def orientate(self):
"""Orientate the character towards the current destination.
"""
direction = self[Movable].direction
if direction:
dx = direction.x
dy = direction.y
if dx:
target_heading = atan(dy / dx) + (pi / 2) * copysign(1, dx)
else:
target_heading = pi if dy > 0 else 0
# Compute remaining rotation
delta = target_heading - self.heading
abs_delta = abs(delta)
if abs_delta > WHOLE_ANGLE / 2:
abs_delta = WHOLE_ANGLE - abs(delta)
delta = -delta
# tweak speed (XXX: make it more rational)
rot_speed = abs_delta * 2 * pi / 40
if abs_delta < rot_speed * 2:
# Rotation is complete within a small error.
# Force it to the exact value:
self.heading = target_heading
return
self.heading += copysign(1, delta) * rot_speed
# normalize angle to be in (-pi, pi)
if self.heading >= WHOLE_ANGLE / 2:
self.heading = -WHOLE_ANGLE + self.heading
if self.heading < -WHOLE_ANGLE / 2:
self.heading = WHOLE_ANGLE + self.heading
def deflectionTo(self, otherPt, preferredDir=None):
'''When interpreting both ExtendedPoints as Vectors, return the deflection
(in units of radians). Negative deflection is left.
:param otherPt: ExtendedPoint to be compared with for computation of deflection
:param longSolution: if True, compute deflection the long way around the circle
:return: a namedTuple of the interior solution azimuth and the exterior solution azimuth
:rtype: namedTuple AzimuthPair
'''
defl = otherPt.azimuth - self.azimuth
if defl < -1.0 * math.pi:
interiorDeflection = defl + 2 * math.pi
exteriorDeflection = defl
elif defl > math.pi:
interiorDeflection = defl - 2 * math.pi
exteriorDeflection = defl
else:
interiorDeflection = defl
if defl > 0.0:
exteriorDeflection = defl - 2 * math.pi
else:
exteriorDeflection = defl + 2 * math.pi
if preferredDir == None:
return AzimuthPair(interiorSolution = interiorDeflection,
exteriorSolution = exteriorDeflection)
elif math.copysign(1, exteriorDeflection) == math.copysign(1, preferredDir):
return exteriorDeflection
return interiorDeflection
def updatePlayerDirectionOnCollision(self):
scale = 1.2 #moves players away from each other by this factor
xDirection = -self.velocity*math.cos(self.angle)
yDirection = -self.velocity*math.sin(self.angle)
xDirection = math.copysign(math.ceil(abs(xDirection)), xDirection)
yDirection = math.copysign(math.ceil(abs(yDirection)), yDirection)
self.move(xDirection*scale, yDirection*scale)
def write_corner(fhandler, r, n, last_id, m_fact=1.0):
"""Write the Ghost particles as well as the common mirror particle, for a
corner.
This method is only for convex bodies, and Ghost particles.
Position arguments:
r -- Mirroring position
n -- Outward normal of the corner
last_id -- Number of already written particles
Keyword arguments:
m_fact -- Mass multiplier factor (To eventually overlap ghost particles)
Returned value:
Number of written particles
"""
if BC != 'GP':
return 0
n_box = 1
write_particle(fhandler, r, n=n, mass=dr, imove=-2)
dir = (math.copysign(1.0, n[0]), math.copysign(1.0, n[1]))
dx = 0.5 * dr
while dx < sep * h:
x = r[0] + dir[0] * dx
dy = 0.5 * dr
while dy < sep * h:
y = r[1] + dir[1] * dy
write_particle(fhandler, (x, y), n=n, mass=m_fact*refd*dr**2,
imove=-1, associated=last_id)
n_box += 1
dy += dr
dx += dr
return n_box
def apply_matching(self,error_type,matching):
""" applies appropriate flips to the array to bring it back to the codespace using the given matching """
channel=0 if error_type=="X" else 1
flips=[]
for pair in matching:
[p0,p1]=pair[0]
[q0,q1]=pair[1]
if channel==1 and (p1==-1 or p1==self.size*2+1)and(q1==-1 or q1==self.size*2+1):
flips+=[]
elif channel==0 and (p0==-1 or p0==self.size*2+1)and(q0==-1 or q0==self.size*2+1):
flips+=[]
else:
s0=int(math.copysign(1,q0-p0))
s1=int(math.copysign(1,q1-p1))
range0=range(1,abs(q0-p0),2)
range1=range(1,abs(q1-p1),2)
for x in range1:
flips+=[[p0,p1+s1*x]]
for y in range0:
flips+=[[p0+s0*y,q1]]
for flip in flips:
self.array[flip[0]][flip[1]][channel]*=-1
def repulsiveFields(self, x=-1, y=-1):
if x != -1 and y != -1:
self.currentTank.x = x
self.currentTank.y = y
radius = 5;
spread = 10;
beta = 20;
if self.currentTank.flag != '-':
return
for tank in self.mytanks:
if tank is self.currentTank:
continue
distance = math.sqrt(math.pow(tank.x - self.currentTank.x, 2) + math.pow(self.currentTank.y - tank.y, 2))
angle = self.normalize_angle(math.atan2(tank.y - self.currentTank.y, tank.x - self.currentTank.x))
if distance < radius:
doX = math.copysign(1, math.cos(angle)) * -9001
doY = math.copysign(1, math.sin(angle)) * -9001
elif radius <= distance and distance <= (spread + radius):
doX = -beta * (spread + radius - distance) * math.cos(angle)
doY = -beta * (spread + radius - distance) * math.sin(angle)
else:
doX = 0;
doY = 0;
self.dx = self.dx + doX
self.dy = self.dy + doY
def assertFloatsAreIdentical(self, x, y):
"""assert that floats x and y are identical, in the sense that:
(1) both x and y are nans, or
(2) both x and y are infinities, with the same sign, or
(3) both x and y are zeros, with the same sign, or
(4) x and y are both finite and nonzero, and x == y
"""
msg = 'floats {!r} and {!r} are not identical'
if isnan(x) or isnan(y):
if isnan(x) and isnan(y):
return
elif x == y:
if x != 0.0:
return
# both zero; check that signs match
elif copysign(1.0, x) == copysign(1.0, y):
return
else:
msg += ': zeros have different signs'
if test_support.due_to_ironpython_bug("http://ironpython.codeplex.com/workitem/28352"):
print msg.format(x, y)
return
self.fail(msg.format(x, y))
def assert_same_sign(a, b, fp_zero=1e-9):
if (a == sp.NaN) or (b == sp.NaN):
raise ValueError("NaN(s) passed to sign comparison functions")
elif (abs(a) < fp_zero) and (abs(b) < fp_zero):
assert True
else:
assert math.copysign(1, a) == math.copysign(1, b)
def scrollEvent(self, dx=0, dy=0): """ Generate scroll events from parametters and displacement @param int dx delta movement from last call on x axis @param int dy delta movement from last call on y axis @param bool free set to true for free ball move @return float absolute distance moved this tick """ # Compute mouse mouvement from interger part of d * scale self._scr_dx += dx * self._scr_xscale self._scr_dy += dy * self._scr_yscale _syn = False if int(self._scr_dx): self.relEvent(rel=Rels.REL_HWHEEL, val=int(copysign(1, self._scr_dx))) self._scr_dx -= int(self._scr_dx) _syn = True if int(self._scr_dy): self.relEvent(rel=Rels.REL_WHEEL, val=int(copysign(1, self._scr_dy))) self._scr_dy -= int(self._scr_dy) _syn = True if _syn: self.synEvent()
def getTangentialField(self, tank, obstacle):
obstacle_x = (obstacle[0][0] + obstacle[2][0])/2
obstacle_y = (obstacle[0][1] + obstacle[2][1])/2
dx = abs(obstacle_x - tank.x)
dy = abs(obstacle_y - tank.y)
distance = math.sqrt((obstacle[2][0]-obstacle[0][0])**2 + (obstacle[2][1]-obstacle[0][1])**2)
radius = distance/2 #flag radius
spread = radius + 20 #spread
beta = 3.6
a = math.atan2(obstacle_y - tank.y, obstacle_x - tank.x)
d = math.sqrt(dx**2 + dy**2)
field = Field()
field.angle = a
field.magnitude = d
if (d < radius):
field.dx = - math.copysign(1, math.cos(a + math.pi/4)) * ((1/d) if d > 0 else 10)
field.dy = - math.copysign(1, math.sin(a + math.pi/4)) * ((1/d) if d > 0 else 10)
elif (radius <= d and d <= spread + radius):
field.dx = -beta * (spread + radius - d) * math.cos(a + math.pi/4)
field.dy = -beta * (spread + radius - d) * math.sin(a+ math.pi/4)
elif (d > spread + radius):
field.dx = 0
field.dy = 0
return field
def move_vector(self):
#horizontal?
if self.x_real == self.x_dest:
self.x_move = 0
#up by default
self.y_move = 1
#whoops, we need down
if(self.y_dest < self.y_real):
self.y_move = -1
#negative safely unreald slope
self.m = (-999,1)
#positive safely unreal slope
else:
self.m = (999,1)
#we have vertical movement, find slope
else:
self.m = ((self.y_dest - self.y_real), (self.x_dest - self.x_real))
self.y_move = self.m[0]/(abs(self.m[0])+abs(self.m[1]))
self.x_move = 1 - self.y_move
#make sure the sign is correct
self.y_move = math.copysign(self.y_move, self.m[0])
self.x_move = math.copysign(self.x_move, self.m[1])
def almostEqualF(a, b, rel_err=2e-15, abs_err = 5e-323):
"""Determine whether floating-point values a and b are equal to within
a (small) rounding error. The default values for rel_err and
abs_err are chosen to be suitable for platforms where a float is
represented by an IEEE 754 double. They allow an error of between
9 and 19 ulps."""
# special values testing
if math.isnan(a):
return math.isnan(b)
if math.isinf(a):
return a == b
# if both a and b are zero, check whether they have the same sign
# (in theory there are examples where it would be legitimate for a
# and b to have opposite signs; in practice these hardly ever
# occur).
if not a and not b:
return math.copysign(1., a) == math.copysign(1., b)
# if a-b overflows, or b is infinite, return False. Again, in
# theory there are examples where a is within a few ulps of the
# max representable float, and then b could legitimately be
# infinite. In practice these examples are rare.
try:
absolute_error = abs(b-a)
except OverflowError:
return False
else:
return absolute_error <= max(abs_err, rel_err * abs(a))
def squashMatching(size,error_type,matching):
channel=0 if error_type=="X" else 1
flip_array=[[1]*(2*size+1) for _ in range(2*size+1)]
for [(pt,p0,p1),(qt,q0,q1)] in matching:
flips = []
if (p0 in [-1,size*2+1] and q0 in [-1,size*2+1]) or (p1 in [-1,size*2+1] and q1 in [-1,size*2+1]):
flips+=[]
else:
s0=int(math.copysign(1,q0-p0))
s1=int(math.copysign(1,q1-p1))
range0=range(1,abs(q0-p0),2)
range1=range(1,abs(q1-p1),2)
for x in range1:
flips+=[[p0,p1+s1*x]]
for y in range0:
flips+=[[p0+s0*y,q1]]
for flip in flips:
flip_array[flip[0]][flip[1]]*=-1
return flip_array
def GetXYZ(self):
"""Returns angles (theta,phi,psi) for:
an x-rotation by theta followed by a y-rotation by phi followed by a z-rotation by psi.
Active rotations are considered here.
This works in all quadrants
Note that if you construct a rotation matrix using three angles, you may not get back the same angles from this function
(i.e. the mapping between xyz-angle-triples and SO(3) is not 1-1)"""
phi=math.asin(-self.item(2,0))
if math.fabs(1.-math.fabs(self.item(2,0)))>.0000001:
# if the phi rotation is not by pi/2 or -pi/2 (two solutions, return one of them)
psi=math.atan2(self.item(1,0),self.item(0,0))
theta=math.atan2(self.item(2,1),self.item(2,2))
else:
# if the phi rotation was in fact by pi/2 or -pi/2 (infinite solutions- pick 0 for psi and solve for theta)
psi=0
if math.fabs(self.item(1,1))>.0000001 and math.fabs(self.item(0,2))>.0000001: #as long as these matrix elements aren't 0
if math.copysign(1,self.item(1,1))==math.copysign(1,self.item(0,2)):
# relative sign of these matrix elements determines theta's quadrant
theta=math.atan2(self.item(0,1),self.item(1,1))
else:
theta=math.atan2(-self.item(0,1),self.item(1,1))
else:
# if one of them was zero then use these matrix elements to test for theta's quadrant instead
if not math.copysign(1,self.item(0,1))==math.copysign(1,self.item(1,2)):
# relative sign of these matrix elements determines theta's quadrant
theta=math.atan2(self.item(0,1),self.item(1,1))
else:
theta=math.atan2(-self.item(0,1),self.item(1,1))
return (theta,phi,psi)
def readline(self):
if self.readList is None:
return ''
n = 0
timeDiff = self.lastTempAt - time.time()
self.lastTempAt = time.time()
if abs(self.temp - self.targetTemp) > 1:
self.temp += math.copysign(timeDiff *
10, self.targetTemp - self.temp)
if self.temp < 0:
self.temp = 0
if abs(self.bedTemp - self.bedTargetTemp) > 1:
self.bedTemp += math.copysign(timeDiff *
10, self.bedTargetTemp - self.bedTemp)
if self.bedTemp < 0:
self.bedTemp = 0
while len(self.readList) < 1:
time.sleep(0.1)
n += 1
if n == 20:
return ''
if self.readList is None:
return ''
time.sleep(0.001)
return self.readList.pop(0)
def update(self):
print(self.children)
self.map_offset = self.parent.offset
if copysign(1, self.velocity[0]) * (self.touch_position[0] - self.map_position[0]) < 0:
self.velocity[0] = 0
if copysign(1, self.velocity[1]) * (self.touch_position[1] - self.map_position[1]) < 0:
self.velocity[1] = 0
if not self.parent.collide_point(self.map_position[0],self.map_position[1]):
self.map_position[0] -= self.velocity[0]
self.map_position[1] -= self.velocity[1]
self.velocity = [0,0]
for child in self.parent.children:
if child.id == self.id or child.id == 'sprite':
continue
if self.collide_widget(child):
self.map_position[0] -= self.velocity[0]
self.map_position[1] -= self.velocity[1]
self.velocity = [0,0]
print(self.id,child.id,self.collide_widget(child))
self.map_position[0] += self.velocity[0]
self.map_position[1] += self.velocity[1]
self.x = self.map_position[0] + self.map_offset[0]
self.y = self.map_position[1] + self.map_offset[1]
# print(self.parent.children[0].map_position)
# print(self.collide_widget(self.parent.children[0]))
return
def GetG4XYZ(self):
"""Returns angles (theta,phi,psi) for:
an x-rotation by theta followed by a y-rotation by phi followed by a z-rotation by psi.
Passive rotations are considered here, as expected for a GEANT4 rotation. That is equivalent to
an Active rotation by -psi,-phi,-theta in the ZYX order.
Note that this is the same algorithm as GetXYZ(), for the INVERSE matrix.
This works in all quadrants
Note that if you construct a rotation matrix using three angles, you may not get back the same angles from this function
(i.e. the mapping between xyz-angle-triples and SO(3) is not 1-1)"""
phi= -math.asin(self.item(0,2))
if math.fabs(1.-math.fabs(self.item(0,2))) > 0.0000001:
psi = math.atan2(self.item(0,1),self.item(0,0))
theta= math.atan2(self.item(1,2),self.item(2,2))
else:
psi = 0
if math.fabs(self.item(1,1)) > 0.0000001 and math.fabs(self.item(2,0))>0.0000001:
if math.copysign(1,self.item(1,1)) == math.copysign(1,self.item(2,0)):
theta=math.atan2(self.item(1,0),self.item(1,1))
else:
theta=math.atan2(-self.item(1,0),self.item(1,1))
else:
if not math.copysign(1,self.item(1,0)) == math.copysign(1,self.item(2,1)):
theta=math.atan2(self.item(1,0),self.item(1,1))
else:
theta=math.atan2(-self.item(1,0),self.item(1,1))
return(theta,phi,psi)
def _roll(cls, start_x, start_y, finish_x, finish_y):
path = []
x = start_x
y = start_y
if math.fabs(finish_x - start_x) > math.fabs(finish_y - start_y):
dx = math.copysign(1.0, finish_x - start_x)
dy = dx * float(finish_y - start_y) / (finish_x - start_x)
else:
dy = math.copysign(1.0, finish_y - start_y)
dx = dy * float(finish_x - start_x) / (finish_y - start_y)
real_x = float(x)
real_y = float(y)
while x != finish_x or y != finish_y:
real_x += dx
real_y += dy
if int(round(real_x)) == x + 1: path.append(PATH_DIRECTION.RIGHT.value)
elif int(round(real_x)) == x - 1: path.append(PATH_DIRECTION.LEFT.value)
if int(round(real_y)) == y + 1: path.append(PATH_DIRECTION.DOWN.value)
elif int(round(real_y)) == y - 1: path.append(PATH_DIRECTION.UP.value)
x = int(round(real_x))
y = int(round(real_y))
return ''.join(path)
def float_round(value, precision_digits=None, precision_rounding=None, rounding_method='HALF-UP'):
"""Return ``value`` rounded to ``precision_digits`` decimal digits,
minimizing IEEE-754 floating point representation errors, and applying
the tie-breaking rule selected with ``rounding_method``, by default
HALF-UP (away from zero).
Precision must be given by ``precision_digits`` or ``precision_rounding``,
not both!
:param float value: the value to round
:param int precision_digits: number of fractional digits to round to.
:param float precision_rounding: decimal number representing the minimum
non-zero value at the desired precision (for example, 0.01 for a
2-digit precision).
:param rounding_method: the rounding method used: 'HALF-UP' or 'UP', the first
one rounding up to the closest number with the rule that number>=0.5 is
rounded up to 1, and the latest one always rounding up.
:return: rounded float
"""
rounding_factor = _float_check_precision(precision_digits=precision_digits,
precision_rounding=precision_rounding)
if rounding_factor == 0 or value == 0: return 0.0
# NORMALIZE - ROUND - DENORMALIZE
# In order to easily support rounding to arbitrary 'steps' (e.g. coin values),
# we normalize the value before rounding it as an integer, and de-normalize
# after rounding: e.g. float_round(1.3, precision_rounding=.5) == 1.5
# TIE-BREAKING: HALF-UP (for normal rounding)
# We want to apply HALF-UP tie-breaking rules, i.e. 0.5 rounds away from 0.
# Due to IEE754 float/double representation limits, the approximation of the
# real value may be slightly below the tie limit, resulting in an error of
# 1 unit in the last place (ulp) after rounding.
# For example 2.675 == 2.6749999999999998.
# To correct this, we add a very small epsilon value, scaled to the
# the order of magnitude of the value, to tip the tie-break in the right
# direction.
# Credit: discussion with OpenERP community members on bug 882036
normalized_value = value / rounding_factor # normalize
epsilon_magnitude = math.log(abs(normalized_value), 2)
epsilon = 2**(epsilon_magnitude-53)
if rounding_method == 'HALF-UP':
normalized_value += math.copysign(epsilon, normalized_value)
rounded_value = round(normalized_value) # round to integer
# TIE-BREAKING: UP (for ceiling operations)
# When rounding the value up, we instead subtract the epsilon value
# as the the approximation of the real value may be slightly *above* the
# tie limit, this would result in incorrectly rounding up to the next number
# The math.ceil operation is applied on the absolute value in order to
# round "away from zero" and not "towards infinity", then the sign is
# restored.
elif rounding_method == 'UP':
sign = math.copysign(1.0, normalized_value)
normalized_value -= sign*epsilon
rounded_value = math.ceil(abs(normalized_value))*sign # ceil to integer
result = rounded_value * rounding_factor # de-normalize
return result
def rowJacobian(x, y, drop_data, tolerances):
[xP, yP, RP, BP, wP] = drop_data.params
# x, y = xy # extract the data points
# s_0 = drop_data.s_0
if ((x - xP) * cos(wP) - (y - yP) * sin(wP)) < 0:
s_0 = drop_data.s_left
else:
s_0 = drop_data.s_right
# if x < xP:
# s_0 = s_left
# else:
# s_0 = s_right
xs, ys, dx_dBs, dy_dBs, e_r, e_z, s_i = minimum_arclength(x, y, s_0, drop_data, tolerances) # functions at s*
if ((x - xP) * cos(wP) - (y - yP) * sin(wP)) < 0:
drop_data.s_left = s_i
else:
drop_data.s_right = s_i
# e_i = sqrt(e_r**2 + e_z**2) # actual residual
e_i = math.copysign(sqrt(e_r**2 + e_z**2), e_r) # actual residual
sgnx = math.copysign(1, ((x - xP) * cos(wP) - (y - yP) * sin(wP))) # calculates the sign for ddi_dX0
ddi_dxP = -( e_r * sgnx * cos(wP) + e_z * sin(wP) ) / e_i # derivative w.r.t. X_0 (x at apex)
ddi_dyP = -(-e_r * sgnx * sin(wP) + e_z * cos(wP) ) / e_i # derivative w.r.t. Y_0 (y at apex)
ddi_dRP = -( e_r * xs + e_z * ys) / e_i # derivative w.r.t. RP (apex radius)
ddi_dBP = - RP * (e_r * dx_dBs + e_z * dy_dBs) / e_i # derivative w.r.t. Bo (Bond number)
ddi_dwP = (e_r * sgnx * (- (x - xP) * sin(wP) - (y - yP) * cos(wP)) + e_z * ( (x - xP) * cos(wP) - (y - yP) * sin(wP))) / e_i
return [[ ddi_dxP, ddi_dyP, ddi_dRP, ddi_dBP, ddi_dwP], e_i]
def glsl_literal(x):
"""Convert the given number to a string that represents a GLSL literal.
:param x: a uint32 or float32
"""
if isinstance(x, uint32):
return "{0}u".format(uint32(x))
elif isinstance(x, float32):
if math.isnan(x):
# GLSL ES 3.00 and GLSL 4.10 do not require implementations to
# support NaN, so we do not test it.
assert(False)
elif math.isinf(x):
# GLSL ES 3.00 lacks a literal for infinity. However, ±1.0e256
# suffices because it lies sufficientlyoutside the range of finite
# float32 values.
#
# From page 31 of the GLSL ES 3.00 spec:
#
# If the value of the floating point number is too large (small)
# to be stored as a single precision value, it is converted to
# positive (negative) infinity.
#
return repr(copysign(1.0e256, x))
elif x == 0 and copysign(1.0, x) == -1.0:
# Workaround for numpy-1.7.0, in which repr(float32(-0.0)) does
# not return a float literal.
# See https://github.com/numpy/numpy/issues/2935 .
return "-0.0"
else:
return repr(x)
else:
assert(False)
def VectorMath(ExtPts):
aDx = ExtPts[1].X-ExtPts[0].X
aDy = ExtPts[1].Y-ExtPts[0].Y
bDx = ExtPts[-2].X-ExtPts[0].X
bDy = ExtPts[-2].Y-ExtPts[0].Y
VectorA=[aDx,aDy]
VectorB=[bDx,bDy]
VectorX=[1,0]
VectorY=[0,1]
A_Len = np.linalg.norm(VectorA)
B_Len = np.linalg.norm(VectorB)
dpAB=dotProduct(VectorA, VectorB)
AngAB=math.acos(dpAB/A_Len/B_Len)
cpAB=(A_Len*B_Len)*math.sin(AngAB)
dpAX=dotProduct(VectorA, VectorX)
AngAx=math.acos(dpAX/A_Len/1.0)*math.copysign(1,aDy)
dpBX=dotProduct(VectorB, VectorX)
AngBx=math.acos(dpBX/B_Len/1.0)*math.copysign(1,bDy)
eParts=[A_Len,B_Len, AngAB, AngAx, AngBx,cpAB]
return(eParts)
def update(self, txn):
if self.sid != txn.sid:
raise Exception('updating position with txn for a '
'different sid')
total_shares = self.amount + txn.amount
if total_shares == 0:
self.cost_basis = 0.0
else:
prev_direction = copysign(1, self.amount)
txn_direction = copysign(1, txn.amount)
if prev_direction != txn_direction:
# we're covering a short or closing a position
if abs(txn.amount) > abs(self.amount):
# we've closed the position and gone short
# or covered the short position and gone long
self.cost_basis = txn.price
else:
prev_cost = self.cost_basis * self.amount
txn_cost = txn.amount * txn.price
total_cost = prev_cost + txn_cost
self.cost_basis = total_cost / total_shares
# Update the last sale price if txn is
# best data we have so far
if self.last_sale_date is None or txn.dt > self.last_sale_date:
self.last_sale_price = txn.price
self.last_sale_date = txn.dt
self.amount = total_shares
def intersection_point(center_x, center_y, source_x, source_y, \
width, height=None):
"""Determines where the rhombus centered at (center_x, center_y)
intersects with a line drawn from (source_x, source_y) to
(center_x, center_y).
@see: ShapeDrawer.intersection_point"""
height = height or width
if height == 0 and width == 0:
return center_x, center_y
delta_x, delta_y = source_x - center_x, source_y - center_y
# Treat edge case when delta_x = 0
if delta_x == 0:
if delta_y == 0:
return center_x, center_y
else:
return center_x, center_y + copysign(height / 2, delta_y)
width = copysign(width, delta_x)
height = copysign(height, delta_y)
f = height / (height + width * delta_y / delta_x)
return center_x + f * width / 2, center_y + (1-f) * height / 2
def update_vel(self, delta_time, desired_vel):
v = float(desired_vel.v)
omega = float(desired_vel.omega)
sigma = max(v/self.max_vel, omega/self.max_rot_vel, 1.0)
if sigma != 1.0:
if v/self.max_vel > omega/self.max_rot_vel:
v = copysign(self.max_vel, v)
omega /= sigma
else: # omega/self.max_rot_vel > v/self.max_vel
v /= sigma
omega = copysign(self.max_rot_vel, omega)
# these are the velocities wheels would get
# if they didn't have to accelerate smoothly
target_lvel = v - 0.5 * self.width * omega
target_rvel = v + 0.5 * self.width * omega
if abs(self.lvel - target_lvel) < delta_time * config.BOT_ACCEL_CAP:
self.lvel = target_lvel
else:
self.lvel += copysign(config.BOT_ACCEL_CAP, target_lvel - self.lvel) * delta_time
if abs(self.rvel - target_rvel) < delta_time * config.BOT_ACCEL_CAP:
self.rvel = target_rvel
else:
self.rvel += copysign(config.BOT_ACCEL_CAP, target_rvel - self.rvel) * delta_time
# cap velocity
v = max(abs(self.lvel), abs(self.rvel))
if v > self.max_vel:
self.lvel *= self.max_vel / v
self.rvel *= self.max_vel / v
def compare(self, flower1, flower2):
if (flower1.height == flower2.height):
return 0 # never happen
if ( self.block(flower1,flower2) ):
return int(math.copysign(1, flower1.height - flower2.height))
else:
return int(math.copysign(1, flower2.height - flower1.height))
def drag3(event):
global x, y, dpx
dpx=max(abs(start3[0]-event.x)/sizex,abs(start3[1]-event.y)/sizey)
x=start3[0]+copysign(dpx*sizex, event.x-start3[0])
y=start3[1]+copysign(dpx*sizey, event.y-start3[1])
canv.coords(rect,start3[0],start3[1],x,y)
canv.itemconfig(rect,state='normal')
def stepThatWay(self):
"""
Not used.
"""
fX = self.goal[0] - self.pos.means[0]
fY = self.goal[1] - self.pos.means[1]
fM = math.hypot(fX, fY)
fD = math.atan2(fY, fX)
# Convert to robot frame
fDR = fD - self.pos.means[2]
if math.fabs(fDR) > math.pi:
fDR -= math.copysign(2 * math.pi, fDR)
if math.fabs(fDR) > math.pi/10.0:
provX = 0.0
else:
provX = min(self.maxSpeed, self.kSpeed * fM)
provZ = math.fabs(self.kTurn * fDR)
provZ = min(self.maxTurn, provZ)
provZ = math.copysign(provZ, fDR)
twist = Twist()
twist.linear.x = provX
twist.angular.z = provZ
return twist
def move_arc(self, radius, theta):
turn_speed = 0.0
initial_distance = self.total_distance
initial_heading = self.heading
arc_length = radius * theta # some calculation
while(self.total_distance - initial_distance < abs(arc_length)):
turn_speed = 0.0
# calculate desired angle based on distance travelled
target_heading = (self.total_distance - initial_distance)/radius
target_heading = math.copysign(target_heading, arc_length)
# offset by starting angle
target_heading += initial_heading
# ensure that 0 <= target_heading <= 2*pi
if target_heading < 0:
target_heading += 2*math.pi
if target_heading > 2*math.pi:
target_heading -= 2*math.pi
error = target_heading - self.heading
if error < -math.pi:
error += 2*math.pi
if error > math.pi:
error -= 2*math.pi
# correct angle
if(abs(error) > 0.008):
if abs(error) < 0.05:
turn_speed = math.copysign(0.3, error)
else:
turn_speed = error*5
self.set_speeds(0.2, turn_speed)
print "relative distance: ", self.total_distance - initial_distance
print "error: ", error
self.stop_all_motion()
return 1
def update(self, dt):
# call parent update (Animation)
super().update(dt)
# Apply gravity if grounded
if not self.grounded:
self.velocity_y += self.gravity*dt
# Set up vars
c_x = self.get_x(); c_y = self.get_y()
vx = math.floor(self.velocity_x)
vy = math.floor(self.velocity_y)
# Collision handling
# Collision x
while not self.can_move(c_x, c_y, c_x + vx, c_y, 0) and not vx == 0:
vx -= math.copysign(1, vx)
# Move x
self.set_position(c_x + vx, c_y)
c_x = self.get_x()
# Collision y
while not self.can_move(c_x, c_y, c_x, c_y + vy, 1) and not vy == 0:
vy -= math.copysign(1, vy)
self.velocity_y = 0
# Check if grounded
self.grounded = not self.can_move(c_x, c_y, c_x, c_y + 1, 1)
# Move y
self.set_position(c_x, c_y + vy)
def remainder(x, y):
"""Difference between x and the closest integer multiple of y.
Return x - n*y where n*y is the closest integer multiple of y.
In the case where x is exactly halfway between two multiples of
y, the nearest even value of n is used. The result is always exact."""
from math import copysign, fabs, fmod, isfinite, isinf, isnan, nan
x = float(x)
y = float(y)
# Deal with most common case first.
if isfinite(x) and isfinite(y):
if y == 0.0:
# return nan
# Merging the logic from math_2 in CPython's mathmodule.c
# nan returned and x and y both not nan -> domain error
raise ValueError("math domain error")
absx = fabs(x)
absy = fabs(y)
m = fmod(absx, absy)
# Warning: some subtlety here. What we *want* to know at this point is
# whether the remainder m is less than, equal to, or greater than half
# of absy. However, we can't do that comparison directly because we
# can't be sure that 0.5*absy is representable (the mutiplication
# might incur precision loss due to underflow). So instead we compare
# m with the complement c = absy - m: m < 0.5*absy if and only if m <
# c, and so on. The catch is that absy - m might also not be
# representable, but it turns out that it doesn't matter:
# - if m > 0.5*absy then absy - m is exactly representable, by
# Sterbenz's lemma, so m > c
# - if m == 0.5*absy then again absy - m is exactly representable
# and m == c
# - if m < 0.5*absy then either (i) 0.5*absy is exactly representable,
# in which case 0.5*absy < absy - m, so 0.5*absy <= c and hence m <
# c, or (ii) absy is tiny, either subnormal or in the lowest normal
# binade. Then absy - m is exactly representable and again m < c.
c = absy - m
if m < c:
r = m
elif m > c:
r = -c
else:
# Here absx is exactly halfway between two multiples of absy,
# and we need to choose the even multiple. x now has the form
# absx = n * absy + m
# for some integer n (recalling that m = 0.5*absy at this point).
# If n is even we want to return m; if n is odd, we need to
# return -m.
# So
# 0.5 * (absx - m) = (n/2) * absy
# and now reducing modulo absy gives us:
# | m, if n is odd
# fmod(0.5 * (absx - m), absy) = |
# | 0, if n is even
# Now m - 2.0 * fmod(...) gives the desired result: m
# if n is even, -m if m is odd.
# Note that all steps in fmod(0.5 * (absx - m), absy)
# will be computed exactly, with no rounding error
# introduced.
assert m == c
r = m - 2.0 * fmod(0.5 * (absx - m), absy)
return copysign(1.0, x) * r
# Special values.
if isnan(x):
return x
if isnan(y):
return y
if isinf(x):
# return nan
# Merging the logic from math_2 in CPython's mathmodule.c
# nan returned and x and y both not nan -> domain error
raise ValueError("math domain error")
assert isinf(y)
return x
def X(b):
return copysign(1, b) * sqrt(pi * abs(b)) * Cf(sqrt(abs(b) / pi))
def yCoord(gamma, alpha, s):
return gamma * copysign(1, alpha) * sqrt(pi / abs(alpha)) * Sf(
sqrt(abs(alpha) / pi) * s)
def _sign(x):
return int(copysign(1, x))
def __init__(self):
# Give the node a name
rospy.init_node('calibrate_linear', anonymous=False)
# Set rospy to execute a shutdown function when terminating the script
rospy.on_shutdown(self.shutdown)
# How fast will we check the odometry values?
self.rate = rospy.get_param('~rate', 20)
r = rospy.Rate(self.rate)
# Set the distance to travel
self.test_distance = rospy.get_param('~test_distance', 1.0) # meters
self.speed = rospy.get_param('~speed', 0.15) # meters per second
self.tolerance = rospy.get_param('~tolerance', 0.01) # meters
self.odom_linear_scale_correction = rospy.get_param(
'~odom_linear_scale_correction', 1.0)
self.start_test = rospy.get_param('~start_test', True)
# Publisher to control the robot's speed
self.cmd_vel = rospy.Publisher('/cmd_vel', Twist, queue_size=5)
# The base frame is base_footprint for the TurtleBot but base_link for Pi Robot
self.base_frame = rospy.get_param('~base_frame', '/base_footprint')
# The odom frame is usually just /odom
#self.odom_frame = rospy.get_param('~odom_frame', '/odom')
self.odom_frame = rospy.get_param('~odom_frame', '/odom_combined')
# Initialize the tf listener
self.tf_listener = tf.TransformListener()
# Give tf some time to fill its buffer
rospy.sleep(2)
# Make sure we see the odom and base frames
self.tf_listener.waitForTransform(self.odom_frame, self.base_frame,
rospy.Time(), rospy.Duration(60.0))
rospy.loginfo("Bring up rqt_reconfigure to control the test.")
self.position = Point()
# Get the starting position from the tf transform between the odom and base frames
self.position = self.get_position()
x_start = self.position.x
y_start = self.position.y
move_cmd = Twist()
while not rospy.is_shutdown():
# Stop the robot by default
move_cmd = Twist()
if self.start_test:
# Get the current position from the tf transform between the odom and base frames
self.position = self.get_position()
# Compute the Euclidean distance from the target point
distance = sqrt(
pow((self.position.x - x_start), 2) +
pow((self.position.y - y_start), 2))
# Correct the estimated distance by the correction factor
distance *= self.odom_linear_scale_correction
# How close are we?
error = distance - self.test_distance
# Are we close enough?
if not self.start_test or abs(error) < self.tolerance:
self.start_test = False
params = {'start_test': False}
rospy.loginfo(params)
else:
# If not, move in the appropriate direction
move_cmd.linear.x = copysign(self.speed, -1 * error)
else:
self.position = self.get_position()
x_start = self.position.x
y_start = self.position.y
self.cmd_vel.publish(move_cmd)
r.sleep()
# Stop the robot
self.cmd_vel.publish(Twist())
def set_cmd_vel(self, msg):
global counter
counter = 0
try:
marker = msg.markers[0]
# rospy.loginfo("the Roll is: %d",roll)
# rospy.loginfo("the Pitch is: %d",pitch)
# rospy.loginfo("the Roll is: %d",yaw)
if not self.target_visible:
rospy.loginfo("FOLLOWER is Tracking Target!")
# quaternion = (
# marker.pose.orientation.x,
# marker.pose.orientation.y,
# marker.pose.orientation.z,
# marker.pose.orientation.w)
# euler = tf.transformations.euler_from_quaternion(quaternion)
# roll = euler[0]
# pitch = euler[1]
# yaw = euler[2]
#counter+=1
#rospy.loginfo("the frame count is : %f", counter)
#print ("Number of succesfully tracked frames so far: %i",counter)
self.move_cmd.angular.z = 0.0
self.target_visible = True
#rospy.sleep(0.09) nice response
except:
# If target is lost, stop the robot by slowing it incrementally
self.move_cmd.linear.x /= 1.9
#if()
self.move_cmd.angular.z = 1.1
if self.target_visible:
rospy.loginfo("FOLLOWER LOST Target!")
self.target_visible = False
counter += 1
return
rospy.loginfo("the frame count is : %f", counter)
quaternion = (marker.pose.pose.orientation.x,
marker.pose.pose.orientation.y,
marker.pose.pose.orientation.z,
marker.pose.pose.orientation.w)
euler = tf.transformations.euler_from_quaternion(quaternion)
roll = euler[0]
pitch = euler[1]
yaw = euler[2]
rospy.loginfo("the Roll is: %f", roll)
rospy.loginfo("the Pitch is: %f", pitch)
rospy.loginfo("the yaw is: %f", yaw)
# Get the displacement of the marker relative to the base
target_offset_y = marker.pose.pose.position.y
# Get the distance of the marker from the base
target_offset_x = marker.pose.pose.position.x
# Get the distance of the marker from the base
target_offset_z = marker.pose.pose.position.z
rospy.loginfo("the target_offset_x is: %f", target_offset_x)
rospy.loginfo("the target_offset_y is: %f", target_offset_y)
rospy.loginfo("the target_offset_z is: %f", target_offset_z)
# Rotate the robot only if the displacement of the target exceeds the threshold
if abs(target_offset_y) > self.y_threshold:
# Set the rotation speed proportional to the displacement of the target
speed = (target_offset_y * self.y_scale)
self.move_cmd.angular.z = copysign(
max(self.min_angular_speed,
min(self.max_angular_speed, abs(speed))), speed)
else:
self.move_cmd.angular.z = 0.0
# Now get the linear speed
if (target_offset_x - self.goal_x) > self.x_threshold:
speed = abs((self.goal_x - (target_offset_x + 0.2))) * self.x_scale
if speed > 0:
speed *= 1.5
self.move_cmd.linear.x = copysign(
min(self.max_linear_speed,
max(self.min_linear_speed, abs(speed))), speed)
else:
self.move_cmd.linear.x /= 1.9
cspeed = self.move_cmd.linear.x
rospy.loginfo("the current speed is : %f", cspeed)
if ((target_offset_x <= 0.8) and (target_offset_x >= 0.05)
and (cspeed <= 0.1)):
self.move_cmd.linear.x = 0.3 # 0.4 worked
rospy.loginfo("increasing Speed \n")
else:
self.move_cmd.linear.x /= 1.01
self.move_cmd.linear.y = 0.0
self.move_cmd.linear.z = 0.0
rospy.loginfo("target achieved\n")
#
import math
def fail(which):
print("fail %s" % which)
exit(1)
#
# Number-theoretic and representation functions
#
if not math.ceil(0.5) == 1: fail("math.ceil(0.5) == 1")
if not math.ceil(-0.5) == 0: fail("math.ceil(-0.5) == 0")
if not math.copysign(1.1, -2) == -1.1: fail("math.copysign(1.1, -2) == -1.1")
if not math.copysign(-1.1, -2) == -1.1: fail("math.copysign(-1.1, -2) == -1.1")
if not math.copysign(1.1, 2) == 1.1: fail("math.copysign(1.1, 2) == 1.1")
if not math.copysign(-1.1, 2) == 1.1: fail("math.copysign(-1.1, 2) == 1.1")
if not math.fabs(-1.1) == 1.1: fail("math.fabs(-1.1) == 1.1")
if not math.fabs(1.1) == 1.1: fail("math.fabs(1.1) == 1.1")
if not math.factorial(9) == 362880: fail("math.factorial(9) == 362880")
if not math.floor(0.5) == 0: fail("math.floor(0.5) == 0")
if not math.floor(-0.5) == -1: fail("math.floor(-0.5) == -1")
if not math.frexp(12.5) == (0.78125, 4):
fail("math.frexp(12.5) == (0.78125, 4)")
if not math.isclose(math.fsum([0.001] * 1000), 1):
fail("math.isclose(math.fsum([0.01] * 100), 1)")
if not math.gcd(21, 14) == 7: fail("math.gcd(21,14) == 7")
big = 10.1
for i in range(40):
def _deriv_copysign(x, y):
if x >= 0:
return math.copysign(1, y)
else:
return -math.copysign(1, y)
def testCopysign(self):
self.assertEqual(math.copysign(1, 42), 1.0)
self.assertEqual(math.copysign(0., 42), 0.0)
self.assertEqual(math.copysign(1., -42), -1.0)
self.assertEqual(math.copysign(3, 0.), 3.0)
self.assertEqual(math.copysign(4., -0.), -4.0)
self.assertRaises(TypeError, math.copysign)
# copysign should let us distinguish signs of zeros
self.assertEqual(math.copysign(1., 0.), 1.)
self.assertEqual(math.copysign(1., -0.), -1.)
self.assertEqual(math.copysign(INF, 0.), INF)
self.assertEqual(math.copysign(INF, -0.), NINF)
self.assertEqual(math.copysign(NINF, 0.), INF)
self.assertEqual(math.copysign(NINF, -0.), NINF)
# and of infinities
self.assertEqual(math.copysign(1., INF), 1.)
self.assertEqual(math.copysign(1., NINF), -1.)
self.assertEqual(math.copysign(INF, INF), INF)
self.assertEqual(math.copysign(INF, NINF), NINF)
self.assertEqual(math.copysign(NINF, INF), INF)
self.assertEqual(math.copysign(NINF, NINF), NINF)
self.assertTrue(math.isnan(math.copysign(NAN, 1.)))
self.assertTrue(math.isnan(math.copysign(NAN, INF)))
self.assertTrue(math.isnan(math.copysign(NAN, NINF)))
self.assertTrue(math.isnan(math.copysign(NAN, NAN)))
# copysign(INF, NAN) may be INF or it may be NINF, since
# we don't know whether the sign bit of NAN is set on any
# given platform.
self.assertTrue(math.isinf(math.copysign(INF, NAN)))
# similarly, copysign(2., NAN) could be 2. or -2.
self.assertEqual(abs(math.copysign(2., NAN)), 2.)
def __init__(self, numer: int, denom: int) -> None:
gcd = math.gcd(numer, denom)
self.numer: int = int(math.copysign(numer, numer * denom)) // gcd
self.denom: int = abs(denom) // gcd
def calc_trade_pnl(
open_qtys: np.ndarray, open_prices: np.ndarray, new_qtys: np.ndarray,
new_prices: np.ndarray, multiplier: float
) -> Tuple[np.ndarray, np.ndarray, float, float, float]:
'''
>>> print(calc_trade_pnl(
... open_qtys = np.array([], dtype = float), open_prices = np.array([], dtype = float),
... new_qtys = np.array([-8, 9, -4]), new_prices = np.array([10, 11, 6]), multiplier = 100))
(array([-3.]), array([6.]), -3.0, 6.0, -1300.0)
>>> print(calc_trade_pnl(open_qtys = np.array([], dtype = float), open_prices = np.array([], dtype = float), new_qtys = np.array([3, 10, -5]),
... new_prices = np.array([51, 50, 45]), multiplier = 100))
(array([8.]), array([50.]), 8.0, 50.0, -2800.0)
>>> print(calc_trade_pnl(open_qtys = np.array([]), open_prices = np.array([]),
... new_qtys = np.array([-58, -5, -5, 6, -8, 5, 5, -5, 19, 7, 5, -5, 39]),
... new_prices = np.array([2080, 2075.25, 2070.75, 2076, 2066.75, 2069.25, 2074.75, 2069.75, 2087.25, 2097.25, 2106, 2088.25, 2085.25]),
... multiplier = 50))
(array([], dtype=float64), array([], dtype=float64), 0.0, 0, -33762.5) '''
# TODO: Cythonize this
realized = 0.
new_qtys = new_qtys.copy()
new_prices = new_prices.copy()
_open_prices = np.zeros(len(open_prices) + len(new_prices), dtype=float)
_open_prices[:len(open_prices)] = open_prices
_open_qtys = np.zeros(len(open_qtys) + len(new_qtys), dtype=float)
_open_qtys[:len(open_qtys)] = open_qtys
new_qty_indices = np.nonzero(new_qtys)[0]
open_qty_indices = np.zeros(len(_open_qtys), dtype=int)
nonzero_indices = np.nonzero(_open_qtys)[0]
open_qty_indices[:len(nonzero_indices)] = nonzero_indices
i = 0 # index into new_qty_indices to get idx of the new qty we are currently netting
o = len(nonzero_indices) # virtual length of open_qty_indices
j = 0 # index into open_qty_indices to get idx of the open qty we are currently netting
k = len(open_qtys) # virtual length of _open_qtys
# Try to net all new trades against existing non-netted trades.
# Append any remaining non-netted new trades to end of existing trades
while i < len(new_qty_indices):
# Always try to net first non-zero new trade against first non-zero existing trade
# FIFO acccounting
new_idx = new_qty_indices[i]
new_qty, new_price = new_qtys[new_idx], new_prices[new_idx]
# print(f'i: {i} j: {j} k: {k} o: {o} oq: {_open_qtys} oqi: {open_qty_indices} op: {_open_prices} nq: {new_qtys} np: {new_prices}')
if j < o: # while we still have open positions to net against
open_idx = open_qty_indices[j]
open_qty, open_price = _open_qtys[open_idx], _open_prices[open_idx]
if math.copysign(1, open_qty) == math.copysign(1, new_qty):
# Nothing to net against so add this trade to the array and wait for the next offsetting trade
_open_qtys[k] = new_qty
_open_prices[k] = new_price
open_qty_indices[o] = k
k += 1
o += 1
new_qtys[new_idx] = 0
i += 1
elif abs(new_qty) > abs(open_qty):
# New trade has more qty than offsetting trade so:
# a. net against offsetting trade
# b. remove the offsetting trade
# c. reduce qty of new trade
open_qty, open_price = _open_qtys[open_idx], _open_prices[
open_idx]
realized += open_qty * (new_price - open_price)
# print(f'open_qty: {open_qty} open_price: {open_price} open_idx: {open_idx} i: {i}
# j: {j} k: {k} l: {l} oq: {_open_qtys} oqi: {open_qty_indices} op: {_open_prices} nq: {new_qtys} np: {new_prices}')
_open_qtys[open_idx] = 0
j += 1
new_qtys[new_idx] += open_qty
else:
# New trade has less qty than offsetting trade so:
# a. net against offsetting trade
# b. remove new trade
# c. reduce qty of offsetting trade
realized += new_qty * (open_price - new_price)
new_qtys[new_idx] = 0
i += 1
_open_qtys[open_idx] += new_qty
else:
# Nothing to net against so add this trade to the open trades array and wait for the next offsetting trade
_open_qtys[k] = new_qty
_open_prices[k] = new_price
open_qty_indices[o] = k
k += 1
o += 1
new_qtys[new_idx] = 0
i += 1
mask = _open_qtys != 0
_open_qtys = _open_qtys[mask]
_open_prices = _open_prices[mask]
open_qty = np.sum(_open_qtys)
if math.isclose(open_qty, 0):
weighted_avg_price = 0
else:
weighted_avg_price = np.sum(_open_qtys * _open_prices) / open_qty
return _open_qtys, _open_prices, open_qty, weighted_avg_price, realized * multiplier
def testTanhSign(self):
# check that tanh(-0.) == -0. on IEEE 754 systems
self.assertEqual(math.tanh(-0.), -0.)
self.assertEqual(math.copysign(1., math.tanh(-0.)),
math.copysign(1., -0.))
#!/bin/python3
import math
import random
sign = lambda x: math.copysign(1, x)
# I searched for an algorithm to get that bounding interval
# without making random choice and enourmous array but I couldn't fund any
# like I can't get results for any num over 1000 because of the enourmous
# array and random choice, let's see how c++ would be different
def bisection_root(c, error=0.1):
function = lambda x: x**2 - c
interval = [
i for i in range(-1 * c * 100, c * 100)
] # this is arbitrary interval from which we would choose a and b
a = b = 0 # and I have the feeling that It won't work for some functions
while True: # but It I guess it would work for finding roots and stuff
# getting the interval
while True:
if sign(function(a)) != sign(function(b)):
break
a = random.choice(interval)
b = random.choice(interval)
m = (a + b) / 2
if sign(function(m)) == 1.0: # that means it is positive
if function(
m
) == 0: # that could happen if we got very very luck ... the algorithm gets it more than you think
def signed_sqare(x):
# converts correlation into R-sqared, but of the same sign
return copysign(x**2, x)
def test_can_generate_both_zeros_when_in_interval(l, r, sign):
assert minimal(st.floats(l, r),
lambda x: math.copysign(1, x) == sign) == sign * 0.0
def draw(self, ani_state):
geometry = self.geometry # little shortcut
fground = self.fground
beatf = ani_state.state['beatf']
light_level = ani_state.state['light']
if fground:
state_part = 'f_'
else:
state_part = 'b_'
sp = ((ani_state.state[state_part + 'speed'] % 20) / 5.0) - 2.0
speedMillisDivider = math.copysign(10**(2.0 - abs(sp)), sp)
animationSpeed = ani_state.millisDelta / speedMillisDivider
if not fground:
# the background should move slower to give a parallax effect
animationSpeed /= 5.0
animationType = (int(
ani_state.state[state_part + 'spin']
)) % 6 # spinZ, spinX, spinY, spinZSpinX, spinXSpinYSpinZ, noise
if animationType == 0:
geometry.rotateIncZ(animationSpeed)
elif animationType == 1:
geometry.rotateIncX(animationSpeed)
elif animationType == 2:
geometry.rotateIncY(animationSpeed)
elif animationType == 3:
geometry.rotateIncZ(animationSpeed)
#if fground:
geometry.rotateIncX(animationSpeed)
elif animationType == 4:
#if fground:
geometry.rotateIncX(animationSpeed)
geometry.rotateIncY(animationSpeed)
geometry.rotateIncZ(animationSpeed)
elif animationType == 5:
#if fground:
geometry.rotateIncX(animationSpeed * uniform(-1, 1))
geometry.rotateIncY(animationSpeed * uniform(-1, 1))
geometry.rotateIncZ(animationSpeed * uniform(-1, 1))
scale = ani_state.state[state_part + 'scale']
if fground:
scale = 1.0 + (scale % 20) / 4.0 # from 0,10 to 1,5
else:
scale = 15.0 + (scale % 20) / 4.0
geometry.scale(scale, scale, scale)
shaderType = (int(ani_state.state[state_part + 'shader'])) % len(
ShaderTypes.shadersTable)
shader = ShaderTypes.shadersTable[shaderType]
geometry.set_shader(shader)
# use the palette scale to invert the colors
paletteInvert = (int(ani_state.state[state_part + 'inv'])) % 2
if ani_state.state['f_paltt'] == 0:
col1 = [i for i in ani_state.state['user1']]
col2 = [i for i in ani_state.state['user2']]
else:
paletteEntry = PaletteTypes.paletteTable[(int(
ani_state.state['f_paltt'])) % len(PaletteTypes.paletteTable)]
col1 = [i for i in paletteEntry[0]]
col2 = [i for i in paletteEntry[1]]
######## light levels ###############
col1 = [i * light_level for i in col1]
col2 = [i * light_level for i in col2]
if paletteInvert:
col1, col2 = col2, col1
# goes from 0 to 5, only the first four do something
# swap, shades, random, flash
# TODO music related function rather than frameCount % 8
swap = ani_state.state[state_part + 'fx1'] % 2
shde = ani_state.state[state_part + 'fx2'] % 2
rndm = ani_state.state[state_part + 'fx3'] % 2
flsh = ani_state.state[state_part + 'fx4'] % 2
fc = ani_state.frameCount % beatf
if swap and fc == 0:
col1, col2 = col2, col1
if shde and fc == 2:
if uniform(0, 1) > 0.5:
col1 = [0.5 + 0.5 * i for i in col1]
col2 = [light_level - i for i in col2]
else:
col1 = [light_level - i for i in col1]
col2 = [light_level - i for i in col2]
if rndm and fc == 4:
col1 = [uniform(0, light_level) for i in col1]
col2 = [uniform(0, light_level) for i in col2]
if flsh and fc == 6:
col1 = [0.8 * light_level + 0.2 * i for i in col1]
col2 = [0.8 * light_level + 0.2 * i for i in col2]
geometry.set_custom_data(48, col1)
geometry.set_custom_data(51, col2)
shaderScale = 1.0 + int(ani_state.state[state_part + 'mult']) % 20.0
# with the dots shader, too few dots don't look super-cool, so adjust
if shaderType == ShaderTypes.dots:
shaderScale = 5.0 + shaderScale
i = int(ani_state.state[state_part + 'param1'])
param1 = ShaderTypes.petalTable[i % len(ShaderTypes.petalTable)]
i = int(ani_state.state[state_part + 'param2'])
param2 = ShaderTypes.powerTable[i % len(ShaderTypes.powerTable)] + (
ani_state.frameCount % 1000) / 250.0 - 2.0
geometry.set_custom_data(
54, [shaderScale, param1, param2]) # number of stripes etc
geometry.draw(camera=self.cameraToUse)
def test_half_bounded_respects_sign_of_lower_bound(x):
assert math.copysign(1, x) == 1
def test_does_not_generate_positive_if_right_boundary_is_negative(x):
assert math.copysign(1, x) == -1
def method_infinity(self, space):
if math.isinf(self.floatvalue):
return space.newint(int(math.copysign(1, self.floatvalue)))
return space.w_nil
def test_can_generate_both_zeros(sign):
assert minimal(
st.floats(),
lambda x: math.copysign(1, x) == sign,
) == sign * 0.0
def Plot3DHits(self, track, color=1, style=0):
'''
Plots the 3D hits from a track.
'''
pix_coords = []
for hit in track.pixelHits():
if hit.isValid():
pix_coords.append(hit.x())
pix_coords.append(hit.y())
pix_coords.append(hit.z())
if pix_coords:
pix_plot = ROOT.TPolyMarker3D(
len(pix_coords) / 3, array('f', pix_coords), 2)
pix_plot.SetMarkerColor(color)
if style == 1: pix_plot.SetMarkerStyle(5)
if style == 2: pix_plot.SetMarkerStyle(4)
self.plots_3D.append(pix_plot)
for hit in track.gluedHits():
if hit.isValid():
x = hit.x()
y = hit.y()
z = hit.z()
if hit.isBarrel():
X = [x, x]
Y = [y, y]
Z = [z - sqrt(hit.zz()), z + sqrt(hit.zz())]
else:
X = [
x - copysign(sqrt(hit.xx()), x),
x + copysign(sqrt(hit.xx()), x)
]
Y = [
y - copysign(sqrt(hit.yy()), y),
y + copysign(sqrt(hit.yy()), y)
]
Z = [hit.z(), hit.z()]
glu_plot = ROOT.TPolyLine3D(len(X), array("f", X),
array("f", Y), array("f", Z))
#glu_plot.SetLineStyle(2)
if style == 1: glu_plot.SetLineStyle(2)
if style == 2: glu_plot.SetLineStyle(3)
glu_plot.SetLineColor(color)
self.plots_3D.append(glu_plot)
for hit in track.stripHits():
if hit.isValid():
x = hit.x()
y = hit.y()
z = hit.z()
if hit.isBarrel():
X = [x, x]
Y = [y, y]
Z = [z - 1.5 * sqrt(hit.zz()), z + 1.5 * sqrt(hit.zz())]
else:
X = [
x - 1.5 * copysign(sqrt(hit.xx()), x),
x + 1.5 * copysign(sqrt(hit.xx()), x)
]
Y = [
y - 1.5 * copysign(sqrt(hit.yy()), y),
y + 1.5 * copysign(sqrt(hit.yy()), y)
]
Z = [hit.z(), hit.z()]
str_plot = ROOT.TPolyLine3D(len(X), array("f", X),
array("f", Y), array("f", Z))
if style == 1: str_plot.SetLineStyle(2)
if style == 2: str_plot.SetLineStyle(3)
str_plot.SetLineColor(color)
self.plots_3D.append(str_plot)
def sign(x):
try:
return math.copysign(1.0, x)
except TypeError:
raise TypeError('Expected float but got %r of type %s' %
(x, type(x).__name__))
def float_round(value, precision_digits=None, precision_rounding=None, rounding_method='HALF-UP'):
"""Return ``value`` rounded to ``precision_digits`` decimal digits,
minimizing IEEE-754 floating point representation errors, and applying
the tie-breaking rule selected with ``rounding_method``, by default
HALF-UP (away from zero).
Precision must be given by ``precision_digits`` or ``precision_rounding``,
not both!
:param float value: the value to round
:param int precision_digits: number of fractional digits to round to.
:param float precision_rounding: decimal number representing the minimum
non-zero value at the desired precision (for example, 0.01 for a
2-digit precision).
:param rounding_method: the rounding method used: 'HALF-UP', 'UP' or 'DOWN',
the first one rounding up to the closest number with the rule that
number>=0.5 is rounded up to 1, the second always rounding up and the
latest one always rounding down.
:return: rounded float
"""
rounding_factor = _float_check_precision(precision_digits=precision_digits,
precision_rounding=precision_rounding)
if rounding_factor == 0 or value == 0:
return 0.0
# NORMALIZE - ROUND - DENORMALIZE
# In order to easily support rounding to arbitrary 'steps' (e.g. coin values),
# we normalize the value before rounding it as an integer, and de-normalize
# after rounding: e.g. float_round(1.3, precision_rounding=.5) == 1.5
# Due to IEE754 float/double representation limits, the approximation of the
# real value may be slightly below the tie limit, resulting in an error of
# 1 unit in the last place (ulp) after rounding.
# For example 2.675 == 2.6749999999999998.
# To correct this, we add a very small epsilon value, scaled to the
# the order of magnitude of the value, to tip the tie-break in the right
# direction.
# Credit: discussion with OpenERP community members on bug 882036
normalized_value = value / rounding_factor # normalize
sign = math.copysign(1.0, normalized_value)
epsilon_magnitude = math.log(abs(normalized_value), 2)
epsilon = 2**(epsilon_magnitude-52)
# TIE-BREAKING: UP/DOWN (for ceiling[resp. flooring] operations)
# When rounding the value up[resp. down], we instead subtract[resp. add] the epsilon value
# as the the approximation of the real value may be slightly *above* the
# tie limit, this would result in incorrectly rounding up[resp. down] to the next number
# The math.ceil[resp. math.floor] operation is applied on the absolute value in order to
# round "away from zero" and not "towards infinity", then the sign is
# restored.
if rounding_method == 'UP':
normalized_value -= sign*epsilon
rounded_value = math.ceil(abs(normalized_value)) * sign
elif rounding_method == 'DOWN':
normalized_value += sign*epsilon
rounded_value = math.floor(abs(normalized_value)) * sign
# TIE-BREAKING: HALF-UP (for normal rounding)
# We want to apply HALF-UP tie-breaking rules, i.e. 0.5 rounds away from 0.
else:
normalized_value += math.copysign(epsilon, normalized_value)
rounded_value = round(normalized_value) # round to integer
result = rounded_value * rounding_factor # de-normalize
return result
def border_point(self, t, s):
s = math.copysign(1.0, s)
Px, Py, Pz = self.progress_frame(t)
w = self.a_width * (1 - t) + self.b_width * t
return Px.deviate(Pz, w * s)
def reverse(self, xyz, y=None, z=None, M=False):
'''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}.
@param xyz: Either an L{Ecef9Tuple}, an C{(x, y, z)} 3-tuple or C{scalar}
ECEF C{x} coordinate in C{meter}.
@keyword y: ECEF C{y} coordinate in C{meter} for C{scalar} B{C{xyz}}
and B{C{z}}.
@keyword z: ECEF C{z} coordinate in C{meter} for C{scalar} B{C{xyz}}
and B{C{y}}.
@keyword M: Optionally, return the rotation L{EcefMatrix} (C{bool}).
@return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
with geodetic coordinates C{(lat, lon, height)} for the given
geocentric ones C{(x, y, z)}, case C{C}, optional L{EcefMatrix}
C{M} and C{datum} if available.
@raise EcefError: If B{C{xyz}} not L{Ecef9Tuple} or C{scalar} C{x}
or B{C{y}} and/or B{C{z}} not C{scalar} for C{scalar}
B{C{xyz}}.
@note: In general, there are multiple solutions and the result
which minimizes C{height} is returned, i.e., C{(lat, lon)}
corresponds to the closest point on the ellipsoid. If
there are still multiple solutions with different latitudes
(applies only if C{z} = 0), then the solution with C{lat} > 0
is returned. If there are still multiple solutions with
different longitudes (applies only if C{x} = C{y} = 0) then
C{lon} = 0 is returned. The returned C{height} value is not
below M{−E.a * (1 − E.e2) / sqrt(1 − E.e2 * sin(lat)**2)}.
The returned C{lon} is in the range [−180°, 180°]. Like
C{forward} above, M{v1 = Transpose(M) ⋅ v0}.
'''
x, y, z, name = _xyzn4(xyz, y, z, Error=EcefError)
sb, cb, d = _sch3(y, x)
h = hypot(d, z) # distance to earth center
if h > self._hmax:
# We really far away (> 12 million light years). Treat the earth
# as a point and h, above, is an acceptable approximation to the
# height. This avoids overflow, e.g., in the computation of d
# below. It's possible that h has overflowed to INF, that's OK.
# Treat finite x, y, but r overflows to +INF by scaling by 2.
sb, cb, r = _sch3(y / 2, x / 2)
sa, ca, _ = _sch3(z / 2, r)
C = 1
elif self.e4a:
# Treat prolate spheroids by swapping R and Z here and by switching
# the arguments to phi = atan2(...) at the end.
p = (d / self.a)**2
q = self.e2m * (z / self.a)**2
if self.f < 0:
p, q = q, p
r = p + q - self.e4a
e = self.e4a * q
if e or r > 0:
# Avoid possible division by zero when r = 0 by multiplying
# equations for s and t by r^3 and r, resp.
s = e * p / 4 # s = r^3 * s
u = r = r / 6
r2 = r**2
r3 = r * r2
t3 = s + r3
disc = s * (r3 + t3)
if disc < 0:
# t is complex, but the way u is defined the result is real.
# There are three possible cube roots. We choose the root
# which avoids cancellation. Note, disc < 0 implies r < 0.
u += 2 * r * cos(atan2(sqrt(-disc), -t3) / 3)
else:
# Pick the sign on the sqrt to maximize abs(T3). This
# minimizes loss of precision due to cancellation. The
# result is unchanged because of the way the T is used
# in definition of u.
if disc > 0:
t3 += copysign(sqrt(disc), t3) # t3 = (r * t)^3
# N.B. cbrt always returns the real root, cbrt(-8) = -2.
t = cbrt(t3) # t = r * t
# t can be zero; but then r2 / t -> 0.
if t:
u += t + r2 / t
v = sqrt(u**2 + e) # guaranteed positive
# Avoid loss of accuracy when u < 0. Underflow doesn't occur in
# E.e4 * q / (v - u) because u ~ e^4 when q is small and u < 0.
uv = (e / (v - u)) if u < 0 else (u + v) # u+v, guaranteed positive
# Need to guard against w going negative due to roundoff in uv - q.
w = max(0.0, self.e2a * (uv - q) / (2 * v))
# Rearrange expression for k to avoid loss of accuracy due to
# subtraction. Division by 0 not possible because uv > 0, w >= 0.
k1 = k2 = uv / (sqrt(uv + w**2) + w)
if self.f < 0:
k1 -= self.e2
else:
k2 += self.e2
sa, ca, h = _sch3(z / k1, d / k2)
h *= k1 - self.e2m
C = 2
else: # e = self.e4a * q == 0 and r <= 0
# This leads to k = 0 (oblate, equatorial plane) and k + E.e^2 = 0
# (prolate, rotation axis) and the generation of 0/0 in the general
# formulas for phi and h, using the general formula and division
# by 0 in formula for h. Handle this case by taking the limits:
# f > 0: z -> 0, k -> E.e2 * sqrt(q) / sqrt(E.e4 - p)
# f < 0: r -> 0, k + E.e2 -> -E.e2 * sqrt(q) / sqrt(E.e4 - p)
q = self.e4a - p
if self.f < 0:
p, q, e = q, p, -1
else:
e = -self.e2m
sa, ca, h = _sch3(sqrt(q / self.e2m), sqrt(p))
h *= self.a * e / self.e2a
if z < 0:
sa = -sa # for tiny negative z, not for prolate
C = 3
else: # self.e4a == 0
# Treat the spherical case. Dealing with underflow in the general
# case with E.e2 = 0 is difficult. Origin maps to North pole, same
# as with ellipsoid.
sa, ca, _ = _sch3(z if h else 1, d)
h -= self.a
C = 4
r = Ecef9Tuple(x, y, z, degrees(atan2(sa, ca)),
degrees(atan2(sb, cb)), h, C,
self._Matrix(sa, ca, sb, cb) if M else None,
self.datum)
return self._xnamed(r, name)
def _addrow(self):
"""
Return cashflow table with one more line or raise an exception if there is no more line to add
The same logic also applies to rem table
关于对于一个基金多个操作存在于同一交易日的说明：无法处理历史买入第一笔同时是分红日的情形, 事实上也不存在这种情形。无法处理一日多笔买卖的情形。
同一日既有卖也有买不现实，多笔买入只能在 csv 上合并记录，由此可能引起份额计算 0.01 的误差。可以处理分红日买入卖出的情形。
分级份额折算日封闭无法买入，所以程序直接忽略当天的买卖。因此不会出现多个操作共存的情形。
"""
# the design on data remtable is disaster, it is very dangerous though works now
# possibly failing cases include:
# 买卖日记录是节假日，而顺延的日期恰好是折算日（理论上无法申赎）或分红日（可能由于 date 和 rdate 的错位而没有考虑到），
# 又比如周日申购记录，周一申购记录，那么周日记录会现金流记在周一，继续现金流标更新将从周二开始，周一数据被丢弃
code = self.aim.code
if len(self.cftable) == 0:
if len(self.status[self.status[code] != 0]) == 0:
raise Exception("no other info to be add into cashflow table")
i = 0
while self.status.iloc[i].loc[code] == 0:
i += 1
value = self.status.iloc[i].loc[code]
date = self.status.iloc[i].date
self.lastdate = date
if len(self.price[self.price["date"] >= date]) > 0:
date = self.price[self.price["date"] >= date].iloc[0]["date"]
else:
date = self.price[self.price["date"] <= date].iloc[-1]["date"]
# 这里没有像下边部分一样仔细处理单独的 lastdate，hopefully 不会出现其他奇怪的问题，有 case 再说
# https://github.com/refraction-ray/xalpha/issues/47
# 凭直觉这个地方的处理很可能还有其他 issue
if value > 0:
feelabel = 100 * value - int(100 * value)
if round(feelabel, 1) == 0.5:
# binary encoding, 10000.005 is actually 10000.0050...1, see issue #59
feelabel = feelabel - 0.5
if abs(feelabel) < 1e-4:
feelabel = 0
else:
feelabel *= 100
else:
feelabel = None
value = int(value * 100) / 100
assert feelabel is None or feelabel >= 0.0, "自定义申购费必须为正值"
rdate, cash, share = self.aim.shengou(value,
date,
fee=feelabel)
rem = rm.buy([], share, rdate)
else:
raise TradeBehaviorError(
"You cannot sell first when you never buy")
elif len(self.cftable) > 0:
# recorddate = list(self.status.date)
if not getattr(self, "lastdate", None):
lastdate = self.cftable.iloc[-1].date + pd.Timedelta(1,
unit="d")
else:
lastdate = self.lastdate + pd.Timedelta(1, unit="d")
while (lastdate not in self.aim.specialdate) and (
(lastdate not in self.recorddate_set) or
((lastdate in self.recorddate_set) and
(self.status[self.status["date"] ==
lastdate].loc[:, code].any() == 0))):
lastdate += pd.Timedelta(1, unit="d")
if (lastdate - yesterdayobj()).days >= 1:
raise Exception(
"no other info to be add into cashflow table")
if (lastdate - yesterdayobj()).days >= 1:
raise Exception("no other info to be add into cashflow table")
date = lastdate
# 无净值日优先后移，无法后移则前移
# 还是建议日期记录准确，不然可能有无法完美兼容的错误出现
if len(self.price[self.price["date"] >= date]) > 0:
date = self.price[self.price["date"] >= date].iloc[0]["date"]
else:
date = self.price[self.price["date"] <= date].iloc[-1]["date"]
if date != lastdate and date in list(self.status.date):
# 日期平移到了其他记录日，很可能出现问题!
logger.warning(
"账单日期 %s 非 %s 的净值记录日期，日期智能平移后 %s 与账单其他日期重合！交易处理极可能出现问题！！ "
"靠后日期的记录被覆盖" % (lastdate, self.code, date))
self.lastdate = lastdate
if date > lastdate:
self.lastdate = date
# see https://github.com/refraction-ray/xalpha/issues/27, begin new date from last one in df is not reliable
label = self.aim.dividend_label # 现金分红 0, 红利再投 1
cash = 0
share = 0
rem = self.remtable.iloc[-1].rem
rdate = date
if (lastdate
in self.recorddate_set) and (date
not in self.aim.zhesuandate):
# deal with buy and sell and label the fenhongzaitouru, namely one label a 0.05 in the original table to label fenhongzaitouru
value = self.status[
self.status["date"] <= lastdate].iloc[-1].loc[code]
if date in self.aim.fenhongdate: # 0.05 的分红行为标记，只有分红日才有效
fenhongmark = round(10 * value - int(10 * value), 1)
if fenhongmark == 0.5 and label == 0:
label = 1 # fenhong reinvest
value = value - math.copysign(0.05, value)
elif fenhongmark == 0.5 and label == 1:
label = 0
value = value - math.copysign(0.05, value)
if value > 0: # value stands for purchase money
feelabel = 100 * value - int(100 * value)
if int(10 * feelabel) == 5:
feelabel = (feelabel - 0.5) * 100
else:
feelabel = None
value = int(value * 100) / 100
rdate, dcash, dshare = self.aim.shengou(
value, date, fee=feelabel
) # shengou fee is in the unit of percent, different than shuhui case
rem = rm.buy(rem, dshare, rdate)
elif value < -0.005: # value stands for redemp share
feelabel = int(100 * value) - 100 * value
if int(10 * feelabel) == 5:
feelabel = feelabel - 0.5
else:
feelabel = None
value = int(value * 100) / 100
rdate, dcash, dshare = self.aim.shuhui(
-value, date, self.remtable.iloc[-1].rem, fee=feelabel)
_, rem = rm.sell(rem, -dshare, rdate)
elif value >= -0.005 and value < 0:
# value now stands for the ratio to be sold in terms of remain positions, -0.005 stand for sell 100%
remainshare = sum(self.cftable[
self.cftable["date"] <= date].loc[:, "share"])
ratio = -value / 0.005
rdate, dcash, dshare = self.aim.shuhui(
remainshare * ratio, date, self.remtable.iloc[-1].rem,
0)
_, rem = rm.sell(rem, -dshare, rdate)
else: # in case value=0, when specialday is in record day
rdate, dcash, dshare = date, 0, 0
cash += dcash
share += dshare
if date in self.aim.specialdate: # deal with fenhong and xiazhe
comment = self.price[self.price["date"] ==
date].iloc[0].loc["comment"]
if isinstance(comment, float):
if comment < 0:
dcash2, dshare2 = (
0,
sum([
myround(sh * (-comment - 1)) for _, sh in rem
]),
) # xiazhe are seperately carried out based on different purchase date
rem = rm.trans(rem, -comment, date)
# myround(sum(cftable.loc[:,'share'])*(-comment-1))
elif comment > 0 and label == 0:
dcash2, dshare2 = (
myround(
sum(self.cftable.loc[:, "share"]) * comment),
0,
)
rem = rm.copy(rem)
elif comment > 0 and label == 1:
dcash2, dshare2 = (
0,
myround(
sum(self.cftable.loc[:, "share"]) *
(comment / self.price[self.price["date"] ==
date].iloc[0].netvalue)),
)
rem = rm.buy(rem, dshare2, date)
cash += dcash2
share += dshare2
else:
raise ParserFailure("comments not recognized")
self.cftable = self.cftable.append(
pd.DataFrame([[rdate, cash, share]],
columns=["date", "cash", "share"]),
ignore_index=True,
)
self.remtable = self.remtable.append(pd.DataFrame(
[[rdate, rem]], columns=["date", "rem"]),
ignore_index=True)
def main():
# create GraphWin
win = GraphWin('Linear Regression', 600, 600)
# Set window coordinates for text entry
win.setCoords(0, 0, 10, 10)
# introduce program
msg = Text(Point(5, 7),
'After user creates points, a linear regression is drawn.')
msg.draw(win)
win.getMouse()
msg.undraw()
# Set window coordinates for graphing (-11, -11, 11, 12)
win.setCoords(-11, -11, 11, 12)
# call drawAxes() to draw axes
drawAxes(win, -10, -10, 10, 10, "Linear Regression")
# draw Done box in lower left corner
buttonLL = Point(-10.5, -10.5)
buttonUR = Point(-8.5, -9.5)
button = Rectangle(buttonLL, buttonUR)
button.draw(win)
buttonText = Text(Point(-9.5, -10), 'Done')
buttonText.draw(win)
# display instructions
msg = Text(
Point(5, 7),
"Create points by clicking on the graph.\nClick 'Done' when finished.\n\nClick anywhere to start."
)
msg.draw(win)
win.getMouse()
msg.undraw()
# initialize Regression object
bestFit = Regresion()
# while True
while True:
# get mouse click
graphPt = win.getMouse()
# if Done, exit loop
# Done is true when mouse click is within borders of Done rectangle (button)
graphPtX = graphPt.getX()
graphPtY = graphPt.getY()
if graphPtX >= buttonLL.getX() and graphPtX <= buttonUR.getX() and \
graphPtY >= buttonLL.getY() and graphPtY <= buttonUR.getY():
break
# otherwise, draw point and add point to bestFit
bestFit.addPoint(graphPt)
Point(graphPtX, graphPtY).draw(win)
# calculate y coordinates for min and max x coordinates (y = meanY + slope(x - meanX))
y1 = bestFit.predict(-10)
y2 = bestFit.predict(10)
# draw line between those two coordinate pairs
Line(Point(-10, y1), Point(10, y2)).draw(win)
# calculate y-intercept
yInt = bestFit.predict(0)
# display equation of line in y = mx + b format
Text(Point(5, copysign(min(abs(y2), 10), y2)),
'y = {:.2f}x + {:.2f}'.format(bestFit.slope(), yInt)).draw(win)
# wait for mouse click
win.getMouse()
def reverse(self, xyz, y=None, z=None, **no_M): # PYCHOK unused M
'''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}
transcribed from I{Chris Veness}' U{JavaScript
<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
Uses B. R. Bowring’s formulation for μm precision in concise
form: U{'The accuracy of geodetic latitude and height equations'
<https://www.ResearchGate.net/publication/
233668213_The_Accuracy_of_Geodetic_Latitude_and_Height_Equations>},
Survey Review, Vol 28, 218, Oct 1985.
@param xyz: Either an L{Ecef9Tuple}, an C{(x, y, z)} 3-tuple or C{scalar}
ECEF C{x} coordinate in C{meter}.
@keyword y: ECEF C{y} coordinate in C{meter} for C{scalar} B{C{xyz}}
and B{C{z}}.
@keyword z: ECEF C{z} coordinate in C{meter} for C{scalar} B{C{xyz}}
and B{C{y}}.
@keyword no_M: Rotation matrix C{M} not available.
@return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
with geodetic coordinates C{(lat, lon, height)} for the given
geocentric ones C{(x, y, z)}, case C{C}, L{EcefMatrix} C{M}
always C{None} and C{datum} if available.
@raise EcefError: If B{C{xyz}} not L{Ecef9Tuple} or C{scalar} C{x}
or B{C{y}} and/or B{C{z}} not C{scalar} for C{scalar}
B{C{xyz}}.
@see: Ralph M. Toms U{'An Efficient Algorithm for Geocentric to Geodetic
Coordinate Conversion'<https://www.OSTI.gov/scitech/biblio/110235>},
Sept 1995 and U{'An Improved Algorithm for Geocentric to Geodetic
Coordinate Conversion'<https://www.OSTI.gov/scitech/servlets/purl/231228>},
Apr 1996, both from Lawrence Livermore National Laboratory (LLNL).
'''
x, y, z, name = _xyzn4(xyz, y, z, Error=EcefError)
E = self.ellipsoid
p = hypot(x, y) # distance from minor axis
r = hypot(p, z) # polar radius
if min(p, r) > EPS:
# parametric latitude (Bowring eqn 17, replaced)
t = (E.b * z) / (E.a * p) * (1 + E.e22 * E.b / r)
c = 1 / hypot1(t)
s = t * c
# geodetic latitude (Bowring eqn 18)
a = atan2(z + E.e22 * E.b * s**3,
p - E.e2 * E.a * c**3)
b = atan2(y, x) # ... and longitude
# height above ellipsoid (Bowring eqn 7)
sa, ca = sincos2(a)
# r = E.a / E.e2s(sa) # length of normal terminated by minor axis
# h = p * ca + z * sa - (E.a * E.a / r)
h = fsum_(p * ca, z * sa, -E.a * E.e2s(sa))
C, lat, lon = 1, degrees90(a), degrees180(b)
# see <https://GIS.StackExchange.com/questions/28446>
elif p > EPS: # lat arbitrarily zero
C, lat, lon, h = 2, 0.0, degrees180(atan2(y, x)), p - E.a
else: # polar lat, lon arbitrarily zero
C, lat, lon, h = 3, copysign(90.0, z), 0.0, abs(z) - E.b
r = Ecef9Tuple(x, y, z, lat, lon, h, C, None, self.datum)
return self._xnamed(r, name)
def legacy_round(number, points=0):
p = 10**points
return float(math.floor((number * p) + math.copysign(0.5, number))) / p
# return log_1arg_der(*args) # Argument number check
#except TypeError:
# return 1/args[0]/math.log(args[1]) # 2-argument form
fixed_derivatives = {
# In alphabetical order, here:
'acos': [lambda x: -1/math.sqrt(1-x**2)],
'acosh': [lambda x: 1/math.sqrt(x**2-1)],
'asin': [lambda x: 1/math.sqrt(1-x**2)],
'asinh': [lambda x: 1/math.sqrt(1+x**2)],
'atan': [lambda x: 1/(1+x**2)],
'atan2': [lambda y, x: x/(x**2+y**2), # Correct for x == 0
lambda y, x: -y/(x**2+y**2)], # Correct for x == 0
'atanh': [lambda x: 1/(1-x**2)],
'ceil': [lambda x: 0],
'copysign': [lambda x, y: (1 if x >= 0 else -1) * math.copysign(1, y),
lambda x, y: 0],
'cos': [lambda x: -math.sin(x)],
'cosh': [math.sinh],
'degrees': [lambda x: math.degrees(1)],
'exp': [math.exp],
'fabs': [lambda x: 1 if x >= 0 else -1],
'floor': [lambda x: 0],
'hypot': [lambda x, y: x/math.hypot(x, y),
lambda x, y: y/math.hypot(x, y)],
'log': [log_der0,
lambda x, y: -math.log(x, y)/y/math.log(y)],
'log10': [lambda x: 1/x/math.log(10)],
'log1p': [lambda x: 1/(1+x)],
'pow': [lambda x, y: y*math.pow(x, y-1),
lambda x, y: math.log(x) * math.pow(x, y)],