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master/_modules/ot/gromov/_lowrank.html

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@@ -176,14 +176,14 @@ <h1>Source code for ot.gromov._lowrank</h1><div class="highlight"><pre>
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<span class="sd"> where :</span>
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<span class="sd"> - :math: `A` is the (`dim_a`, `dim_a`) square pairwise cost matrix of the source domain.</span>
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<span class="sd"> - :math: `B` is the (`dim_a`, `dim_a`) square pairwise cost matrix of the target domain.</span>
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<span class="sd"> - :math: `\mathcal{Q}_{A,B}` is quadratic objective function of the Gromov Wasserstein plan.</span>
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<span class="sd"> - :math: `Q` and `R` are the low-rank matrix decomposition of the Gromov-Wasserstein plan.</span>
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<span class="sd"> - :math: `g` is the weight vector for the low-rank decomposition of the Gromov-Wasserstein plan.</span>
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<span class="sd"> - :math:`A` is the (`dim_a`, `dim_a`) square pairwise cost matrix of the source domain.</span>
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<span class="sd"> - :math:`B` is the (`dim_a`, `dim_a`) square pairwise cost matrix of the target domain.</span>
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<span class="sd"> - :math:`\mathcal{Q}_{A,B}` is quadratic objective function of the Gromov Wasserstein plan.</span>
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<span class="sd"> - :math:`Q` and `R` are the low-rank matrix decomposition of the Gromov-Wasserstein plan.</span>
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<span class="sd"> - :math:`g` is the weight vector for the low-rank decomposition of the Gromov-Wasserstein plan.</span>
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<span class="sd"> - :math:`\mathbf{a}` and :math:`\mathbf{b}` are source and target weights (histograms, both sum to 1).</span>
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<span class="sd"> - :math: `r` is the rank of the Gromov-Wasserstein plan.</span>
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<span class="sd"> - :math: `\mathcal{C(a,b,r)}` are the low-rank couplings of the OT problem.</span>
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<span class="sd"> - :math:`r` is the rank of the Gromov-Wasserstein plan.</span>
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<span class="sd"> - :math:`\mathcal{C(a,b,r)}` are the low-rank couplings of the OT problem.</span>
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<span class="sd"> - :math:`H((Q,R,g))` is the values of the three respective entropies evaluated for each term.</span>
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master/_modules/ot/gromov/_partial.html

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@@ -1098,18 +1098,18 @@ <h1>Source code for ot.gromov._partial</h1><div class="highlight"><pre>
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<span class="sd"> Parameters</span>
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<span class="sd"> ----------</span>
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<span class="sd"> G : array-like, shape(ns,nt)</span>
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<span class="sd"> G : array-like, shape(ns, nt)</span>
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<span class="sd"> The transport map at a given iteration of the FW</span>
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<span class="sd"> deltaG : array-like (ns,nt)</span>
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<span class="sd"> deltaG : array-like, shape (ns, nt)</span>
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<span class="sd"> Difference between the optimal map `Gc` found by linearization in the</span>
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<span class="sd"> FW algorithm and the value at a given iteration</span>
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<span class="sd"> cost_G : float</span>
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<span class="sd"> Value of the cost at `G`</span>
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<span class="sd"> df_G : array-like (ns,nt)</span>
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<span class="sd"> df_G : array-like, shape (ns, nt)</span>
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<span class="sd"> Gradient of the GW cost at `G`</span>
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<span class="sd"> df_Gc : array-like (ns,nt)</span>
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<span class="sd"> df_Gc : array-like, shape (ns, nt)</span>
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<span class="sd"> Gradient of the GW cost at `Gc`</span>
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<span class="sd"> M : array-like (ns,nt)</span>
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<span class="sd"> M : array-like, shape (ns, nt)</span>
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<span class="sd"> Cost matrix between the features.</span>
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<span class="sd"> reg : float</span>
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<span class="sd"> Regularization parameter.</span>
@@ -1128,7 +1128,7 @@ <h1>Source code for ot.gromov._partial</h1><div class="highlight"><pre>
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<span class="sd"> nb of function call. Useless here</span>
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<span class="sd"> cost_G : float</span>
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<span class="sd"> The value of the cost for the next iteration</span>
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<span class="sd"> df_G : array-like (ns,nt)</span>
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<span class="sd"> df_G : array-like, shape (ns, nt)</span>
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<span class="sd"> Updated gradient of the GW cost</span>
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<span class="sd"> References</span>
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<span class="sd"> Returns</span>
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<span class="sd"> -------</span>
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<span class="sd"> :math: `gamma` : (dim_a, dim_b) ndarray</span>
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<span class="sd"> :math:`gamma` : ndarray, shape (dim_a, dim_b)</span>
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<span class="sd"> Optimal transportation matrix for the given parameters</span>
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<span class="sd"> log : dict</span>
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<span class="sd"> log dictionary returned only if `log` is `True`</span>

master/_modules/ot/lp/solver_1d.html

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@@ -247,7 +247,7 @@ <h1>Source code for ot.lp.solver_1d</h1><div class="highlight"><pre>
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<span class="sd"> where :</span>
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<span class="sd"> - d is the metric</span>
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<span class="sd"> - x_a and x_b are the samples</span>
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<span class="sd"> - :math:`x_a` and :math:`x_b` are the samples</span>
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<span class="sd"> - a and b are the sample weights</span>
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<span class="sd"> This implementation only supports metrics</span>
@@ -257,21 +257,21 @@ <h1>Source code for ot.lp.solver_1d</h1><div class="highlight"><pre>
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<span class="sd"> Parameters</span>
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<span class="sd"> ----------</span>
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<span class="sd"> x_a : (ns,) or (ns, 1) ndarray, float64</span>
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<span class="sd"> x_a : ndarray of float64, shape (ns,) or (ns, 1)</span>
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<span class="sd"> Source dirac locations (on the real line)</span>
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<span class="sd"> x_b : (nt,) or (ns, 1) ndarray, float64</span>
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<span class="sd"> x_b : ndarray of float64, shape (nt,) or (ns, 1)</span>
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<span class="sd"> Target dirac locations (on the real line)</span>
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<span class="sd"> a : (ns,) ndarray, float64, optional</span>
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<span class="sd"> a : ndarray of float64, shape (ns,), optional</span>
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<span class="sd"> Source histogram (default is uniform weight)</span>
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<span class="sd"> b : (nt,) ndarray, float64, optional</span>
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<span class="sd"> b : ndarray of float64, shape (nt,), optional</span>
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<span class="sd"> Target histogram (default is uniform weight)</span>
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<span class="sd"> metric: str, optional (default=&#39;sqeuclidean&#39;)</span>
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<span class="sd"> Metric to be used. Only works with either of the strings</span>
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<span class="sd"> `&#39;sqeuclidean&#39;`, `&#39;minkowski&#39;`, `&#39;cityblock&#39;`, or `&#39;euclidean&#39;`.</span>
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<span class="sd"> p: float, optional (default=1.0)</span>
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<span class="sd"> The p-norm to apply for if metric=&#39;minkowski&#39;</span>
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<span class="sd"> dense: boolean, optional (default=True)</span>
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<span class="sd"> If True, returns math:`\gamma` as a dense ndarray of shape (ns, nt).</span>
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<span class="sd"> If True, returns :math:`\gamma` as a dense ndarray of shape (ns, nt).</span>
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<span class="sd"> Otherwise returns a sparse representation using scipy&#39;s `coo_matrix`</span>
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<span class="sd"> format. Due to implementation details, this function runs faster when</span>
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<span class="sd"> `&#39;sqeuclidean&#39;`, `&#39;minkowski&#39;`, `&#39;cityblock&#39;`, or `&#39;euclidean&#39;` metrics</span>
@@ -285,7 +285,7 @@ <h1>Source code for ot.lp.solver_1d</h1><div class="highlight"><pre>
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<span class="sd"> Returns</span>
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<span class="sd"> -------</span>
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<span class="sd"> gamma: (ns, nt) ndarray</span>
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<span class="sd"> gamma: ndarray, shape (ns, nt)</span>
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<span class="sd"> Optimal transportation matrix for the given parameters</span>
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<span class="sd"> log: dict</span>
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<span class="sd"> If input log is True, a dictionary containing the cost</span>
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<span class="sd"> where :</span>
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<span class="sd"> - d is the metric</span>
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<span class="sd"> - x_a and x_b are the samples</span>
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<span class="sd"> - :math:`x_a` and :math:`x_b` are the samples</span>
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<span class="sd"> - a and b are the sample weights</span>
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<span class="sd"> This implementation only supports metrics</span>
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<span class="sd"> Parameters</span>
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<span class="sd"> ----------</span>
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<span class="sd"> x_a : (ns,) or (ns, 1) ndarray, float64</span>
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<span class="sd"> x_a : ndarray of float64, shape (ns,) or (ns, 1)</span>
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<span class="sd"> Source dirac locations (on the real line)</span>
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<span class="sd"> x_b : (nt,) or (ns, 1) ndarray, float64</span>
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<span class="sd"> x_b : ndarray of float64, shape (nt,) or (ns, 1)</span>
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<span class="sd"> Target dirac locations (on the real line)</span>
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<span class="sd"> a : (ns,) ndarray, float64, optional</span>
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<span class="sd"> a : ndarray of float64, shape (ns,), optional</span>
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<span class="sd"> Source histogram (default is uniform weight)</span>
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<span class="sd"> b : (nt,) ndarray, float64, optional</span>
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<span class="sd"> b : ndarray of float64, shape (nt,), optional</span>
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<span class="sd"> Target histogram (default is uniform weight)</span>
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<span class="sd"> metric: str, optional (default=&#39;sqeuclidean&#39;)</span>
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<span class="sd"> Metric to be used. Only works with either of the strings</span>
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<span class="sd"> `&#39;sqeuclidean&#39;`, `&#39;minkowski&#39;`, `&#39;cityblock&#39;`, or `&#39;euclidean&#39;`.</span>
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<span class="sd"> p: float, optional (default=1.0)</span>
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<span class="sd"> The p-norm to apply for if metric=&#39;minkowski&#39;</span>
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<span class="sd"> dense: boolean, optional (default=True)</span>
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<span class="sd"> If True, returns math:`\gamma` as a dense ndarray of shape (ns, nt).</span>
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<span class="sd"> If True, returns :math:`\gamma` as a dense ndarray of shape (ns, nt).</span>
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<span class="sd"> Otherwise returns a sparse representation using scipy&#39;s `coo_matrix`</span>
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<span class="sd"> format. Only used if log is set to True. Due to implementation details,</span>
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<span class="sd"> this function runs faster when dense is set to False.</span>
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<span class="sd"> Parameters</span>
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<span class="sd"> ----------</span>
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<span class="sd"> M : (nr, nc) ndarray</span>
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<span class="sd"> M : ndarray, shape (nr, nc)</span>
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<span class="sd"> Matrix to shift</span>
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<span class="sd"> shifts: int or (nr,) ndarray</span>
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<span class="sd"> shifts: int or ndarray, shape (nr,)</span>
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<span class="sd"> Returns</span>
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<span class="sd"> -------</span>
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<span class="sd"> Parameters</span>
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<span class="sd"> ----------</span>
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<span class="sd"> u_values: ndarray, shape (n, ...)</span>
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<span class="sd"> u_values : ndarray, shape (n, ...)</span>
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<span class="sd"> Samples</span>
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<span class="sd"> u_weights : ndarray, shape (n, ...), optional</span>
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<span class="sd"> samples weights in the source domain</span>

master/_modules/ot/plot.html

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@@ -116,7 +116,7 @@ <h1>Source code for ot.plot</h1><div class="highlight"><pre>
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<span class="w"> </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;Plot matrix :math:`\mathbf{M}` with the source and target 1D distributions.</span>
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<span class="sd"> Creates a subplot with the source distribution :math:`\mathbf{a}` and target</span>
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<span class="sd"> distribution :math:`\mathbf{b}`t.</span>
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<span class="sd"> distribution :math:`\mathbf{b}`.</span>
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<span class="sd"> In &#39;yx&#39; mode (default), the source is on the left and</span>
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<span class="sd"> the target on the top, and in &#39;xy&#39; mode, source on the bottom (upside</span>
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<span class="sd"> down) and the target on the left.</span>
@@ -153,8 +153,9 @@ <h1>Source code for ot.plot</h1><div class="highlight"><pre>
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<span class="sd"> ax2 : target plot ax</span>
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<span class="sd"> ax3 : coupling plot ax</span>
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<span class="sd"> .. seealso::</span>
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<span class="sd"> :func:`rescale_for_imshow_plot`</span>
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<span class="sd"> See Also</span>
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<span class="sd"> --------</span>
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<span class="sd"> :func:`rescale_for_imshow_plot`</span>
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<span class="sd"> &quot;&quot;&quot;</span>
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<span class="k">assert</span> <span class="n">plot_style</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;yx&quot;</span><span class="p">,</span> <span class="s2">&quot;xy&quot;</span><span class="p">],</span> <span class="s2">&quot;plot_style should be &#39;yx&#39; or &#39;xy&#39;&quot;</span>
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<span class="n">na</span><span class="p">,</span> <span class="n">nb</span> <span class="o">=</span> <span class="n">M</span><span class="o">.</span><span class="n">shape</span>
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<span class="sd"> yr : ndarray, shape (nx,)</span>
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<span class="sd"> Rescaled y values (due to slicing, may have less elements than y)</span>
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<span class="sd"> .. seealso::</span>
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<span class="sd"> :func:`plot1D_mat`</span>
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<span class="sd"> See Also</span>
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<span class="sd"> --------</span>
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<span class="sd"> :func:`plot1D_mat`</span>
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<span class="sd"> &quot;&quot;&quot;</span>
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<span class="c1"># slice over the y values that are in the y range</span>

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