def authorizedMove(self, move, possibleNorm=NORM_MOVES):
'''
Returns if the move is authorized given a optional direction for the collision constraints
:param move: the move to check
:param possibleNorm: check only the norm provided
:return: a boolean true if the position is authorized
'''
head = self.head()
# backward moves are forbidden
if move.direction() == utils.mult(self.orientation(), -1):
return False
target = move.applyDirection(head)
# If a collision already occurred we can't do another one
if (self.on_tail and self.onSnakeExceptLastOrNotGrid(target, 1)):
return False
# If we would need two collisions in a row there is a problem
next_target = move.applyDirection(head, mu=2)
if (self.onSnakeExceptLastOrNotGrid(target, 1)
and self.onSnakeExceptLastOrNotGrid(next_target, 2)):
return False
if move.norm() == 2 and 2 in possibleNorm:
# We can only accelerate when the snake is big enough
if self.size() <= 2:
return False
next_acc_target = move.applyDirection(head, mu=3)
# We make sure that we can move without causing death at the next time
if (self.onSnakeExceptLastOrNotGrid(next_acc_target, 3)
and self.onSnakeExceptLastOrNotGrid(next_target)):
return False
return True
def getRate(self):
return (
len(self.scalas),
len(self.getAllNotes()),
reduce(utils.lcm, self.scalas),
utils.mult(self.scalas),
)
def tree(primes, check, level, r = ()):
if r == ():
if not check(1): return
for p in primes():
if level < p: break # ugly !!!
r1 = (p,) + r
if not check(utils.mult(r1)): return # skip other primes
RangeSearcher.tree(primes, check, p, r1)
def getFundamentals(self):
result = Spectrum()
keys = sorted(self.keys(), key=float) # might be not sorted
variations = list(utils.variations(len(keys)))[1:]
for v in variations: # (0,0,1), (0,1,0), (0,1,1),.. (1,1,1)
ks = [k for (b, k) in zip(v, keys) if b]
d = Rational.gcd(*ks)
value = utils.mult(self[k] for k in ks)
value **= 1.0 / len(ks) # geometric mean
result[d] += value
return result
def run(self):
"""
Run the network simulation by evaluating model equations at every time
step.
"""
# integration constant
rho_a = 1./(self.stim_len)
# simulation time
time = np.arange(0, self.t_max)
for t in time[1:]:
# stop simulation if target found or max guesses
if self._terminate_condition(t):
break
# ----- Semantic Layer -----
# winning/active units
self.z[t-1] = step(self.w[t-1], self.theta_w)
# unit activities
self.a[t] = self.a[t-1] + rho_a*(mult(self.W,
self.z[t-1],
self.a[t-1]) +
self.I[t-1])
# ----- WTA Layer -----
eta = np.random.random(self.N) - self.noise_offset
# normalise activities to 0-1
divisor = np.max([1., self.a[t-1].max()])
self.w[t] = self.w[t-1] + self.rho_w * \
(self.c1*self.z[t-1] +
self.c2*self.a[t-1]/divisor -
self.c3*self.y[t-1] -
self.c4*self.r[t-1] +
self.c5*eta)
self.y[t] = self.z[t-1].sum()
# ----- Inhibitory Layer -----
# -2 added because of discreete update lags
self.r[t] = (self.r[t-1] +
step(self.z[t-self.stim_len:t].sum(axis=0),
self.stim_len-2)).clip(max=1)
# several winners are not allowed
if self.y[t] > 1:
raise Exception('Multiple winners')
# rectify WTA activities to 0 (if needed)
self.w[t] = self.w[t].clip(min=0)
def run(self):
"""
Run the network simulation by evaluating model equations at every time
step.
"""
# integration constant
rho_a = 1. / (self.stim_len)
# simulation time
time = np.arange(0, self.t_max)
for t in time[1:]:
# stop simulation if target found or max guesses
if self._terminate_condition(t):
break
# ----- Semantic Layer -----
# winning/active units
self.z[t - 1] = step(self.w[t - 1], self.theta_w)
# unit activities
self.a[t] = self.a[t - 1] + rho_a * (
mult(self.W, self.z[t - 1], self.a[t - 1]) + self.I[t - 1])
# ----- WTA Layer -----
eta = np.random.random(self.N) - self.noise_offset
# normalise activities to 0-1
divisor = np.max([1., self.a[t - 1].max()])
self.w[t] = self.w[t-1] + self.rho_w * \
(self.c1*self.z[t-1] +
self.c2*self.a[t-1]/divisor -
self.c3*self.y[t-1] -
self.c4*self.r[t-1] +
self.c5*eta)
self.y[t] = self.z[t - 1].sum()
# ----- Inhibitory Layer -----
# -2 added because of discreete update lags
self.r[t] = (self.r[t - 1] +
step(self.z[t - self.stim_len:t].sum(axis=0),
self.stim_len - 2)).clip(max=1)
# several winners are not allowed
if self.y[t] > 1:
raise Exception('Multiple winners')
# rectify WTA activities to 0 (if needed)
self.w[t] = self.w[t].clip(min=0)
def getHarmonicDistance(chord, weights=()):
"chord as a list of integers, weights - floats"
from rationals import Rational
import harmonicity
#print chord, weights
if not weights: weights = (1.0, ) * len(chord)
variations = list(utils.variations(len(chord)))
distance = 0.0
for var in variations:
ns = [n for (n, b) in zip(chord, var) if b]
if len(ns) >= 2:
gcd = reduce(utils.gcd, ns)
ns = [n / gcd for n in ns] # reduce notes
d = sum([harmonicity.simple(5)(Rational(n)) for n in ns])
dw = d * utils.mult([w for (w, b) in zip(weights, var) if b])
#print " ", ns, lcm, `r`, d #, dw
distance += dw
return distance
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"""
table = [[int(j) for j in i.split(" ")] for i in table.splitlines()]
values = []
w, h = len(table[0]), len(table)
take = 4
for x in range(w):
for y in range(h):
if y + take <= h:
values.append([table[y + i][x] for i in range(take)])
if x + take <= w:
values.append([table[y + i][x + i] for i in range(take)])
if x - take >= -1:
values.append([table[y + i][x - i] for i in range(take)])
values.append(table[y][x:x + take])
print(max(mult(i) for i in values))
def n_totient(n):
f = factors[n]
if f:
return 1 / (mult(1 - 1 / i for i in f))
return n / (n - 1)