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additional_utilities.html
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<div class="section" id="additional-utilities">
<span id="id1"></span><h1>Additional utilities<a class="headerlink" href="#additional-utilities" title="Permalink to this headline">¶</a></h1>
<p>MDP offers some additional utilities of general interest
in the <code class="docutils literal"><span class="pre">mdp.utils</span></code> module. Refer to the
<a class="reference external" href="https://mdp-toolkit.github.io/docs/api/index.html">API</a>
for the full documentation and interface description.</p>
<dl class="docutils">
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils.CovarianceMatrix-class.html">mdp.utils.CovarianceMatrix</a></dt>
<dd><p class="first">This class stores an empirical covariance matrix that can be updated
incrementally. A call to the <code class="docutils literal"><span class="pre">fix</span></code> method returns the current state
of the covariance matrix, the average and the number of observations,
and resets the internal data.</p>
<p class="last">Note that the internal sum is a standard <code class="docutils literal"><span class="pre">__add__</span></code> operation. We are not
using any of the fancy sum algorithms to avoid round off errors when
adding many numbers. If you want to contribute a <code class="docutils literal"><span class="pre">CovarianceMatrix</span></code>
class that uses such algorithms we would be happy to include it in
MDP. For a start see the <a class="reference external" href="http://code.activestate.com/recipes/393090/">Python recipe</a>
by Raymond Hettinger. For a
review about floating point arithmetic and its pitfalls see
<em>What every computer scientist should know about floating-point
arithmetic</em> by David Goldberg, ACM Computing Surveys, Vol 23, No
1, March 1991.</p>
</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils.VartimeCovarianceMatrix-class.html">mdp.utils.VartimeCovarianceMatrix</a></dt>
<dd><p class="first">This class stores an empirical covariance matrix that can be updated
incrementally. A call to the <code class="docutils literal"><span class="pre">fix</span></code> method returns the current state
of the covariance matrix, the average and the number of observations,
and resets the internal data.</p>
<p class="last">As compared to the <code class="docutils literal"><span class="pre">CovarianceMatrix</span></code> class, this class accepts sampled
input in conjunction with a non-constant time increment between samples.
The covariance matrix is then computed as a (centered) scalar product
between functions, that is sampled unevenly, using the trapezoid rule.</p>
</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils.DelayCovarianceMatrix-class.html">mdp.utils.DelayCovarianceMatrix</a></dt>
<dd>This class stores an empirical covariance matrix between the signal and
time delayed signal that can be updated incrementally.</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils.MultipleCovarianceMatrices-class.html">mdp.utils.MultipleCovarianceMatrices</a></dt>
<dd>Container class for multiple covariance matrices to easily
execute operations on all matrices at the same time.</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#dig_node">mdp.utils.dig_node</a> (node)</dt>
<dd>Crawl recursively an MDP <code class="docutils literal"><span class="pre">Node</span></code> looking for arrays.
Return (dictionary, string), where the dictionary is:
{ attribute_name: (size_in_bytes, array_reference)}
and string is a nice string representation of it.</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#get_node_size">mdp.utils.get_node_size</a> (node)</dt>
<dd>Get <code class="docutils literal"><span class="pre">node</span></code> total byte-size using <code class="docutils literal"><span class="pre">cPickle</span></code> with protocol=2.
(The byte-size is related the memory needed by the node).</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#progressinfo">mdp.utils.progressinfo</a> (sequence, length, style, custom)</dt>
<dd><p class="first">A fully configurable text-mode progress info box tailored to the
command-line die-hards.
To get a progress info box for your loops use it like this:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">progressinfo</span><span class="p">(</span><span class="n">sequence</span><span class="p">):</span>
<span class="gp">... </span> <span class="n">do_something</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
</pre></div>
</div>
<p>You can also use it with generators, files or any other iterable object,
but in this case you have to specify the total length of the sequence:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">progressinfo</span><span class="p">(</span><span class="n">open_file</span><span class="p">,</span> <span class="n">nlines</span><span class="p">):</span>
<span class="gp">... </span> <span class="n">do_something</span><span class="p">(</span><span class="n">line</span><span class="p">)</span>
</pre></div>
</div>
<p>A few examples of the available layouts:</p>
<div class="last highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span><span class="o">===================================</span><span class="mi">73</span><span class="o">%==============>...................</span><span class="p">]</span>
<span class="n">Progress</span><span class="p">:</span> <span class="mi">67</span><span class="o">%</span><span class="p">[</span><span class="o">======================================></span> <span class="p">]</span>
<span class="mi">23</span><span class="o">%</span> <span class="p">[</span><span class="mi">02</span><span class="p">:</span><span class="mi">01</span><span class="p">:</span><span class="mi">28</span><span class="p">]</span> <span class="o">-</span> <span class="p">[</span><span class="mi">00</span><span class="p">:</span><span class="mi">12</span><span class="p">:</span><span class="mi">37</span><span class="p">]</span>
</pre></div>
</div>
</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils.QuadraticForm-class.html">mdp.utils.QuadraticForm</a></dt>
<dd>Define an inhomogeneous quadratic form as <code class="docutils literal"><span class="pre">1/2</span> <span class="pre">x'Hx</span> <span class="pre">+</span> <span class="pre">f'x</span> <span class="pre">+</span> <span class="pre">c</span></code>.
This class implements the quadratic form analysis methods
presented in:
Berkes, P. and Wiskott, L. On the analysis and interpretation
of inhomogeneous quadratic forms as receptive fields. <em>Neural
Computation</em>, 18(8): 1868-1895. (2006).</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#refcast">mdp.utils.refcast</a> (array, dtype)</dt>
<dd>Cast the array to <code class="docutils literal"><span class="pre">dtype</span></code> only if necessary,
otherwise return a reference.</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#rotate">mdp.utils.rotate</a> (mat, angle, columns, units)</dt>
<dd><p class="first">Rotate in-place a NxM data matrix in the plane defined by the <code class="docutils literal"><span class="pre">columns</span></code>
when observation are stored on rows. Observations are rotated
counterclockwise. This corresponds to the following matrix-multiplication
for each data-point (unchanged elements omitted):</p>
<div class="last highlight-default"><div class="highlight"><pre><span></span><span class="p">[</span> <span class="n">cos</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="p">[</span> <span class="n">x_i</span> <span class="p">]</span>
<span class="n">sin</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="n">cos</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="p">]</span> <span class="o">*</span> <span class="p">[</span> <span class="n">x_j</span> <span class="p">]</span>
</pre></div>
</div>
</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#random_rot">mdp.utils.random_rot</a> (dim, dtype)</dt>
<dd>Return a random rotation matrix, drawn from the Haar distribution
(the only uniform distribution on SO(n)).
The algorithm is described in the paper
Stewart, G.W., <em>The efficient generation of random orthogonal
matrices with an application to condition estimators</em>, SIAM Journal
on Numerical Analysis, 17(3), pp. 403-409, 1980.
For more information see this <a class="reference external" href="http://en.wikipedia.org/wiki/Orthogonal_matrix#Randomization">Wikipedia entry</a>.</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#symeig_semidefinite_ldl">mdp.utils.symeig_semidefinite_ldl</a> (A, B, eigenvectors, turbo, rng, type, overwrite, rank_threshold, dfc_out)</dt>
<dd><p class="first">LDL-based routine to solve generalized symmetric positive semidefinite
eigenvalue problems.
This can be used in case the normal <code class="docutils literal"><span class="pre">symeig()</span></code> call in
<code class="docutils literal"><span class="pre">_stop_training()</span></code> throws
<code class="docutils literal"><span class="pre">SymeigException</span> <span class="pre">('Covariance</span> <span class="pre">matrices</span> <span class="pre">may</span> <span class="pre">be</span> <span class="pre">singular')</span></code>.</p>
<p>This solver uses SciPy’s raw LAPACK interface to access LDL decomposition.</p>
<p class="last">Roughly as efficient as ordinary eigenvalue solving. Can exploit range
parameter for performance just as well as the backend for ordinary symmetric
eigenvalue solving enables. This is the recommended and most efficient
approach, but it requires SciPy 1.0 or newer.</p>
</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#symeig_semidefinite_pca">mdp.utils.symeig_semidefinite_pca</a> (A, B, eigenvectors, turbo, range, type, overwrite, rank_threshold, dfc_out)</dt>
<dd><p class="first">PCA-based routine to solve generalized symmetric positive semidefinite
eigenvalue problems.
This can be used in case the normal <code class="docutils literal"><span class="pre">symeig()</span></code>
call in <code class="docutils literal"><span class="pre">_stop_training()</span></code> throws
<code class="docutils literal"><span class="pre">SymeigException</span> <span class="pre">('Covariance</span> <span class="pre">matrices</span> <span class="pre">may</span> <span class="pre">be</span> <span class="pre">singular')</span></code>.</p>
<p>It applies PCA to B and filters out rank deficit before it applies
symeig() to A.
It is roughly twice as expensive as the ordinary eigh implementation.</p>
<p class="last">One of the most stable and accurate approaches.
Roughly twice as expensive as ordinary symmetric eigenvalue solving as
it solves two symmetric eigenvalue problems.
Only the second one can exploit range parameter for performance.</p>
</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#symeig_semidefinite_reg">mdp.utils.symeig_semidefinite_reg</a> (A, B, eigenvectors, turbo, range, type, overwrite, rank_threshold, dfc_out)</dt>
<dd><p class="first">Regularization-based routine to solve generalized symmetric positive
semidefinite eigenvalue problems.
This can be used in case the normal <code class="docutils literal"><span class="pre">symeig()</span></code>
call in <code class="docutils literal"><span class="pre">_stop_training()</span></code> throws
<code class="docutils literal"><span class="pre">SymeigException</span> <span class="pre">('Covariance</span> <span class="pre">matrices</span> <span class="pre">may</span> <span class="pre">be</span> <span class="pre">singular')</span></code>.</p>
<p>This solver applies a moderate regularization to B before applying
eigh/symeig. Afterwards it properly detects the rank deficit and
filters out malformed features.
For full range, this procedure is (approximately) as efficient as the
ordinary eigh implementation, because all additional steps are
computationally cheap.
For shorter range, the LDL method should be preferred.</p>
<p class="last">Roughly as efficient as ordinary eigenvalue solving if no range is given.
If range is given, depending on the backend for ordinary symmetric
eigenvalue solving, this method can be much slower than an ordinary
symmetric eigenvalue solver that can exploit range for performance.</p>
</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#symeig_semidefinite_svd">mdp.utils.symeig_semidefinite_svd</a> (A, B, eigenvectors, turbo, range, type, overwrite, rank_threshold, dfc_out)</dt>
<dd><p class="first">SVD-based routine to solve generalized symmetric positive semidefinite
eigenvalue problems.
This can be used in case the normal <code class="docutils literal"><span class="pre">symeig()</span></code>
call in <code class="docutils literal"><span class="pre">_stop_training()</span></code> throws
<code class="docutils literal"><span class="pre">SymeigException</span> <span class="pre">('Covariance</span> <span class="pre">matrices</span> <span class="pre">may</span> <span class="pre">be</span> <span class="pre">singular')</span></code>.</p>
<p class="last">One of the most stable and accurate approaches.
Involves solving two svd problems. Computational cost can vary greatly
depending on the backends used. E.g. SVD from SciPy appears to be much
faster than SVD from NumPy. Based on this it can be faster or slower
than the PCA based approach.</p>
</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#symrand">mdp.utils.symrand</a> (dim_or_eigv, dtype)</dt>
<dd>Return a random symmetric (Hermitian) matrix with eigenvalues
uniformly distributed on (0,1].</dd>
</dl>
<div class="section" id="html-slideshows">
<h2>HTML Slideshows<a class="headerlink" href="#html-slideshows" title="Permalink to this headline">¶</a></h2>
<p>The <code class="docutils literal"><span class="pre">mdp.utils</span></code> module contains some classes and helper function to
display animated results in a Webbrowser. This works by creating an
HTML file with embedded JavaScript code, which dynamically loads
image files (the images contain the content that you want to animate
and can for example be created with matplotlib).
MDP internally uses the open source <a class="reference external" href="http://davidbau.com/downloads/templet.py">Templete templating libray,
written by David Bau</a>.</p>
<p>The easiest way to create a slideshow it to use one of these two helper
function:</p>
<dl class="docutils">
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#show_image_slideshow">mdp.utils.show_image_slideshow</a> (filenames, image_size, filename=None, title=None, **kwargs)</dt>
<dd>Write the slideshow into a HTML file, open it in the browser and
return the file name. <code class="docutils literal"><span class="pre">filenames</span></code> is a list of the images files
that you want to display in the slideshow. <code class="docutils literal"><span class="pre">image_size</span></code> is a
2-tuple containing the width and height at which the images should
be displayed. There are also a couple of additional arguments,
which are documented in the docstring.</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.utils-module.html#image_slideshow">mdp.utils.image_slideshow</a> (filenames, image_size, title=None, **kwargs)</dt>
<dd>This function is similar to <code class="docutils literal"><span class="pre">show_image_slideshow</span></code>, but it simply
returns the slideshow HTML code (including the JavaScript code)
which you can then embed into your own HTML file. Note that
the default slideshow CSS code is not included, but it can be
accessed in <code class="docutils literal"><span class="pre">mdp.utils.IMAGE_SLIDESHOW_STYLE</span></code>.</dd>
</dl>
<p>Note that there are also two demos in the Examples section <a class="reference internal" href="examples/slideshow/slideshow.html#slideshow"><span class="std std-ref">Slideshow</span></a>.</p>
</div>
<div class="section" id="graph-module">
<h2>Graph module<a class="headerlink" href="#graph-module" title="Permalink to this headline">¶</a></h2>
<p>MDP contains <code class="docutils literal"><span class="pre">mdp.graph</span></code>, a lightweight package to handle directed graphs.</p>
<dl class="docutils">
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.graph.Graph-class.html">mdp.graph.Graph</a></dt>
<dd><p class="first">Represent a directed graph. This class contains several methods
to create graph structures and manipulate them, among which</p>
<ul class="last">
<li><dl class="first docutils">
<dt><code class="docutils literal"><span class="pre">add_tree</span></code>: Add a tree to the graph.</dt>
<dd><p class="first">The tree is specified with a nested list of tuple, in a LISP-like
notation. The values specified in the list become the values of
the single nodes.
Return an equivalent nested list with the nodes instead of the values.</p>
<p>Example::</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">g</span> <span class="o">=</span> <span class="n">mdp</span><span class="o">.</span><span class="n">graph</span><span class="o">.</span><span class="n">Graph</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">b</span> <span class="o">=</span> <span class="n">c</span> <span class="o">=</span> <span class="n">d</span> <span class="o">=</span> <span class="n">e</span> <span class="o">=</span> <span class="kc">None</span>
<span class="gp">>>> </span><span class="n">nodes</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">add_tree</span><span class="p">(</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="p">,</span><span class="n">e</span><span class="p">))</span> <span class="p">)</span>
</pre></div>
</div>
<p>Graph <code class="docutils literal"><span class="pre">g</span></code> corresponds to this tree, with all node values
being <code class="docutils literal"><span class="pre">None</span></code>:</p>
<div class="last highlight-default"><div class="highlight"><pre><span></span> <span class="n">a</span>
<span class="o">/</span> \
<span class="n">b</span> <span class="n">c</span>
<span class="o">/</span> \
<span class="n">d</span> <span class="n">e</span>
</pre></div>
</div>
</dd>
</dl>
</li>
<li><p class="first"><code class="docutils literal"><span class="pre">topological_sort</span></code>: Perform a topological sort of the nodes.</p>
</li>
<li><p class="first"><code class="docutils literal"><span class="pre">dfs</span></code>, <code class="docutils literal"><span class="pre">undirected_dfs</span></code>: Perform Depth First sort.</p>
</li>
<li><p class="first"><code class="docutils literal"><span class="pre">bfs</span></code>, <code class="docutils literal"><span class="pre">undirected_bfs</span></code>: Perform Breadth First sort.</p>
</li>
<li><p class="first"><code class="docutils literal"><span class="pre">connected_components</span></code>: Return a list of lists containing
the nodes of all connected components of the graph.</p>
</li>
<li><p class="first"><code class="docutils literal"><span class="pre">is_weakly_connected</span></code>: Return True if the graph is weakly connected.</p>
</li>
</ul>
</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.graph.GraphEdge-class.html">mdp.graph.GraphEdge</a></dt>
<dd>Represent a graph edge and all information attached to it.</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.graph.GraphNode-class.html">mdp.graph.GraphNode</a></dt>
<dd>Represent a graph node and all information attached to it.</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.graph-module.html#recursive_map">mdp.graph.recursive_map</a> (fun, seq)</dt>
<dd>Apply a function recursively on a sequence and all subsequences.</dd>
<dt><a class="reference external" href="https://mdp-toolkit.github.io/api/mdp.graph-module.html#recursive_reduce">mdp.graph.recursive_reduce</a> (func, seq, *argv)</dt>
<dd>Apply <code class="docutils literal"><span class="pre">reduce(func,</span> <span class="pre">seq)</span></code> recursively to a sequence and all its
subsequences.</dd>
</dl>
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