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469 KiB
469 KiB
In [1]:
import numpy as np
from SimPEG import *
import SeogiUtils as SeUtils
import simpegEM.Utils.Solver.Mumps as Mumps
from simpegPF import MagAnalytics
from SeogiUtils.Optimize import ProjectedGNCG
% pylab inlineEfficiency Warning: Interpolation will be slow, use setup.py!
python setup.py build_ext --inplace
[1;31m---------------------------------------------------------------------------[0m [1;31mImportError[0m Traceback (most recent call last) [1;32m<ipython-input-1-d87eabd27cc5>[0m in [0;36m<module>[1;34m()[0m [0;32m 1[0m [1;32mimport[0m [0mnumpy[0m [1;32mas[0m [0mnp[0m[1;33m[0m[0m [0;32m 2[0m [1;32mfrom[0m [0mSimPEG[0m [1;32mimport[0m [1;33m*[0m[1;33m[0m[0m [1;32m----> 3[1;33m [1;32mimport[0m [0mSeogiUtils[0m [1;32mas[0m [0mSeUtils[0m[1;33m[0m[0m [0m[0;32m 4[0m [1;32mimport[0m [0msimpegEM[0m[1;33m.[0m[0mUtils[0m[1;33m.[0m[0mSolver[0m[1;33m.[0m[0mMumps[0m [1;32mas[0m [0mMumps[0m[1;33m[0m[0m [0;32m 5[0m [1;32mfrom[0m [0msimpegPF[0m [1;32mimport[0m [0mMagAnalytics[0m[1;33m[0m[0m [1;31mImportError[0m: No module named SeogiUtils
In [2]:
cs, ncx, ncy, ncz, npad = 20., 31, 31, 1, 0
hx = [(cs,npad,-1.3), (cs,ncx), (cs,npad,1.3)]
hy = [(cs,npad,-1.3), (cs,ncy), (cs,npad,1.3)]
hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)]
mesh = Mesh.TensorMesh([hx,hy,hz], 'CCC')In [3]:
sph_ind = MagAnalytics.spheremodel(mesh, 0., 0., -200, 200)
model = np.zeros(mesh.nC)
model[sph_ind] = 10.[1;31m---------------------------------------------------------------------------[0m [1;31mNameError[0m Traceback (most recent call last) [1;32m<ipython-input-3-63af893581c4>[0m in [0;36m<module>[1;34m()[0m [1;32m----> 1[1;33m [0msph_ind[0m [1;33m=[0m [0mMagAnalytics[0m[1;33m.[0m[0mspheremodel[0m[1;33m([0m[0mmesh[0m[1;33m,[0m [1;36m0.[0m[1;33m,[0m [1;36m0.[0m[1;33m,[0m [1;33m-[0m[1;36m200[0m[1;33m,[0m [1;36m200[0m[1;33m)[0m[1;33m[0m[0m [0m[0;32m 2[0m [0mmodel[0m [1;33m=[0m [0mnp[0m[1;33m.[0m[0mzeros[0m[1;33m([0m[0mmesh[0m[1;33m.[0m[0mnC[0m[1;33m)[0m[1;33m[0m[0m [0;32m 3[0m [0mmodel[0m[1;33m[[0m[0msph_ind[0m[1;33m][0m [1;33m=[0m [1;36m10.[0m[1;33m[0m[0m [1;31mNameError[0m: name 'MagAnalytics' is not defined
In [902]:
from simpegEM import SourcesIn [903]:
txloc = np.ones((1,3))
txloc[0,0] = 0.
txloc[0,1] = 0.
txloc[0,2] = 0.In [904]:
xr = np.arange(-125., 126., 25.)
nrx_x = xr.size
yr = np.arange(-125., 126., 25.)
nrx_y = yr.size
xyz_tx = Utils.ndgrid(xr, yr, np.r_[0.])In [905]:
plt.plot(xyz_tx[:,0], xyz_tx[:,1], '.')Out [905]:
[<matplotlib.lines.Line2D at 0x1a392550>]
In [906]:
ax = Sources.MagneticLoopVectorPotential(txloc, mesh.gridEx, 'x', 200.)
ay = Sources.MagneticLoopVectorPotential(txloc, mesh.gridEy, 'y', 200.)
az = Sources.MagneticLoopVectorPotential(txloc, mesh.gridEz, 'z', 200.)In [907]:
a = np.r_[ax, ay, az]In [908]:
mesh.edgeCurl.shapeOut [908]:
(3906, 4992)
In [909]:
a.shapeOut [909]:
(4992,)
In [910]:
b = mesh.edgeCurl*aIn [911]:
P = mesh.getInterpolationMat(xyz_tx, 'Fz')In [912]:
b_primary = P*bIn [913]:
X = xyz_tx[:,0].reshape((nrx_x, nrx_y), order='F')
Y = xyz_tx[:,1].reshape((nrx_x, nrx_y), order='F')
B_prim = b_primary.reshape((nrx_x, nrx_y), order='F')In [914]:
Circ1 = SeUtils.View.Circle2D(np.r_[0.,0.], 200, 50)In [915]:
import matplotlib
matplotlib.rcParams.update({'font.size': 16, 'text.usetex': True})In [916]:
fig, ax = plt.subplots(1,1,figsize = (7,5))
dat1 = ax.contourf(X, Y, B_prim, 30)
ax.plot(Circ1[:,0], Circ1[:,1], 'r--', lw = 2)
ax.plot(xyz_tx[:,0], xyz_tx[:,1], 'k.')
cb = plt.colorbar(dat1)
cb.set_label("$b_z$ field (T)")
fig.savefig("/home/seogi/Google Drive/Ideas/obs.png", dpi=100)
In [918]:
ntx = xyz_tx.shape[0]In [919]:
G = SeUtils.BiotSavart.BiotSavartFun(mesh, xyz_tx, component = 'z')In [920]:
from SimPEG.Maps import IdentityMap
class VecMap(IdentityMap):
@property
def nP(self):
return self.mesh.nC*3In [921]:
# O = Utils.spzeros(mesh.nC, mesh.nC)
# J = G*sp.vstack((Utils.speye(mesh.nC), O, O))In [922]:
# active = mesh.gridCC[:,2]<0.
# actMap = Maps.ActiveCells(mesh, active, 0.)
# mapping = actMap
mapping = VecMap(mesh)In [923]:
prb = SeUtils.LinearIP.LinearProblem(mesh, mapping)
prb.J = G
prb.Solver = Utils.SolverUtils.SolverWrapD(Mumps, factorize=True)
survey = SeUtils.LinearIP.AirbornSurvey()
prb.unpair()
prb.pair(survey)In [924]:
# dtrue = survey.dpred(ones(mesh.nC*3))
dtrue = b_primaryIn [925]:
# fig, ax = plt.subplots(1,2, figsize = (15, 5))
# X = xyz_tx[:,0].reshape(nrx_x, nrx_y, order = 'F')
# Y = xyz_tx[:,1].reshape(nrx_x, nrx_y, order = 'F')
# Dtrue = dtrue.reshape(nrx_x, nrx_y, order = 'F')
# dat1 = ax[0].contourf(X, Y, Dtrue, 30)
# dat2 = ax[1].contourf(X, Y, Dtrue, 30)
# plt.colorbar(dat1, ax = ax[0])
# plt.colorbar(dat2, ax = ax[1])In [926]:
# plt.pcolor(dtrue.reshape((nrx_x, nrx_y), order='F'))In [927]:
survey.dtrue = dtrue
std = 0.05
noise = std*abs(survey.dtrue)*np.random.randn(*survey.dtrue.shape)
survey.dobs = survey.dtrue+noise
survey.std = survey.dobs*0 + stdIn [984]:
dmisfit = DataMisfit.l2_DataMisfit(survey)
# dmisfit.Wd = 1./(np.ones(survey.dobs.size)*abs(np.max(survey.dobs)))
dmisfit.Wd = 1./(np.ones(survey.dobs.size)*abs(survey.dobs)+1e-9)In [929]:
m0 = np.zeros(mesh.nC*3)In [1190]:
class SparseRegularization(Regularization.BaseRegularization):
perturbation0 = None
perturbation = None
rate = None
m_before = None
Wm = None
Rm = None
alpha = None
alpha_before = None
phim_before = None
p = 0.
vec_store = []
def __init__(self, mesh, mapping=None, **kwargs):
Regularization.BaseRegularization.__init__(self, mesh, mapping=mapping, **kwargs)
def W(self):
"""Full regularization weighting matrix W."""
iteration = self.opt.iter
dec = (self.rate)**iteration
self.Rm = self.R(self.m_before, dec)
# print ("dec = %5e")%(dec)
return self.Rm*sp.identity(self.mapping.nP)
def R(self, m, dec):
self.perturbation = self.perturbation0*dec
R = Utils.sdiag( 1./ ((self.mapping *(m**2+self.perturbation**2)**(1-self.p/2) ) )**0.5 )
return R
@Utils.timeIt
def eval(self, m):
r = self.Wm * ( self.mapping * (m) )
return 0.5*r.dot(r)*self.alpha
@Utils.timeIt
def evalDeriv(self, m):
mD = self.mapping.deriv(m)
r = self.Wm * ( self.mapping * (m) )
return mD.T * ( self.Wm.T * r )*self.alpha
@Utils.timeIt
def eval2Deriv(self, m, v=None):
if self.m_before == None:
self.m_before = m
self.Wm = self.W()
rm = self.Rm.dot(self.m_before)
if self.opt.iter==0:
self.alpha = m.dot(m)/(rm.dot(rm))
else:
self.alpha = self.phim_before/(rm.dot(rm))
self.phim_before = (rm.dot(rm))*self.alpha
self.m_before = m
mD = self.mapping.deriv(m)
self.vec_store.append(self.Rm.T*(self.Rm*m))
print ("alpha= %5e, peturb= %5e")%(self.alpha, self.perturbation)
if v is None:
return mD.T * self.Wm.T * self.Wm * mD*self.alpha
return mD.T * ( self.Wm.T * ( self.Wm * ( mD * v) ) )*self.alphaIn [1194]:
figsize(10, 5)
hist(abs(mopt_l2))Out [1194]:
(array([ 2.05600000e+03, 4.99000000e+02, 1.55000000e+02,
6.10000000e+01, 5.90000000e+01, 1.00000000e+00,
8.00000000e+00, 1.70000000e+01, 1.90000000e+01,
8.00000000e+00]),
array([ 0.00000000e+00, 6.42532598e-05, 1.28506520e-04,
1.92759779e-04, 2.57013039e-04, 3.21266299e-04,
3.85519559e-04, 4.49772819e-04, 5.14026079e-04,
5.78279338e-04, 6.42532598e-04]),
<a list of 10 Patch objects>)
In [1356]:
reg0 = Regularization.BaseRegularization(mesh, mapping = mapping)
reg1 = SparseRegularization(mesh, mapping = mapping)
# reg1.rate = 0.5
# reg1.perturbation0 = 0.00065
reg1.rate = 0.8
reg1.perturbation0 = 0.0001
reg1.p = 0.
opt = Optimization.InexactGaussNewton(maxIter = 10, maxIterLS=15)
# opt = Optimization.ProjectedGNCG(maxIter = 15)
# opt = Optimization.ProjectedGradient(maxIter = 15)
# opt.lower = 0.
# invProb = InvProblem.BaseInvProblem(dmisfit, reg0, opt)
invProb = InvProblem.BaseInvProblem(dmisfit, reg1, opt)
# Create an inversion object
beta = Directives.BetaSchedule(coolingFactor=1, coolingRate=1)
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e-1)
# betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e-1)
# betaest = Directives.BetaSchedule(beta=)
# BetaEstimate_ByEig(beta0_ratio=1e-1)
inv = Inversion.BaseInversion(invProb, directiveList=[beta,betaest])
# reg.alpha_s = 1.
# reg.alpha_x = 1.
# reg.alpha_y = 1.
# reg.alpha_z = 1.
reg1.mref = 0.
prb.counter = opt.counter = Utils.Counter()
opt.LSshorten = 0.5
opt.remember('xc')In [1357]:
mopt = inv.run(mopt_l2)
# mopt = inv.run(m0)SimPEG.InvProblem is setting bfgsH0 to the inverse of the eval2Deriv.
***Done using same solver as the problem***
alpha= 5.424578e-08, peturb= 1.000000e-04
alpha= 5.424578e-08, peturb= 1.000000e-04
============================ Inexact Gauss Newton ============================
# beta phi_d phi_m f |proj(x-g)-x| LS Comment
-----------------------------------------------------------------------------
0 1.35e+04 1.11e-01 1.59e-05 3.26e-01 5.86e+02 0
alpha= 5.424578e-08, peturb= 1.000000e-04
alpha= 5.424578e-08, peturb= 1.000000e-04
alpha= 5.424578e-08, peturb= 1.000000e-04
alpha= 5.424578e-08, peturb= 1.000000e-04
alpha= 5.424578e-08, peturb= 1.000000e-04
1 1.35e+04 6.94e-03 1.62e-05 2.25e-01 5.19e+02 0
alpha= 4.525803e-08, peturb= 8.000000e-05
alpha= 4.634058e-08, peturb= 8.000000e-05
alpha= 4.634058e-08, peturb= 8.000000e-05
alpha= 4.634058e-08, peturb= 8.000000e-05
alpha= 4.634058e-08, peturb= 8.000000e-05
2 1.35e+04 8.51e-03 1.45e-05 2.03e-01 4.59e+02 0
alpha= 3.940438e-08, peturb= 6.400000e-05
alpha= 4.115360e-08, peturb= 6.400000e-05
alpha= 4.115360e-08, peturb= 6.400000e-05
alpha= 4.115360e-08, peturb= 6.400000e-05
alpha= 4.115360e-08, peturb= 6.400000e-05
3 1.35e+04 3.36e-02 8.19e-06 1.44e-01 5.02e+02 0
alpha= 3.550353e-08, peturb= 5.120000e-05
alpha= 5.054731e-08, peturb= 5.120000e-05
alpha= 5.054731e-08, peturb= 5.120000e-05
alpha= 5.054731e-08, peturb= 5.120000e-05
alpha= 5.054731e-08, peturb= 5.120000e-05
------------------------------------------------------------------
0 : ft = 2.4841e-01 <= alp*descent = 1.4399e-01
1 : maxIterLS = 15 <= iterLS = 15
------------------------- End Linesearch -------------------------
The linesearch got broken. Boo.
In [1358]:
opt.counter.summary()
xc = opt.recall('xc')
# dpredall = [survey.dpred(xc_i) for xc_i in xc]Counters: InexactGaussNewton.doEndIteration : 3 InexactGaussNewton.doStartIteration : 4 InexactGaussNewton.modifySearchDirectionBreak: 1 InexactGaussNewton.scaleSearchDirection : 4 Times: mean sum InexactGaussNewton.findSearchDirection : 2.51e-02, 1.00e-01, 4x InexactGaussNewton.minimize : 1.07e+01, 1.07e+01, 1x InexactGaussNewton.modifySearchDirection: 2.17e+00, 8.69e+00, 4x InexactGaussNewton.projection : 5.83e-05, 1.81e-03, 31x LinearProblem.Jtvec_approx : 5.19e-04, 1.09e-02, 21x LinearProblem.Jvec_approx : 1.78e-04, 3.74e-03, 21x
In [1359]:
# plt.plot(np.sort(abs(reg1.vec_store[1])), '.')In [1360]:
# plot(abs(mopt))
# iteration = 2
# mopt = xc[iteration]In [1380]:
mopt_sort = np.sort(mopt)
ind = np.argsort(mopt)In [1387]:
rm = abs(reg1.Rm.T*(reg1.Rm*mopt))In [1399]:
fig = plt.figure()
ax = plt.subplot(111)
ax1 = plt.twinx()
ax1.hist(abs(mopt), alpha = 0.5)
ax.plot(abs(mopt[ind]), abs(rm[ind])/4, 'ro', lw=2)Out [1399]:
[<matplotlib.lines.Line2D at 0x3ab907d0>]
In [1400]:
# xc = opt.recall('xc')
# opt.iterIn [1401]:
# fig, ax = plt.subplots(1,2, figsize = (15, 3))
# dat1 = mesh.plotSlice(mx, normal = 'X', ax = ax[0])
# cb = colorbar(dat1[0], ax = ax[0])
# dat2 = mesh.plotSlice(mx, normal = 'X', ax = ax[1])
# cb = colorbar(dat2[0], ax = ax[1])
# # ax[0].set_ylim(-600., 0.)
# # ax[1].set_ylim(-600., 0.)In [1402]:
area = 20**2
# mx = xc[iteration].reshape((mesh.nC, 3), order='F')[:,0] * area
# my = xc[iteration].reshape((mesh.nC, 3), order='F')[:,1] * area
# mz = xc[iteration].reshape((mesh.nC, 3), order='F')[:,2] * area
mx = mopt.reshape((mesh.nC, 3), order='F')[:,0] * area
my = mopt.reshape((mesh.nC, 3), order='F')[:,1] * area
mz = mopt.reshape((mesh.nC, 3), order='F')[:,2] * area
mx_l2 = mopt_l2.reshape((mesh.nC, 3), order='F')[:,0] * area
my_l2 = mopt_l2.reshape((mesh.nC, 3), order='F')[:,1] * area
mz_l2 = mopt_l2.reshape((mesh.nC, 3), order='F')[:,2] * area
xy = Utils.ndgrid(mesh.vectorCCx, mesh.vectorCCy)
Xxy = xy[:,0].reshape((mesh.vnC[:2]), order='F')
Yxy = xy[:,1].reshape((mesh.vnC[:2]), order='F')
Mx = mx.reshape((mesh.vnC[:2]), order='F')
My = my.reshape((mesh.vnC[:2]), order='F')
Mx_l2 = mx_l2.reshape((mesh.vnC[:2]), order='F')
My_l2 = my_l2.reshape((mesh.vnC[:2]), order='F')In [1403]:
fig, ax = plt.subplots(1,2, figsize = (15, 5))
dat1 = mesh.plotSlice(mx, normal = 'Z', ax = ax[0], ind = 0, clim = (-0.4, 0.4))
ax[0].plot(Circ1[:,0], Circ1[:,1], 'r--', lw = 2)
ax[0].quiver(Xxy, Yxy, Mx, My, scale=5)
cb = colorbar(dat1[0], ax = ax[0])
dat2 = mesh.plotSlice(my, normal = 'Z', ax = ax[1], ind = 0, clim = (-0.4, 0.4))
cb = colorbar(dat2[0], ax = ax[1])
ax[1].plot(Circ1[:,0], Circ1[:,1], 'r--', lw = 2)
ax[1].quiver(Xxy, Yxy, Mx, My, scale=5)
ax[0].set_title("$\\vec{j}_x$")
ax[1].set_title("$\\vec{j}_x$")
fig.savefig("/home/seogi/Google Drive/Ideas/recovered_j.png", dpi=100)
In [1404]:
fig, ax = plt.subplots(1,2, figsize = (15, 5))
dat1 = mesh.plotSlice(mx_l2, normal = 'Z', ax = ax[0], ind = 0, clim = (-0.4, 0.4))
ax[0].plot(Circ1[:,0], Circ1[:,1], 'r--', lw = 2)
ax[0].quiver(Xxy, Yxy, Mx_l2, My_l2, scale=5)
cb = colorbar(dat1[0], ax = ax[0])
dat2 = mesh.plotSlice(my_l2, normal = 'Z', ax = ax[1], ind = 0, clim = (-0.4, 0.4))
cb = colorbar(dat2[0], ax = ax[1])
ax[1].plot(Circ1[:,0], Circ1[:,1], 'r--', lw = 2)
ax[1].quiver(Xxy, Yxy, Mx_l2, My_l2, scale=5)
ax[0].set_title("$\\vec{j}_x$")
ax[1].set_title("$\\vec{j}_x$")
# fig.savefig("/home/seogi/Google Drive/Ideas/recovered_j.png", dpi=100)Out [1404]:
<matplotlib.text.Text at 0x3b48f110>
In [1405]:
plt.plot(np.sort(abs(mopt)), 'r.')
plt.plot(np.sort(abs(mopt_l2)), 'k.')Out [1405]:
[<matplotlib.lines.Line2D at 0x39384510>]
In [1406]:
np.median(abs(mx))Out [1406]:
0.010629142125980437
In [1407]:
plt.plot(survey.dobs)
plt.plot(invProb.dpred)Out [1407]:
[<matplotlib.lines.Line2D at 0x39384410>]
In [1408]:
fig, ax = plt.subplots(1,2, figsize = (15, 5))
dat1 = ax[0].contourf(X, Y, invProb.dpred.reshape((nrx_x, nrx_y), order='F'), 15)
ax[0].plot(Circ1[:,0], Circ1[:,1], 'r--', lw = 2)
ax[0].plot(xyz_tx[:,0], xyz_tx[:,1], 'k.')
cb = colorbar(dat1, ax = ax[0])
dat2 = ax[1].contourf(X, Y, survey.dobs.reshape((nrx_x, nrx_y), order='F'), 15)
cb = colorbar(dat2, ax = ax[1])
ax[1].plot(Circ1[:,0], Circ1[:,1], 'r--', lw = 2)
ax[1].plot(xyz_tx[:,0], xyz_tx[:,1], 'k.')
ax[0].set_title("Observed data")
ax[1].set_title("Predicted data")
fig.savefig("/home/seogi/Google Drive/Ideas/obspred_bz.png", dpi=100)
In [1409]:
Utils.meshutils.writeUBCTensorModel("/home/seogi/Google Drive/Ideas/mx.j", mesh, mx)
Utils.meshutils.writeUBCTensorModel("/home/seogi/Google Drive/Ideas/my.j", mesh, my)
Utils.meshutils.writeUBCTensorModel("/home/seogi/Google Drive/Ideas/mz.j", mesh, mz)
Utils.meshutils.writeUBCTensorMesh("/home/seogi/Google Drive/Ideas/mesh.msh", mesh)In [1410]:
tempx = np.loadtxt("/home/seogi/Google Drive/Ideas/mx.j")
tempy = np.loadtxt("/home/seogi/Google Drive/Ideas/my.j")
tempz = np.loadtxt("/home/seogi/Google Drive/Ideas/mz.j")
np.savetxt("/home/seogi/Google Drive/Ideas/mxyz.j", np.c_[tempx, tempy, tempz])
np.savetxt("/home/seogi/Google Drive/Ideas/txloc.txt", np.hstack((Circ1, np.ones((Circ1.shape[0],1)))))In [ ]: