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GRIMMER_SD.py
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import math
import re
##this is a stand alone function for standard deviations along with code for testing
def round_up(number,places):
if type(number)==type('string'):
pass
else:
number=repr(number)
if number[-1]=='5':
decimals=len(number.split('.')[-1])
if places<decimals:
return round(float(number[:-1]+'6'),places)
else:
return round(float(number),places)
else:
return round(float(number),places)
var_precision=12
#use floats for values except for size and Type, size is int Type is either "Sample", "Population", or random string
def grimmer(sd,sd_decimals,size,Type,mean=None,mean_decimals=None):
global possibilities
global averages_even
global averages_odd
global pattern_even
global pattern_odd
global averages_zero
global low
global high
global pattern
import importlib
mod = importlib.import_module('patterns.'+str(size))
pattern_zero=mod.pattern_zero[:]
pattern_even=mod.pattern_even[:]
pattern_odd=mod.pattern_odd[:]
averages_even=sorted(zip(mod.averages_even.copy().keys(),mod.averages_even.copy().values()))
averages_odd=sorted(zip(mod.averages_odd.copy().keys(),mod.averages_odd.copy().values()))
pattern_zero_rounded=[round_up('.'+repr(n).split('.')[1],5) for n in pattern_zero]
averages_zero={round_up('.'+repr(n).split('.')[1],5):mod.averages_even.copy()[n] for n in mod.averages_even.copy() if round_up('.'+repr(n).split('.')[1],5) in pattern_zero_rounded}
averages_zero=sorted(zip(averages_zero.copy().keys(),averages_zero.copy().values()))
def loop(low,high):
possibilities=[]
if low==0:
for index,i in enumerate(pattern_zero):
possibilities.append([i,index])
low=1
loop=0
X=True
if low%2==0:
pattern_1=pattern_even
pattern_2=pattern_odd
else:
pattern_1=pattern_odd
pattern_2=pattern_even
while True:
if X==True:
for index,i in enumerate(pattern_1):
value=low+i+loop
possibilities.append([value,index])
if value>=high:
X=False
break
loop+=1
if X==False:
break
for index,i in enumerate(pattern_2):
value=low+i+loop
possibilities.append([value,index])
if value>=high:
X=False
break
loop+=1
else:
break
return possibilities
if mean==None:
grim=False
else:
if round_up(round_up(mean*size,0)/size,mean_decimals)==mean:
grim=True
else:
return "GRIM failed"
lower=sd-.5/(10**sd_decimals)
higher=sd+.5/(10**sd_decimals)
low=math.floor(lower**2)
high=math.ceil(higher**2)
sample_count=0
population_count=0
if Type!='Sample':
possibilities=loop(low,high)
if grim:
for j in possibilities:
## print j
if int(j[0])==0:
if round_up('.'+repr(mean).split('.')[1],mean_decimals) in [round_up(ave,mean_decimals) for ave in averages_zero[j[1]][1]]:
if round_up(j[0]**.5,sd_decimals)==sd:
population_count+=1
elif int(j[0])%2==0:
if round_up('.'+repr(mean).split('.')[1],mean_decimals) in [round_up(ave,mean_decimals) for ave in averages_even[j[1]][1]]:
if round_up(j[0]**.5,sd_decimals)==sd:
population_count+=1
else:
if round_up('.'+repr(mean).split('.')[1],mean_decimals) in [round_up(ave,mean_decimals) for ave in averages_odd[j[1]][1]]:
if round_up(j[0]**.5,sd_decimals)==sd:
population_count+=1
else:
for j in possibilities:
if round_up(j[0]**.5,sd_decimals)==sd:
population_count+=1
if Type!='Population':
#recalculate low and high for sample variance
low=math.floor(low*(size-1)/size)
high=math.ceil(high*(size-1)/size)
possibilities=loop(low,high)
if grim:
for j in possibilities:
if int(j[0])==0:
if round_up('.'+repr(mean).split('.')[1],mean_decimals) in [round_up(ave,mean_decimals) for ave in averages_zero[j[1]][1]]:
if round_up((j[0]*size/(size-1))**.5,sd_decimals)==sd:
sample_count+=1
elif int(j[0])%2==0:
if round_up('.'+repr(mean).split('.')[1],mean_decimals) in [round_up(ave,mean_decimals) for ave in averages_even[j[1]][1]]:
if round_up((j[0]*size/(size-1))**.5,sd_decimals)==sd:
sample_count+=1
else:
if round_up('.'+repr(mean).split('.')[1],mean_decimals) in [round_up(ave,mean_decimals) for ave in averages_odd[j[1]][1]]:
if round_up((j[0]*size/(size-1))**.5,sd_decimals)==sd:
sample_count+=1
else:
for j in possibilities:
if round_up((j[0]*size/(size-1))**.5,sd_decimals)==sd:
sample_count+=1
return sample_count,population_count
#######thorough testing
#######note, it might be possible to get a key error if large standard deviations are tested here
#######this is fixable but this test shouldn't be using large values anyways
std_places=2
ave_places=2
##for r in range(5,100):
## import importlib
## mod = importlib.import_module('patterns.'+str(r))
## global_pattern_zero=mod.pattern_zero[:]
## global_pattern_even=mod.pattern_even[:]
## global_pattern_odd=mod.pattern_odd[:]
## global_averages_even=mod.averages_even.copy()
## global_averages_odd=mod.averages_odd.copy()
## global_pattern_zero_rounded=[round_up('.'+repr(n).split('.')[1],5) for n in global_pattern_zero]
## global_averages_zero={round_up('.'+repr(n).split('.')[1],5):global_averages_even[n] for n in global_averages_even if round_up('.'+repr(n).split('.')[1],5) in global_pattern_zero_rounded}
## test=global_pattern_zero[:]
## for n in range(1,3):
## if n%2==0:
## for value in global_pattern_even:
## test.append(value+n)
## else:
## for value in global_pattern_odd:
## test.append(value+n)
## print r, len(test),test[-1]
## pattern_zero=mod.pattern_zero[:]
## pattern_even=mod.pattern_even[:]
## pattern_odd=mod.pattern_odd[:]
## averages_even=mod.averages_even.copy()
## averages_odd=mod.averages_odd.copy()
## pattern_zero_rounded=[round_up('.'+repr(n).split('.')[1],5) for n in pattern_zero]
## averages_zero={round_up('.'+repr(n).split('.')[1],5):averages_even[n] for n in averages_even if round_up('.'+repr(n).split('.')[1],5) in pattern_zero_rounded}
## for i in test:
## #for 'Population':
#### std=round_up(i**.5,std_places)
## ##for 'Sample':
## std=round_up((i*float(r)/(r-1))**.5,std_places)
## if int(i)==0:
## ave=round_up(repr(global_averages_zero[round_up('.'+repr(i).split('.')[1],5)][0]),ave_places)
## elif int(i)%2==0:
## ave=round_up(repr(global_averages_even[round_up('.'+repr(i).split('.')[1],var_precision)][0]),ave_places)
## else:
## ave=round_up(repr(global_averages_odd[round_up('.'+repr(i).split('.')[1],var_precision)][0]),ave_places)
## ##for 'Population'
#### if grimmer(std,std_places,r,'Population',ave,ave_places)[1]!=1:
#### print i,std,ave,r,low,high,grimmer(std,std_places,r,'Population',ave,ave_places)
##
## ##for 'Sample':
## if grimmer(std,std_places,r,'Sample',ave,ave_places)[0]!=1:
## print i,std,ave,r,low,high,grimmer(std,std_places,r,'Sample',ave,ave_places)
######random testing
import random
def variance(data,u):
return sum([(i-u)**2 for i in data])/len(data)
for r in range(5,100):
print r
std_places=2
ave_places=2
for i in range(1):
test=[random.randint(0,10) for k in range(r)]
mean=round_up(sum(test)/float(len(test)),ave_places)
true_mean=round_up(sum(test)/float(len(test)),16)
#for 'Population':
std=round_up(variance(test,true_mean)**.5,std_places)
## if grimmer(std,std_places,r,'Population',mean,ave_places)[1]<1:
## print grimmer(std,std_places,r,'Population',mean,ave_places),test
print grimmer(std,std_places,r,'Population',mean,ave_places),std,std**2,mean
#for 'Sample'
## std=round_up((variance(test,true_mean)*len(test)/(len(test)-1))**.5,std_places)
## if grimmer(std,std_places,r,'Sample',mean,ave_places)[0]<1:
## print grimmer(std,std_places,r,'Sample',mean,ave_places),test
## print grimmer(std,std_places,r,'Sample',mean,ave_places),std,std**2,mean