#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Python module containing detrend methods.
:copyright:
The ObsPy Development Team (devs@obspy.org)
:license:
GNU Lesser General Public License, Version 3
(https://www.gnu.org/copyleft/lesser.html)
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
from future.builtins import * # NOQA
import numpy as np
from scipy.interpolate import LSQUnivariateSpline
[docs]def simple(data):
"""
Detrend signal simply by subtracting a line through the first and last
point of the trace
:param data: Data to detrend, type numpy.ndarray.
:return: Detrended data. Returns the original array which has been
modified in-place if possible but it might have to return a copy in
case the dtype has to be changed.
"""
# Convert data if it's not a floating point type.
if not np.issubdtype(data.dtype, np.floating):
data = np.require(data, dtype=np.float64)
ndat = len(data)
x1, x2 = data[0], data[-1]
data -= x1 + np.arange(ndat) * (x2 - x1) / float(ndat - 1)
return data
[docs]def _plotting_helper(data, fit, plot):
import matplotlib.pyplot as plt
fig, axes = plt.subplots(2, 1, figsize=(8, 5))
plt.subplots_adjust(hspace=0)
axes[0].plot(data, color="k", label="Original Data")
axes[0].plot(fit, color="red", lw=2, label="Fitted Trend")
axes[0].legend(loc="best")
axes[0].label_outer()
axes[0].set_yticks(axes[0].get_yticks()[1:])
axes[1].plot(data - fit, color="k", label="Result")
axes[1].legend(loc="best")
axes[1].label_outer()
axes[1].set_yticks(axes[1].get_yticks()[:-1])
axes[1].set_xlabel("Samples")
plt.tight_layout(h_pad=0)
if plot is True:
plt.show()
else:
plt.savefig(plot)
plt.close(fig)
[docs]def polynomial(data, order, plot=False):
"""
Removes a polynomial trend from the data.
:param data: The data to detrend. Will be modified in-place.
:type data: :class:`numpy.ndarray`
:param order: The order of the polynomial to fit.
:type order: int
:param plot: If True, a plot of the operation happening will be shown.
If a string is given that plot will be saved to the given file name.
:type plot: bool or str
.. note::
In a real world application please make sure to use the convenience
:meth:`obspy.core.trace.Trace.detrend` method.
.. rubric:: Example
>>> import obspy
>>> from obspy.signal.detrend import polynomial
Prepare some example data.
>>> tr = obspy.read()[0].filter("highpass", freq=2)
>>> tr.data += 6000 + 4 * tr.times() ** 2
>>> tr.data -= 0.1 * tr.times() ** 3 + 0.00001 * tr.times() ** 5
>>> data = tr.data
Remove the trend.
>>> polynomial(data, order=3, plot=True) # doctest: +SKIP
.. plot::
import obspy
from obspy.signal.detrend import polynomial
tr = obspy.read()[0].filter("highpass", freq=2)
tr.data += 6000 + 4 * tr.times() ** 2 - 0.1 * tr.times() ** 3 - \
0.00001 * tr.times() ** 5
polynomial(tr.data, order=3, plot=True)
"""
# Convert data if it's not a floating point type.
if not np.issubdtype(data.dtype, np.floating):
data = np.require(data, dtype=np.float64)
x = np.arange(len(data))
fit = np.polyval(np.polyfit(x, data, deg=order), x)
if plot:
_plotting_helper(data, fit, plot)
data -= fit
return data
[docs]def spline(data, order, dspline, plot=False):
"""
Remove a trend by fitting splines.
:param data: The data to detrend. Will be modified in-place.
:type data: :class:`numpy.ndarray`
:param order: The order/degree of the smoothing spline to fit.
Must be 1 <= order <= 5.
:type order: int
:param dspline: The distance in samples between two spline nodes.
:type dspline: int
:param plot: If True, a plot of the operation happening will be shown.
If a string is given that plot will be saved to the given file name.
:type plot: bool or str
.. note::
In a real world application please make sure to use the convenience
:meth:`obspy.core.trace.Trace.detrend` method.
.. rubric:: Example
>>> import obspy
>>> from obspy.signal.detrend import spline
Prepare some example data.
>>> tr = obspy.read()[0].filter("highpass", freq=2)
>>> tr.data += 6000 + 4 * tr.times() ** 2
>>> tr.data -= 0.1 * tr.times() ** 3 + 0.00001 * tr.times() ** 5
>>> data = tr.data
Remove the trend.
>>> spline(data, order=2, dspline=1000, plot=True) # doctest: +SKIP
.. plot::
import obspy
from obspy.signal.detrend import spline
tr = obspy.read()[0].filter("highpass", freq=2)
tr.data += 6000 + 4 * tr.times() ** 2 - 0.1 * tr.times() ** 3 - \
0.00001 * tr.times() ** 5
spline(tr.data, order=2, dspline=1000, plot=True)
"""
# Convert data if it's not a floating point type.
if not np.issubdtype(data.dtype, np.floating):
data = np.require(data, dtype=np.float64)
x = np.arange(len(data))
splknots = np.arange(dspline / 2.0, len(data) - dspline / 2.0 + 2,
dspline)
spl = LSQUnivariateSpline(x=x, y=data, t=splknots, k=order)
fit = spl(x)
if plot:
_plotting_helper(data, fit, plot)
data -= fit
return data
if __name__ == '__main__':
import doctest
doctest.testmod(exclude_empty=True)