PythonOT
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@@ -1257,16 +1257,17 @@ <h1>Source code for ot.backend</h1><div class="highlight"><pre>
 
 <div class="viewcode-block" id="Backend.kl_div">
 <a class="viewcode-back" href="../../gen_modules/ot.backend.html#ot.backend.Backend.kl_div">[docs]</a>
-    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
+    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">mass</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
 <span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="sd">        Computes the Kullback-Leibler divergence.</span>
+<span class="sd">        Computes the (Generalized) Kullback-Leibler divergence.</span>
 
 <span class="sd">        This function follows the api from :any:`scipy.stats.entropy`.</span>
 
 <span class="sd">        Parameter eps is used to avoid numerical errors and is added in the log.</span>
 
 <span class="sd">        .. math::</span>
-<span class="sd">             KL(p,q) = \sum_i p(i) \log (\frac{p(i)}{q(i)}+\epsilon)</span>
+<span class="sd">             KL(p,q) = \langle \mathbf{p}, log(\mathbf{p} / \mathbf{q} + eps \rangle</span>
+<span class="sd">             + \mathbb{1}_{mass=True} \langle \mathbf{q} - \mathbf{p}, \mathbf{1} \rangle</span>
 
 <span class="sd">        See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.entropy.html</span>
 <span class="sd">        &quot;&quot;&quot;</span>
@@ -1908,8 +1909,11 @@ <h1>Source code for ot.backend</h1><div class="highlight"><pre>
 
 <div class="viewcode-block" id="NumpyBackend.kl_div">
 <a class="viewcode-back" href="../../gen_modules/ot.backend.html#ot.backend.NumpyBackend.kl_div">[docs]</a>
-    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
-        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">p</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="n">p</span> <span class="o">/</span> <span class="n">q</span> <span class="o">+</span> <span class="n">eps</span><span class="p">))</span></div>
+    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">mass</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
+        <span class="n">value</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">p</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="n">p</span> <span class="o">/</span> <span class="n">q</span> <span class="o">+</span> <span class="n">eps</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">mass</span><span class="p">:</span>
+            <span class="n">value</span> <span class="o">=</span> <span class="n">value</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">q</span> <span class="o">-</span> <span class="n">p</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">value</span></div>
 
 
 <div class="viewcode-block" id="NumpyBackend.isfinite">
@@ -2550,8 +2554,11 @@ <h1>Source code for ot.backend</h1><div class="highlight"><pre>
 
 <div class="viewcode-block" id="JaxBackend.kl_div">
 <a class="viewcode-back" href="../../gen_modules/ot.backend.html#ot.backend.JaxBackend.kl_div">[docs]</a>
-    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
-        <span class="k">return</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">p</span> <span class="o">*</span> <span class="n">jnp</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">p</span> <span class="o">/</span> <span class="n">q</span> <span class="o">+</span> <span class="n">eps</span><span class="p">))</span></div>
+    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">mass</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
+        <span class="n">value</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">p</span> <span class="o">*</span> <span class="n">jnp</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">p</span> <span class="o">/</span> <span class="n">q</span> <span class="o">+</span> <span class="n">eps</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">mass</span><span class="p">:</span>
+            <span class="n">value</span> <span class="o">=</span> <span class="n">value</span> <span class="o">+</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">q</span> <span class="o">-</span> <span class="n">p</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">value</span></div>
 
 
 <div class="viewcode-block" id="JaxBackend.isfinite">
@@ -3280,8 +3287,11 @@ <h1>Source code for ot.backend</h1><div class="highlight"><pre>
 
 <div class="viewcode-block" id="TorchBackend.kl_div">
 <a class="viewcode-back" href="../../gen_modules/ot.backend.html#ot.backend.TorchBackend.kl_div">[docs]</a>
-    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
-        <span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">p</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">p</span> <span class="o">/</span> <span class="n">q</span> <span class="o">+</span> <span class="n">eps</span><span class="p">))</span></div>
+    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">mass</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
+        <span class="n">value</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">p</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">p</span> <span class="o">/</span> <span class="n">q</span> <span class="o">+</span> <span class="n">eps</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">mass</span><span class="p">:</span>
+            <span class="n">value</span> <span class="o">=</span> <span class="n">value</span> <span class="o">+</span> <span class="n">torch</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">q</span> <span class="o">-</span> <span class="n">p</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">value</span></div>
 
 
 <div class="viewcode-block" id="TorchBackend.isfinite">
@@ -3924,8 +3934,11 @@ <h1>Source code for ot.backend</h1><div class="highlight"><pre>
 
 <div class="viewcode-block" id="CupyBackend.kl_div">
 <a class="viewcode-back" href="../../gen_modules/ot.backend.html#ot.backend.CupyBackend.kl_div">[docs]</a>
-    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
-        <span class="k">return</span> <span class="n">cp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">p</span> <span class="o">*</span> <span class="n">cp</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">p</span> <span class="o">/</span> <span class="n">q</span> <span class="o">+</span> <span class="n">eps</span><span class="p">))</span></div>
+    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">mass</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
+        <span class="n">value</span> <span class="o">=</span> <span class="n">cp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">p</span> <span class="o">*</span> <span class="n">cp</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">p</span> <span class="o">/</span> <span class="n">q</span> <span class="o">+</span> <span class="n">eps</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">mass</span><span class="p">:</span>
+            <span class="n">value</span> <span class="o">=</span> <span class="n">value</span> <span class="o">+</span> <span class="n">cp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">q</span> <span class="o">-</span> <span class="n">p</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">value</span></div>
 
 
 <div class="viewcode-block" id="CupyBackend.isfinite">
@@ -4591,8 +4604,11 @@ <h1>Source code for ot.backend</h1><div class="highlight"><pre>
 
 <div class="viewcode-block" id="TensorflowBackend.kl_div">
 <a class="viewcode-back" href="../../gen_modules/ot.backend.html#ot.backend.TensorflowBackend.kl_div">[docs]</a>
-    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
-        <span class="k">return</span> <span class="n">tnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">p</span> <span class="o">*</span> <span class="n">tnp</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">p</span> <span class="o">/</span> <span class="n">q</span> <span class="o">+</span> <span class="n">eps</span><span class="p">))</span></div>
+    <span class="k">def</span> <span class="nf">kl_div</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span><span class="p">,</span> <span class="n">mass</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-16</span><span class="p">):</span>
+        <span class="n">value</span> <span class="o">=</span> <span class="n">tnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">p</span> <span class="o">*</span> <span class="n">tnp</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">p</span> <span class="o">/</span> <span class="n">q</span> <span class="o">+</span> <span class="n">eps</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">mass</span><span class="p">:</span>
+            <span class="n">value</span> <span class="o">=</span> <span class="n">value</span> <span class="o">+</span> <span class="n">tnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">q</span> <span class="o">-</span> <span class="n">p</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">value</span></div>
 
 
 <div class="viewcode-block" id="TensorflowBackend.isfinite">
 
@@ -460,7 +460,7 @@ <h1>Source code for ot.bregman._barycenter</h1><div class="highlight"><pre>
         <span class="n">log</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;err&#39;</span><span class="p">:</span> <span class="p">[]}</span>
 
     <span class="n">M</span> <span class="o">=</span> <span class="o">-</span> <span class="n">M</span> <span class="o">/</span> <span class="n">reg</span>
-    <span class="n">logA</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">A</span> <span class="o">+</span> <span class="mf">1e-15</span><span class="p">)</span>
+    <span class="n">logA</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">A</span> <span class="o">+</span> <span class="mf">1e-16</span><span class="p">)</span>
     <span class="n">log_KU</span><span class="p">,</span> <span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="o">*</span><span class="n">logA</span><span class="o">.</span><span class="n">shape</span><span class="p">),</span> <span class="n">type_as</span><span class="o">=</span><span class="n">A</span><span class="p">)</span>
     <span class="n">err</span> <span class="o">=</span> <span class="mi">1</span>
     <span class="k">for</span> <span class="n">ii</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">numItermax</span><span class="p">):</span>
@@ -804,7 +804,7 @@ <h1>Source code for ot.bregman._barycenter</h1><div class="highlight"><pre>
         <span class="n">log</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;err&#39;</span><span class="p">:</span> <span class="p">[]}</span>
 
     <span class="n">M</span> <span class="o">=</span> <span class="o">-</span> <span class="n">M</span> <span class="o">/</span> <span class="n">reg</span>
-    <span class="n">logA</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">A</span> <span class="o">+</span> <span class="mf">1e-15</span><span class="p">)</span>
+    <span class="n">logA</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">A</span> <span class="o">+</span> <span class="mf">1e-16</span><span class="p">)</span>
     <span class="n">log_KU</span><span class="p">,</span> <span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="o">*</span><span class="n">logA</span><span class="o">.</span><span class="n">shape</span><span class="p">),</span> <span class="n">type_as</span><span class="o">=</span><span class="n">A</span><span class="p">)</span>
     <span class="n">c</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">dim</span><span class="p">,</span> <span class="n">type_as</span><span class="o">=</span><span class="n">A</span><span class="p">)</span>
     <span class="n">err</span> <span class="o">=</span> <span class="mi">1</span>