Math Utilities¶

Useful math functions for LWA work.

lsl.misc.mathutils.cimag(cmplx)¶: Return the imaginary rectilinear component from complex values expressed in polar form (magnitude, phase).

lsl.misc.mathutils.cmagnitude(cmplx)¶: Return the polar magnitudes of complex values.

lsl.misc.mathutils.cphase(cmplx)¶: Return the polar phases of complex values as radians.

lsl.misc.mathutils.cpolar(cmplx)¶: Return the polar (magnitude, phase) representation of complex values (real, imaginary). The return value is an array of shape (N,2), where N is the length of the cmplx input array.

lsl.misc.mathutils.creal(cmplx)¶: Return the real rectilinear component from complex values expressed in polar form (magnitude, phase).

lsl.misc.mathutils.crect(cmplx)¶: Return the rectilinear (real, imaginary) representation of complex values (magnitude, phase).

lsl.misc.mathutils.downsample(vector, factor, rescale=True)¶: Downsample (i.e. co-add consecutive numbers) a vector by an integer factor. Trims the input timeseries to be a multiple of the downsample factor, if needed. If rescale == True, then divides each sum by factor to produce a mean value, otherwise just adds the values in the vector.

lsl.misc.mathutils.from_dB(dB)¶: Convert from decibels to linear units.

lsl.misc.mathutils.gaussian1d(height, center, width)¶

Return a function that generates a 1-D gaussian with the specified height, mean, and standard deviation.

Example: >>> height = 1 >>> center = 5.0 >>> width = 2.1 >>> gauFnc = guassian1d(height, center, width) >>> value = gauFnc(numpy.arange(0, 100))

Based on: http://code.google.com/p/agpy/source/browse/trunk/agpy/gaussfitter.py

lsl.misc.mathutils.gaussian2d(height, centerX, centerY, widthMaj, widthMin, angle=0.0)¶

Return a function that generates a 2-D gaussian with the specified height, mean (for both X and Y), standard deviation (for both major and minor axes), and rotation angle from the X axis in degrees.

Based on: http://code.google.com/p/agpy/source/browse/trunk/agpy/gaussfitter.py

lsl.misc.mathutils.gaussparams(data, x=None, y=None)¶: Estimate the parameters (height, center, width) for a gaussian. The return order is:

1-D: height, center, width 2-D: height, center x, center y, width x, width y, position angle

Note

The 2-D fits always return a position angle of zero since the routine decomposes the process into two 1-D fits.

lsl.misc.mathutils.ndft(t, x)¶: Given a list of times and a list of data values, compute a non-uniform discrete Fourier transform (NDFT) of the data. Returns a two element tuple of frequency and the complex NDFT result.

lsl.misc.mathutils.regrid(x, y, newx, allow_extrapolation=False, method='spline')¶

Regrid data from x,y onto newx. If allow_extrapolation is True, extrapolation is attempted if the method supports it. Supported methods are:

linear

spline

Use of this function may require the scipy extension package.

lsl.misc.mathutils.smooth(x, window_len=10, window='hanning')¶

Smooth the data using a window with requested size. Stolen from SciPy Cookbook at http://www.scipy.org/Cookbook/SignalSmooth

This method is based on the convolution of a scaled window with the signal. The signal is prepared by introducing reflected copies of the signal (with the window size) in both ends so that transient parts are minimized in the begining and end part of the output signal.

Input:

x: the input signal
window_len: the dimension of the smoothing window
window: the type of window from ‘flat’, ‘hanning’, ‘hamming’,
‘bartlett’, ‘blackman’ flat window will produce a moving average smoothing.

Output:

the smoothed signal

Example:

>>> from numpy import *
>>> t=linspace(-2,2,0.1)
>>> x=sin(t)+randn(len(t))*0.1
>>> y=smooth(x)