/usr/share/pyshared/openopt/solvers/UkrOpt/Dilation2.py is in python-openopt 0.38+svn1589-1.
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import numpy
from numpy.linalg import norm
class DilationUnit():
#vectorNorm = 0 # TODO: remove it?
#dilationCoeff = 1.0
maxScalarComponentsLength = 2
def __init__(self, vector, dilationCoeff):
#self.vectorDirection = None
self.scalarComponents = []
nv = norm(vector)
assert nv != 0
#self.vectorDirection, self.vectorNorm, self.dilationCoeff = vector/nv, nv, dilationCoeff
self.vectorDirection, self.dilationCoeff = vector/nv, dilationCoeff
class Dilation():
#maxUnits = 10
#treshhold = 1.01
th_phi = 0.1
dilationCoeffThreshold = 0.999999
prevRest = None
#maxVectorNum = 50
def __init__(self, maxUnitsNum):
self.maxUnitsNum = maxUnitsNum
self.units = []
self.unitsNum = 0
self.T = numpy.float64
if hasattr(numpy, 'float128'):
pass
self.T = numpy.float128
def addDilationUnit(self, vector, dilationCoeff = 0.99999):
assert all(isfinite(vector))
self.unitsNum += 1
v = self.T(vector.copy())
nv = norm(v)
v /= nv
# TODO: COMMENT IT OUT
# M = 0
# for i, unit in enumerate(self.units):
# M = max((M, abs(dot(unit.vectorDirection, v))))
# if M > 1e-2:
# print 'warning: max M=', M, 'nv=', nv
# return
#self.units.add(DilationUnit(vector.copy(), dilationCoeff))
self.units.append(DilationUnit(v, dilationCoeff))
print 'add new dilation vector; curr num: ', len(self.units)
def getProjections(self, vv):
#assert len(self.units) != 0
V = self.T(vv)
NV = norm(V)
V /= NV
r= []
#print 'norm(V):', norm(V)
for unit in self.units:
# TODO: try to involve less multiplication ops
scalarComponent = dot(unit.vectorDirection, V)
# print 'norm(unit.vectorDirection):', norm(unit.vectorDirection)
# print 'scalarComponent>>>', scalarComponent
component = unit.vectorDirection * scalarComponent#V
r.append((scalarComponent, component, unit))
for scalarComponent, component, unit in r:
V -= component
return r, V#*NV
def getDilatedDirection(self, direction):
projectionsInfo, rest = self.getProjections(direction)
dilatedDirection = zeros(direction.size)
for scalarComponent, component, unit in projectionsInfo:
dilatedDirection += component * unit.dilationCoeff
return projectionsInfo, dilatedDirection+rest
def getRestrictedDilatedDirection(self, direction):
projectionsInfo, rest = self.getProjections(direction)
dilatedDirection = zeros(direction.size)
s, ns = [], []
for scalarComponent, component, unit in projectionsInfo:
t = component * unit.dilationCoeff
s.append(t)
ns.append(norm(t))
dilatedDirection += t
r = dilatedDirection+rest
nr = norm(r)
for i in xrange(len(s)):
if ns[i] < 1e-10*nr:
r += 1e-10*nr*s[i]/ns[i]-s[i]
return projectionsInfo, r
def getMostInsufficientUnit(self, scalarComponents):
assert self.unitsNum != 0
ind, miUnit, miValue = 0, self.units[0], self.units[0].dilationCoeff#abs(scalarComponents[0])*(1-self.units[0].dilationCoeff)
for i, unit in enumerate(self.units):
#newValue = unit.dilationCoeff*abs(scalarComponents[i])
newValue = unit.dilationCoeff#abs(scalarComponents[i])*(1-unit.dilationCoeff)
if newValue > miValue:
ind, miUnit, miValue = i, unit, newValue
return ind, miUnit
def updateDilationCoeffs2(self, scalarComponents, rest):
arr_u = array([unit.dilationCoeff for unit in self.units])
if self.unitsNum == 1:
self.units[0].dilationCoeff /= 2.0
return
m = self.unitsNum
n = rest.size
#th = norm(rest) * sqrt(n-m)
for i, unit in enumerate(self.units):
c = unit.dilationCoeff * abs(scalarComponents[i]) / n
if c < 0.125:
unit.dilationCoeff *= 2.0
elif c > 0.25 :
unit.dilationCoeff /= 2.0
print i, unit.dilationCoeff
def updateDilationCoeffs(self, scalarComponents, rest):
arr_u = array([unit.dilationCoeff for unit in self.units])
# if self.unitsNum == 1:
# self.units[0].dilationCoeff /= 2.0
# return
Ui2 = arr_u ** 2
UiSCi = abs(array([unit.dilationCoeff*scalarComponents[i] for i, unit in enumerate(self.units)]))
Ui2SCi2 = array(UiSCi) ** 2
S, S2 = sum(Ui2), sum(Ui2SCi2)
SCi = abs(array(scalarComponents))
SCi2 = SCi ** 2
alp = 2.0
beta = 1.0 / alp
#k = sqrt(S2 / (alp*sum((1.0-UiSCi)**2 * UiSCi2)))
#rr = k * sqrt(1.0-UiSCi)**2
m, n = self.unitsNum, rest.size
b = abs(beta)
#b = min((abs(beta), m/(16*n*sqrt(sum(UiSCi)))))
#b = m/(n*sqrt(sum(UiSCi)))
nr2 = norm(rest) ** 2
k = b*sqrt(S2 / sum(Ui2SCi2*(1.0-UiSCi)))
#k = sqrt(((b2-1)*nr2 + b2 * S2) / sum(Ui2SCi2*(1.0-UiSCi)))
# k1 = sqrt(b2 * S2 / sum(Ui2SCi2*(1.0-UiSCi)))
# m, n = self.unitsNum, rest.size
# rr1 = k1 * (1-UiSCi)
# u1 = rr1 * arr_u
rr = k * (1-UiSCi)
assert k > 0
#k = sqrt(S2 / (alp*sum((1.0-SCi)**2 * Ui2SCi2)))
#rr = k * sqrt(1.0-SCi)**2
rr[rr>4.0] = 4.0
rr[rr<0.25] = 0.25
r = rr * arr_u
#r[r<1e-20] = 1e-20
assert len(r) == self.unitsNum == len(self.units)
#print '--------------------'
for i, unit in enumerate(self.units):
unit.dilationCoeff = r[i]
print 'nU=%d k=%0.1g r_min=%0.1g r_max=%0.1g' % (self.unitsNum, k, min(r), max(r))
#print r
#print i, unit.dilationCoeff
# print 'old sum:', S2,'new sum:', sum(array([unit.dilationCoeff*scalarComponents[i] for i, unit in enumerate(self.units)])**2)
# print '====================='
def _updateDilationInfo(self, _dilationDirection_, ls, _moveDirection_):
r = {'increased':0, 'decreased':0}
#projectionsInfo, dilatedDirectionComponent, rest = self.getDilatedDirection(_moveDirection_)
projectionsInfo, rest = self.getProjections(_dilationDirection_)
# for scalarComponent, component, unit in projectionsInfo1:
# scs = unit.scalarComponents
# if len(scs) >= unit.maxScalarComponentsLength:
# scs.pop(0)
# scs.append(scalarComponent)
print 'norm(rest1):', norm(rest)
#cond_add = norm(rest1) > 1e-2
s = abs(asfarray([scalarComponent for (scalarComponent, component, unit) in projectionsInfo]))
#cond_add = self.unitsNum == 0 or any(norm(rest1) > 64.0*asfarray([unit.dilationCoeff * s[i] for i, unit in enumerate(self.units)]))
cond_add = norm(rest) > 1e-3 #or (self.prevRest is not None and dot(self.prevRest, rest1) <= 0)
if cond_add:
self.addDilationUnit(rest)
projectionsInfo, rest = self.getProjections(_dilationDirection_)
print 'norm(rest11):', norm(rest)
#print '!>', dot(dilatedDirectionComponent1, rest1) / norm(dilatedDirectionComponent1) / norm(rest1)
#print '!!>', dilatedDirectionComponent1, rest1
#assert norm(dilatedDirectionComponent1) > 1e-10
# mostUnusefulUnitNumber = -1
# mostUnusefulUnitCoeff = -1
# for i, u in enumerate(self.units):
# if u.dilationCoeff > mostUnusefulUnitCoeff:
# mostUnusefulUnitNumber, mostUnusefulUnitCoeff = i, u.dilationCoeff
#print 'norm(_dilationDirection_) :', norm(_dilationDirection_)
#s = norm(rest1) / norm(dilatedDirectionComponent1)
#print 's:', s
scalarComponents = [scalarComponent for (scalarComponent, component, unit) in projectionsInfo]
#print argmax(scalarComponents)
#m = len(self.units)
#n = _dilationDirection_.size
#print 'norm(rest1), norm(scalarComponents, inf):', norm(rest1) , norm(scalarComponents, inf)
#print ''
#condReasonableBigRest = self.unitsNum == 0 or norm(rest1) > norm(scalarComponents, inf)#miUnit.dilationCoeff* abs(scalarComponents[ind_mi]) # s > 0.05
#print 'norm(rest1):', norm(rest1), 'miUnit.dilationCoeff:', miUnit.dilationCoeff, 'miUnit.sc:', scalarComponents[ind_mi]
#if 1 or norm(rest1) > 0.9:
#print '>', rest1/norm(rest1), norm(rest1), [Unit.dilationCoeff for Unit in self.units], [Unit.vectorDirection for Unit in self.units]
#and self.prevRest is not None and (True or dot(self.prevRest, rest) <= 0)
#projectionsInfo2, dilatedDirectionComponent2, rest2 = self.getDilatedDirection( dilatedDirectionComponent1 + rest1)
#assert norm(dilatedDirectionComponent2) > 1e-10
#projectionsInfo3, dilatedDirectionComponent, rest = self.getDilatedDirection( dilatedDirectionComponent + rest)
#print 'norm(r1), norm(d1):', norm(rest1), norm(dilatedDirectionComponent1)
#abs_tan_phi = norm(rest1) / norm(dilatedDirectionComponent1)
#projectionsInfo, dilatedDirectionComponent, rest = projectionsInfo2, dilatedDirectionComponent2, rest2
#print 'norm(r2), norm(d2):', norm(rest2), norm(dilatedDirectionComponent2)
#cond_drift = self.prevRest is not None and dot(self.prevRest, rest1) > 0
# TODO: what if self.prevRest is None?
#haveToAdd = condReasonableBigRest and any(rest1!=0) #and not cond_drift
self.updateDilationCoeffs(scalarComponents, rest)
self.prevRest = rest.copy()
#print 'self.unitsNum, self.maxUnitsNum:', self.unitsNum, self.maxUnitsNum
if self.unitsNum >= self.maxUnitsNum:
self.unitsNum = 0
self.units = []
# ind_mi, miUnit = self.getMostInsufficientUnit(scalarComponents)
# self.units.pop(ind_mi)
# self.unitsNum -= 1
# for unit in self.units:
# unit.dilationCoeff /= miUnit.dilationCoeff
#print 'mi removed:', ind_mi
nRemoved = self.cleanUnnessesaryDilationUnits()
if nRemoved: print 'nRemoved:', nRemoved
return r
#d = 1.0
#projectionsInfo, dilatedDirectionComponent, rest = self.getDilatedDirection(_dilationDirection_)
# for scalarComponent, component, unit in projectionsInfo:
# # angle between ort and dilation direction
# angle = arccos(scalarComponent) # values from 0 to pi
# if angle > pi/2: angle = pi - angle
# if d < 1.0:
# unit.dilationCoeff *= max((0.5, sin(d*angle)))
# elif d > 1.0:
# unit.dilationCoeff *= max((2.0, d/sqrt(1-scalarComponent**2)))
#
# if cond_overdilated:
# #TODO - omit repeated calculations
# nRemoved = self.cleanUnnessesaryDilationUnits()
# print 'REMOVED: ', nRemoved#, 'increaseMultiplier:', increaseMultiplier
# if sign(dot(_moveDirection_, component)) == sign(scalarComponent):
# #print 'case 1'
# unit.dilationCoeff *= multiplier
# if unit.dilationCoeff > 1.0: unit.dilationCoeff = 1.0
# else:
# reduceMultiplier = max((0.5, sqrt(1 - scalarComponent**2)))
# unit.dilationCoeff *= reduceMultiplier
#unit.dilationCoeff /= 2.0#multiplier
#print 'case 2'
# #cond_overDilated = abs_tan_phi > 0.5#min((2.0, 1.0 / self.th_phi))
# if abs_tan_phi < self.th_phi: #abs_tan_phi < 0.1 * len(self.units) / (_dilationDirection_.size-len(self.units)):
# koeff = 0.5
# for scalarComponent, component, unit in projectionsInfo:
# unit.dilationCoeff *= koeff * max((0.1, sqrt(1 - scalarComponent**2)))
# #elif cond_overDilated: # TODO: use separate parameter instead of (1.0 / self.th_phi)
# else:
# #elif abs_tan_phi >
# multiplier = self.th_phi / abs_tan_phi
# if multiplier > 2.0: multiplier = 2.0
# elif multiplier < 1.3: multiplier = 1.3
# for scalarComponent, component, unit in projectionsInfo:
# if sign(dot(_moveDirection_, component)) == sign(scalarComponent):
# unit.dilationCoeff *= multiplier
# #pass
# for scalarComponent, component, unit in projectionsInfo:
# pass
#reduceMultiplier = max((0.25, sqrt(1 - scalarComponent**2)))
#unit.dilationCoeff *= reduceMultiplier
##########################################
# get NEW rest
# TODO - omit repeated calculations
#projectionsInfo, dilatedDirectionComponent, rest = self.getDilatedDirection(_dilationDirection_)
##########################################
#if self.prevRest is not None:print 'sign dot:', sign(dot(self.prevRest, rest))
#print 'norm(rest) / norm(dilatedDirectionComponent:', norm(rest)/ norm(dilatedDirectionComponent)
#haveToAdd = True
def cleanUnnessesaryDilationUnits(self):
indUnitsToRemove = []
for i, unit in enumerate(self.units):
if unit.dilationCoeff > self.dilationCoeffThreshold:
print '>>', unit.dilationCoeff , self.dilationCoeffThreshold
indUnitsToRemove.append(i)
#unitsToRemove.add(unit)
for j in xrange(len(indUnitsToRemove)):
self.units.pop(indUnitsToRemove[-1-j])
nRemoved = len(indUnitsToRemove)
self.unitsNum -= nRemoved
#if nRemoved!=0: print 'dilation units: removed = %d left=%d' % (nRemoved, len(self.units))
return nRemoved
# def cleanUnnessesaryDilationUnits(self):
# unitsToRemove = set()
# for unit in self.units:
# if unit.dilationCoeff >= self.treshhold:
# unitsToRemove.add(unit)
# self.units = self.units.difference(unitsToRemove)
# def updateDilationInfo(self, projectionsInfo, ls):
# r = {'increased':0, 'decreased':0}
#
# for scalarComponent, component, unit in projectionsInfo:
# scs = unit.scalarComponents
# if len(scs) >= unit.maxScalarComponentsLength:
# scs.pop(0)
# scs.append(scalarComponent)
# signs = sign(scs)
#
# #cond_1 = norm(unit.vectorDirection - array([1.0]+[0]*(unit.vectorDirection.size-1)))<1e-4
# #cond_1 = any(unit.vectorDirection[:10]==1)
#
# # TODO: remove cycles
#
# if len(signs)>1: # TODO: handle signs[-1-i] == 0 case
# if ls <= 1:
# if signs[-1] == signs[-2]:
# pass
# else:
# unit.dilationCoeff /= 2.0
# r['decreased'] += 1
# elif ls > 1:
# if signs[-1] == signs[-2]:
# unit.dilationCoeff *= 1 + 0.1#ls/3.0
# r['increased'] += 1
# else:
# pass
# return r
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