def fast_power_iterative(A, n, modulus):
result = [[dirac(i, j) for i in range(len(A))] for j in range(len(A))]
while n > 0:
print n
if n % 2 == 1:
result = mult(result, A, modulus)
A = mult(A, A, modulus)
n /= 2
return result
def fast_power_iterative(A, n, modulus):
result = [[dirac(i, j) for i in range(len(A))] for j in range(len(A))]
while n > 0:
print n
if n % 2 == 1:
result = mult(result, A, modulus)
A = mult(A, A, modulus)
n /= 2
return result
def fast_a(n, p):
A = [[3, 1], [1, 0]]
exponent_reducing_modulus = (p * p - 1) * (p * p - p)
reduced_exponent = pow(2, n, exponent_reducing_modulus)
six_times_answer = mult(fast_power_iterative(A, reduced_exponent, p),
[[3], [2]], p)[1][-1] - 5
answer = crt([(six_times_answer, p), (0, 6)]) / 6
return answer
def main(numSets, accuracy, flag, length=3):
if flag == 2:
n = int(allio.sanitizeInput("Input the block size here:"))
mostRandom = int(
allio.sanitizeInput(
"Print 1 for purely random, 0 for predefined clusters"))
increaseN(n, mostRandom, numSets)
return
else:
testnum = allio.sanitizeInput("Input the test number here:")
filepath = "../Testing/test" + testnum + ".csv"
points = allio.readFile(filepath)
# low = helpers.theMin(points)
# high = helpers.theMax(points)
# spacing = ()
# for i in range(length):
# spacing = spacing + ((high[i]-low[i])/numSets,)
means = []
n = len(points)
thePoint = ()
midpoint = ()
for j in range(length - 1):
thePoint = thePoint + (0, )
midpoint = midpoint + (1 / float(length - 1), )
thePoint = thePoint + (1, )
midpoint = midpoint + (0, )
increment = helpers.add(midpoint, helpers.mult(-1, thePoint))
# print thePoint, midpoint, increment
thePoint = helpers.add(thePoint, helpers.mult(0.25, increment))
increment = helpers.mult(0.5, increment)
# print thePoint, increment
for i in range(numSets):
means.append(
helpers.add(thePoint,
helpers.mult(float(i + 0.5) / numSets, increment)))
means = gen.meanInit(numSets)
# print means
pausebuffer = float(allio.sanitizeInput("Input the pause buffer here:"))
means, sets = doKMeans3(points, means, pausebuffer)
def main(numSets,accuracy,flag,length=3):
if flag == 2:
n = int(sanitizeInput("Input the block size here:"))
mostRandom = int(sanitizeInput("Print 1 for purely random, 0 for predefined clusters"))
increaseN(n,mostRandom,numSets)
return
elif flag == 1:
n = int(sanitizeInput("Input the sample size here:") )
low = float(sanitizeInput("Input the range minimum here:"))
high = float(sanitizeInput("Input the range maximum here:"))
points = []
theRange = high - low
spacing = float(theRange)/numSets
means = []
thePoint = ()
midpoint = ()
for j in range(length-1):
thePoint = thePoint + (0,)
midpoint = midpoint + (1/(numSets-1)**0.5,)
thePoint = thePoint + (1,)
midpoint = midpoint + (0,)
increment = helpers.add(thePoint,helpers.mult(-1,midpoint))
for i in range(numSets):
means.append(helpers.add(thePoint,helpers.mult(float(i+0.5)/numSets,increment)))
for i in range(n):
thePoint = ()
j = 0
while j < length:
thePoint = thePoint + (rand.uniform(low,high),)
j = j + 1
points.append(thePoint)
else:
testnum = sanitizeInput("Input the test number here:")
filepath = "../Testing/test"+testnum+".csv"
points = fileio.readFile(filepath)
# low = helpers.theMin(points)
# high = helpers.theMax(points)
# spacing = ()
# for i in range(length):
# spacing = spacing + ((high[i]-low[i])/numSets,)
means = []
n = len(points)
thePoint = ()
midpoint = ()
for j in range(length-1):
thePoint = thePoint + (0,)
midpoint = midpoint + (1/float(length-1),)
thePoint = thePoint + (1,)
midpoint = midpoint + (0,)
increment = helpers.add(midpoint,helpers.mult(-1,thePoint))
# print thePoint, midpoint, increment
thePoint = helpers.add(thePoint,helpers.mult(0.25,increment))
increment = helpers.mult(0.5,increment)
# print thePoint, increment
for i in range(numSets):
means.append(helpers.add(thePoint,helpers.mult(float(i+0.5)/numSets,increment)))
# print means
doKMeans(points,means)
def basic(sa, sb):
return helpers.mult(sa, sb)
modulus = 987898789 # For c = 1, the total is 10 * number of values for a and b, which is 10 * L * L total = L * L * 10 for c in range(L, 1, -1): print c if c % 2 == 0: matrix = recurrence_matrix([10, 1]) total += even_c_counts['n_equals_0'] * T(0, modulus) total += even_c_counts[0] * T(1, modulus) for exponent in range(1, L + 1): matrix = fast_power_iterative(matrix, c, modulus) xn = mult(matrix, x0, modulus) count = even_c_counts[exponent] total += count * xn[-1][0] total %= modulus ''' for (key, count) in even_c_counts.items(): if key == 'n_equals_0': total += count * T(0, modulus) else: total += count * T(c**key, modulus) total %= modulus ''' else: matrix = recurrence_matrix([10, 1])
print len(odd_c_counts), len(even_c_counts)
modulus = 987898789
# For c = 1, the total is 10 * number of values for a and b, which is 10 * L * L
total = L * L * 10
for c in range(L, 1, -1):
print c
if c % 2 == 0:
matrix = recurrence_matrix([10, 1])
total += even_c_counts['n_equals_0'] * T(0, modulus)
total += even_c_counts[0] * T(1, modulus)
for exponent in range(1, L + 1):
matrix = fast_power_iterative(matrix, c, modulus)
xn = mult(matrix, x0, modulus)
count = even_c_counts[exponent]
total += count * xn[-1][0]
total %= modulus
'''
for (key, count) in even_c_counts.items():
if key == 'n_equals_0':
total += count * T(0, modulus)
else:
total += count * T(c**key, modulus)
total %= modulus
'''
else:
matrix = recurrence_matrix([10, 1])
from helpers import fast_power, mult n = 10 ** 12 modulus = 10 ** 9 A = [[1, 1, 1, 1, 1, 1], [6, 1, 1, 1, 1, 1], [0, 5, 1, 1, 1, 1], [0, 0, 4, 1, 1, 1], [0, 0, 0, 3, 1, 1], [0, 0, 0, 0, 2, 1]] x1 = [[7], [0], [0], [0], [0], [0]] # n - 1 since we have x1 instead of x0. print sum([i[0] for i in mult(fast_power(A, n - 1, modulus), x1, modulus)]) % modulus