""" Statistical methods used to define or modify position of glyphs.
References:
Wilkinson L. The Grammer of Graphics, sections 7, 7.1
Method Types:
- Bin: Partitions a space before statistical calculation
- Summary: Produces a single value comprising a statistical summary
- Region: Produces two values bounding an interval.
- Smooth: Produces values representing smoothed versions of the input data.
- Link: Produces edges from pairs of nodes in a graph.
"""
from __future__ import absolute_import
import numpy as np
import pandas as pd
from bokeh.models.sources import ColumnDataSource
from bokeh.core.properties import (HasProps, Float, Either, String, Date, Datetime, Int,
Bool, List, Instance)
from .properties import Column, EitherColumn, ColumnLabel
class Stat(HasProps):
"""Represents a statistical operation to summarize a column of data.
Can be computed from either a ColumnLabel with a ColumnDataSource, *or*, a
discrete column of data.
"""
# inputs
column = ColumnLabel(help="""A column to use for the stat calculation. Required
when providing a ColumnDataSource as input.""")
source = Instance(ColumnDataSource, help="""One option for providing the data
source for stat calculation.""")
values = EitherColumn(Column(Float), Column(Int), Column(String),
Column(Date), Column(Datetime), Column(Bool), default=None, help="""
Second option for providing values for stat calculation is by
passing the actual column of data.""")
# output
value = Float(help="""The value calculated for the stat. Some stats could use
multiple properties to provide the calculation if required.""")
def __init__(self, **properties):
source = properties.pop('source', None)
if source is not None:
if isinstance(source, pd.DataFrame):
source = ColumnDataSource(source)
properties['source'] = source
super(Stat, self).__init__(**properties)
self._refresh()
def _refresh(self):
"""Lazy update of properties, used for initial transform init."""
if self.get_data() is not None:
self.update()
self.calculate()
def set_data(self, data, column=None):
"""Set data properties and update all dependent properties."""
if isinstance(data, pd.DataFrame):
data = ColumnDataSource(data)
if isinstance(data, ColumnDataSource):
self.source = data
if column is not None:
self.column = column
else:
self.values = data
self.update()
self.calculate()
def get_data(self, column=None):
"""Returns the available columnlabel/source values or column values."""
if self.source is not None and (self.column is not None or column is not None):
if column is not None:
col = column
else:
col = self.column
return pd.Series(self.source.data[col])
elif self.values is None and self.source is not None:
return pd.Series(self.source.to_df().index)
elif self.values is not None:
return self.values
else:
return None
def calculate(self):
"""Return transformed value from column label/source or column-like data."""
raise NotImplementedError('You must implement the calculate method '
'for each stat type.')
def update(self):
"""Perform any initial work before the actual calculation is performed."""
pass
class Sum(Stat):
def calculate(self):
self.value = self.get_data().sum()
class Mean(Stat):
def calculate(self):
self.value = self.get_data().mean()
class Count(Stat):
def calculate(self):
self.value = self.get_data().count()
class CountDistinct(Stat):
def calculate(self):
self.value = self.get_data().nunique()
class Median(Stat):
def calculate(self):
self.value = self.get_data().median()
class StdDeviation(Stat):
def calculate(self):
self.value = self.get_data().std()
class Min(Stat):
def calculate(self):
self.value = self.get_data().min()
class Max(Stat):
def calculate(self):
self.value = self.get_data().max()
class Quantile(Stat):
"""Produces the cutpoint that divides the input data by the interval.
Quartiles are a special case of quartiles that divide a dataset into four
equal-size groups. (https://en.wikipedia.org/wiki/Quantile)
"""
interval = Float(default=0.5)
def calculate(self):
self.value = self.get_data().quantile(self.interval)
class Bin(Stat):
"""Represents a single bin of data values and attributes of the bin."""
label = Either(String, List(String))
start = Either(Float, List(Float))
stop = Either(Float, List(Float))
start_label = String()
stop_label = String()
center = Either(Float, List(Float))
stat = Instance(Stat, default=Count())
def __init__(self, bin_label, values=None, source=None, **properties):
if isinstance(bin_label, tuple):
bin_label = list(bin_label)
else:
bin_label = [bin_label]
properties['label'] = bin_label
bounds = self.process_bounds(bin_label)
starts, stops = zip(*bounds)
centers = [(start + stop)/2.0 for start, stop in zip(starts, stops)]
if len(starts) == 1:
starts = starts[0]
stops = stops[0]
centers = centers[0]
else:
starts = list(starts)
stops = list(stops)
centers = list(centers)
properties['start'] = starts
properties['stop'] = stops
properties['center'] = centers
properties['values'] = values
super(Bin, self).__init__(**properties)
@staticmethod
def binstr_to_list(bins):
"""Produce a consistent display of a bin of data."""
value_chunks = bins.split(',')
value_chunks = [val.replace('[', '').replace(']', '').replace('(', '').replace(')', '') for val in value_chunks]
bin_values = [float(value) for value in value_chunks]
return bin_values[0], bin_values[1]
def process_bounds(self, bin_label):
if isinstance(bin_label, list):
return [self.binstr_to_list(dim) for dim in bin_label]
else:
return [self.binstr_to_list(bin_label)]
def update(self):
self.stat.set_data(self.values)
def calculate(self):
self.value = self.stat.value
class BinStats(Stat):
"""A set of statistical calculations for binning values.
Bin counts using: https://en.wikipedia.org/wiki/Freedman%E2%80%93Diaconis_rule
"""
bin_count = Either(Int, Float)
bin_width = Float(default=None, help='Use Freedman-Diaconis rule if None.')
q1 = Quantile(interval=0.25)
q3 = Quantile(interval=0.75)
labels = List(String)
def __init__(self, values=None, column=None, **properties):
properties['values'] = values
properties['column'] = column or 'values'
super(BinStats, self).__init__(**properties)
def update(self):
values = self.get_data()
self.q1.set_data(values)
self.q3.set_data(values)
if self.bin_count is None:
self.calc_num_bins(values)
def calc_num_bins(self, values):
"""Calculate optimal number of bins using IQR.
From: http://stats.stackexchange.com/questions/114490/optimal-bin-width-for-two-dimensional-histogram
"""
iqr = self.q3.value - self.q1.value
if iqr == 0:
self.bin_width = np.sqrt(values.size)
else:
self.bin_width = 2 * iqr * (len(values) ** -(1. / 3.))
self.bin_count = int(np.ceil((values.max() - values.min()) / self.bin_width))
if self.bin_count == 1:
self.bin_count = 3
def calculate(self):
pass
class Bins(Stat):
"""Bins and aggregates dimensions for plotting.
Takes the inputs and produces a list of bins that can be iterated over and
inspected for their metadata. The bins provide easy access to consistent labeling,
bounds, and values.
"""
bin_stat = Instance(BinStats, help="""
A mapping between each dimension and associated binning calculations.
""")
bins = List(Instance(Bin), help="""
A list of the `Bin` instances that were produced as result of the inputs.
Iterating over `Bins` will iterate over this list. Each `Bin` can be inspected
for metadata about the bin and the values associated with it.
""")
stat = Instance(Stat, default=Count(), help="""
The statistical operation to be used on the values in each bin.
""")
bin_count = Int(help="""
An optional list of the number of bins to use for each dimension. If a single
value is provided, then the same number of bins will be used for each.
""")
bin_column = String()
centers_column = String()
aggregate = Bool(default=True)
bin_values = Bool(default=False)
bin_width = Float()
def __init__(self, values=None, column=None, bins=None,
stat='count', source=None, **properties):
if isinstance(stat, str):
stat = stats[stat]()
properties['column'] = column or 'vals'
properties['bins'] = bins
properties['stat'] = stat
properties['values'] = values
properties['source'] = source
super(Bins, self).__init__(**properties)
def _get_stat(self):
stat_kwargs = {}
if self.source is not None:
stat_kwargs['source'] = self.source
stat_kwargs['column'] = self.column
elif self.values is not None:
stat_kwargs['values'] = self.values
stat_kwargs['bin_count'] = self.bin_count
return BinStats(**stat_kwargs)
def update(self):
self.bin_stat = self._get_stat()
self.bin_stat.update()
def calculate(self):
bin_str = '_bin'
self.bin_column = self.column + bin_str
bin_models = []
binned, bin_bounds = pd.cut(self.bin_stat.get_data(), self.bin_stat.bin_count,
retbins=True, include_lowest=True, precision=0)
self.bin_width = np.round(bin_bounds[2] - bin_bounds[1], 1)
if self.source is not None:
# add bin column to data source
self.source.add(binned.tolist(), name=self.bin_column)
df = self.source.to_df()
else:
df = pd.DataFrame({self.column: self.values, self.bin_column: binned})
for name, group in df.groupby(self.bin_column):
bin_models.append(Bin(bin_label=name, values=group[self.column],
stat=self.stat))
self.bins = bin_models
centers = binned.copy()
centers = centers.astype(str)
for bin in self.bins:
centers[binned == bin.label] = bin.center
self.centers_column = self.column + '_center'
if self.source is not None:
self.source.add(centers.tolist(), name=self.centers_column)
else:
df[self.centers_column] = centers
def __getitem__(self, item):
return self.bins[item]
def apply(self, data):
self.set_data(data.source)
return self.source.to_df()
def sort(self, ascending=True):
if self.bins is not None:
self.bins = list(sorted(self.bins, key=lambda x: x.center,
reverse=~ascending))
def bins(data, values=None, column=None, bin_count=None, labels=None,
**kwargs):
"""Specify binning or bins to be used for column or values."""
if isinstance(data, str):
column = data
values = None
else:
column = None
return Bins(values=values, column=column, bin_count=bin_count, **kwargs)
stats = {
'sum': Sum,
'mean': Mean,
'count': Count,
'nunique': CountDistinct,
'median': Median,
'stddev': StdDeviation,
'min': Min,
'max': Max,
'quantile': Quantile
}