"""
Interactivity functions and classes using matplotlib and IPython widgets
**Gravity forward modeling**
* :class:`~fatiando.gravmag.interactive.Moulder`: a matplitlib GUI for 2D
forward modeling using polygons
----
"""
from __future__ import division
import cPickle as pickle
import numpy
from matplotlib import pyplot, widgets, patches
from matplotlib.lines import Line2D
from IPython.core.pylabtools import print_figure
from IPython.display import Image
from .. import utils
from . import talwani
from ..mesher import Polygon
[docs]class Moulder(object):
"""
Interactive 2D forward modeling using polygons.
A matplotlib GUI application. Allows drawing and manipulating polygons and
computes their predicted data automatically. Also permits contaminating the
data with gaussian pseudo-random error for producing synthetic data sets.
Uses :mod:`fatiando.gravmag.talwani` for computations.
*Moulder* objects can be persisted to Python pickle files using the
:meth:`~fatiando.gravmag.interactive.Moulder.save` method and later
restored using :meth:`~fatiando.gravmag.interactive.Moulder.load`.
.. warning::
Cannot be used with ``%matplotlib inline`` on IPython notebooks because
the app uses the matplotlib plot window. You can still embed the
generated model and data figure on notebooks using the
:meth:`~fatiando.gravmag.interactive.Moulder.plot` method.
Parameters:
* area : list = (x1, x2, z1, z2)
The limits of the model drawing area, in meters.
* x, z : 1d-arrays
The x- and z-coordinates of the computation points (places where
predicted data will be computed). In meters.
* data : None or 1d-array
Observed data measured at *x* and *z*. Will plot this with black dots
along the predicted data.
* density_range : list = [min, max]
The minimum and maximum values allowed for the density. Determines the
limits of the density slider of the application. In kg.m^-3. Defaults
to [-2000, 2000].
* kwargs : dict
Other keyword arguments used to restore the state of the application.
Used by the :meth:`~fatiando.gravmag.interactive.Moulder.load` method.
Not intended for general use.
Examples:
Make the Moulder object and start the app::
import numpy as np
area = (0, 10e3, 0, 5e3)
# Calculate on 100 points
x = np.linspace(area[0], area[1], 100)
z = np.zeros_like(x)
app = Moulder(area, x, z)
app.run()
# This will pop-up a window with the application (like the screenshot
# below). Start drawing (follow the instruction in the figure title).
# When satisfied, close the window to resume execution.
.. image:: ../_static/images/Moulder-screenshot.png
:alt: Screenshot of the Moulder GUI
After closing the plot window, you can access the model and data from the
*Moulder* object::
app.model # The drawn model as fatiando.mesher.Polygon
app.predicted # 1d-array with the data predicted by the model
# You can save the predicted data to use later
app.save_predicted('data.txt')
# You can also save the application and resume it later
app.save('application.pkl')
# Close this session/IPython notebook/etc.
# To resume drawing later:
app = Moulder.load('application.pkl')
app.run()
"""
# The tolerance range for mouse clicks on vertices. In pixels.
epsilon = 5
# App instructions printed in the figure suptitle
instructions = ' | '.join([
'n: New polygon', 'd: delete', 'click: select/move', 'esc: cancel'])
def __init__(self, area, x, z, data=None, density_range=[-2000, 2000],
**kwargs):
self.area = area
self.x, self.z = numpy.asarray(x), numpy.asarray(z)
self.density_range = density_range
self.data = data
# Used to set the ylims for the data axes.
if data is None:
self.dmin, self.dmax = 0, 0
else:
self.dmin, self.dmax = data.min(), data.max()
self.predicted = kwargs.get('predicted', numpy.zeros_like(x))
self.error = kwargs.get('error', 0)
self.cmap = kwargs.get('cmap', pyplot.cm.RdBu_r)
self.line_args = dict(
linewidth=2, linestyle='-', color='k', marker='o',
markerfacecolor='k', markersize=5, animated=False, alpha=0.6)
self.polygons = []
self.lines = []
self.densities = kwargs.get('densities', [])
vertices = kwargs.get('vertices', [])
for xy, dens in zip(vertices, self.densities):
poly, line = self._make_polygon(xy, dens)
self.polygons.append(poly)
self.lines.append(line)
[docs] def save_predicted(self, fname):
"""
Save the predicted data to a text file.
Data will be saved in 3 columns separated by spaces: x z data
Parameters:
* fname : string or file-like object
The name of the output file or an open file-like object.
"""
numpy.savetxt(fname, numpy.transpose([self.x, self.z, self.predicted]))
[docs] def save(self, fname):
"""
Save the application state into a pickle file.
Use this to persist the application. You can later reload the entire
object, with the drawn model and data, using the
:meth:`~fatiando.gravmag.interactive.Moulder.load` method.
Parameters:
* fname : string
The name of the file to save the application. The extension doesn't
matter (use ``.pkl`` if in doubt).
"""
with open(fname, 'w') as f:
vertices = [numpy.asarray(p.xy) for p in self.polygons]
state = dict(area=self.area, x=self.x,
z=self.z, data=self.data,
density_range=self.density_range,
cmap=self.cmap,
predicted=self.predicted,
vertices=vertices,
densities=self.densities,
error=self.error)
pickle.dump(state, f)
@classmethod
[docs] def load(cls, fname):
"""
Restore an application from a pickle file.
The pickle file should have been generated by the
:meth:`~fatiando.gravmag.interactive.Moulder.save` method.
Parameters:
* fname : string
The name of the file.
Returns:
* app : Moulder object
The restored application. You can continue using it as if nothing
had happened.
"""
with open(fname) as f:
state = pickle.load(f)
app = cls(**state)
return app
@property
def model(self):
"""
The polygon model drawn as :class:`fatiando.mesher.Polygon` objects.
"""
m = [Polygon(p.xy, {'density': d})
for p, d in zip(self.polygons, self.densities)]
return m
[docs] def run(self):
"""
Start the application for drawing.
Will pop-up a window with a place for drawing the model (below) and a
place with the predicted (and, optionally, observed) data (top).
Follow the instruction on the figure title.
When done, close the window to resume program execution.
"""
fig = self._figure_setup()
# Sliders to control the density and the error in the data
self.density_slider = widgets.Slider(
fig.add_axes([0.10, 0.01, 0.30, 0.02]), 'Density',
self.density_range[0], self.density_range[1], valinit=0.,
valfmt='%6.0f kg/m3')
self.error_slider = widgets.Slider(
fig.add_axes([0.60, 0.01, 0.30, 0.02]), 'Error',
0, 5, valinit=self.error, valfmt='%1.2f mGal')
# Put instructions on figure title
self.dataax.set_title(self.instructions)
# Markers for mouse click events
self._ivert = None
self._ipoly = None
self._lastevent = None
self._drawing = False
self._xy = []
self._drawing_plot = None
# Used to blit the model plot and make
# rendering faster
self.background = None
# Connect event callbacks
self._connect()
self._update_data()
self._update_data_plot()
self.canvas.draw()
pyplot.show()
def _connect(self):
"""
Connect the matplotlib events to their callback methods.
"""
# Make the proper callback connections
self.canvas.mpl_connect('button_press_event',
self._button_press_callback)
self.canvas.mpl_connect('key_press_event',
self._key_press_callback)
self.canvas.mpl_connect('button_release_event',
self._button_release_callback)
self.canvas.mpl_connect('motion_notify_event',
self._mouse_move_callback)
self.canvas.mpl_connect('draw_event',
self._draw_callback)
# Call the cleanup and extra code for a draw event when resizing as
# well. This is needed so that tight_layout adjusts the figure when
# resized. Otherwise, tight_layout snaps only when the user clicks on
# the figure to do something.
self.canvas.mpl_connect('resize_event',
self._draw_callback)
self.density_slider.on_changed(self._set_density_callback)
self.error_slider.on_changed(self._set_error_callback)
[docs] def plot(self, figsize=(10, 8), dpi=70):
"""
Make a plot of the data and model for embedding in IPython notebooks
Doesn't require ``%matplotlib inline`` to embed the plot (as that would
not allow the app to run).
Parameters:
* figsize : list = (width, height)
The figure size in inches.
* dpi : float
The number of dots-per-inch for the figure resolution.
"""
fig = self._figure_setup(figsize=figsize, facecolor='white')
self._update_data_plot()
pyplot.close(fig)
data = print_figure(fig, dpi=dpi)
return Image(data=data)
def _figure_setup(self, **kwargs):
"""
Setup the plot figure with labels, titles, ticks, etc.
Sets the *canvas*, *dataax*, *modelax*, *polygons* and *lines*
attributes.
Parameters:
* kwargs : dict
Keyword arguments passed to ``pyplot.subplots``.
Returns:
* fig : matplotlib figure object
The created figure
"""
fig, axes = pyplot.subplots(2, 1, **kwargs)
ax1, ax2 = axes
self.predicted_line, = ax1.plot(self.x, self.predicted, '-r')
if self.data is not None:
self.data_line, = ax1.plot(self.x, self.data, '.k')
ax1.set_ylabel('Gravity anomaly (mGal)')
ax1.set_xlabel('x (m)', labelpad=-10)
ax1.set_xlim(self.area[:2])
ax1.set_ylim((-200, 200))
ax1.grid(True)
tmp = ax2.pcolor(numpy.array([self.density_range]), cmap=self.cmap)
tmp.set_visible(False)
pyplot.colorbar(tmp, orientation='horizontal',
pad=0.08, aspect=80).set_label(r'Density (kg/cm3)')
# Remake the polygons and lines to make sure they belong to the right
# axis coordinates
vertices = [p.xy for p in self.polygons]
newpolygons, newlines = [], []
for xy, dens in zip(vertices, self.densities):
poly, line = self._make_polygon(xy, dens)
newpolygons.append(poly)
newlines.append(line)
ax2.add_patch(poly)
ax2.add_line(line)
self.polygons = newpolygons
self.lines = newlines
ax2.set_xlim(self.area[:2])
ax2.set_ylim(self.area[2:])
ax2.grid(True)
ax2.invert_yaxis()
ax2.set_ylabel('z (m)')
fig.subplots_adjust(top=0.95, left=0.1, right=0.95, bottom=0.06,
hspace=0.1)
self.figure = fig
self.canvas = fig.canvas
self.dataax = axes[0]
self.modelax = axes[1]
fig.canvas.draw()
return fig
def _density2color(self, density):
"""
Map density values to colors using the given *cmap* attribute.
Parameters:
* density : 1d-array
The density values of the model polygons
Returns
* colors : 1d-array
The colors mapped to each density value (returned by a matplotlib
colormap object.
"""
dmin, dmax = self.density_range
return self.cmap((density - dmin)/(dmax - dmin))
def _make_polygon(self, vertices, density):
"""
Create a polygon for drawing.
Polygons are matplitlib.patches.Polygon objects for the fill and
matplotlib.lines.Line2D for the contour.
Parameters:
* vertices : list of [x, z]
List of the [x, z] coordinate pairs of each vertex of the polygon
* density : float
The density of the polygon (used to set the color)
Returns:
* polygon, line
The matplotlib Polygon and Line2D objects
"""
poly = patches.Polygon(vertices, animated=False, alpha=0.9,
color=self._density2color(density))
x, y = zip(*poly.xy)
line = Line2D(x, y, **self.line_args)
return poly, line
def _update_data(self):
"""
Recalculate the predicted data (optionally with random error)
"""
self.predicted = talwani.gz(self.x, self.z, self.model)
if self.error > 0:
self.predicted = utils.contaminate(self.predicted, self.error)
def _update_data_plot(self):
"""
Update the predicted data plot in the *dataax*.
Adjusts the xlim of the axes to fit the data.
"""
self.predicted_line.set_ydata(self.predicted)
vmin = 1.2*min(self.predicted.min(), self.dmin)
vmax = 1.2*max(self.predicted.max(), self.dmax)
self.dataax.set_ylim(vmin, vmax)
self.dataax.grid(True)
self.canvas.draw()
def _draw_callback(self, value):
"""
Callback for the canvas.draw() event.
This is called everytime the figure is redrawn. Used to do some
clean up and tunning whenever this is called as well, like calling
``tight_layout``.
"""
self.figure.tight_layout()
def _set_error_callback(self, value):
"""
Callback when error slider is edited
"""
self.error = value
self._update_data()
self._update_data_plot()
def _set_density_callback(self, value):
"""
Callback when density slider is edited
"""
if self._ipoly is not None:
self.densities[self._ipoly] = value
self.polygons[self._ipoly].set_color(self._density2color(value))
self._update_data()
self._update_data_plot()
self.canvas.draw()
def _get_polygon_vertice_id(self, event):
"""
Find out which vertex of which polygon the event happened in.
If the click was inside a polygon (not on a vertex), identify that
polygon.
Returns:
* p, v : int, int
p: the index of the polygon the event happened in or None if
outside all polygons.
v: the index of the polygon vertex that was clicked or None if the
click was not on a vertex.
"""
distances = []
indices = []
for poly in self.polygons:
x, y = poly.get_transform().transform(poly.xy).T
d = numpy.sqrt((x - event.x)**2 + (y - event.y)**2)
distances.append(d.min())
indices.append(numpy.argmin(d))
p = numpy.argmin(distances)
if distances[p] >= self.epsilon:
# Check if the event was inside a polygon
x, y = event.x, event.y
p, v = None, None
for i, poly in enumerate(self.polygons):
if poly.contains_point([x, y]):
p = i
break
else:
v = indices[p]
last = len(self.polygons[p].xy) - 1
if v == 0 or v == last:
v = [0, last]
return p, v
def _button_press_callback(self, event):
"""
What actions to perform when a mouse button is clicked
"""
if event.inaxes != self.modelax:
return
if event.button == 1 and not self._drawing and self.polygons:
self._lastevent = event
for line, poly in zip(self.lines, self.polygons):
poly.set_animated(False)
line.set_animated(False)
line.set_color([0, 0, 0, 0])
self.canvas.draw()
# Find out if a click happened on a vertice
# and which vertice of which polygon
self._ipoly, self._ivert = self._get_polygon_vertice_id(event)
if self._ipoly is not None:
self.density_slider.set_val(self.densities[self._ipoly])
self.polygons[self._ipoly].set_animated(True)
self.lines[self._ipoly].set_animated(True)
self.lines[self._ipoly].set_color([0, 1, 0, 0])
self.canvas.draw()
self.background = self.canvas.copy_from_bbox(self.modelax.bbox)
self.modelax.draw_artist(self.polygons[self._ipoly])
self.modelax.draw_artist(self.lines[self._ipoly])
self.canvas.blit(self.modelax.bbox)
elif self._drawing:
if event.button == 1:
self._xy.append([event.xdata, event.ydata])
self._drawing_plot.set_data(zip(*self._xy))
self.canvas.restore_region(self.background)
self.modelax.draw_artist(self._drawing_plot)
self.canvas.blit(self.modelax.bbox)
elif event.button == 3:
if len(self._xy) >= 3:
density = self.density_slider.val
poly, line = self._make_polygon(self._xy, density)
self.polygons.append(poly)
self.lines.append(line)
self.densities.append(density)
self.modelax.add_patch(poly)
self.modelax.add_line(line)
self._drawing_plot.remove()
self._drawing_plot = None
self._xy = None
self._drawing = False
self._ipoly = len(self.polygons) - 1
self.lines[self._ipoly].set_color([0, 1, 0, 0])
self.dataax.set_title(self.instructions)
self.canvas.draw()
self._update_data()
self._update_data_plot()
def _button_release_callback(self, event):
"""
Reset place markers on mouse button release
"""
if event.inaxes != self.modelax:
return
if event.button != 1:
return
if self._ivert is None and self._ipoly is None:
return
self.background = None
for line, poly in zip(self.lines, self.polygons):
poly.set_animated(False)
line.set_animated(False)
self.canvas.draw()
self._ivert = None
# self._ipoly is only released when clicking outside
# the polygons
self._lastevent = None
self._update_data()
self._update_data_plot()
def _key_press_callback(self, event):
"""
What to do when a key is pressed on the keyboard.
"""
if event.inaxes is None:
return
if event.key == 'd':
if self._drawing and self._xy:
self._xy.pop()
if self._xy:
self._drawing_plot.set_data(zip(*self._xy))
else:
self._drawing_plot.set_data([], [])
self.canvas.restore_region(self.background)
self.modelax.draw_artist(self._drawing_plot)
self.canvas.blit(self.modelax.bbox)
elif self._ivert is not None:
poly = self.polygons[self._ipoly]
line = self.lines[self._ipoly]
if len(poly.xy) > 4:
verts = numpy.atleast_1d(self._ivert)
poly.xy = numpy.array([xy for i, xy in enumerate(poly.xy)
if i not in verts])
line.set_data(zip(*poly.xy))
self._update_data()
self._update_data_plot()
self.canvas.restore_region(self.background)
self.modelax.draw_artist(poly)
self.modelax.draw_artist(line)
self.canvas.blit(self.modelax.bbox)
self._ivert = None
elif self._ipoly is not None:
self.polygons[self._ipoly].remove()
self.lines[self._ipoly].remove()
self.polygons.pop(self._ipoly)
self.lines.pop(self._ipoly)
self.densities.pop(self._ipoly)
self._ipoly = None
self.canvas.draw()
self._update_data()
self._update_data_plot()
elif event.key == 'n':
self._ivert = None
self._ipoly = None
for line, poly in zip(self.lines, self.polygons):
poly.set_animated(False)
line.set_animated(False)
line.set_color([0, 0, 0, 0])
self.canvas.draw()
self.background = self.canvas.copy_from_bbox(self.modelax.bbox)
self._drawing = True
self._xy = []
self._drawing_plot = Line2D([], [], **self.line_args)
self._drawing_plot.set_animated(True)
self.modelax.add_line(self._drawing_plot)
self.dataax.set_title(' | '.join([
'left click: set vertice', 'right click: finish',
'esc: cancel']))
self.canvas.draw()
elif event.key == 'escape':
self._drawing = False
self._xy = []
if self._drawing_plot is not None:
self._drawing_plot.remove()
self._drawing_plot = None
for line, poly in zip(self.lines, self.polygons):
poly.set_animated(False)
line.set_animated(False)
line.set_color([0, 0, 0, 0])
self.canvas.draw()
def _mouse_move_callback(self, event):
"""
Handle things when the mouse move.
"""
if event.inaxes != self.modelax:
return
if event.button != 1:
return
if self._ivert is None and self._ipoly is None:
return
x, y = event.xdata, event.ydata
p = self._ipoly
v = self._ivert
if self._ivert is not None:
self.polygons[p].xy[v] = x, y
else:
dx = x - self._lastevent.xdata
dy = y - self._lastevent.ydata
self.polygons[p].xy[:, 0] += dx
self.polygons[p].xy[:, 1] += dy
self.lines[p].set_data(zip(*self.polygons[p].xy))
self._lastevent = event
self.canvas.restore_region(self.background)
self.modelax.draw_artist(self.polygons[p])
self.modelax.draw_artist(self.lines[p])
self.canvas.blit(self.modelax.bbox)
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