def _createBox(proxy, size, colour, moiScale, withMesh):
"""
Private function.
Use createBox() or createArticulatedBox() instead.
"""
# Mesh and cdps will be set manually
proxy.meshes = None
proxy.cdps = None
# Compute box moi
size = PyUtils.toVector3d(size)
proxy.moi = MathLib.Vector3d(
size.y * size.y + size.z * size.z,
size.x * size.x + size.z * size.z,
size.x * size.x + size.y * size.y,
) * 1.0 / 12.0 * proxy.mass * moiScale
box = proxy.createAndFillObject()
cdp = Physics.BoxCDP()
halfSize = PyUtils.toVector3d(size) * 0.5
cdp.setPoint1(MathLib.Point3d(halfSize * -1))
cdp.setPoint2(MathLib.Point3d(halfSize))
box.addCollisionDetectionPrimitive(cdp)
if withMesh:
mesh = Mesh.createBox(size=size, colour=colour)
box.addMesh(mesh)
return box
def load(self):
assert not self._loaded, "Cannot load scenario twice!"
self._loaded = True
# Create the rigid bodies for the main staircase
orientation = PyUtils.angleAxisToQuaternion((self._angle, (0, 1, 0)))
size = MathLib.Vector3d(self._staircaseWidth, self._riserHeight,
self._threadDepth)
pos = PyUtils.toPoint3d(self._position) + MathLib.Vector3d(
0, -self._riserHeight / 2.0, 0)
delta = MathLib.Vector3d(size)
delta.x = 0
delta = orientation.rotate(delta)
for i in range(self._stepCount):
box = PyUtils.RigidBody.createBox(size,
pos=pos + delta * (i + 1),
locked=True,
orientation=orientation)
Physics.world().addRigidBody(box)
# Create the rigid bodies for both ramps
rampHeights = (self._leftRampHeight, self._rightRampHeight)
deltaRamp = MathLib.Vector3d(self._staircaseWidth / 2.0, 0, 0)
deltaRamp = orientation.rotate(deltaRamp)
deltaRamps = (deltaRamp, deltaRamp * -1)
for deltaRamp, rampHeight in zip(deltaRamps, rampHeights):
if rampHeight is None: continue
deltaRamp.y = rampHeight / 2.0
box = PyUtils.RigidBody.createBox((0.02, rampHeight, 0.02),
pos=pos + deltaRamp + delta,
locked=True,
orientation=orientation)
Physics.world().addRigidBody(box)
box = PyUtils.RigidBody.createBox(
(0.02, rampHeight, 0.02),
pos=pos + deltaRamp + (delta * self._stepCount),
locked=True,
orientation=orientation)
Physics.world().addRigidBody(box)
deltaRamp.y = rampHeight
rampOrientation = orientation * PyUtils.angleAxisToQuaternion(
(math.atan2(self._riserHeight, self._threadDepth), (-1, 0, 0)))
rampLen = self._stepCount * math.sqrt(
self._riserHeight * self._riserHeight +
self._threadDepth * self._threadDepth)
box = PyUtils.RigidBody.createBox(
(0.04, 0.02, rampLen),
pos=pos + deltaRamp + (delta * ((self._stepCount + 1) * 0.5)),
locked=True,
orientation=rampOrientation)
Physics.world().addRigidBody(box)
def createBox(size=(1, 1, 1), position=(0, 0, 0), colour=(0.6, 0.6, 0.6)):
"""
Creates the mesh for a box having the specified size and a specified position.
The size should be a 3-tuple (xSize, ySize, zSize).
The position should be a 3-tuple.
Colour should be a 3-tuple (R,G,B) or a 4-tuple (R,G,B,A)
"""
size = PyUtils.toVector3d(size)
position = PyUtils.toPoint3d(position)
vertices = []
delta = MathLib.Vector3d()
for repeat in range(3):
for x in (-0.5, 0.5):
delta.x = size.x * x
for y in (-0.5, 0.5):
delta.y = size.y * y
for z in (-0.5, 0.5):
delta.z = size.z * z
vertices.append(position + delta)
faces = [
(0, 1, 3, 2),
(5, 4, 6, 7), # YZ Faces
(9, 13, 15, 11),
(12, 8, 10, 14), # XY Faces
(18, 19, 23, 22),
(17, 16, 20, 21)
] # XZ Faces
return create(vertices, faces, colour)
def single(d):
n, factors = d
# merge some of the primes together
for grouping in partition(factors):
# print ("\tGrouping:", grouping)
joined = list(map(MathLib.product, grouping))
counts = Counter(joined)
modified_sum_of_div = MathLib.product(
(p**(1 + c) - 1) // (p - 1) for p, c in counts.items())
if 2 * n == modified_sum_of_div:
print(n, "\t", factors, grouping)
return n
return None
def __init__(self,
controller,
jointName,
componentIndex,
type='unknown',
posInChild=MathLib.Point3d(),
oppositeJointName=None,
reverseOppositeJoint=False,
minValue=-1000,
maxValue=1000):
"""
Creates a handle that can be used to access a specific component in a controller in a standard (direct) way.
type should be 'circular', 'reverseCircular', 'perpendicular', 'reversePerpendicular' or 'unknown' to indicate how the handle behaves
posInChild should be of type MathLib.Point3d
reverse should be True if the handle works in a reverse way (i.e. going clockwise increase the angle (?))
oppositeJointName should be the name of the corresponding joint on the other stance.
reverseOppositeJoint should be True if the opposite joint sign is different
"""
self._controller = controller
self._jointName = jointName
trajectory = controller.getState(0).getTrajectory(
jointName).getTrajectoryComponent(
componentIndex).getBaseTrajectory()
self._oppositeJointName = oppositeJointName
self._posInChild = posInChild
if oppositeJointName is not None:
oppositeTrajectory = controller.getState(0).getTrajectory(
oppositeJointName).getTrajectoryComponent(
componentIndex).getBaseTrajectory()
else:
oppositeTrajectory = None
self._type = type
super(Handle, self).__init__(trajectory, oppositeTrajectory,
reverseOppositeJoint, minValue, maxValue)
import MathLib x = MathLib.Vector3d() x.setValues(10, 0.44, -132) print "x = ", x._print() y = MathLib.Vector3d() y.setValues(3, 11, 2) print "y = ", y._print() x.addScaledVector(y, 0.5) print "x + 0.5y = ", x._print()
import MathLib
from collections import Counter
from tqdm import tqdm
import multiprocessing
print("Factoring")
factors = MathLib.sieveOfFactors(10**5)
print("Factored!")
# Max factors is ~20 (2^20), so number of partition is small (674)
def partition(values):
if len(values) == 0:
return
if len(values) == 1:
yield ((values[0], ), )
return
first, *rest = values
for smaller in partition(rest):
for n, subset in enumerate(smaller):
yield smaller[:n] + (((first, ) + subset), ) + smaller[n + 1:]
yield ((first, ), ) + smaller
def single(d):
n, factors = d
# merge some of the primes together
for grouping in partition(factors):
def gsplot(self):
ffit = open(os.path.join(self.p.fit_path, self.p.scannum + '.fit'))
trfit = ffit.read()[:-1].split('\n')
ffit.close()
trfit = [e for e in trfit if not e.startswith('#')]
try:
srcname = trfit[0].split()[0]
except IndexError:
print('No data found in FITS file !!!')
return
fdat = open(os.path.join(self.p.fit_path, self.p.scannum + '.dat'))
trdat = fdat.readlines()
fdat.close()
trdat = [
e[:-1] for e in trdat if (e[0] != '#' or e[:2] == '#!' or (
e[0] == '#' and len(e.split()) == 6))
]
trdat = trdat[1:]
tr = [e for e in trdat if re.match('#! SUBSCAN', e)]
keys = [trdat.index(e) for e in tr]
keys.append(len(trdat))
subs = len(trfit)
amp, eamp = np.zeros(subs), np.zeros(subs)
scandir = np.array([])
n1 = int((subs + 1)**0.5)
n2 = n1 * 1
while n1 * n2 < subs + 1:
n2 = n2 + 1
self.Figure.clf()
gsp = gridspec.GridSpec(n1, n2)
sub_flag = np.array([True] * subs)
for i in range(subs):
ax = self.Figure.add_subplot(gsp[i])
trf = trfit[i].split()
scandir = np.append(scandir, trf[2])
mjd = float(trf[4])
tsys = float(trf[14])
amp[i], eamp[i] = float(trf[7]), float(trf[8])
off = float(trf[9])
hpbw = float(trf[11])
az, el, sunang = float(trf[5]), float(trf[6]), float(trf[16])
del trf
trd = trdat[keys[i] + 2:keys[i + 1]]
trd = [e.split()[0:3][::2] for e in trd]
trd = np.array(trd).transpose()
dataX = trd[0].astype(np.float)
dataY = trd[1].astype(np.float)
del trd
if amp[i] != 0:
fitY = ML.Gauss(1,
1).fGauss(np.array([amp[i], off, hpbw, 0, 0]),
dataX)
else:
fitY = dataY * 1.0
ampcolor, offcolor, hpbwcolor = 'white', 'white', 'white'
titlecolor, titlebackcolor = 'black', '#00FF00'
xmin, xmax = min(dataX), max(dataX)
dy = max(dataY) - min(dataY)
if self.p.flag == False:
ymin = max(min(dataY), -0.1 * dy)
ymax = min(max(dataY) + 0.1 * dy, 1.5 * amp[i])
else:
if (amp[i] <= 0) or (eamp[i] / amp[i] > self.p.rerr):
ampcolor = 'red'
elif eamp[i] / amp[i] > 0.5 * self.p.rerr:
ampcolor = 'yellow'
if np.fabs(off) > self.p.doff:
offcolor = 'red'
elif np.fabs(off) > 0.5 * self.p.doff:
offcolor = 'yellow'
if np.fabs(hpbw / self.p.beam - 1) > self.p.dwidth:
hpbwcolor = 'red'
elif np.fabs(hpbw / self.p.beam - 1) > 0.5 * self.p.dwidth:
hpbwcolor = 'yellow'
if 'red' in [ampcolor, offcolor, hpbwcolor]:
sub_flag[i] = False
ymin = min(dataY)
ymax = max(dataY) + 0.1 * dy
else:
ymin = max(min(dataY), -0.1 * dy)
ymax = min(max(dataY) + 0.1 * dy, 1.5 * amp[i])
ax.text(0.05*xmax+0.95*xmin, 0.9*ymax+0.1*ymin, \
'Amp=%0.4f' %amp[i], \
fontsize=14, \
horizontalalignment='left',\
verticalalignment='top',\
linespacing=1.5,\
color=ampcolor)
ax.text(0.05*xmax+0.95*xmin, 0.815*ymax+0.185*ymin, \
'Off=%0.2f' %off, \
fontsize=14, \
horizontalalignment='left',\
verticalalignment='top',\
linespacing=1.5,\
color=offcolor)
ax.text(0.05*xmax+0.95*xmin, 0.73*ymax+0.27*ymin, \
'HPBW=%0.2f' %hpbw, \
fontsize=14, \
horizontalalignment='left',\
verticalalignment='top',\
linespacing=1.5,\
color=hpbwcolor)
ax.text(0.95*xmax+0.05*xmin, 0.9*ymax+0.1*ymin, \
'Az=%0.1f\nEl=%0.1f\nSun=%0.1f' %(az, el, sunang), \
fontsize=14, \
horizontalalignment='right',\
verticalalignment='top',\
linespacing=1.5,\
color='white')
ax.set_xlim(xmin, xmax)
ax.set_ylim(ymin, ymax)
ax.set_xlabel('%s-OFF (arcsec.)' % scandir[i])
ax.set_ylabel('COUNTS')
ax.plot(dataX, dataY, color='white', linewidth=1)
if amp[i] != 0:
ax.plot(dataX, fitY, color='#00FF00', linewidth=2)
ax.grid(True)
ax = self.Figure.add_subplot(gsp[subs])
_amp0 = amp + eamp
_amp1 = amp - eamp
dy = max(_amp0) - min(_amp1)
ymin = 1.1 * min(_amp1) - 0.1 * max(_amp0)
ymax = 1.1 * max(_amp0) - 0.1 * min(_amp1)
ax.set_xlim(0, subs + 1)
ax.set_ylim(ymin, ymax)
del _amp0, _amp1
ax.set_xlabel('Comparison of Subscans')
if self.p.flag == True:
if True not in sub_flag[scandir=='ALON'] or \
True not in sub_flag[scandir=='ALAT']:
titlecolor, titlebackcolor = 'white', 'red'
inv_flag = np.array([not e for e in sub_flag])
ax.errorbar(np.arange(1,subs+1)[sub_flag], \
amp[sub_flag], yerr=eamp[sub_flag], fmt='d', \
ecolor='white', mfc='white', mec='white', \
ms=8, lw=2)
ax.errorbar(np.arange(1,subs+1)[inv_flag], \
amp[inv_flag], yerr=eamp[inv_flag], fmt='o', \
ecolor='red', mfc='red', mec='red', \
ms=10, lw=2)
else:
ax.errorbar(np.arange(subs)+1, amp, yerr=eamp, fmt='d',\
ecolor='white', mfc='white', mec='white', \
ms=8, lw=2)
ax.plot([0, subs + 1], [np.mean(amp)] * 2, color='white', linewidth=2)
self.Figure.suptitle('\nScan: %4s %s @%0.1fMHz' \
%(self.p.scannum, srcname, self.p.freq), \
weight='bold', ha='center', \
linespacing=0.3, fontsize=20, \
backgroundcolor=titlebackcolor,\
color=titlecolor)
self.UpdatePlot()
del ax
MAX_DIGITS = 2000
SIEVE_MAX = 5000
to_test = [[[True, True, False, True, True] for a in range(10)]
for d in range(MAX_DIGITS + 1)]
# Filter the 6 silly patterns
for a in (3, 6, 9):
for b in (3, 9):
for test_d in range(MAX_DIGITS + 1):
assert (a * pow(10, test_d, 3) + b) % 3 == 0
to_test[test_d][a][b // 2] = False
# Sieve out "small" prime factors and mark those numbers not to test.
small_primes = MathLib.sieveOfErat(SIEVE_MAX)
factors = MathLib.sieveOfFactors(SIEVE_MAX)
print("\t PrimePi({}) = {}".format(SIEVE_MAX, len(small_primes)))
for p in small_primes:
if p in (2, 5):
continue
divisible_mods = defaultdict(list)
for a in range(1, 10):
if a % p == 0:
continue
modular_inverse = MathLib.modularInverse(a, p)
[-1.0,0.0,0.0],
[0.0,0.0,1.0],
[0.0,1.0,0.0],
[1.0,0.0,0.0]
])
m2 = np.array([
[0.0,0.0,-1.0],
[0.0,-1.0,0.0],
[-1.0,0.0,0.0],
[0.0,0.0,1.0],
[0.0,1.0,0.0],
[1.0,0.0,0.0]
])
r = np.array([-90.0,110.0,10.0])
u = np.array([0.0,0.0,1.0])
print(m.VneshPole(0, mU))
print(m.SteerOttalk(mK,u,r))
print(m.Moment(n,mK,mU,u,r))
print(m.Sila(n,mK,mU,u,r))
print(m.MathKernel(mK,mU,m1,m2,0, 0))
print(m.PorvrkaGrani(mK))
# koordi = MatrixUglSkorostiы
# fig = plt.figure(figsize=(12, 12))
# ax = fig.add_subplot(111, projection='3d')
# x, y, z = xp.copy(koordi[:, :1]), xp.copy(koordi[:, 1:2]), xp.copy(koordi[:, 2:3])
# ax.scatter(x, y, z, marker = 'o')
# plt.show()