate(Parameter):
"""BetaEstimate"""
beta0 = 'guess' #: The initial Beta (regularization parameter)
beta0_ratio = 0.1 #: When beta0 is set to 'guess', estimateBeta0 is used with this ratio
beta = None #: Beta parameter
def __init__(self, **kwargs):
Parameter.__init__(self, **kwargs)
def initialize(self):
self.beta = self.beta0
@Utils.requires('parent')
def nextIter(self):
if self.beta is 'guess':
if self.debug: print 'BetaSchedule is estimating Beta0.'
self.beta = self.estimateBeta0()
return self.beta
@Utils.requires('parent')
def estimateBeta0(self):
"""estimateBeta0(u=None)
The initial beta is calculated by comparing the estimated
eigenvalues of JtJ and WtW.
To estimate the eigenvector of **A**, we will use one iteration
of the *Power Method*:
.. math::
\mathbf{x_1 = A x_0}
Given this (very course) approximation of the eigenvector,
we can use the *Rayleigh quotient* to approximate the largest eigenvalue.
.. math::
\lambda_0 = \\frac{\mathbf{x^\\top A x}}{\mathbf{x^\\top x}}
We will approximate the largest eigenvalue for both JtJ and WtW, and
use some ratio of the quotient to estimate beta0.
.. math::
\\beta_0 = \gamma \\frac{\mathbf{x^\\top J^\\top J x}}{\mathbf{x^\\top W^\\top W x}}
:rtype: float
:return: beta0
"""
objFunc = self.parent
data = objFunc.data
m = objFunc.m_current
u = objFunc.u_current
if u is None:
u = data.prob.field(m)
x0 = np.random.rand(*m.shape)
t = x0.dot(objFunc.dataObj2Deriv(m,x0,u=u))
b = x0.dot(objFunc.reg.modelObj2Deriv()*x0)
return self.beta0_ratio*(t/b)
class BetaSchedule(BetaEstimate):
"""BetaSchedule"""
coolingFactor = 2.
coolingRate = 3
@Utils.requires('parent')
def nextIter(self):
if self.beta is 'guess':
if self.debug: print 'BetaSchedule is estimating Beta0.'
self.beta = self.estimateBeta0()
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.beta /= self.coolingFactor
return self.beta
SimPEG/forward/Problem.py → SimPEG/Problem.py
+38 -92
View File
@@ -1,8 +1,7 @@
from SimPEG import utils, data, np, sp
norm = np.linalg.norm
import Utils, Data, numpy as np, scipy.sparse as sp
class Problem(object):
class BaseProblem(object):
"""
Problem is the base class for all geophysical forward problems in SimPEG.
@@ -35,71 +34,42 @@ class Problem(object):
to (locally) find how model parameters change the data, and optimize!
"""
__metaclass__ = utils.Save.Savable
__metaclass__ = Utils.Save.Savable
counter = None #: A SimPEG.utils.Counter object
counter = None #: A SimPEG.Utils.Counter object
dataPair = Data.BaseData
def __init__(self, mesh, *args, **kwargs):
utils.setKwargs(self, **kwargs)
def __init__(self, mesh, model, *args, **kwargs):
Utils.setKwargs(self, **kwargs)
self.mesh = mesh
self.model = model
@property
def RHS(self):
def data(self):
"""
Source matrix.
The data object for this problem.
"""
return self._RHS
@RHS.setter
def RHS(self, value):
self._RHS = value
return getattr(self, '_data', None)
def pair(self, d):
"""Bind a data to this problem instance using pointers."""
assert isinstance(d, self.dataPair), "Data object must be an instance of a %s class."%(self.dataPair.__name__)
if d.ispaired:
raise Exception("The data object is already paired to a problem. Use data.unpair()")
self._data = d
d._prob = self
def unpair(self):
"""Unbind a data from this problem instance."""
if not self.ispaired: return
self.data._prob = None
self._data = None
@property
def P(self):
"""
Projection matrix.
def ispaired(self): return self.data is not None
.. math::
d_\\text{pred} = Pu(m)
"""
return self._P
@P.setter
def P(self, value):
self._P = value
@utils.count
def dpred(self, m, u=None):
"""
Predicted data.
.. math::
d_\\text{pred} = Pu(m)
"""
if u is None:
u = self.field(m)
return self.P*u
@utils.count
def dataResidual(self, m, data, u=None):
"""
:param numpy.array m: geophysical model
:param numpy.array u: fields
:rtype: float
:return: data misfit
The data misfit:
.. math::
\mu_\\text{data} = \mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}
Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
u is the field of interest; d_obs is the observed data.
"""
return self.dpred(m, u=u) - data.dobs
@utils.timeIt
@Utils.timeIt
def J(self, m, v, u=None):
"""
:param numpy.array m: model
@@ -129,7 +99,7 @@ class Problem(object):
"""
raise NotImplementedError('J is not yet implemented.')
@utils.timeIt
@Utils.timeIt
def Jt(self, m, v, u=None):
"""
:param numpy.array m: model
@@ -143,7 +113,7 @@ class Problem(object):
raise NotImplementedError('Jt is not yet implemented.')
@utils.timeIt
@Utils.timeIt
def J_approx(self, m, v, u=None):
"""
@@ -158,7 +128,7 @@ class Problem(object):
"""
return self.J(m, v, u)
@utils.timeIt
@Utils.timeIt
def Jt_approx(self, m, v, u=None):
"""
:param numpy.array m: model
@@ -182,33 +152,7 @@ class Problem(object):
"""
pass
def modelTransform(self, m):
"""
:param numpy.array m: model
:rtype: numpy.array
:return: transformed model
The modelTransform changes the model into the physical property.
A common example of this is to invert for electrical conductivity
in log space. In this case, your model will be log(sigma) and to
get back to sigma, you can take the exponential:
"""
return m
def modelTransformDeriv(self, m):
"""
:param numpy.array m: model
:rtype: scipy.csr_matrix
:return: derivative of transformed model
The modelTransform changes the model into the physical property.
The modelTransformDeriv provides the derivative of the modelTransform.
"""
return sp.identity(m.size)
def createSyntheticData(self, m, std=0.05, u=None):
def createSyntheticData(self, m, std=0.05, u=None, **geometry_kwargs):
"""
Create synthetic data given a model, and a standard deviation.
@@ -220,11 +164,13 @@ class Problem(object):
Returns the observed data with random Gaussian noise
and Wd which is the same size as data, and can be used to weight the inversion.
"""
dtrue = self.dpred(m,u=u)
noise = std*abs(dtrue)*np.random.randn(*dtrue.shape)
dobs = dtrue+noise
stdev = dobs*0 + std
return data.SimPEGData(self, dobs=dobs, std=stdev, dtrue=dtrue, mtrue=m)
data = self.dataPair(mtrue=m, **geometry_kwargs)
data.pair(self)
data.dtrue = data.dpred(m, u=u)
noise = std*abs(data.dtrue)*np.random.randn(*data.dtrue.shape)
data.dobs = data.dtrue+noise
data.std = data.dobs*0 + std
return data
SimPEG/inverse/Regularization.py → SimPEG/Regularization.py
+121 -78
View File
@@ -1,7 +1,109 @@
from SimPEG import utils, np, sp
import Utils, Model, Parameters, numpy as np, scipy.sparse as sp
class Regularization(object):
"""**Regularization**
class BaseRegularization(object):
"""
**Base Regularization Class**
This is used to regularize the model space::
reg = Regularization(mesh, model)
"""
__metaclass__ = Utils.Save.Savable
modelPair = Model.BaseModel #: Some regularizations only work on specific models
model = None #: A SimPEG.Model instance.
counter = None
def __init__(self, model, **kwargs):
Utils.setKwargs(self, **kwargs)
assert isinstance(model, self.modelPair), "Incorrect model for this regularization"
self.model = model
mref = Parameters.ParameterProperty('mref', default=None, doc='Reference model.')
@property
def parent(self):
"""This is the parent of the regularization."""
return getattr(self,'_parent',None)
@parent.setter
def parent(self, p):
if getattr(self,'_parent',None) is not None:
print 'Regularization has switched to a new parent!'
self._parent = p
@property
def inv(self): return self.parent.inv
@property
def objFunc(self): return self.parent
@property
def reg(self): return self
@property
def opt(self): return self.parent.opt
@property
def prob(self): return self.parent.prob
@property
def data(self): return self.parent.data
@property
def mesh(self): return self.model.mesh
@property
def W(self):
"""Full regularization weighting matrix W."""
return sp.identity(self.model.nP)
@Utils.timeIt
def modelObj(self, m):
r = self.W * (m - self.mref)
return 0.5*r.dot(r)
@Utils.timeIt
def modelObjDeriv(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.W.T * ( self.W * (m - self.mref) )
@Utils.timeIt
def modelObj2Deriv(self):
"""
The regularization is:
.. math::
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top W(m-m_\\text{ref})}
So the second derivative is straight forward:
.. math::
R(m) = \mathbf{W^\\top W}
"""
return self.W.T * self.W
class Tikhonov(BaseRegularization):
"""**Tikhonov Regularization**
Here we will define regularization of a model, m, in general however, this should be thought of as (m-m_ref) but otherwise it is exactly the same:
@@ -83,36 +185,22 @@ class Regularization(object):
"""
__metaclass__ = utils.Save.Savable
alpha_s = Utils.dependentProperty('_alpha_s', 1e-6, ['_W', '_Ws'], "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")
alpha_xx = Utils.dependentProperty('_alpha_xx', 0.0, ['_W', '_Wxx'], "Weight for the second derivative in the x direction")
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")
alpha_s = utils.dependentProperty('_alpha_s', 1e-6, ['_W', '_Ws'], "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")
alpha_xx = utils.dependentProperty('_alpha_xx', 0.0, ['_W', '_Wxx'], "Weight for the second derivative in the x direction")
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")
counter = None
def __init__(self, mesh, **kwargs):
utils.setKwargs(self, **kwargs)
self.mesh = mesh
@property
def mref(self):
if getattr(self, '_mref', None) is None:
return np.zeros(self.mesh.nC);
return self._mref
@mref.setter
def mref(self, value):
self._mref = value
def __init__(self, model, **kwargs):
BaseRegularization.__init__(self, model, **kwargs)
@property
def Ws(self):
"""Regularization matrix Ws"""
if getattr(self,'_Ws', None) is None:
self._Ws = utils.sdiag((self.mesh.vol*self.alpha_s)**0.5)
self._Ws = Utils.sdiag((self.mesh.vol*self.alpha_s)**0.5)
return self._Ws
@property
@@ -120,7 +208,7 @@ class Regularization(object):
"""Regularization matrix Wx"""
if getattr(self, '_Wx', None) is None:
Ave_x_vol = self.mesh.aveF2CC[:,:self.mesh.nFv[0]].T*self.mesh.vol
self._Wx = utils.sdiag((Ave_x_vol*self.alpha_x)**0.5)*self.mesh.cellGradx
self._Wx = Utils.sdiag((Ave_x_vol*self.alpha_x)**0.5)*self.mesh.cellGradx
return self._Wx
@property
@@ -128,7 +216,7 @@ class Regularization(object):
"""Regularization matrix Wy"""
if getattr(self, '_Wy', None) is None:
Ave_y_vol = self.mesh.aveF2CC[:,self.mesh.nFv[0]:np.sum(self.mesh.nFv[:2])].T*self.mesh.vol
self._Wy = utils.sdiag((Ave_y_vol*self.alpha_y)**0.5)*self.mesh.cellGrady
self._Wy = Utils.sdiag((Ave_y_vol*self.alpha_y)**0.5)*self.mesh.cellGrady
return self._Wy
@property
@@ -136,31 +224,30 @@ class Regularization(object):
"""Regularization matrix Wz"""
if getattr(self, '_Wz', None) is None:
Ave_z_vol = self.mesh.aveF2CC[:,np.sum(self.mesh.nFv[:2]):].T*self.mesh.vol
self._Wz = utils.sdiag((Ave_z_vol*self.alpha_z)**0.5)*self.mesh.cellGradz
self._Wz = Utils.sdiag((Ave_z_vol*self.alpha_z)**0.5)*self.mesh.cellGradz
return self._Wz
@property
def Wxx(self):
"""Regularization matrix Wxx"""
if getattr(self, '_Wxx', None) is None:
self._Wxx = utils.sdiag((self.mesh.vol*self.alpha_xx)**0.5)*self.mesh.faceDivx*self.mesh.cellGradx
self._Wxx = Utils.sdiag((self.mesh.vol*self.alpha_xx)**0.5)*self.mesh.faceDivx*self.mesh.cellGradx
return self._Wxx
@property
def Wyy(self):
"""Regularization matrix Wyy"""
if getattr(self, '_Wyy', None) is None:
self._Wyy = utils.sdiag((self.mesh.vol*self.alpha_yy)**0.5)*self.mesh.faceDivy*self.mesh.cellGrady
self._Wyy = Utils.sdiag((self.mesh.vol*self.alpha_yy)**0.5)*self.mesh.faceDivy*self.mesh.cellGrady
return self._Wyy
@property
def Wzz(self):
"""Regularization matrix Wzz"""
if getattr(self, '_Wzz', None) is None:
self._Wzz = utils.sdiag((self.mesh.vol*self.alpha_zz)**0.5)*self.mesh.faceDivz*self.mesh.cellGradz
self._Wzz = Utils.sdiag((self.mesh.vol*self.alpha_zz)**0.5)*self.mesh.faceDivz*self.mesh.cellGradz
return self._Wzz
@property
def W(self):
"""Full regularization matrix W"""
@@ -173,47 +260,3 @@ class Regularization(object):
self._W = sp.vstack(wlist)
return self._W
@utils.timeIt
def modelObj(self, m):
r = self.W * (m - self.mref)
return 0.5*r.dot(r)
@utils.timeIt
def modelObjDeriv(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.W.T * ( self.W * (m - self.mref) )
@utils.timeIt
def modelObj2Deriv(self):
"""
The regularization is:
.. math::
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top W(m-m_\\text{ref})}
So the second derivative is straight forward:
.. math::
R(m) = \mathbf{W^\\top W}
"""
return self.W.T * self.W
SimPEG/utils/Solver.py → SimPEG/Solver.py
+4 -3
View File
@@ -1,14 +1,15 @@
import numpy as np
import scipy.sparse as sp
import scipy.sparse.linalg as linalg
from SimPEG.utils import mkvc, sdiag
from Utils.matutils import mkvc
from Utils.sputils import sdiag
import warnings
DEFAULTS = {'direct':'scipy', 'iter':'scipy', 'triangular':'fortran', 'diagonal':'python'}
OPTIONS = {'direct':['scipy'], 'iter':['scipy'], 'triangular':['python'], 'diagonal':['python']}
try:
import TriSolve
import Utils.TriSolve as TriSolve
OPTIONS['triangular'].append('fortran')
except Exception, e:
print 'Warning: Python backend is being used for solver. Run setup.py from the command line.'
@@ -319,7 +320,7 @@ class Solver(object):
if __name__ == '__main__':
from SimPEG.mesh import TensorMesh
from SimPEG.Mesh import TensorMesh
from time import time
h1 = np.ones(20)*100.
h2 = np.ones(20)*100.
SimPEG/tests/TestUtils.py → SimPEG/Tests/TestUtils.py
+9 -11
View File
@@ -1,9 +1,9 @@
import numpy as np
import matplotlib.pyplot as plt
from pylab import norm
from SimPEG.utils import mkvc, sdiag
from SimPEG import utils
from SimPEG.mesh import TensorMesh, LogicallyOrthogonalMesh
from numpy.linalg import norm
from SimPEG.Utils import mkvc, sdiag
from SimPEG import Utils
from SimPEG.Mesh import TensorMesh, LogicallyOrthogonalMesh
import numpy as np
import scipy.sparse as sp
import unittest
@@ -112,10 +112,10 @@ class OrderTest(unittest.TestCase):
else:
raise Exception('Unexpected meshType')
if self.meshDimension == 2:
X, Y = utils.exampleLomGird([nc, nc], kwrd)
X, Y = Utils.exampleLomGird([nc, nc], kwrd)
self.M = LogicallyOrthogonalMesh([X, Y])
if self.meshDimension == 3:
X, Y, Z = utils.exampleLomGird([nc, nc, nc], kwrd)
X, Y, Z = Utils.exampleLomGird([nc, nc, nc], kwrd)
self.M = LogicallyOrthogonalMesh([X, Y, Z])
return 1./nc
@@ -211,12 +211,10 @@ def checkDerivative(fctn, x0, num=7, plotIt=True, dx=None, expectedOrder=2, tole
.. plot::
:include-source:
from SimPEG.tests import checkDerivative
from SimPEG.utils import sdiag
import numpy as np
from SimPEG import Tests, Utils, np
def simplePass(x):
return np.sin(x), sdiag(np.cos(x))
checkDerivative(simplePass, np.random.randn(5))
return np.sin(x), Utils.sdiag(np.cos(x))
Tests.checkDerivative(simplePass, np.random.randn(5))
"""
print "%s checkDerivative %s" % ('='*20, '='*20)
SimPEG/Tests/__init__.py
+14
View File
@@ -0,0 +1,14 @@
from TestUtils import checkDerivative, Rosenbrock, OrderTest, getQuadratic
if __name__ == '__main__':
import os
import glob
import unittest
test_file_strings = glob.glob('test_*.py')
module_strings = [str[0:len(str)-3] for str in test_file_strings]
suites = [unittest.defaultTestLoader.loadTestsFromName(str) for str
in module_strings]
testSuite = unittest.TestSuite(suites)
unittest.TextTestRunner(verbosity=2).run(testSuite)
SimPEG/tests/test_LogicallyOrthogonalMesh.py → SimPEG/Tests/test_LogicallyOrthogonalMesh.py
+2 -2
View File
@@ -1,7 +1,7 @@
import numpy as np
import unittest
from SimPEG.mesh import TensorMesh, LogicallyOrthogonalMesh
from SimPEG.utils import ndgrid
from SimPEG.Mesh import TensorMesh, LogicallyOrthogonalMesh
from SimPEG.Utils import ndgrid
class BasicLOMTests(unittest.TestCase):
SimPEG/tests/test_Solver.py → SimPEG/Tests/test_Solver.py
+2 -2
View File
@@ -1,7 +1,7 @@
import unittest
from SimPEG import Solver
from SimPEG.mesh import TensorMesh
from SimPEG.utils import sdiag
from SimPEG.Mesh import TensorMesh
from SimPEG.Utils import sdiag
import numpy as np
import scipy.sparse as sparse
SimPEG/tests/test_basemesh.py → SimPEG/Tests/test_basemesh.py
+8 -8
View File
@@ -1,6 +1,6 @@
import unittest
import sys
from SimPEG.mesh import BaseMesh
from SimPEG.Mesh import BaseMesh
import numpy as np
@@ -13,7 +13,7 @@ class TestBaseMesh(unittest.TestCase):
self.assertTrue(self.mesh.dim, 3)
def test_mesh_nc(self):
self.assertTrue(np.all(self.mesh.n == [6, 2, 3]))
self.assertTrue(np.all(self.mesh.nCv == [6, 2, 3]))
def test_mesh_nc_xyz(self):
x = np.all(self.mesh.nCx == 6)
@@ -106,9 +106,9 @@ class TestBaseMesh(unittest.TestCase):
g[:, 1] = 2
g[:, 2] = 3
Xc, Yc, Zc = self.mesh.r(g, 'CC', 'CC', 'M')
self.assertTrue(np.all(Xc.shape == self.mesh.n))
self.assertTrue(np.all(Yc.shape == self.mesh.n))
self.assertTrue(np.all(Zc.shape == self.mesh.n))
self.assertTrue(np.all(Xc.shape == self.mesh.nCv))
self.assertTrue(np.all(Yc.shape == self.mesh.nCv))
self.assertTrue(np.all(Zc.shape == self.mesh.nCv))
self.assertTrue(np.all(Xc == 1))
self.assertTrue(np.all(Yc == 2))
self.assertTrue(np.all(Zc == 3))
@@ -123,7 +123,7 @@ class TestMeshNumbers2D(unittest.TestCase):
self.assertTrue(self.mesh.dim, 2)
def test_mesh_nc(self):
self.assertTrue(np.all(self.mesh.n == [6, 2]))
self.assertTrue(np.all(self.mesh.nCv == [6, 2]))
def test_mesh_nc_xyz(self):
x = np.all(self.mesh.nCx == 6)
@@ -203,8 +203,8 @@ class TestMeshNumbers2D(unittest.TestCase):
g = np.ones((self.mesh.nC, 2))
g[:, 1] = 2
Xc, Yc = self.mesh.r(g, 'CC', 'CC', 'M')
self.assertTrue(np.all(Xc.shape == self.mesh.n))
self.assertTrue(np.all(Yc.shape == self.mesh.n))
self.assertTrue(np.all(Xc.shape == self.mesh.nCv))
self.assertTrue(np.all(Yc.shape == self.mesh.nCv))
self.assertTrue(np.all(Xc == 1))
self.assertTrue(np.all(Yc == 2))
SimPEG/Tests/test_forward_DCproblem.py
+85
View File
@@ -0,0 +1,85 @@
# import numpy as np
# import unittest
# from SimPEG.mesh import TensorMesh
# from SimPEG.Utils import ModelBuilder, sdiag
# from SimPEG.forward import Problem
# from SimPEG.examples.DC import *
# from TestUtils import checkDerivative
# from scipy.sparse.linalg import dsolve
# from SimPEG import inverse
# class DCProblemTests(unittest.TestCase):
# def setUp(self):
# # Create the mesh
# h1 = np.ones(20)
# h2 = np.ones(20)
# mesh = TensorMesh([h1,h2])
# # Create some parameters for the model
# sig1 = 1
# sig2 = 0.01
# # Create a synthetic model from a block in a half-space
# p0 = [2, 2]
# p1 = [5, 5]
# condVals = [sig1, sig2]
# mSynth = ModelBuilder.defineBlockConductivity(p0,p1,mesh.gridCC,condVals)
# # Set up the projection
# nelec = 10
# spacelec = 2
# surfloc = 0.5
# elecini = 0.5
# elecend = 0.5+spacelec*(nelec-1)
# elecLocR = np.linspace(elecini, elecend, nelec)
# rxmidLoc = (elecLocR[0:nelec-1]+elecLocR[1:nelec])*0.5
# q, Q, rxmidloc = genTxRxmat(nelec, spacelec, surfloc, elecini, mesh)
# P = Q.T
# # Create some data
# problem = DCProblem(mesh)
# problem.P = P
# problem.RHS = q
# data = problem.createSyntheticData(mSynth, std=0.05)
# # Now set up the problem to do some minimization
# opt = inverse.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6)
# reg = inverse.Regularization(mesh)
# inv = inverse.Inversion(problem, reg, opt, data, beta0=1e4)
# self.inv = inv
# self.reg = reg
# self.p = problem
# self.mesh = mesh
# self.m0 = mSynth
# self.data = data
# def test_misfit(self):
# derChk = lambda m: [self.p.dpred(m), lambda mx: self.p.J(self.m0, mx)]
# passed = checkDerivative(derChk, self.m0, plotIt=False)
# self.assertTrue(passed)
# def test_adjoint(self):
# # Adjoint Test
# u = np.random.rand(self.mesh.nC*self.p.RHS.shape[1])
# v = np.random.rand(self.mesh.nC)
# w = np.random.rand(self.data.dobs.shape[0])
# wtJv = w.dot(self.p.J(self.m0, v, u=u))
# vtJtw = v.dot(self.p.Jt(self.m0, w, u=u))
# passed = (wtJv - vtJtw) < 1e-10
# self.assertTrue(passed)
# def test_dataObj(self):
# derChk = lambda m: [self.inv.dataObj(m), self.inv.dataObjDeriv(m)]
# checkDerivative(derChk, self.m0, plotIt=False)
# def test_modelObj(self):
# derChk = lambda m: [self.reg.modelObj(m), self.reg.modelObjDeriv(m)]
# checkDerivative(derChk, self.m0, plotIt=False)
# if __name__ == '__main__':
# unittest.main()
SimPEG/tests/test_interpolation.py → SimPEG/Tests/test_interpolation.py
+1 -1
View File
@@ -1,7 +1,7 @@
import numpy as np
import unittest
from TestUtils import OrderTest
from SimPEG.utils import mkvc
from SimPEG.Utils import mkvc
MESHTYPES = ['uniformTensorMesh', 'randomTensorMesh']
TOLERANCES = [0.9, 0.55]
SimPEG/tests/test_massMatrices.py → SimPEG/Tests/test_massMatrices.py
View File
File renamed without changes.
SimPEG/Tests/test_model.py
+27
View File
@@ -0,0 +1,27 @@
import numpy as np
import unittest
from SimPEG import *
from TestUtils import checkDerivative
from scipy.sparse.linalg import dsolve
class ModelTests(unittest.TestCase):
def setUp(self):
a = np.array([1, 1, 1])
b = np.array([1, 2])
c = np.array([1, 4])
self.mesh2 = Mesh.TensorMesh([a, b], np.array([3, 5]))
def test_modelTransforms(self):
print 'SimPEG.Model.BaseModel: Testing Model Transform'
for M in dir(Model):
if 'Model' not in M: continue
model = getattr(Model, M)(self.mesh2)
m = model.example()
passed = checkDerivative(lambda m : [model.transform(m), model.transformDeriv(m)], m, plotIt=False)
self.assertTrue(passed)
if __name__ == '__main__':
unittest.main()
SimPEG/tests/test_operators.py → SimPEG/Tests/test_operators.py
View File
File renamed without changes.
SimPEG/tests/test_optimizers.py → SimPEG/Tests/test_optimizers.py
+9 -9
View File
@@ -1,11 +1,11 @@
import unittest
from SimPEG import Solver
from SimPEG.mesh import TensorMesh
from SimPEG.utils import sdiag
from SimPEG.Mesh import TensorMesh
from SimPEG.Utils import sdiag
import numpy as np
import scipy.sparse as sp
from SimPEG import inverse
from SimPEG.tests import getQuadratic, Rosenbrock
from SimPEG import Optimization
from SimPEG.Tests import getQuadratic, Rosenbrock
TOL = 1e-2
@@ -16,7 +16,7 @@ class TestOptimizers(unittest.TestCase):
self.b = np.array([-5,-5])
def test_GN_Rosenbrock(self):
GN = inverse.GaussNewton()
GN = Optimization.GaussNewton()
xopt = GN.minimize(Rosenbrock,np.array([0,0]))
x_true = np.array([1.,1.])
print 'xopt: ', xopt
@@ -24,7 +24,7 @@ class TestOptimizers(unittest.TestCase):
self.assertTrue(np.linalg.norm(xopt-x_true,2) < TOL, True)
def test_GN_quadratic(self):
GN = inverse.GaussNewton()
GN = Optimization.GaussNewton()
xopt = GN.minimize(getQuadratic(self.A,self.b),np.array([0,0]))
x_true = np.array([5.,5.])
print 'xopt: ', xopt
@@ -32,7 +32,7 @@ class TestOptimizers(unittest.TestCase):
self.assertTrue(np.linalg.norm(xopt-x_true,2) < TOL, True)
def test_ProjGradient_quadraticBounded(self):
PG = inverse.ProjectedGradient(debug=True)
PG = Optimization.ProjectedGradient(debug=True)
PG.lower, PG.upper = -2, 2
xopt = PG.minimize(getQuadratic(self.A,self.b),np.array([0,0]))
x_true = np.array([2.,2.])
@@ -42,7 +42,7 @@ class TestOptimizers(unittest.TestCase):
def test_ProjGradient_quadratic1Bound(self):
myB = np.array([-5,1])
PG = inverse.ProjectedGradient()
PG = Optimization.ProjectedGradient()
PG.lower, PG.upper = -2, 2
xopt = PG.minimize(getQuadratic(self.A,myB),np.array([0,0]))
x_true = np.array([2.,-1.])
@@ -53,7 +53,7 @@ class TestOptimizers(unittest.TestCase):
def test_NewtonRoot(self):
fun = lambda x, return_g=True: np.sin(x) if not return_g else ( np.sin(x), sdiag( np.cos(x) ) )
x = np.array([np.pi-0.3, np.pi+0.1, 0])
xopt = inverse.NewtonRoot(comments=False).root(fun,x)
xopt = Optimization.NewtonRoot(comments=False).root(fun,x)
x_true = np.array([np.pi,np.pi,0])
print 'Newton Root Finding'
print 'xopt: ', xopt
SimPEG/Tests/test_regularization.py
+31
View File
@@ -0,0 +1,31 @@
import numpy as np
import unittest
from SimPEG import *
from TestUtils import checkDerivative
from scipy.sparse.linalg import dsolve
import inspect
class RegularizationTests(unittest.TestCase):
def setUp(self):
self.mesh2 = Mesh.TensorMesh([3, 2])
def test_regularization(self):
for R in dir(Regularization):
r = getattr(Regularization, R)
if not inspect.isclass(r): continue
if not issubclass(r, Regularization.BaseRegularization):
continue
# if 'Regularization' not in R: continue
print 'Check:', R
model = r.modelPair(self.mesh2)
reg = r(model)
m = model.example()
reg.mref = model.example()*0
passed = checkDerivative(lambda m : [reg.modelObj(m), reg.modelObjDeriv(m)], m, plotIt=False)
self.assertTrue(passed)
if __name__ == '__main__':
unittest.main()
SimPEG/tests/test_tensorMesh.py → SimPEG/Tests/test_tensorMesh.py
+1 -1
View File
@@ -1,6 +1,6 @@
import numpy as np
import unittest
from SimPEG.mesh import TensorMesh
from SimPEG.Mesh import TensorMesh
from TestUtils import OrderTest
from scipy.sparse.linalg import dsolve
SimPEG/tests/test_utils.py → SimPEG/Tests/test_utils.py
+2 -2
View File
@@ -1,7 +1,7 @@
import numpy as np
import unittest
from SimPEG.utils import mkvc, ndgrid, indexCube, sdiag, inv3X3BlockDiagonal, inv2X2BlockDiagonal
from SimPEG.tests import checkDerivative
from SimPEG.Utils import mkvc, ndgrid, indexCube, sdiag, inv3X3BlockDiagonal, inv2X2BlockDiagonal
from SimPEG.Tests import checkDerivative
class TestCheckDerivative(unittest.TestCase):
SimPEG/utils/Geophysics/__init__.py → SimPEG/Utils/Geophysics/__init__.py
View File
File renamed without changes.
SimPEG/utils/Geophysics/emSources/__init__.py → SimPEG/Utils/Geophysics/emSources/__init__.py
View File
File renamed without changes.
SimPEG/utils/Geophysics/emSources/emSources.py → SimPEG/Utils/Geophysics/emSources/emSources.py
View File
File renamed without changes.
SimPEG/utils/ModelBuilder.py → SimPEG/Utils/ModelBuilder.py
+9 -6
View File
@@ -27,6 +27,9 @@ def getIndecesBlock(p0,p1,ccMesh):
dimMesh = np.size(ccMesh[0,:])
assert len(p0) == dimMesh, "Dimension mismatch. len(p0) != dimMesh"
for ii in range(len(p0)):
p0[ii], p1[ii] = np.min([p0[ii], p1[ii]]), np.max([p0[ii], p1[ii]])
if dimMesh == 1:
# Define the reference points
x1 = p0[0]
@@ -67,7 +70,7 @@ def getIndecesBlock(p0,p1,ccMesh):
# Return a tuple
return ind
def defineBlockConductivity(p0,p1,ccMesh,condVals):
def defineBlockConductivity(ccMesh,p0,p1,condVals):
"""
Build a block with the conductivity specified by condVal. Returns an array.
condVals[0] conductivity of the block
@@ -80,7 +83,7 @@ def defineBlockConductivity(p0,p1,ccMesh,condVals):
return sigma
def defineTwoLayeredConductivity(depth,ccMesh,condVals):
def defineTwoLayeredConductivity(ccMesh,depth,condVals):
"""
Define a two layered model. Depth of the first layer must be specified.
CondVals vector with the conductivity values of the layers. Eg:
@@ -151,7 +154,7 @@ def randomModel(shape, seed=None, anisotropy=None, its=100, bounds=[0,1]):
.. plot::
import matplotlib.pyplot as plt
import SimPEG.utils.ModelBuilder as MB
import SimPEG.Utils.ModelBuilder as MB
plt.colorbar(plt.imshow(MB.randomModel((50,50),bounds=[-4,0])))
plt.title('A very cool, yet completely random model.')
plt.show()
@@ -196,7 +199,7 @@ def randomModel(shape, seed=None, anisotropy=None, its=100, bounds=[0,1]):
if __name__ == '__main__':
from SimPEG.mesh import TensorMesh
from SimPEG.Mesh import TensorMesh
from matplotlib import pyplot as plt
# Define the mesh
@@ -229,7 +232,7 @@ if __name__ == '__main__':
p1 = np.array([1.0,1.0,1.0])[:testDim]
condVals = np.array([100,1e-6])
sigma = defineBlockConductivity(p0,p1,ccMesh,condVals)
sigma = defineBlockConductivity(ccMesh,p0,p1,condVals)
# Plot sigma model
print sigma.shape
@@ -242,7 +245,7 @@ if __name__ == '__main__':
condVals = np.array([100,1e-5]);
depth = 1.0;
sigma = defineTwoLayeredConductivity(depth,ccMesh,condVals)
sigma = defineTwoLayeredConductivity(ccMesh,depth,condVals)
M.plotImage(sigma)
print sigma
SimPEG/utils/Save.py → SimPEG/Utils/Save.py
+8 -4
View File
@@ -5,7 +5,7 @@ import re
try:
import h5py
except Exception, e:
print 'Warning: SimPEG.utils.Save needs h5py to be installed.'
print 'Warning: SimPEG.Utils.Save needs h5py to be installed.'
SAVEABLES = {}
@@ -57,7 +57,7 @@ class SimPEGTable:
# At the start of every iteration we will create a inversion iteration node.
def _doStartIteration_hdf5_inv(invObj):
invObj._invNodeIt = invObj._invNode.addGroup('%d'%(invObj._iter+1))
invObj._invNodeIt = invObj._invNode.addGroup('%d'%(invObj.iter+1))
preIteration(invObj._invNodeIt)
invObj.hook(_doStartIteration_hdf5_inv, overwrite=True)
@@ -78,7 +78,7 @@ class SimPEGTable:
invObj.hook(_finish_hdf5_inv, overwrite=True)
def _doStartIteration_hdf5_opt(optObj):
optObj._optNodeIt = optObj.parent._invNode.addGroup('%d.%d'%(optObj.parent._iter, optObj._iter))
optObj._optNodeIt = optObj.parent._invNode.addGroup('%d.%d'%(optObj.parent.iter, optObj.iter))
preIteration(optObj._optNodeIt)
invObj.opt.hook(_doStartIteration_hdf5_opt, overwrite=True)
@@ -208,6 +208,10 @@ class hdf5Inversion(hdf5Group):
def rebuild(self):
return loadSavable(self['rebuild'])
@property
def results(self): return self['results']
class hdf5InversionResults(hdf5Group):
def __init__(self, T, groupNode):
hdf5Group.__init__(self, T, groupNode)
@@ -343,6 +347,6 @@ def loadSavable(node, pointers=None):
print 'KWARGS: ', KWARGS
return (cls, ARGS, KWARGS, node)
else:
print 'Warning: %s Class not found in SimPEG.utils.Save.SAVABLES' % cls
print 'Warning: %s Class not found in SimPEG.Utils.Save.SAVABLES' % cls
return (cls, ARGS, KWARGS, node)
SimPEG/utils/TriSolve.f → SimPEG/Utils/TriSolve.f
View File
File renamed without changes.
SimPEG/utils/__init__.py → SimPEG/Utils/__init__.py
+60 -16
View File
@@ -1,19 +1,12 @@
import matutils
import sputils
import lomutils
import interputils
import ModelBuilder
import meshutils
from matutils import getSubArray, mkvc, ndgrid, ind2sub, sub2ind
from sputils import spzeros, kron3, speye, sdiag, ddx, av, avExtrap
from meshutils import exampleLomGird, meshTensors
from lomutils import volTetra, faceInfo, inv2X2BlockDiagonal, inv3X3BlockDiagonal, indexCube
from interputils import interpmat
from ipythonUtils import easyAnimate as animate
import Solver
from Solver import Solver
from ipythonutils import easyAnimate as animate
import Save
import Geophysics
import ModelBuilder
import types
import time
@@ -90,7 +83,7 @@ def printStoppers(obj, stoppers, pad='', stop='STOP!', done='DONE!'):
print pad + stopper['str'] % (l<=r,l,r)
print pad + "%s%s%s" % ('-'*25,done,'-'*25)
def callHooks(match):
def callHooks(match, mainFirst=False):
"""
Use this to wrap a funciton::
@@ -99,16 +92,28 @@ def callHooks(match):
pass
This will call everything named _doEndIteration* at the beginning of the function call.
By default the master method (doEndIteration) is run after all of the sub methods (_doEndIteration*).
This can be reversed by adding the mainFirst=True kwarg.
"""
def callHooksWrap(f):
@wraps(f)
def wrapper(self,*args,**kwargs):
for method in [posible for posible in dir(self) if ('_'+match) in posible]:
if getattr(self,'debug',False): print (match+' is calling self.'+method)
getattr(self,method)(*args, **kwargs)
if not mainFirst:
for method in [posible for posible in dir(self) if ('_'+match) in posible]:
if getattr(self,'debug',False): print (match+' is calling self.'+method)
getattr(self,method)(*args, **kwargs)
return f(self,*args,**kwargs)
else:
out = f(self,*args,**kwargs)
for method in [posible for posible in dir(self) if ('_'+match) in posible]:
if getattr(self,'debug',False): print (match+' is calling self.'+method)
getattr(self,method)(*args, **kwargs)
return out
return f(self,*args,**kwargs)
extra = """
If you have things that also need to run in the method %s, you can create a method::
@@ -119,8 +124,8 @@ def callHooks(match):
Where the * can be any string. If present, _%s* will be called at the start of the default %s call.
You may also completely overwrite this function.
""" % (match, match, match, match)
wrapper.__doc__ += extra
doc = wrapper.__doc__
wrapper.__doc__ = ('' if doc is None else doc) + extra
return wrapper
return callHooksWrap
@@ -133,6 +138,45 @@ def dependentProperty(name, value, children, doc):
setattr(self, name, val)
return property(fget=fget, fset=fset, doc=doc)
def requires(var):
"""
Use this to wrap a funciton::
@requires('prob')
def dpred(self):
pass
This wrapper will ensure that a problem has been bound to the data.
If a problem is not bound an Exception will be raised, and an nice error message printed.
"""
def requiresVar(f):
if var is 'prob':
extra = """
.. note::
To use data.%s(), SimPEG requires that a problem be bound to the data.
If a problem has not been bound, an Exception will be raised.
To bind a problem to the Data object::
data.pair(myProblem)
""" % f.__name__
else:
extra = """
To use *%s* method, SimPEG requires that the %s be specified.
""" % (f.__name__, var)
@wraps(f)
def requiresVarWrapper(self,*args,**kwargs):
if getattr(self, var, None) is None:
raise Exception(extra)
return f(self,*args,**kwargs)
doc = requiresVarWrapper.__doc__
requiresVarWrapper.__doc__ = ('' if doc is None else doc) + extra
return requiresVarWrapper
return requiresVar
class Counter(object):
"""
SimPEG/utils/interputils.py → SimPEG/Utils/interputils.py
+4 -4
View File
@@ -14,10 +14,10 @@ def _interp_point_1D(x, xr_i):
"""
# TODO: This fails if the point is on the outside of the mesh. We may want to replace this by extrapolation?
im = np.argmin(abs(x-xr_i))
if xr_i - x[im] >= 0: # Point on the left
if xr_i - x[im] >= 0: # Point on the left
ind_x1 = im
ind_x2 = im+1
elif xr_i - x[im] < 0: # Point on the right
elif xr_i - x[im] < 0: # Point on the right
ind_x1 = im-1
ind_x2 = im
dx1 = xr_i - x[ind_x1]
@@ -45,7 +45,7 @@ def interpmat(locs, x, y=None, z=None):
x = np.linspace(0,1,7)
dense = np.linspace(0,1,200)
fun = lambda x: np.cos(2*np.pi*x)
Q = SimPEG.utils.interpmat(locs, x)
Q = SimPEG.Utils.interpmat(locs, x)
plt.plot(x, fun(x), 'bs-')
plt.plot(dense, fun(dense), 'y:')
plt.plot(locs, Q*fun(x), 'mo')
@@ -173,7 +173,7 @@ if __name__ == '__main__':
x = np.linspace(0,1,7)
dense = np.linspace(0,1,200)
fun = lambda x: np.cos(2*np.pi*x)
Q = SimPEG.utils.interpmat(locs, x)
Q = SimPEG.Utils.interpmat(locs, x)
plt.plot(x, fun(x), 'bs-')
plt.plot(dense, fun(dense), 'y:')
plt.plot(locs, Q*fun(x), 'mo')
SimPEG/utils/ipythonUtils.py → SimPEG/Utils/ipythonutils.py
View File
File renamed without changes.
SimPEG/utils/lomutils.py → SimPEG/Utils/lomutils.py
View File
File renamed without changes.
SimPEG/utils/matutils.py → SimPEG/Utils/matutils.py
View File
File renamed without changes.
SimPEG/utils/meshutils.py → SimPEG/Utils/meshutils.py
+3 -3
View File
@@ -30,12 +30,12 @@ def meshTensors(*args):
"""
**meshTensors** takes any number of tuples that have the form::
h1 = ( (numPad, sizeStart [, increaseFactor]), (numCore, sizeCode), (numPad, sizeStart [, increaseFactor]) )
h1 = ( (numPad, sizeStart [, increaseFactor]), (numCore, sizeCore), (numPad, sizeStart [, increaseFactor]) )
.. plot::
from SimPEG import mesh, utils
M = mesh.TensorMesh(utils.meshTensors(((10,10),(40,10),(10,10)), ((10,10),(20,10),(0,0))))
from SimPEG import Mesh, Utils
M = Mesh.TensorMesh(Utils.meshTensors(((10,10),(40,10),(10,10)), ((10,10),(20,10),(0,0))))
M.plotGrid()
"""
SimPEG/utils/sputils.py → SimPEG/Utils/sputils.py
View File
File renamed without changes.
SimPEG/__init__.py
+14 -8
View File
@@ -1,13 +1,19 @@
import numpy as np
import scipy.sparse as sp
import utils
from utils import Solver
import mesh
import data
import forward
import inverse
import visualize
import examples
import Utils
from Solver import Solver
import Mesh
import Model
import Problem
import Data
import Regularization
import ObjFunction
import Optimization
import Inversion
import Parameters
import Examples
import Tests
import scipy.version as _v
if _v.version < '0.13.0':
SimPEG/data/__init__.py
-20
View File
@@ -1,20 +0,0 @@
from SimPEG import utils
class SimPEGData(object):
"""Data holds the observed data, and the standard deviations."""
__metaclass__ = utils.Save.Savable
std = None #: Estimated Standard Deviations
dobs = None #: Observed data
dtrue = None #: True data, if data is synthetic
mtrue = None #: True model, if data is synthetic
def __init__(self, prob, **kwargs):
utils.setKwargs(self, **kwargs)
self.prob = prob
def isSynthetic(self):
"Check if the data is synthetic."
return self.mtrue is not None
SimPEG/forward/ModelTransforms.py
-49
View File
@@ -1,49 +0,0 @@
import numpy as np
from SimPEG.utils import mkvc, sdiag
class LogModel(object):
"""docstring for LogModel"""
def modelTransform(self, m):
"""
:param numpy.array m: model
:rtype: numpy.array
:return: transformed model
The modelTransform changes the model into the physical property.
A common example of this is to invert for electrical conductivity
in log space. In this case, your model will be log(sigma) and to
get back to sigma, you can take the exponential:
.. math::
m = \log{\sigma}
\exp{m} = \exp{\log{\sigma}} = \sigma
"""
return np.exp(mkvc(m))
def modelTransformDeriv(self, m):
"""
:param numpy.array m: model
:rtype: scipy.csr_matrix
:return: derivative of transformed model
The modelTransform changes the model into the physical property.
The modelTransformDeriv provides the derivative of the modelTransform.
If the model transform is:
.. math::
m = \log{\sigma}
\exp{m} = \exp{\log{\sigma}} = \sigma
Then the derivative is:
.. math::
\\frac{\partial \exp{m}}{\partial m} = \\text{sdiag}(\exp{m})
"""
return sdiag(np.exp(mkvc(m)))
SimPEG/forward/__init__.py
-2
View File
@@ -1,2 +0,0 @@
from Problem import *
import ModelTransforms
SimPEG/inverse/BetaSchedule.py
-12
View File
@@ -1,12 +0,0 @@
class Cooling(object):
"""Simple Beta Schedule"""
beta0 = None #: The initial beta value, set to none means that it will be approximated in the first iteration.
beta_coolingFactor = 2.
def getBeta(self):
if self._beta is None:
return self.beta0
return self._beta / self.beta_coolingFactor
SimPEG/inverse/Inversion.py
-396
View File
@@ -1,396 +0,0 @@
import SimPEG
from SimPEG import utils, sp, np
from Optimize import Remember
from BetaSchedule import Cooling
from SimPEG.inverse import IterationPrinters, StoppingCriteria
class BaseInversion(object):
"""BaseInversion(prob, reg, opt, data, **kwargs)
"""
__metaclass__ = utils.Save.Savable
maxIter = 1 #: Maximum number of iterations
name = 'BaseInversion'
debug = False #: Print debugging information
comment = '' #: Used by some functions to indicate what is going on in the algorithm
counter = None #: Set this to a SimPEG.utils.Counter() if you want to count things
beta0 = None #: The initial Beta (regularization parameter)
beta0_ratio = 0.1 #: When beta0 is set to None, estimateBeta0 is used with this ratio
def __init__(self, prob, reg, opt, data, **kwargs):
utils.setKwargs(self, **kwargs)
self.prob = prob
self.reg = reg
self.opt = opt
self.data = data
self.opt.parent = self
self.stoppers = [StoppingCriteria.iteration]
# Check if we have inserted printers into the optimization
if IterationPrinters.phi_d not in self.opt.printers:
self.opt.printers.insert(1,IterationPrinters.beta)
self.opt.printers.insert(2,IterationPrinters.phi_d)
self.opt.printers.insert(3,IterationPrinters.phi_m)
if not hasattr(opt, '_bfgsH0') and hasattr(opt, 'bfgsH0'): # Check if it has been set by the user and the default is not being used.
print 'Setting bfgsH0 to the inverse of the modelObj2Deriv. Done using direct methods.'
opt.bfgsH0 = SimPEG.Solver(reg.modelObj2Deriv())
@property
def Wd(self):
"""
Standard deviation weighting matrix.
"""
if getattr(self,'_Wd',None) is None:
eps = np.linalg.norm(utils.mkvc(self.data.dobs),2)*1e-5
self._Wd = 1/(abs(self.data.dobs)*self.data.std+eps)
return self._Wd
@Wd.setter
def Wd(self, value):
self._Wd = value
@property
def phi_d_target(self):
"""
target for phi_d
By default this is the number of data.
Note that we do not set the target if it is None, but we return the default value.
"""
if getattr(self, '_phi_d_target', None) is None:
return self.data.dobs.size #
return self._phi_d_target
@phi_d_target.setter
def phi_d_target(self, value):
self._phi_d_target = value
@utils.timeIt
def run(self, m0):
"""run(m0)
Runs the inversion!
"""
self.startup(m0)
while True:
self.doStartIteration()
self.m = self.opt.minimize(self.evalFunction, self.m)
self.doEndIteration()
if self.stoppingCriteria(): break
self.printDone()
self.finish()
return self.m
@utils.callHooks('startup')
def startup(self, m0):
"""
**startup** is called at the start of any new run call.
:param numpy.ndarray x0: initial x
:rtype: None
:return: None
"""
if not hasattr(self.reg, '_mref'):
print 'Regularization has not set mref. SimPEG will set it to m0.'
self.reg.mref = m0
self.m = m0
self._iter = 0
self._beta = None
self.phi_d_last = np.nan
self.phi_m_last = np.nan
@utils.callHooks('doStartIteration')
def doStartIteration(self):
"""
**doStartIteration** is called at the end of each run iteration.
:rtype: None
:return: None
"""
self._beta = self.getBeta()
@utils.callHooks('doEndIteration')
def doEndIteration(self):
"""
**doEndIteration** is called at the end of each run iteration.
:rtype: None
:return: None
"""
# store old values
self.phi_d_last = self.phi_d
self.phi_m_last = self.phi_m
self._iter += 1
def getBeta(self):
return self.beta0
def estimateBeta0(self, u=None, ratio=0.1):
"""estimateBeta0(u=None, ratio=0.1)
The initial beta is calculated by comparing the estimated
eigenvalues of JtJ and WtW.
To estimate the eigenvector of **A**, we will use one iteration
of the *Power Method*:
.. math::
\mathbf{x_1 = A x_0}
Given this (very course) approximation of the eigenvector,
we can use the *Rayleigh quotient* to approximate the largest eigenvalue.
.. math::
\lambda_0 = \\frac{\mathbf{x^\\top A x}}{\mathbf{x^\\top x}}
We will approximate the largest eigenvalue for both JtJ and WtW, and
use some ratio of the quotient to estimate beta0.
.. math::
\\beta_0 = \gamma \\frac{\mathbf{x^\\top J^\\top J x}}{\mathbf{x^\\top W^\\top W x}}
:param numpy.array u: fields
:param float ratio: desired ratio of the eigenvalues, default is 0.1
:rtype: float
:return: beta0
"""
if u is None:
u = self.prob.field(self.m)
x0 = np.random.rand(*self.m.shape)
t = x0.dot(self.dataObj2Deriv(self.m,x0,u=u))
b = x0.dot(self.reg.modelObj2Deriv()*x0)
return ratio*(t/b)
def stoppingCriteria(self):
if self.debug: print 'checking stoppingCriteria'
return utils.checkStoppers(self, self.stoppers)
def printDone(self):
"""
**printDone** is called at the end of the inversion routine.
"""
utils.printStoppers(self, self.stoppers)
@utils.callHooks('finish')
def finish(self):
"""finish()
**finish** is called at the end of the optimization.
"""
pass
@utils.timeIt
def evalFunction(self, m, return_g=True, return_H=True):
"""evalFunction(m, return_g=True, return_H=True)
"""
u = self.prob.field(m)
if self._iter is 0 and self._beta is None:
self._beta = self.beta0 = self.estimateBeta0(u=u,ratio=self.beta0_ratio)
phi_d = self.dataObj(m, u)
phi_m = self.reg.modelObj(m)
self.dpred = self.prob.dpred(m, u=u) # This is a cheap matrix vector calculation.
self.phi_d = phi_d
self.phi_m = phi_m
f = phi_d + self._beta * phi_m
out = (f,)
if return_g:
phi_dDeriv = self.dataObjDeriv(m, u=u)
phi_mDeriv = self.reg.modelObjDeriv(m)
g = phi_dDeriv + self._beta * phi_mDeriv
out += (g,)
if return_H:
def H_fun(v):
phi_d2Deriv = self.dataObj2Deriv(m, v, u=u)
phi_m2Deriv = self.reg.modelObj2Deriv()*v
return phi_d2Deriv + self._beta * phi_m2Deriv
operator = sp.linalg.LinearOperator( (m.size, m.size), H_fun, dtype=m.dtype )
out += (operator,)
return out if len(out) > 1 else out[0]
@utils.timeIt
def dataObj(self, m, u=None):
"""dataObj(m, u=None)
:param numpy.array m: geophysical model
:param numpy.array u: fields
:rtype: float
:return: data misfit
The data misfit using an l_2 norm is:
.. math::
\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
"""
# TODO: ensure that this is a data is vector and Wd is a matrix.
R = self.Wd*self.prob.dataResidual(m, self.data, u=u)
R = utils.mkvc(R)
return 0.5*np.vdot(R, R)
@utils.timeIt
def dataObjDeriv(self, m, u=None):
"""dataObjDeriv(m, u=None)
:param numpy.array m: geophysical model
:param numpy.array u: fields
:rtype: numpy.array
:return: data misfit derivative
The data misfit using an l_2 norm is:
.. math::
\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
If the field, u, is provided, the calculation of the data is fast:
.. math::
\mathbf{d}_\\text{pred} = \mathbf{Pu(m)}
\mathbf{R} = \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs})
Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
The derivative of this, with respect to the model, is:
.. math::
\\frac{\partial \mu_\\text{data}}{\partial \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ R}
"""
if u is None:
u = self.prob.field(m)
R = self.Wd*self.prob.dataResidual(m, self.data, u=u)
dmisfit = self.prob.Jt(m, self.Wd * R, u=u)
return dmisfit
@utils.timeIt
def dataObj2Deriv(self, m, v, u=None):
"""dataObj2Deriv(m, v, u=None)
:param numpy.array m: geophysical model
:param numpy.array v: vector to multiply
:param numpy.array u: fields
:rtype: numpy.array
:return: data misfit derivative
The data misfit using an l_2 norm is:
.. math::
\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
If the field, u, is provided, the calculation of the data is fast:
.. math::
\mathbf{d}_\\text{pred} = \mathbf{Pu(m)}
\mathbf{R} = \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs})
Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
The derivative of this, with respect to the model, is:
.. math::
\\frac{\partial \mu_\\text{data}}{\partial \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ R}
\\frac{\partial^2 \mu_\\text{data}}{\partial^2 \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ W J}
"""
if u is None:
u = self.prob.field(m)
R = self.Wd*self.prob.dataResidual(m, self.data, u=u)
# TODO: abstract to different norms a little cleaner.
# \/ it goes here. in l2 it is the identity.
dmisfit = self.prob.Jt_approx(m, self.Wd * self.Wd * self.prob.J_approx(m, v, u=u), u=u)
return dmisfit
def save(self, group):
group.attrs['phi_d'] = self.phi_d
group.attrs['phi_m'] = self.phi_m
group.setArray('m', self.m)
group.setArray('dpred', self.dpred)
class Inversion(Cooling, Remember, BaseInversion):
maxIter = 10
name = "SimPEG Inversion"
def __init__(self, prob, reg, opt, data, **kwargs):
BaseInversion.__init__(self, prob, reg, opt, data, **kwargs)
self.stoppers.append(StoppingCriteria.phi_d_target_Inversion)
if StoppingCriteria.phi_d_target_Minimize not in self.opt.stoppers:
self.opt.stoppers.append(StoppingCriteria.phi_d_target_Minimize)
class TimeSteppingInversion(Remember, BaseInversion):
"""
A slightly different view on regularization parameters,
let Beta be viewed as 1/dt, and timestep by updating the
reference model every optimization iteration.
"""
maxIter = 1
name = "Time-Stepping SimPEG Inversion"
def __init__(self, prob, reg, opt, data, **kwargs):
BaseInversion.__init__(self, prob, reg, opt, data, **kwargs)
self.stoppers.append(StoppingCriteria.phi_d_target_Inversion)
if StoppingCriteria.phi_d_target_Minimize not in self.opt.stoppers:
self.opt.stoppers.append(StoppingCriteria.phi_d_target_Minimize)
def _startup_TimeSteppingInversion(self, m0):
def _doEndIteration_updateMref(self, xt):
if self.debug: 'Updating the reference model.'
self.parent.reg.mref = self.xc
self.opt.hook(_doEndIteration_updateMref, overwrite=True)
SimPEG/inverse/__init__.py
-4
View File
@@ -1,4 +0,0 @@
from Optimize import *
from Inversion import *
from Regularization import Regularization
import BetaSchedule
SimPEG/license.txt
-21
View File
@@ -1,21 +0,0 @@
The MIT License (MIT)
Copyright (c) 2013 SimPEG Developers
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
SimPEG/setup.py
+2 -2
View File
@@ -1,8 +1,8 @@
import os
print 'Compiling TriSolve.'
os.system('f2py -c utils/TriSolve.f -m TriSolve')
os.system('f2py -c Utils/TriSolve.f -m TriSolve')
print 'TriSolve Compiled! yay.'
print 'Moving TriSolve into Utils.'
os.system('mv TriSolve.so utils/TriSolve.so')
os.system('mv TriSolve.so Utils/TriSolve.so')
print 'Thats it. Well Done Computer.'
SimPEG/tests/HTMLTestRunner.py
-825
View File
@@ -1,825 +0,0 @@
"""
A TestRunner for use with the Python unit testing framework. It
generates a HTML report to show the result at a glance.
The simplest way to use this is to invoke its main method. E.g.
import unittest
import HTMLTestRunner
... define your tests ...
if __name__ == '__main__':
HTMLTestRunner.main()
For more customization options, instantiates a HTMLTestRunner object.
HTMLTestRunner is a counterpart to unittest's TextTestRunner. E.g.
# output to a file
fp = file('my_report.html', 'wb')
runner = HTMLTestRunner.HTMLTestRunner(
stream=fp,
title='My unit test',
description='This demonstrates the report output by HTMLTestRunner.'
)
# Use an external stylesheet.
# See the Template_mixin class for more customizable options
runner.STYLESHEET_TMPL = '<link rel="stylesheet" href="my_stylesheet.css" type="text/css">'
# run the test
runner.run(my_test_suite)
------------------------------------------------------------------------
Copyright (c) 2004-2007, Wai Yip Tung
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name Wai Yip Tung nor the names of its contributors may be
used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
"""
# URL: http://tungwaiyip.info/software/HTMLTestRunner.html
__author__ = "Wai Yip Tung"
__version__ = "0.8.2"
"""
Change History
Version 0.8.2
* Show output inline instead of popup window (Viorel Lupu).
Version in 0.8.1
* Validated XHTML (Wolfgang Borgert).
* Added description of test classes and test cases.
Version in 0.8.0
* Define Template_mixin class for customization.
* Workaround a IE 6 bug that it does not treat <script> block as CDATA.
Version in 0.7.1
* Back port to Python 2.3 (Frank Horowitz).
* Fix missing scroll bars in detail log (Podi).
"""
# TODO: color stderr
# TODO: simplify javascript using ,ore than 1 class in the class attribute?
import datetime
import StringIO
import sys
import time
import unittest
from xml.sax import saxutils
# ------------------------------------------------------------------------
# The redirectors below are used to capture output during testing. Output
# sent to sys.stdout and sys.stderr are automatically captured. However
# in some cases sys.stdout is already cached before HTMLTestRunner is
# invoked (e.g. calling logging.basicConfig). In order to capture those
# output, use the redirectors for the cached stream.
#
# e.g.
# >>> logging.basicConfig(stream=HTMLTestRunner.stdout_redirector)
# >>>
class OutputRedirector(object):
""" Wrapper to redirect stdout or stderr """
def __init__(self, fp):
self.fp = fp
def write(self, s):
self.fp.write(s)
def writelines(self, lines):
self.fp.writelines(lines)
def flush(self):
self.fp.flush()
stdout_redirector = OutputRedirector(sys.stdout)
stderr_redirector = OutputRedirector(sys.stderr)
# ----------------------------------------------------------------------
# Template
class Template_mixin(object):
"""
Define a HTML template for report customerization and generation.
Overall structure of an HTML report
HTML
+------------------------+
|<html> |
| <head> |
| |
| STYLESHEET |
| +----------------+ |
| | | |
| +----------------+ |
| |
| </head> |
| |
| <body> |
| |
| HEADING |
| +----------------+ |
| | | |
| +----------------+ |
| |
| REPORT |
| +----------------+ |
| | | |
| +----------------+ |
| |
| ENDING |
| +----------------+ |
| | | |
| +----------------+ |
| |
| </body> |
|</html> |
+------------------------+
"""
STATUS = {
0: 'pass',
1: 'fail',
2: 'error',
}
DEFAULT_TITLE = 'Unit Test Report'
DEFAULT_DESCRIPTION = ''
# ------------------------------------------------------------------------
# HTML Template
HTML_TMPL = r"""<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title>%(title)s</title>
<meta name="generator" content="%(generator)s"/>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
%(stylesheet)s
</head>
<body>
<script language="javascript" type="text/javascript"><!--
output_list = Array();
/* level - 0:Summary; 1:Failed; 2:All */
function showCase(level) {
trs = document.getElementsByTagName("tr");
for (var i = 0; i < trs.length; i++) {
tr = trs[i];
id = tr.id;
if (id.substr(0,2) == 'ft') {
if (level < 1) {
tr.className = 'hiddenRow';
}
else {
tr.className = '';
}
}
if (id.substr(0,2) == 'pt') {
if (level > 1) {
tr.className = '';
}
else {
tr.className = 'hiddenRow';
}
}
}
}
function showClassDetail(cid, count) {
var id_list = Array(count);
var toHide = 1;
for (var i = 0; i < count; i++) {
tid0 = 't' + cid.substr(1) + '.' + (i+1);
tid = 'f' + tid0;
tr = document.getElementById(tid);
if (!tr) {
tid = 'p' + tid0;
tr = document.getElementById(tid);
}
id_list[i] = tid;
if (tr.className) {
toHide = 0;
}
}
for (var i = 0; i < count; i++) {
tid = id_list[i];
if (toHide) {
var divTid = document.getElementById('div_'+tid);
if(divTid !== null){divTid.style.display = 'none';}
document.getElementById(tid).className = 'hiddenRow';
}
else {
document.getElementById(tid).className = '';
}
}
}
function showTestDetail(div_id){
var details_div = document.getElementById(div_id)
var displayState = details_div.style.display
// alert(displayState)
if (displayState != 'block' ) {
displayState = 'block'
details_div.style.display = 'block'
}
else {
details_div.style.display = 'none'
}
}
function html_escape(s) {
s = s.replace(/&/g,'&amp;');
s = s.replace(/</g,'&lt;');
s = s.replace(/>/g,'&gt;');
return s;
}
/* obsoleted by detail in <div>
function showOutput(id, name) {
var w = window.open("", //url
name,
"resizable,scrollbars,status,width=800,height=450");
d = w.document;
d.write("<pre>");
d.write(html_escape(output_list[id]));
d.write("\n");
d.write("<a href='javascript:window.close()'>close</a>\n");
d.write("</pre>\n");
d.close();
}
*/
--></script>
%(heading)s
%(report)s
%(ending)s
</body>
</html>
"""
# variables: (title, generator, stylesheet, heading, report, ending)
# ------------------------------------------------------------------------
# Stylesheet
#
# alternatively use a <link> for external style sheet, e.g.
# <link rel="stylesheet" href="$url" type="text/css">
STYLESHEET_TMPL = """
<style type="text/css" media="screen">
body { font-family: verdana, arial, helvetica, sans-serif; font-size: 80%; }
table { font-size: 100%; }
pre { }
/* -- heading ---------------------------------------------------------------------- */
h1 {
font-size: 16pt;
color: gray;
}
.heading {
margin-top: 0ex;
margin-bottom: 1ex;
}
.heading .attribute {
margin-top: 1ex;
margin-bottom: 0;
}
.heading .description {
margin-top: 4ex;
margin-bottom: 6ex;
}
/* -- css div popup ------------------------------------------------------------------------ */
a.popup_link {
}
a.popup_link:hover {
color: red;
}
.popup_window {
display: none;
position: relative;
left: 0px;
top: 0px;
/*border: solid #627173 1px; */
padding: 10px;
background-color: #E6E6D6;
font-family: "Lucida Console", "Courier New", Courier, monospace;
text-align: left;
font-size: 8pt;
width: 500px;
}
}
/* -- report ------------------------------------------------------------------------ */
#show_detail_line {
margin-top: 3ex;
margin-bottom: 1ex;
}
#result_table {
width: 80%;
border-collapse: collapse;
border: 1px solid #777;
}
#header_row {
font-weight: bold;
color: white;
background-color: #777;
}
#result_table td {
border: 1px solid #777;
padding: 2px;
}
#total_row { font-weight: bold; }
.passClass { background-color: #6c6; }
.failClass { background-color: #c60; }
.errorClass { background-color: #c00; }
.passCase { color: #6c6; }
.failCase { color: #c60; font-weight: bold; }
.errorCase { color: #c00; font-weight: bold; }
.hiddenRow { display: none; }
.testcase { margin-left: 2em; }
/* -- ending ---------------------------------------------------------------------- */
#ending {
}
</style>
"""
# ------------------------------------------------------------------------
# Heading
#
HEADING_TMPL = """<div class='heading'>
<h1>%(title)s</h1>
%(parameters)s
<p class='description'>%(description)s</p>
</div>
""" # variables: (title, parameters, description)
HEADING_ATTRIBUTE_TMPL = """<p class='attribute'><strong>%(name)s:</strong> %(value)s</p>
""" # variables: (name, value)
# ------------------------------------------------------------------------
# Report
#
REPORT_TMPL = """
<p id='show_detail_line'>Show
<a href='javascript:showCase(0)'>Summary</a>
<a href='javascript:showCase(1)'>Failed</a>
<a href='javascript:showCase(2)'>All</a>
</p>
<table id='result_table'>
<colgroup>
<col align='left' />
<col align='right' />
<col align='right' />
<col align='right' />
<col align='right' />
<col align='right' />
</colgroup>
<tr id='header_row'>
<td>Test Group/Test case</td>
<td>Count</td>
<td>Pass</td>
<td>Fail</td>
<td>Error</td>
<td>View</td>
</tr>
%(test_list)s
<tr id='total_row'>
<td>Total</td>
<td>%(count)s</td>
<td>%(Pass)s</td>
<td>%(fail)s</td>
<td>%(error)s</td>
<td>&nbsp;</td>
</tr>
</table>
""" # variables: (test_list, count, Pass, fail, error)
REPORT_CLASS_TMPL = r"""
<tr class='%(style)s'>
<td>%(desc)s</td>
<td>%(count)s</td>
<td>%(Pass)s</td>
<td>%(fail)s</td>
<td>%(error)s</td>
<td><a href="javascript:showClassDetail('%(cid)s',%(count)s)">Detail</a></td>
</tr>
""" # variables: (style, desc, count, Pass, fail, error, cid)
REPORT_TEST_WITH_OUTPUT_TMPL = r"""
<tr id='%(tid)s' class='%(Class)s'>
<td class='%(style)s'><div class='testcase'>%(desc)s</div></td>
<td colspan='5' align='center'>
<!--css div popup start-->
<a class="popup_link" onfocus='this.blur();' href="javascript:showTestDetail('div_%(tid)s')" >
%(status)s</a>
<div id='div_%(tid)s' class="popup_window">
<div style='text-align: right; color:red;cursor:pointer'>
<a onfocus='this.blur();' onclick="document.getElementById('div_%(tid)s').style.display = 'none' " >
[x]</a>
</div>
<pre>
%(script)s
</pre>
</div>
<!--css div popup end-->
</td>
</tr>
""" # variables: (tid, Class, style, desc, status)
REPORT_TEST_NO_OUTPUT_TMPL = r"""
<tr id='%(tid)s' class='%(Class)s'>
<td class='%(style)s'><div class='testcase'>%(desc)s</div></td>
<td colspan='5' align='center'>%(status)s</td>
</tr>
""" # variables: (tid, Class, style, desc, status)
REPORT_TEST_OUTPUT_TMPL = r"""
%(id)s: %(output)s
""" # variables: (id, output)
# ------------------------------------------------------------------------
# ENDING
#
ENDING_TMPL = """<div id='ending'>&nbsp;</div>"""
# -------------------- The end of the Template class -------------------
TestResult = unittest.TestResult
class _TestResult(TestResult):
# note: _TestResult is a pure representation of results.
# It lacks the output and reporting ability compares to unittest._TextTestResult.
def __init__(self, verbosity=1):
TestResult.__init__(self)
self.stdout0 = None
self.stderr0 = None
self.success_count = 0
self.failure_count = 0
self.error_count = 0
self.verbosity = verbosity
# result is a list of result in 4 tuple
# (
# result code (0: success; 1: fail; 2: error),
# TestCase object,
# Test output (byte string),
# stack trace,
# )
self.result = []
def startTest(self, test):
TestResult.startTest(self, test)
# just one buffer for both stdout and stderr
self.outputBuffer = StringIO.StringIO()
stdout_redirector.fp = self.outputBuffer
stderr_redirector.fp = self.outputBuffer
self.stdout0 = sys.stdout
self.stderr0 = sys.stderr
sys.stdout = stdout_redirector
sys.stderr = stderr_redirector
def complete_output(self):
"""
Disconnect output redirection and return buffer.
Safe to call multiple times.
"""
if self.stdout0:
sys.stdout = self.stdout0
sys.stderr = self.stderr0
self.stdout0 = None
self.stderr0 = None
return self.outputBuffer.getvalue()
def stopTest(self, test):
# Usually one of addSuccess, addError or addFailure would have been called.
# But there are some path in unittest that would bypass this.
# We must disconnect stdout in stopTest(), which is guaranteed to be called.
self.complete_output()
def addSuccess(self, test):
self.success_count += 1
TestResult.addSuccess(self, test)
output = self.complete_output()
self.result.append((0, test, output, ''))
if self.verbosity > 1:
sys.stderr.write('ok ')
sys.stderr.write(str(test))
sys.stderr.write('\n')
else:
sys.stderr.write('.')
def addError(self, test, err):
self.error_count += 1
TestResult.addError(self, test, err)
_, _exc_str = self.errors[-1]
output = self.complete_output()
self.result.append((2, test, output, _exc_str))
if self.verbosity > 1:
sys.stderr.write('E ')
sys.stderr.write(str(test))
sys.stderr.write('\n')
else:
sys.stderr.write('E')
def addFailure(self, test, err):
self.failure_count += 1
TestResult.addFailure(self, test, err)
_, _exc_str = self.failures[-1]
output = self.complete_output()
self.result.append((1, test, output, _exc_str))
if self.verbosity > 1:
sys.stderr.write('F ')
sys.stderr.write(str(test))
sys.stderr.write('\n')
else:
sys.stderr.write('F')
class HTMLTestRunner(Template_mixin):
"""
"""
def __init__(self, stream=sys.stdout, verbosity=1, title=None, description=None):
self.stream = stream
self.verbosity = verbosity
if title is None:
self.title = self.DEFAULT_TITLE
else:
self.title = title
if description is None:
self.description = self.DEFAULT_DESCRIPTION
else:
self.description = description
self.startTime = datetime.datetime.now()
def run(self, test):
"Run the given test case or test suite."
result = _TestResult(self.verbosity)
test(result)
self.stopTime = datetime.datetime.now()
self.generateReport(test, result)
print >>sys.stderr, '\nTime Elapsed: %s' % (self.stopTime-self.startTime)
return result
def sortResult(self, result_list):
# unittest does not seems to run in any particular order.
# Here at least we want to group them together by class.
rmap = {}
classes = []
for n,t,o,e in result_list:
cls = t.__class__
if not rmap.has_key(cls):
rmap[cls] = []
classes.append(cls)
rmap[cls].append((n,t,o,e))
r = [(cls, rmap[cls]) for cls in classes]
return r
def getReportAttributes(self, result):
"""
Return report attributes as a list of (name, value).
Override this to add custom attributes.
"""
startTime = str(self.startTime)[:19]
duration = str(self.stopTime - self.startTime)
status = []
if result.success_count: status.append('Pass %s' % result.success_count)
if result.failure_count: status.append('Failure %s' % result.failure_count)
if result.error_count: status.append('Error %s' % result.error_count )
if status:
status = ' '.join(status)
else:
status = 'none'
return [
('Start Time', startTime),
('Duration', duration),
('Status', status),
]
def generateReport(self, test, result):
report_attrs = self.getReportAttributes(result)
generator = 'HTMLTestRunner %s' % __version__
stylesheet = self._generate_stylesheet()
heading = self._generate_heading(report_attrs)
report = self._generate_report(result)
ending = self._generate_ending()
output = self.HTML_TMPL % dict(
title = saxutils.escape(self.title),
generator = generator,
stylesheet = stylesheet,
heading = heading,
report = report,
ending = ending,
)
self.stream.write(output.encode('utf8'))
def _generate_stylesheet(self):
return self.STYLESHEET_TMPL
def _generate_heading(self, report_attrs):
a_lines = []
for name, value in report_attrs:
line = self.HEADING_ATTRIBUTE_TMPL % dict(
name = saxutils.escape(name),
value = saxutils.escape(value),
)
a_lines.append(line)
heading = self.HEADING_TMPL % dict(
title = saxutils.escape(self.title),
parameters = ''.join(a_lines),
description = saxutils.escape(self.description),
)
return heading
def _generate_report(self, result):
rows = []
sortedResult = self.sortResult(result.result)
for cid, (cls, cls_results) in enumerate(sortedResult):
# subtotal for a class
np = nf = ne = 0
for n,t,o,e in cls_results:
if n == 0: np += 1
elif n == 1: nf += 1
else: ne += 1
# format class description
if cls.__module__ == "__main__":
name = cls.__name__
else:
name = "%s.%s" % (cls.__module__, cls.__name__)
doc = cls.__doc__ and cls.__doc__.split("\n")[0] or ""
desc = doc and '%s: %s' % (name, doc) or name
row = self.REPORT_CLASS_TMPL % dict(
style = ne > 0 and 'errorClass' or nf > 0 and 'failClass' or 'passClass',
desc = desc,
count = np+nf+ne,
Pass = np,
fail = nf,
error = ne,
cid = 'c%s' % (cid+1),
)
rows.append(row)
for tid, (n,t,o,e) in enumerate(cls_results):
self._generate_report_test(rows, cid, tid, n, t, o, e)
report = self.REPORT_TMPL % dict(
test_list = ''.join(rows),
count = str(result.success_count+result.failure_count+result.error_count),
Pass = str(result.success_count),
fail = str(result.failure_count),
error = str(result.error_count),
)
return report
def _generate_report_test(self, rows, cid, tid, n, t, o, e):
# e.g. 'pt1.1', 'ft1.1', etc
has_output = bool(o or e)
tid = (n == 0 and 'p' or 'f') + 't%s.%s' % (cid+1,tid+1)
name = t.id().split('.')[-1]
doc = t.shortDescription() or ""
desc = doc and ('%s: %s' % (name, doc)) or name
tmpl = has_output and self.REPORT_TEST_WITH_OUTPUT_TMPL or self.REPORT_TEST_NO_OUTPUT_TMPL
# o and e should be byte string because they are collected from stdout and stderr?
if isinstance(o,str):
# TODO: some problem with 'string_escape': it escape \n and mess up formating
# uo = unicode(o.encode('string_escape'))
uo = o.decode('latin-1')
else:
uo = o
if isinstance(e,str):
# TODO: some problem with 'string_escape': it escape \n and mess up formating
# ue = unicode(e.encode('string_escape'))
ue = e.decode('latin-1')
else:
ue = e
script = self.REPORT_TEST_OUTPUT_TMPL % dict(
id = tid,
output = saxutils.escape(uo+ue),
)
row = tmpl % dict(
tid = tid,
Class = (n == 0 and 'hiddenRow' or 'none'),
style = n == 2 and 'errorCase' or (n == 1 and 'failCase' or 'none'),
desc = desc,
script = script,
status = self.STATUS[n],
)
rows.append(row)
if not has_output:
return
def _generate_ending(self):
return self.ENDING_TMPL
##############################################################################
# Facilities for running tests from the command line
##############################################################################
# Note: Reuse unittest.TestProgram to launch test. In the future we may
# build our own launcher to support more specific command line
# parameters like test title, CSS, etc.
class TestProgram(unittest.TestProgram):
"""
A variation of the unittest.TestProgram. Please refer to the base
class for command line parameters.
"""
def runTests(self):
# Pick HTMLTestRunner as the default test runner.
# base class's testRunner parameter is not useful because it means
# we have to instantiate HTMLTestRunner before we know self.verbosity.
if self.testRunner is None:
self.testRunner = HTMLTestRunner(verbosity=self.verbosity)
unittest.TestProgram.runTests(self)
main = TestProgram
##############################################################################
# Executing this module from the command line
##############################################################################
if __name__ == "__main__":
main(module=None)
SimPEG/tests/__init__.py
-2
View File
@@ -1,2 +0,0 @@
import TestUtils
from TestUtils import checkDerivative, Rosenbrock, OrderTest, getQuadratic
SimPEG/tests/runTests.py
-57
View File
@@ -1,57 +0,0 @@
import os
import glob
import unittest
import HTMLTestRunner
# This code will run all tests in directory named test_*.py
def main(html=False):
TITLE = 'Test Results'
test_file_strings = glob.glob('test_*.py')
module_strings = [str[0:len(str)-3] for str in test_file_strings]
suites = [unittest.defaultTestLoader.loadTestsFromName(str) for str
in module_strings]
testSuite = unittest.TestSuite(suites)
if not html:
unittest.TextTestRunner(verbosity=2).run(testSuite)
return
outfile = open("report.html", "w")
runner = HTMLTestRunner.HTMLTestRunner(
stream=outfile,
title=TITLE,
description='SimPEG Test Report was automatically generated.',
verbosity=2
)
runner.run(testSuite)
outfile.close()
reader = open("report.html", "r")
writer = open("../../docs/api_TestResults.rst", "w")
writer.write('.. _api_TestResults:\n\nTest Results\n============\n\n.. raw:: html\n\n')
go = False
for line in reader:
skip = False
if line == '<style type="text/css" media="screen">\n':
go = True
elif line == "<div id='ending'>&nbsp;</div>\n":
go = False
elif line == '</head>\n':
skip = True
elif line == '<h1>'+TITLE+'</h1>\n':
skip = True
elif line == '<body>\n':
skip = True
if go and not skip:
writer.write(' '+line)
writer.close()
reader.close()
os.remove("report.html")
if __name__ == '__main__':
main(True)
SimPEG/tests/runTests.sh
-3
View File
@@ -1,3 +0,0 @@
#!/bin/sh
python -m unittest discover
SimPEG/tests/test_forward_DCproblem.py
-85
View File
@@ -1,85 +0,0 @@
import numpy as np
import unittest
from SimPEG.mesh import TensorMesh
from SimPEG.utils import ModelBuilder, sdiag
from SimPEG.forward import Problem
from SimPEG.examples.DC import *
from TestUtils import checkDerivative
from scipy.sparse.linalg import dsolve
from SimPEG import inverse
class DCProblemTests(unittest.TestCase):
def setUp(self):
# Create the mesh
h1 = np.ones(20)
h2 = np.ones(20)
mesh = TensorMesh([h1,h2])
# Create some parameters for the model
sig1 = 1
sig2 = 0.01
# Create a synthetic model from a block in a half-space
p0 = [2, 2]
p1 = [5, 5]
condVals = [sig1, sig2]
mSynth = ModelBuilder.defineBlockConductivity(p0,p1,mesh.gridCC,condVals)
# Set up the projection
nelec = 10
spacelec = 2
surfloc = 0.5
elecini = 0.5
elecend = 0.5+spacelec*(nelec-1)
elecLocR = np.linspace(elecini, elecend, nelec)
rxmidLoc = (elecLocR[0:nelec-1]+elecLocR[1:nelec])*0.5
q, Q, rxmidloc = genTxRxmat(nelec, spacelec, surfloc, elecini, mesh)
P = Q.T
# Create some data
problem = DCProblem(mesh)
problem.P = P
problem.RHS = q
data = problem.createSyntheticData(mSynth, std=0.05)
# Now set up the problem to do some minimization
opt = inverse.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6)
reg = inverse.Regularization(mesh)
inv = inverse.Inversion(problem, reg, opt, data, beta0=1e4)
self.inv = inv
self.reg = reg
self.p = problem
self.mesh = mesh
self.m0 = mSynth
self.data = data
def test_misfit(self):
derChk = lambda m: [self.p.dpred(m), lambda mx: self.p.J(self.m0, mx)]
passed = checkDerivative(derChk, self.m0, plotIt=False)
self.assertTrue(passed)
def test_adjoint(self):
# Adjoint Test
u = np.random.rand(self.mesh.nC*self.p.RHS.shape[1])
v = np.random.rand(self.mesh.nC)
w = np.random.rand(self.data.dobs.shape[0])
wtJv = w.dot(self.p.J(self.m0, v, u=u))
vtJtw = v.dot(self.p.Jt(self.m0, w, u=u))
passed = (wtJv - vtJtw) < 1e-10
self.assertTrue(passed)
def test_dataObj(self):
derChk = lambda m: [self.inv.dataObj(m), self.inv.dataObjDeriv(m)]
checkDerivative(derChk, self.m0, plotIt=False)
def test_modelObj(self):
derChk = lambda m: [self.reg.modelObj(m), self.reg.modelObjDeriv(m)]
checkDerivative(derChk, self.m0, plotIt=False)
if __name__ == '__main__':
unittest.main()
SimPEG/tests/test_forward_problem.py
-34
View File
@@ -1,34 +0,0 @@
import numpy as np
import unittest
from SimPEG import mesh, forward, inverse
from TestUtils import checkDerivative
from scipy.sparse.linalg import dsolve
class ProblemTests(unittest.TestCase):
def setUp(self):
a = np.array([1, 1, 1])
b = np.array([1, 2])
c = np.array([1, 4])
self.mesh2 = mesh.TensorMesh([a, b], np.array([3, 5]))
self.p2 = forward.Problem(self.mesh2)
self.reg = inverse.Regularization(self.mesh2)
def test_modelTransform(self):
print 'SimPEG.forward.Problem: Testing Model Transform'
m = np.random.rand(self.mesh2.nC)
passed = checkDerivative(lambda m : [self.p2.modelTransform(m), self.p2.modelTransformDeriv(m)], m, plotIt=False)
self.assertTrue(passed)
def test_regularization(self):
derChk = lambda m: [self.reg.modelObj(m), self.reg.modelObjDeriv(m)]
mSynth = np.random.randn(self.mesh2.nC)
checkDerivative(derChk, mSynth, plotIt=False)
if __name__ == '__main__':
unittest.main()
SimPEG/visualize/vtk/vtkTools.py
+1 -1
View File
@@ -3,7 +3,7 @@ try:
import vtk, vtk.util.numpy_support as npsup, pdb
except Exception, e:
print 'VTK import error. Please ensure you have VTK installed to use this visualization package.'
from SimPEG.utils import mkvc
from SimPEG.Utils import mkvc
class vtkTools(object):
docs/api_BaseMesh.rst
+1 -1
View File
@@ -3,6 +3,6 @@
Base Mesh
*********
.. automodule:: SimPEG.mesh.BaseMesh
.. automodule:: SimPEG.Mesh.BaseMesh
:members:
:undoc-members:
docs/api_Cyl1DMesh.rst
+2 -2
View File
@@ -3,6 +3,6 @@
Cylindrical 1D Mesh
*******************
.. automodule:: SimPEG.mesh.Cyl1DMesh
.. automodule:: SimPEG.Mesh.Cyl1DMesh
:members:
:undoc-members:
:undoc-members:
docs/api_DiffOperators.rst
+1 -1
View File
@@ -3,6 +3,6 @@
Differential Operators
**********************
.. automodule:: SimPEG.mesh.DiffOperators
.. automodule:: SimPEG.Mesh.DiffOperators
:members:
:undoc-members:
docs/api_Problem.rst → docs/api_Forward.rst
+20 -22
View File
@@ -1,32 +1,30 @@
.. _api_Problem:
.. _api_Forward:
Model
*****
.. automodule:: SimPEG.Model
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
Data
****
.. automodule:: SimPEG.Data
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
Problem
*******
.. automodule:: SimPEG.forward.Problem
.. automodule:: SimPEG.Problem
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
DCProblem
*********
.. automodule:: SimPEG.examples.DC
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
Linear Problem
**************
.. automodule:: SimPEG.examples.Linear
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
docs/api_InnerProducts.rst
+1 -1
View File
@@ -3,6 +3,6 @@
Inner Products
**************
.. automodule:: SimPEG.mesh.InnerProducts
.. automodule:: SimPEG.Mesh.InnerProducts
:members:
:undoc-members:
docs/api_Optimize.rst → docs/api_Inverse.rst
+29 -26
View File
@@ -1,35 +1,38 @@
.. _api_Inverse:
Optimize
********
.. automodule:: SimPEG.inverse.Optimize
:show-inheritance:
:private-members:
:members:
:undoc-members:
Inversion
*********
.. automodule:: SimPEG.inverse.Inversion
:show-inheritance:
:members:
:undoc-members:
Beta Schedule
*************
.. automodule:: SimPEG.inverse.BetaSchedule
:members:
:undoc-members:
Regularization
**************
.. automodule:: SimPEG.inverse.Regularization
.. automodule:: SimPEG.Regularization
:show-inheritance:
:members:
:undoc-members:
Objective Function
******************
.. automodule:: SimPEG.ObjFunction
:members:
:undoc-members:
Optimize
********
.. automodule:: SimPEG.Optimization
:show-inheritance:
:private-members:
:members:
:undoc-members:
Inversion
*********
.. automodule:: SimPEG.Inversion
:show-inheritance:
:members:
:undoc-members:
docs/api_LogicallyOrthogonalMesh.rst
+1 -9
View File
@@ -3,16 +3,8 @@
Logically Orthogonal Mesh
*************************
.. automodule:: SimPEG.mesh.LogicallyOrthogonalMesh
.. automodule:: SimPEG.Mesh.LogicallyOrthogonalMesh
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
LOM View
********
.. automodule:: SimPEG.mesh.LomView
:members:
:undoc-members:
docs/api_Parameters.rst
+11
View File
@@ -0,0 +1,11 @@
.. _api_Parameters:
Parameters
**********
.. automodule:: SimPEG.Parameters
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
docs/api_TensorMesh.rst
+1 -8
View File
@@ -3,15 +3,8 @@
Tensor Mesh
***********
.. automodule:: SimPEG.mesh.TensorMesh
.. automodule:: SimPEG.Mesh.TensorMesh
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
Tensor View
***********
.. automodule:: SimPEG.mesh.TensorView
:members:
:undoc-members:
docs/api_TestResults.rst
-3994
View File
File diff suppressed because it is too large. Load diff
docs/api_Tests.rst
+1 -1
View File
@@ -3,6 +3,6 @@
Testing SimPEG
**************
.. automodule:: SimPEG.tests.TestUtils
.. automodule:: SimPEG.Tests.TestUtils
:members:
:undoc-members:
docs/api_Utils.rst
+8 -8
View File
@@ -4,7 +4,7 @@
Solver
******
.. automodule:: SimPEG.utils.Solver
.. automodule:: SimPEG.Solver
:members:
:undoc-members:
@@ -12,49 +12,49 @@ Solver
Utilities
*********
.. automodule:: SimPEG.utils
.. automodule:: SimPEG.Utils
:members:
:undoc-members:
Matrix Utilities
****************
.. automodule:: SimPEG.utils.matutils
.. automodule:: SimPEG.Utils.matutils
:members:
:undoc-members:
Sparse Utilities
****************
.. automodule:: SimPEG.utils.sputils
.. automodule:: SimPEG.Utils.sputils
:members:
:undoc-members:
LOM Utilities
*************
.. automodule:: SimPEG.utils.lomutils
.. automodule:: SimPEG.Utils.lomutils
:members:
:undoc-members:
Mesh Utilities
**************
.. automodule:: SimPEG.utils.meshutils
.. automodule:: SimPEG.Utils.meshutils
:members:
:undoc-members:
Model Builder Utilities
***********************
.. automodule:: SimPEG.utils.ModelBuilder
.. automodule:: SimPEG.Utils.ModelBuilder
:members:
:undoc-members:
Interpolation Utilities
***********************
.. automodule:: SimPEG.utils.interputils
.. automodule:: SimPEG.Utils.interputils
:members:
:undoc-members:
docs/examples/mesh/plot_LogicallyOrthogonalMesh.py
-7
View File
@@ -1,7 +0,0 @@
from SimPEG.mesh import LogicallyOrthogonalMesh
from SimPEG import utils
import matplotlib.pyplot as plt
X, Y = utils.exampleLomGird([3,3],'rotate')
M = LogicallyOrthogonalMesh([X, Y])
M.plotGrid()
plt.show()
docs/examples/mesh/plot_grid_2D.py
-11
View File
@@ -1,11 +0,0 @@
import numpy as np
import matplotlib.pyplot as plt
from SimPEG.mesh import TensorMesh
h1 = np.linspace(.1,.5,3)
h2 = np.linspace(.1,.5,5)
mesh = TensorMesh([h1, h2])
mesh.plotGrid(nodes=True, faces=True, centers=True, lines=True)
plt.show()
docs/examples/mesh/plot_grid_3D.py
-12
View File
@@ -1,12 +0,0 @@
import numpy as np
import matplotlib.pyplot as plt
from SimPEG.mesh import TensorMesh
h1 = np.linspace(.1,.5,3)
h2 = np.linspace(.1,.5,5)
h3 = np.linspace(.1,.5,3)
mesh = TensorMesh([h1,h2,h3])
mesh.plotGrid(nodes=True, faces=True, centers=True, lines=True)
plt.show()
docs/examples/mesh/plot_image_2D.py
-11
View File
@@ -1,11 +0,0 @@
import numpy as np
import matplotlib.pyplot as plt
from SimPEG.mesh import TensorMesh
n = 20
h = np.ones(n)/n
M = TensorMesh([h, h])
I = np.sin(M.gridCC[:,0]*2*np.pi)*np.sin(M.gridCC[:,1]*2*np.pi)
M.plotImage(I)
plt.show()
docs/examples/mesh/plot_image_3D.py
-12
View File
@@ -1,12 +0,0 @@
import numpy as np
import matplotlib.pyplot as plt
from SimPEG.mesh import TensorMesh
n = 20
h = np.ones(n)/n
M = TensorMesh([h,h,h])
I = np.sin(M.gridCC[:,0]*2*np.pi)*np.sin(M.gridCC[:,1]*2*np.pi)*np.sin(M.gridCC[:,2]*2*np.pi)
M.plotImage(I, annotationColor='k')
plt.show()
docs/examples/mesh/plot_nodes.py
-13
View File
@@ -1,13 +0,0 @@
import numpy as np
import matplotlib.pyplot as plt
from SimPEG.mesh import TensorMesh
x0 = np.zeros(2)
h1 = np.linspace(.1,.5,3)
h2 = np.linspace(.1,.5,5)
M = TensorMesh([h1,h2],x0)
M.plotGrid()
plt.hold()
plt.plot(M.gridN[:,0], M.gridN[:,1], 'ks', markersize=10)
plt.show()
docs/index.rst
+16 -20
View File
@@ -3,7 +3,7 @@
:alt: SimPEG
:align: center
SimPEG (Simulation and Parameter Estimation in Geoscience) is a python
SimPEG (Simulation and Parameter Estimation in Geophysics) is a python
package for simulation and gradient based parameter estimation in the
context of geoscience applications.
@@ -16,11 +16,10 @@ these goals, this package has the following features:
* provides a framework for geophysical and hydrogeologic problems
* supports 1D, 2D and 3D problems
.. raw:: html
<iframe src="http://row1.ca/labs/simpegvis" width="100%" height="500px" style="border:none;background:#eee;margin:50px 0;"></iframe>
.. image:: simpeg-framework.png
:width: 400 px
:alt: Framework
:align: center
Meshing & Operators
===================
@@ -41,7 +40,7 @@ Forward Problems
.. toctree::
:maxdepth: 2
api_Problem
api_Forward
Inversion
=========
@@ -49,7 +48,8 @@ Inversion
.. toctree::
:maxdepth: 2
api_Optimize
api_Inverse
api_Parameters
Testing SimPEG
==============
@@ -58,22 +58,18 @@ Testing SimPEG
:maxdepth: 2
api_Tests
api_TestResults
Build Results
=============
* Master Branch
.. image:: https://travis-ci.org/simpeg/simpeg.png?branch=master
:target: https://travis-ci.org/simpeg/simpeg
:alt: Master Branch
:align: center
.. image:: https://travis-ci.org/simpeg/simpeg.png?branch=master
:target: https://travis-ci.org/simpeg/simpeg
:alt: Master Branch
:align: center
* Develop Branch
.. image:: https://travis-ci.org/simpeg/simpeg.png?branch=develop
:target: https://travis-ci.org/simpeg/simpeg
:alt: Develop Branch
:align: center
.. image:: https://travis-ci.org/simpeg/simpeg.png?branch=develop
:target: https://travis-ci.org/simpeg/simpeg
:alt: Develop Branch
:align: center
Utility Codes
docs/simpeg-framework.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 16 KiB

notebooks/BFGS.ipynb
-158
View File
@@ -1,158 +0,0 @@
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import SimPEG\n",
"from SimPEG import Solver\n",
"from SimPEG.mesh import TensorMesh\n",
"from SimPEG.regularization import Regularization\n",
"import SimPEG.inverse as inverse\n",
"from SimPEG.inverse import Minimize, Remember, IterationPrinters\n",
"import numpy as np\n",
"import scipy.sparse as sp"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"FUN = SimPEG.tests.Rosenbrock\n",
"FUN = SimPEG.tests.getQuadratic(sp.csr_matrix(([100,1],([0,1],[0,1])),shape=(2,2)),np.array([-5,-5]),100)\n",
"\n",
"x0 = np.array([1,0])\n",
"opt = inverse.BFGS()\n",
"xopt = opt.minimize(FUN,x0)\n",
"print xopt\n",
"opt = inverse.GaussNewton()\n",
"xopt = opt.minimize(FUN,x0)\n",
"print xopt\n",
"opt = inverse.SteepestDescent()\n",
"xopt = opt.minimize(FUN,x0)\n",
"print xopt"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"===================== BFGS =====================\n",
" # f |proj(x-g)-x| LS Comment \n",
"-----------------------------------------------\n",
" 0 1.45e+02 9.51e+01 0 \n",
" 1 1.14e+02 5.37e+01 6 \n",
" 2 1.04e+02 3.04e+01 6 \n",
" 3 8.83e+01 1.37e+01 0 \n",
" 4 8.76e+01 5.97e+00 0 Skip BFGS \n",
" 5 8.74e+01 2.61e+00 0 Skip BFGS \n",
" 6 8.74e+01 1.14e+00 0 Skip BFGS \n",
" 7 8.74e+01 5.01e-01 0 Skip BFGS \n",
" 8 8.74e+01 2.19e-01 0 Skip BFGS \n",
" 9 8.74e+01 9.60e-02 0 Skip BFGS \n",
"------------------------- STOP! -------------------------\n",
"1 : |fc-fOld| = 1.9437e-04 <= tolF*(1+|f0|) = 1.4600e+01\n",
"1 : |xc-x_last| = 1.2663e-03 <= tolX*(1+|x0|) = 2.0000e-01\n",
"1 : |proj(x-g)-x| = 9.5952e-02 <= tolG = 1.0000e-01\n",
"0 : |proj(x-g)-x| = 9.5952e-02 <= 1e3*eps = 1.0000e-02\n",
"0 : maxIter = 20 <= iter = 9\n",
"------------------------- DONE! -------------------------\n",
"[ 0.05095952 4.99977449]\n",
"=========== Gauss Newton ===========\n",
" # f |proj(x-g)-x| LS \n",
"-----------------------------------\n",
" 0 1.45e+02 9.51e+01 0 \n",
" 1 8.74e+01 4.44e-15 0 \n",
"------------------------- STOP! -------------------------\n",
"0 : |fc-fOld| = 5.7625e+01 <= tolF*(1+|f0|) = 1.4600e+01\n",
"0 : |xc-x_last| = 5.0894e+00 <= tolX*(1+|x0|) = 2.0000e-01\n",
"1 : |proj(x-g)-x| = 4.4409e-15 <= tolG = 1.0000e-01\n",
"1 : |proj(x-g)-x| = 4.4409e-15 <= 1e3*eps = 1.0000e-02\n",
"0 : maxIter = 20 <= iter = 1\n",
"------------------------- DONE! -------------------------\n",
"[ 0.05 5. ]\n",
"========= Steepest Descent =========\n",
" # f |proj(x-g)-x| LS \n",
"-----------------------------------\n",
" 0 1.45e+02 9.51e+01 0 \n",
" 1 1.14e+02 5.37e+01 6 \n",
" 2 1.04e+02 3.04e+01 6 \n",
" 3 1.00e+02 1.76e+01 6 \n",
" 4 9.88e+01 1.06e+01 6 \n",
" 5 9.82e+01 7.07e+00 6 \n",
" 6 9.80e+01 1.22e+01 5 \n",
" 7 9.73e+01 7.77e+00 6 \n",
" 8 9.68e+01 5.64e+00 6 \n",
" 9 9.65e+01 8.72e+00 5 \n",
" 10 9.60e+01 5.97e+00 6 \n",
" 11 9.58e+01 9.98e+00 5 \n",
" 12 9.53e+01 6.48e+00 6 \n",
" 13 9.53e+01 1.16e+01 5 \n",
" 14 9.46e+01 7.20e+00 6 \n",
" 15 9.43e+01 5.07e+00 6 \n",
" 16 9.41e+01 8.17e+00 5 \n",
" 17 9.37e+01 5.43e+00 6 \n",
" 18 9.36e+01 9.42e+00 5 \n",
" 19 9.32e+01 5.98e+00 6 \n",
" 20 9.29e+01 4.32e+00 6 \n",
"------------------------- STOP! -------------------------\n",
"1 : |fc-fOld| = 2.5913e-01 <= tolF*(1+|f0|) = 1.4600e+01\n",
"1 : |xc-x_last| = 9.3379e-02 <= tolX*(1+|x0|) = 2.0000e-01\n",
"0 : |proj(x-g)-x| = 4.3246e+00 <= tolG = 1.0000e-01\n",
"0 : |proj(x-g)-x| = 4.3246e+00 <= 1e3*eps = 1.0000e-02\n",
"1 : maxIter = 20 <= iter = 20\n",
"------------------------- DONE! -------------------------\n",
"[ 0.07777107 1.6849632 ]\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"/Users/rowan/git/simpeg/SimPEG/inverse/Optimize.py:664: RuntimeWarning: divide by zero encountered in remainder\n",
" khat = np.mod(n-nn+k,nn)\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"A = sp.identity(2)\n",
"S = Solver(A)\n",
"\n",
"assert type(S) is Solver"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
notebooks/Bound Constraint Problem.ipynb
-620
View File
@@ -1,620 +0,0 @@
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import SimPEG\n",
"from SimPEG.mesh import TensorMesh\n",
"from SimPEG.regularization import Regularization\n",
"import SimPEG.inverse as inverse\n",
"from SimPEG.inverse import Minimize\n",
"import numpy as np\n",
"import scipy.sparse as sp"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from SimPEG.forward.LinearProblem import example as LinExample\n",
"\n",
"prob, m_true = LinExample(1000)\n",
"M = prob.mesh\n",
"\n",
"reg = Regularization(M)\n",
"opt = inverse.InexactGaussNewton(maxIter=100,maxStep=0.2,debug=False,LSreduction=0.3,maxIterLS=50)\n",
"opt.remember('f', ('norm_g', lambda M:np.linalg.norm(M.g)))\n",
"inv = inverse.Inversion(prob,reg,opt,beta0=1e-4,maxIter=2,debug=False)\n",
"m0 = np.zeros_like(m_true)\n",
"\n",
"mrec = inv.run(m0)\n",
"\n",
"plt.plot(M.vectorCCx, m_true, 'b-')\n",
"plt.plot(M.vectorCCx, mrec, 'r-')\n",
"\n",
"figure()\n",
"plot(opt.recall('f'))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"====================== Inexact Gauss Newton ======================\n",
" # beta phi_d phi_m f |proj(x-g)-x| LS \n",
"-----------------------------------------------------------------\n",
" 0 1.00e-04 9.62e+02 0.00e+00 9.62e+02 1.02e+04 0 \n",
" 1 1.00e-04 6.63e+02 7.73e+02 6.63e+02 8.47e+03 0 \n",
" 2 1.00e-04 4.15e+02 4.39e+03 4.15e+02 6.63e+03 0 \n",
" 3 1.00e-04 2.26e+02 6.85e+03 2.27e+02 4.80e+03 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 4 1.00e-04 9.74e+01 1.07e+04 9.84e+01 3.02e+03 0 \n",
" 5 1.00e-04 2.42e+01 1.64e+04 2.58e+01 1.35e+03 0 \n",
" 6 1.00e-04 1.06e+00 2.34e+04 3.39e+00 9.21e+00 0 \n",
"------------------------- STOP! -------------------------\n",
"1 : |fc-fOld| = 2.2421e+01 <= tolF*(1+|f0|) = 9.6325e+01\n",
"0 : |xc-x_last| = 2.1351e+00 <= tolX*(1+|x0|) = 1.0000e-01\n",
"0 : |proj(x-g)-x| = 9.2073e+00 <= tolG = 1.0000e-01\n",
"0 : |proj(x-g)-x| = 9.2073e+00 <= 1e3*eps = 1.0000e-02\n",
"0 : maxIter = 100 <= iter = 6\n",
"1 : phi_d = 1.0595e+00 <= phi_d_target = 2.0000e+01 \n",
"------------------------- DONE! -------------------------\n",
"-------------------------STOP!-------------------------\n",
"0 : maxIter = 2 <= iter = 1\n",
"1 : phi_d = 1.0595e+00 <= phi_d_target = 2.0000e+01 \n",
"-------------------------DONE!-------------------------\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
"[<matplotlib.lines.Line2D at 0x10ebf9f10>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEACAYAAAC08h1NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x10ecafa10>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x10ecbec90>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"FUN = SimPEG.tests.getQuadratic(sp.identity(2),np.array([-5,-5]))\n",
"# FUN = SimPEG.tests.Rosenbrock\n",
"\n",
"f = FUN(np.array([1,2]))\n",
"print f\n",
"n,l,u = 50,-10,10\n",
"I = np.zeros((n,n))\n",
"X = np.linspace(l,u,n)\n",
"for i, x in enumerate(X):\n",
" for j, y in enumerate(X):\n",
" f, g, H = FUN(np.array([x,y]))\n",
" I[i,j] = f\n",
"\n",
"colorbar(contourf(X,X, I.T))\n",
"\n",
"GN = inverse.GaussNewton()\n",
"xopt = GN.minimize(FUN,np.array([0,0]))\n",
"print xopt"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(-12.5, array([-4., -3.]), <2x2 sparse matrix of type '<type 'numpy.float64'>'\n",
"\twith 2 stored elements (1 diagonals) in DIAgonal format>)\n",
"=========== Gauss Newton ==========="
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" # f |proj(x-g)-x| LS \n",
"-----------------------------------\n",
" 0 0.00e+00 7.07e+00 0 \n",
" 1 -2.50e+01 0.00e+00 0 \n",
"------------------------- STOP! -------------------------\n",
"0 : |fc-fOld| = 2.5000e+01 <= tolF*(1+|f0|) = 1.0000e-01\n",
"0 : |xc-x_last| = 7.0711e+00 <= tolX*(1+|x0|) = 1.0000e-01\n",
"1 : |proj(x-g)-x| = 0.0000e+00 <= tolG = 1.0000e-01\n",
"1 : |proj(x-g)-x| = 0.0000e+00 <= 1e3*eps = 1.0000e-02\n",
"0 : maxIter = 20 <= iter = 1\n",
"------------------------- DONE! -------------------------\n",
"[ 5. 5.]\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAAEACAYAAACEfgxsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAH/lJREFUeJzt3X1wVOX5N/DvRppQJQ8FbZfMJAszGLIbiLDxSTbtr4QQ\neQnQkFTaqbQVh+RxYLEEBdJfLWgPTJVB7aAwEtLWtNNamF+lIjgtBEJdMsGyG95E01ChQGMZNCZ9\nHljeqinn+QN3zXvOvpy973PO9zOzM+7Zk3Nf7sKXK9ees2tTVVUFEREJlyS6ACIiuo2BTEQkCQYy\nEZEkGMhERJJgIBMRSYKBTEQkiZgDuaKiAna7HTk5OeFtwWAQZWVlcDgcKC8vx9WrV2NdhohImA8+\n+ADTp0/HxIkTUVRUhO3btwMAXnvtNUycOBF33HEHjh8/3uNnNm/ejMzMTGRnZ6OpqUnTOjEH8uLF\ni7Fv374e22pqauBwOHDmzBmkp6dj27ZtsS5DRCTMF77wBWzatAktLS3YuXMn1q5di2AwiJycHOza\ntQuFhYU99m9vb8fWrVtx8OBB1NTUoKqqStM6MQfy1KlTMWrUqB7bAoEAKisrkZKSgoqKCvj9/liX\nISISZsyYMZgyZQoA4J577sHEiRNx9OhROJ1OTJgwoc/+fr8fJSUlcDgcmDZtGlRVRTAYHHIdXWbI\nzc3NcDqdAACn04lAIKDHMkRECXf27Fm0tLQgPz9/wH0CgQBcLlf4flZWlqYc1CWQeTU2EZlRMBjE\nd77zHWzatAl33XXXgPv1l4E2m23I4w+LqboB5OXlobW1FW63G62trcjLy+uzz5h7v4iP/n5Tj+WJ\nyGTGjx+Ps2fPxnSM/2WzYeihwW0jRozoM2L49NNPsWDBAjz88MMoKysb9Oc9Hg8aGhrC90+fPt1v\nDvamSyB7PB7U1dXhueeeQ11dHQoKCvrs89Hfb2K3OmvQ42zDEj3K02Rv44OJW+xXCrBYGXo/DbsY\n2lt+AL8A8KjoSiTB5yLk73/vmyGRCgLQdq4D8PVeZ4apqorKykpMmjQJjz/+eL8/070rzs/PR3V1\nNdra2nDu3DkkJSUhNTV1yHVjHlksXLgQX/va1/D+++8jIyMDv/rVr+D1etHW1oasrCxcvHgRS5cu\njXWZhEpoGNNtb/GNX5LX4cOH8eqrr+LPf/4z3G433G439u7dizfeeAMZGRk4cuQI5s2bhzlz5gAA\n7HY7vF4viouLsWzZMrz00kua1om5Q96xY0e/23fv3h3roak7RXQBOmIYk+S+/vWv49atW/0+Vl5e\n3u/2FStWYMWKFRGtI+2VeqLGFUK64ylFiV9TFn3COFdIGXLic2E10gaypbiLBn9cSUQRAvTbGd+f\n8DLkxefCahjIJAbHFER9SBnIlhpXDEURXYAOGMZE/ZIykOkziugCdMAwJhqQdIHM7tjEGMZEg5Iu\nkOkziugC4oxhTDQkBjIRkSQYyJBwXKGILiDO2B0TaSJVIIv87ArSCcOYSDOpAlkEdsc6YhgTRcTy\ngUw6YRgTRUyaQOa4goisTppAFoHjCp2wOyaKiqUDmXTAMCaKmhSBzHEFzNMdE1HUpAhkEaQbV5gB\nu2OimFg2kImIZMNAloEiuoA4YHdMFDPhgcz5sQkwjMnkKioqYLfbkZOTE97217/+Fd/4xjcwZcoU\nlJaWorW1NfzY5s2bkZmZiezsbDQ1af2uawkCWQTOj4koEosXL8a+fft6bFu/fj0WLVqEkydP4rvf\n/S7Wr18PAGhvb8fWrVtx8OBB1NTUoKqqSvM6MX/rNMVIEV1AjNgdkwVMnToVFy5c6LFt5MiR6Ozs\nxK1bt9DZ2YlRo0YBAPx+P0pKSuBwOOBwOKCqKoLBIFJTU4dch4FMRBSF559/Hvn5+fjRj36EtLQ0\nHD16FAAQCATgcrnC+2VlZSEQCOCBBx4Y8piWHFlQnLA7JgurqKjA8uXL0dnZCa/Xi4qKCgCAqqp9\n9rXZbJqOKbRDFvGGnlTzY0V0AUTW8l8L+9/u+wjwtXfb8N7Qx2pqasJvf/tbDBs2DJWVldiwYQMA\nwOPxoKGhIbzf6dOnkZeXp6k+dshEZHlFdkDJ+fymxfTp07Fnzx4AwO7duzFz5kwAQH5+Purr69HW\n1gafz4ekpCRN82OAM2SKFscVZCELFy7EoUOH0NHRgYyMDKxfvx5r167FT3/6Uzz77LOYNGkSnnrq\nKQCA3W6H1+tFcXExkpOTUVtbq3kdm9rfwCMBbDYb5qh/SPi60owsFNEFxIiBTAlV0O9sNhI2mw3q\nACOLPvvu6H8WrDdLjSykCWOjYxgT6cJSgUxEJDMGMhGRJBjIFBmOK4h0w0AWQRFdABHJiIFMRCQJ\nywQyz7CIA44riHRlmUAmIpIdA5mISBIM5ERTRBdARLJiIBMRSYKBTNrwDT0i3TGQiYgkwUAmIpIE\nA5mISBIMZCIiSVgikHmVHhEZgSUCmWLEMyyIEoKBTEQkCV0Dedy4cbjvvvvgdruRn5+v51LGoIgu\ngIiiUVFRAbvdjpycz7+SWlEUpKenw+12w+12Y+/eveHHNm/ejMzMTGRnZ6OpqUnzOrp+67TNZoPP\n58Po0aP1XIaISFeLFy/G8uXLsWjRovA2m82GlStXYuXKlT32bW9vx9atW3Hw4EGcP38eVVVVOH78\nuKZ1dA1kQMw3txIRxdPUqVNx4cKFPtv7yze/34+SkhI4HA44HA6oqopgMIjU1NQh19F1ZGGz2VBc\nXIzy8nLs2bNHz6WIiBJuy5YtKCgowMaNGxEMBgEAgUAALpcrvE9WVhYCgYCm4+naIR8+fBhpaWlo\nbW1FaWkp8vPzMWbMmPDjZ5T/Cf/36KKJuLtokp7lEJFhHAOg7df8ePB9BPjaI/sZr9eLp59+Gleu\nXEF1dTVqa2uxevXqfrtmm82m6Zi6BnJaWhoAwOVyYf78+XjzzTfx6KOPhh/PVL6j5/JEZFj3f3YL\neSU+h/3v/jcXfXYLWTdl6EN95StfAQCMHDkSjz32GJYtW4bVq1fD4/GgoaEhvN/p06eRl5enqTzd\nRhbXr18Pt/Aff/wx6uvrUVJSotdyREQJdenSJQBAV1cXtm/fjrlz5wIA8vPzUV9fj7a2Nvh8PiQl\nJWmaHwM6dsgfffQRvvnNbwIA7r77bqxatQoZGRl6LUdEpJuFCxfi0KFD6OjoQEZGBtatWwefz4eT\nJ08iOTkZhYWF8Hq9AAC73Q6v14vi4mIkJyejtrZW8zo2VdBpEDabDXPUPyRkLakunVZEFxAFXqlH\nwhXEfMaWzWaDelLjvlPEnCHGK/WIiCTBQKahTfeIroDIEhjIRESSsEQgzyl8XXQJRERDskQgExEZ\nAQOZiEgSDGQiIkkwkImIJMFAJm146huR7hjIRESSYCAnmiK6ACKSFQOZiEgSDGTSjnNkIl1ZJpB5\ntR4Ryc4ygUxEJDsGsgiK6AKISEYMZIoM58hEumEgExFJwlKBzDf2iEhmlgpkqSiiC4gBxxZkMRUV\nFbDb7cjJyQlvq66uhsvlQm5uLh5//HHcuHEj/NjmzZuRmZmJ7OxsNDU1aV6HgUxENITFixdj3759\nPbbNmjULLS0tOHr0KK5du4bt27cDANrb27F161YcPHgQNTU1qKqq0rwOA5miwy6ZLGTq1KkYNWpU\nj20zZ85EUlISkpKSMHv2bBw6dAgA4Pf7UVJSAofDgWnTpkFVVQSDQU3rMJCJiGL0i1/8AqWlpQCA\nQCAAl8sVfiwrKwuBQEDTcYQG8lLUJnxNqd7YU0QXECN2yWQSvmZAqfn8Fon169cjNTUV3/72twEA\nqqr22cdms2k61rDIliYiMq49k2f1/8BkIPf/dLtfu1/T8X7961+jvr4eBw8eDG/zeDxoaGgI3z99\n+jTy8vI0HY8jC4oNu2SyqH379uH555/Hnj17MHz48PD2/Px81NfXo62tDT6fD0lJSUhNTdV0THbI\noikw/uiCyOQWLlyIQ4cOoaOjAxkZGVi3bh02bNiATz75BDNmzAAAfPWrX8XWrVtht9vh9XpRXFyM\n5ORk1NZqH83a1P4GHglgs9mwW73968M2LEn4+nsbH0z4mgNSRBcQB2/5RVdAplbQ72w2Et0zZyhl\ntv0xrxcNjiyIiCTBQJaBIrqAOOAsmShmlg1kqU5/IyKCJIEs4nxk0gG7ZKKYSBHIBHOMLQCGMlEM\nGMhERJKwdCBLN0dWRBcQJ+ySiaIiTSBzjmwyDGWiiEkTyPQZRXQBRCSK5QNZurGFmbBLJoqIVIHM\nsYUJMZSJNJMqkEWRrktWRBcQZwxlIk0YyJQYDGWiIUkXyBxbfEYRXQARJZp0gSyKdGMLwHyhzC6Z\naFAMZEoshjLRgKQMZFFjC3bJCcJQJuqXlIFMFsBQJuqDgdwLu+QEYigT9aBbIDc2NsLlciEzMxNb\ntmyJ+Od5toVFMJTJILZv345p06Zh4sSJ+OUvfwkACAaDKCsrg8PhQHl5Oa5evRrTGroF8ooVK1Bb\nW4uGhga8/PLL6Ojo0Gspa1BEF6AjhjJJ7vLly1i3bh3eeOMN+P1+/PznP8fly5dRU1MDh8OBM2fO\nID09Hdu2bYtpHV0C+fLlywCAwsJCjB07FrNmzYLfH/m3EvPNvV4U0QXoiKFMEnv77beRm5uLUaNG\nYcSIEZg+fTr+8pe/IBAIoLKyEikpKaioqIgq57rTJZCbm5vhdDrD97Ozs3HkyBE9liIzme5hMJOU\nCgsLEQgEcP78eVy6dAl/+tOf8Pbbb/fIOqfTiUAgENM6w+JRbLR2KGfD/z2paDRyikYLrKanOYWv\nY2/jg6LL6EuBuTtl4HYovxVbp0FGdwzA8dv/OS4duKDvau/6/oX3fP8a8PG77roLL774IhLine truncated
"text": [
"<matplotlib.figure.Figure at 0x10ebd9750>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"opt = inverse.ProjectedGradient(maxIter=50,maxStep=np.inf, maxIterLS=20, debug=False)\n",
"opt.remember('f')\n",
"opt.lower = -2\n",
"opt.upper = 2\n",
"opt.minimize(FUN,np.array([0,0]))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"======================= Projected Gradient =======================\n",
" # f |proj(x-g)-x| LS itType aSet bSet Comment\n",
"------------------------------------------------------------------\n",
" 0 0.00e+00 2.83e+00 0 SD 0 0 \n",
" 1 -1.60e+01 0.00e+00 0 SD 2 2 \n",
"------------------------- STOP! -------------------------\n",
"0 : |fc-fOld| = 1.6000e+01 <= tolF*(1+|f0|) = 1.0000e-01\n",
"0 : |xc-x_last| = 2.8284e+00 <= tolX*(1+|x0|) = 1.0000e-01\n",
"1 : |proj(x-g)-x| = 0.0000e+00 <= tolG = 1.0000e-01\n",
"1 : |proj(x-g)-x| = 0.0000e+00 <= 1e3*eps = 1.0000e-02\n",
"0 : maxIter = 50 <= iter = 1\n",
"1 : probSize = 2 <= bindingSet = 2\n",
"------------------------- DONE! -------------------------\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
"array([ 2., 2.])"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"opt = inverse.ProjectedGradient(maxIter=50, maxStep=0.3,debug=False, maxIterLS=20, tolCG=1e-5, maxIterCG=1000)\n",
"opt.lower, opt.upper = -0.4, 0.9\n",
"opt.remember('f', 'xc', ('norm_g', lambda M: np.linalg.norm(M.g)), 'phi_d', 'phi_m')\n",
"inv = inverse.Inversion(prob,reg,opt,beta0=1e-3,debug=False)\n",
"inv.remember(('phi_d',lambda I:I.opt.recall('phi_d')),('phi_m',lambda I:I.opt.recall('phi_m')))\n",
"m0 = np.zeros_like(m_true)\n",
"mrecB = inv.run(m0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"====================================== Projected Gradient ======================================\n",
" # beta phi_d phi_m f |proj(x-g)-x| LS itType aSet bSet Comment\n",
"------------------------------------------------------------------------------------------------\n",
" 0 1.00e-03 9.62e+02 0.00e+00 9.62e+02 2.14e+01 0 SD 0 0 \n",
" 1 1.00e-03 9.53e+02 8.49e-03 9.53e+02 2.18e+01 9 SD 0 0 \n",
" 2 1.00e-03 5.32e+02 1.42e+03 5.33e+02 2.20e+01 0 .CG. 0 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 3 1.00e-03 2.32e+02 5.66e+03 2.38e+02 2.26e+01 0 .CG. 0 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 4 1.00e-03 1.29e+02 8.85e+03 1.38e+02 2.30e+01 1 .CG. 0 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 5 1.00e-03 1.10e+02 9.74e+03 1.20e+02 2.15e+01 3 .CG. 22 22 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 6 1.00e-03 1.09e+02 9.74e+03 1.19e+02 2.36e+01 10 SD 22 0 Stop SD\n",
" 7 1.00e-03 7.65e+01 1.33e+04 8.98e+01 2.21e+01 1 .CG. 85 75 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 8 1.00e-03 5.11e+01 1.33e+04 6.44e+01 2.38e+01 9 SD 75 3 \n",
" 9 1.00e-03 5.07e+01 1.33e+04 6.41e+01 2.11e+01 12 SD 4 4 \n",
" 10 1.00e-03 5.06e+01 1.33e+04 6.40e+01 2.20e+01 12 SD 17 9 Stop SD\n",
" 11 1.00e-03 5.04e+01 1.34e+04 6.37e+01 2.05e+01 8 .CG. 85 81 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 12 1.00e-03 5.03e+01 1.34e+04 6.37e+01 1.65e+01 13 SD 81 26 \n",
" 13 1.00e-03 5.03e+01 1.34e+04 6.37e+01 1.67e+01 15 SD 30 30 \n",
" 14 1.00e-03 5.03e+01 1.34e+04 6.36e+01 1.42e+01 15 SD 84 84 Stop SD\n",
" 15 1.00e-03 2.65e+01 2.26e+04 4.91e+01 2.52e+01 0 .CG. 190 50 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 16 1.00e-03 1.51e+01 2.26e+04 3.77e+01 2.24e+01 10 SD 50 1 \n",
"------------------------- STOP! -------------------------\n",
"1 : |fc-fOld| = 1.1392e+01 <= tolF*(1+|f0|) = 9.6325e+01\n",
"1 : |xc-x_last| = 3.4809e-03 <= tolX*(1+|x0|) = 1.0000e-01\n",
"0 : |proj(x-g)-x| = 2.2369e+01 <= tolG = 1.0000e-01\n",
"0 : |proj(x-g)-x| = 2.2369e+01 <= 1e3*eps = 1.0000e-02\n",
"0 : maxIter = 50 <= iter = 16\n",
"0 : probSize = 1000 <= bindingSet = 1\n",
"1 : phi_d = 1.5077e+01 <= phi_d_target = 2.0000e+01 \n",
"------------------------- DONE! -------------------------\n",
"-------------------------STOP!-------------------------\n",
"0 : maxIter = 10 <= iter = 1\n",
"1 : phi_d = 1.5077e+01 <= phi_d_target = 2.0000e+01 \n",
"-------------------------DONE!-------------------------\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# First set up the figure, the axis, and the plot element we want to animate\n",
"fig = plt.figure()\n",
"ax = plt.axes()\n",
"ax.plot(M.vectorCCx, m_true, 'b-')\n",
"txt = plt.text(0.8,0.9,'')\n",
"line, = ax.plot([], [], 'r-', lw=1)\n",
"\n",
"def animate(i):\n",
" txt.set_text('iteration %d'%i)\n",
" line.set_data(M.vectorCCx, np.array(opt.recall('xc')[i]))\n",
"\n",
"SimPEG.utils.animate(fig, animate, frames=len(opt.recall('xc')))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<video controls loop>\n",
" <source src=\"data:video/x-m4v;base64,AAAAIGZ0eXBpc29tAAACAGlzb21pc28yYXZjMW1wNDEAAAAIZnJlZQAALXFtZGF0AAACoQYF//+d\n",
"3EXpvebZSLeWLNgg2SPu73gyNjQgLSBjb3JlIDEyNSAtIEguMjY0L01QRUctNCBBVkMgY29kZWMg\n",
"LSBDb3B5bGVmdCAyMDAzLTIwMTIgLSBodHRwOi8vd3d3LnZpZGVvbGFuLm9yZy94MjY0Lmh0bWwg\n",
"LSBvcHRpb25zOiBjYWJhYz0xIHJlZj0zIGRlYmxvY2s9MTowOjAgYW5hbHlzZT0weDM6MHgxMTMg\n",
"bWU9aGV4IHN1Ym1lPTcgcHN5PTEgcHN5X3JkPTEuMDA6MC4wMCBtaXhlZF9yZWY9MSBtZV9yYW5n\n",
"ZT0xNiBjaHJvbWFfbWU9MSB0cmVsbGlzPTEgOHg4ZGN0PTEgY3FtPTAgZGVhZHpvbmU9MjEsMTEg\n",
"ZmFzdF9wc2tpcD0xIGNocm9tYV9xcF9vZmZzZXQ9LTIgdGhyZWFkcz0xMiBsb29rYWhlYWRfdGhy\n",
"ZWFkcz0yIHNsaWNlZF90aHJlYWRzPTAgbnI9MCBkZWNpbWF0ZT0xIGludGVybGFjZWQ9MCBibHVy\n",
"YXlfY29tcGF0PTAgY29uc3RyYWluZWRfaW50cmE9MCBiZnJhbWVzPTMgYl9weXJhbWlkPTIgYl9h\n",
"ZGFwdD0xIGJfYmlhcz0wIGRpcmVjdD0xIHdlaWdodGI9MSBvcGVuX2dvcD0wIHdlaWdodHA9MiBr\n",
"ZXlpbnQ9MjUwIGtleWludF9taW49MjAgc2NlbmVjdXQ9NDAgaW50cmFfcmVmcmVzaD0wIHJjX2xv\n",
"b2thaGVhZD00MCByYz1jcmYgbWJ0cmVlPTEgY3JmPTIzLjAgcWNvbXA9MC42MCBxcG1pbj0wIHFw\n",
"bWF4PTY5IHFwc3RlcD00IGlwX3JhdGlvPTEuNDAgYXE9MToxLjAwAIAAAAlFZYiEAFf9EwAD0rwK\n",
"a/s12U1hg0FMgMmMOVNcwAAAAwANFchWCs4PnSPLHgxFeZ2MBPwOINxDCInVnrlTnaSkcTqCnVwZ\n",
"C32ci4e4iEXqjfabfM26fKQmxb+v+i35CIUYvwFed9H6aEX+hZ9g90vyHpRRW3xSWaZ4rATX4Ful\n",
"X1PY/KHFJqojGxHWguFGV15/GBkVjfpjE9uqjYsd6Bt8CVRl/mvAHDEXYS/zFAfmrQU60ITF965L\n",
"Z/72ajw7MJlEfjucLdUWfQd0optIg36XkpkI2TJsfjLEQmpiJ81K6Lkkwpxo3Yz4oQbL2NSiGXvH\n",
"ptbV/ua2wolNPsqounXqYGot+QHwiUPfVwvdkdrwR5Cj40fjXsR4XowPkN9WnSAZNJJMTDNE2/Md\n",
"gG71sBn25gK1zE7+bhNsOj+dScDbYdEG3KIoDZsTq8MZytZ68/Vpy1RcUYFf9dTLxRw5Ipm5m0ru\n",
"j7V7D9ijr0jkKFusPzsMBU1EhcMQRka1hTRqmuD0m+vOqCwiFYLOUZIIpi4h0uB4PlfRinMkUuY2\n",
"kMU2qmbrE5Wm9vsg8Fm7seMdwx+ho6BKqYLHWti2aitk0eV3AChBd/JcGzDRksLet7eiWrgCEEST\n",
"jR0vUhkfLqy0ZO0Cdr4RQWZJP3C37cnoyUA9TIoL0cRmE9lOFvhvgksc2zFuZci3Hh5feHKPVeBf\n",
"l32EaqVeVAMOTWR5TkodkPZzGC7HQ/mivKJsE7e9m+5pBvhV0w08qOUoH1yni1Igrx/OxWUhmOnm\n",
"yklYRg/9KxYtkyR/41KsLR1vws1W8U+cYW/oDNdYRsSoFHoT8o/L317+Y3t+uKdJb88f/+iFotNf\n",
"7oHM3BiXGLq3ivXqk9UkVbWgzRJbBrL76mhMOktDlRJRwOYlI0iTc4/jMKJaUoM5h/iTqK14Dkq0\n",
"J9yodSB0CaNq5IADEyWfGP7hgOR+7xcii4HL21EAa7K7ImitBqOBAS7bxaPKM8L7hxgRC7JdePvA\n",
"2aupg0jsgty8+6gWx3l2Ze37WQZLJ71uSuiMKCHCnEwwyP/SWJc3CkKPEKQXVvRDn5g1oYla/Prm\n",
"ODl9WqhVmDfQ86JROF/YYkUfEKlLA6RkyUwoqJb8WpjT1lRG/WzGEc8oRAkpJLcCeLFR7Rb9G8a3\n",
"94Z/ACtdk1FrK4szZOdURDJ80T1gqJeKfVM0UXY3Za8mCt6RWmVMR/FB5d8zl9dcMSV6qkjUrmah\n",
"grcw6L/XvGDrC2/WawKiccCYNmY9vMP2xbj0K+zaAeuV0ibqjaifYRcDBJsCjA3cKmek8mPWHg8h\n",
"W0D7sY1kYaPOWg2ZnhHz7S0kZKRStPaNeNXuENWj/lUMPdiWnu7D74aMgNSnXU/o2t3QE12SRWOx\n",
"VHnVgAmnb1E+rh4m02fPjqPszu3FOXnm9/tQGpv0RN81cTzFhfSPV9FUDB9lr6fpHzEgaaqvnpjB\n",
"I5or0rrhY5rEr9C+CcR4Q1zcSPF1cDVBS9Z8pmre3w5qtaUKHKIvWA9LP0C5TmCuxPL023dQz7Xe\n",
"NVRLHO7gq8tApGJmZETIpsdECo6WOnI18i/mv/4PpR7xvICUqNgMapVOkmRA724DDmk3GshB3bjT\n",
"DJ9I7k4CLpfK8CxOCV1VQY7Audf6MPcEkI7RFdEzxsaktih9JXAGEcR5XhP1ul1qfxUNM13Vw4CI\n",
"PWlmXtXAX/DyMw+IMwg6J6zU+qcymJFwcyO5RdJGkFIO5RUcvTCXx/4D6Dl0gVACgsvzIGYuVuCk\n",
"F1yQY2Slk7Gv98qf/E9XKelR+KwrUfeRzBNnGq2Kni+SRj9tt73ZLW98kOTSdrOiqAIajRfX+bkC\n",
"eRN2CouZ0NKNfn/PHxNaFJtwwpgUPut0Z2i9GsHMyF+17l4WiT+ED4FSxbT3PQA7gc0Zuy3jE8yk\n",
"jjNN5c7Po21uFr+spVXB0sF4Jzm9kGAmwW7pqcyZJex6h5vYGjkMqO+AAD5RbsMnzs3Es2PBwGSP\n",
"kwAnSp3yQtvfk/ZOZuQgEdrTsqhEB/sSwJREgYHeNHWv0i4mdLsb4ONbyiZPLhS5SehZe+LxDC+t\n",
"nw3ZzxhxnHCJnyeboo/bPg7jivmd4WptC2Uv1PWrNs/qnBQH83AcpM0tzrkX59jxem6Qh2QsKOVW\n",
"TOsaM2jgZOedSg8PiC1EZ879LqrJszy3kNhsbUSTqEYreq+0CMYqRo4d3h/dfcBBad8LN0TwRw3H\n",
"OVDqb2r4urW0AeLSwlEqEd9anrQK+hQRwbaB+GdjZcjIo2xv/RQhF+hltcfNrJt04AK4dkkpMN/B\n",
"43uYVaeNO7u0/1H0UwsezF8Mywz86l+5upm4WYbdOpi5IMJaneXE+rukRHK+U1GEu8OlCdJglnBD\n",
"L2kKnlR/GGaYF9HOJvs2dpM3Y0aNm5c+dIRTu8H8r+01n93q/m2Sra9gKv3e5XJGIm8TXOzV3U5c\n",
"IE/yw2grWivvo3jr/Xo2xJkxG7MPuXkDxFThpj/WYkviz8F++//zev/jqWyoXjEGKa+jL/thkvR0\n",
"hhwo+ZDeZLAYNwBUJXy2nAdFATDb479pxsCpd2lB3iSrU05RjPztU1Gs3jpWPigmiRmaWKURFsHo\n",
"PDfu+wybU4p7o+svv9JGpGRCNej7dPhjrUb2+JsE/L/2KyZG/+5N6c0xyJJgqDSsWEKnyvGIRA3P\n",
"WT10RE+TrzoGN5hzv4HCq7z6T6xD28DzBLrHJ8Rkb7oSI1Fj454dhChjFwmZwam4OIQiAeLroTRL\n",
"QCniEHPl8p0TLgT24DLxLz6tryKjzOIVWiFPfbLaSlOxQw6ledXn0HgR2cTOhJ/cX+V6E5QmDlnB\n",
"DmEN1Bypx0LRlXbCN/dRum9C5l4n2vOJVexMqkmhmPg5nFCRGBQ0lCjGPOMZVIMfcBoFqgaTPmbs\n",
"R+vb68Q2UFp3i8pHFPh+/evVnhdV88IHOR8k4RrvNFCw6Gi/jwpLnmF0R1Eq4plwN5aSY5fBZkdc\n",
"NeyaAdzNOltXsYEfY7B/GYag0TpYvu08B2U0PFj7ylvIwQeTpKwWvW9kW16KHSnLm3COrIQ2JXsC\n",
"RL2eWVDQ12ibeYHLS9GVX9m8OY1TO4CdHWkUHSVUIs/aF8fbeSjvPtOjBmVRyWhabeI1d+0VPw0p\n",
"knz6FlwB/zZFWJFcxVti2ScggAAWWDLBAAAJVkGaJGxFfwAetnPo34UTgfc9ZdjMf3994gez/4R0\n",
"Ra9vVJYxtJcNGbQ8YOjK3nKuouKdCUiqAkiS0DuoY3wN88kAzNtfTxb19oF0sEhoLtTPUoGj3HVV\n",
"mcor7V47f+juJW0/iONRyDMwsMvwhnfcNOfYxN+qlT6SdejharOYiADeCFPlfFP3v0QfYaU4IPLQ\n",
"zxUOH84B4WD52GfHrZ5hqNb30TmoPsGRNMYOXEa3KLU+BLqqKc8aItiDQHsffua0dl8ZJLTfzQiU\n",
"gPxlz+MlVH3o/rwg3xAae8A//R3VVO5+gxA6QhIWe4DGYu4bhhF6MlOE3E5VvX/4YAEsUDraJDUj\n",
"gLiXDaDBSySGDlD7HOvCSvAdhipdQNZinwLWQp65n5+pauJ27y5jWQMcNwl/f8veaDi9/ZsOLE2J\n",
"+IuDM8KDM6Z0EpfqP7BvixAcfyccuoL9qOvjmytvrYDYrz8VaYMHqdQZwo9dFqRR60mhEtTkRrC9\n",
"xqWyFmF+Qyv7KTlOfkOTXFaL6yLiIXJdEXNKtLlXgAQ6t0VaqEotzY91sJkUQhpmC2IIAFbIBdRP\n",
"h+F26NvtlMm7VtEctcr00f5cThPOqsK7ux910q8ZWPZfCvV17UN3bN9VU0KjjGEXB7EACHYvtbV2\n",
"vOO+nyBsjKssfGwC2RCzNq4q71YS5a5GxqaVDVUgOXNcg5SJ2me991F3Bu+PK2OzXg9G0jndusZC\n",
"4WnxANuqQZZkrW4/FA8HdrwX+lJKj/KHwtDWV7urypOL2bWw5JAn4swP9kkcQ8To4G4KdIy7adSR\n",
"sYcTNP93QqWEvUDyfaALlii3xHG8TxK+2nq4sylEZ4k9/nOevozKHzbj+gWgwCWsBgp+wFr4jnfN\n",
"IV3J+g08KizNYq9DW7Ae71hw6/Sx4s32NPmfnWd9sw/L9MwRQryEBtMvoWVeJpI7Ubynyk4OX0oL\n",
"RLHWRwRqYeZdaL9pfjsCw5YI2tBYK89cnsPZ28sSgAVjrhcyg99AWFgG90AImGvB0zt/v76MepIt\n",
"/Omzu1L30daaYqgo4b8WN59CbRcfaI2KNpUwkq0VOTwU3YFiahffWj8sVVoTTOa9+hcroattpelG\n",
"s+R0uNRKBZf/QIPjedqtdEYdN8jGhzDIXKDKmsdw1vEVgt2qGwfEzkc6SUO5V6dSwbCkMzgdCNBG\n",
"fJ4zd3SQBEOq8HG0zpRqCNgcSVgc3yw7J/TBJeTOusP8NzCDLFZn4FxsCsM03nXSvFOsGlTblban\n",
"Rs5vwRpZ+8wwlmJ0k9st4fQtGG41LQqD3XA432Ktz3XahUoA+mOBQwLICYfCAb8xCle8t+StYtnu\n",
"xYf3RfpfO69jMdRbUl6IcVPet08s4Za8UaxVuZKOW60tbhfDiYjvJ+V7mDrmVLWUlydXjdIZ6ivy\n",
"2JhqeOn6lGAU205nuIBho6K/n+Sq3AryVklpLVVQOhZAVcU1Rlpu1Xd+yv2RKAngs4Br8AuLP68g\n",
"JdCKIflKAbz2yY1dydWJ7H4fSo1vDHN60ULK/0Vd4HOB38hIVu2DIOHwgT2yw2ou5evRdJQTzjeV\n",
"MjkgrH9VZ+euDJ3eVA8C5ddMkjoMbKmdBDQZMuShK8YjT3E0c8zGthRtVbRSZdl7b5VuFBGkKHMG\n",
"7VRcs/EdkDoik+mUWioKSpOf1E7O9vIGr1IOKcTgf50ad2KN2An7NajZT+yB83uhXbL6DkTlDK0D\n",
"0Zs/k0n2dhDfwP2BmheuAOAPGRjcrDTwF36oU1/9tCjzix1z/InNYkDSoPlXSAiW8eK6OtWrpQ4W\n",
"csGs1gn4HNQhjixy6g0XMe2HpuqkNn7V7JYe/uc9yQcErA/ks9roppYhsN7HhiikFLq4crrLmHgJ\n",
"BXi9TJn0pu91hTONu+GpuoQbAt6XFGNnBLjSJlL3+xznqXoP//X8rQmm5d3EYyiBSbdOnReweB4H\n",
"TE6waaPq8/6KKySTwoEKXo9AVC9a4Sp1hn7th6NcoqilYXx6dubj8CpL/vzT19S3Uzd4xvdoPcPU\n",
"01j2Gs71X5/b+P12kVc99r1NYIR5V79O/1i4JN/Im0JGhXKz5MvJx90eq20lNOyr8A7opk1JQxou\n",
"5ppOv5M4ZKjb6ue8zOLSMcMcY+KfZLcdeRiAv0O5/IQMi7lDOLmait8IEE2J4/KSQfv5tgZPBjFj\n",
"Xr1s/IRLdS2EbUBRvw7+AX7Kns3MzKqtPSeRTyC6M0YOjcbDmoUlIJ+lqYifYhskO/89X0xUJDyk\n",
"bH3jt+wATOz6WQJtGhXbAfByxQcL3vtUL5BK1ouEAGyd+tk243CzewPnO71BHc+2t76jAb/ylYtl\n",
"nts1xa2+jUKX5q/DsBxVACNNsXzQYG+YWqEqCKnRhSkJjxHxjc3ydUOu6wYt4fh1pDwdZW7uKeWH\n",
"TgjQ1O1LzZLggrs2LiNxmByrTqLojBTvUK44U5z99kOa6WGED+Shecy97zZMTUsJZaoQvQ5H+GFm\n",
"17cWlwkBEiiWAQ+5LtYRlLCLDShtqMdC0O19c+ANTOruTt1FJrHuKhVJvU8eYxLbKR3oFIUCZ9D4\n",
"r84o+vfk3FlLQRwvAo51xtNKLrqdwkR7jvFAUVikWYgArfSpeKJMzHYpoLaBBPC5pA+TcsmM066G\n",
"HegMHJvrpLMa6Br79yAt2ZBWCwaO7UNPAzLSCUM9C2jvYNh0LpGtRVQ1eAphrAOjQhjNfFdD0aQF\n",
"O2063dQcKoJZUI/vKJ1inTUGD26UjdFvWACWlToMaQsIK30MrfSG1eQe+ucKNSJ/a2akg3w/lA3M\n",
"H/arbp0YMrumABX3Ce31RhaGMDo2K8+tboqZ8PJo5LvSZFK+WCAuxTJ2qd7j1huADPQHE3/5LTqg\n",
"OY24OmE7BuSGfdUGh6JjjoYB+K8CZWtdiLMteVw1+dNAKV//8Yai0j8wSrCICOwtnPvLnPe5NyaA\n",
"QI3K7Cra56fXo0u2PgXtl6B+FjwUKGPQgm4muf4MDcUr0tJqPeKoKDcv7XFcdH1kdrkIXmyVWNED\n",
"WZCU9QcQMJZEzRfLHihY31rmOfZHsoioTsyg81KQgr+O5unedG+AAbu7e+vOsukFNWiMo+LARdfN\n",
"KzVyKzdd3QLRNoo0h03SlGdQtOuylyH99pfIbXXE8Rg0w363mZx5L6wqkFlJsrnDliq/V3ReHjPI\n",
"lNkiOgRN88HVQL/P2V1nGGpiCy9S/ubgAAAD6UGeQniK/who5pcZnp3WgrbWXwQKnBRYyPaJuIpv\n",
"WFOoscmmvq3rFyHuxBJ4V/FtoQc7mypCRcEgSxGcECiyRzWnQWFxfdzWGvkRBVYufaF2BAbf6HUO\n",
"MyL3sW47XAeR4OnKcogAPXVzR0BvoXRd4O1KQbkN4BBGamMnnBF2aIjz66wptRqrOfygl7kWmJa4\n",
"QNyMcA2WbBjkx/XAq4JgAw9sYyMzejwKRP0Wgc3lBO6niy0XiYK7t1Q5gAx0CWyIF2RMX59pC9IR\n",
"X82JMG4fNC17CjmXqiPnkZNcmZRawXsaJ3nuzZ0hRJKQtzFSCKHwlqoYXU5Bxbaa1+GPWMW2EXDJ\n",
"qsPCze1eN33T1ILPk6KdX1fmp9XZ9pBP+mxJ8uNJO4DauBLwJxHoe6aZ5+6idiYVoiRaE4cweiiR\n",
"x9lIcSVlc55vEETwznMe4BfjnV1lghpP0H4GJlUawszCO47hqYDkkuka9Rtf44KgTkTjj6cu3rTx\n",
"f5t60dlwf6CG6/uXiDZDfgkDZMVpXzU7qmyx6J1ewstqI8xila5DK3ciPM98J2JZFGiYN6W44ctE\n",
"u8IEHEnYqAH/D8x3wDizCJShZVOyd/r6wQbg0VhKeFP47JK+/5qioHV67f4W+O7G64AXhQWq//qK\n",
"GsR+puhPc00kIoaxQ7kc2DOkiRT2AaepioePyXKD/zGxExG8AKkZl+Xk14taDQlmDzkHfX/KyRAt\n",
"Lf+R6NAVYKh5f6IpwjYwIRd6fnTudS9xv8yCM5KVsq7QCSKrVi05KmPP4YBIogotYZfuut3mN1jd\n",
"Njzmk6ZJnpeE080SNbyHq92gNOlJ0ZJfQheP3rol34B0munX7e9HrBdEh2xoCRDBJP7yX3gVcj/M\n",
"7GLh1ugFD5V49fm8rEQj5xJV5UCm6rKaYJdm3nfG8zfv0/mEYYqJaGoUeNa1+dNj6NMDezKGw4s2\n",
"Tjf+C6L0uvFI0TIBMHSzWC0PTv4/8wChciRE/Bedwopn8s/zCXIotrCQcZdQesjmqeWI+G0kdldO\n",
"BgpYNQxq0zTAzztMHrbLJfUFaf5W3iOadMihMakI3H+q7RrMXGPj7TIUbqsuzyn2mAJsyOL1fRpw\n",
"VNxwiYyW103hCGpXs9N1koJUHNZzEopAVWNPawlmyfe263+hAFvj9SCKsa2RtVac4EtvUin5mnGN\n",
"qNn7kmTFaoh1HZeeGV3rwefM56mf32QcDZG3E2+Zcp0S2i5fXbW+NJQtoofZ11hj4/1BM+wpshfm\n",
"1PHWYj6/s6ZeiIwLRbRk5AUweOXyujPafezOsVGqxtldKpR4Pjv+ShkqEe7atYyR3z7zRA/Zovt5\n",
"v6+LAAABKwGeYXRFfwhoacf2QXzGFACvjPKz80P5FCQ+t3mrEN2ykbw11Nh+EWCJhNDnd8Rmf+Qa\n",
"xHx2uF6SrjizcufswW8+4bn76sq98fw3xmRNTzNzpFxTDKy+5KFns0cldjbDdgbI6PMq2Hp3cmHZ\n",
"dcp2dq+s64K080FTpljypdxuPEmnIiPtyHlvmv01yNtM/dDQWxhU1A/4AQGyU8pUamtRg/ZeGs2b\n",
"RbmPokLEoAN/WOc9MN1t1mVpQELj73EKwQfL3OKS8Y8rWh9tZZ6A+BC3UHi2GVn/UnxkGc5bOQ7X\n",
"mnOpnzLRpehXk6Oz+Ixp1O92ycxz3WAWsVCbrAJyPMmkrrvcTG1BVV2JVa/qOjSBOAfR4UDLP8/A\n",
"o31HoszulNTt24hEoP6xDupB00+gAAAC2wGeY2pFfwg1UoTXGN70Zx+Uy7GUir+kVrxauZotEgxp\n",
"LLl/HW1GW21hvPSD95TzwYBBhfBSOEmGh7O+9XCNCrldUtS2VtcL8eEKaO2sb/4t/P6H8I5FUNkZ\n",
"4fr9JiuLZkF9iHipvPjAsWFffk6FD26g8W62J9SyCmyTJK5jH4Dr31A3JspD0AAh9/175tmVdQ2w\n",
"CfCt2TAL3hg94XTaYNslmTvKdaIkWel6VmTFs/mCD9KeJN8wMUCuh1pi8mzg3dl3Yt0yAW3tBE+t\n",
"GQ2MotdqPS9zzP6HvvDNk3olpDU78HEEIRaQQzg2y70nXoq2FEPgs+FGf7EKeKAueq1p546v27RM\n",
"AfvCxjNA9eODCkl5G6eHFkcgjQSo7PtoFSbkwQjDRjJQ2nUWvu/f9XHSRZ/VbEMFvUgTT6g5udmD\n",
"PFxDLDTJPFrJHJCzRk4b3Rwx03aINXdIvEIQQ0hmyMxLLnz5wDPkPCt2EBotJlpyH/rV7/1gfKZT\n",
"pFmMJ/j6c655dB+nH+/o1uO/wcPEiSTstwVORou55ybPlKe53aS2rc7LkDhLRA+PK9tUPWQHMut7\n",
"wrbTe8Mfl8s4F9elaCAk+Vp1ttRjrEYkcPoTItSKLjOU3w1u26DX7vvws/UGRZEzxlJLLkQ7ZQIF\n",
"2vdlbjV44MkOCr/IvffYxRq4syenOBjor7P1bxNKGld0Z/I3UEfQU54iPp5y//n4oUXvNHu2+ImS\n",
"Mepx3qRElO2sQPo3No9SUlirpafeazOuV2AplyPN86GB2OYdDoUvbiDORovCTfpgjXIpvuHWLImX\n",
"Repe4XxdGiEarsJYa0f1IUtoVByd7Uw9/yH4Due6V4CbOkLbHJ88g3n+zEIl8vZ70KMG1jlpPRiH\n",
"pS0WJw6Nt3gGAiQCFcLsph6D7kIqr3p2rRH/ek8e4uKTjM3na0/ap/PIMvL5kwSh0mkqta276pIu\n",
"iqe41sJEas4nMDCCVEVVAAAFBUGaaEmoQWiZTAivAB57ryOsVCgwwe/Ej/IXkjarLuReuPraHXlw\n",
"SGZhAXQeWxLbKybw/9hTPICY6yZLcr71K2CszWQCXbRFPOqHb2B8uq6+K4/W1N85tVQSZNsraQ4m\n",
"a6Zk0i/H3KNyLZVlfdCBvvWwy9oVZ6l0XGWPKEKnQHQ6kqxsl3uDDPSmbjtNhYWNQ61HqxbC4TJL\n",
"PW8r5RjEH35avRC2nkLzPrv2otr+8oeyOXhUqZlw5uPAo4ne3IZ8iWIz1Xtifjw8M13AAPlO9vpC\n",
"ZnvCP62+6+uZQT+dR0hVB9Q+opraRY/rQEBtM7FU350LxZ4/YJrrMJ6ZGgIoGMMqgH0//Qb7b+x4\n",
"gpYHQTRj9BYtMuUJSPxg1Pg9gd3dFi3DFI/r6BVldNtse8GK08IUMd9BAw7iKPnDk7AfbQ9OoRZ9\n",
"kJHi9mWXlifpp9j7vmXNMavu2Hd0v4Rln4itKixcOXgLLxIeB85VGwy1sYNf/9BWViBmGe0UmUSJ\n",
"pnrzQJvkSG1Os7TEeQQsCYnSRjFtLHhDwg91CyOqlCu0FP0GGk7yXjpTDSGaGzEOs4vw4bAMqmQX\n",
"uuCG8pWiaX8LDhH42KCIPNswfq+U2yL7l97op2fTf75o6Qqbh7IgzmOwCg58+BhiVUbLLwRq9Ri6\n",
"vyMqmY5bTa+nF2BnAoGzuXuiRAzzryQoAsq0iZtElDq3PdBadkqu8tVbWhQwDdl4TLN9/XgCDzS3\n",
"oChcyWBFfUdQKOkrIQljUxEsnRde+CX+jMUs/CqpzGPiyD2GIe1cm6xCj18dCISG6RnhqsTI0dbz\n",
"fuzwb7kfDuNBmCHqmkiXqZUI33m6r9Vd8EM1wX/rFblN7GjbLxaccQD3p9pe3rxgjki+llmQAsUm\n",
"C6ajLasp5JH++0fVGAn9yCs3iPGBMnD31K7zQovgNCWOXYoLrwBih+YkyIE8GuGsVmVd+Dr7gIAp\n",
"7+C/ar6F7HzccDxprUHon7+eBc1ElCOvWpEoFxYzCQSttSaFLnXXv01ejIZaXTMWFrQh77Oab9g3\n",
"TyYomseLoL+cshXQ0MX9ffJUgAUfqTDXXnmfQtDQqcQYUNz22j1okZ2WGqv6T6CHFlS3vevRjSQC\n",
"Bs7iWbOT8uCyUHXfmpTMdvsLqtTSAnsTXPzaL4ZYq8Ou2AfjDxnDP8Zw5DU3tW/C1/7vxEiMAWSf\n",
"PIYWrZw3zyGsp9x5hytlLSJJ2/EKEl9AzRg36DixePqMS01k72aVD2eTRCMP00Fqto5P52E7lKqe\n",
"azl1L7kbRIPmx3JsgX/9/ZyHfpWNSbfdOAQgCYnjqaplBv/yseW339+d4qdOYURFFaxKkkXSNDTG\n",
"K01YDLS77OTGRambgcrJGNyusSiQTLUrK2G76xIqq9Vm1D/ab/gtdEsePbVX6xGSTZMjxXwflPSt\n",
"VpJlaMVrwnsF0WdBwac5NABOgB0+l8A9K7ck8XfD8ZnVwF0Ma73BIEgmW9SacLrDM/JQUWdrotA4\n",
"7bEQvkryU5gMoU+IAbA4q1ltfNCqRl/wiucF/6Vz1tYCM1mtz9xHn3/dv2soRnW1a6jhE7ojpnsi\n",
"uAmPK1BUYv5MbMWy7n6J1wsG+8dqEhPHcILzMAhq5H1Y9GQCC0fI9ByZHw07mx8wQ0Gngc4LqXNk\n",
"muHCca/AEPZveSnTx4Pe6CpIivr9K5q9OqLGOX9TGLOFahJK/uzsVLD3FCJMnAzFFbEAAAFLQZ6G\n",
"RREsVwh/OGVXCtYozBusXu+yEQUVkAxqPgKY4fboRWRClGLkKKhnATAlz5su9fTeN2OofHbiifK6\n",
"PK7bsweRYEIIoQB6tKSIZRJK9TxV7+jSHHm2KXGVHhHH9HG+Unw29m8n+pb/5UN7X9sIKW5q8Ii/\n",
"JPVStxjltntvrwKRvVONfOYOabzMUU6nlWnl0/UFeH95FWpiECxdYjW8pHbtXOdiMmjngpopTshy\n",
"eYSAZRJ+b9HOM3hmByUUlQgLy8V0C7qm+iWBqaOlVgrIcMnkE1//b8dOnpAn1O1z0yvRzoABZLfC\n",
"m42DEFi9XQXQYO4aAiKupdIGcd4DBCd1RvMf8b/gXWCyZf+MTJJb1EovxBELk83IxH1FwxTtvBeU\n",
"oCIg7fnOWJ97iY3GqAHPBYwbtPO7jMDmBNR9/yXrGSeSXShjTVnvMgXvwQAAAIUBnqV0RX8IRqhR\n",
"CN5v5BxmyxhKLXEXl6TGFvXjiTqv39HC7e++QXjIFJk4qLwRcpxfygfvDKEAzlTBtSyZdca8WG8W\n",
"qzXgYSDvVZYR+g3bWG1nLKjeG5GI+o+8fwB09qQIhts6ltXkQuZ0mWfB64glwOoYTJrXWDmBN1Rx\n",
"roSXRu72EQFDAAAAlgGep2pFfwh/OGVbKr6BsUVV2LqoD8TnFfs/N8CeO7kNNX5ni1iPC+2WvqgY\n",
"O+lJaa3EpAxP9OGul3wDU/m4ZdYojX0Nl3Qndcufk1khwwMxhpRDiUY3Xcpf9+SNRb24JeXT+OiV\n",
"pJydPIPmvyO8ROCLxx71ZQ/bf3lxiZ0mXADQSGYc++p4D/MmYc289K+UMUQj2HcBoQAAALZBmqxJ\n",
"qEFsmUwIrwAe4knKedAjQ5NuiDSz80P5FCQsfG8wRlHL/v9J2W9/bzhBBm+JWUuz9aFzreFBYfTv\n",
"HnRYNesxA2cy2wQKFDVm18K6uh49qT4iFIEJo2cojCQmr9Xd6OvJtThwOYk8T+eAJzpPsPVbQADl\n",
"zrlipi/WkOSRY5lumwmTeRzoMvcfkrHkxDYc8MGSd2IdAk03gk0bvFd/OspxXbdYrrfnvioCzP+t\n",
"NeNNwUwIQAAAAH5BnspFFSxXCGqIOLHSeyOWrrVc6p9JUi9Tpxza5c1epYoQT3F1WiEoTyvTeuO8\n",
"h1OQz9eP+FPFW2ce+iN3Oo3zqCwBf0hUWoNcWPDqiDIKLASYIXN81MTKE3huRiPqLhim8N1sWMNU\n",
"itkjF2dkG7eyDmUUg5ezu/0Jjf4gdKUAAABuAZ7pdEV/CHepJXWTkudR4Mc6DD883bIaHAwKsmnl\n",
"8lWKOSeh36McySaUhfHCBB6936JLwZrz5yG0d+Dg7ycKcmSVFCawZHb3bSr+EfqNN3wJhnmVR5V6\n",
"C1BrzpMt7KjyBPIhGRKj/yh1TwTGZzgAAABsAZ7rakV/CGmzR9rP+s6mD/QFuqteC9/v+qhuZGAA\n",
"I0W5ZmVO1OLaBTG+dHM2VPSua48I0XoTQrK8ITjUc1/S+E7PF0/K8qOvM15+m8NyMR9RcMU3hutm\n",
"FAiHYy64R/D5Eniln4ajkJ355WHdAAAFrEGa70moQWyZTAivABf6BuTI4u6LB5CeqClc/mVqcXNs\n",
"eUzfx5Vw1hVjbcu3onAhD9jH6j239ZgofEOkbIe1/7m989Hvka3NB9STh4iFCAtRHneNZM68CB4u\n",
"1b/08O6l+jOxYeN4lWX7hzSHbfvfikvBO8M0psiziNIJV3V8q17v3fP+ZobqvsFZFkJsNnZ/bV5O\n",
"+HVWCEVQ3SlLo3rwIYBtkrvrTDh5Wjs/ezxUuQCOdBbB3JpLzu3FXptW8/Uxb63gkSSWfc5BypIW\n",
"IzWqp9cBIAwOEu9dtC2MRTN1b3hRALvJ/RobTdGjwbkRGsdcf4LGPCG67El9WR1yWJMb/iiZnzTF\n",
"kP1qW3F1dncLo6Ahji7bdbNNIKoJzQ6JKiOWeZ73znfNy2Kf+Y2B2ASBXMzGoJf/aDlWoeVvsBHa\n",
"VSMq+C0zAkpIepnSEcOhOAPIHVWO4Jn+kA1gjmnChUan6xaI00i68uHElbF9DljNuA4emGXTp9QR\n",
"2L0BgsMxJyyL0x26fZ5fl3jv/nkPRieZnVh476cbT0TJuxa790DPtKYz4ZBdYuSaFdqtepvNvBuw\n",
"SkVXQSReMNHd31GsxRnJzjC6YLSWFmZTmUMVxvUoe42e/zp5WmbSYm7OvX5oAWa6wRnaRFQ8bpH1\n",
"xSzNDwrijcRkcu2oKg/0zkEgEWHUib1gHZNdtKavaLPVlSLdfnL//5vwf04D8MXPKRY8/i7Xvf5U\n",
"Hv67lzEwDXAheYDa+wAKU9VfcgVA6IU38Qu0kBpLQ7RUrXvnqZKGwyHMAVk6cQ4T0OBpn31gIgeG\n",
"rahLKuSBQoPIzJ2Q3WK9uxl3CZqgYROGgjM+xUM4lVciukw/xwckjJPHxf7h/LTQxg0MomkSrwGc\n",
"tuMcGK77ZROH2JajQJBK2TSAfpY005+izomM5UaWCWJEoeaIym6772Jq4niOtxhv5QV5A8BVIPZT\n",
"hLyUIti9QTXE/BZTEXg8eJAbNsfgP6+8A0uPTo7Z9U4IyfUIv7yOKIay+eWgnqs1KThF5pguHCA6\n",
"HDKiUiQA1omcWHrg3/RtvilJmQ72YsPTepsRMyio/+8BOcpBwKSt+h2a1HJ6EhSraAXdfvDdPn3N\n",
"IhgWykMkLaKuRaxcULJiSl04wGlfeE9hLuUnIn7g+86RujHiXefVIGqfGgjD15dOyJ0JrT3b9ouM\n",
"rzxyrvNxSeSyS2cO/jwQMbUzibALhUV0cBduOqucIgn+vUnKMeMzdQhH0NKwvWDwO3ZdwTwcMSI0\n",
"2lfRRdqGkL96nAIC07gtqRvk6gqb2EQWurg6mDaDtH/HF6WclaPhCojETJrcK3J2+IvfPqaFlSyB\n",
"MPcJC0fi/rqeZyJMu4g6AiLv/1tvqjyap80ovIwEPwFY3VNPKkJYSXT/qibMVghSVkRGEp9Awsvq\n",
"pRc3DGrfSijw79PXU5x0Sn2gfdj1Zx7b/vgHuoshfMb8pupiw+XJXL6OoRY1cBaYCVVYHD52aLQB\n",
"jCULajCjpdk3BOeohmS4xN19NcMGdj/Z9yDcuB4ahB4toJVRr2Z3TzfJVQoEkp6we8elE003b9kc\n",
"wNbEQVxfi27XcgfkwenvZWB+vgrLrXAPRo4w3/UYpCgTJfnUilHFwaeY9anSxQ+BZQLNXQRDpIBd\n",
"OywwJt1xE2v1xfQwnwd4wW0aR31MXkKPzR5e49Gmq7x7QzhpR8bmWUHePhmigopBJ/qJbOAGbS7T\n",
"yiL0HXiZ7KcQ90+MzmxR8H/urQ+7oL++5E7HjJLYPB9SJZF0BysRL2UsWBQWNHMmWeDYT+P5pt9o\n",
"d8JDJuWNq5gOqp/0fxQKpHGuQNtaY5eRXv7LIezMgNiA/UB/zhxwZ0lgpfDUxINwxf+TyQSfdIqy\n",
"4f28YbHDq33/tOiKOo/nbSwN2haKz1Cz6T9i9hVury97x/AHCSGJFd9Uv9ust62trKIFhQAAAJNB\n",
"nw5CK/8ISLXm8HMrvSE/GxGj2zgBPpY/22vp9lNp/bh0UfyCN5ngBlbBlaTyrHGCMyEtX4+rAlrC\n",
"mlIbVlrhrRLaa1CkycbQmeHZyX//6yZ9+KiNuKaygoTrDC5eHVBTY8RkHU4XR+LBv6cgSUZyXa8j\n",
"cf7d86o97YuULg8vsgXjqFihxtXnXpaezvxSrOWLxWEAAABCAZ8taRFfCCq9mFu54b/QktcVX5of\n",
"2v4xafyUbOmlXvTGasy/p4p0v0oiE7P0+47SGxMe41H5rBt0BLxFPKJ1gEKBAAAD0m1vb3YAAABs\n",
"bXZoZAAAAAAAAAAAAAAAAAAAA+gAAAMgAAEAAAEAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAAAA\n",
"AQAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIAAAL8dHJhawAA\n",
"AFx0a2hkAAAADwAAAAAAAAAAAAAAAQAAAAAAAAMgAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAA\n",
"AAAAAAAAAQAAAAAAAAAAAAAAAAAAQAAAAAGwAAABIAAAAAAAJGVkdHMAAAAcZWxzdAAAAAAAAAAB\n",
"AAADIAAABAAAAQAAAAACdG1kaWEAAAAgbWRoZAAAAAAAAAAAAAAAAAAAKAAAACAAVcQAAAAAAC1o\n",
"ZGxyAAAAAAAAAAB2aWRlAAAAAAAAAAAAAAAAVmlkZW9IYW5kbGVyAAAAAh9taW5mAAAAFHZtaGQA\n",
"AAABAAAAAAAAAAAAAAAkZGluZgAAABxkcmVmAAAAAAAAAAEAAAAMdXJsIAAAAAEAAAHfc3RibAAA\n",
"AJdzdHNkAAAAAAAAAAEAAACHYXZjMQAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAGwASAASAAAAEgA\n",
"AAAAAAAAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABj//wAAADFhdmNDAWQAFf/h\n",
"ABhnZAAVrNlBsJaEAAADAAQAAAMAoDxYtlgBAAZo6+PLIsAAAAAYc3R0cwAAAAAAAAABAAAAEAAA\n",
"AgAAAAAUc3RzcwAAAAAAAAABAAAAAQAAAJBjdHRzAAAAAAAAABAAAAABAAAEAAAAAAEAAAoAAAAA\n",
"AQAABAAAAAABAAAAAAAAAAEAAAIAAAAAAQAACgAAAAABAAAEAAAAAAEAAAAAAAAAAQAAAgAAAAAB\n",
"AAAKAAAAAAEAAAQAAAAAAQAAAAAAAAABAAACAAAAAAEAAAgAAAAAAQAABAAAAAABAAAAAAAAABxz\n",
"dHNjAAAAAAAAAAEAAAABAAAAEAAAAAEAAABUc3RzegAAAAAAAAAAAAAAEAAAC+4AAAlaAAAD7QAA\n",
"AS8AAALfAAAFCQAAAU8AAACJAAAAmgAAALoAAACCAAAAcgAAAHAAAAWwAAAAlwAAAEYAAAAUc3Rj\n",
"bwAAAAAAAAABAAAAMAAAAGJ1ZHRhAAAAWm1ldGEAAAAAAAAAIWhkbHIAAAAAAAAAAG1kaXJhcHBs\n",
"AAAAAAAAAAAAAAAALWlsc3QAAAAlqXRvbwAAAB1kYXRhAAAAAQAAAABMYXZmNTQuNjMuMTA0\n",
"\" type=\"video/mp4\">\n",
" Your browser does not support the video tag.\n",
"</video>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 9,
"text": [
"<matplotlib.animation.FuncAnimation at 0x10ee35450>"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(opt.recall('phi_d'))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 10,
"text": [
"[<matplotlib.lines.Line2D at 0x10eb01450>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEACAYAAAC08h1NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x11030ec90>"
]
}
],
"prompt_number": 10
}
],
"metadata": {}
}
]
}
notebooks/SliceThroughModel.ipynb
-3048
View File
File diff suppressed because it is too large. Load diff
notebooks/VisualizeWithvtkView-updated.ipynb
-142
View File
@@ -1,142 +0,0 @@
{
"metadata": {
"name": "VisualizeWithvtkView-updated"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import SimPEG as simpeg, matplotlib as mpl"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The history saving thread hit an unexpected error (OperationalError('disk I/O error',)).History will not be written to the database.\n",
"Warning: mumps solver not available."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Simple notebook of how to use vtkView to visualize SimPEG models. It will pop-up external vtk windows."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Make a mesh and model\n",
"x0 = np.zeros(3)\n",
"h1 = np.ones(60)*50\n",
"h2 = np.ones(60)*100\n",
"h3 = np.ones(50)*200\n",
"\n",
"mesh = simpeg.mesh.TensorMesh([h1,h2,h3],x0)\n",
"\n",
"# Make a models that correspond to the cells, faces and edges.\n",
"t = np.ones(mesh.nC)\n",
"t[10000:50000] = 100\n",
"t[100000:120000] = 100\n",
"t[100000:120000] = 50\n",
"# Make models called 'Test' for all with a range. \n",
"models = {'C':{'Test':np.arange(0,mesh.nC),'Model':t},'F':{'Test':np.arange(0,mesh.nF)},'E':{'Test':np.arange(0,mesh.nE)}}\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Make the vtk viewer object.\n",
"vtkViewer = simpeg.visualize.vtk.vtkView(mesh,models)\n",
"# Set the .viewprop for which model to view\n",
"vtkViewer.viewprop = {'F':'Test'}\n",
"# Show the image\n",
"vtkViewer.Show()\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Set subset of the mesh to view (remove padding)\n",
"vtkViewer.extent = [4,14,0,7,0,3]\n",
"vtkViewer.Show()\n",
"\n",
"# Change viewing property \n",
"vtkViewer.viewprop = {'C':'Model'}\n",
"# Set the color range\n",
"# Reset extent. Error check will reset the limits correctly.\n",
"vtkViewer.extent = [-1,1000,-1,1000,-1,1000]\n",
"# Set the range\n",
"vtkViewer.range = [0.,100.]\n",
"# Show\n",
"vtkViewer.Show()\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"/home/Gudni/Codes/python/simpeg/SimPEG/visualize/vtk/vtkView.py:116: UserWarning: Lower bounds smaller then 0\n",
" warnings.warn('Lower bounds smaller then 0')\n",
"/home/Gudni/Codes/python/simpeg/SimPEG/visualize/vtk/vtkView.py:128: UserWarning: Upper bounds greater then number of cells\n",
" warnings.warn('Upper bounds greater then number of cells')\n",
"/home/Gudni/Codes/python/simpeg/SimPEG/visualize/vtk/vtkView.py:137: UserWarning: Changed given extent from [-1, 1000, -1, 1000, -1, 1000] to [0, 59, 0, 59, 0, 49]\n",
" warnings.warn('Changed given extent from {:s} to {:s}'.format(value,valnp.tolist()))\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Change color scale, has to be set to bytes=True.\n",
"vtkViewer.cmap = mpl.cm.copper(np.arange(0.,1.,0.01),bytes=True)\n",
"vtkViewer.Show()\n",
"# Set limits of values to view \n",
"vtkViewer.limits = [5.0,100.0]\n",
"vtkViewer.Show()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
}
],
"metadata": {}
}
]
}
notebooks/exLomPlots.ipynb
-122
View File
@@ -1,122 +0,0 @@
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import sys\n",
"sys.path.append('../')\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from SimPEG import LogicallyOrthogonalMesh, utils\n",
"mkvc = utils.mkvc"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test 2D Plots\n",
"\n",
"For 2D nodal or cell-centered plots are supported.\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X, Y = utils.exampleLomGird([3,3],'rotate')\n",
"M = LogicallyOrthogonalMesh([X, Y])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"M.plotGrid()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEPCAYAAACtCNj2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x10b6cc110>"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test 3D Plots\n",
"\n",
"Plot x, y, and z coordinates of cell-centred points"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X, Y, Z = utils.exampleLomGird([3,3,3],'rotate')\n",
"M = LogicallyOrthogonalMesh([X, Y, Z])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"M.plotGrid()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADtCAYAAAAcNaZ2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x10d796110>"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 42
}
],
"metadata": {}
}
]
}
notebooks/exPlotImage2D.ipynb
-235
View File
@@ -1,235 +0,0 @@
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import sys\n",
"sys.path.append('../')\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from SimPEG import TensorMesh\n",
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test 1D Plots\n",
"\n",
"For 1D nodal or cell-centered plots are supported.\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x0 = np.zeros(1)\n",
"h = np.random.rand(32)\n",
"mesh = TensorMesh([h],x0)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ax1 = plt.subplot()\n",
"ax1.set_title('sin(x) on CC grid')\n",
"ph1 = mesh.plotImage(np.sin(mesh.gridCC),ax=ax1)\n",
"ax2 = plt.subplot()\n",
"ax2.set_title('sin(x) on N grid')\n",
"ph2 = mesh.plotImage(np.sin(mesh.gridN), ax=ax2,imageType='N')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEZCAYAAABsPmXUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x10c1e9910>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEZCAYAAABsPmXUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x10dd96ed0>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test 2D Plots\n",
"\n",
"Plot x and y coordinates of cell-centred points"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x0 = np.zeros(2)\n",
"h1 = np.linspace(.1,.5,3)\n",
"h2 = np.linspace(.1,.5,5)\n",
"mesh = TensorMesh([h1,h2],x0)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(1)\n",
"ax1 = plt.subplot()\n",
"ax1.set_title('mesh.gridCC[:,0]')\n",
"mesh.plotImage(mesh.gridCC[:,0],ax = ax1)\n",
"ax2 = plt.subplot()\n",
"ax2.set_title('mesh.gridFx[:,1]')\n",
"mesh.plotImage(mesh.gridFx[:,1],ax = ax2,imageType='Fx')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEZCAYAAACTsIJzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x10ddc1ad0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEZCAYAAACTsIJzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x10df9cf50>"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 5,
"text": [
"<matplotlib.collections.QuadMesh at 0x10dfc4f50>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test 3D Plots\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x0 = np.zeros(3)\n",
"h1 = np.linspace(.1,.5,3)\n",
"h1 = np.r_[1,2,1]\n",
"h2 = np.r_[1,3]\n",
"h3 = np.linspace(.1,.5,10)\n",
"\n",
"mesh = TensorMesh([h1,h2,h3],x0)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ax1 = plt.subplot()\n",
"ax1.set_title('mesh.gridCC[:,0]')\n",
"a1 = mesh.plotImage(mesh.gridCC[:,0],ax=ax1,annotationColor='w')\n",
"ax2 = plt.subplot()\n",
"ax2.set_title('mesh.gridFx[:,1]')\n",
"a2 = mesh.plotImage(mesh.gridFx[:,1],ax=ax2,imageType='Fx')\n",
"ax3 = plt.subplot()\n",
"ax3.set_title('mesh.gridEz[:,2]')\n",
"mesh.plotImage(mesh.gridEz[:,2],ax=ax3,imageType='Ez')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXEAAAEKCAYAAADkYmWmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x10dfd5c50>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXEAAAEKCAYAAADkYmWmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x10dfa5990>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXEAAAEKCAYAAADkYmWmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text": [
"<matplotlib.figure.Figure at 0x10f09be50>"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
"<matplotlib.collections.QuadMesh at 0x10f2d2a90>"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}