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<h1>Source code for astroML.resample</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">warnings</span>
<span class="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <span class="n">check_random_state</span>
<div class="viewcode-block" id="bootstrap"><a class="viewcode-back" href="../../modules/generated/astroML.resample.bootstrap.html#astroML.resample.bootstrap">[docs]</a><span class="k">def</span> <span class="nf">bootstrap</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">n_bootstraps</span><span class="p">,</span> <span class="n">user_statistic</span><span class="p">,</span> <span class="n">kwargs</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">pass_indices</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">"""Compute bootstraped statistics of a dataset.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> data : array_like</span>
<span class="sd"> An n-dimensional data array of size n_samples by n_attributes</span>
<span class="sd"> n_bootstraps : integer</span>
<span class="sd"> the number of bootstrap samples to compute. Note that internally,</span>
<span class="sd"> two arrays of size (n_bootstraps, n_samples) will be allocated.</span>
<span class="sd"> For very large numbers of bootstraps, this can cause memory issues.</span>
<span class="sd"> user_statistic : function</span>
<span class="sd"> The statistic to be computed. This should take an array of data</span>
<span class="sd"> of size (n_bootstraps, n_samples) and return the row-wise statistics</span>
<span class="sd"> of the data.</span>
<span class="sd"> kwargs : dictionary (optional)</span>
<span class="sd"> A dictionary of keyword arguments to be passed to the</span>
<span class="sd"> user_statistic function.</span>
<span class="sd"> pass_indices : boolean (optional)</span>
<span class="sd"> if True, then the indices of the points rather than the points</span>
<span class="sd"> themselves are passed to `user_statistic`</span>
<span class="sd"> random_state: RandomState or an int seed (0 by default)</span>
<span class="sd"> A random number generator instance</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> distribution : ndarray</span>
<span class="sd"> the bootstrapped distribution of statistics (length = n_bootstraps)</span>
<span class="sd"> """</span>
<span class="c1"># we don't set kwargs={} by default in the argument list, because using</span>
<span class="c1"># a mutable type as a default argument can lead to strange results</span>
<span class="k">if</span> <span class="n">kwargs</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">kwargs</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">rng</span> <span class="o">=</span> <span class="n">check_random_state</span><span class="p">(</span><span class="n">random_state</span><span class="p">)</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="k">if</span> <span class="n">data</span><span class="o">.</span><span class="n">ndim</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"bootstrap data are n-dimensional: "</span>
<span class="s2">"assuming ordered n_samples by n_attributes"</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">size</span>
<span class="c1"># Generate random indices with repetition</span>
<span class="n">ind</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">n_bootstraps</span><span class="p">,</span> <span class="n">n_samples</span><span class="p">))</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="c1"># Call the function</span>
<span class="k">if</span> <span class="n">pass_indices</span><span class="p">:</span>
<span class="n">stat_bootstrap</span> <span class="o">=</span> <span class="n">user_statistic</span><span class="p">(</span><span class="n">ind</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">stat_bootstrap</span> <span class="o">=</span> <span class="n">user_statistic</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="c1"># compute the statistic on the data</span>
<span class="k">return</span> <span class="n">stat_bootstrap</span></div>
<div class="viewcode-block" id="jackknife"><a class="viewcode-back" href="../../modules/generated/astroML.resample.jackknife.html#astroML.resample.jackknife">[docs]</a><span class="k">def</span> <span class="nf">jackknife</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">user_statistic</span><span class="p">,</span> <span class="n">kwargs</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">return_raw_distribution</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">pass_indices</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="sd">"""Compute first-order jackknife statistics of the data.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> data : array_like</span>
<span class="sd"> A 1-dimensional data array of size n_samples</span>
<span class="sd"> user_statistic : function</span>
<span class="sd"> The statistic to be computed. This should take an array of data</span>
<span class="sd"> of size (n_samples, n_samples - 1) and return an array of size</span>
<span class="sd"> n_samples or tuple of arrays of size n_samples, representing the</span>
<span class="sd"> row-wise statistics of the input.</span>
<span class="sd"> kwargs : dictionary (optional)</span>
<span class="sd"> A dictionary of keyword arguments to be passed to the</span>
<span class="sd"> user_statistic function.</span>
<span class="sd"> return_raw_distribution : boolean (optional)</span>
<span class="sd"> if True, return the raw jackknife distribution. Be aware that</span>
<span class="sd"> this distribution is not reflective of the true distribution:</span>
<span class="sd"> it is simply an intermediate step in the jackknife calculation</span>
<span class="sd"> pass_indices : boolean (optional)</span>
<span class="sd"> if True, then the indices of the points rather than the points</span>
<span class="sd"> themselves are passed to `user_statistic`</span>
<span class="sd"> Returns</span>
<span class="sd"> -------</span>
<span class="sd"> mean, stdev : floats</span>
<span class="sd"> The mean and standard deviation of the jackknifed distribution</span>
<span class="sd"> raw_distribution : ndarray</span>
<span class="sd"> Returned only if `return_raw_distribution` is True</span>
<span class="sd"> The array containing the raw distribution (length n_samples)</span>
<span class="sd"> Be aware that this distribution is not reflective of the true</span>
<span class="sd"> distribution: it is simply an intermediate step in the jackknife</span>
<span class="sd"> calculation</span>
<span class="sd"> Notes</span>
<span class="sd"> -----</span>
<span class="sd"> This implementation is a leave-one-out jackknife.</span>
<span class="sd"> Jackknife resampling is known to fail on rank-based statistics</span>
<span class="sd"> (e.g. median, quartiles, etc.) It works well on smooth statistics</span>
<span class="sd"> (e.g. mean, standard deviation, etc.)</span>
<span class="sd"> """</span>
<span class="c1"># we don't set kwargs={} by default in the argument list, because using</span>
<span class="c1"># a mutable type as a default argument can lead to strange results</span>
<span class="k">if</span> <span class="n">kwargs</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">kwargs</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">size</span>
<span class="k">if</span> <span class="n">data</span><span class="o">.</span><span class="n">ndim</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"bootstrap expects 1-dimensional data"</span><span class="p">)</span>
<span class="c1"># generate indices for the entire dataset, converting to row vector</span>
<span class="n">ind0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n_samples</span><span class="p">)[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="p">:]</span>
<span class="c1"># generate sets of indices where a single datapoint is left-out</span>
<span class="n">ind</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">int</span><span class="p">)</span>
<span class="n">ind</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">ind</span><span class="p">[:</span><span class="n">i</span><span class="p">],</span> <span class="n">ind</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">:]))</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">ind</span><span class="p">])</span>
<span class="c1"># compute the statistic for the whole dataset</span>
<span class="k">if</span> <span class="n">pass_indices</span><span class="p">:</span>
<span class="n">stat_data</span> <span class="o">=</span> <span class="n">user_statistic</span><span class="p">(</span><span class="n">ind0</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="n">stat_jackknife</span> <span class="o">=</span> <span class="n">user_statistic</span><span class="p">(</span><span class="n">ind</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">stat_data</span> <span class="o">=</span> <span class="n">user_statistic</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">ind0</span><span class="p">],</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="n">stat_jackknife</span> <span class="o">=</span> <span class="n">user_statistic</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">ind</span><span class="p">],</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="c1"># handle multiple statistics:</span>
<span class="c1"># if ndim=0, then the statistic is not operating on rows (error).</span>
<span class="c1"># if ndim=1, then it's a single statistic returned</span>
<span class="c1"># if ndim=2, then a tuple has been returned</span>
<span class="n">stat_data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">stat_data</span><span class="p">)</span>
<span class="n">ndim</span> <span class="o">=</span> <span class="n">stat_data</span><span class="o">.</span><span class="n">ndim</span>
<span class="k">if</span> <span class="n">ndim</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"user_statistic should return row-wise statistics"</span><span class="p">)</span>
<span class="n">stat_data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">atleast_2d</span><span class="p">(</span><span class="n">stat_data</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
<span class="n">stat_jackknife</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">atleast_2d</span><span class="p">(</span><span class="n">stat_jackknife</span><span class="p">)</span>
<span class="c1"># compute the jackknife correction formula</span>
<span class="n">delta_stat</span> <span class="o">=</span> <span class="p">(</span><span class="n">n_samples</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">stat_data</span> <span class="o">-</span> <span class="n">stat_jackknife</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="mi">1</span><span class="p">))</span>
<span class="n">stat_corrected</span> <span class="o">=</span> <span class="p">(</span><span class="n">stat_data</span> <span class="o">+</span> <span class="n">delta_stat</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">sigma_stat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">1.</span> <span class="o">/</span> <span class="n">n_samples</span> <span class="o">/</span> <span class="p">(</span><span class="n">n_samples</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">n_samples</span> <span class="o">*</span> <span class="n">stat_data</span> <span class="o">-</span> <span class="n">stat_corrected</span>
<span class="o">-</span> <span class="p">(</span><span class="n">n_samples</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<span class="o">*</span> <span class="n">stat_jackknife</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<span class="k">if</span> <span class="n">return_raw_distribution</span><span class="p">:</span>
<span class="n">results</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">stat_corrected</span><span class="p">,</span> <span class="n">sigma_stat</span><span class="p">,</span> <span class="n">stat_jackknife</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">results</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">stat_corrected</span><span class="p">,</span> <span class="n">sigma_stat</span><span class="p">))</span>
<span class="k">if</span> <span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">results</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">results</span></div>
</pre></div>
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