update readme

3 files changed, 80 insertions, 8 deletions

diff --git a/README.md b/README.md
index 09da51b..4aa4cc5 100644
--- a/README.md
+++ b/README.md
@@ -72,9 +72,42 @@ obviously you need CUDA installed and a compatible GPU.
 
 ## Examples
 
-The examples folder contain several examples and use case for the library. The full documentation is available on [Readthedocs](http://pot.readthedocs.io/)
+### Short examples
 
- Here is a list of the Python notebooks if you want a quick look:
+* Import the toolbox
+```python
+import ot
+```
+* Compute Wasserstein distances
+```python
+# a,b are 1D histograms (sum to 1 and positive)
+# M is the ground cost matrix
+Wd=ot.emd2(a,b,M) # exact linear program
+# if b is a matrix compute all distances to a and return a vector
+```
+* Compute OT matrix
+```python
+# a,b are 1D histograms (sum to 1 and positive)
+# M is the ground cost matrix
+Totp=ot.emd(a,b,M) # exact linear program
+Totp_reg=ot.sinkhorn(a,b,M,reg) # entropic regularized OT
+```
+* Compute Wasserstein barycenter
+```python
+# A is a n*d matrix containing d  1D histograms
+# M is the ground cost matrix
+ba=ot.barycenter(A,M,reg) # reg is regularization parameter
+```
+
+
+
+
+### Examples and Notebooks
+
+The examples folder contain several examples and use case for the library. The full documentation is available on [Readthedocs](http://pot.readthedocs.io/).
+
+
+Here is a list of the Python notebooks available [here](https://github.com/rflamary/POT/blob/master/notebooks/) if you want a quick look:
 
 * [1D optimal transport](https://github.com/rflamary/POT/blob/master/notebooks/Demo_1D_OT.ipynb)
 * [OT Ground Loss](https://github.com/rflamary/POT/blob/master/notebooks/Demo_Ground_Loss.ipynb)
@@ -88,8 +121,7 @@ The examples folder contain several examples and use case for the library. The f
 * [OT mapping estimation for color transfer in images](https://github.com/rflamary/POT/blob/master/notebooks/Demo_Image_ColorAdaptation_mapping.ipynb)
 * [Wasserstein Discriminant Analysis](https://github.com/rflamary/POT/blob/master/notebooks/Demo_Wasserstein_Discriminant_Analysis.ipynb)
 
-
-You can also see the notebooks with [Jupyter nbviewer](https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/examples/).
+You can also see the notebooks with [Jupyter nbviewer](https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/notebooks/).
 
 ## Acknowledgements
 
diff --git a/docs/source/readme.rst b/docs/source/readme.rst
index 6898296..611001b 100644
--- a/docs/source/readme.rst
+++ b/docs/source/readme.rst
@@ -93,11 +93,51 @@ obviously you need CUDA installed and a compatible GPU.
 Examples
 --------
 
+Short examples
+~~~~~~~~~~~~~~
+
+-  Import the toolbox
+
+   .. code:: python
+
+       import ot
+
+-  Compute Wasserstein distances
+
+   .. code:: python
+
+       # a,b are 1D histograms (sum to 1 and positive)
+       # M is the ground cost matrix
+       Wd=ot.emd2(a,b,M) # exact linear program
+       # if b is a matrix compute all distances to a and return a vector
+
+-  Compute OT matrix
+
+   .. code:: python
+
+       # a,b are 1D histograms (sum to 1 and positive)
+       # M is the ground cost matrix
+       Totp=ot.emd(a,b,M) # exact linear program
+       Totp_reg=ot.sinkhorn(a,b,M,reg) # entropic regularized OT
+
+-  Compute Wasserstein barycenter
+
+   .. code:: python
+
+       # A is a n*d matrix containing d  1D histograms
+       # M is the ground cost matrix
+       ba=ot.barycenter(A,M,reg) # reg is regularization parameter
+
+Examples and Notebooks
+~~~~~~~~~~~~~~~~~~~~~~
+
 The examples folder contain several examples and use case for the
 library. The full documentation is available on
-`Readthedocs <http://pot.readthedocs.io/>`__
+`Readthedocs <http://pot.readthedocs.io/>`__.
 
-Here is a list of the Python notebooks if you want a quick look:
+Here is a list of the Python notebooks available
+`here <https://github.com/rflamary/POT/blob/master/notebooks/>`__ if you
+want a quick look:
 
 -  `1D optimal
    transport <https://github.com/rflamary/POT/blob/master/notebooks/Demo_1D_OT.ipynb>`__
@@ -123,7 +163,7 @@ Here is a list of the Python notebooks if you want a quick look:
    Analysis <https://github.com/rflamary/POT/blob/master/notebooks/Demo_Wasserstein_Discriminant_Analysis.ipynb>`__
 
 You can also see the notebooks with `Jupyter
-nbviewer <https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/examples/>`__.
+nbviewer <https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/notebooks/>`__.
 
 Acknowledgements
 ----------------
diff --git a/setup.py b/setup.py
index 347c882..9e08ccc 100755
--- a/setup.py
+++ b/setup.py
@@ -21,7 +21,7 @@ __version__ = re.search(
 ROOT = os.path.abspath(os.path.dirname(__file__))
 
 
-# convert markdown readme to rst in pypandoc installed
+# convert markdown readme to rst if pypandoc installed
 try:
    import pypandoc
    README = pypandoc.convert('README.md', 'rst')