Minor change in optimal_transport

optimal_transport.ipynb

@@ -43,7 +43,7 @@
     "from ipywidgets import interact, fixed, FloatSlider, RadioButtons\n",
     "rcParams['figure.figsize'] = (8., 6.)  # Enlarge figure\n",
     "# A slider for p\n",
-    "sliderd = dict(min=-1., max=2., step=0.1, value=1.1, continuous_update=False)\n",
+    "sliderd = dict(min=-1., max=2., step=0.05, value=1.1, continuous_update=False)\n",
     "\n",
     "from earth_movers import EarthMovers1D, EarthMovers2D"
    ]
@@ -105,7 +105,8 @@
     }
    },
    "source": [
-    "Solve the earth movers problem for 1000-position samples."
+    "Solve the earth movers problem for 1000-position samples.\n",
+    "The darker the line, the longer the distance."
    ]
   },
   {
 %% Cell type:markdown id: tags:
 
 # Course of Dario Trevisan: Optimal transport
 
 %% Cell type:markdown id: tags:
 
 We solve the earth movers problem using the [POT](https://pot.readthedocs.io/en/stable/index.html) library.
 
 First, some python initializations.
 
 %% Cell type:code id: tags:
 
 ``` python
 %matplotlib inline
 from matplotlib import rcParams
 from ipywidgets import interact, fixed, FloatSlider, RadioButtons
 rcParams['figure.figsize'] = (8., 6.)  # Enlarge figure
 # A slider for p
-sliderd = dict(min=-1., max=2., step=0.1, value=1.1, continuous_update=False)
+sliderd = dict(min=-1., max=2., step=0.05, value=1.1, continuous_update=False)
 
 from earth_movers import EarthMovers1D, EarthMovers2D
 ```
 
 %% Cell type:markdown id: tags:
 
 ## 1D case
 
 
 Solve the earth movers problem for 50-position samples.
 
 %% Cell type:code id: tags:
 
 ``` python
 em1D = EarthMovers1D(50)
 interact(em1D.plot_ot, p=FloatSlider(**sliderd), plot_points=fixed(True));
 ```
 
 %% Cell type:markdown id: tags:
 
 ## 2D case
 
 Solve the earth movers problem for 50-position samples.
 
 %% Cell type:code id: tags:
 
 ``` python
 em2D = EarthMovers2D(100)
 interact(em2D.plot_ot, p=FloatSlider(**sliderd), plot_points=fixed(True));
 ```
 
 %% Cell type:markdown id: tags:
 
 Solve the earth movers problem for 1000-position samples.
+The darker the line, the longer the distance.
 
 %% Cell type:code id: tags:
 
 ``` python
 em2D_large = EarthMovers2D(1000)
 interact(em2D_large.plot_ot, p=FloatSlider(**sliderd), plot_points=fixed(False));
 ```
 
 %% Cell type:markdown id: tags:
 
 ## Histogram of distance
 
 %% Cell type:markdown id: tags:
 
 Plot the histogram of distance for 2000-position samples on the 1D and 2D problems.
 
 %% Cell type:code id: tags:
 
 ``` python
 def plot_histogram(dimension=2, p=1.1):
     nsim = 2000
     em = EarthMovers1D(nsim) if dimension == 1 else EarthMovers2D(nsim)
     return em.plot_distance_histogram(p, bins=20)
 
 interact(plot_histogram, dimension=RadioButtons(options=[1, 2], value=2), p=FloatSlider(**sliderd));
 ```
 
 %% Cell type:markdown id: tags:
 
 ## Todo
 
 - Uniform random blue and red points on a square #
 - Its optimal mathching, with p=1, n=500 #
 - Histogram of matching length in d=1,2,3 #
 - one dimensional matching for p=1.1 and p=0.9, comparison
 - The scaling algorithm for local optimal matching
 
 PoT: <https://pot.readthedocs.io/en/stable/auto_examples/plot_OT_2D_samples.html>