def mdc_reduce(machine):
stack = [machine]
while stack:
m = stack.pop()
if m.is_trivial():
return True
m = m.md_reduce()
fs = factor.factor(m)
if not fs:
m = m.dual()
if m.is_trivial():
return True
fs = factor.factor(m)
if not fs:
continue
for a, b in fs:
c = mealy.product(b, a)
d = c.md_reduce()
if d.is_trivial() or d.dual().is_trivial():
return True
if d != c and d.dual() != c:
stack.append(d)
return False
def smallest_multiple(divisors):
"""
Returns the smallest positive integer evenly divisible by all of the
integers in divisors.
"""
# Maps each prime factor to a count (e.g. 8 factors into three 2s, so its
# map would look like {2 : 3}).
factor_counts = defaultdict(int)
# Factor all integers in the list of divisors.
for d in divisors:
t = tree.Tree(d)
f.factor(t)
# Count up the num of occurrences of each prime factor.
leaf_counts = defaultdict(int) # defaultdict sets initial counts to 0
for leaf in t.get_leaves():
leaf_counts[leaf] += 1
# If num of occurrences of a factor exceeds what we already have,
# change count to the larger value (e.g. a number needs at least three
# 2s in its list of prime factors in order to be divisible by 8).
for leaf in leaf_counts:
if (factor_counts[leaf] < leaf_counts[leaf]):
factor_counts[leaf] = leaf_counts[leaf]
# Now that we have a count of all prime factors for our smallest multiple,
# we multiply them all together.
smallest_multiple = 1
for factor in factor_counts:
smallest_multiple *= factor ** factor_counts[factor]
return smallest_multiple
def is_primitive(x, p):
for q in factor(p - 1):
if len(factor(q)) == 0:
v = (x**((p - 1) / q) % p)
# print('testing {}**(({} - 1)/{}) % {} = {}'.format(x, p, q, p, v))
if v == 1:
return False
return True
def largest_prime_factor(n):
"""
Generates a factor tree then performs depth-first search to find largest
prime factor.
"""
t = tree.Tree(n)
factor.factor(t)
largest = dfs(t)
return largest
def _evaluate_one(self, n, num_p):
start_init_time = time()
pqs = PQSieve(n, h=[], num_p=num_p,
progress=False
)
end_init_time = time()
start_search_time = time()
res = pqs.search()
end_search_time = time()
self.init_times.append(end_init_time - start_init_time)
self.search_times.append(end_search_time - start_search_time)
self.res_list.append(res)
self.primes_used_list.append(pqs.primes_used)
self.R_size_list.append(pqs.R_size)
self.total_i_list.append(pqs.total_i)
self.last_j_list.append(pqs.last_j)
self.last_r_list.append(pqs.p_plus_q)
self.T_list.append(pqs.p_plus_q - pqs.sqrt_n + 1)
Tp = pqs.last_j - pqs.b0_ind + 1 if pqs.total_i == 0 else (pqs.R_size - pqs.b0_ind) + (pqs.total_i - 1) * pqs.R_size + (pqs.last_j + 1)
self.Tp_list.append(Tp)
del pqs
start_qs_time = time()
qs_res = qs.factor(n)
end_qs_time = time()
self.qs_times.append(end_qs_time - start_qs_time)
self.qs_res_list.append(qs_res)
def _evaluate_fermat(self, n):
start_init_time = time()
fermat = Fermat(n, progress=False)
end_init_time = time()
start_search_time = time()
res = fermat.search()
end_search_time = time()
self.init_times.append(end_init_time - start_init_time)
self.search_times.append(end_search_time - start_search_time)
self.res_list.append(res)
self.primes_used_list.append([])
self.R_size_list.append(0)
self.total_i_list.append(fermat.total_i)
self.last_j_list.append(0)
self.last_r_list.append(fermat.p_plus_q)
self.T_list.append(fermat.p_plus_q - fermat.sqrt_n + 1)
Tp = fermat.total_i + 1
self.Tp_list.append(Tp)
del fermat
start_qs_time = time()
qs_res = qs.factor(n)
end_qs_time = time()
self.qs_times.append(end_qs_time - start_qs_time)
self.qs_res_list.append(qs_res)
def minG(m):
p = phi(m)
mp = factor(p)
checkLst = [p // i for i in mp]
i = 2
while 1:
if all((i**n - 1) % m != 0 for n in checkLst): return i
i += 1
def gs(m, num=100):
'''return list of m's primary roots below num'''
p = phi(m)
mp = factor(p)
checkLst = [p // i for i in mp]
return [
i for i in range(2, num) if all((i**n - 1) % m != 0 for n in checkLst)
]
def test_factor(self):
for k in range(5):
for _ in range(500):
expected = sorted(random.choices(PRIMES, k=k))
N = product(expected)
with self.subTest(N=N, expected=expected):
found = sorted(factor(N))
self.assertEqual(expected, found)
def is_prim_root(x: int, modulus: int) -> bool:
phi_modulus = phi.phi(modulus)
phi_factor_dict = factor.factor(phi_modulus)
for single_factor in phi_factor_dict.keys():
if (modular_exp.modular_exp(x, phi_modulus // single_factor, \
modulus) == 1):
return False
return True
def print_solution(ret):
# print solution
out = []
prod = 1
for x,y in zip(P, ret):
if y:
out.append(x)
prod *= x
print N, prod, prod%N, out
print tm(out),"%",tm(factor(N)[0]),"==",prod%N
def addtl_augs(strength, img_in, lbl_in, i=0):
print('\nCreate additional variation {0}'.format(str(i + 1)))
addtl_choices = {
0: img_in,
1: HighContrast,
2: LowContrast,
3: Sharpen,
4: Blur,
5: UniformNoise,
6: TV_Chambolle,
7: HistogramEqualization,
8: [img_in, Skew],
9: [HighContrast, Skew],
10: [LowContrast, Skew],
11: [Sharpen, Skew],
12: [Blur, ElasticDistortion],
13: [UniformNoise, ElasticDistortion],
14: [TV_Chambolle, ElasticDistortion],
15: [HistogramEqualization, ElasticDistortion]
}
if factor(strength, i) == 0:
img_out, lbl_out = img_in, lbl_in
else:
if i == 0:
img_out, lbl_out = img_in, lbl_in
elif i < 8:
img_out, lbl_out = addtl_choices[i](img_in, factor(strength,
i)), lbl_in
else:
if i == 8:
img1 = img_in
else:
img1 = addtl_choices[i][0](img_in, factor(strength, i - 8))
if i < 12:
img_out, lbl_out = addtl_choices[i][1](img1, lbl_in,
factor(strength, 8))
else:
img_out, lbl_out = addtl_choices[i][1](img1, lbl_in,
factor(strength, 9))
return img_out, lbl_out, addtl_choices
def phi(n: int) -> int:
if (n == 1):
return 1
factor_dict = factor.factor(n)
result = functools.reduce(operator.mul,
map(lambda x: n - n // x, factor_dict.keys()))
result = result // exp.exp(n, len(factor_dict.keys()) - 1)
return result
def create_key():
"""
return (pub_key, priv_key) pair
"""
while True:
p = get_rand_prime(2**10, 2**16)
q = get_rand_prime(2**10, 2**16)
if gcd(p, q) == 2:
break
phi = (p - 1) * (q - 1)
f = factor(p - 1) + factor(q - 1)
d, dp, dq = 0, 0, 0
while True:
e = get_rand_prime(1, phi)
if e not in f:
d = eea(e, phi)[1]
dp = d % (p - 1)
dq = d % (q - 1)
if dp & 1 == dq & 1:
break
return (e, p * q), (p, q, dp, dq)
def experiment(k, lamb):
print(f"Process {k} {lamb} start")
folder = f"./record/k_{k}_lambda_{lamb}"
if not os.path.exists(folder):
os.makedirs(folder)
with open(os.path.join(folder, "log.txt"), 'w+') as f:
Xtrain = np.array(load_npz("train.npz").todense())
Xtest = np.array(load_npz("test.npz").todense())
U, V, record = factor(Xtrain, Xtest, k, 1e-2, lamb, 500, rmse_thd=1e-5, f=f)
np.savetxt(os.path.join(folder, "U.txt"), U)
np.savetxt(os.path.join(folder, "V.txt"), V)
with open(os.path.join(folder, "record.json"), "w") as f:
record = [(float(x[0]), float(x[1])) for x in record]
f.write(json.dumps(record))
print(f"process k: {k}, lambda {lamb} finish")
def get_prim_root_generic(n: int) -> int:
stats = get_prim_root_stats(n)
p = stats[2]
l = stats[3]
if (stats[0] == False):
raise ValueError("get_prim_root_generic: no primitive " + \
"root of %d" % n)
# 若 p == 2，则一定 n == 2 或 n == 4
if (p == 2):
# n == 4
if stats[1]:
return 3
# n == 2
else:
return 1
if stats[1]:
modulus = n // 2
else:
modulus = n
phi_modulus = phi.phi_prime_power(p, l)
phi_factor_dict = factor.factor(p - 1)
# 不存在的因数不应该加入字典
if (l != 1):
phi_factor_dict[p] = l - 1
for i in range(2, n):
failed_flag = False
for single_factor in phi_factor_dict.keys():
if (modular_exp.modular_exp(i, \
phi_modulus // single_factor, modulus) == 1):
failed_flag = True
break
if (failed_flag):
continue
else:
return i
# 不应该运行到这里
raise RuntimeError("get_prim_root_generic: cannot find " + \
"primitive root of %d while it must have one" % n)
def get_prim_root_list(n: int) -> int:
stats = get_prim_root_stats(n)
p = stats[2]
l = stats[3]
if (stats[0] == False):
raise ValueError("get_prim_root_generic: no primitive " + \
"root of %d" % n)
# 若 p == 2，则一定 n == 2 或 n == 4
if (p == 2):
# n == 4
if stats[1]:
return 3
# n == 2
else:
return 1
result = []
modulus = exp.exp(p, l)
phi_modulus = phi.phi_prime_power(p, l)
phi_factor_dict = factor.factor(p - 1)
# 不存在的因数不应该加入字典
if (l != 1):
phi_factor_dict[p] = l - 1
for i in range(2, p):
failed_flag = False
for single_factor in phi_factor_dict.keys():
if (modular_exp.modular_exp(i, \
phi_modulus // single_factor, modulus) == 1):
failed_flag = True
break
if (failed_flag):
continue
else:
result.append(i)
return result
#!/usr/bin/python
import itertools
import factor
dlimit = 20
if dlimit < 3:
dlimit
else:
common_factors = {}
for x in range(3, dlimit):
factors = factor.factor(x)
mcf = []
for k, g in itertools.groupby(sorted(factors)):
z = list(g)
mcf = z if len(z) > len(mcf) else mcf
if mcf[0] not in common_factors or len(mcf) > common_factors[mcf[0]]:
common_factors[mcf[0]] = len(mcf)
prod = 1
print(common_factors)
for x in common_factors:
prod *= x ** common_factors[x]
print(prod)
def generator(x): fact, phi = factor(x-1) #g = sorted(fact)[::-1][0] return fact
def factorUnary(inString):
M = len(inString)
return factor(str(M))
def factsuff():
if tk.token.code == CodeTable['*'] or tk.token.code == CodeTable['/']:
muloper()
factor()
factsuff()
def test_factor_7_return_7_in_list(self):
self.assertEqual(factor.factor(7), [7])
#!/usr/bin/python #acleetus from factor import factor from triangle import triangle from doubling import doubling from factorial import factorial from pascal import pascal from occurrences import num_occurrences print factor(60) print factor(45) print factor(35) print factor(13) triangle(3) triangle(5) print doubling(0.1) print doubling(0.05) print doubling(0.01) print factorial(4) print factorial(0) pascal(10) print num_occurrences(["a", "b", "a", "b", "c", "b", "d", "e"], "b")
def test_factor_9_return_3_3_in_list(self):
self.assertEqual(factor.factor(9), [3, 3])
def get_expts(nrange):
nums = factor(this_num)
return [nums.get(n, 0)
for n in nrange]
def test_factor_one_return_empty_list(self):
self.assertEqual(factor.factor(1), [])
def test_factor_zero_return_empty_list(self):
self.assertEqual(factor.factor(0), [])
def test_factor_big_return_correct_in_list(self):
self.assertEqual(factor.factor(2 * 2 * 3 * 5 * 5 * 7 * 11 * 17 * 19),
[2, 2, 3, 5, 5, 7, 11, 17, 19])
#problem3.py
import sys, math
sys.path.append('/Users/nathanielgentile/Documents/OCW/compsci101/Python')
import factor
factlist = []
for i in range(1, int(math.sqrt(600851475143))+1):
if factor.factor(i, 600851475143):
factlist.append(i)
print factlist
def test_factor_8_return_2_2_2_in_list(self):
self.assertEqual(factor.factor(8), [2, 2, 2])
#!/usr/bin/python3
from factor import factor
from collections import Counter
n = 10000
factors_last = factor(n)
while True:
n += 1
factors_n = factors_last
factors_n1 = factor(n+1)
factors_last = factors_n1
factors_triangular = Counter(factors_n) #+ factors_n1
factors_triangular += Counter(factors_n1)
factors_triangular[2] -= 1 # simulate dividing by 2
# Get the factor exponents
exp = factors_triangular.values()
num_divisors = 1
for i in exp:
num_divisors *= int(i)+1
if num_divisors >= 500:
triangular = (n+1)*n/2
print(triangular)
print(factors_triangular)
break
def primitives_of(m):
assert len(factor(m)) == 0
for i in range(1, m):
if is_primitive(i, m):
print(i)
def test_factor_big2_return_correct_in_list(self):
self.assertEqual(factor.factor(5993), [13, 461])
def match(self,patname,srcname):
"""
given a pattern image and a source image, return the match result and
the scaling factor
"""
p = Image.open(patname).convert('L')
pa = numpy.array(p)
pa *= 255.0/pa.max()
s = Image.open(srcname).convert('L')
sa = numpy.array(s)
sa *= 255.0/sa.max()
pre = process.process()
ex= findextrema.findextrema()
des = descriptor.descriptor()
scale = factor.factor()
pdata = pre.creatdog(pa)
sdata = pre.creatdog(sa)
pDes = []
sDes = []
# dict to store all the feature matching result
result = {}
pFeatures = ex.get_Patextremes(pdata,pa)
sFeatures = ex.get_Srcextremes(sdata,sa)
# assign decriptors for each feature points
pDes = des.creatDes(pFeatures,pa)
sDes = des.creatDes(sFeatures,sa)
tree = []
if sDes=={} or pDes=={}:
return False
else:
# use cKD tree struture to compute the two similar pixels
tree = scipy.spatial.cKDTree(sDes.values())
slocList = sDes.keys()
pDict = {}
sDict = {}
for p in pDes.keys():
x = pDes[p]
re = tree.query(x,k=2,eps=self.distanceThresh,p=2,
distance_upper_bound=numpy.inf)
if re[0][1]!=0 and re[0][0]/re[0][1] < self.similarityThresh:
pLoc = p
sLoc = slocList[re[1][0]]
distance = re[0][0]
# did not been compared before
if sDict.has_key(sLoc)==False:
# add the result and compared pattern pixel
# and source pixel
result[(pLoc,sLoc)] = distance
pDict[pLoc] = sLoc
sDict[sLoc] = pLoc
elif distance < result.get((sDict[sLoc],sLoc)):
# updates the result and compared pattern pixel
# and source pixel
del result[(sDict[sLoc],sLoc)]
result[(pLoc,sLoc)] = distance
del pDict[sDict[sLoc]]
pDict[pLoc] = sLoc
sDict[sLoc] = pLoc
elif re[0][1]==0:
pLoc = p
sLoc = slocList[re[1][0]]
distance = re[0][0]
# did not been compared before
if sDict.has_key(sLoc)==False:
# add the result and compared pattern pixel
# and source pixel
result[(pLoc,sLoc)] = distance
pDict[pLoc] = sLoc
sDict[sLoc] = pLoc
elif distance < result.get((sDict[sLoc],sLoc)):
# updates the result and compared pattern pixel
# and source pixel
del result[(sDict[sLoc],sLoc)]
result[(pLoc,sLoc)] = distance
del pDict[sDict[sLoc]]
pDict[pLoc] = sLoc
sDict[sLoc] = pLoc
# the list of matched pixels, sorted by the distance
finResult = sorted(result.items(), reverse=False, key=lambda d: d[1])
match1 = finResult[0][0]
match2 = finResult[1][0]
match3 = finResult[2][0]
scalingFactor = scale.cal_factor(match1,match2,match3)
return finResult,scalingFactor
# instasolve #P = primes[20:47] #N = reduce(lambda x,y: x*y, primes[0:9]) #P = primes[20:90] #N = reduce(lambda x,y: x*y, primes[0:4]) # testing P = primes[20:56] N = reduce(lambda x,y: x*y, primes[0:11]) #print P print "2^%d" % len(P) print "finding", N ret, phi = factor(N) print phi ret = sorted(list(set(ret))) print ret #exit(0) odds = log(phi)/log(2) print "2^%f" % odds print "will find",len(P)-odds if len(P)-odds < 1.0: exit(-1) pass """
#!/usr/bin/python3
import numpy as np
from collections import defaultdict
from factor import factor
lcm_factors = defaultdict(int)
N=20
for i in range(2,N+1):
f = factor(i)
for k,v in f.items():
lcm_factors[k] = max(lcm_factors[k], v)
n = 1
for k,v in lcm_factors.items():
print(k)
print(v)
n *= k**v
print(n)
print(lcm_factors)
print(n)
##problem 5.py
import sys, math
sys.path.append('/Users/nathanielgentile/Documents/OCW/compsci101/Python')
import factor
t = True
init = 24504480
while t:
init += 1
for i in range(20, 0, -1):
if i == 1:
t = False
elif factor.factor(i, init):
continue
else:
break
print init
#takes a while
def factor_to_string(num):
facs = factor(num)
facs = ["{}**{}".format(n, p)
for n, p in sorted(facs.items(), key=lambda n: n[0])]
return ' * '.join(facs)
def pow_orders(d, n):
fs = [1, d] + factor(d)
for x in range(1, n):
if order(x, n) in fs:
print(x)
def match(self,patname,srcname):
"""
given a pattern image and a source image, return the match result and
the scaling factor
"""
p = Image.open(patname).convert('L')
pa = numpy.array(p)
pa *= 255.0/pa.max()
s = Image.open(srcname).convert('L')
sa = numpy.array(s)
sa *= 255.0/sa.max()
pre = process.process()
ex= findextrema.findextrema()
des = descriptor.descriptor()
scale = factor.factor()
pdata = pre.creatdog(pa)
sdata = pre.creatdog(sa)
pDes = []
sDes = []
# dict to store all the feature matching result
result = {}
pFeatures = ex.get_Patextremes(pdata,pa)
sFeatures = ex.get_Srcextremes(sdata,sa)
# assign decriptors for each feature points
pDes = des.creatDes(pFeatures,pa)
sDes = des.creatDes(sFeatures,sa)
tree = []
if sDes=={} or pDes=={}:
return False
else:
# use cKD tree struture to compute the two similar pixels
tree = scipy.spatial.cKDTree(sDes.values())
slocList = sDes.keys()
pDict = {}
sDict = {}
for p in pDes.keys():
x = pDes[p]
re = tree.query(x,k=2,eps=self.distanceThresh,p=2,
distance_upper_bound=numpy.inf)
if re[0][1]!=0 and re[0][0]/re[0][1] < self.similarityThresh:
pLoc = p
sLoc = slocList[re[1][0]]
distance = re[0][0]
# did not been compared before
if sDict.has_key(sLoc)==False:
# add the result and compared pattern pixel
# and source pixel
result[(pLoc,sLoc)] = distance
pDict[pLoc] = sLoc
sDict[sLoc] = pLoc
elif distance < result.get((sDict[sLoc],sLoc)):
# updates the result and compared pattern pixel
# and source pixel
del result[(sDict[sLoc],sLoc)]
result[(pLoc,sLoc)] = distance
del pDict[sDict[sLoc]]
pDict[pLoc] = sLoc
sDict[sLoc] = pLoc
elif re[0][1]==0:
pLoc = p
sLoc = slocList[re[1][0]]
distance = re[0][0]
# did not been compared before
if sDict.has_key(sLoc)==False:
# add the result and compared pattern pixel
# and source pixel
result[(pLoc,sLoc)] = distance
pDict[pLoc] = sLoc
sDict[sLoc] = pLoc
elif distance < result.get((sDict[sLoc],sLoc)):
# updates the result and compared pattern pixel
# and source pixel
del result[(sDict[sLoc],sLoc)]
result[(pLoc,sLoc)] = distance
del pDict[sDict[sLoc]]
pDict[pLoc] = sLoc
sDict[sLoc] = pLoc
# the list of matched pixels, sorted by the distance
finResult = sorted(result.items(), reverse=False, key=lambda d: d[1])
match1 = finResult[0][0]
match2 = finResult[1][0]
match3 = finResult[2][0]
scalingFactor = scale.cal_factor(match1,match2,match3)
return finResult,scalingFactor
def spike(A, b, config, output = True, debug = False) :
# Check the values
if (config['partitionNumber'] < 2) :
raise ValueError("The partitionNumber has to be at least 2 but it is", config['partitionNumber'])
elif (config['matrixSize'] / config['partitionNumber'] < config['bandwidth']) :
raise ValueError("The number of partitions must be smaller or equal to", config['matrixSize'] / config['bandwidth'], "but it is", config['partitionNumber'])
elif (config['matrixSize'] % config['partitionNumber'] != 0) :
raise ValueError("The matrixSize should be devideable by the number of partitions. given:", config['matrixSize'], config['partitionNumber'])
else :
# Determine the size of each partition
config['partitionSize'] = config['matrixSize'] / config['partitionNumber']
# make bandwidth even
if (config['bandwidth'] % 2 != 0) :
config['bandwidth'] += 1
config['rhsSize'] = b.shape[1]
config['offdiagonalSize'] = config['bandwidth']/2 #(bandwidth-1)/2
if (output) :
print config
print "input A:"
print A.todense()
print "input b:"
print b.todense()
# create prerequirements for OpenCL
ctx = cl.create_some_context(True)
#for platform in cl.get_platforms() :
# devices = platform.get_devices(cl.device_type.CPU)
# ctx = cl.Context(devices)
queue = cl.CommandQueue(ctx)
# compile programm code for CL
directory = os.path.dirname(os.path.realpath(__file__))
gaussFile = open(os.path.join(directory, "gauss.cl"), 'r')
gaussCode = ''.join(gaussFile.readlines())
program = cl.Program(ctx, gaussCode).build()
# 1. Pre-processing
# 1.1 Partitioning of the original system onto different processors
start = time()
buffers = partition.partition(config, ctx, A, b, debug)
# 1.2 Factorization of each diagonal block
# solve A_j[V_j, W_j, G_j] = [(0 ... 0 B_j)T, (C_j 0 ... 0)T, F_j]
# this step also involves solving of A_j G_j = F_j from (2.1)
factor.factor(config, ctx, queue, program, buffers)
# At this point we can free the A buffer (buffers[0])
# TODO make the memory release dependent on some event
#buffers[0].release()
# 2. Post-processing
# 2.1 Solving the reduced system
buffers = solve.reduced(config, ctx, queue, program, buffers, debug)
# At this point we can free the SG buffer (buffers[2])
#buffers[2].release()
# 2.2 Retrieving the overall solution
x = solve.final(config, ctx, queue, program, buffers, debug)
stop = time()
rt = stop-start
return [x, rt]