[MRG] New Quickstart guide and revamp User guide (#726)

* rrme to user guide and add quicksrat script

* remoe import of deprecated module

* premier jet quckstart guide

* working on the guide

* add stuff

* comment unbalanced Gromov

* rename section

* first shot done

* better verison quickstart guide

* better verison quickstart guide

* fix doc

* cleanup exmaple

* fix?

* add test

* remove sentence

* call it the unified vs classic API

Author: rflamary

Diff for: RELEASES.md

@@ -15,6 +15,7 @@
 - Added `ot.gaussian.bures_wasserstein_distance` (PR #680)
 - `ot.gaussian.bures_wasserstein_distance` can be batched (PR #680)
 - Backend implementation of `ot.dist` for (PR #701)
+- Updated documentation Quickstart guide and User guide with new API (PR #726)
 
 #### Closed issues
 - Fixed `ot.mapping` solvers which depended on deprecated `cvxpy` `ECOS` solver (PR #692, Issue #668)

Diff for: docs/source/conf.py

@@ -347,7 +347,7 @@ def __getattr__(cls, name):
 }
 
 sphinx_gallery_conf = {
-    "examples_dirs": ["../../examples", "../../examples/da"],
+    "examples_dirs": ["../../examples"],
     "gallery_dirs": "auto_examples",
     "filename_pattern": "plot_",  # (?!barycenter_fgw)
     "nested_sections": False,

Diff for: docs/source/index.rst

@@ -17,9 +17,10 @@ Contents
    :maxdepth: 1
 
    self
-   quickstart
-   all
+   auto_examples/plot_quickstart_guide
    auto_examples/index
+   user_guide
+   all
    releases
    contributors
    contributing

Diff for: docs/source/quickstart.rst renamed to docs/source/user_guide.rst

@@ -1,6 +1,6 @@
 
-Quick start guide
-=================
+User guide
+==========
 
 In the following we provide some pointers about which functions and classes
 to use for different problems related to optimal transport (OT) and machine
@@ -136,12 +136,12 @@ instance the memory cost for an OT problem is always :math:`\mathcal{O}(n^2)` in
 memory because the cost matrix has to be computed. The exact solver in of time
 complexity :math:`\mathcal{O}(n^3\log(n))` and the Sinkhorn solver has been
 proven to be nearly :math:`\mathcal{O}(n^2)` which is still too complex for very
-large scale solvers.
+large scale solvers. For all the generic solvers we need to compute the cost
+matrix and the OT matrix of memory size :math:`\mathcal{O}(n^2)` which can be
+prohibitive for very large scale problems. 
 
-
-If you need to solve OT with large number of samples, we recommend to use
-entropic regularization and memory efficient implementation of Sinkhorn as
-proposed in `GeomLoss <https://www.kernel-operations.io/geomloss/>`_. This
+If you need to solve OT with large number of samples, we provide "lazy" memory efficient implementation of Sinkhorn in pure
+python and using `GeomLoss <https://www.kernel-operations.io/geomloss/>`_. This
 implementation is compatible with Pytorch and can handle large number of
 samples. Another approach to estimate the Wasserstein distance for very large
 number of sample is to use the trick from `Wasserstein GAN
@@ -193,15 +193,19 @@ that will return the optimal transport matrix :math:`\gamma^*`:
 
     # a and b are 1D histograms (sum to 1 and positive)
     # M is the ground cost matrix
+
+    # unified API
+    T = ot.solve(M, a, b).plan  # exact linear program
+
+    # classical API
     T = ot.emd(a, b, M)  # exact linear program
 
 The method implemented for solving the OT problem is the network simplex. It is
 implemented in C from [1]_. It has a complexity of :math:`O(n^3)` but the
 solver is quite efficient and uses sparsity of the solution.
 
 
-
-.. minigallery:: ot.emd
+.. minigallery:: ot.emd, ot.solve
     :add-heading: Examples of use for :any:`ot.emd`
     :heading-level: "
 
@@ -226,7 +230,12 @@ It can computed from an already estimated OT matrix with
 
     # a and b are 1D histograms (sum to 1 and positive)
     # M is the ground cost matrix
-    W = ot.emd2(a, b, M)  # Wasserstein distance / EMD value
+
+    # Wasserstein distance / EMD value with unified API
+    W = ot.solve(M, a, b, return_matrix=False).value  
+
+    # with classical API
+    W = ot.emd2(a, b, M)  
 
 Note that the well known  `Wasserstein distance
 <https://en.wikipedia.org/wiki/Wasserstein_metric>`_ between distributions a and
@@ -246,7 +255,7 @@ the :math:`W_1` Wasserstein distance can be done directly with :any:`ot.emd2`
 when providing :code:`M = ot.dist(xs, xt, metric='euclidean')` to use the Euclidean
 distance.
 
-.. minigallery:: ot.emd2
+.. minigallery:: ot.emd2, ot.solve
     :add-heading: Examples of use for :any:`ot.emd2`
     :heading-level: "
 
@@ -274,6 +283,10 @@ distributions. In the case when the finite sample dataset is supposed Gaussian,
 we provide :any:`ot.gaussian.bures_wasserstein_mapping` that returns the parameters for the
 Monge mapping.
 
+All those special cases are accessible with the unified API of POT through the
+function :any:`ot.solve_sample` with the parameter :code:`method` that allows to
+choose the method used to solve the problem (with :code:`method='1D'` or :code:`method='gaussian'`).
+
 
 Regularized Optimal Transport
 -----------------------------
@@ -330,13 +343,15 @@ The Sinkhorn-Knopp algorithm is implemented in :any:`ot.sinkhorn` and
 linear term. Note that the regularization parameter :math:`\lambda` in the
 equation above is given to those functions with the parameter :code:`reg`.
 
-    >>> import ot
-    >>> a = [.5, .5]
-    >>> b = [.5, .5]
-    >>> M = [[0., 1.], [1., 0.]]
-    >>> ot.sinkhorn(a, b, M, 1)
-    array([[ 0.36552929,  0.13447071],
-        [ 0.13447071,  0.36552929]])
+.. code:: python
+
+    # unified API
+    P = ot.solve(M, a, b, reg=1).plan  # OT Sinkhorn matrix
+    loss = ot.solve(M, a, b, reg=1).value # OT Sinkhorn value
+
+    # classical API
+    P = ot.sinkhorn(a, b, M, reg=1)  # OT Sinkhorn matrix
+    loss = ot.sinkhorn2(a, b, M, reg=1)  # OT Sinkhorn value
 
 More details about the algorithms used are given in the following note.
 
@@ -406,13 +421,10 @@ implementations are not optimized for speed but provide a robust implementation
 of algorithms in [18]_ [19]_.
 
 
-.. minigallery:: ot.sinkhorn
-    :add-heading: Examples of use for :any:`ot.sinkhorn`
+.. minigallery:: ot.sinkhorn ot.sinkhorn2
+    :add-heading: Examples of use for Sinkhorn algorithm
     :heading-level: "
 
-.. minigallery:: ot.sinkhorn2
-    :add-heading: Examples of use for :any:`ot.sinkhorn2`
-    :heading-level: "
 
 
 Other regularizations
@@ -969,18 +981,6 @@ For instance, to disable TensorFlow, set `export POT_BACKEND_DISABLE_TENSORFLOW=
 It's important to note that the `numpy` backend cannot be disabled.
 
 
-List of compatible modules
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-This list will get longer for new releases and will hopefully disappear when POT
-become fully implemented with the backend.
-
-- :any:`ot.bregman`
-- :any:`ot.gromov` (some functions use CPU only solvers with copy overhead)
-- :any:`ot.optim` (some functions use CPU only solvers with copy overhead)
-- :any:`ot.sliced`
-- :any:`ot.utils` (partial)
-
 
 FAQ
 ---

Diff for: examples/plot_OT_2D_samples.py

@@ -65,7 +65,7 @@
 
 # %% EMD
 
-G0 = ot.emd(a, b, M)
+G0 = ot.solve(M, a, b).plan
 
 pl.figure(3)
 pl.imshow(G0, interpolation="nearest")