def generate_forward_data():
"""Generate synthetic forward data that we then invert"""
scheme = get_scheme()
mesh = get_fwd_mesh()
rhomap = [
[1, pg.utils.complex.toComplex(100, 0 / 1000)],
# Magnitude: 50 ohm m, Phase: -50 mrad
[2, pg.utils.complex.toComplex(50, 0 / 1000)],
[3, pg.utils.complex.toComplex(100, -50 / 1000)],
]
rho = pg.solver.parseArgToArray(rhomap, mesh.cellCount(), mesh)
fig, axes = plt.subplots(2, 1, figsize=(16 / 2.54, 16 / 2.54))
pg.show(
mesh,
data=np.log(np.abs(rho)),
ax=axes[0],
label=r"$log_{10}(|\rho|~[\Omega m])$"
)
pg.show(mesh, data=np.abs(rho), ax=axes[1], label=r"$|\rho|~[\Omega m]$")
pg.show(
mesh, data=np.arctan2(np.imag(rho), np.real(rho)) * 1000,
ax=axes[1],
label=r"$\phi$ [mrad]",
cMap='jet_r'
)
data = ert.simulate(
mesh,
res=rhomap,
scheme=scheme,
# noiseAbs=0.0,
# noiseLevel=0.0,
)
r_complex = data['rhoa'].array() * np.exp(1j * data['phia'].array())
# Please note the apparent negative (resistivity) phases!
fig, axes = plt.subplots(2, 2, figsize=(16 / 2.54, 16 / 2.54))
ert.showERTData(data, vals=data['rhoa'], ax=axes[0, 0])
# phia is stored in radians, but usually plotted in milliradians
ert.showERTData(
data, vals=data['phia'] * 1000, label=r'$\phi$ [mrad]', ax=axes[0, 1])
ert.showERTData(
data, vals=np.real(r_complex), ax=axes[1, 0],
label=r"$Z'$~[$\Omega$m"
)
ert.showERTData(
data, vals=np.imag(r_complex), ax=axes[1, 1],
label=r"$Z''$~[$\Omega$]"
)
fig.tight_layout()
fig.show()
return r_complex
def plot_inv_pars(filename, d, response, Wd, iteration='start'):
"""Plot error-weighted residuals"""
fig, axes = plt.subplots(1, 2, figsize=(20 / 2.54, 10 / 2.54))
psi = Wd.dot(d - response)
ert.showERTData(
scheme, vals=psi.real, ax=axes[0],
label=r"$(d' - f') / \epsilon$"
)
ert.showERTData(
scheme, vals=psi.imag, ax=axes[1],
label=r"$(d'' - f'') / \epsilon$"
)
fig.suptitle(
'Error weighted residuals of iteration {}'.format(iteration), y=1.00)
fig.tight_layout()
rm.fillConstraints(Wm)
Wm = pg.utils.sparseMatrix2coo(Wm)
###############################################################################
# read-in data and determine error parameters
filename = pg.getExampleFile(
'CR/synthetic_modeling/data_rre_rim.dat', load=False, verbose=True)
data_rre_rim = np.loadtxt(filename)
N = int(data_rre_rim.size / 2)
d_rcomplex = data_rre_rim[:N] + 1j * data_rre_rim[N:]
dmag = np.abs(d_rcomplex)
dpha = np.arctan2(d_rcomplex.imag, d_rcomplex.real) * 1000
fig, axes = plt.subplots(1, 2, figsize=(20 / 2.54, 10 / 2.54))
k = np.array(ert.createGeometricFactors(scheme))
ert.showERTData(
scheme, vals=dmag * k, ax=axes[0], label=r'$|\rho_a|~[\Omega$m]')
ert.showERTData(scheme, vals=dpha, ax=axes[1], label=r'$\phi_a~[mrad]$')
# real part: log-magnitude
# imaginary part: phase [rad]
d_rlog = np.log(d_rcomplex)
# add some noise
np.random.seed(42)
noise_magnitude = np.random.normal(
loc=0,
scale=np.exp(d_rlog.real) * 0.04
)
# absolute phase error
def show(obj=None, data=None, **kwargs):
"""Mesh and model visualization.
Syntactic sugar to show a obj with data. Forwards to
a known visualization for obj. Typical is
:py:mod:`pygimli.viewer.showMesh` or
:py:mod:`pygimli.viewer.mayaview.showMesh3D` to show most of the typical 2D
and 3D content.
See tutorials and examples for usage hints. An empty show
call creates an empty ax window.
Parameters
----------
obj: obj
obj can be so far.
* :gimliapi:`GIMLI::Mesh` or list of meshes
* DataContainer
* pg.core.Sparse[Map]Matrix
data: iterable
Optionally data to visualize. See appropriate show function.
Keyword Arguments
-----------------
**kwargs
Additional kwargs forward to appropriate show functions.
* ax : axe [None]
Matplotlib axes object. Create a new if necessary.
* fitView : bool [True]
Scale x and y limits to match the view.
Returns
-------
Return the results from the showMesh* functions. Usually the axe object
and a colorbar.
See Also
--------
showMesh
"""
if "axes" in kwargs:
print("Deprecation Warning: Please use keyword `ax` instead of `axes`")
kwargs['ax'] = kwargs.pop('axes', None)
if isinstance(obj, pg.DataContainerERT):
from pygimli.physics.ert import showERTData
return showERTData(obj, vals=kwargs.pop('vals', data), **kwargs)
if isinstance(obj, pg.core.MatrixBase):
ax, _ = pg.show()
return drawMatrix(ax, obj, **kwargs)
mesh = kwargs.pop('mesh', obj)
if isinstance(mesh, list):
ax = kwargs.pop('ax', None)
fitView = kwargs.pop('fitView', ax is None)
ax, cBar = show(mesh[0],
data,
hold=1,
ax=ax,
fitView=fitView,
**kwargs)
xMin = mesh[0].xMin()
xMax = mesh[0].xMax()
yMin = mesh[0].yMin()
yMax = mesh[0].yMax()
for m in mesh[1:]:
ax, cBar = show(m, data, ax=ax, hold=1, fitView=False, **kwargs)
xMin = min(xMin, m.xMin())
xMax = max(xMax, m.xMax())
yMin = min(yMin, m.yMin())
yMax = max(yMax, m.yMax())
# ax.relim()
# ax.autoscale_view(tight=True)
if fitView is not False:
ax.set_xlim([xMin, xMax])
ax.set_ylim([yMin, yMax])
# print(ax.get_data_interval())
return ax, cBar
if isinstance(mesh, pg.Mesh):
if mesh.dim() == 2:
if pg.zero(pg.y(mesh)):
pg.info("swap z<->y coordinates for visualization.")
meshSwap = pg.Mesh(mesh)
for n in meshSwap.nodes():
n.pos()[1] = n.pos()[2]
return showMesh(meshSwap, data, **kwargs)
return showMesh(mesh, data, **kwargs)
elif mesh.dim() == 3:
from .vistaview import showMesh3D
return showMesh3D(mesh, data, **kwargs)
else:
pg.error("ERROR: Mesh not valid.", mesh)
ax = kwargs.pop('ax', None)
if ax is None:
ax = plt.subplots()[1]
return ax, None
def show(obj=None, data=None, **kwargs):
"""Mesh and model visualization.
Syntactic sugar to show a obj with data. Forwards to
a known visualization for obj. Typical is
:py:mod:`pygimli.viewer.showMesh` or
:py:mod:`pygimli.viewer.mayaview.showMesh3D` to show most of the typical 2D
and 3D content.
See tutorials and examples for usage hints. An empty show
call creates an empty ax window.
Parameters
----------
obj: obj
obj can be so far.
* :gimliapi:`GIMLI::Mesh` or list of meshes
* DataContainer
* pg.core.Sparse[Map]Matrix
data: iterable
Optionally data to visualize. See appropriate show function.
Keyword Arguments
-----------------
**kwargs
Additional kwargs forward to appropriate show functions.
* ax : axe [None]
Matplotlib axes object. Create a new if necessary.
* fitView : bool [True]
Scale x and y limits to match the view.
Returns
-------
Return the results from the showMesh* functions. Usually the axe object
and a colorbar.
See Also
--------
showMesh
"""
if "axes" in kwargs: # remove me in 1.2 #20200515
print("Deprecation Warning: Please use keyword `ax` instead of `axes`")
kwargs['ax'] = kwargs.pop('axes', None)
### Empty call just to create a axes
if obj is None and not 'mesh' in kwargs.keys():
ax = kwargs.pop('ax', None)
if ax is None:
ax = plt.subplots(figsize=kwargs.pop('figsize', None))[1]
return ax, None
### try to interprete obj containes a mesh
if hasattr(obj, 'mesh'):
return pg.show(obj.mesh, obj, **kwargs)
### try to interprete obj as ERT Data
if isinstance(obj, pg.DataContainerERT):
from pygimli.physics.ert import showERTData
return showERTData(obj, vals=kwargs.pop('vals', data), **kwargs)
### try to interprete obj as matrices
if isinstance(obj, pg.core.MatrixBase) or \
(isinstance(obj, np.ndarray) and obj.ndim == 2):
return showMatrix(obj, **kwargs)
try:
from scipy.sparse import spmatrix
if isinstance(obj, spmatrix):
return showMatrix(obj, **kwargs)
except ImportError:
pass
### try to interprete obj as mesh or list of meshes
mesh = kwargs.pop('mesh', obj)
fitView = kwargs.get('fitView', True)
if isinstance(mesh, list):
ax = kwargs.pop('ax', None)
ax, cBar = show(mesh[0],
data,
hold=1,
ax=ax,
fitView=fitView,
**kwargs)
for m in mesh[1:]:
ax, cBar = show(m, data, ax=ax, hold=1, fitView=False, **kwargs)
if fitView is not False:
ax.autoscale(enable=True, axis='both', tight=True)
ax.set_aspect('equal')
return ax, cBar
if isinstance(mesh, pg.Mesh):
if mesh.dim() == 2:
if pg.zero(pg.y(mesh)):
pg.info("swap z<->y coordinates for visualization.")
meshSwap = pg.Mesh(mesh)
for n in meshSwap.nodes():
n.pos()[1] = n.pos()[2]
return showMesh(meshSwap, data, **kwargs)
return showMesh(mesh, data, **kwargs)
elif mesh.dim() == 3:
from .vistaview import showMesh3D
return showMesh3D(mesh, data, **kwargs)
else:
pg.error("ERROR: Mesh not valid.", mesh)
pg.error("Can't interprete obj: {0} to show.".format(obj))
return None, None
data = ert.simulate(
mesh,
res=rhomap,
scheme=scheme,
# noiseAbs=0.0,
# noiseLevel=0.0,
)
###############################################################################
# Visualize the modeled data
# Convert magnitude and phase into a complex apparent resistivity
rho_a_complex = data['rhoa'].array() * np.exp(1j * data['phia'].array())
# Please note the apparent negative (resistivity) phases!
fig, axes = plt.subplots(2, 2, figsize=(16 / 2.54, 16 / 2.54))
ert.showERTData(data, vals=data['rhoa'], ax=axes[0, 0])
# phia is stored in radians, but usually plotted in milliradians
ert.showERTData(data,
vals=data['phia'] * 1000,
label=r'$\phi$ [mrad]',
ax=axes[0, 1])
ert.showERTData(data,
vals=np.real(rho_a_complex),
ax=axes[1, 0],
label=r"$\rho_a'$~[$\Omega$m]")
ert.showERTData(data,
vals=np.imag(rho_a_complex),
ax=axes[1, 1],
label=r"$\rho_a''$~[$\Omega$m]")
fig.tight_layout()