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862 lines
24 KiB
Python
862 lines
24 KiB
Python
#Titan Robotics Team 2022: Data Analysis Module
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#Written by Arthur Lu & Jacob Levine
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#Notes:
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# this should be imported as a python module using 'import analysis'
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# this should be included in the local directory or environment variable
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# this module has not been optimized for multhreaded computing
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#Number of easter eggs: 2
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#setup:
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__version__ = "1.0.3.008"
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__author__ = (
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"Arthur Lu <arthurlu@ttic.edu>, "
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"Jacob Levine <jlevine@ttic.edu>,"
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)
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__all__ = [
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'_init_device',
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'c_entities',
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'nc_entities',
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'obstacles',
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'objectives',
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'load_csv',
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'basic_stats',
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'z_score',
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'stdev_z_split',
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'histo_analysis', #histo_analysis_old is intentionally left out as it has been depreciated since v 1.0.1.005
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'poly_regression',
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'r_squared',
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'rms',
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'basic_analysis',
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#all statistics functions left out due to integration in other functions
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]
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#now back to your regularly scheduled programming:
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#imports (now in alphabetical order! v 1.0.3.006):
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from bisect import bisect_left, bisect_right
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import collections
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import csv
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from decimal import Decimal
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import functools
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from fractions import Fraction
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from itertools import groupby
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import math
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import matplotlib
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import numbers
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import numpy as np
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import random
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import scipy
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from sklearn import *
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#import statistics <-- statistics.py functions have been integrated into analysis.py as of v 1.0.3.002
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import time
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import torch
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def _init_device (setting, arg): #initiates computation device for ANNs
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if setting == "cuda":
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temp = setting + ":" + str(arg)
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the_device_woman = torch.device(temp if torch.cuda.is_available() else "cpu")
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return the_device_woman #name that reference
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elif setting == "cpu":
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the_device_woman = torch.device("cpu")
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return the_device_woman #name that reference
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else:
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return "error: specified device does not exist"
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class c_entities:
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c_names = []
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c_ids = []
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c_pos = []
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c_properties = []
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c_logic = []
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def debug(self):
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print("c_entities has attributes names, ids, positions, properties, and logic. __init__ takes self, 1d array of names, 1d array of ids, 2d array of positions, nd array of properties, and nd array of logic")
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return[self.c_names, self.c_ids, self.c_pos, self.c_properties, self.c_logic]
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def __init__(self, names, ids, pos, properties, logic):
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self.c_names = names
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self.c_ids = ids
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self.c_pos = pos
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self.c_properties = properties
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self.c_logic = logic
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return None
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def append(self, n_name, n_id, n_pos, n_property, n_logic):
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self.c_names.append(n_name)
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self.c_ids.append(n_id)
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self.c_pos.append(n_pos)
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self.c_properties.append(n_property)
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self.c_logic.append(n_logic)
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return None
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def edit(self, search, n_name, n_id, n_pos, n_property, n_logic):
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position = 0
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for i in range(0, len(self.c_ids), 1):
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if self.c_ids[i] == search:
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position = i
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if n_name != "null":
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self.c_names[position] = n_name
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if n_id != "null":
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self.c_ids[position] = n_id
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if n_pos != "null":
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self.c_pos[position] = n_pos
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if n_property != "null":
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self.c_properties[position] = n_property
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if n_logic != "null":
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self.c_logic[position] = n_logic
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return None
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def search(self, search):
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position = 0
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for i in range(0, len(self.c_ids), 1):
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if self.c_ids[i] == search:
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position = i
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return [self.c_names[position], self.c_ids[position], self.c_pos[position], self.c_properties[position], self.c_logic[position]]
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def regurgitate(self):
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return[self.c_names, self.c_ids, self.c_pos, self.c_properties, self.c_logic]
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class nc_entities:
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c_names = []
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c_ids = []
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c_pos = []
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c_properties = []
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c_effects = []
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def debug(self):
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print ("nc_entities (non-controlable entities) has attributes names, ids, positions, properties, and effects. __init__ takes self, 1d array of names, 1d array of ids, 2d array of positions, 2d array of properties, and 2d array of effects.")
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return[self.c_names, self.c_ids, self.c_pos, self.c_properties, self.c_effects]
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def __init__(self, names, ids, pos, properties, effects):
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self.c_names = names
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self.c_ids = ids
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self.c_pos = pos
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self.c_properties = properties
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self.c_effects = effects
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return None
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def append(self, n_name, n_id, n_pos, n_property, n_effect):
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self.c_names.append(n_name)
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self.c_ids.append(n_id)
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self.c_pos.append(n_pos)
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self.c_properties.append(n_property)
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self.c_effects.append(n_effect)
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return None
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def edit(self, search, n_name, n_id, n_pos, n_property, n_effect):
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position = 0
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for i in range(0, len(self.c_ids), 1):
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if self.c_ids[i] == search:
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position = i
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if n_name != "null":
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self.c_names[position] = n_name
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if n_id != "null":
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self.c_ids[position] = n_id
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if n_pos != "null":
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self.c_pos[position] = n_pos
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if n_property != "null":
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self.c_properties[position] = n_property
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if n_effect != "null":
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self.c_effects[position] = n_effect
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return None
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def search(self, search):
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position = 0
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for i in range(0, len(self.c_ids), 1):
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if self.c_ids[i] == search:
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position = i
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return [self.c_names[position], self.c_ids[position], self.c_pos[position], self.c_properties[position], self.c_effects[position]]
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def regurgitate(self):
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return[self.c_names, self.c_ids, self.c_pos, self.c_properties, self.c_effects]
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class obstacles:
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c_names = []
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c_ids = []
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c_perim = []
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c_effects = []
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def debug(self):
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print("obstacles has atributes names, ids, positions, perimeters, and effects. __init__ takes self, 1d array of names, 1d array of ids, 2d array of position, 3d array of perimeters, 2d array of effects.")
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return [self.c_names, self.c_ids, self.c_perim, self.c_effects]
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def __init__(self, names, ids, perims, effects):
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self.c_names = names
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self.c_ids = ids
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self.c_perim = perims
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self.c_effects = effects
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return None
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def append(self, n_name, n_id, n_perim, n_effect):
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self.c_names.append(n_name)
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self.c_ids.append(n_id)
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self.c_perim.append(n_perim)
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self.c_effects.append(n_effect)
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return None
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def edit(self, search, n_name, n_id, n_perim, n_effect):
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position = 0
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for i in range(0, len(self.c_ids), 1):
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if self.c_ids[i] == search:
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position = i
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if n_name != "null":
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self.c_names[position] = n_name
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if n_id != "null":
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self.c_ids[position] = n_id
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if n_perim != "null":
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self.c_perim[position] = n_perim
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if n_effect != "null":
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self.c_effects[position] = n_effect
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return None
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def search(self, search):
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position = 0
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for i in range(0, len(self.c_ids), 1):
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if self.c_ids[i] == search:
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position = i
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return [self.c_names[position], self.c_ids[position], self.c_perim[position], self.c_effects[position]]
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def regurgitate(self):
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return[self.c_names, self.c_ids, self.c_perim, self.c_effects]
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class objectives:
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c_names = []
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c_ids = []
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c_pos = []
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c_effects = []
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def debug(self):
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print("objectives has atributes names, ids, positions, and effects. __init__ takes self, 1d array of names, 1d array of ids, 2d array of position, 1d array of effects.")
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return [self.c_names, self.c_ids, self.c_pos, self.c_effects]
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def __init__(self, names, ids, pos, effects):
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self.c_names = names
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self.c_ids = ids
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self.c_pos = pos
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self.c_effects = effects
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return None
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def append(self, n_name, n_id, n_pos, n_effect):
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self.c_names.append(n_name)
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self.c_ids.append(n_id)
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self.c_pos.append(n_pos)
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self.c_effects.append(n_effect)
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return None
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def edit(self, search, n_name, n_id, n_pos, n_effect):
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position = 0
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print(self.c_ids)
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for i in range(0, len(self.c_ids), 1):
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if self.c_ids[i] == search:
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position = i
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if n_name != "null":
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self.c_names[position] = n_name
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if n_id != "null":
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self.c_ids[position] = n_id
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if n_pos != "null":
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self.c_pos[position] = n_pos
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if n_effect != "null":
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self.c_effects[position] = n_effect
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return None
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def search(self, search):
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position = 0
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for i in range(0, len(self.c_ids), 1):
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if self.c_ids[i] == search:
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position = i
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return [self.c_names[position], self.c_ids[position], self.c_pos[position], self.c_effects[position]]
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def regurgitate(self):
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return[self.c_names, self.c_ids, self.c_pos, self.c_effects]
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def load_csv(filepath):
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with open(filepath, newline = '') as csvfile:
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file_array = list(csv.reader(csvfile))
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return file_array
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def basic_stats(data, method, arg): # data=array, mode = ['1d':1d_basic_stats, 'column':c_basic_stats, 'row':r_basic_stats], arg for mode 1 or mode 2 for column or row
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if method == 'debug':
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out = "basic_stats requires 3 args: data, mode, arg; where data is data to be analyzed, mode is an int from 0 - 2 depending on type of analysis (by column or by row) and is only applicable to 2d arrays (for 1d arrays use mode 1), and arg is row/column number for mode 1 or mode 2; function returns: [mean, median, mode, stdev, variance]"
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return out
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if method == "1d" or method == 0:
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data_t = []
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for i in range (0, len(data) - 1, 1):
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data_t.append(float(data[i]))
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_mean = mean(data_t)
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_median = median(data_t)
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try:
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_mode = mode(data_t)
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except:
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_mode = None
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try:
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_stdev = stdev(data_t)
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except:
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_stdev = None
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try:
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_variance = variance(data_t)
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except:
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_variance = None
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out = [_mean, _median, _mode, _stdev, _variance]
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return out
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elif method == "column" or method == 1:
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c_data = []
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c_data_sorted = []
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for i in data:
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try:
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c_data.append(float(i[arg]))
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except:
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pass
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_mean = mean(c_data)
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_median = median(c_data)
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try:
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_mode = mode(c_data)
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except:
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_mode = None
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try:
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_stdev = stdev(c_data)
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except:
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_stdev = None
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try:
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_variance = variance(c_data)
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except:
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_variance = None
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out = [_mean, _median, _mode, _stdev, _variance]
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return out
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elif method == "row" or method == 2:
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r_data = []
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for i in range(len(data[arg])):
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r_data.append(float(data[arg][i]))
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_mean = mean(r_data)
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_median = median(r_data)
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try:
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_mode = mode(r_data)
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except:
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_mode = None
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try:
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_stdev = stdev(r_data)
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except:
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_stdev = None
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try:
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_variance = variance(r_data)
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except:
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_variance = None
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out = [_mean, _median, _mode, _stdev, _variance]
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return out
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else:
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return ["ERROR: method error"]
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def z_score(point, mean, stdev): #returns z score with inputs of point, mean and standard deviation of spread
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score = (point - mean)/stdev
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return score
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def stdev_z_split(mean, stdev, delta, low_bound, high_bound): #returns n-th percentile of spread given mean, standard deviation, lower z-score, and upper z-score
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z_split = []
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i = low_bound
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while True:
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z_split.append(float((1 / (stdev * math.sqrt(2 * math.pi))) * math.e ** (-0.5 * (((i - mean) / stdev) ** 2))))
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i = i + delta
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if i > high_bound:
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break
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return z_split
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def histo_analysis_old(hist_data): #note: depreciated since v 1.0.1.005
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if hist_data == 'debug':
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return['lower estimate (5%)', 'lower middle estimate (25%)', 'middle estimate (50%)', 'higher middle estimate (75%)', 'high estimate (95%)', 'standard deviation', 'note: this has been depreciated']
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derivative = []
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for i in range(0, len(hist_data) - 1, 1):
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derivative.append(float(hist_data[i+1]) - float(hist_data[i]))
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derivative_sorted = sorted(derivative, key=int)
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mean_derivative = basic_stats(derivative_sorted, "1d", 0)[0]
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print(mean_derivative)
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stdev_derivative = basic_stats(derivative_sorted, "1d", 0)[3]
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low_bound = mean_derivative + -1.645 * stdev_derivative
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lm_bound = mean_derivative + -0.674 * stdev_derivative
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mid_bound = mean_derivative * 0 * stdev_derivative
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hm_bound = mean_derivative + 0.674 * stdev_derivative
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high_bound = mean_derivative + 1.645 * stdev_derivative
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low_est = float(hist_data[-1:][0]) + low_bound
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lm_est = float(hist_data[-1:][0]) + lm_bound
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mid_est = float(hist_data[-1:][0]) + mid_bound
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hm_est = float(hist_data[-1:][0]) + hm_bound
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high_est = float(hist_data[-1:][0]) + high_bound
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return [low_est, lm_est, mid_est, hm_est, high_est, stdev_derivative]
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def histo_analysis(hist_data, delta, low_bound, high_bound):
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if hist_data == 'debug':
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return ('returns list of predicted values based on historical data; input delta for delta step in z-score and lower and higher bounds in number for standard deviations')
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derivative = []
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for i in range(0, len(hist_data) - 1, 1):
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derivative.append(float(hist_data[i + 1]) - float(hist_data [i]))
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derivative_sorted = sorted(derivative, key=int)
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mean_derivative = basic_stats(derivative_sorted,"1d", 0)[0]
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stdev_derivative = basic_stats(derivative_sorted, "1d", 0)[3]
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predictions = []
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pred_change = 0
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i = low_bound
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while True:
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if i > high_bound:
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break
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try:
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pred_change = mean_derivative + i * stdev_derivative
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except:
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pred_change = mean_derivative
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predictions.append(float(hist_data[-1:][0]) + pred_change)
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i = i + delta
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return predictions
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def poly_regression(x, y, power):
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if x == "null": #if x is 'null', then x will be filled with integer points between 1 and the size of y
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x = []
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for i in range(len(y)):
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print(i)
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x.append(i+1)
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reg_eq = scipy.polyfit(x, y, deg = power)
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print(reg_eq)
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eq_str = ""
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for i in range(0, len(reg_eq), 1):
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if i < len(reg_eq)- 1:
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eq_str = eq_str + str(reg_eq[i]) + "*(z**" + str(len(reg_eq) - i - 1) + ")+"
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else:
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eq_str = eq_str + str(reg_eq[i]) + "*(z**" + str(len(reg_eq) - i - 1) + ")"
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vals = []
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for i in range(0, len(x), 1):
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print(x[i])
|
|
z = x[i]
|
|
|
|
exec("vals.append(" + eq_str + ")")
|
|
|
|
print(vals)
|
|
|
|
_rms = rms(vals, y)
|
|
|
|
r2_d2 = r_squared(vals, y)
|
|
|
|
return [eq_str, _rms, r2_d2]
|
|
|
|
def r_squared(predictions, targets): # assumes equal size inputs
|
|
|
|
out = metrics.r2_score(targets, predictions)
|
|
|
|
return out
|
|
|
|
def rms(predictions, targets): # assumes equal size inputs
|
|
|
|
out = 0
|
|
|
|
_sum = 0
|
|
|
|
avg = 0
|
|
|
|
for i in range(0, len(targets), 1):
|
|
|
|
_sum = (targets[i] - predictions[i]) ** 2
|
|
|
|
avg = _sum/len(targets)
|
|
|
|
out = math.sqrt(avg)
|
|
|
|
return float(out)
|
|
|
|
def basic_analysis(filepath): #assumes that rows are the independent variable and columns are the dependant. also assumes that time flows from lowest column to highest column.
|
|
|
|
data = load_csv(filepath)
|
|
row = len(data)
|
|
|
|
column = []
|
|
|
|
for i in range(0, row, 1):
|
|
|
|
column.append(len(data[i]))
|
|
|
|
column_max = max(column)
|
|
row_b_stats = []
|
|
row_histo = []
|
|
|
|
for i in range(0, row, 1):
|
|
row_b_stats.append(basic_stats(data, "row", i))
|
|
row_histo.append(histo_analysis(data[i], 0.67449, -0.67449, 0.67449))
|
|
|
|
column_b_stats = []
|
|
|
|
for i in range(0, column_max, 1):
|
|
column_b_stats.append(basic_stats(data, "column", i))
|
|
|
|
return[row_b_stats, column_b_stats, row_histo]
|
|
|
|
def benchmark(x, y):
|
|
|
|
start_g = time.time()
|
|
generate_data("benchmark_data.csv", x, y, -10, 10)
|
|
end_g = time.time()
|
|
|
|
start_a = time.time()
|
|
basic_analysis("benchmark_data.csv")
|
|
end_a = time.time()
|
|
|
|
return [(end_g - start_g), (end_a - start_a)]
|
|
|
|
def generate_data(filename, x, y, low, high):
|
|
|
|
file = open(filename, "w")
|
|
|
|
for i in range (0, y, 1):
|
|
|
|
temp = ""
|
|
|
|
for j in range (0, x - 1, 1):
|
|
|
|
temp = str(random.uniform(low, high)) + "," + temp
|
|
|
|
temp = temp + str(random.uniform(low, high))
|
|
file.write(temp + "\n")
|
|
|
|
def debug():
|
|
|
|
data = load_csv('data.txt')
|
|
|
|
print("--------------------------------")
|
|
|
|
print(basic_stats(0, 'debug', 0))
|
|
print(basic_stats(data, "column", 0))
|
|
print(basic_stats(data, "row", 0))
|
|
print(z_score(10, basic_stats(data, "column", 0)[0], basic_stats(data, "column", 0)[3]))
|
|
print(histo_analysis(data[0], 0.01, -1, 1))
|
|
print(stdev_z_split(3.3, 0.2, 0.1, -5, 5))
|
|
|
|
print("--------------------------------")
|
|
|
|
game_c_entities = c_entities(["bot", "bot", "bot"], [0, 1, 2], [[10, 10], [-10, -10], [10, -10]], ["shit", "bad", "worse"], ["triangle", "square", "circle"])
|
|
game_c_entities.append("bot", 3, [-10, 10], "useless", "pentagram")
|
|
game_c_entities.edit(0, "null", "null", "null", "null", "triagon")
|
|
print(game_c_entities.search(0))
|
|
print(game_c_entities.debug())
|
|
print(game_c_entities.regurgitate())
|
|
|
|
print("--------------------------------")
|
|
|
|
game_nc_entities = nc_entities(["cube", "cube", "ball"], [0, 1, 2], [[0, 0.5], [1, 1.5], [2, 2]], ["1;1;1;10', '2;1;1;20", "r=0.5, 5"], ["1", "1", "0"])
|
|
game_nc_entities.append("cone", 3, [1, -1], "property", "effect")
|
|
game_nc_entities.edit(2, "sphere", 10, [5, -5], "new prop", "new effect")
|
|
print(game_nc_entities.search(10))
|
|
print(game_nc_entities.debug())
|
|
print(game_nc_entities.regurgitate())
|
|
|
|
print("--------------------------------")
|
|
|
|
game_obstacles = obstacles(["wall", "fortress", "castle"], [0, 1, 2],[[[10, 10], [10, 9], [9, 10], [9, 9]], [[-10, 9], [-10, -9], [-9, -10]], [[5, 0], [4, -1], [-4, -1]]] , [0, 0.01, 10])
|
|
game_obstacles.append("bastion", 3, [[50, 50], [49, 50], [50, 49], [49, 49]], 75)
|
|
game_obstacles.edit(0, "motte and bailey", "null", [[10, 10], [9, 10], [10, 9], [9, 9]], 0.01)
|
|
print(game_obstacles.search(0))
|
|
print(game_obstacles.debug())
|
|
print(game_obstacles.regurgitate())
|
|
|
|
print("--------------------------------")
|
|
|
|
game_objectives = objectives(["switch", "scale", "climb"], [0,1,2], [[0,0],[1,1],[2,0]], ["0,1", "1,1", "0,5"])
|
|
game_objectives.append("auto", 3, [0, 10], "1, 10")
|
|
game_objectives.edit(3, "null", 4, "null", "null")
|
|
print(game_objectives.search(4))
|
|
print(game_objectives.debug())
|
|
print(game_objectives.regurgitate())
|
|
|
|
print("--------------------------------")
|
|
|
|
print(poly_regression([1, 2, 3, 4, 5], [1, 2, 4, 8, 16], 2))
|
|
|
|
#statistics def below------------------------------------------------------------------------------------------------------------------------------------------------------
|
|
|
|
class StatisticsError(ValueError):
|
|
pass
|
|
|
|
def _sum(data, start=0):
|
|
count = 0
|
|
n, d = _exact_ratio(start)
|
|
partials = {d: n}
|
|
partials_get = partials.get
|
|
T = _coerce(int, type(start))
|
|
for typ, values in groupby(data, type):
|
|
T = _coerce(T, typ) # or raise TypeError
|
|
for n,d in map(_exact_ratio, values):
|
|
count += 1
|
|
partials[d] = partials_get(d, 0) + n
|
|
if None in partials:
|
|
|
|
total = partials[None]
|
|
assert not _isfinite(total)
|
|
else:
|
|
|
|
total = sum(Fraction(n, d) for d, n in sorted(partials.items()))
|
|
return (T, total, count)
|
|
|
|
def _isfinite(x):
|
|
try:
|
|
return x.is_finite() # Likely a Decimal.
|
|
except AttributeError:
|
|
return math.isfinite(x) # Coerces to float first.
|
|
|
|
def _coerce(T, S):
|
|
|
|
assert T is not bool, "initial type T is bool"
|
|
|
|
if T is S: return T
|
|
|
|
if S is int or S is bool: return T
|
|
if T is int: return S
|
|
|
|
if issubclass(S, T): return S
|
|
if issubclass(T, S): return T
|
|
|
|
if issubclass(T, int): return S
|
|
if issubclass(S, int): return T
|
|
|
|
if issubclass(T, Fraction) and issubclass(S, float):
|
|
return S
|
|
if issubclass(T, float) and issubclass(S, Fraction):
|
|
return T
|
|
|
|
msg = "don't know how to coerce %s and %s"
|
|
raise TypeError(msg % (T.__name__, S.__name__))
|
|
|
|
def _exact_ratio(x):
|
|
|
|
try:
|
|
|
|
if type(x) is float or type(x) is Decimal:
|
|
return x.as_integer_ratio()
|
|
try:
|
|
|
|
return (x.numerator, x.denominator)
|
|
except AttributeError:
|
|
try:
|
|
|
|
return x.as_integer_ratio()
|
|
except AttributeError:
|
|
|
|
pass
|
|
except (OverflowError, ValueError):
|
|
|
|
assert not _isfinite(x)
|
|
return (x, None)
|
|
msg = "can't convert type '{}' to numerator/denominator"
|
|
raise TypeError(msg.format(type(x).__name__))
|
|
|
|
def _convert(value, T):
|
|
|
|
if type(value) is T:
|
|
|
|
return value
|
|
if issubclass(T, int) and value.denominator != 1:
|
|
T = float
|
|
try:
|
|
|
|
return T(value)
|
|
except TypeError:
|
|
if issubclass(T, Decimal):
|
|
return T(value.numerator)/T(value.denominator)
|
|
else:
|
|
raise
|
|
|
|
def _counts(data):
|
|
|
|
table = collections.Counter(iter(data)).most_common()
|
|
if not table:
|
|
return table
|
|
|
|
maxfreq = table[0][1]
|
|
for i in range(1, len(table)):
|
|
if table[i][1] != maxfreq:
|
|
table = table[:i]
|
|
break
|
|
return table
|
|
|
|
|
|
def _find_lteq(a, x):
|
|
|
|
i = bisect_left(a, x)
|
|
if i != len(a) and a[i] == x:
|
|
return i
|
|
raise ValueError
|
|
|
|
|
|
def _find_rteq(a, l, x):
|
|
|
|
i = bisect_right(a, x, lo=l)
|
|
if i != (len(a)+1) and a[i-1] == x:
|
|
return i-1
|
|
raise ValueError
|
|
|
|
|
|
def _fail_neg(values, errmsg='negative value'):
|
|
|
|
for x in values:
|
|
if x < 0:
|
|
raise StatisticsError(errmsg)
|
|
yield x
|
|
|
|
def mean(data):
|
|
|
|
if iter(data) is data:
|
|
data = list(data)
|
|
n = len(data)
|
|
if n < 1:
|
|
raise StatisticsError('mean requires at least one data point')
|
|
T, total, count = _sum(data)
|
|
assert count == n
|
|
return _convert(total/n, T)
|
|
|
|
def median(data):
|
|
|
|
data = sorted(data)
|
|
n = len(data)
|
|
if n == 0:
|
|
raise StatisticsError("no median for empty data")
|
|
if n%2 == 1:
|
|
return data[n//2]
|
|
else:
|
|
i = n//2
|
|
return (data[i - 1] + data[i])/2
|
|
|
|
def mode(data):
|
|
|
|
table = _counts(data)
|
|
if len(table) == 1:
|
|
return table[0][0]
|
|
elif table:
|
|
raise StatisticsError(
|
|
'no unique mode; found %d equally common values' % len(table)
|
|
)
|
|
else:
|
|
raise StatisticsError('no mode for empty data')
|
|
|
|
def _ss(data, c=None):
|
|
|
|
if c is None:
|
|
c = mean(data)
|
|
T, total, count = _sum((x-c)**2 for x in data)
|
|
|
|
U, total2, count2 = _sum((x-c) for x in data)
|
|
assert T == U and count == count2
|
|
total -= total2**2/len(data)
|
|
assert not total < 0, 'negative sum of square deviations: %f' % total
|
|
return (T, total)
|
|
|
|
def variance(data, xbar=None):
|
|
|
|
if iter(data) is data:
|
|
data = list(data)
|
|
n = len(data)
|
|
if n < 2:
|
|
raise StatisticsError('variance requires at least two data points')
|
|
T, ss = _ss(data, xbar)
|
|
return _convert(ss/(n-1), T)
|
|
|
|
def stdev(data, xbar=None):
|
|
|
|
var = variance(data, xbar)
|
|
try:
|
|
return var.sqrt()
|
|
except AttributeError:
|
|
return math.sqrt(var)
|