T-Digest data structure

## Project description

# tdigest
### Efficient percentile estimation of streaming or distributed data
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This is a Python implementation of Ted Dunning's [t-digest](https://github.com/tdunning/t-digest) data structure. The t-digest data structure is designed around computing accurate estimates from either streaming data, or distributed data. These estimates are percentiles, quantiles, trimmed means, etc. Two t-digests can be added, making the data structure ideal for map-reduce settings, and can be serialized into much less than 10kB (instead of storing the entire list of data).

See a blog post about it here: [Percentile and Quantile Estimation of Big Data: The t-Digest](http://dataorigami.net/blogs/napkin-folding/19055451-percentile-and-quantile-estimation-of-big-data-the-t-digest)

### Installation
*tdigest* is compatible with both Python 2 and Python 3.

```
pip install tdigest
```

### Usage

#### Update the digest sequentially

```
from tdigest import TDigest
from numpy.random import random

digest = TDigest()
for x in range(5000):
digest.update(random())

print(digest.percentile(15)) # about 0.15, as 0.15 is the 15th percentile of the Uniform(0,1) distribution
```

#### Update the digest in batches

```
another_digest = TDigest()
another_digest.batch_update(random(5000))
print(another_digest.percentile(15))
```

#### Sum two digests to create a new digest

```
sum_digest = digest + another_digest
```

#### To dict or serializing a digest with JSON

You can use the to_dict() method to turn a TDigest object into a standard Python dictionary.
```
digest = TDigest()
digest.update(1)
digest.update(2)
digest.update(3)
print(digest.to_dict())
```
Or you can get only a list of Centroids with `centroids_to_list()`.
```
digest.centroids_to_list()
```

Similarly, you can restore a Python dict of digest values with `update_from_dict()`. Centroids are merged with any existing ones in the digest.
For example, make a fresh digest and restore values from a python dictionary.
```
digest = TDigest()
digest.update_from_dict({'K': 25, 'delta': 0.01, 'centroids': [{'c': 1.0, 'm': 1.0}, {'c': 1.0, 'm': 2.0}, {'c': 1.0, 'm': 3.0}]})
```

K and delta values are optional, or you can provide only a list of centroids with `update_centroids_from_list()`.
```
digest = TDigest()
digest.update_centroids([{'c': 1.0, 'm': 1.0}, {'c': 1.0, 'm': 2.0}, {'c': 1.0, 'm': 3.0}])
```

If you want to serialize with other tools like JSON, you can first convert to_dict().
```
json.dumps(digest.to_dict())
```

Alternatively, make a custom encoder function to provide as default to the standard json module.
```
def encoder(digest_obj):
return digest_obj.to_dict()
```
Then pass the encoder function as the default parameter.
```
json.dumps(digest, default=encoder)
```

### API

`TDigest.`

- `update(x, w=1)`: update the tdigest with value `x` and weight `w`.
- `batch_update(x, w=1)`: update the tdigest with values in array `x` and weight `w`.
- `compress()`: perform a compression on the underlying data structure that will shrink the memory footprint of it, without hurting accuracy. Good to perform after adding many values.
- `percentile(p)`: return the `p`th percentile. Example: `p=50` is the median.
- `cdf(x)`: return the CDF the value `x` is at.
- `trimmed_mean(p1, p2)`: return the mean of data set without the values below and above the `p1` and `p2` percentile respectively.
- `to_dict()`: return a Python dictionary of the TDigest and internal Centroid values.
- `update_from_dict(dict_values)`: update from serialized dictionary values into the TDigest object.
- `centroids_to_list()`: return a Python list of the TDigest object's internal Centroid values.
- `update_centroids_from_list(list_values)`: update Centroids from a python list.

## Project details

This version 0.5.2.2 0.5.2.1 0.5.2.0 0.5.1.0 0.5.0.0 0.4.1.0 0.4.0.2 0.4.0.1 0.4.0 0.3.0 0.2.0 0.1.2 0.1.1 0.1.0

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