def quadraticMinSearcherTest( repeats , f ):
eps = 0.00001
fails = 0
while repeats > 0:
print( repeats )
repeats -= 1
P = rP.getRandomPolygon( 5 )
cD = cV.getConeVol( P )
result = quadraticMinSearcher( cD , [ f , eps ] )[0]
if M.dist( cV.gamma( cD , result) , P[0]) > 0.1:
if cV.sigma( result , cD ) < eps:
print( 'not unique solution' )
print( P )
print(result)
print( cV.gamma( cD , result ) )
fails += 1
break
else:
print('quadratic searcher failed by by')
print( cV.sigma( result , cD ) )
print(P)
print(result)
print(cV.gamma(cD, result))
fails += 1
return fails
def vizLowValue( cD , n , first_bound, second_bound , third_bound):
grid = pS.getGrid(n)
x_1 = []
y_1 = []
x_2 = []
y_2 = []
x_3 = []
y_3 = []
b = 0
d = 0
for point in grid:
while (True):
try:
value = cV.phi(point, cD)
if value <= first_bound:
x_1.append(point[0])
y_1.append(point[1])
else:
if value <= second_bound:
x_2.append(point[0])
y_2.append(point[1])
else:
if value <= third_bound:
x_3.append(point[0])
y_3.append(point[1])
if point[0] > b:
b = point[0]
if point[1] > d:
d = point[1]
break
except ZeroDivisionError:
# print('zero division at',pair)
break
mp.plot(x_1 , y_1 , 'go')
mp.plot(x_2 , y_2 , 'yo')
mp.plot(x_3, y_3, 'ro')
mp.axis( [ 0, b, 0, d ] )
# print(vertices)
mp.show()
if len(x_1) > 0 :
params = [ x_1[0] , y_1[0] ]
vertex = cV.gamma(cD, params)
print( ' Point near to result , gamma params , phi-value , gradient ')
print(vertex)
print( params)
print( cV.phi( params , cD ) )
print( cV.gradPhi( params , cD) )
if len(x_1) > 1 :
lastIndex = len( x_1 ) - 1
params = [x_1[lastIndex],y_1[lastIndex]]
print(' ANOTHER one is ')
vertex = cV.gamma(cD, params)
print(vertex)
print(params)
print(cV.phi(params, cD))
print(cV.gradPhi(params, cD))
def preSolverPlot( cD , params ):
x = cV.domain( 0.22 , 0.223 , 0.0001 )
v = cV.gamma( cD , params )
for x_value in x:
stretchedParams = M.scaleVek( x_value , v )
y_value = preSolverPhi( stretchedParams , cD )
mp.plot( x_value , y_value , 'ro' )
mp.show()
def preSolverPhi( params , cD ):
v = cV.gamma( cD , params )
t = M.norm(v)
n = len( cD )
if t >= 1 :
return ( t ** ( 2 * n ) * cV.phi( params , cD ) )
else:
return cV.phi( params , cD )
def coneVolumeDescend(cD, start):
result = start
previous = [-1, -1]
n = 0
print('gehe in while schleife ')
while (cV.phi(result, cD) > eps_descend):
if M.dist(previous, result) > 0.1:
previous[0] = result[0]
previous[1] = result[1]
d = M.scaleVek(-1, cV.gradPhiApprox(result, cD, 0.0001))
# d = M.scaleVek( 1 / M.norm(d) , d )
alpha = sS.stepSize_posGrad(cD, result, d, n)
result = M.addVek(result, M.scaleVek(alpha, d))
n = n + 1
else:
print('versuche es mit BFGS und BFGSApprox, Start bei:')
print(cV.gamma(cD, result))
result_2 = coneVolumeDescendBFGS(cD, result, previous, crease_test,
efficiency_test, beta_1test,
beta_2test)
print('BFGS ist fertig mit:')
print(cV.gamma(cD, result_2))
result_1 = coneVolumeDescendBFGSApprox(cD, result, previous,
crease_test,
efficiency_test, beta_1test,
beta_2test)
print('BFGS Approx ist fertig!')
if cV.phi(result_1, cD) < cV.phi(result_2, cD):
return result_1
else:
return result_2
return result
def compareResults(P, alternativeParams):
cD = cV.getConeVol(P)
alternatePoint = cV.gamma(cD, alternativeParams)
P_alternative = polygonReconstruct(cD, alternatePoint)
cD_alternative = cV.getConeVol(P_alternative)
pT.plotPoly(P, 'b')
pT.plotPoly(P_alternative, 'r')
print(len(P_alternative))
print('difference in coneVolume matrices')
print(M.distMatrix(M.Matrix(cD), M.Matrix(cD_alternative)))
print(' sigma value of alternative params')
print(cV.sigma(alternativeParams, cD))
eps_test)
sigma_result = cV.sigma(result, cD_test)
if (sigma_result < eps_test):
noFail += 1
else:
if (sigma_result < eps_test * 100):
fail_soft += 1
else:
if (sigma_result < eps_test * 100 * 100):
fail_medium += 1
else:
fail_hard += 1
if M.dist(cV.gamma(cD_test, result), P_test[0]) > 0.01:
if sigma_result < eps_test:
print(
' not unique!!! polygon, result, gamma result , phi value, sigma value:'
)
print(P_test)
print(result)
print(cV.gamma(cD_test, result))
print(cV.phi(result, cD_test))
print(cV.sigma(result, cD_test))
else:
print(
' FAIL!! polygon, result, gamma result , phi value, sigma value:'
)
print(P_test)
def lineSolution( cD , params ):
v = cV.gamma( cD , params )
stepsize = 0.5
import coneVol2 as cV
import matrix as M
import machEps as mE
import vizualization as v
polygon_test2 = [[2.673368179682499, 3.09152986544487],
[1.2086453601351808, 4.28111986768648],
[-1.1761317014903958, -0.022433820601322707],
[-3.4952312190856785, -4.881491593765966],
[0.789349380758395, -2.4687243187640626]]
cD = cV.getConeVol(polygon_test2)
params_now = [4.7, 1.6152821997297826]
print(cV.gamma(cD, params_now))
print(cV.phi(params_now, cD))
d = [
-0.2083940408151545, -0.9780449497608644
] # should come from a BFGS algorithm to test the efficiency of BFGS directions
grad = M.scaleVek(1.0 / M.norm(cV.gradPhi(params_now, cD)),
cV.gradPhi(params_now, cD))
grad_approx = cV.gradPhiApprox(params_now, cD, 0.00001)
stepSize = 1
params_next = M.addVek(params_now, M.scaleVek(stepSize, d))
v.visiualizeLowValueOnGrid(0.001, 0.00001, cD, params_now, 0.02405, 0.024059,
0.02406)
v.vizNiveauGradOnGrid(0.001, 0.00001, cD, params_now, d, 0.000001)
v.vizNiveauGradOnGrid(0.001, 0.00001, cD, params_now, grad, 0.000001)
v.vizNiveauGradOnGrid(0.001, 0.00001, cD, params_now, grad_approx, 0.000001)
n = 0
diff = (1 * cV.phi(params_now, cD)) - (1 * cV.phi(params_next, cD))
d = [-1, 2]