def coneVolumeDescendArmijo(cD, start, crease, efficiency, beta_1, beta_2):
result = start
n = 0
previous = [-1, -1]
print('gehe in while schleife ')
while (cV.phi(result, cD) > eps_descend):
if M.dist(previous, result) > minimalStep_descendArmijo:
previous[0] = result[0]
previous[1] = result[1]
d = M.scaleVek(-1, cV.gradPhi(result, cD))
#d = M.scaleVek( 1 / M.norm(d) , d )
alpha = sS.stepSizeArmijo(cD, result, d, crease, efficiency,
beta_1, beta_2)
result = M.addVek(result, M.scaleVek(alpha, d))
else:
print('versuche es mit BFGS und BFGSApprox')
result_1 = coneVolumeDescendBFGSApprox(cD, result, previous,
crease, efficiency, beta_1,
beta_2)
result_2 = coneVolumeDescendBFGS(cD, result, previous, crease,
efficiency, beta_1, beta_2)
if cV.phi(result_1, cD) < cV.phi(result_2, cD):
return result_1
else:
return result_2
n = n + 1
return result
def powellFunction_1(cD, params, d, step):
dividend = cV.phi(M.addScaleVek(params, step, d), cD) - cV.phi(params, cD)
divisor = step * M.scal(cV.gradPhi(params, cD), d)
if (step <= eps):
return 1
return dividend / divisor
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 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 vizNiveauGradOnGrid( size , stepSize , cD , param , grad , eps):
grid = []
value_param = cV.phi( param , cD )
n = math.floor(size * 1.0/stepSize)
for i in range(n):
for j in range(n):
grid.append( [ i * stepSize - size / 2.0 + param[0], j *stepSize - size / 2.0 + param[1]])
print('grid ist fertig')
x_1 = []
y_1 = []
for point in grid:
while(True):
try:
value= cV.phi(point , cD )
if math.fabs(value - value_param) < eps:
x_1.append(point[0])
y_1.append([point[1]])
break
except ZeroDivisionError:
break
d= M.scaleVek( 1.0 / M.norm(grad) , grad )
x_d = []
y_d = []
stepBound = 0.71 * size
step = - stepBound
while( step <= stepBound ):
point = M.addVek( param , M.scaleVek( step , d ) )
x_d.append( point[0] )
y_d.append( point[1] )
step = step + stepSize
a_x = param[0] - size / 2.0
b_x = param[0] + size / 2.0 + 5
a_y = param[1] - size / 2.0
b_y = param[1] + size / 2.0 + 5
mp.plot( x_1 , y_1 , 'go')
mp.plot( x_d , y_d , 'yo')
mp.plot([param[0]], [param[1]], 'wo')
mp.axes( [a_x , b_x , a_y , b_y])
#print('here comes minimal point, gamma , value, gradient:')
#print( point_min )
#print( cV.gamma( cD , point_min ))
#print( cV.phi( point_min , cD ))
#print( cV.gradPhi( point_min , cD))
mp.show()
def stepSize_posGrad(cD, point, d, n):
alpha = 0.5
nextPoint = M.addVek(point, M.scaleVek(alpha, d))
while (cV.phi(point, cD) + eps < cV.phi(
nextPoint, cD)): #or pS.scalGrad( cD , nextPoint ) < 0 ):
alpha = alpha * 0.5
nextPoint = M.addVek(point, M.scaleVek(alpha, d))
if n % 300 == 0:
print(alpha)
if alpha < eps == 1:
return 0
return alpha
def coneVolumeDescendBFGSApprox(cD, params_new, params_prev, crease,
efficiency, beta_1, beta_2):
A_k = M.idMatrix(2)
n = 0
while (cV.phi(params_new, cD) > eps_descend):
while (True):
try:
A_k = BFGS.getBFGSApprox(cD, params_new, params_prev, A_k)
break
except ZeroDivisionError:
print('es geht nicht besser mit BFGSApprox')
return params_new
break
antiGrad = M.scaleVek(-1, cV.gradPhiApprox(params_new, cD, 0.0001))
d = A_k.lgsSolve(antiGrad)
d = M.scaleVek(1.0 / M.norm(d), d)
alpha = sS.stepSizeArmijo(cD, params_new, d, crease, efficiency,
beta_1, beta_2)
d = M.scaleVek(alpha, d)
params_prev = [params_new[0], params_new[1]]
params_new = M.addVek(params_new, d)
if (M.dist(params_new, params_prev) < minimalStep_BFGSApprox):
print(' distance is lower than minimalStep of BFGSApprox ')
break
n = n + 1
return params_new
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 getLowPointOnGrid( grid , cD , upperBound ):
result = []
value_result = upperBound
for point in grid:
while (True):
try:
value = cV.phi( point , cD )
if value_result >= value:
result = point
value_result = value
break
except ZeroDivisionError:
# print('zero division at',pair)
break
return result
def coneVolumeDescendBFGS(cD, params_new, params_prev, crease, efficiency,
beta_1, beta_2):
A_k = M.idMatrix(2)
n = 0
while (cV.phi(params_new, cD) > eps_descend):
# ICH VERÄNDERE HIER MEIN CREASE...
crease = 0.000001 #cV.phi( params_new , cD) * 0.00000001
while (True):
try:
A_k = BFGS.getBFGS(cD, params_new, params_prev, A_k)
break
except ZeroDivisionError:
print('es geht nicht besser')
return params_new
break
antiGrad = M.scaleVek(-1, cV.gradPhi(params_new, cD))
d = A_k.lgsSolve(antiGrad)
d = M.scaleVek(1.0 / M.norm(d), d)
alpha = sS.stepSize_posGrad(
cD, params_new, d, n) # crease , efficiency , beta_1 , beta_2 )
d = M.scaleVek(alpha, d)
params_prev = [params_new[0], params_new[1]]
params_new = M.addVek(params_new, d)
if (M.dist(params_new, params_prev) < minimalStep_BFGS):
print(' distance is lower than minimalStep of BFGS ')
break
n = n + 1
return params_new
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)
print(result)
print(cV.gamma(cD_test, result))
print(cV.phi(result, cD_test))
print(cV.sigma(result, cD_test))
repeats += 1
print(repeats)
print([noFail, fail_soft, fail_medium, fail_hard])
def notEfficient(cD, point, d, stepSize, crease):
v = M.addVek(point, M.scaleVek(stepSize, d))
upper_bound = cV.phi(point, cD) + crease * stepSize * M.scal(
cV.gradPhi(point, cD), d) / M.norm(d)
return cV.phi(v, cD) > upper_bound
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]
def visiualizeLowValueOnGrid( size , stepSize , cD , param , value_1 , value_2 , value_3 ):
grid = []
n = math.floor(size * 1.0/stepSize)
for i in range(n):
for j in range(n):
grid.append( [ i * stepSize - size / 2.0 + param[0], j *stepSize - size / 2.0 + param[1]])
print('grid ist fertig')
min = math.inf
point_min = param
x_1 = []
y_1 = []
x_2 = []
y_2 = []
x_3 = []
y_3 = []
x_4 = []
y_4 = []
for point in grid:
while(True):
try:
value= cV.phi(point , cD )
if value < min:
point_min = point
min = value
if value < value_1:
x_1.append(point[0])
y_1.append([point[1]])
else:
if value < value_2:
x_2.append(point[0])
y_2.append([point[1]])
else:
if value < value_3:
x_3.append(point[0])
y_3.append([point[1]])
else:
x_4.append(point[0])
y_4.append(point[1])
break
except ZeroDivisionError:
break
a_x = param[0] - size / 2.0
b_x = param[0] + size / 2.0 + 5
a_y = param[1] - size / 2.0
b_y = param[1] + size / 2.0 + 5
mp.plot( x_1 , y_1 , 'go')
mp.plot( x_2 , y_2 , 'yo')
mp.plot( x_3 , y_3 , 'ro')
mp.plot( x_4 , y_4 , 'bo')
mp.plot([param[0]], [param[1]], 'wo')
mp.axes( [a_x , b_x , a_y , b_y])
#print('here comes minimal point, gamma , value, gradient:')
#print( point_min )
#print( cV.gamma( cD , point_min ))
#print( cV.phi( point_min , cD ))
#print( cV.gradPhi( point_min , cD))
mp.show()
def phiNormScaled( params , cD):
return cV.phi( params , cD ) * ( ( M.norm( params ) ) ** n + 1 )