# `binary`

## `sokal_dist_matrix`

```
Calculates the Sokal distance matrix for a data matrix `X` using SciPy.

Parameters (inputs)
----------
X: a pandas/polars DataFrame or a NumPy array. It represents a data matrix.

Returns (outputs)
-------
M: the Sokal distance matrix between the rows of X.
```

## `sokal_dist`


```
Calculates the Sokal distance between a pair of vectors.

Parameters (inputs)
----------
xi, xr: a pair of quantitative vectors. They represent a couple of statistical observations.

Returns (outputs)
-------
The Sokal distance between the observations `xi` and `xr`.
```

## `jaccard_dist_matrix`


```
Calculates the Jaccard distance matrix for a data matrix `X` using SciPy.

Parameters (inputs)
----------
X: a pandas/polars DataFrame or a NumPy array. It represents a data matrix.

Returns (outputs)
-------
M: the Jaccard distance matrix between the rows of X.
```

## `jaccard_dist` 

```
Calculates the Jaccard distance between a pair of vectors.

Parameters (inputs)
----------
xi, xr: a pair of quantitative vectors. They represent a couple of statistical observations.

Returns (outputs)
-------
The Jaccard distance between the observations `xi` and `xr`.
```