| | |
- appromatrix(matrix, s, sparse=None, testing=False, verbose=False)
- Returns an approximate (sparse) matrix.
Parameters:
-----------
matrix : a 2d numpy array holding the transition matrix
s : a cutoff value for the column sum in the interval ]0.0; 1.0]
At least one value per column will always be kept.
sparse : output format for the approximated matrix
See sparse matrix classes in the scipy.sparse documentation.
The most frequent will be:
- "csc" (compressed column; fast calculations)
- "lil" (list of lists; strong compression)
Defaults to None, i.e. no sparse format applied
testing : execute efficiency test and an accuracy test
If True, the function gives out a tuple of values instead of just the
matrix: (matrix, efficiency ratio, accuracy p-value)
verbose : boolean
If True, print out intermediate results of the approximation process
Returns:
--------
sparsematrix : 2d scipy sparse array or 2d numpy array
The approximate matrix, optionally in a sparse format.
If testing is True:
sparsematrix : 2d scipy sparse array or 2d numpy array
The approximate matrix, optionally in a sparse format.
efficiency: float
One minus sparse matrix to original matrix bytesize ratio.
p_value: float
P-value of a G-test on the eigenvectors of the sparse vs. original
matrix. SciPy's own G-test function is used from SciPy version 0.13.0
upwards.
- eigenone(matrix, alg='linalg', throwex=False, verbose=False)
- Returns the eigenvector corresponding to a single maximal eigenvalue of
one of a matrix.
Parameters:
-----------
matrix : a 2d numpy array or a 2d scipy sparse array
alg : string, an algorithm to calculate the vector.
Either "linalg" for using LAPACK (numpy matrix) or ARPACK (sparse
matrix), or "power" for the power method (accuracy = 1e-15).
throwex : boolean
If true, throw exception in case of bad behavior of the function.
For the power method, this occurs when there is no convergence after
100 steps; for the linalg method, this occurs if the maximal
eigenvalue of the matrix is not single or not equal to 1.0.
If false, there will only be a printed warning.
verbose : boolean
If true, diagnostic intermediate results will be printed out.
Note:
-----
It will not be checked previously if the matrix actually has a single
maximal eigenvalue of one. If in doubt, use the "linalg" algorithm
and turn on the "throwex" option.
Returns:
--------
vector : 1d numpy array
The eigenvector corresponding to a single (= of multiplicity one)
maximal eigenvalue of one of a matrix.
Warning:
--------
This function automatically returns the normalized absolute of the
desired eigenvector. Small negative values may arise due to numerical
errors (see LAPACK/ARPACK documentation).
- histo3d(matrix, visualize=False, axes=None, scaling=None, statenames=None, spacing=0.1, angle=[20, 12], *args, **kwargs)
- Create a 3d histogram of a 2d numpy array.
Parameters:
-----------
matrix : a 2d numpy array holding the transition matrix
visualize: boolean
If True, the resulting diagram will be shown directly.
axes : an axes object to draw to; None means drawing to current axes.
scaling : a scaling applied to all values in the matrix
========== =============== =========================================
value range description
========== =============== =========================================
None (0,1) no scaling, values are taken as they are
"log10" (-inf, 0) log10 scaling on the values
"-log10" (0, +inf) negative log10 scaling on the values
"logit" (-inf, +inf) logit scaling on the values
========== =============== =========================================
statenames : labels for the states
========== =============== =========================================
value range description
========== =============== =========================================
None (0, n-1) python array indexes
"1N" (1, n) count index of each state
[...] list of stings empty list : print no statenames
========== =============== =========================================
spacing : float, half distance between bars
angle : tuple of numbers, viewing angle (azimut, elevation)
Plus any arguments which can be used on Axes3D bar3d objects.
Returns:
--------
axes : matplotlib 3d axes object
Matrix columns are displayed on the y-axis, rows on the x-axis.
Warning:
--------
As per version 1.3.1, the 3D plotting function in matplotlib has a bug
which results in an incorrect display of the bars at certain viewing
angles (wrong plotting order). This also produces a runtime warning
("invalid value encountered in divide for n in normals"). Please
ignore the warning and use the "angle" argument to find a correct
display angle.
- histogrid(matrix, visualize=False, axes=None, scaling=None, statenames=None, *args, **kwargs)
- Create a color coded 2d histogram of a 2d numpy array.
Parameters:
-----------
matrix : a 2d numpy array holding the transition matrix
visualize: boolean
If True, the resulting diagram will be shown directly.
axes : an axes object to draw to; None means drawing to current axes.
scaling : a scaling applied to all values in the matrix
========== =============== =========================================
value range description
========== =============== =========================================
None (0,1) no scaling, values are taken as they are
"log10" (-inf, 0) log10 scaling on the values
"-log10" (0, +inf) negative log10 scaling on the values
"logit" (-inf, +inf) logit scaling on the values
========== =============== =========================================
statenames : labels for the states
========== =============== =========================================
value range description
========== =============== =========================================
None (0, n-1) python array indexes
"1N" (1, n) count index of each state
[...] list of stings empty list : print no statenames
========== =============== =========================================
Plus any arguments the matplotlib.pyplot.imshow() function would take.
Returns:
--------
axes : matplotlib axes object
The default colormap is greyscale with increasing luminosity - see
comments at matplotlib.pyplot.colormaps() for more information about
using color in scientific illustrations.
- loadmatrix(filepath=None, loadnames=False, comments=None, verbose=False)
- Ask for a filepath and import matrix from there.
Parameters:
-----------
filepath : string
Optional, gives the path (incl. filename) of a tab-delimited
.txt-like matrix file;has to be entered in a prompt if not provided
in the function call.
loadnames : boolean
Optional, wether or not to read in statenames from the first line of
the matrix file
comments : string
Optional, set a character which turns the following text into a
comment; text lines marked as comment will not be imported
verbose : boolean
If True, print out status messages & intermediate results
Returns:
--------
matrix : a 2d numpy array with datatype float
If the upper left cell of the input file holds "#", row and column
names are cut off automatically.
If loadnames is True, matrix and names are returned as a tuple:
matrix : a 2d numpy array with datatype float
Without row and column names.
statenames : a list
Reads out the column names in the input file.
- networkplot(matrix, visualize=False, axes=None, mode='', special=[0, 1], openout=True, *args, **kwargs)
- Customizable network display of a matrix.
Parameters:
-----------
matrix : a 2d numpy array holding the transition matrix
visualize: boolean
If True, the resulting diagram will be shown directly.
axes : an axes object to draw to; None means drawing to current axes.
mode: different ways to display the data; combine from I & II:
================ =============================================================================
value description
================ =============================================================================
I. edges are drawn:
"mp_neighbor" from each node to its most probable neighbor(s)
"mp_path" along the most probable path from the first "special" node to the second
"percolation" according to a percolation threshold set via "special"
"eachedge" all edges are drawn if none of three options above are specified
"noedge" overrides edge drawing
II. nodes are colored according to:
"p_eig" their probability to be occupied during an infinite run (power method)
"p_stay" the probability to stay at them for the next time step
"p_out" the probability to move out of them at the next time step
"p_in_raw" the probability to arrive at them from anywhere else with equal probability
"p_in_inf" the average probability to arrive at them during an infinite run
"btw_cent" their value of betweenness-centrality
"d_in" their degree of incoming edges
"d_out" their degree of outgoing edges
"d_all" their degree counting edges in both directions
"special" wether they are the special nodes (orange) or not (70% grey)
"t_spec" the expected time to a special state
"nonode" overrides node drawing
================ =============================================================================
special : a list of two nodes specified by their indices in the matrix
This list will be used as the source and target for the "percolation threshold" and
"shortest path" algorithms.
statenames : a list of labels
Alias for networkx labels.
openout : boolean
If true, plotting is performed as a block, if false the components
are returned one by one (more convenient for making legends).
Plus any arguments the networkx.draw_networkx() function would take.
Returns:
--------
nodes : matplotlib artist or False
The network nodes.
edges : matplotlib artist(s) or False
The network edges.
labels : matplotlib artist or False
The labels.
if open is False:
axes : matplotlib axes object
Nodelabeling and axis plotting is turned off per default.
- percolation(matrix, source, target, verbose=False)
- Returns a graph where percolation is just possible between source and
target.
Parameters:
-----------
matrix : a 2d numpy array holding the transition matrix
source : a node, given by its index in the matrix
target : a node, given by its index in the matrix
verbose : print out percentage of edges retained & minimal edge weight
Returns:
--------
graph : networkx graph object
Contains all nodes, but only edges whose weight is above the
percolation threshold defined by the two nodes provided. This also
works correctly if source and target node are identical.
- testvectors(original, fake, ignorext=True, verbose=False)
- G-test comparing two vectors.
Parameters:
-----------
original : 1D numpy array
Distribution against which the test will be performed
fake : 1D numpy array
Distribution to be tested
ignorext : boolean
Ignore zeros and negative values in the vector and compare only
positive vector entries
verbose : boolean
If True, print out the summands for the G-statistic
Returns:
--------
g_value : float
The value of G
p_value : float
P-value of the G-test
Note:
------
Compare the scipy.stats.power_divergence() function in scipy >= 0.13.0
for a better implementation. P-values for G are determined on a
chi-squared distribution.
|