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---

Drawing Unravelled Persistence Diagrams
=======================================

First we create and plot a point cloud of a sphere
and of a torus.

```{code-cell} ipython3
from tadasets import sphere, torus, plot3d

my_sphere = sphere( r = 2, n = 100 )
my_torus  = torus( c = 2, a = 1, n = 100 )

plot3d( my_sphere );
plot3d( my_torus  );
```

Then we compute persistence intervals for each point cloud.

```{code-cell} ipython3
import numpy as np
import torch
import gudhi

simplex_trees = [
    gudhi.AlphaComplex( points = point_cloud ).create_simplex_tree() for
    point_cloud in ( my_sphere, my_torus )
]

[ simplex_tree.compute_persistence() for simplex_tree in simplex_trees ];

persistence_intervals = [
    [ torch.from_numpy( 
        np.float32( simplex_tree.persistence_intervals_in_dimension(dim) )
    ) for dim in range(3) ] for
    simplex_tree in simplex_trees
]
```

Then we complement the notebook to allow us
to draw several unravelled persistence diagrams
without rendering the HTML document invalid
and we instantiate the
<a href="../persunraveltorch.draw.html#persunraveltorch.draw.Draw">
  class `Draw`</a>
with its default parameters.

```{code-cell} ipython3
from functools import partial
from persunraveltorch.draw import Draw

Draw.complement_notebook()

draw = Draw()
```

Then we draw unravelled persistence diagrams
corresponding to the previously created point clouds
using the arctan function to map all intervals
into the range between 0 and π/2.
(You can choose different bounds when instantiating
<a href="../persunraveltorch.draw.html#persunraveltorch.draw.Draw">
  `Draw`</a>
using the `range_intervals` keyword argument.)

```{code-cell} ipython3
draw( list(
    map( partial(map, torch.atan), persistence_intervals )
) )
```

Then we draw the same diagrams again except that we scale
all persistence intervals with a factor of 1.7 before applying
arctan.

```{code-cell} ipython3
draw( list(
    map(
        partial(map, lambda intervals_d: torch.atan(1.7 * intervals_d)),
        persistence_intervals
    )
) )
```

Finally,
we save the first version as a standalone SVG file.

```{code-cell} ipython3
with open('unravelled-diagrams.svg', 'w') as svg_file:
    svg_file.write(
        draw(
            standalone = True,
            intervals = list(
                map( partial(map, torch.atan), persistence_intervals )
            )
        )
    )
```