def fget(self):
if(self._area is None or self._normals is None):
# Compute areas of cell faces
if(self.dim == 2):
xy = self.gridN
A, B = Utils.indexCube('AB', self.vnC+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.vnC+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._normals = [normalize2D(normal1), normalize2D(normal2)]
elif(self.dim == 3):
A, E, F, B = Utils.indexCube('AEFB', self.vnC+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.vnC+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.vnC+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._normals = [normal1, normal2, normal3]
return self._area
def plotGrid(self, ax=None, text=False, centers=False, faces=False, edges=False, lines=True, nodes=False, showIt=False):
self.number()
axOpts = {'projection':'3d'} if self.dim == 3 else {}
if ax is None: ax = plt.subplot(111, **axOpts)
if lines:
[f.plotGrid(ax, text=text) for f in self.faces]
if centers:
[c.plotGrid(ax, text=text) for c in self.cells]
if faces:
fX = np.array([f.center for f in self.sortedFaceX])
ax.plot(fX[:,0],fX[:,1],'g>')
fY = np.array([f.center for f in self.sortedFaceY])
ax.plot(fY[:,0],fY[:,1],'g^')
if edges:
eX = np.array([e.center for e in self.sortedFaceY])
ax.plot(eX[:,0],eX[:,1],'c>')
eY = np.array([e.center for e in self.sortedFaceX])
ax.plot(eY[:,0],eY[:,1],'c^')
if nodes:
ns = np.array([n.x0 for n in self.sortedNodes])
ax.plot(ns[:,0],ns[:,1],'bs')
ax.set_xlim((self.x0[0], self.h[0].sum()))
ax.set_ylim((self.x0[1], self.h[1].sum()))
if self.dim == 3:
ax.set_zlim((self.x0[2], self.h[2].sum()))
ax.grid(True)
ax.hold(False)
ax.set_xlabel('x1')
ax.set_ylabel('x2')
if showIt: plt.show()
def fget(self):
if(self._area is None or self._normals is None):
# Compute areas of cell faces
if(self.dim == 2):
xy = self.gridN
A, B = Utils.indexCube('AB', self.vnC+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.vnC+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._normals = [normalize2D(normal1), normalize2D(normal2)]
elif(self.dim == 3):
A, E, F, B = Utils.indexCube('AEFB', self.vnC+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.vnC+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.vnC+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._normals = [normal1, normal2, normal3]
return self._area
def __init__(self, h_in, x0=None):
assert type(h_in) is list, 'h_in must be a list'
assert len(h_in) > 1, "len(h_in) must be greater than 1"
h = range(len(h_in))
for i, h_i in enumerate(h_in):
if type(h_i) in [int, long, float]:
# This gives you something over the unit cube.
h_i = np.ones(int(h_i))/int(h_i)
assert isinstance(h_i, np.ndarray), ("h[%i] is not a numpy array." % i)
assert len(h_i.shape) == 1, ("h[%i] must be a 1D numpy array." % i)
h[i] = h_i[:] # make a copy.
self.h = h
if x0 is None:
x0 = np.zeros(self.dim)
else:
assert type(x0) in [list, np.ndarray], 'x0 must be a numpy array or a list'
x0 = np.array(x0, dtype=float)
assert len(x0) == self.dim, 'x0 must have the same dimensions as the mesh'
# TODO: this has a lot of stuff which doesn't work for this style of mesh...
BaseMesh.__init__(self, np.array([x.size for x in h]), x0)
# set the sets for holding the cells, nodes, faces, and edges
self.cells = set()
self.nodes = set()
self.faces = set()
self.facesX = set()
self.facesY = set()
if self.dim == 3:
self.facesZ = set()
self.edges = set()
self.edgesX = set()
self.edgesY = set()
self.edgesZ = set()
self.children = np.empty([hi.size for hi in h],dtype=TreeCell)
if self.dim == 2:
for i in range(h[0].size):
for j in range(h[1].size):
fXm = None if i is 0 else self.children[i-1][j].fXp
fYm = None if j is 0 else self.children[i][j-1].fYp
x0i = (np.r_[x0[0], h[0][:i]]).sum()
x0j = (np.r_[x0[1], h[1][:j]]).sum()
self.children[i][j] = TreeCell(self, x0=[x0i, x0j], depth=0, sz=[h[0][i], h[1][j]], fXm=fXm, fYm=fYm)
elif self.dim == 3:
for i in range(h[0].size):
for j in range(h[1].size):
for k in range(h[2].size):
fXm = None if i is 0 else self.children[i-1][j][k].fXp
fYm = None if j is 0 else self.children[i][j-1][k].fYp
fZm = None if k is 0 else self.children[i][j][k-1].fZp
x0i = (np.r_[x0[0], h[0][:i]]).sum()
x0j = (np.r_[x0[1], h[1][:j]]).sum()
x0k = (np.r_[x0[2], h[2][:k]]).sum()
self.children[i][j][k] = TreeCell(self, x0=[x0i, x0j, x0k], depth=0, sz=[h[0][i], h[1][j], h[2][k]], fXm=fXm, fYm=fYm, fZm=fZm)
def Jtvec(self, m, v, u=None):
"""
Sensitivity transpose times a vector
:param numpy.array m: inversion model (nP,)
:param numpy.array v: vector which we take adjoint product with (nP,)
:param SimPEG.EM.FDEM.Fields u: fields object
:rtype numpy.array:
:return: Jv (ndata,)
"""
if u is None:
u = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
for freq in self.survey.freqs:
AT = self.getA(freq).T
ATinv = self.Solver(AT, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
ftype = self._fieldType + 'Solution'
u_src = u[src, ftype]
for rx in src.rxList:
PTv = rx.projectFieldsDeriv(src, self.mesh, u, v[src, rx], adjoint=True) # wrt u, need possibility wrt m
df_duTFun = getattr(u, '_%sDeriv_u'%rx.projField, None)
df_duT = df_duTFun(src, PTv, adjoint=True)
ATinvdf_duT = ATinv * df_duT
dA_dmT = self.getADeriv_m(freq, u_src, ATinvdf_duT, adjoint=True)
dRHS_dmT = self.getRHSDeriv_m(freq,src, ATinvdf_duT, adjoint=True)
du_dmT = -dA_dmT + dRHS_dmT
df_dmFun = getattr(u, '_%sDeriv_m'%rx.projField, None)
dfT_dm = df_dmFun(src, PTv, adjoint=True)
du_dmT += dfT_dm
# TODO: this should be taken care of by the reciever
real_or_imag = rx.projComp
if real_or_imag is 'real':
Jtv += np.array(du_dmT,dtype=complex).real
elif real_or_imag is 'imag':
Jtv += - np.array(du_dmT,dtype=complex).real
else:
raise Exception('Must be real or imag')
ATinv.clean()
return Utils.mkvc(Jtv)
def test_ndgrid_2D(self):
XY = ndgrid([self.a, self.b])
X1_test = np.array([1, 2, 3, 1, 2, 3])
X2_test = np.array([1, 1, 1, 2, 2, 2])
self.assertTrue(np.all(XY[:, 0] == X1_test))
self.assertTrue(np.all(XY[:, 1] == X2_test))
def test_ndgrid_2D(self):
XY = ndgrid([self.a, self.b])
X1_test = np.array([1, 2, 3, 1, 2, 3])
X2_test = np.array([1, 1, 1, 2, 2, 2])
self.assertTrue(np.all(XY[:, 0] == X1_test))
self.assertTrue(np.all(XY[:, 1] == X2_test))
def read_GOCAD_ts(tsfile):
"""Read GOCAD triangulated surface (*.ts) file
INPUT:
tsfile: Triangulated surface
OUTPUT:
vrts : Array of vertices in XYZ coordinates [n x 3]
trgl : Array of index for triangles [m x 3]. The order of the vertices
is important and describes the normal
n = cross( (P2 - P1 ) , (P3 - P1) )
Created on Jan 13th, 2016
Author: @fourndo
"""
fid = open(tsfile,'r')
line = fid.readline()
# Skip all the lines until the vertices
while re.match('TFACE',line)==None:
line = fid.readline()
line = fid.readline()
vrtx = []
# Run down all the vertices and save in array
while re.match('VRTX',line):
l_input = re.split('[\s*]',line)
temp = np.array(l_input[2:5])
vrtx.append(temp.astype(np.float))
# Read next line
line = fid.readline()
vrtx = np.asarray(vrtx)
# Skip lines to the triangles
while re.match('TRGL',line)==None:
line = fid.readline()
# Run down the list of triangles
trgl = []
# Run down all the vertices and save in array
while re.match('TRGL',line):
l_input = re.split('[\s*]',line)
temp = np.array(l_input[1:4])
trgl.append(temp.astype(np.int))
# Read next line
line = fid.readline()
trgl = np.asarray(trgl)
return vrtx, trgl
def __init__(self, rxList, freq, S_m, integrate = True, ePrimary=None, bPrimary=None, hPrimary=None, jPrimary=None):
self._S_m = np.array(S_m,dtype=complex)
self.freq = float(freq)
self.integrate = integrate
self._ePrimary = np.array(ePrimary,dtype=complex)
self._bPrimary = np.array(bPrimary,dtype=complex)
self._hPrimary = np.array(hPrimary,dtype=complex)
self._jPrimary = np.array(jPrimary,dtype=complex)
SrcFDEM.__init__(self, rxList)
def test_ndgrid_3D(self):
XYZ = ndgrid([self.a, self.b, self.c])
X1_test = np.array([1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3])
X2_test = np.array([1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2])
X3_test = np.array([1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4])
self.assertTrue(np.all(XYZ[:, 0] == X1_test))
self.assertTrue(np.all(XYZ[:, 1] == X2_test))
self.assertTrue(np.all(XYZ[:, 2] == X3_test))
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"):
cs, ncx, ncz, npad = 20., 25, 25, 15
hx = [(cs, ncx), (cs, npad, 1.3)]
hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)]
mesh = Mesh.CylMesh([hx, 1, hz], '00C')
sighalf = 1e-2
siginf = np.ones(mesh.nC) * 1e-8
siginf[mesh.gridCC[:, -1] < 0.] = sighalf
eta = np.ones(mesh.nC) * 0.2
tau = np.ones(mesh.nC) * 0.005
c = np.ones(mesh.nC) * 0.7
m = np.r_[siginf, eta, tau, c]
iMap = Maps.IdentityMap(nP=int(mesh.nC))
maps = [('sigmaInf', iMap), ('eta', iMap), ('tau', iMap), ('c', iMap)]
prb = ProblemATEMIP_b(mesh, mapping=maps)
if waveformType == "GENERAL":
# timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4])
timeon = np.cumsum(np.r_[np.ones(10) * 1e-3,
np.ones(10) * 5e-4,
np.ones(10) * 1e-4])
timeon -= timeon.max()
timeoff = np.cumsum(np.r_[np.ones(20) * 1e-5,
np.ones(20) * 1e-4,
np.ones(20) * 1e-3])
time = np.r_[timeon, timeoff]
current_on = np.ones_like(timeon)
current_on[[0, -1]] = 0.
current = np.r_[current_on, np.zeros_like(timeoff)]
wave = np.c_[time, current]
prb.waveformType = "GENERAL"
prb.currentwaveform(wave)
prb.t0 = time.min()
elif waveformType == "STEPOFF":
prb.timeSteps = [(1e-5, 20), (1e-4, 20), (1e-3, 10)]
offset = 20.
tobs = np.logspace(-4, -2, 21)
rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz")
src = EM.TDEM.SrcTDEM_VMD_MVP([rx],
np.array([[0., 0., 0.]]),
waveformType=waveformType)
survey = EM.TDEM.SurveyTDEM([src])
prb.Solver = MumpsSolver
prb.pair(survey)
out = survey.dpred(m)
bz_ana = mu_0 * hzAnalyticDipoleT_CC(
offset, rx.times, sigmaInf=sighalf, eta=eta[0], tau=tau[0], c=c[0])
err = np.linalg.norm(bz_ana - out) / np.linalg.norm(bz_ana)
print '>> Relative error = ', err
if showIt:
plt.loglog(rx.times, abs(bz_ana), 'k')
plt.loglog(rx.times, abs(out), 'b.')
plt.show()
return err
def readUBC_DC2DLoc(fileName):
from SimPEG import np
"""
Read UBC GIF 2D observation file and generate arrays for tx-rx location
Input:
:param fileName, path to the UBC GIF 2D model file
Output:
:param rx, tx
:return
Created on Thu Nov 12 13:14:10 2015
@author: dominiquef
"""
# Open fileand skip header... assume that we know the mesh already
#==============================================================================
# fopen = open(fileName,'r')
# lines = fopen.readlines()
# fopen.close()
#==============================================================================
# Load file
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
# Check first line and figure out if 2D or 3D file format
line = np.array(obsfile[0].split(),dtype=float)
tx_A = []
tx_B = []
rx_M = []
rx_N = []
d = []
wd = []
for ii in range(obsfile.shape[0]):
# If len==3, then simple format where tx-rx is listed on each line
if len(line) == 4:
temp = np.fromstring(obsfile[ii], dtype=float,sep=' ')
tx_A = np.hstack((tx_A,temp[0]))
tx_B = np.hstack((tx_B,temp[1]))
rx_M = np.hstack((rx_M,temp[2]))
rx_N = np.hstack((rx_N,temp[3]))
rx = np.transpose(np.array((rx_M,rx_N)))
tx = np.transpose(np.array((tx_A,tx_B)))
return tx, rx, d, wd
def Jtvec(self, m, v, u=None):
"""
Sensitivity transpose times a vector
:param numpy.array m: inversion model (nP,)
:param numpy.array v: vector which we take adjoint product with (nP,)
:param SimPEG.EM.FDEM.Fields u: fields object
:rtype numpy.array:
:return: Jv (ndata,)
"""
if u is None:
u = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
for freq in self.survey.freqs:
AT = self.getA(freq).T
ATinv = self.Solver(AT, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
u_src = u[src, self._solutionType]
for rx in src.rxList:
PTv = rx.evalDeriv(src, self.mesh, u, v[src, rx], adjoint=True) # wrt u, need possibility wrt m
df_duTFun = getattr(u, '_%sDeriv'%rx.projField, None)
df_duT, df_dmT = df_duTFun(src, None, PTv, adjoint=True)
ATinvdf_duT = ATinv * df_duT
dA_dmT = self.getADeriv(freq, u_src, ATinvdf_duT, adjoint=True)
dRHS_dmT = self.getRHSDeriv(freq, src, ATinvdf_duT, adjoint=True)
du_dmT = -dA_dmT + dRHS_dmT
df_dmT = df_dmT + du_dmT
# TODO: this should be taken care of by the reciever?
real_or_imag = rx.projComp
if real_or_imag is 'real':
Jtv += np.array(df_dmT, dtype=complex).real
elif real_or_imag is 'imag':
Jtv += - np.array(df_dmT, dtype=complex).real
else:
raise Exception('Must be real or imag')
ATinv.clean()
return Utils.mkvc(Jtv)
def test_indexCube_3D(self):
nN = np.array([3, 3, 3])
self.assertTrue(
np.all(
indexCube('A', nN) == np.array([0, 1, 3, 4, 9, 10, 12, 13])))
self.assertTrue(
np.all(
indexCube('B', nN) == np.array([3, 4, 6, 7, 12, 13, 15, 16])))
self.assertTrue(
np.all(
indexCube('C', nN) == np.array([4, 5, 7, 8, 13, 14, 16, 17])))
self.assertTrue(
np.all(
indexCube('D', nN) == np.array([1, 2, 4, 5, 10, 11, 13, 14])))
self.assertTrue(
np.all(
indexCube('E', nN) == np.array([9, 10, 12, 13, 18, 19, 21, 22
])))
self.assertTrue(
np.all(
indexCube('F', nN) == np.array(
[12, 13, 15, 16, 21, 22, 24, 25])))
self.assertTrue(
np.all(
indexCube('G', nN) == np.array(
[13, 14, 16, 17, 22, 23, 25, 26])))
self.assertTrue(
np.all(
indexCube('H', nN) == np.array(
[10, 11, 13, 14, 19, 20, 22, 23])))
def Jtvec(self, m, v, f=None):
"""
Sensitivity transpose times a vector
:param numpy.array m: inversion model (nP,)
:param numpy.array v: vector which we take adjoint product with (nP,)
:param SimPEG.EM.FDEM.FieldsFDEM.FieldsFDEM u: fields object
:rtype numpy.array:
:return: Jv (ndata,)
"""
if f is None:
f = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
for freq in self.survey.freqs:
AT = self.getA(freq).T
ATinv = self.Solver(AT, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
u_src = f[src, self._solutionType]
for rx in src.rxList:
PTv = rx.evalDeriv(src, self.mesh, f, v[src, rx], adjoint=True) # wrt f, need possibility wrt m
df_duTFun = getattr(f, '_{0}Deriv'.format(rx.projField), None)
df_duT, df_dmT = df_duTFun(src, None, PTv, adjoint=True)
ATinvdf_duT = ATinv * df_duT
dA_dmT = self.getADeriv(freq, u_src, ATinvdf_duT, adjoint=True)
dRHS_dmT = self.getRHSDeriv(freq, src, ATinvdf_duT, adjoint=True)
du_dmT = -dA_dmT + dRHS_dmT
df_dmT = df_dmT + du_dmT
# TODO: this should be taken care of by the reciever?
if rx.component is 'real':
Jtv += np.array(df_dmT, dtype=complex).real
elif rx.component is 'imag':
Jtv += - np.array(df_dmT, dtype=complex).real
else:
raise Exception('Must be real or imag')
ATinv.clean()
return Utils.mkvc(Jtv)
def toRecArray(self,returnType='RealImag'):
'''
Function that returns a numpy.recarray for a SimpegMT impedance data object.
:param str returnType: Switches between returning a rec array where the impedance is split to real and imaginary ('RealImag') or is a complex ('Complex')
'''
# Define the record fields
dtRI = [('freq',float),('x',float),('y',float),('z',float),('zxxr',float),('zxxi',float),('zxyr',float),('zxyi',float),
('zyxr',float),('zyxi',float),('zyyr',float),('zyyi',float),('tzxr',float),('tzxi',float),('tzyr',float),('tzyi',float)]
dtCP = [('freq',float),('x',float),('y',float),('z',float),('zxx',complex),('zxy',complex),('zyx',complex),('zyy',complex),('tzx',complex),('tzy',complex)]
impList = ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi']
for src in self.survey.srcList:
# Temp array for all the receivers of the source.
# Note: needs to be written more generally, using diffterent rxTypes and not all the data at the locaitons
# Assume the same locs for all RX
locs = src.rxList[0].locs
if locs.shape[1] == 1:
locs = np.hstack((np.array([[0.0,0.0]]),locs))
elif locs.shape[1] == 2:
locs = np.hstack((np.array([[0.0]]),locs))
tArrRec = np.concatenate((src.freq*np.ones((locs.shape[0],1)),locs,np.nan*np.ones((locs.shape[0],12))),axis=1).view(dtRI)
# np.array([(src.freq,rx.locs[0,0],rx.locs[0,1],rx.locs[0,2],np.nan ,np.nan ,np.nan ,np.nan ,np.nan ,np.nan ,np.nan ,np.nan ) for rx in src.rxList],dtype=dtRI)
# Get the type and the value for the DataMT object as a list
typeList = [[rx.rxType.replace('z1d','zyx'),self[src,rx]] for rx in src.rxList]
# Insert the values to the temp array
for nr,(key,val) in enumerate(typeList):
tArrRec[key] = mkvc(val,2)
# Masked array
mArrRec = np.ma.MaskedArray(rec2ndarr(tArrRec),mask=np.isnan(rec2ndarr(tArrRec))).view(dtype=tArrRec.dtype)
# Unique freq and loc of the masked array
uniFLmarr = np.unique(mArrRec[['freq','x','y','z']]).copy()
try:
outTemp = recFunc.stack_arrays((outTemp,mArrRec))
#outTemp = np.concatenate((outTemp,dataBlock),axis=0)
except NameError as e:
outTemp = mArrRec
if 'RealImag' in returnType:
outArr = outTemp
elif 'Complex' in returnType:
# Add the real and imaginary to a complex number
outArr = np.empty(outTemp.shape,dtype=dtCP)
for comp in ['freq','x','y','z']:
outArr[comp] = outTemp[comp].copy()
for comp in ['zxx','zxy','zyx','zyy','tzx','tzy']:
outArr[comp] = outTemp[comp+'r'].copy() + 1j*outTemp[comp+'i'].copy()
else:
raise NotImplementedError('{:s} is not implemented, as to be RealImag or Complex.')
# Return
return outArr
def readUBC_DC2DModel(fileName):
from SimPEG import np, mkvc
"""
Read UBC GIF 2DTensor model and generate 2D Tensor model in simpeg
Input:
:param fileName, path to the UBC GIF 2D model file
Output:
:param SimPEG TensorMesh 2D object
:return
Created on Thu Nov 12 13:14:10 2015
@author: dominiquef
"""
# Open fileand skip header... assume that we know the mesh already
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
dim = np.array(obsfile[0].split(),dtype=float)
temp = np.array(obsfile[1].split(),dtype=float)
if len(temp) > 1:
model = np.zeros(dim)
for ii in range(len(obsfile)-1):
mm = np.array(obsfile[ii+1].split(),dtype=float)
model[:,ii] = mm
model = model[:,::-1]
else:
if len(obsfile[1:])==1:
mm = np.array(obsfile[1:].split(),dtype=float)
else:
mm = np.array(obsfile[1:],dtype=float)
# Permute the second dimension to flip the order
model = mm.reshape(dim[1],dim[0])
model = model[::-1,:]
model = np.transpose(model, (1, 0))
model = mkvc(model)
return model
def readMagneticsObservations(self, obs_file):
"""
Read and write UBC mag file format
INPUT:
:param fileName, path to the UBC obs mag file
OUTPUT:
:param survey
:param M, magnetization orentiaton (MI, MD)
"""
fid = open(self.basePath + obs_file, 'r')
# First line has the inclination,declination and amplitude of B0
line = fid.readline()
B = np.array(line.split(), dtype=float)
# Second line has the magnetization orientation and a flag
line = fid.readline()
M = np.array(line.split(), dtype=float)
# Third line has the number of rows
line = fid.readline()
ndat = np.array(line.split(), dtype=int)
# Pre-allocate space for obsx, obsy, obsz, data, uncert
line = fid.readline()
temp = np.array(line.split(), dtype=float)
d = np.zeros(ndat, dtype=float)
wd = np.zeros(ndat, dtype=float)
locXYZ = np.zeros((ndat[0], 3), dtype=float)
for ii in range(ndat):
temp = np.array(line.split(), dtype=float)
locXYZ[ii, :] = temp[:3]
if len(temp) > 3:
d[ii] = temp[3]
if len(temp) == 5:
wd[ii] = temp[4]
line = fid.readline()
rxLoc = BaseMag.RxObs(locXYZ)
srcField = BaseMag.SrcField([rxLoc], param=(B[2], B[0], B[1]))
survey = BaseMag.LinearSurvey(srcField)
survey.dobs = d
survey.std = wd
return survey
def readMagneticsObservations(self, obs_file):
"""
Read and write UBC mag file format
INPUT:
:param fileName, path to the UBC obs mag file
OUTPUT:
:param survey
:param M, magnetization orentiaton (MI, MD)
"""
fid = open(self.basePath + obs_file, 'r')
# First line has the inclination,declination and amplitude of B0
line = fid.readline()
B = np.array(line.split(), dtype=float)
# Second line has the magnetization orientation and a flag
line = fid.readline()
M = np.array(line.split(), dtype=float)
# Third line has the number of rows
line = fid.readline()
ndat = np.array(line.split(), dtype=int)
# Pre-allocate space for obsx, obsy, obsz, data, uncert
line = fid.readline()
temp = np.array(line.split(), dtype=float)
d = np.zeros(ndat, dtype=float)
wd = np.zeros(ndat, dtype=float)
locXYZ = np.zeros((ndat[0], 3), dtype=float)
for ii in range(ndat):
temp = np.array(line.split(), dtype=float)
locXYZ[ii, :] = temp[:3]
if len(temp) > 3:
d[ii] = temp[3]
if len(temp) == 5:
wd[ii] = temp[4]
line = fid.readline()
rxLoc = BaseMag.RxObs(locXYZ)
srcField = BaseMag.SrcField([rxLoc], param=(B[2], B[0], B[1]))
survey = BaseMag.LinearSurvey(srcField)
survey.dobs = d
survey.std = wd
return survey
def readUBC_DC2DModel(fileName):
"""
Read UBC GIF 2DTensor model and generate 2D Tensor model in simpeg
Input:
:param fileName, path to the UBC GIF 2D model file
Output:
:param SimPEG TensorMesh 2D object
:return
Created on Thu Nov 12 13:14:10 2015
@author: dominiquef
"""
from SimPEG import np, mkvc
# Open fileand skip header... assume that we know the mesh already
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
dim = np.array(obsfile[0].split(),dtype=float)
temp = np.array(obsfile[1].split(),dtype=float)
if len(temp) > 1:
model = np.zeros(dim)
for ii in range(len(obsfile)-1):
mm = np.array(obsfile[ii+1].split(),dtype=float)
model[:,ii] = mm
model = model[:,::-1]
else:
if len(obsfile[1:])==1:
mm = np.array(obsfile[1:].split(),dtype=float)
else:
mm = np.array(obsfile[1:],dtype=float)
# Permute the second dimension to flip the order
model = mm.reshape(dim[1],dim[0])
model = model[::-1,:]
model = np.transpose(model, (1, 0))
model = mkvc(model)
return model
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"):
cs, ncx, ncz, npad = 20., 25, 25, 15
hx = [(cs, ncx), (cs, npad, 1.3)]
hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)]
mesh = Mesh.CylMesh([hx, 1, hz], '00C')
prb = ProblemATEM_b(mesh)
if waveformType == "GENERAL":
timeon = np.cumsum(np.r_[np.ones(10) * 1e-3,
np.ones(10) * 5e-4,
np.ones(10) * 1e-4])
timeon -= timeon.max()
timeoff = np.cumsum(np.r_[np.ones(10) * 5e-5,
np.ones(10) * 1e-4,
np.ones(10) * 5e-4,
np.ones(10) * 1e-3,
np.ones(10) * 5e-3])
time = np.r_[timeon, timeoff]
current_on = np.ones_like(timeon)
current_on[[0, -1]] = 0.
current = np.r_[current_on, np.zeros_like(timeoff)]
wave = np.c_[time, current]
prb.waveformType = "GENERAL"
prb.currentwaveform(wave)
prb.t0 = time.min()
elif waveformType == "STEPOFF":
prb.timeSteps = [(1e-5, 10), (5e-5, 10), (1e-4, 10), (5e-4, 10),
(1e-3, 10), (5e-3, 10)]
offset = 20.
tobs = np.logspace(-4, -2, 21)
rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz")
src = EM.TDEM.SrcTDEM_VMD_MVP([rx],
np.array([[0., 0., 0.]]),
waveformType=waveformType)
survey = EM.TDEM.SurveyTDEM([src])
prb.Solver = MumpsSolver
sigma = np.ones(mesh.nC) * 1e-8
active = mesh.gridCC[:, 2] < 0.
sig_half = 1e-2
sigma[active] = sig_half
prb.pair(survey)
out = survey.dpred(sigma)
bz_ana = mu_0 * hzAnalyticDipoleT(offset, rx.times, sig_half)
err = np.linalg.norm(bz_ana - out) / np.linalg.norm(bz_ana)
print '>> Relative error = ', err
if showIt:
plt.loglog(rx.times, bz_ana, 'k')
plt.loglog(rx.times, out, 'b.')
plt.show()
return err
def test_indexCube_3D(self):
nN = np.array([3, 3, 3])
self.assertTrue(np.all(indexCube('A', nN) == np.array([0, 1, 3, 4, 9, 10, 12, 13])))
self.assertTrue(np.all(indexCube('B', nN) == np.array([3, 4, 6, 7, 12, 13, 15, 16])))
self.assertTrue(np.all(indexCube('C', nN) == np.array([4, 5, 7, 8, 13, 14, 16, 17])))
self.assertTrue(np.all(indexCube('D', nN) == np.array([1, 2, 4, 5, 10, 11, 13, 14])))
self.assertTrue(np.all(indexCube('E', nN) == np.array([9, 10, 12, 13, 18, 19, 21, 22])))
self.assertTrue(np.all(indexCube('F', nN) == np.array([12, 13, 15, 16, 21, 22, 24, 25])))
self.assertTrue(np.all(indexCube('G', nN) == np.array([13, 14, 16, 17, 22, 23, 25, 26])))
self.assertTrue(np.all(indexCube('H', nN) == np.array([10, 11, 13, 14, 19, 20, 22, 23])))
def Jtvec(self, m, v, f=None):
"""
Sensitivity transpose times a vector
"""
if f is None:
f = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
for freq in self.survey.freqs:
AT = self.getA(freq).T
ATinv = self.Solver(AT, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
ftype = self._fieldType + 'Solution'
u_src = f[src, ftype]
for rx in src.rxList:
PTv = rx.projectFieldsDeriv(src, self.mesh, f, v[src, rx], adjoint=True) # wrt u, need possibility wrt m
df_duTFun = getattr(f, '_%sDeriv_u'%rx.projField, None)
df_duT = df_duTFun(src, PTv, adjoint=True)
ATinvdf_duT = ATinv * df_duT
dA_dmT = self.getADeriv_m(freq, u_src, ATinvdf_duT, adjoint=True)
dRHS_dmT = self.getRHSDeriv_m(freq,src, ATinvdf_duT, adjoint=True)
du_dmT = -dA_dmT + dRHS_dmT
df_dmFun = getattr(f, '_%sDeriv_m'%rx.projField, None)
dfT_dm = df_dmFun(src, PTv, adjoint=True)
du_dmT += dfT_dm
real_or_imag = rx.projComp
if real_or_imag is 'real':
Jtv += np.array(du_dmT,dtype=complex).real
elif real_or_imag is 'imag':
Jtv += - np.array(du_dmT,dtype=complex).real
else:
raise Exception('Must be real or imag')
return Jtv
def readUBC_DC2Dobs(fileName):
"""
------- NEEDS TO BE UPDATED ------
Read UBC GIF 2D observation file and generate arrays for tx-rx location
Input:
:param fileName, path to the UBC GIF 2D model file
Output:
:param rx, tx
:return
Created on Thu Nov 12 13:14:10 2015
@author: dominiquef
"""
from SimPEG import np
# Load file
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
# Check first line and figure out if 2D or 3D file format
line = np.array(obsfile[0].split(),dtype=float)
tx_A = []
tx_B = []
rx_M = []
rx_N = []
d = []
wd = []
for ii in range(obsfile.shape[0]):
# If len==3, then simple format where tx-rx is listed on each line
if len(line) == 4:
temp = np.fromstring(obsfile[ii], dtype=float,sep=' ')
tx_A = np.hstack((tx_A,temp[0]))
tx_B = np.hstack((tx_B,temp[1]))
rx_M = np.hstack((rx_M,temp[2]))
rx_N = np.hstack((rx_N,temp[3]))
rx = np.transpose(np.array((rx_M,rx_N)))
tx = np.transpose(np.array((tx_A,tx_B)))
return tx, rx, d, wd
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"):
cs, ncx, ncz, npad = 20., 25, 25, 15
hx = [(cs,ncx), (cs,npad,1.3)]
hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)]
mesh = Mesh.CylMesh([hx,1,hz], '00C')
sighalf = 1e-2
siginf = np.ones(mesh.nC)*1e-8
siginf[mesh.gridCC[:,-1]<0.] = sighalf
eta = np.ones(mesh.nC)*0.2
tau = np.ones(mesh.nC)*0.005
c = np.ones(mesh.nC)*0.7
m = np.r_[siginf, eta, tau, c]
iMap = Maps.IdentityMap(nP=int(mesh.nC))
maps = [('sigmaInf', iMap), ('eta', iMap), ('tau', iMap), ('c', iMap)]
prb = ProblemATEMIP_b(mesh, mapping = maps)
if waveformType =="GENERAL":
# timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4])
timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4])
timeon -= timeon.max()
timeoff = np.cumsum(np.r_[np.ones(20)*1e-5, np.ones(20)*1e-4, np.ones(20)*1e-3])
time = np.r_[timeon, timeoff]
current_on = np.ones_like(timeon)
current_on[[0,-1]] = 0.
current = np.r_[current_on, np.zeros_like(timeoff)]
wave = np.c_[time, current]
prb.waveformType = "GENERAL"
prb.currentwaveform(wave)
prb.t0 = time.min()
elif waveformType =="STEPOFF":
prb.timeSteps = [(1e-5, 20), (1e-4, 20), (1e-3, 10)]
offset = 20.
tobs = np.logspace(-4, -2, 21)
rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz")
src = EM.TDEM.SrcTDEM_VMD_MVP([rx], np.array([[0., 0., 0.]]), waveformType=waveformType)
survey = EM.TDEM.SurveyTDEM([src])
prb.Solver = MumpsSolver
prb.pair(survey)
out = survey.dpred(m)
bz_ana = mu_0*hzAnalyticDipoleT_CC(offset, rx.times, sigmaInf=sighalf, eta=eta[0], tau=tau[0], c=c[0])
err = np.linalg.norm(bz_ana-out)/np.linalg.norm(bz_ana)
print '>> Relative error = ', err
if showIt:
plt.loglog(rx.times, abs(bz_ana), 'k')
plt.loglog(rx.times, abs(out), 'b.')
plt.show()
return err
def edge(self):
self.number()
if self.dim == 2:
edges = self.sortedFaceY + self.sortedFaceX
elif self.dim == 3:
edges = self.sortedEdgeX + self.sortedEdgeY + self.sortedEdgeZ
return np.array([e.length for e in edges], dtype=float)
def __init__(
self, rxList, freq, s_m, **kwargs
): # ePrimary=Zero(), bPrimary=Zero(), hPrimary=Zero(), jPrimary=Zero()):
self._s_m = np.array(s_m, dtype=complex)
self.freq = float(freq)
BaseSrc.__init__(self, rxList, **kwargs)
def __init__(
self, rxList, freq, s_m, **kwargs
): #ePrimary=Zero(), bPrimary=Zero(), hPrimary=Zero(), jPrimary=Zero()):
self._s_m = np.array(s_m, dtype=complex)
self.freq = float(freq)
BaseSrc.__init__(self, rxList, **kwargs)
def __init__(self, h_in, x0_in=None):
assert type(h_in) in [list, tuple], 'h_in must be a list'
assert len(h_in) in [1,2,3], 'h_in must be of dimension 1, 2, or 3'
h = range(len(h_in))
for i, h_i in enumerate(h_in):
if Utils.isScalar(h_i) and type(h_i) is not np.ndarray:
# This gives you something over the unit cube.
h_i = self._unitDimensions[i] * np.ones(int(h_i))/int(h_i)
elif type(h_i) is list:
h_i = Utils.meshTensor(h_i)
assert isinstance(h_i, np.ndarray), ("h[%i] is not a numpy array." % i)
assert len(h_i.shape) == 1, ("h[%i] must be a 1D numpy array." % i)
h[i] = h_i[:] # make a copy.
x0 = np.zeros(len(h))
if x0_in is not None:
assert len(h) == len(x0_in), "Dimension mismatch. x0 != len(h)"
for i in range(len(h)):
x_i, h_i = x0_in[i], h[i]
if Utils.isScalar(x_i):
x0[i] = x_i
elif x_i == '0':
x0[i] = 0.0
elif x_i == 'C':
x0[i] = -h_i.sum()*0.5
elif x_i == 'N':
x0[i] = -h_i.sum()
else:
raise Exception("x0[%i] must be a scalar or '0' to be zero, 'C' to center, or 'N' to be negative." % i)
BaseRectangularMesh.__init__(self, np.array([x.size for x in h]), x0)
# Ensure h contains 1D vectors
self._h = [Utils.mkvc(x.astype(float)) for x in h]
def test_ana_boundary_computation(self):
hxind = [(0, 25, 1.3), (21, 12.5), (0, 25, 1.3)]
hyind = [(0, 25, 1.3), (21, 12.5), (0, 25, 1.3)]
hzind = [(0, 25, 1.3), (20, 12.5), (0, 25, 1.3)]
# hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)
M3 = Mesh.TensorMesh([hxind, hyind, hzind], "CCC")
indxd, indxu, indyd, indyu, indzd, indzu = M3.faceBoundaryInd
mu0 = 4*np.pi*1e-7
chibkg = 0.
chiblk = 0.01
chi = np.ones(M3.nC)*chibkg
sph_ind = PF.MagAnalytics.spheremodel(M3, 0, 0, 0, 100)
chi[sph_ind] = chiblk
mu = (1.+chi)*mu0
Bbc, const = PF.MagAnalytics.CongruousMagBC(M3, np.array([1., 0., 0.]), chi)
flag = 'secondary'
Box = 1.
H0 = Box/mu_0
Bbcxx, Bbcxy, Bbcxz = PF.MagAnalytics.MagSphereAnaFun(M3.gridFx[(indxd|indxu),0], M3.gridFx[(indxd|indxu),1], M3.gridFx[(indxd|indxu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbcyx, Bbcyy, Bbcyz = PF.MagAnalytics.MagSphereAnaFun(M3.gridFy[(indyd|indyu),0], M3.gridFy[(indyd|indyu),1], M3.gridFy[(indyd|indyu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbczx, Bbczy, Bbczz = PF.MagAnalytics.MagSphereAnaFun(M3.gridFz[(indzd|indzu),0], M3.gridFz[(indzd|indzu),1], M3.gridFz[(indzd|indzu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbc_ana = np.r_[Bbcxx, Bbcyy, Bbczz]
if plotIt:
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1,1, figsize = (10, 10))
ax.plot(Bbc_ana)
ax.plot(Bbc)
plt.show()
err = np.linalg.norm(Bbc-Bbc_ana) / np.linalg.norm(Bbc_ana)
assert err < 0.1, 'Mag Boundary computation is wrong!!, err = {}'.format(err)
def __init__(self, rxList, freq, S_e, ePrimary=None, bPrimary=None, hPrimary=None, jPrimary=None):
self._S_e = np.array(S_e,dtype=complex)
self._ePrimary = ePrimary
self._bPrimary = bPrimary
self._hPrimary = hPrimary
self._jPrimary = jPrimary
self.freq = float(freq)
SrcFDEM.__init__(self, rxList)
def test_ndgrid_3D(self):
XYZ = ndgrid([self.a, self.b, self.c])
X1_test = np.array([
1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1,
2, 3
])
X2_test = np.array([
1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2,
2, 2
])
X3_test = np.array([
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4,
4, 4
])
self.assertTrue(np.all(XYZ[:, 0] == X1_test))
self.assertTrue(np.all(XYZ[:, 1] == X2_test))
self.assertTrue(np.all(XYZ[:, 2] == X3_test))
def __init__(self, h_in, x0_in=None):
assert type(h_in) in [list, tuple], 'h_in must be a list'
assert len(h_in) in [1, 2, 3], 'h_in must be of dimension 1, 2, or 3'
h = list(range(len(h_in)))
for i, h_i in enumerate(h_in):
if Utils.isScalar(h_i) and type(h_i) is not np.ndarray:
# This gives you something over the unit cube.
h_i = self._unitDimensions[i] * np.ones(int(h_i)) / int(h_i)
elif type(h_i) is list:
h_i = Utils.meshTensor(h_i)
assert isinstance(
h_i, np.ndarray), ("h[{0:d}] is not a numpy array.".format(i))
assert len(h_i.shape) == 1, (
"h[{0:d}] must be a 1D numpy array.".format(i))
h[i] = h_i[:] # make a copy.
x0 = np.zeros(len(h))
if x0_in is not None:
assert len(h) == len(x0_in), "Dimension mismatch. x0 != len(h)"
for i in range(len(h)):
x_i, h_i = x0_in[i], h[i]
if Utils.isScalar(x_i):
x0[i] = x_i
elif x_i == '0':
x0[i] = 0.0
elif x_i == 'C':
x0[i] = -h_i.sum() * 0.5
elif x_i == 'N':
x0[i] = -h_i.sum()
else:
raise Exception(
"x0[{0:d}] must be a scalar or '0' to be zero, "
"'C' to center, or 'N' to be negative.".format(i))
if isinstance(self, BaseRectangularMesh):
BaseRectangularMesh.__init__(self, np.array([x.size for x in h]),
x0)
else:
BaseMesh.__init__(self, np.array([x.size for x in h]), x0)
# Ensure h contains 1D vectors
self._h = [Utils.mkvc(x.astype(float)) for x in h]
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"): cs, ncx, ncz, npad = 20., 25, 25, 15 hx = [(cs,ncx), (cs,npad,1.3)] hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)] mesh = Mesh.CylMesh([hx,1,hz], '00C') prb = ProblemATEM_b(mesh) if waveformType =="GENERAL": timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4]) timeon -= timeon.max() timeoff = np.cumsum(np.r_[np.ones(10)*5e-5, np.ones(10)*1e-4, np.ones(10)*5e-4, np.ones(10)*1e-3, np.ones(10)*5e-3]) time = np.r_[timeon, timeoff] current_on = np.ones_like(timeon) current_on[[0,-1]] = 0. current = np.r_[current_on, np.zeros_like(timeoff)] wave = np.c_[time, current] prb.waveformType = "GENERAL" prb.currentwaveform(wave) prb.t0 = time.min() elif waveformType =="STEPOFF": prb.timeSteps = [(1e-5, 10), (5e-5, 10), (1e-4, 10), (5e-4, 10), (1e-3, 10),(5e-3, 10)] offset = 20. tobs = np.logspace(-4, -2, 21) rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz") src = EM.TDEM.SrcTDEM_VMD_MVP([rx], np.array([[0., 0., 0.]]), waveformType=waveformType) survey = EM.TDEM.SurveyTDEM([src]) prb.Solver = MumpsSolver sigma = np.ones(mesh.nC)*1e-8 active = mesh.gridCC[:,2]<0. sig_half = 1e-2 sigma[active] = sig_half prb.pair(survey) out = survey.dpred(sigma) bz_ana = mu_0*hzAnalyticDipoleT(offset, rx.times, sig_half) err = np.linalg.norm(bz_ana-out)/np.linalg.norm(bz_ana) print '>> Relative error = ', err if showIt: plt.loglog(rx.times, bz_ana, 'k') plt.loglog(rx.times, out, 'b.') plt.show() return err
def test_asArray_N_x_Dim(self):
true = np.array([[1, 2, 3]])
listArray = asArray_N_x_Dim([1, 2, 3], 3)
self.assertTrue(np.all(true == listArray))
self.assertTrue(true.shape == listArray.shape)
listArray = asArray_N_x_Dim(np.r_[1, 2, 3], 3)
self.assertTrue(np.all(true == listArray))
self.assertTrue(true.shape == listArray.shape)
listArray = asArray_N_x_Dim(np.array([[1, 2, 3.]]), 3)
self.assertTrue(np.all(true == listArray))
self.assertTrue(true.shape == listArray.shape)
true = np.array([[1, 2], [4, 5]])
listArray = asArray_N_x_Dim([[1, 2], [4, 5]], 2)
self.assertTrue(np.all(true == listArray))
self.assertTrue(true.shape == listArray.shape)
def __init__(
self,
rxList,
freq,
S_e,
integrate=True
): #, ePrimary=None, bPrimary=None, hPrimary=None, jPrimary=None):
self._S_e = np.array(S_e, dtype=complex)
self.freq = float(freq)
self.integrate = integrate
BaseSrc.__init__(self, rxList)
def __init__(
self,
rxList,
freq,
S_m,
integrate=True
): #ePrimary=Zero(), bPrimary=Zero(), hPrimary=Zero(), jPrimary=Zero()):
self._S_m = np.array(S_m, dtype=complex)
self.freq = float(freq)
self.integrate = integrate
BaseSrc.__init__(self, rxList)
def fget(self):
if(self._edge is None or self._tangents is None):
if(self.dim == 2):
xy = self.gridN
A, D = Utils.indexCube('AD', self.vnC+1, np.array([self.nCx, self.nNy]))
edge1 = xy[D, :] - xy[A, :]
A, B = Utils.indexCube('AB', self.vnC+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._tangents = np.r_[edge1, edge2]/np.c_[self._edge, self._edge]
elif(self.dim == 3):
xyz = self.gridN
A, D = Utils.indexCube('AD', self.vnC+1, np.array([self.nCx, self.nNy, self.nNz]))
edge1 = xyz[D, :] - xyz[A, :]
A, B = Utils.indexCube('AB', self.vnC+1, np.array([self.nNx, self.nCy, self.nNz]))
edge2 = xyz[B, :] - xyz[A, :]
A, E = Utils.indexCube('AE', self.vnC+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._tangents = np.r_[edge1, edge2, edge3]/np.c_[self._edge, self._edge, self._edge]
return self._edge
def fget(self):
if(self._edge is None or self._tangents is None):
if(self.dim == 2):
xy = self.gridN
A, D = Utils.indexCube('AD', self.vnC+1, np.array([self.nCx, self.nNy]))
edge1 = xy[D, :] - xy[A, :]
A, B = Utils.indexCube('AB', self.vnC+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._tangents = np.r_[edge1, edge2]/np.c_[self._edge, self._edge]
elif(self.dim == 3):
xyz = self.gridN
A, D = Utils.indexCube('AD', self.vnC+1, np.array([self.nCx, self.nNy, self.nNz]))
edge1 = xyz[D, :] - xyz[A, :]
A, B = Utils.indexCube('AB', self.vnC+1, np.array([self.nNx, self.nCy, self.nNz]))
edge2 = xyz[B, :] - xyz[A, :]
A, E = Utils.indexCube('AE', self.vnC+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._tangents = np.r_[edge1, edge2, edge3]/np.c_[self._edge, self._edge, self._edge]
return self._edge
def test_asArray_N_x_Dim(self):
true = np.array([[1,2,3]])
listArray = asArray_N_x_Dim([1,2,3],3)
self.assertTrue(np.all(true == listArray))
self.assertTrue(true.shape == listArray.shape)
listArray = asArray_N_x_Dim(np.r_[1,2,3],3)
self.assertTrue(np.all(true == listArray))
self.assertTrue(true.shape == listArray.shape)
listArray = asArray_N_x_Dim(np.array([[1,2,3.]]),3)
self.assertTrue(np.all(true == listArray))
self.assertTrue(true.shape == listArray.shape)
true = np.array([[1,2],[4,5]])
listArray = asArray_N_x_Dim([[1,2],[4,5]],2)
self.assertTrue(np.all(true == listArray))
self.assertTrue(true.shape == listArray.shape)
def readGravityObservations(self, obs_file):
"""
Read UBC grav file format
INPUT:
:param fileName, path to the UBC obs grav file
OUTPUT:
:param survey
"""
fid = open(obs_file, 'r')
# First line has the number of rows
line = fid.readline()
ndat = np.array(line.split(), dtype=int)
# Pre-allocate space for obsx, obsy, obsz, data, uncert
line = fid.readline()
temp = np.array(line.split(), dtype=float)
d = np.zeros(ndat, dtype=float)
wd = np.zeros(ndat, dtype=float)
locXYZ = np.zeros((ndat[0], 3), dtype=float)
for ii in range(ndat):
temp = np.array(line.split(), dtype=float)
locXYZ[ii, :] = temp[:3]
d[ii] = temp[3]
wd[ii] = temp[4]
line = fid.readline()
rxLoc = BaseGrav.RxObs(locXYZ)
srcField = BaseGrav.SrcField([rxLoc])
survey = BaseGrav.LinearSurvey(srcField)
survey.dobs = d
survey.std = wd
return survey
def readGravityObservations(self, obs_file):
"""
Read UBC grav file format
INPUT:
:param fileName, path to the UBC obs grav file
OUTPUT:
:param survey
"""
fid = open(obs_file,'r')
# First line has the number of rows
line = fid.readline()
ndat = np.array(line.split(),dtype=int)
# Pre-allocate space for obsx, obsy, obsz, data, uncert
line = fid.readline()
temp = np.array(line.split(),dtype=float)
d = np.zeros(ndat, dtype=float)
wd = np.zeros(ndat, dtype=float)
locXYZ = np.zeros( (ndat,3), dtype=float)
for ii in range(ndat):
temp = np.array(line.split(),dtype=float)
locXYZ[ii,:] = temp[:3]
d[ii] = temp[3]
wd[ii] = temp[4]
line = fid.readline()
rxLoc = BaseGrav.RxObs(locXYZ)
srcField = BaseGrav.SrcField([rxLoc])
survey = BaseGrav.LinearSurvey(srcField)
survey.dobs = d
survey.std = wd
return survey
def getInterpolationMat(self, loc, locType, zerosOutside=False):
""" Produces interpolation matrix
:param numpy.ndarray loc: Location of points to interpolate to
:param str locType: What to interpolate (see below)
:rtype: scipy.sparse.csr.csr_matrix
:return: M, the interpolation matrix
locType can be::
'Ex' -> x-component of field defined on edges
'Ey' -> y-component of field defined on edges
'Ez' -> z-component of field defined on edges
'Fx' -> x-component of field defined on faces
'Fy' -> y-component of field defined on faces
'Fz' -> z-component of field defined on faces
'N' -> scalar field defined on nodes
'CC' -> scalar field defined on cell centers
"""
if self._meshType == 'CYL' and self.isSymmetric and locType in ['Ex','Ez','Fy']:
raise Exception('Symmetric CylMesh does not support %s interpolation, as this variable does not exist.' % locType)
loc = Utils.asArray_N_x_Dim(loc, self.dim)
if zerosOutside is False:
assert np.all(self.isInside(loc)), "Points outside of mesh"
else:
indZeros = np.logical_not(self.isInside(loc))
loc[indZeros, :] = np.array([v.mean() for v in self.getTensor('CC')])
if locType in ['Fx','Fy','Fz','Ex','Ey','Ez']:
ind = {'x':0, 'y':1, 'z':2}[locType[1]]
assert self.dim >= ind, 'mesh is not high enough dimension.'
nF_nE = self.vnF if 'F' in locType else self.vnE
components = [Utils.spzeros(loc.shape[0], n) for n in nF_nE]
components[ind] = Utils.interpmat(loc, *self.getTensor(locType))
# remove any zero blocks (hstack complains)
components = [comp for comp in components if comp.shape[1] > 0]
Q = sp.hstack(components)
elif locType in ['CC', 'N']:
Q = Utils.interpmat(loc, *self.getTensor(locType))
else:
raise NotImplementedError('getInterpolationMat: locType=='+locType+' and mesh.dim=='+str(self.dim))
if zerosOutside:
Q[indZeros, :] = 0
return Q.tocsr()
def unpackdx(fid,nrows):
for ii in range(nrows):
line = fid.readline()
var = np.array(line.split(),dtype=float)
if ii==0:
x0= var[0]
xvec = np.ones(int(var[2])) * (var[1] - var[0]) / int(var[2])
xend = var[1]
else:
xvec = np.hstack((xvec,np.ones(int(var[1])) * (var[0] - xend) / int(var[1])))
xend = var[0]
return x0, xvec
def unpackdx(fid,nrows):
for ii in range(nrows):
line = fid.readline()
var = np.array(line.split(),dtype=float)
if ii==0:
x0= var[0]
xvec = np.ones(int(var[2])) * (var[1] - var[0]) / int(var[2])
xend = var[1]
else:
xvec = np.hstack((xvec,np.ones(int(var[1])) * (var[0] - xend) / int(var[1])))
xend = var[0]
return x0, xvec
def __init__(self, nodes):
assert type(nodes) == list, "'nodes' variable must be a list of np.ndarray"
assert len(nodes) > 1, "len(node) must be greater than 1"
for i, nodes_i in enumerate(nodes):
assert isinstance(nodes_i, np.ndarray), ("nodes[%i] is not a numpy array." % i)
assert nodes_i.shape == nodes[0].shape, ("nodes[%i] is not the same shape as nodes[0]" % i)
assert len(nodes[0].shape) == len(nodes), "Dimension mismatch"
assert len(nodes[0].shape) > 1, "Not worth using Curv for a 1D mesh."
BaseRectangularMesh.__init__(self, np.array(nodes[0].shape)-1, None)
# 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))
def __init__(self, nodes):
assert type(nodes) == list, "'nodes' variable must be a list of np.ndarray"
assert len(nodes) > 1, "len(node) must be greater than 1"
for i, nodes_i in enumerate(nodes):
assert isinstance(nodes_i, np.ndarray), ("nodes[%i] is not a numpy array." % i)
assert nodes_i.shape == nodes[0].shape, ("nodes[%i] is not the same shape as nodes[0]" % i)
assert len(nodes[0].shape) == len(nodes), "Dimension mismatch"
assert len(nodes[0].shape) > 1, "Not worth using Curv for a 1D mesh."
BaseRectangularMesh.__init__(self, np.array(nodes[0].shape)-1, None)
# 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))
def Jvec(self, m, v, u=None):
"""
Sensitivity times a vector.
:param numpy.array m: inversion model (nP,)
:param numpy.array v: vector which we take sensitivity product with (nP,)
:param SimPEG.EM.FDEM.Fields u: fields object
:rtype numpy.array:
:return: Jv (ndata,)
"""
if u is None:
u = self.fields(m)
self.curModel = m
Jv = self.dataPair(self.survey)
for freq in self.survey.freqs:
A = self.getA(freq) #
Ainv = self.Solver(A, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
ftype = self._fieldType + 'Solution'
u_src = u[src, ftype]
dA_dm = self.getADeriv_m(freq, u_src, v)
dRHS_dm = self.getRHSDeriv_m(freq, src, v)
du_dm = Ainv * ( - dA_dm + dRHS_dm )
for rx in src.rxList:
df_duFun = getattr(u, '_%sDeriv_u'%rx.projField, None)
df_dudu_dm = df_duFun(src, du_dm, adjoint=False)
df_dmFun = getattr(u, '_%sDeriv_m'%rx.projField, None)
df_dm = df_dmFun(src, v, adjoint=False)
Df_Dm = np.array(df_dudu_dm + df_dm,dtype=complex)
P = lambda v: rx.projectFieldsDeriv(src, self.mesh, u, v) # wrt u, also have wrt m
Jv[src, rx] = P(Df_Dm)
Ainv.clean()
return Utils.mkvc(Jv)
def appResNorm(sigmaHalf):
nFreq = 26
m1d = Mesh.TensorMesh([[(100,5,1.5),(100.,10),(100,5,1.5)]], x0=['C'])
sigma = np.zeros(m1d.nC) + sigmaHalf
sigma[m1d.gridCC[:]>200] = 1e-8
# Calculate the analytic fields
freqs = np.logspace(4,-4,nFreq)
Z = []
for freq in freqs:
Ed, Eu, Hd, Hu = NSEM.Utils.getEHfields(m1d,sigma,freq,np.array([200]))
Z.append((Ed + Eu)/(Hd + Hu))
Zarr = np.concatenate(Z)
app_r, app_p = NSEM.Utils.appResPhs(freqs,Zarr)
return np.linalg.norm(np.abs(app_r - np.ones(nFreq)/sigmaHalf)) / np.log10(sigmaHalf)
def __init__(self, rxList, freq, s_m, s_e, **kwargs):
self._s_m = np.array(s_m, dtype=complex)
self._s_e = np.array(s_e, dtype=complex)
self.freq = float(freq)
BaseSrc.__init__(self, rxList, **kwargs)
def evalDeriv(self, src, mesh, f, v, adjoint=False):
"""
The derivative of the projection wrt u
:param MTsrc src: MT source
:param TensorMesh mesh: Mesh defining the topology of the problem
:param MTfields f: MT fields object of the source
:param numpy.ndarray v: Random vector of size
"""
real_or_imag = self.projComp
if not adjoint:
if self.projType is 'Z1D':
Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
# ex = Pex*mkvc(f[src,'e_1d'],2)
# bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
dP_de = -mkvc(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Pex*v),2)
dP_db = mkvc( Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)))*(Pbx*f._bDeriv_u(src,v)/mu_0),2)
PDeriv_complex = np.sum(np.hstack((dP_de,dP_db)),1)
elif self.projType is 'Z2D':
raise NotImplementedError('Has not been implement for 2D impedance tensor')
elif self.projType is 'Z3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pex = mesh.getInterpolationMat(eFLocs,'Ex')
Pey = mesh.getInterpolationMat(eFLocs,'Ey')
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
# Get the fields at location
# px: x-polaration and py: y-polaration.
ex_px = Pex*f[src,'e_px']
ey_px = Pey*f[src,'e_px']
ex_py = Pex*f[src,'e_py']
ey_py = Pey*f[src,'e_py']
hx_px = Pbx*f[src,'b_px']/mu_0
hy_px = Pby*f[src,'b_px']/mu_0
hx_py = Pbx*f[src,'b_py']/mu_0
hy_py = Pby*f[src,'b_py']/mu_0
# Derivatives as lambda functions
# The size of the diratives should be nD,nU
ex_px_u = lambda vec: Pex*f._e_pxDeriv_u(src,vec)
ey_px_u = lambda vec: Pey*f._e_pxDeriv_u(src,vec)
ex_py_u = lambda vec: Pex*f._e_pyDeriv_u(src,vec)
ey_py_u = lambda vec: Pey*f._e_pyDeriv_u(src,vec)
# NOTE: Think b_p?Deriv_u should return a 2*nF size matrix
hx_px_u = lambda vec: Pbx*f._b_pxDeriv_u(src,vec)/mu_0
hy_px_u = lambda vec: Pby*f._b_pxDeriv_u(src,vec)/mu_0
hx_py_u = lambda vec: Pbx*f._b_pyDeriv_u(src,vec)/mu_0
hy_py_u = lambda vec: Pby*f._b_pyDeriv_u(src,vec)/mu_0
# Update the input vector
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
# Define the components of the derivative
Hd = sDiag(1./(sDiag(hx_px)*hy_py - sDiag(hx_py)*hy_px))
Hd_uV = sDiag(hy_py)*hx_px_u(v) + sDiag(hx_px)*hy_py_u(v) - sDiag(hx_py)*hy_px_u(v) - sDiag(hy_px)*hx_py_u(v)
# Calculate components
if 'zxx' in self.rxType:
Zij = sDiag(Hd*( sDiag(ex_px)*hy_py - sDiag(ex_py)*hy_px ))
ZijN_uV = sDiag(hy_py)*ex_px_u(v) + sDiag(ex_px)*hy_py_u(v) - sDiag(ex_py)*hy_px_u(v) - sDiag(hy_px)*ex_py_u(v)
elif 'zxy' in self.rxType:
Zij = sDiag(Hd*(-sDiag(ex_px)*hx_py + sDiag(ex_py)*hx_px ))
ZijN_uV = -sDiag(hx_py)*ex_px_u(v) - sDiag(ex_px)*hx_py_u(v) + sDiag(ex_py)*hx_px_u(v) + sDiag(hx_px)*ex_py_u(v)
elif 'zyx' in self.rxType:
Zij = sDiag(Hd*( sDiag(ey_px)*hy_py - sDiag(ey_py)*hy_px ))
ZijN_uV = sDiag(hy_py)*ey_px_u(v) + sDiag(ey_px)*hy_py_u(v) - sDiag(ey_py)*hy_px_u(v) - sDiag(hy_px)*ey_py_u(v)
elif 'zyy' in self.rxType:
Zij = sDiag(Hd*(-sDiag(ey_px)*hx_py + sDiag(ey_py)*hx_px ))
ZijN_uV = -sDiag(hx_py)*ey_px_u(v) - sDiag(ey_px)*hx_py_u(v) + sDiag(ey_py)*hx_px_u(v) + sDiag(hx_px)*ey_py_u(v)
# Calculate the complex derivative
PDeriv_complex = Hd * (ZijN_uV - Zij * Hd_uV )
elif self.projType is 'T3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
Pbz = mesh.getInterpolationMat(bFLocs,'Fz')
# Get the fields at location
# px: x-polaration and py: y-polaration.
bx_px = Pbx*f[src,'b_px']
by_px = Pby*f[src,'b_px']
bz_px = Pbz*f[src,'b_px']
bx_py = Pbx*f[src,'b_py']
by_py = Pby*f[src,'b_py']
bz_py = Pbz*f[src,'b_py']
# Derivatives as lambda functions
# NOTE: Think b_p?Deriv_u should return a 2*nF size matrix
bx_px_u = lambda vec: Pbx*f._b_pxDeriv_u(src,vec)
by_px_u = lambda vec: Pby*f._b_pxDeriv_u(src,vec)
bz_px_u = lambda vec: Pbz*f._b_pxDeriv_u(src,vec)
bx_py_u = lambda vec: Pbx*f._b_pyDeriv_u(src,vec)
by_py_u = lambda vec: Pby*f._b_pyDeriv_u(src,vec)
bz_py_u = lambda vec: Pbz*f._b_pyDeriv_u(src,vec)
# Update the input vector
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
# Define the components of the derivative
Hd = sDiag(1./(sDiag(bx_px)*by_py - sDiag(bx_py)*by_px))
Hd_uV = sDiag(by_py)*bx_px_u(v) + sDiag(bx_px)*by_py_u(v) - sDiag(bx_py)*by_px_u(v) - sDiag(by_px)*bx_py_u(v)
if 'tzx' in self.rxType:
Tij = sDiag(Hd*( - sDiag(by_px)*bz_py + sDiag(by_py)*bz_px ))
TijN_uV = -sDiag(by_px)*bz_py_u(v) - sDiag(bz_py)*by_px_u(v) + sDiag(by_py)*bz_px_u(v) + sDiag(bz_px)*by_py_u(v)
elif 'tzy' in self.rxType:
Tij = sDiag(Hd*( sDiag(bx_px)*bz_py - sDiag(bx_py)*bz_px ))
TijN_uV = sDiag(bz_py)*bx_px_u(v) + sDiag(bx_px)*bz_py_u(v) - sDiag(bx_py)*bz_px_u(v) - sDiag(bz_px)*bx_py_u(v)
# Calculate the complex derivative
PDeriv_complex = Hd * (TijN_uV - Tij * Hd_uV )
# Extract the real number for the real/imag components.
Pv = np.array(getattr(PDeriv_complex, real_or_imag))
elif adjoint:
# Note: The v vector is real and the return should be complex
if self.projType is 'Z1D':
Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
# ex = Pex*mkvc(f[src,'e_1d'],2)
# bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
dP_deTv = -mkvc(Pex.T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*v,2)
db_duv = Pbx.T/mu_0*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))).T*Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2)).T*v
dP_dbTv = mkvc(f._bDeriv_u(src,db_duv,adjoint=True),2)
PDeriv_real = np.sum(np.hstack((dP_deTv,dP_dbTv)),1)
elif self.projType is 'Z2D':
raise NotImplementedError('Has not be implement for 2D impedance tensor')
elif self.projType is 'Z3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pex = mesh.getInterpolationMat(eFLocs,'Ex')
Pey = mesh.getInterpolationMat(eFLocs,'Ey')
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
# Get the fields at location
# px: x-polaration and py: y-polaration.
aex_px = mkvc(mkvc(f[src,'e_px'],2).T*Pex.T)
aey_px = mkvc(mkvc(f[src,'e_px'],2).T*Pey.T)
aex_py = mkvc(mkvc(f[src,'e_py'],2).T*Pex.T)
aey_py = mkvc(mkvc(f[src,'e_py'],2).T*Pey.T)
ahx_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pbx.T)
ahy_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pby.T)
ahx_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pbx.T)
ahy_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pby.T)
# Derivatives as lambda functions
aex_px_u = lambda vec: f._e_pxDeriv_u(src,Pex.T*vec,adjoint=True)
aey_px_u = lambda vec: f._e_pxDeriv_u(src,Pey.T*vec,adjoint=True)
aex_py_u = lambda vec: f._e_pyDeriv_u(src,Pex.T*vec,adjoint=True)
aey_py_u = lambda vec: f._e_pyDeriv_u(src,Pey.T*vec,adjoint=True)
ahx_px_u = lambda vec: f._b_pxDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
ahy_px_u = lambda vec: f._b_pxDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
ahx_py_u = lambda vec: f._b_pyDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
ahy_py_u = lambda vec: f._b_pyDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
# Update the input vector
# Define shortcuts
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
sVec = lambda t: Utils.sp.csr_matrix(mkvc(t,2))
# Define the components of the derivative
aHd = sDiag(1./(sDiag(ahx_px)*ahy_py - sDiag(ahx_py)*ahy_px))
aHd_uV = lambda x: ahx_px_u(sDiag(ahy_py)*x) + ahx_px_u(sDiag(ahy_py)*x) - ahy_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(ahy_px)*x)
# Need to fix this to reflect the adjoint
if 'zxx' in self.rxType:
Zij = sDiag(aHd*( sDiag(ahy_py)*aex_px - sDiag(ahy_px)*aex_py))
ZijN_uV = lambda x: aex_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aex_px)*x) - ahy_px_u(sDiag(aex_py)*x) - aex_py_u(sDiag(ahy_px)*x)
elif 'zxy' in self.rxType:
Zij = sDiag(aHd*(-sDiag(ahx_py)*aex_px + sDiag(ahx_px)*aex_py))
ZijN_uV = lambda x:-aex_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aex_px)*x) + ahx_px_u(sDiag(aex_py)*x) + aex_py_u(sDiag(ahx_px)*x)
elif 'zyx' in self.rxType:
Zij = sDiag(aHd*( sDiag(ahy_py)*aey_px - sDiag(ahy_px)*aey_py))
ZijN_uV = lambda x: aey_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aey_px)*x) - ahy_px_u(sDiag(aey_py)*x) - aey_py_u(sDiag(ahy_px)*x)
elif 'zyy' in self.rxType:
Zij = sDiag(aHd*(-sDiag(ahx_py)*aey_px + sDiag(ahx_px)*aey_py))
ZijN_uV = lambda x:-aey_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aey_px)*x) + ahx_px_u(sDiag(aey_py)*x) + aey_py_u(sDiag(ahx_px)*x)
# Calculate the complex derivative
PDeriv_real = ZijN_uV(aHd*v) - aHd_uV(Zij.T*aHd*v)#
# NOTE: Need to reshape the output to go from 2*nU array to a (nU,2) matrix for each polarization
# PDeriv_real = np.hstack((mkvc(PDeriv_real[:len(PDeriv_real)/2],2),mkvc(PDeriv_real[len(PDeriv_real)/2::],2)))
PDeriv_real = PDeriv_real.reshape((2,mesh.nE)).T
elif self.projType is 'T3D':
if self.locs.ndim == 3:
bFLocs = self.locs[:,:,1]
else:
bFLocs = self.locs
# Get the projection
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
Pbz = mesh.getInterpolationMat(bFLocs,'Fz')
# Get the fields at location
# px: x-polaration and py: y-polaration.
abx_px = mkvc(mkvc(f[src,'b_px'],2).T*Pbx.T)
aby_px = mkvc(mkvc(f[src,'b_px'],2).T*Pby.T)
abz_px = mkvc(mkvc(f[src,'b_px'],2).T*Pbz.T)
abx_py = mkvc(mkvc(f[src,'b_py'],2).T*Pbx.T)
aby_py = mkvc(mkvc(f[src,'b_py'],2).T*Pby.T)
abz_py = mkvc(mkvc(f[src,'b_py'],2).T*Pbz.T)
# Derivatives as lambda functions
abx_px_u = lambda vec: f._b_pxDeriv_u(src,Pbx.T*vec,adjoint=True)
aby_px_u = lambda vec: f._b_pxDeriv_u(src,Pby.T*vec,adjoint=True)
abz_px_u = lambda vec: f._b_pxDeriv_u(src,Pbz.T*vec,adjoint=True)
abx_py_u = lambda vec: f._b_pyDeriv_u(src,Pbx.T*vec,adjoint=True)
aby_py_u = lambda vec: f._b_pyDeriv_u(src,Pby.T*vec,adjoint=True)
abz_py_u = lambda vec: f._b_pyDeriv_u(src,Pbz.T*vec,adjoint=True)
# Update the input vector
# Define shortcuts
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
sVec = lambda t: Utils.sp.csr_matrix(mkvc(t,2))
# Define the components of the derivative
aHd = sDiag(1./(sDiag(abx_px)*aby_py - sDiag(abx_py)*aby_px))
aHd_uV = lambda x: abx_px_u(sDiag(aby_py)*x) + abx_px_u(sDiag(aby_py)*x) - aby_px_u(sDiag(abx_py)*x) - abx_py_u(sDiag(aby_px)*x)
# Need to fix this to reflect the adjoint
if 'tzx' in self.rxType:
Tij = sDiag(aHd*( -sDiag(abz_py)*aby_px + sDiag(abz_px)*aby_py))
TijN_uV = lambda x: -abz_py_u(sDiag(aby_px)*x) - aby_px_u(sDiag(abz_py)*x) + aby_py_u(sDiag(abz_px)*x) + abz_px_u(sDiag(aby_py)*x)
elif 'tzy' in self.rxType:
Tij = sDiag(aHd*( sDiag(abz_py)*abx_px - sDiag(abz_px)*abx_py))
TijN_uV = lambda x: abx_px_u(sDiag(abz_py)*x) + abz_py_u(sDiag(abx_px)*x) - abx_py_u(sDiag(abz_px)*x) - abz_px_u(sDiag(abx_py)*x)
# Calculate the complex derivative
PDeriv_real = TijN_uV(aHd*v) - aHd_uV(Tij.T*aHd*v)#
# NOTE: Need to reshape the output to go from 2*nU array to a (nU,2) matrix for each polarization
# PDeriv_real = np.hstack((mkvc(PDeriv_real[:len(PDeriv_real)/2],2),mkvc(PDeriv_real[len(PDeriv_real)/2::],2)))
PDeriv_real = PDeriv_real.reshape((2,mesh.nE)).T
# Extract the data
if real_or_imag == 'imag':
Pv = 1j*PDeriv_real
elif real_or_imag == 'real':
Pv = PDeriv_real.astype(complex)
return Pv
def MagneticDipoleVectorPotential(srcLoc, obsLoc, component, moment=1.,
orientation=np.r_[0., 0., 1.],
mu=mu_0):
"""
Calculate the vector potential of a set of magnetic dipoles
at given locations 'ref. <http://en.wikipedia.org/wiki/Dipole#Magnetic_vector_potential>'
:param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
:param numpy.ndarray,SimPEG.Mesh obsLoc: Where the potentials will be
calculated (x, y, z) or a
SimPEG Mesh
:param str,list component: The component to calculate - 'x', 'y', or
'z' if an array, or grid type if mesh, can
be a list
:param numpy.ndarray orientation: The vector dipole moment
:rtype: numpy.ndarray
:return: The vector potential each dipole at each observation location
"""
# TODO: break this out!
if isinstance(orientation, str):
orientation = orientationDict[orientation]
assert np.linalg.norm(np.array(orientation), 2) == 1., ("orientation must "
"be a unit vector")
if type(component) in [list, tuple]:
out = range(len(component))
for i, comp in enumerate(component):
out[i] = MagneticDipoleVectorPotential(srcLoc, obsLoc, comp,
orientation=orientation,
mu=mu)
return np.concatenate(out)
if isinstance(obsLoc, Mesh.BaseMesh):
mesh = obsLoc
assert component in ['Ex', 'Ey', 'Ez', 'Fx', 'Fy', 'Fz'], ("Components"
"must be in: ['Ex','Ey','Ez','Fx','Fy','Fz']")
return MagneticDipoleVectorPotential(srcLoc, getattr(mesh, 'grid' +
component),
component[1],
orientation=orientation)
if component == 'x':
dimInd = 0
elif component == 'y':
dimInd = 1
elif component == 'z':
dimInd = 2
else:
raise ValueError('Invalid component')
srcLoc = np.atleast_2d(srcLoc)
obsLoc = np.atleast_2d(obsLoc)
orientation = np.atleast_2d(orientation)
nObs = obsLoc.shape[0]
nSrc = srcLoc.shape[0]
m = moment*np.array(orientation).repeat(nObs, axis=0)
A = np.empty((nObs, nSrc))
for i in range(nSrc):
dR = obsLoc - srcLoc[i, np.newaxis].repeat(nObs, axis=0)
mCr = np.cross(m, dR)
r = np.sqrt((dR**2).sum(axis=1))
A[:, i] = +(mu/(4*np.pi)) * mCr[:, dimInd]/(r**3)
if nSrc == 1:
return A.flatten()
return A
def setUp(self):
self.a = np.array([1, 2, 3])
self.b = np.array([1, 2])
self.c = np.array([1, 2, 3, 4])
def readDriverFile(self, input_file):
"""
Read input files for forward modeling MAG data with integral form
INPUT:
input_file: File name containing the forward parameter
OUTPUT:
mshfile
obsfile
topofile
start model
ref model
mag model
weightfile
chi_target
as, ax ,ay, az
upper, lower bounds
lp, lqx, lqy, lqz
# All files should be in the working directory,
# otherwise the path must be specified.
"""
fid = open(self.basePath + input_file, 'r')
# Line 1: Mesh
line = fid.readline()
l_input = re.split('[!\s]', line)
mshfile = l_input[1].rstrip()
# Line 2: Observation file
line = fid.readline()
l_input = re.split('[!\s]', line)
obsfile = l_input[1].rstrip()
# Line 3: Topo, active-dyn, active-static
topofile = None
staticInput = None
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0] == 'TOPO':
topofile = l_input[1].rstrip()
elif l_input[0] == 'VALUE':
staticInput = float(l_input[1])
elif l_input[0] == 'FILE':
staticInput = l_input[1].rstrip()
# Line 4: Starting model
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0] == 'VALUE':
mstart = float(l_input[1])
elif l_input[0] == 'FILE':
mstart = l_input[1].rstrip()
# Line 5: Reference model
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0] == 'VALUE':
mref = float(l_input[1])
elif l_input[0] == 'FILE':
mref = l_input[1].rstrip()
# Line 6: Magnetization model
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0] == 'DEFAULT':
magfile = None
elif l_input[0] == 'FILE':
magfile = l_input[1].rstrip()
# Line 7: Cell weights
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0] == 'DEFAULT':
wgtfile = []
elif l_input[0] == 'FILE':
wgtfile = l_input[1].rstrip()
# Line 8: Target chi-factor
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0] == 'DEFAULT':
chi = 1.
elif l_input[0] == 'VALUE':
chi = float(l_input[1])
# Line 9: Alpha values
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0] == 'VALUE':
val = np.array(l_input[1:5])
alphas = val.astype(np.float)
elif l_input[0] == 'DEFAULT':
alphas = np.ones(4)
# Line 10: Bounds
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0] == 'VALUE':
val = np.array(l_input[1:3])
bounds = val.astype(np.float)
elif l_input[0] == 'FILE':
bounds = l_input[1].rstrip()
else:
bounds = [-np.inf, np.inf]
# Line 11: Norms
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0] == 'VALUE':
val = np.array(l_input[1:6])
lpnorms = val.astype(np.float)
elif l_input[0] == 'FILE':
lpnorms = l_input[1].rstrip()
# Line 12: Treshold values
line = fid.readline()
l_input = re.split('[!\s]', line)
if l_input[0] == 'VALUE':
val = np.array(l_input[1:3])
eps = val.astype(np.float)
elif l_input[0] == 'DEFAULT':
eps = None
self.mshfile = mshfile
self.obsfile = obsfile
self.topofile = topofile
self.mstart = mstart
self._mrefInput = mref
self._staticInput = staticInput
self.magfile = magfile
self.wgtfile = wgtfile
self.chi = chi
self.alphas = alphas
self.bounds = bounds
self.lpnorms = lpnorms
self.eps = eps
def test_indexCube_2D(self):
nN = np.array([3, 3])
self.assertTrue(np.all(indexCube('A', nN) == np.array([0, 1, 3, 4])))
self.assertTrue(np.all(indexCube('B', nN) == np.array([3, 4, 6, 7])))
self.assertTrue(np.all(indexCube('C', nN) == np.array([4, 5, 7, 8])))
self.assertTrue(np.all(indexCube('D', nN) == np.array([1, 2, 4, 5])))
def gen_DCIPsurvey(endl, mesh, stype, a, b, n):
"""
Load in endpoints and survey specifications to generate Tx, Rx location
stations.
Assumes flat topo for now...
Input:
:param endl -> input endpoints [x1, y1, z1, x2, y2, z2]
:object mesh -> SimPEG mesh object
:switch stype -> "dpdp" (dipole-dipole) | "pdp" (pole-dipole) | 'gradient'
: param a, n -> pole seperation, number of rx dipoles per tx
Output:
:param Tx, Rx -> List objects for each tx location
Lines: P1x, P1y, P1z, P2x, P2y, P2z
Created on Wed December 9th, 2015
@author: dominiquef
!! Require clean up to deal with DCsurvey
"""
from SimPEG import np
def xy_2_r(x1, x2, y1, y2):
r = np.sqrt(np.sum((x2 - x1)**2 + (y2 - y1)**2))
return r
## Evenly distribute electrodes and put on surface
# Mesure survey length and direction
dl_len = xy_2_r(endl[0, 0], endl[1, 0], endl[0, 1], endl[1, 1])
dl_x = (endl[1, 0] - endl[0, 0]) / dl_len
dl_y = (endl[1, 1] - endl[0, 1]) / dl_len
nstn = np.floor(dl_len / a)
# Compute discrete pole location along line
stn_x = endl[0, 0] + np.array(range(int(nstn))) * dl_x * a
stn_y = endl[0, 1] + np.array(range(int(nstn))) * dl_y * a
if mesh.dim == 2:
ztop = mesh.vectorNy[-1]
# Create line of P1 locations
M = np.c_[stn_x, np.ones(nstn).T * ztop]
# Create line of P2 locations
N = np.c_[stn_x + a * dl_x, np.ones(nstn).T * ztop]
elif mesh.dim == 3:
ztop = mesh.vectorNz[-1]
# Create line of P1 locations
M = np.c_[stn_x, stn_y, np.ones(nstn).T * ztop]
# Create line of P2 locations
N = np.c_[stn_x + a * dl_x, stn_y + a * dl_y, np.ones(nstn).T * ztop]
## Build list of Tx-Rx locations depending on survey type
# Dipole-dipole: Moving tx with [a] spacing -> [AB a MN1 a MN2 ... a MNn]
# Pole-dipole: Moving pole on one end -> [A a MN1 a MN2 ... MNn a B]
SrcList = []
if stype != 'gradient':
for ii in range(0, int(nstn) - 1):
if stype == 'dipole-dipole':
tx = np.c_[M[ii, :], N[ii, :]]
elif stype == 'pole-dipole':
tx = np.c_[M[ii, :], M[ii, :]]
else:
raise Exception(
'The stype must be "dipole-dipole" or "pole-dipole"')
# Rx.append(np.c_[M[ii+1:indx,:],N[ii+1:indx,:]])
# Current elctrode seperation
AB = xy_2_r(tx[0, 1], endl[1, 0], tx[1, 1], endl[1, 1])
# Number of receivers to fit
nstn = np.min([np.floor((AB - b) / a), n])
# Check if there is enough space, else break the loop
if nstn <= 0:
continue
# Compute discrete pole location along line
stn_x = N[ii, 0] + dl_x * b + np.array(range(int(nstn))) * dl_x * a
stn_y = N[ii, 1] + dl_y * b + np.array(range(int(nstn))) * dl_y * a
# Create receiver poles
if mesh.dim == 3:
# Create line of P1 locations
P1 = np.c_[stn_x, stn_y, np.ones(nstn).T * ztop]
# Create line of P2 locations
P2 = np.c_[stn_x + a * dl_x, stn_y + a * dl_y,
np.ones(nstn).T * ztop]
rxClass = DC.Rx.Dipole(P1, P2)
elif mesh.dim == 2:
# Create line of P1 locations
P1 = np.c_[stn_x, np.ones(nstn).T * ztop]
# Create line of P2 locations
P2 = np.c_[stn_x + a * dl_x, np.ones(nstn).T * ztop]
rxClass = DC.Rx.Dipole_ky(P1, P2)
if stype == 'dipole-dipole':
srcClass = DC.Src.Dipole([rxClass], M[ii, :], N[ii, :])
elif stype == 'pole-dipole':
srcClass = DC.Src.Pole([rxClass], M[ii, :])
SrcList.append(srcClass)
elif stype == 'gradient':
# Gradient survey only requires Tx at end of line and creates a square
# grid of receivers at in the middle at a pre-set minimum distance
# Get the edge limit of survey area
min_x = endl[0, 0] + dl_x * b
min_y = endl[0, 1] + dl_y * b
max_x = endl[1, 0] - dl_x * b
max_y = endl[1, 1] - dl_y * b
box_l = np.sqrt((min_x - max_x)**2 + (min_y - max_y)**2)
box_w = box_l / 2.
nstn = np.floor(box_l / a)
# Compute discrete pole location along line
stn_x = min_x + np.array(range(int(nstn))) * dl_x * a
stn_y = min_y + np.array(range(int(nstn))) * dl_y * a
# Define number of cross lines
nlin = int(np.floor(box_w / a))
lind = range(-nlin, nlin + 1)
ngrad = nstn * len(lind)
rx = np.zeros([ngrad, 6])
for ii in range(len(lind)):
# Move line in perpendicular direction by dipole spacing
lxx = stn_x - lind[ii] * a * dl_y
lyy = stn_y + lind[ii] * a * dl_x
M = np.c_[lxx, lyy, np.ones(nstn).T * ztop]
N = np.c_[lxx + a * dl_x, lyy + a * dl_y, np.ones(nstn).T * ztop]
rx[(ii * nstn):((ii + 1) * nstn), :] = np.c_[M, N]
if mesh.dim == 3:
rxClass = DC.Rx.Dipole(rx[:, :3], rx[:, 3:])
elif mesh.dim == 2:
M = M[:, [0, 2]]
N = N[:, [0, 2]]
rxClass = DC.Rx.Dipole_ky(rx[:, [0, 2]], rx[:, [3, 5]])
srcClass = DC.Src.Dipole([rxClass], M[0, :], N[-1, :])
SrcList.append(srcClass)
else:
print """stype must be either 'pole-dipole', 'dipole-dipole' or 'gradient'. """
return SrcList
def getInterpolationMat(self, loc, locType='CC', zerosOutside=False):
""" Produces interpolation matrix
:param numpy.ndarray loc: Location of points to interpolate to
:param str locType: What to interpolate (see below)
:rtype: scipy.sparse.csr.csr_matrix
:return: M, the interpolation matrix
locType can be::
'Ex' -> x-component of field defined on edges
'Ey' -> y-component of field defined on edges
'Ez' -> z-component of field defined on edges
'Fx' -> x-component of field defined on faces
'Fy' -> y-component of field defined on faces
'Fz' -> z-component of field defined on faces
'N' -> scalar field defined on nodes
'CC' -> scalar field defined on cell centers
'CCVx' -> x-component of vector field defined on cell centers
'CCVy' -> y-component of vector field defined on cell centers
'CCVz' -> z-component of vector field defined on cell centers
"""
if self._meshType == 'CYL' and self.isSymmetric and locType in [
'Ex', 'Ez', 'Fy'
]:
raise Exception(
'Symmetric CylMesh does not support %s interpolation, as this variable does not exist.'
% locType)
loc = Utils.asArray_N_x_Dim(loc, self.dim)
if zerosOutside is False:
assert np.all(self.isInside(loc)), "Points outside of mesh"
else:
indZeros = np.logical_not(self.isInside(loc))
loc[indZeros, :] = np.array(
[v.mean() for v in self.getTensor('CC')])
if locType in ['Fx', 'Fy', 'Fz', 'Ex', 'Ey', 'Ez']:
ind = {'x': 0, 'y': 1, 'z': 2}[locType[1]]
assert self.dim >= ind, 'mesh is not high enough dimension.'
nF_nE = self.vnF if 'F' in locType else self.vnE
components = [Utils.spzeros(loc.shape[0], n) for n in nF_nE]
components[ind] = Utils.interpmat(loc, *self.getTensor(locType))
# remove any zero blocks (hstack complains)
components = [comp for comp in components if comp.shape[1] > 0]
Q = sp.hstack(components)
elif locType in ['CC', 'N']:
Q = Utils.interpmat(loc, *self.getTensor(locType))
elif locType in ['CCVx', 'CCVy', 'CCVz']:
Q = Utils.interpmat(loc, *self.getTensor('CC'))
Z = Utils.spzeros(loc.shape[0], self.nC)
if locType == 'CCVx':
Q = sp.hstack([Q, Z, Z])
elif locType == 'CCVy':
Q = sp.hstack([Z, Q, Z])
elif locType == 'CCVz':
Q = sp.hstack([Z, Z, Q])
else:
raise NotImplementedError('getInterpolationMat: locType==' +
locType + ' and mesh.dim==' +
str(self.dim))
if zerosOutside:
Q[indZeros, :] = 0
return Q.tocsr()
def run(plotIt=True):
"""
FLOW: Richards: 1D: Celia1990
=============================
There are two different forms of Richards equation that differ
on how they deal with the non-linearity in the time-stepping term.
The most fundamental form, referred to as the
'mixed'-form of Richards Equation Celia1990_
.. math::
\\frac{\partial \\theta(\psi)}{\partial t} -
\\nabla \cdot k(\psi) \\nabla \psi -
\\frac{\partial k(\psi)}{\partial z} = 0
\quad \psi \in \Omega
where \\\\(\\\\theta\\\\) is water content, and \\\\(\\\\psi\\\\)
is pressure head. This formulation of Richards equation is called the
'mixed'-form because the equation is parameterized in \\\\(\\\\psi\\\\)
but the time-stepping is in terms of \\\\(\\\\theta\\\\).
As noted in Celia1990_ the 'head'-based form of Richards
equation can be written in the continuous form as:
.. math::
\\frac{\partial \\theta}{\partial \psi}
\\frac{\partial \psi}{\partial t} -
\\nabla \cdot k(\psi) \\nabla \psi -
\\frac{\partial k(\psi)}{\partial z} = 0
\quad \psi \in \Omega
However, it can be shown that this does not conserve mass in the
discrete formulation.
Here we reproduce the results from Celia1990_ demonstrating the
head-based formulation and the mixed-formulation.
.. _Celia1990: http://www.webpages.uidaho.edu/ch/papers/Celia.pdf
"""
M = Mesh.TensorMesh([np.ones(40)])
M.setCellGradBC('dirichlet')
params = Richards.Empirical.HaverkampParams().celia1990
params['Ks'] = np.log(params['Ks'])
E = Richards.Empirical.Haverkamp(M, **params)
bc = np.array([-61.5, -20.7])
h = np.zeros(M.nC) + bc[0]
# bc = np.array([-20.7, -61.5])
# h = np.zeros(M.nC) + bc[1]
def getFields(timeStep, method):
timeSteps = np.ones(360 / timeStep) * timeStep
prob = Richards.RichardsProblem(M,
modelMap=E,
boundaryConditions=bc,
initialConditions=h,
doNewton=False,
method=method)
prob.timeSteps = timeSteps
return prob.fields(params['Ks'])
Hs_M010 = getFields(10., 'mixed')
Hs_M030 = getFields(30., 'mixed')
Hs_M120 = getFields(120., 'mixed')
Hs_H010 = getFields(10., 'head')
Hs_H030 = getFields(30., 'head')
Hs_H120 = getFields(120., 'head')
if not plotIt:
return
plt.figure(figsize=(13, 5))
plt.subplot(121)
plt.plot(40 - M.gridCC, Hs_M010[-1], 'b-')
plt.plot(40 - M.gridCC, Hs_M030[-1], 'r-')
plt.plot(40 - M.gridCC, Hs_M120[-1], 'k-')
plt.ylim([-70, -10])
plt.title('Mixed Method')
plt.xlabel('Depth, cm')
plt.ylabel('Pressure Head, cm')
plt.legend(
('$\Delta t$ = 10 sec', '$\Delta t$ = 30 sec', '$\Delta t$ = 120 sec'))
plt.subplot(122)
plt.plot(40 - M.gridCC, Hs_H010[-1], 'b-')
plt.plot(40 - M.gridCC, Hs_H030[-1], 'r-')
plt.plot(40 - M.gridCC, Hs_H120[-1], 'k-')
plt.ylim([-70, -10])
plt.title('Head-Based Method')
plt.xlabel('Depth, cm')
plt.ylabel('Pressure Head, cm')
plt.legend(
('$\Delta t$ = 10 sec', '$\Delta t$ = 30 sec', '$\Delta t$ = 120 sec'))