# Welcome to triarray’s documentation!¶

triarray is a Python package for working with symmetric matrices in non- redundant format. This format stores only the elements in the upper or lower triangle, thus halving memory requirements.

When storing symmetric matrices in standard array format about half of the elements are redundant, meaning you are using twice as much memory or disk space as you need to. This is especially common in scientific applications when working with large distance or similarity matrices.

Space can be saved by storing only the lower or upper triangle of the array, but standard operations like getting an element by row and column become awkward. triarray provides tools for working with data in this format.

triarray uses Numba ‘s just-in-time compilation to generate high-performance C code that works with any data type and is easily extendable (including within a Jupyter notebook).

## Example¶

The `scipy.spatial.distance.pdist()` function calculates pairwise distances between all rows of a matrix and returns only the upper triangle of the full distance matrix:

```import numpy as np
from scipy.spatial.distance import pdist

vectors = np.random.rand(1000, 10)

dists = pdist(vectors)  # Shape is (499500,) instead of (1000, 1000)
```

The `TriMatrix` class wraps a 1D Numpy array storing the condensed data and exposes an interface that lets you treat it as if it was still in matrix format:

```from triarray import TriMatrix

matrix = TriMatrix(dists, upper=True, diag_val=0)

matrix.size  # Number of rows/columns in matrix
>>> 1000

matrix[0, 1]  # Distance between 0th and 1st vector
>>> 1.1610289956390953

matrix[0, 0]  # Diagonals are zero
>>> 0.0

matrix[0]  # 0th row of matrix
>>> array([ 0.        ,  1.161029  ,  1.03467554,  1.32559121,  1.26185034,
...
```

It even supports Numpy’s advanced indexing with integer arrays of arbitrary shape:

```rows, cols = np.ix_([0, 1, 2], [3, 4, 5])
rows, cols
>>> (array([[0],
[1],
[3]]), array([[4, 5, 6]]))

matrix[rows, cols]
>>> array([[ 1.26185034,  1.08800206,  1.30490993],
[ 0.99262394,  1.33044029,  1.20373382],
[ 1.42524039,  1.36195143,  1.70404005]])
```