# Titan Robotics Team 2022: Data Analysis Module
# Written by Arthur Lu & Jacob Levine
# Notes:
# this should be imported as a python module using 'import analysis'
# this should be included in the local directory or environment variable
# this module has not been optimized for multhreaded computing
# number of easter eggs: 2
# setup:
__version__ = "1.0.9.000"
# changelog should be viewed using print(analysis.__changelog__)
__changelog__ = """changelog:
1.0.9.000:
- refactored
- numpyed everything
- removed stats in favor of numpy functions
1.0.8.005:
- minor fixes
1.0.8.004:
- removed a few unused dependencies
1.0.8.003:
- added p_value function
1.0.8.002:
- updated __all__ correctly to contain changes made in v 1.0.8.000 and v 1.0.8.001
1.0.8.001:
- refactors
- bugfixes
1.0.8.000:
- depreciated histo_analysis_old
- depreciated debug
- altered basic_analysis to take array data instead of filepath
- refactor
- optimization
1.0.7.002:
- bug fixes
1.0.7.001:
- bug fixes
1.0.7.000:
- added tanh_regression (logistical regression)
- bug fixes
1.0.6.005:
- added z_normalize function to normalize dataset
- bug fixes
1.0.6.004:
- bug fixes
1.0.6.003:
- bug fixes
1.0.6.002:
- bug fixes
1.0.6.001:
- corrected __all__ to contain all of the functions
1.0.6.000:
- added calc_overfit, which calculates two measures of overfit, error and performance
- added calculating overfit to optimize_regression
1.0.5.000:
- added optimize_regression function, which is a sample function to find the optimal regressions
- optimize_regression function filters out some overfit funtions (functions with r^2 = 1)
- planned addition: overfit detection in the optimize_regression function
1.0.4.002:
- added __changelog__
- updated debug function with log and exponential regressions
1.0.4.001:
- added log regressions
- added exponential regressions
- added log_regression and exp_regression to __all__
1.0.3.008:
- added debug function to further consolidate functions
1.0.3.007:
- added builtin benchmark function
- added builtin random (linear) data generation function
- added device initialization (_init_device)
1.0.3.006:
- reorganized the imports list to be in alphabetical order
- added search and regurgitate functions to c_entities, nc_entities, obstacles, objectives
1.0.3.005:
- major bug fixes
- updated historical analysis
- depreciated old historical analysis
1.0.3.004:
- added __version__, __author__, __all__
- added polynomial regression
- added root mean squared function
- added r squared function
1.0.3.003:
- bug fixes
- added c_entities
1.0.3.002:
- bug fixes
- added nc_entities, obstacles, objectives
- consolidated statistics.py to analysis.py
1.0.3.001:
- compiled 1d, column, and row basic stats into basic stats function
1.0.3.000:
- added historical analysis function
1.0.2.xxx:
- added z score test
1.0.1.xxx:
- major bug fixes
1.0.0.xxx:
- added loading csv
- added 1d, column, row basic stats
"""
__author__ = (
"Arthur Lu <arthurlu@ttic.edu>, "
"Jacob Levine <jlevine@ttic.edu>,"
)
__all__ = [
'_init_device',
'c_entities',
'nc_entities',
'obstacles',
'objectives',
'load_csv',
'basic_stats',
'z_score',
'z_normalize',
'stdev_z_split',
'histo_analysis',
'poly_regression',
'log_regression',
'exp_regression',
'r_squared',
'rms',
'calc_overfit',
'strip_data',
'optimize_regression',
'select_best_regression',
'basic_analysis',
# all statistics functions left out due to integration in other functions
]
# now back to your regularly scheduled programming:
# imports (now in alphabetical order! v 1.0.3.006):
from bisect import bisect_left, bisect_right
import collections
import csv
from decimal import Decimal
import functools
from fractions import Fraction
from itertools import groupby
import math
import matplotlib
import numbers
import numpy as np
import pandas
import random
import scipy
from scipy.optimize import curve_fit
from scipy import stats
from sklearn import *
# import statistics <-- statistics.py functions have been integrated into analysis.py as of v 1.0.3.002
import time
import torch
class error(ValueError):
pass
def _init_device(setting, arg): # initiates computation device for ANNs
if setting == "cuda":
try:
return torch.device(setting + ":" + str(arg) if torch.cuda.is_available() else "cpu")
except:
raise error("could not assign cuda or cpu")
elif setting == "cpu":
try:
return torch.device("cpu")
except:
raise error("could not assign cpu")
else:
raise error("specified device does not exist")
def load_csv(filepath):
with open(filepath, newline='') as csvfile:
file_array = np.array(list(csv.reader(csvfile)))
csvfile.close()
return file_array
# 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
def basic_stats(data, method, arg):
if method == 'debug':
return "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]"
if method == "1d" or method == 0:
data_t = np.array(data).astype(float)
_mean = mean(data_t)
_median = median(data_t)
try:
_mode = mode(data_t)
except:
_mode = None
try:
_stdev = stdev(data_t)
except:
_stdev = None
try:
_variance = variance(data_t)
except:
_variance = None
return _mean, _median, _mode, _stdev, _variance
"""
elif method == "column" or method == 1:
c_data = []
c_data_sorted = []
for i in data:
try:
c_data.append(float(i[arg]))
except:
pass
_mean = mean(c_data)
_median = median(c_data)
try:
_mode = mode(c_data)
except:
_mode = None
try:
_stdev = stdev(c_data)
except:
_stdev = None
try:
_variance = variance(c_data)
except:
_variance = None
return _mean, _median, _mode, _stdev, _variance
elif method == "row" or method == 2:
r_data = []
for i in range(len(data[arg])):
r_data.append(float(data[arg][i]))
_mean = mean(r_data)
_median = median(r_data)
try:
_mode = mode(r_data)
except:
_mode = None
try:
_stdev = stdev(r_data)
except:
_stdev = None
try:
_variance = variance(r_data)
except:
_variance = None
return _mean, _median, _mode, _stdev, _variance
else:
raise error("method error")
"""
# returns z score with inputs of point, mean and standard deviation of spread
def z_score(point, mean, stdev):
score = (point - mean) / stdev
return score
# mode is either 'x' or 'y' or 'both' depending on the variable(s) to be normalized
def z_normalize(x, y, mode):
x_norm = np.array().astype(float)
y_norm = np.array().astype(float)
mean = 0
stdev = 0
if mode == 'x':
_mean, _median, _mode, _stdev, _variance = basic_stats(x, "1d", 0)
for i in range(0, len(x), 1):
x_norm.append(z_score(x[i], _mean, _stdev))
return x_norm, y
if mode == 'y':
_mean, _median, _mode, _stdev, _variance = basic_stats(y, "1d", 0)
for i in range(0, len(y), 1):
y_norm.append(z_score(y[i], _mean, _stdev))
return x, y_norm
if mode == 'both':
_mean, _median, _mode, _stdev, _variance = basic_stats(x, "1d", 0)
for i in range(0, len(x), 1):
x_norm.append(z_score(x[i], _mean, _stdev))
_mean, _median, _mode, _stdev, _variance = basic_stats(y, "1d", 0)
for i in range(0, len(y), 1):
y_norm.append(z_score(y[i], _mean, _stdev))
return x_norm, y_norm
else:
return error('method error')
# returns n-th percentile of spread given mean, standard deviation, lower z-score, and upper z-score
def stdev_z_split(mean, stdev, delta, low_bound, high_bound):
z_split = np.array().astype(float)
i = low_bound
while True:
z_split.append(float((1 / (stdev * math.sqrt(2 * math.pi))) *
math.e ** (-0.5 * (((i - mean) / stdev) ** 2))))
i = i + delta
if i > high_bound:
break
return z_split
def histo_analysis(hist_data, delta, low_bound, high_bound):
if hist_data == 'debug':
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 of standard deviations')
derivative = []
for i in range(0, len(hist_data), 1):
try:
derivative.append(float(hist_data[i - 1]) - float(hist_data[i]))
except:
pass
derivative_sorted = sorted(derivative, key=int)
mean_derivative = basic_stats(derivative_sorted, "1d", 0)[0]
stdev_derivative = basic_stats(derivative_sorted, "1d", 0)[3]
predictions = []
pred_change = 0
i = low_bound
while True:
if i > high_bound:
break
try:
pred_change = mean_derivative + i * stdev_derivative
except:
pred_change = mean_derivative
predictions.append(float(hist_data[-1:][0]) + pred_change)
i = i + delta
return predictions
def poly_regression(x, y, power):
if x == "null": # if x is 'null', then x will be filled with integer points between 1 and the size of y
x = []
for i in range(len(y)):
print(i)
x.append(i + 1)
reg_eq = scipy.polyfit(x, y, deg=power)
eq_str = ""
for i in range(0, len(reg_eq), 1):
if i < len(reg_eq) - 1:
eq_str = eq_str + str(reg_eq[i]) + \
"*(z**" + str(len(reg_eq) - i - 1) + ")+"
else:
eq_str = eq_str + str(reg_eq[i]) + \
"*(z**" + str(len(reg_eq) - i - 1) + ")"
vals = []
for i in range(0, len(x), 1):
z = x[i]
try:
exec("vals.append(" + eq_str + ")")
except:
pass
_rms = rms(vals, y)
r2_d2 = r_squared(vals, y)
return [eq_str, _rms, r2_d2]
def log_regression(x, y, base):
x_fit = []
for i in range(len(x)):
try:
# change of base for logs
x_fit.append(np.log(x[i]) / np.log(base))
except:
pass
# y = reg_eq[0] * log(x, base) + reg_eq[1]
reg_eq = np.polyfit(x_fit, y, 1)
q_str = str(reg_eq[0]) + "* (np.log(z) / np.log(" + \
str(base) + "))+" + str(reg_eq[1])
vals = []
for i in range(len(x)):
z = x[i]
try:
exec("vals.append(" + eq_str + ")")
except:
pass
_rms = rms(vals, y)
r2_d2 = r_squared(vals, y)
return eq_str, _rms, r2_d2
def exp_regression(x, y, base):
y_fit = []
for i in range(len(y)):
try:
# change of base for logs
y_fit.append(np.log(y[i]) / np.log(base))
except:
pass
# y = base ^ (reg_eq[0] * x) * base ^ (reg_eq[1])
reg_eq = np.polyfit(x, y_fit, 1, w=np.sqrt(y_fit))
eq_str = "(" + str(base) + "**(" + \
str(reg_eq[0]) + "*z))*(" + str(base) + "**(" + str(reg_eq[1]) + "))"
vals = []
for i in range(len(x)):
z = x[i]
try:
exec("vals.append(" + eq_str + ")")
except:
pass
_rms = rms(vals, y)
r2_d2 = r_squared(vals, y)
return eq_str, _rms, r2_d2
def tanh_regression(x, y):
def tanh(x, a, b, c, d):
return a * np.tanh(b * (x - c)) + d
reg_eq = np.float64(curve_fit(tanh, np.array(x), np.array(y))[0]).tolist()
eq_str = str(reg_eq[0]) + " * np.tanh(" + str(reg_eq[1]) + \
"*(z - " + str(reg_eq[2]) + ")) + " + str(reg_eq[3])
vals = []
for i in range(len(x)):
z = x[i]
try:
exec("vals.append(" + eq_str + ")")
except:
pass
_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
return metrics.r2_score(np.array(targets), np.array(predictions))
def rms(predictions, targets): # assumes equal size inputs
_sum = 0
for i in range(0, len(targets), 1):
_sum = (targets[i] - predictions[i]) ** 2
return float(math.sqrt(_sum / len(targets)))
def calc_overfit(equation, rms_train, r2_train, x_test, y_test):
# performance overfit = performance(train) - performance(test) where performance is r^2
# error overfit = error(train) - error(test) where error is rms; biased towards smaller values
vals = []
for i in range(0, len(x_test), 1):
z = x_test[i]
exec("vals.append(" + equation + ")")
r2_test = r_squared(vals, y_test)
rms_test = rms(vals, y_test)
return r2_train - r2_test
def strip_data(data, mode):
if mode == "adam": # x is the row number, y are the data
pass
if mode == "eve": # x are the data, y is the column number
pass
else:
raise error("mode error")
# _range in poly regression is the range of powers tried, and in log/exp it is the inverse of the stepsize taken from -1000 to 1000
def optimize_regression(x, y, _range, resolution):
# usage not: for demonstration purpose only, performance is shit
if type(resolution) != int:
raise error("resolution must be int")
x_train = x
y_train = []
for i in range(len(y)):
y_train.append(float(y[i]))
x_test = []
y_test = []
for i in range(0, math.floor(len(x) * 0.5), 1):
index = random.randint(0, len(x) - 1)
x_test.append(x[index])
y_test.append(float(y[index]))
x_train.pop(index)
y_train.pop(index)
#print(x_train, x_test)
#print(y_train, y_test)
eqs = []
rmss = []
r2s = []
for i in range(0, _range + 1, 1):
try:
x, y, z = poly_regression(x_train, y_train, i)
eqs.append(x)
rmss.append(y)
r2s.append(z)
except:
pass
for i in range(1, 100 * resolution + 1):
try:
x, y, z = exp_regression(x_train, y_train, float(i / resolution))
eqs.append(x)
rmss.append(y)
r2s.append(z)
except:
pass
for i in range(1, 100 * resolution + 1):
try:
x, y, z = log_regression(x_train, y_train, float(i / resolution))
eqs.append(x)
rmss.append(y)
r2s.append(z)
except:
pass
try:
x, y, z = tanh_regression(x_train, y_train)
eqs.append(x)
rmss.append(y)
r2s.append(z)
except:
pass
# marks all equations where r2 = 1 as they 95% of the time overfit the data
for i in range(0, len(eqs), 1):
if r2s[i] == 1:
eqs[i] = ""
rmss[i] = ""
r2s[i] = ""
while True: # removes all equations marked for removal
try:
eqs.remove('')
rmss.remove('')
r2s.remove('')
except:
break
overfit = []
for i in range(0, len(eqs), 1):
overfit.append(calc_overfit(eqs[i], rmss[i], r2s[i], x_test, y_test))
return eqs, rmss, r2s, overfit
def select_best_regression(eqs, rmss, r2s, overfit, selector):
b_eq = ""
b_rms = 0
b_r2 = 0
b_overfit = 0
ind = 0
if selector == "min_overfit":
ind = np.argmin(overfit)
b_eq = eqs[ind]
b_rms = rmss[ind]
b_r2 = r2s[ind]
b_overfit = overfit[ind]
if selector == "max_r2s":
ind = np.argmax(r2s)
b_eq = eqs[ind]
b_rms = rmss[ind]
b_r2 = r2s[ind]
b_overfit = overfit[ind]
return b_eq, b_rms, b_r2, b_overfit
def p_value(x, y): # takes 2 1d arrays
return stats.ttest_ind(x, y)[1]
# assumes that rows are the independent variable and columns are the dependant. also assumes that time flows from lowest column to highest column.
def basic_analysis(data):
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("data/data.csv", x, y, -10, 10)
end_g = time.time()
start_a = time.time()
basic_analysis("data/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 mean(data):
return np.mean(data)
def median(data):
return np.median(data)
def mode(data):
return np.argmax(np.bincount(data))
def stdev(data):
return np.std(data)
def variance(data):
return np.var(data)
"""
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)
"""