def getNextPosAndResult(self, pos, e):
left = pos + e* (-self.stepSize)
right = pos + e * (self.stepSize)
left2 = pos + e* (-self.stepSize/4)
right2 = pos + e * (self.stepSize/4)
mini = goldenSectionSearch(self.variables, self.getFunctionResult, left, right, self.epsilon)
miniVal = self.getFunctionResult(dict(zip(self.variables, mini)))
return mini, miniVal
def tilt_d_s_given_center(pointset, c):
'''Tilt, foci spacing, and string length given center. '''
tlo,thi = 0,math.pi
def area(t):
d,s = d_s_given_center_tilt(pointset, c, t)
return 0.25*math.pi*s*math.sqrt(s**2-d**2)
b = tlo+resphi*(thi-tlo)
T = goldenSectionSearch(area, zip((tlo,b,thi),3*[None]), 0.05*thi)
return T, + d_s_given_center_tilt(c,T)
def tilt_d_s_given_center(pointset, c):
'''Tilt, foci spacing, and string length given center. '''
tlo, thi = 0, math.pi
def area(t):
d, s = d_s_given_center_tilt(pointset, c, t)
return 0.25 * math.pi * s * math.sqrt(s**2 - d**2)
b = tlo + resphi * (thi - tlo)
T = goldenSectionSearch(area, zip((tlo, b, thi), 3 * [None]), 0.05 * thi)
return T, +d_s_given_center_tilt(c, T)
def d_s_given_center_tilt(pointset, c, t):
'''Foci spacing and string length given center and tilt.'''
dlo,dhi = (0, 2*max([math.sqrt(np.dot(*(2*[c-p]))) for p in pointset]))
def s_given_d(d):
delta = 0.5*d*np.array([math.cos(t),math.sin(t)])
foci = [c+delta,c-delta]
return s_given_foci(pointset, foci)
def area(d):
s = s_given_d(d)
a = 0.25*math.pi*s*math.sqrt(s**2-d**2)
return a
b = dlo+resphi*(dhi-dlo)
D = goldenSectionSearch(area, zip((dlo,b,dhi),3*[None]), 0.0001*dhi)
return D , s_given_d(D)
def d_s_given_center_tilt(pointset, c, t):
'''Foci spacing and string length given center and tilt.'''
dlo, dhi = (0,
2 * max([math.sqrt(np.dot(*(2 * [c - p]))) for p in pointset]))
def s_given_d(d):
delta = 0.5 * d * np.array([math.cos(t), math.sin(t)])
foci = [c + delta, c - delta]
return s_given_foci(pointset, foci)
def area(d):
s = s_given_d(d)
a = 0.25 * math.pi * s * math.sqrt(s**2 - d**2)
return a
b = dlo + resphi * (dhi - dlo)
D = goldenSectionSearch(area, zip((dlo, b, dhi), 3 * [None]), 0.0001 * dhi)
return D, s_given_d(D)