def _checkInitialValue(x0, G, h, A, b):
if x0 is None:
if G is None:
if A is None:
raise Exception("Fail to obtain an initial value")
else:
x = scipy.linalg.lstsq(A,b)[0]
if not feasiblePoint(x, G, h):
raise Exception("Fail to obtain an initial value")
else:
x = feasibleStartingValue(G, h)
else:
x = checkArrayType(x0)
x = x.reshape(len(x),1)
if G is not None:
if not feasiblePoint(x, G, h):
x = feasibleStartingValue(G, h)
# else (we do not care as we can use infeasible Newton steps
return x
def trustRegion(func, grad, hessian=None, x0=None,
maxiter=100,
method='exact',
disp=0, full_output=False):
x = checkArrayType(x0)
p = len(x)
if grad is None:
def finiteForward(x,func,p):
def finiteForward1(x):
return forward(func,x.ravel())
return finiteForward1
grad = finiteForward(x,func,p)
if hessian is None:
approxH = BFGS
elif type(hessian) is str:
if hessian.lower()=='bfgs':
approxH = BFGS
elif hessian.lower()=='sr1':
approxH = SR1
elif hessian.lower()=='dfp':
approxH = DFP
else:
raise Exception("Input name of hessian is not recognizable")
hessian = None
if method is None:
trustMethod = trustExact
elif type(method) is str:
if method.lower()=='exact':
trustMethod = trustExact
else:
raise Exception("Input name of hessian is not recognizable")
fx = None
oldGrad = None
deltaX = None
oldFx = numpy.inf
i = 0
oldi = -1
j = 0
tau = 1.0
radius = 1.0
maxRadius = 1.0
dispObj = Disp(disp)
while maxiter>i:
# if we have successfully moved on, then
# we would need to recompute some of the quantities
if i!=oldi:
g = grad(x)
fx = func(x)
if hessian is None:
if oldGrad is None:
H = numpy.eye(len(x))
else:
diffG = numpy.array(g - oldGrad)
H = approxH(H, diffG, deltaX)
else:
H = hessian(x)
deltaX, tau = trustMethod(x, g, H, radius)
deltaX = deltaX.real
M = diffM(deltaX, g, H)
# print x
# print deltaX
newFx = func(x + deltaX)
predRatio = (fx - newFx) / M(deltaX)
if predRatio>=0.75:
if tau>0.0:
radius = min(2.0*radius, maxRadius)
elif predRatio<=0.25:
radius *= 0.25
if predRatio>=0.25:
oldGrad = g
x += deltaX
oldFx = fx
fx = newFx
i +=1
oldi = i - 1
# we only allow termination if we make a move
if (abs(fx-oldFx)/fx)<=reltol:
break
if abs(deltaX.dot(g))<=atol:
break
else:
oldi = i
dispObj.d(j, x , fx, deltaX, g, i)
j += 1
if full_output:
output = dict()
output['totalIter'] = i
output['outerIter'] = j
output['fx'] = func(x)
output['H'] = H
output['g'] = g
return x, output
else:
return x
