multipletau reference¶
General¶
This package provides a multiple-τ algorithm for Python 2.7 and
Python 3.x and requires the package numpy
.
Multipe-τ correlation is computed on a logarithmic scale (less
data points are computed) and is thus much faster than conventional
correlation on a linear scale such as numpy.correlate()
.
Recommended literature¶
- Klaus Schaetzel and Rainer Peters; Noise on multiple-tau photon correlation data. Proc. SPIE 1430, Photon Correlation Spectroscopy: Multicomponent Systems, 109 (June 1, 1991); http://doi.org/10.1117/12.44160
- Thorsten Wohland, Rudolf Rigler, and Horst Vogel; The Standard Deviation in Fluorescence Correlation Spectroscopy. Biophysical Journal, 80 (June 1, 2001); http://dx.doi.org/10.1016/S0006-3495(01)76264-9
Obtaining multipletau¶
If you have Python and numpy
installed, simply run
pip install multipletau
The source code of multipletau is available at https://github.com/FCS-analysis/multipletau.
Citing multipletau¶
The multipletau package should be cited like this (replace “x.x.x” with the actual version of multipletau that you used and “DD Month YYYY” with a matching date).
cite
Paul Müller (2012) Python multiple-tau algorithm (Version x.x.x) [Computer program]. Available at https://pypi.python.org/pypi/multipletau/ (Accessed DD Month YYYY)
You can find out what version you are using by typing (in a Python console):
>>> import multipletau
>>> multipletau.__version__
'0.1.4'
Usage¶
The package is straightforward to use. Here is a quick example:
>>> import numpy as np
>>> import multipletau
>>> a = np.linspace(2,5,42)
>>> v = np.linspace(1,6,42)
>>> multipletau.correlate(a, v, m=2)
array([[ 1. , 549.87804878],
[ 2. , 530.37477692],
[ 4. , 491.85812017],
[ 8. , 386.39500297]])
Methods¶
Summary:
autocorrelate (a[, m, deltat, normalize, ...]) |
Autocorrelation of a 1-dimensional sequence on a log2-scale. |
correlate (a, v[, m, deltat, normalize, ...]) |
Cross-correlation of two 1-dimensional sequences on a log2-scale. |
correlate_numpy (a, v[, deltat, normalize, ...]) |
Convenience function that wraps around numpy.correlate and returns the data as multipletau.correlate does. |
For a quick overview, see Index.
Autocorrelation¶
-
multipletau.
autocorrelate
(a, m=16, deltat=1, normalize=False, copy=True, dtype=None)[source]¶ Autocorrelation of a 1-dimensional sequence on a log2-scale.
This computes the correlation according to
numpy.correlate()
for positive \(k\) on a base 2 logarithmic scale.numpy.correlate(a, a, mode="full")[len(a)-1:]()
\(z_k = \Sigma_n a_n a_{n+k}\)
Note that only the correlation in the positive direction is computed.
Parameters: a : array_like
input sequence of real numbers
m : even integer
defines the number of points on one level, must be an even integer
deltat : float
distance between bins
normalize : bool
normalize the result to the square of the average input signal and the factor M-k.
copy : bool
copy input array, set to False to save memory
dtype : dtype, optional
The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of a is used.
Returns: autocorrelation : ndarray
Nx2 array containing lag time and autocorrelation
Notes
The algorithm computes the correlation with the convention of the curve decaying to zero.
For experiments like e.g. fluorescence correlation spectroscopy, the signal can be normalized to M-k by invoking:
normalize = TrueFor emulating the numpy.correlate behavior on a logarithmic scale (default behavior) use:
normalize = FalseExamples
>>> from numpy import dtype >>> from multipletau import autocorrelate >>> autocorrelate(range(42), m=2, dtype=dtype(float)) array([[ 1.00000000e+00, 2.29600000e+04], [ 2.00000000e+00, 2.21000000e+04], [ 4.00000000e+00, 2.03775000e+04], [ 8.00000000e+00, 1.50612000e+04]])
Cross-correlation¶
-
multipletau.
correlate
(a, v, m=16, deltat=1, normalize=False, copy=True, dtype=None)[source]¶ Cross-correlation of two 1-dimensional sequences on a log2-scale.
This computes the cross-correlation according to
numpy.correlate()
for positive \(k\) on a base 2 logarithmic scale.numpy.correlate(a, v, mode=”full”)[len(a)-1:]
\(z_k = \Sigma_n a_n v_{n+k}\)
Note that only the correlation in the positive direction is computed.
Parameters: a, v : array_like
input sequences with equal length
m : even integer
defines the number of points on one level, must be an even integer
deltat : float
distance between bins
normalize : bool
normalize the result to the square of the average input signal and the factor M-k.
copy : bool
copy input array, set to False to save memory
dtype : dtype, optional
The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of a is used.
Returns: crosscorrelation : ndarray
Nx2 array containing lag time and cross-correlation
Notes
The algorithm computes the correlation with the convention of the curve decaying to zero.
For experiments like e.g. fluorescence correlation spectroscopy, the signal can be normalized to M-k by invoking:
normalize = TrueFor emulating the numpy.correlate behavior on a logarithmic scale (default behavior) use:
normalize = FalseExamples
>>> from numpy import dtype >>> from multipletau import correlate >>> correlate(range(42), range(1,43), m=2, dtype=dtype(float)) array([[ 1.00000000e+00, 2.38210000e+04], [ 2.00000000e+00, 2.29600000e+04], [ 4.00000000e+00, 2.12325000e+04], [ 8.00000000e+00, 1.58508000e+04]])
Cross-correlation (NumPy)¶
-
multipletau.
correlate_numpy
(a, v, deltat=1, normalize=False, dtype=None, copy=True)[source]¶ Convenience function that wraps around numpy.correlate and returns the data as multipletau.correlate does.
Parameters: a, v : array_like
input sequences
deltat : float
distance between bins
normalize : bool
normalize the result to the square of the average input signal and the factor (M-k). The resulting curve follows the convention of decaying to zero for large lag times.
copy : bool
copy input array, set to False to save memory
dtype : dtype, optional
The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of a is used.
Returns: crosscorrelation : ndarray
Nx2 array containing lag time and cross-correlation
Examples¶
Comparison of correlation methods¶
Illustration of the difference between
multipletau.correlate()
and numpy.correlate()
.

Download the
full example
.