def part2(busses):
step = 1
time = 0
for offset, bus in busses:
while ((time + offset) % bus != 0):
time += step
step = np.lcm(bus, step)
return (time)
def compute(M,N): m,n,p,q = len(M), len(M[0]), len(N), len(N[0]) s = np.lcm(n,p) i1,i2 = s//n,s//p I1 = np.identity(i1) I2 = np.identity(i2) MI = np.kron(M,I1) NI = np.kron(N,I2) return np.matmul(MI,NI)
def createCsv(sampleRate, filename, wave):
rpts = int(np.lcm(len(wave), 128)/len(wave))
f = open (filename, 'w')
f.write("SampleRate={}\n".format(int(sampleRate)))
f.write("SetConfig=true\n")
f.write("Y1\n")
for sample in np.tile(wave, rpts):
f.write("{}\n".format(sample))
f.close()
def run2(self):
first_bus_id = None
bus_ids_dict = {}
diff_from_first_bus = 0
with open(self.path, "r") as f:
line_number = 0
for line in f:
line = line.strip()
if line_number == 0:
my_timestamp = int(line)
elif line_number == 1:
for id in line.split(","):
if id != "x":
if first_bus_id is None:
first_bus_id = int(id)
bus_ids_dict[int(id)] = diff_from_first_bus
diff_from_first_bus += 1
else:
raise Exception(f"Invalid line number {line_number}")
line_number += 1
largest_bus_id = max(bus_ids_dict.keys())
largest_diff_from_first_bus = bus_ids_dict[largest_bus_id]
bus_ids_sorted = list(bus_ids_dict.keys())
bus_ids_sorted.sort(reverse=True)
bus_ids_sorted.remove(largest_bus_id)
time_differences_sorted = []
for bus_id in bus_ids_sorted:
time_differences_sorted.append(bus_ids_dict[bus_id])
starting_timestamp = int(my_timestamp / largest_bus_id) * largest_bus_id
largest_factor = bus_ids_sorted[0]
largest_factor_start = self.get_first_match(starting_timestamp, largest_bus_id, largest_factor,
time_differences_sorted[0] - largest_diff_from_first_bus)
bus_ids_sorted.remove(bus_ids_sorted[0])
time_differences_sorted.remove(time_differences_sorted[0])
timestamp = largest_factor_start
while bus_ids_sorted:
firsts_timestamp = timestamp - largest_diff_from_first_bus
while bus_ids_sorted:
bus_id = bus_ids_sorted[0]
time_difference = time_differences_sorted[0]
if (firsts_timestamp + time_difference) % bus_id != 0:
break
else:
largest_factor = np.lcm(largest_factor, bus_id, dtype='int64')
bus_ids_sorted.remove(bus_ids_sorted[0])
time_differences_sorted.remove(time_differences_sorted[0])
if not bus_ids_sorted:
print(f"part2: {timestamp - largest_diff_from_first_bus}")
break
timestamp += largest_bus_id*largest_factor
def test_dygraph(self):
paddle.disable_static()
x1 = paddle.to_tensor(self.x_np)
x2 = paddle.to_tensor(self.y_np)
result = paddle.lcm(x1, x2)
self.assertEqual(
np.allclose(np.lcm(self.x_np, self.y_np), result.numpy()), True)
paddle.enable_static()
def ajax():
form = InputForm()
if form.validate_on_submit():
x = form.x.data
y = form.y.data
result = str(np.lcm(x, y)) # calculate & parse to string for jsonify
return jsonify(result=result)
return jsonify(result=form.errors)
def createMat(sampleRate, filename, wave):
rpts = int(np.lcm(len(wave), 128)/len(wave))
XDelta = 1 / sampleRate
matparams = {'InputZoom':[[1]],
'XDelta':XDelta,
'XStart':[[0]],
'Y': np.tile(wave, rpts)}
sio.savemat(filename, matparams)
def diff_resize_area(tensor, new_height_width):
"""Performs a resize op that passes gradients evenly.
The tensor goes through a resize and pool where the resize and pool
operations are determined by the Least Common Multiplier. Since resize with
nearest_neighbors and avg_pool distributes the gradients from the
output to input evenly, there's less of a chance of learning artifacts. First
we resize to the LCM then avg_pool to new_height_width. This resize operation
is only efficient in cases where LCM is small. This is typically the case when
upsampling or downsampling by a factor of 2 (e.g H = 0.5 * new_H).
Args:
tensor: a tensor of shape [B, H, W, D]
new_height_width: A tuple of length two which specifies new height, width
respectively.
Returns:
The resize area tensor [B, H_new, W_new, D].
Raises:
RuntimeError: If the LCM is larger than 10 x new_height_width, then
raise an error to prevent inefficient memory usage.
"""
new_h, new_w = new_height_width
unused_b, curr_h, curr_w, unused_d = tensor.shape.as_list()
# The least common multiplier used to determine the intermediate resize
# operation.
l_h = np.lcm(curr_h, new_h)
l_w = np.lcm(curr_w, new_w)
if l_h == curr_h and l_w == curr_w:
im = tensor
elif (l_h < (10 * new_h) and l_w < (10 * new_w)):
im = tf.compat.v1.image.resize_bilinear(tensor, [l_h, l_w],
half_pixel_centers=True)
else:
raise RuntimeError("DifferentiableResizeArea is memory inefficient"
"for resizing from (%d, %d) -> (%d, %d)" %
(curr_h, curr_w, new_h, new_w))
lh_factor = l_h // new_h
lw_factor = l_w // new_w
if lh_factor == lw_factor == 1:
return im
return tf.nn.avg_pool2d(im, [lh_factor, lw_factor], [lh_factor, lw_factor],
padding="VALID")
def simulate_moons_2(moons):
i = 0
initial_state = [state(moons, x) for x in range(3)]
cycle_len = [0, 0, 0]
while (cycle_len[0] == 0 or cycle_len[1] == 0 or cycle_len[2] == 0):
step(moons)
i += 1
if i % 100 == 0:
print(i, cycle_len)
for d in range(3):
if cycle_len[d] == 0 and state(moons, d) == initial_state[d]:
cycle_len[d] = i
print(cycle_len)
print(cycle_len)
result = np.lcm(cycle_len[0], np.lcm(cycle_len[1], cycle_len[2]))
return result
def calculate_greatest_common_denominator(denominators):
GCD = 0
if len(denominators) == 1:
return denominators
else:
for i in range(len(denominators) - 1):
cur_GCD = np.lcm(denominators[i], denominators[i + 1])
if cur_GCD > GCD:
GCD = cur_GCD
return GCD
def np_LCM():
x = 4
y = 6
print(np.lcm(x, y))
arr = np.array([3, 6, 9])
x = np.lcm.reduce(arr)
print(x)
arr = np.arange(1, 10)
x = np.lcm.reduce(arr)
print(x)
def calculate_digit(sum_cache, i, int_signal, times=1):
window_length = ((i + 1) * 4)
reminder = len(int_signal) % window_length
if reminder == 0:
fft = signle_cycle_fft(sum_cache, i, int_signal, window_length)
return (fft * times) % 10
else:
cycle = np.lcm(reminder, window_length) / reminder
remaining_times = times % cycle
effective_signal = int_signal * int(remaining_times)
return signle_cycle_fft(sum_cache, i, effective_signal, window_length)
def cancel(arr, i, j, k):
a = arr[j][i]
b = arr[j][k]
if b != 0:
try:
lcm = int(numpy.lcm(a, b))
except:
return []
for t in range(len(arr)):
arr[t].row[k] = arr[t][k] * (lcm //
b) - arr[t][i] * (lcm // a)
def adjust_block_compatibility(self, ws, bs, gs):
"""Adjusts the compatibility of widths, bottlenecks, and groups."""
assert len(ws) == len(bs) == len(gs)
assert all(w > 0 and b > 0 and g > 0 for w, b, g in zip(ws, bs, gs))
vs = [int(max(1, w * b)) for w, b in zip(ws, bs)]
gs = [int(min(g, v)) for g, v in zip(gs, vs)]
ms = [np.lcm(g, b) if b > 1 else g for g, b in zip(gs, bs)]
vs = [max(m, int(round(v / m) * m)) for v, m in zip(vs, ms)]
ws = [int(v / b) for v, b in zip(vs, bs)]
assert all(w * b % g == 0 for w, b, g in zip(ws, bs, gs))
return ws, bs, gs
def combine(buses: List[Tuple[int, int]]) -> Tuple[int, int]:
*buses_to_combine, (bus_time_period, wait_time) = buses
if not buses_to_combine:
return 0, bus_time_period
curr_time, time_period = combine(buses_to_combine)
while True:
if get_wait_time(curr_time, bus_time_period) == wait_time:
return curr_time, numpy.lcm(time_period, bus_time_period)
curr_time += time_period
def solve(data=None):
"""
Simulate the motion of the moons in time steps.
Within each time step, first update the velocity of every moon by applying gravity.
Then, once all moons' velocities have been updated,
update the position of every moon by applying velocity.
Time progresses by one step once all of the positions are updated.
"""
moons = parse_input(data)
x_moons = []
y_moons = []
z_moons = []
for moon in moons:
x_moons.append(Moon(Point(moon.position[0]), Point(moon.velocity[0])))
y_moons.append(Moon(Point(moon.position[1]), Point(moon.velocity[1])))
z_moons.append(Moon(Point(moon.position[2]), Point(moon.velocity[2])))
x = find_loop(x_moons)
y = find_loop(y_moons)
z = find_loop(z_moons)
return np.lcm(x, np.lcm(y, z))
def main():
pos = np.array(lmap(parse, read_lines()), dtype=np.int32)
vel = np.zeros_like(pos, np.int32)
initial_pos = pos.copy()
periods = np.zeros(pos.shape[1], np.int64)
periods_left = list(range(pos.shape[1]))
assert len(periods_left) == 3
for i in range(1000):
gravity = compute_gravity(pos)
vel += gravity
pos += vel
vel = np.abs(vel)
pos = np.abs(pos)
energy = np.sum(vel.sum(axis=1) * pos.sum(axis=1))
print("1.)", energy)
pos = initial_pos.copy()
vel = np.zeros_like(pos)
for i in range(240000):
gravity = compute_gravity(pos)
vel += gravity
pos += vel
period_found = None
for j in periods_left:
if np.all(pos[:, j] == initial_pos[:, j]):
period_found = j
periods[j] = i + 1
break # hopefully no similar periods
if period_found is not None:
periods_left.remove(period_found)
if not periods_left:
break
periods += 1 # next step starts the period
lcm = np.lcm(periods[0], np.lcm(periods[1], periods[2]))
print("2.)", lcm)
def execute(self, context):
r = round(self.r, 6)
R = round(self.R, 6)
d = round(self.d, 6)
Rmr = round(R - r, 6) # R-r
Rpr = round(R + r, 6) # R +r
Rpror = round(Rpr / r, 6) # (R+r)/r
Rmror = round(Rmr / r, 6) # (R-r)/r
maxangle = 2 * math.pi * (
(np.lcm(round(self.R * 1000), round(self.r * 1000)) / (R * 1000)))
if self.typecurve == "hypo":
xstring = str(Rmr) + "*cos(t)+" + str(d) + "*cos(" + str(
Rmror) + "*t)"
ystring = str(Rmr) + "*sin(t)-" + str(d) + "*sin(" + str(
Rmror) + "*t)"
else:
xstring = str(Rpr) + "*cos(t)-" + str(d) + "*cos(" + str(
Rpror) + "*t)"
ystring = str(Rpr) + "*sin(t)-" + str(d) + "*sin(" + str(
Rpror) + "*t)"
zstring = '(' + str(round(
self.dip,
6)) + '*(sqrt(((' + xstring + ')**2)+((' + ystring + ')**2))))'
print("x= " + str(xstring))
print("y= " + str(ystring))
print("z= " + str(zstring))
print("maxangle " + str(maxangle))
x = Expression(xstring, ["t"]) # make equation from string
y = Expression(ystring, ["t"]) # make equation from string
z = Expression(zstring, ["t"]) # make equation from string
# build function to be passed to create parametric curve ()
def f(t, offset: float = 0.0):
c = (x(t), y(t), z(t))
return c
iter = int(maxangle * 10)
if iter > 10000: # do not calculate more than 10000 points
print("limiting calculatons to 10000 points")
iter = 10000
parametric.create_parametric_curve(f,
offset=0.0,
min=0,
max=maxangle,
use_cubic=True,
iterations=iter)
return {'FINISHED'}
def get_output_digit(self, d):
kernel_period = 4 * (d + 1)
read_length = lcm(self.period, kernel_period)
full_reads = self.data.length // read_length
frag_reads = self.data.length % read_length
out = 0
if 1 <= full_reads <= 9:
for j in range(min(read_length, self.data.length)):
out += self.data[j] * self.kernel[(j + 1) // (d + 1)]
for j in range(frag_reads):
out += self.data[j] * self.kernel[(j + 1) // (d + 1)]
return abs(out) % 10
def generate(p=number.getPrime(randint(660, 700)),
q=number.getPrime(randint(660, 700))):
n = p * q
phi = (p - 1) * (q - 1)
carm_func = np.lcm(p - 1, q - 1)
while True:
e = randint(2, carm_func)
if np.gcd(e, carm_func) == 1: break
d = int(modinv(e, phi))
return (n, e, d)
def part_two(timetable: list, max_iter: int) -> int:
num1 = timetable[0]
# The step can get very large, np uses int32 by default, make sure it is initialized as int64
step = np.int64(num1)
counter = 0
for num2 in timetable:
# Find the LCM with offset for the previous aggregated number and the new one
num1 = get_lcm(num1, num2, counter, step, max_iter)
# Calculate the step for the next LCM calculation (major speed-up)
step = np.lcm(step, num2)
counter = counter + 1
return num1
def __abc_smc_plotting(fig: plt.Figure, y_obs: [[float]],
priors: ["stats.Distribution"],
fitting_model: Models.Model, model_hat: Models.Model,
accepted_params: [[float]],
weights: [float]) -> plt.Figure:
n_params = (fitting_model.n_params - 2) if (
type(fitting_model) is Models.SIRModel) else fitting_model.n_params
n_rows = max([1, np.lcm(n_params, fitting_model.dim_obs)])
gs = fig.add_gridspec(n_rows, 2)
# plot fitted model
row_step = n_rows // fitting_model.dim_obs
for i in range(fitting_model.dim_obs):
ax = fig.add_subplot(gs[i * row_step:(i + 1) * row_step, -1])
y_obs_dim = [y[i] for y in y_obs]
Plotting.plot_accepted_observations(ax,
fitting_model.x_obs,
y_obs_dim, [],
model_hat,
dim=i)
row_step = n_rows // n_params
if (type(fitting_model) is Models.SIRModel):
for i in range(2, fitting_model.n_params):
ax = fig.add_subplot(gs[(i - 2) * row_step:(i - 2 + 1) * row_step,
0])
name = "theta_{}".format(i)
accepted_parameter_values = [theta[i] for theta in accepted_params]
Plotting.plot_parameter_posterior(
ax,
name,
accepted_parameter_values,
predicted_val=model_hat.params[i],
prior=priors[i],
dim=i,
weights=weights)
else:
for i in range(fitting_model.n_params):
ax = fig.add_subplot(gs[i * row_step:(i + 1) * row_step, 0])
name = "theta_{}".format(i)
parameter_values = [theta[i] for theta in accepted_params]
Plotting.plot_parameter_posterior(
ax,
name,
accepted_parameter_values,
predicted_val=model_hat.params[i],
prior=priors[i],
dim=i,
weights=weights)
return fig
def main():
# Command line arguments
process_args()
# Load vr data
vr_data = preprocessing.load_vr_file(vr_file)
vr_vec = vr_data.frames[:, 1]
vr_fps = vr_data.fps
vr_vec = (vr_vec - np.mean(vr_vec)) / np.std(vr_vec)
# Load mocap data
mocap_data = preprocessing.load_mocap_file_helper(open(mocap_file, "r"))
mocap_vec = mocap_data.frames[:, 1]
mocap_fps = mocap_data.fps
mocap_vec = (mocap_vec - np.mean(mocap_vec)) / np.std(mocap_vec)
# Upsample both sequences
fps = np.lcm(vr_fps, mocap_fps)
vr_vec_upsampled = np.interp(np.arange(0, vr_vec.size, vr_fps / fps),
np.arange(vr_vec.size), vr_vec)
mocap_vec_upsampled = np.interp(
np.arange(0, mocap_vec.size, mocap_fps / fps),
np.arange(mocap_vec.size), mocap_vec)
predicted_offset = get_temporal_offset(mocap_vec_upsampled,
vr_vec_upsampled, fps, 0, 10)
print("Predicted Offset:", predicted_offset)
#"""
start, end, window, gap = 0, 60, 1, 30
offsets = []
while end < vr_vec.size / vr_fps:
offset = get_temporal_offset(mocap_vec_upsampled,
vr_vec_upsampled,
fps,
predicted_offset,
10,
start=start,
end=end)
offsets.append(offset)
start, end = start + gap, end + gap
variability = np.array(offsets) - predicted_offset
print("Variability:", variability)
print("Average variability: ", np.mean(variability))
#"""
plt.plot(
np.arange(mocap_vec.size) / mocap_fps + predicted_offset, mocap_vec,
'b')
plt.plot(np.arange(vr_vec.size) / vr_fps, vr_vec, 'r')
plt.show()
def get_minimum_sample_time(self):
"""
Method to generate a minimum time-array as
long as is needed to be to garantie every
tooth mesh combination has been considered.
"""
# Get meshing time between two tooth
time2tooth = (1 / self.rotational_frequency_in) / self.GearPropIn['no_teeth']
# Get lowest common multiple
toothmeshlcm = np.lcm(self.GearPropIn['no_teeth'],
self.GearPropOut['no_teeth'])
min_time = time2tooth * toothmeshlcm
return(min_time)
def part2(data):
data = [(d, idx) for idx, d in enumerate(data) if d]
guess, skip = data[0][0], data[0][0]
idx = 1
total_len = len(data)
while idx < total_len:
x, i = data[idx]
while (guess + i) % x != 0:
guess += skip
skip = np.lcm(skip, data[idx][0])
idx += 1
return guess
def löse2(self):
kgv_old = kgv = uint64(1)
id = dt = time = uint64(0)
for dt, id in self.ids2:
dt = dt % id # SollWartezeit > BusID == "ZyklusZeit des Busses"
kgv_old = kgv
kgv = lcm(
kgv, uint64(id)
) #least common multiple from numpy (10 times faster as native *)
for _ in range(id):
if ((id - time) % id) == dt: break
time += kgv_old
return time
def adjust_block_compatibility(ws, bs, gs):
"""Adjusts the compatibility of widths, bottlenecks, and groups."""
assert len(ws) == len(bs) == len(gs)
assert all(w > 0 and b > 0 and g > 0 for w, b, g in zip(ws, bs, gs))
vs = [int(max(1, w * b)) for w, b in zip(ws, bs)]
# make sure widths not smaller than groups
gs = [int(min(g, v)) for g, v in zip(gs, vs)]
ms = [np.lcm(g, b) if b > 1 else g for g, b in zip(gs, bs)]
# make suer that widths in bottlenecks are common multiple of bs and gs
vs = [max(m, int(round(v / m) * m)) for v, m in zip(vs, ms)]
ws = [int(v / b) for v, b in zip(vs, bs)]
assert all(w * b % g == 0 for w, b, g in zip(ws, bs, gs))
return ws, bs, gs
def __sub__(self, other): # frac1-frac2, frac-int
if not isinstance(other, (Frac, int)):
raise ValueError("Invalid value format, it must be Frac or Integer value.")
if isinstance(other, Frac):
if self.y == other.y:
self.x -= other.x
return Frac(self.x, self.y)
lcm = np.lcm(self.y, other.y)
return Frac(self.x * (lcm // self.y) - other.x * (lcm // other.y), lcm)
if isinstance(other, int):
return Frac(self.x - self.y * other, self.y)
def generate_keys():
global private_key, n, g
# hard code these
# set these to be higher than SSS
p = 5
q = 7
private_key = numpy.lcm(p - 1, q - 1)
n = p * q
g = n + 1
print("n", n)
print("g", g)
return n, g
def AWG_Sinewave(ifreq, Ioffset, Qoffset, Iamp, Qamp, Iphase, Qphase):
'''
ifreq: IF frequency in MHz
'''
AWG.Clear_ArbMemory(awgsess)
WAVE = []
ifvoltag = [min(abs(Qamp), 1), min(abs(Iamp),
1)] # contain amplitude within 1V
iffunction = ['sin', 'cos']
iffreq = [ifreq, ifreq]
ifoffset = [Qoffset, Ioffset]
ifphase = [Qphase, Iphase]
# construct waveform:
for ch in range(2):
channel = str(ch + 1)
Nperiod = lcm(round(1000 / iffreq[ch] / dt * 100), 800) // 100
print("Waveform contains %s points per sequence" % Nperiod)
wavefom = [
ifvoltag[ch] *
eval(iffunction[ch] + '(x*%s*%s/1000*2*pi + %s/180*pi)' %
(dt, iffreq[ch], ifphase[ch])) + ifoffset[ch]
for x in range(Nperiod)
]
stat, wave = AWG.CreateArbWaveform(awgsess, wavefom)
# print('Waveform channel %s: %s <%s>' %(channel, wave, status_code(stat)))
WAVE.append(wave)
# Building Sequences:
for ch in range(2):
channel = str(ch + 1)
status, seqhandl = AWG.CreateArbSequence(
awgsess, [WAVE[ch]],
[1]) # loop# canbe >1 if longer sequence is needed in the future!
# print('Sequence channel %s: %s <%s>' %(channel, seqhandl, status_code(status)))
# Channel Assignment:
stat = AWG.arb_sequence_handle(awgsess,
RepCap=channel,
action=["Set", seqhandl])
# print('Sequence channel %s embeded: %s <%s>' %(channel, stat[1], status_code(stat[0])))
# Trigger Settings:
for ch in range(2):
channel = str(ch + 1)
AWG.operation_mode(awgsess, RepCap=channel, action=["Set", 0])
AWG.trigger_source_adv(awgsess, RepCap=channel, action=["Set", 0])
AWG.Init_Gen(awgsess)
AWG.Send_Pulse(awgsess, 1)
return
