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  <div class="section" id="using-patsy-in-your-library">
<span id="library-developers"></span><h1>Using Patsy in your library<a class="headerlink" href="#using-patsy-in-your-library" title="Permalink to this headline"></a></h1>
<p>Our goal is to make Patsy the de facto standard for describing
models in Python, regardless of the underlying package in use &#8211; just
as formulas are the standard interface to all R packages. Therefore
we&#8217;ve tried to make it as easy as possible for you to build Patsy
support into your libraries.</p>
<p>Patsy is a good houseguest:</p>
<ul class="simple">
<li>Pure Python, no compilation necessary.</li>
<li>Exhaustive tests (&gt;98% statement coverage at time of writing) and
documentation (you&#8217;re looking at it).</li>
<li>No dependencies besides numpy.</li>
<li>Tested and supported on every version of Python since 2.5. (And 2.4
probably still works too if you really want it, it&#8217;s just become too
hard to keep a working 2.4 environment on the test server.)</li>
</ul>
<p>So you can be pretty confident that adding a dependency on Patsy
won&#8217;t create much hassle for your users.</p>
<p>And, of course, the fundamental design is very conservative &#8211; the
formula mini-language in S was first described in Chambers and Hastie
(1992), more than two decades ago. It&#8217;s still in heavy use today in R,
which is one of the most popular environments for statistical
programming. Many of your users may already be familiar with it. So we
can be pretty certain that it will hold up to real-world usage.</p>
<div class="section" id="using-the-high-level-interface">
<h2>Using the high-level interface<a class="headerlink" href="#using-the-high-level-interface" title="Permalink to this headline"></a></h2>
<p>If you have a function whose signature currently looks like this:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">mymodel2</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">...</span><span class="p">):</span>
    <span class="o">...</span>
</pre></div>
</div>
<p>or this:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">mymodel1</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="o">...</span><span class="p">):</span>
    <span class="o">...</span>
</pre></div>
</div>
<p>then adding Patsy support is extremely easy (though of course like
any other API change, you may have to deprecate the old interface, or
provide two interfaces in parallel, depending on your situation). Just
write something like:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">mymodel2_patsy</span><span class="p">(</span><span class="n">formula_like</span><span class="p">,</span> <span class="n">data</span><span class="o">=</span><span class="p">{},</span> <span class="o">...</span><span class="p">):</span>
    <span class="n">y</span><span class="p">,</span> <span class="n">X</span> <span class="o">=</span> <span class="n">patsy</span><span class="o">.</span><span class="n">dmatrices</span><span class="p">(</span><span class="n">formula_like</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
    <span class="o">...</span>
</pre></div>
</div>
<p>or:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">mymodel1_patsy</span><span class="p">(</span><span class="n">formula_like</span><span class="p">,</span> <span class="n">data</span><span class="o">=</span><span class="p">{},</span> <span class="o">...</span><span class="p">):</span>
    <span class="n">X</span> <span class="o">=</span> <span class="n">patsy</span><span class="o">.</span><span class="n">dmatrix</span><span class="p">(</span><span class="n">formula_like</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
    <span class="o">...</span>
</pre></div>
</div>
<p>(See <a class="reference internal" href="API-reference.html#patsy.dmatrices" title="patsy.dmatrices"><code class="xref py py-func docutils literal"><span class="pre">dmatrices()</span></code></a> and <a class="reference internal" href="API-reference.html#patsy.dmatrix" title="patsy.dmatrix"><code class="xref py py-func docutils literal"><span class="pre">dmatrix()</span></code></a> for details.) This won&#8217;t
force your users to switch to formulas immediately; they can replace
code that looks like this:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">build_matrices_laboriously</span><span class="p">()</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">mymodel2</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
<span class="n">other_result</span> <span class="o">=</span> <span class="n">mymodel1</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
</pre></div>
</div>
<p>with code like this:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">build_matrices_laboriously</span><span class="p">()</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">mymodel2</span><span class="p">((</span><span class="n">y</span><span class="p">,</span> <span class="n">X</span><span class="p">),</span> <span class="n">data</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
<span class="n">other_result</span> <span class="o">=</span> <span class="n">mymodel1</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">data</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
</pre></div>
</div>
<p>Of course in the long run they might want to throw away that
<code class="xref py py-func docutils literal"><span class="pre">build_matrices_laboriously()</span></code> function and start using formulas,
but they aren&#8217;t forced to just to start using your new interface.</p>
<div class="section" id="working-with-metadata">
<h3>Working with metadata<a class="headerlink" href="#working-with-metadata" title="Permalink to this headline"></a></h3>
<p>Once you&#8217;ve started using Patsy to handle formulas, you&#8217;ll probably
want to take advantage of the metadata that Patsy provides, so that
you can display regression coefficients by name and so forth. Design
matrices processed by Patsy always have a <code class="docutils literal"><span class="pre">.design_info</span></code>
attribute which contains lots of information about the design: see
<a class="reference internal" href="API-reference.html#patsy.DesignInfo" title="patsy.DesignInfo"><code class="xref py py-class docutils literal"><span class="pre">DesignInfo</span></code></a> for details.</p>
</div>
<div class="section" id="predictions">
<h3>Predictions<a class="headerlink" href="#predictions" title="Permalink to this headline"></a></h3>
<p>Another nice feature is making predictions on new data. But this
requires that we can take in new data, and transform it to create a
new <cite>X</cite> matrix. Or if we want to compute the likelihood of our model
on new data, we need both new <cite>X</cite> and <cite>y</cite> matrices.</p>
<p>This is also easily done with Patsy &#8211; first fetch the relevant
<a class="reference internal" href="API-reference.html#patsy.DesignInfo" title="patsy.DesignInfo"><code class="xref py py-class docutils literal"><span class="pre">DesignInfo</span></code></a> objects by doing <code class="docutils literal"><span class="pre">input_data.design_info</span></code>, and
then pass them to <a class="reference internal" href="API-reference.html#patsy.build_design_matrices" title="patsy.build_design_matrices"><code class="xref py py-func docutils literal"><span class="pre">build_design_matrices()</span></code></a> along with the new
data.</p>
</div>
<div class="section" id="example">
<h3>Example<a class="headerlink" href="#example" title="Permalink to this headline"></a></h3>
<p>Here&#8217;s a simplified class for doing ordinary least-squares regression,
demonstrating the above techniques:</p>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p class="last">This code has not been validated for numerical
correctness.</p>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">patsy</span> <span class="kn">import</span> <span class="n">dmatrices</span><span class="p">,</span> <span class="n">build_design_matrices</span>

<span class="k">class</span> <span class="nc">LM</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;An example ordinary least squares linear model class, analogous to R&#39;s</span>
<span class="sd">    lm() function. Don&#39;t use this in real life, it isn&#39;t properly tested.&quot;&quot;&quot;</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">formula_like</span><span class="p">,</span> <span class="n">data</span><span class="o">=</span><span class="p">{}):</span>
        <span class="n">y</span><span class="p">,</span> <span class="n">x</span> <span class="o">=</span> <span class="n">dmatrices</span><span class="p">(</span><span class="n">formula_like</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">nobs</span> <span class="o">=</span> <span class="n">x</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="bp">self</span><span class="o">.</span><span class="n">betas</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">rss</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">lstsq</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_y_design_info</span> <span class="o">=</span> <span class="n">y</span><span class="o">.</span><span class="n">design_info</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">_x_design_info</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">design_info</span>

    <span class="k">def</span> <span class="nf">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="n">summary</span> <span class="o">=</span> <span class="p">(</span><span class="s">&quot;Ordinary least-squares regression</span><span class="se">\n</span><span class="s">&quot;</span>
                   <span class="s">&quot;  Model: </span><span class="si">%s</span><span class="s"> ~ </span><span class="si">%s</span><span class="se">\n</span><span class="s">&quot;</span>
                   <span class="s">&quot;  Regression (beta) coefficients:</span><span class="se">\n</span><span class="s">&quot;</span>
                   <span class="o">%</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_y_design_info</span><span class="o">.</span><span class="n">describe</span><span class="p">(),</span>
                      <span class="bp">self</span><span class="o">.</span><span class="n">_x_design_info</span><span class="o">.</span><span class="n">describe</span><span class="p">()))</span>
        <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_x_design_info</span><span class="o">.</span><span class="n">column_names</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">betas</span><span class="p">):</span>
            <span class="n">summary</span> <span class="o">+=</span> <span class="s">&quot;    </span><span class="si">%s</span><span class="s">:  </span><span class="si">%0.3g</span><span class="se">\n</span><span class="s">&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">value</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
        <span class="k">return</span> <span class="n">summary</span>

    <span class="k">def</span> <span class="nf">predict</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">new_data</span><span class="p">):</span>
        <span class="p">(</span><span class="n">new_x</span><span class="p">,)</span> <span class="o">=</span> <span class="n">build_design_matrices</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">_x_design_info</span><span class="p">],</span>
                                         <span class="n">new_data</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">new_x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">betas</span><span class="p">)</span>

    <span class="k">def</span> <span class="nf">loglik</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">new_data</span><span class="p">):</span>
        <span class="p">(</span><span class="n">new_y</span><span class="p">,</span> <span class="n">new_x</span><span class="p">)</span> <span class="o">=</span> <span class="n">build_design_matrices</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">_y_design_info</span><span class="p">,</span>
                                                <span class="bp">self</span><span class="o">.</span><span class="n">_x_design_info</span><span class="p">],</span>
                                               <span class="n">new_data</span><span class="p">)</span>
        <span class="n">new_pred</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">new_x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">betas</span><span class="p">)</span>
        <span class="n">sigma2</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rss</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">nobs</span>
        <span class="c"># It&#39;d be more elegant to use scipy.stats.norm.logpdf here, but adding</span>
        <span class="c"># a dependency on scipy makes the docs build more complicated:</span>
        <span class="n">Z</span> <span class="o">=</span> <span class="o">-</span><span class="mf">0.5</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">sigma2</span><span class="p">)</span>
        <span class="k">return</span> <span class="n">Z</span> <span class="o">+</span> <span class="o">-</span><span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="n">new_y</span> <span class="o">-</span> <span class="n">new_x</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="o">/</span><span class="n">sigma2</span>
</pre></div>
</div>
<p>And here&#8217;s how it can be used:</p>
<div class="highlight-ipython"><div class="highlight"><pre><span class="gp">In [1]: </span><span class="kn">from</span> <span class="nn">patsy</span> <span class="kn">import</span> <span class="n">demo_data</span>

<span class="gp">In [2]: </span><span class="n">data</span> <span class="o">=</span> <span class="n">demo_data</span><span class="p">(</span><span class="s">&quot;x&quot;</span><span class="p">,</span> <span class="s">&quot;y&quot;</span><span class="p">,</span> <span class="s">&quot;a&quot;</span><span class="p">)</span>

<span class="go"># Old and boring approach (but it still works):</span>
<span class="gp">In [3]: </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">column_stack</span><span class="p">(([</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="s">&quot;y&quot;</span><span class="p">]),</span> <span class="n">data</span><span class="p">[</span><span class="s">&quot;x&quot;</span><span class="p">]))</span>

<span class="gp">In [4]: </span><span class="n">LM</span><span class="p">((</span><span class="n">data</span><span class="p">[</span><span class="s">&quot;y&quot;</span><span class="p">],</span> <span class="n">X</span><span class="p">))</span>
<span class="gh">Out[4]: </span><span class="go"></span>
<span class="go">Ordinary least-squares regression</span>
<span class="go">  Model: y0 ~ x0 + x1</span>
<span class="go">  Regression (beta) coefficients:</span>
<span class="go">    x0:  0.677</span>
<span class="go">    x1:  -0.217</span>

<span class="go"># Fancy new way:</span>
<span class="gp">In [5]: </span><span class="n">m</span> <span class="o">=</span> <span class="n">LM</span><span class="p">(</span><span class="s">&quot;y ~ x&quot;</span><span class="p">,</span> <span class="n">data</span><span class="p">)</span>

<span class="gp">In [6]: </span><span class="n">m</span>
<span class="gh">Out[6]: </span><span class="go"></span>
<span class="go">Ordinary least-squares regression</span>
<span class="go">  Model: y ~ 1 + x</span>
<span class="go">  Regression (beta) coefficients:</span>
<span class="go">    Intercept:  0.677</span>
<span class="go">    x:  -0.217</span>

<span class="gp">In [7]: </span><span class="n">m</span><span class="o">.</span><span class="n">predict</span><span class="p">({</span><span class="s">&quot;x&quot;</span><span class="p">:</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">]})</span>
<span class="gh">Out[7]: </span><span class="go"></span>
<span class="go">array([[-1.48944498],</span>
<span class="go">       [-3.65620297],</span>
<span class="go">       [-5.82296096]])</span>

<span class="gp">In [8]: </span><span class="n">m</span><span class="o">.</span><span class="n">loglik</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="gh">Out[8]: </span><span class="go"></span>
<span class="go">array([[ -0.28884193,  -1.46289596],</span>
<span class="go">       [ -2.64235743,  -0.8254485 ],</span>
<span class="go">       [ -2.44930737,  -2.36666465],</span>
<span class="go">       [ -0.90233651,  -6.24317017],</span>
<span class="go">       [ -1.58762894,  -5.56817766],</span>
<span class="go">       [ -0.65148056, -10.80114045]])</span>

<span class="gp">In [9]: </span><span class="n">m</span><span class="o">.</span><span class="n">loglik</span><span class="p">({</span><span class="s">&quot;x&quot;</span><span class="p">:</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">],</span> <span class="s">&quot;y&quot;</span><span class="p">:</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">3</span><span class="p">]})</span>
<span class="gh">Out[9]: </span><span class="go"></span>
<span class="go">array([[   -7.39939265,  -215.51261221],</span>
<span class="go">       [  -16.29311998,  -861.19721649],</span>
<span class="go">       [  -28.74433824, -1937.33822362]])</span>

<span class="go"># Your users get support for categorical predictors for free:</span>
<span class="gp">In [10]: </span><span class="n">LM</span><span class="p">(</span><span class="s">&quot;y ~ a&quot;</span><span class="p">,</span> <span class="n">data</span><span class="p">)</span>
<span class="gh">Out[10]: </span><span class="go"></span>
<span class="go">Ordinary least-squares regression</span>
<span class="go">  Model: y ~ 1 + a</span>
<span class="go">  Regression (beta) coefficients:</span>
<span class="go">    Intercept:  0.33</span>
<span class="go">    a[T.a2]:  0.241</span>

<span class="go"># And variable transformations too:</span>
<span class="gp">In [11]: </span><span class="n">LM</span><span class="p">(</span><span class="s">&quot;y ~ np.log(x ** 2)&quot;</span><span class="p">,</span> <span class="n">data</span><span class="p">)</span>
<span class="gh">Out[11]: </span><span class="go"></span>
<span class="go">Ordinary least-squares regression</span>
<span class="go">  Model: y ~ 1 + np.log(x ** 2)</span>
<span class="go">  Regression (beta) coefficients:</span>
<span class="go">    Intercept:  0.399</span>
<span class="go">    np.log(x ** 2):  0.148</span>
</pre></div>
</div>
</div>
<div class="section" id="other-cool-tricks">
<h3>Other cool tricks<a class="headerlink" href="#other-cool-tricks" title="Permalink to this headline"></a></h3>
<p>If you want to compute ANOVAs, then check out
<a class="reference internal" href="API-reference.html#patsy.DesignInfo.term_name_slices" title="patsy.DesignInfo.term_name_slices"><code class="xref py py-attr docutils literal"><span class="pre">DesignInfo.term_name_slices</span></code></a>, <a class="reference internal" href="API-reference.html#patsy.DesignInfo.slice" title="patsy.DesignInfo.slice"><code class="xref py py-meth docutils literal"><span class="pre">DesignInfo.slice()</span></code></a>.</p>
<p>If you support linear hypothesis tests or otherwise allow your users
to specify linear constraints on model parameters, consider taking
advantage of <a class="reference internal" href="API-reference.html#patsy.DesignInfo.linear_constraint" title="patsy.DesignInfo.linear_constraint"><code class="xref py py-meth docutils literal"><span class="pre">DesignInfo.linear_constraint()</span></code></a>.</p>
</div>
</div>
<div class="section" id="extending-the-formula-syntax">
<h2>Extending the formula syntax<a class="headerlink" href="#extending-the-formula-syntax" title="Permalink to this headline"></a></h2>
<p>The above documentation assumes that you have a relatively simple
model that can be described by one or two matrices (plus whatever
other arguments you take). This covers many of the most popular
models, but it&#8217;s definitely not sufficient for every model out there.</p>
<p>Internally, Patsy is designed to be very flexible &#8211; for example,
it&#8217;s quite straightforward to add custom operators to the formula
parser, or otherwise extend the formula evaluation machinery. (Heck,
it only took an hour or two to repurpose it for a totally different
purpose, parsing linear constraints.)  But extending Patsy in a
more fundamental way then this will require just a wee bit more complicated
API than just calling <a class="reference internal" href="API-reference.html#patsy.dmatrices" title="patsy.dmatrices"><code class="xref py py-func docutils literal"><span class="pre">dmatrices()</span></code></a>, and for this initial release,
we&#8217;ve been busy enough getting the basics working that we haven&#8217;t yet
taken the time to pin down a public extension API we can support.</p>
<p>So, if you want something fancier &#8211; please give us a nudge, it&#8217;s
entirely likely we can work something out.</p>
</div>
</div>


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  <h3><a href="index.html">Table Of Contents</a></h3>
  <ul>
<li><a class="reference internal" href="#">Using Patsy in your library</a><ul>
<li><a class="reference internal" href="#using-the-high-level-interface">Using the high-level interface</a><ul>
<li><a class="reference internal" href="#working-with-metadata">Working with metadata</a></li>
<li><a class="reference internal" href="#predictions">Predictions</a></li>
<li><a class="reference internal" href="#example">Example</a></li>
<li><a class="reference internal" href="#other-cool-tricks">Other cool tricks</a></li>
</ul>
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<li><a class="reference internal" href="#extending-the-formula-syntax">Extending the formula syntax</a></li>
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