update readme

1 files changed, 36 insertions, 4 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