/usr/share/pyshared/openopt/kernel/Point.py is in python-openopt 0.38+svn1589-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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from numpy import copy, isnan, array, argmax, abs, vstack, zeros, any, isfinite, all, where, asscalar, \
sign, dot, sqrt, array_equal, nanmax, inf, hstack, isscalar, logical_or, matrix, asfarray, prod, arange, ndarray, asarray, sum
from ooMisc import norm
from nonOptMisc import Copy, isPyPy
from pointProjection import pointProjection
empty_arr = array(())
try:
from scipy.sparse import isspmatrix, csr_matrix
scipyInstalled = True
except ImportError:
scipyInstalled = False
isspmatrix = lambda *args, **kwargs: False
class Point:
"""
the class is used to prevent calling non-linear constraints more than once
f, c, h are funcs for obtaining objFunc, non-lin ineq and eq constraints.
df, dc, dh are funcs for obtaining 1st derivatives.
"""
__expectedArgs__ = ['x', 'f', 'mr']
def __init__(self, p, x, *args, **kwargs):
self.p = p
self.x = copy(x)
for i, arg in enumerate(args):
setattr(self, '_' + self.__expectedArgs__[i], args[i])
for name, val in kwargs.items():
setattr(self, '_' + name, val)
#assert self.x is not None
def f(self):
if not hasattr(self, '_f'):
# TODO: rework this: self.p.probType!='IP'
if self.p._baseClassName == 'NonLin' and self.p.probType!='IP':
self._f = self.p.f(self.x) if self.p.isObjFunValueASingleNumber else self.p.F(self.x)
else:
self._f = self.p.objFunc(self.x)
return copy(self._f)
def df(self):
if not hasattr(self, '_df'): self._df = self.p.df(self.x)
return Copy(self._df)
def c(self, ind=None):
if not self.p.userProvided.c: return empty_arr.copy()
if ind is None:
if not hasattr(self, '_c'): self._c = self.p.c(self.x)
return copy(self._c)
else:
if hasattr(self, '_c'): return copy(self._c[ind])
else: return copy(self.p.c(self.x, ind))
def dc(self, ind=None):
if not self.p.userProvided.c: return empty_arr.copy().reshape(0, self.p.n)
if ind is None:
if not hasattr(self, '_dc'): self._dc = self.p.dc(self.x)
return Copy(self._dc)
else:
if hasattr(self, '_dc'): return Copy(self._dc[ind])
else: return Copy(self.p.dc(self.x, ind))
def h(self, ind=None):
if not self.p.userProvided.h: return empty_arr.copy()
if ind is None:
if not hasattr(self, '_h'): self._h = self.p.h(self.x)
return copy(self._h)
else:
if hasattr(self, '_h'): return copy(self._h[ind])
else: return copy(self.p.h(self.x, ind))
def dh(self, ind=None):
if not self.p.userProvided.h: return empty_arr.copy().reshape(0, self.p.n)
#raise 0
if ind is None:
if not hasattr(self, '_dh'): self._dh = self.p.dh(self.x)
return Copy(self._dh)
else:
if hasattr(self, '_dh'):
return Copy(self._dh[ind])
else:
return Copy(self.p.dh(self.x, ind))
def d2f(self):
if not hasattr(self, '_d2f'): self._d2f = self.p.d2f(self.x)
return copy(self._d2f)
# def intConstraints(self):
# if self.p.intVars == {} or self.p.intVars == []: return 0
# if not hasattr(self, '_intConstraint'):
# r = [norm(self.x[k]-self.p.intVars[k], -inf) for k in self.p.intVars.keys()]
# self._intConstraints = max(r)
#
# return copy(self._intConstraints)
def lin_ineq(self):
if not hasattr(self, '_lin_ineq'): self._lin_ineq = self.p._get_AX_Less_B_residuals(self.x)
return copy(self._lin_ineq)
def lin_eq(self):
if not hasattr(self, '_lin_eq'): self._lin_eq = self.p._get_AeqX_eq_Beq_residuals(self.x)
return copy(self._lin_eq)
def lb(self):
if not hasattr(self, '_lb'): self._lb = self.p.lb - self.x
return copy(self._lb)
def ub(self):
if not hasattr(self, '_ub'): self._ub = self.x - self.p.ub
return copy(self._ub)
def mr(self, retAll = False):
# returns max residual
if not hasattr(self, '_mr'):
r, fname, ind = 0, None, 0
ineqs = ['lin_ineq', 'lb', 'ub']
eqs = ['lin_eq']
if self.p._baseClassName == 'NonLin':
ineqs.append('c')
eqs.append('h')
elif self.p.probType in ['MILP', 'MINLP']:
pass
#ineqs.append('intConstraints')
for field in ineqs:
fv = array(getattr(self, field)()).flatten()
if fv.size > 0:
#ind_max = argmax(fv)
#val_max = fv[ind_max
val_max = nanmax(fv)
if not isnan(val_max):
ind_max = where(fv==val_max)[0][0]
if r < val_max:
r, ind, fname = val_max, ind_max, field
for field in eqs:
fv = array(getattr(self, field)()).flatten()
if fv.size > 0:
fv = abs(fv)
ind_max = argmax(fv)
val_max = fv[ind_max]
if r < val_max:
r, ind, fname = val_max, ind_max, field
self._mr, self._mrName, self._mrInd= r, fname, ind
if retAll:
return asscalar(copy(self._mr)), self._mrName, asscalar(copy(self._mrInd))
else: return asscalar(copy(self._mr))
def sum_of_all_active_constraints(self):
if not hasattr(self, '_sum_of_all_active_constraints'):
p = self.p
if p.solver.__name__ == 'ralg':
tol = p.contol / 2.0
else:
tol = 0.0
# elif p.solver.__name__ == 'gsubg':
# tol = 0.0
# else:
# p.err('unimplemented case in Point.py')
c, h= self.c(), self.h()
all_lin = self.all_lin()
self._sum_of_all_active_constraints = (c[c>0] - 0).sum() + (h[h>tol] - tol).sum() - (h[h<-tol] + tol).sum() + all_lin
return Copy(self._sum_of_all_active_constraints)
def mr_alt(self, retAll = False, bestFeasiblePoint=None):
# TODO: add fix wrt bestFeasiblePoint handling
###################################################
# DEBUG!
# IT SAVES DIFFERENT VALUES WRT WITH OR WITHOUT bestFeasiblePoint
# IT HAS BEEN CALLED 1ST TIME
if hasattr(self, '_mr_alt'): delattr(self, '_mr_alt')
###################################################
if not hasattr(self, '_mr_alt'):
p = self.p
if not hasattr(p.solver, 'approach') or p.solver.approach == 'all active':
val = self.sum_of_all_active_constraints()
if bestFeasiblePoint is not None:
# not "+="!!!!! Else some problems with array shapes can occur
#print self.f()-bestFeasiblePoint.f()
# val = val + max((0, self.f()-bestFeasiblePoint.f())) * p.contol / p.fTol
pass
self._mr_alt, self._mrName_alt, self._mrInd_alt = val, 'all active', 0
else:
p.err('bug in openopt kernel, inform developers')
# r = 0.0
# if c.size != 0:
# ind_max = argmax(c)
# val_max = c[ind_max]
# if val_max > r:
# r = val_max
# Type = 'c'
# ind = ind_max
# if h.size != 0:
# h = abs(h)
# ind_max = argmax(h)
# val_max = h[ind_max]
# #hm = abs(h).max()
# if val_max > r:
# r = val_max
# Type = 'h'
# ind = ind_max
# lin_eq = self.lin_eq()
# if lin_eq.size != 0:
# l_eq = abs(lin_eq)
# ind_max = argmax(l_eq)
# val_max = l_eq[ind_max]
# if val_max > r:
# r = val_max
# Type = 'lin_eq'
# ind = ind_max
# lin_ineq = self.lin_ineq()
# # TODO: implement it
# val = r
# self._mr_alt, self._mrName_alt, self._mrInd_alt = val, Type, 0
if retAll:
return asscalar(copy(self._mr_alt)), self._mrName_alt, asscalar(copy(self._mrInd_alt))
else: return asscalar(copy(self._mr_alt))
def dmr(self, retAll = False):
# returns direction for max residual decrease
#( gradient for equality < 0 residuals ! )
if not hasattr(self, '_dmr') or (retAll and not hasattr(self, '_dmrInd')):
g = zeros(self.p.n)
maxResidual, resType, ind = self.mr(retAll=True)
if resType == 'lb':
g[ind] -= 1 # N * (-1), -1 = dConstr/dx = d(lb-x)/dx
elif resType == 'ub':
g[ind] += 1 # N * (+1), +1 = dConstr/dx = d(x-ub)/dx
elif resType == 'lin_ineq':
g += self.p.A[ind]
elif resType == 'lin_eq':
rr = self.p.matmult(self.p.Aeq[ind], self.x)-self.p.beq[ind]
if rr < 0: g -= self.p.Aeq[ind]
else: g += self.p.Aeq[ind]
elif resType == 'c':
dc = self.dc(ind=ind).flatten()
g += dc
elif resType == 'h':
dh = self.dh(ind=ind).flatten()
if self.p.h(self.x, ind) < 0: g -= dh#CHECKME!!
else: g += dh#CHECKME!!
else:
# TODO: error or debug warning
pass
#self.p.err('incorrect resType')
self._dmr, self._dmrName, self._dmrInd = g, resType, ind
if retAll:
return copy(self._dmr), self._dmrName, copy(self._dmrInd)
else:
return copy(self._dmr)
def betterThan(self, point2compare, altLinInEq = False, bestFeasiblePoint = None):
"""
usage: result = involvedPoint.better(pointToCompare)
returns True if the involvedPoint is better than pointToCompare
and False otherwise
(if NOT better, mb same fval and same residuals or residuals less than desired contol)
"""
if self.p.isUC:
return self.f() < point2compare.f()
contol = self.p.contol
if altLinInEq:
mr, point2compareResidual = self.mr_alt(bestFeasiblePoint=bestFeasiblePoint), point2compare.mr_alt(bestFeasiblePoint=bestFeasiblePoint)
else:
mr, point2compareResidual = self.mr(), point2compare.mr()
# if altLinInEq and bestFeasiblePoint is not None and isfinite(self.f()) and isfinite(point2compare.f()):
# fTol = self.p.fTol
# mr += (self.f() - bestFeasiblePoint.f() + fTol) *contol / fTol
# point2compareResidual += (point2compare.f() - bestFeasiblePoint.f()+fTol) *contol / fTol
# mr += max((0, self.f() - bestFeasiblePoint.f())) *contol/ fTol
# point2compareResidual += max((0, point2compare.f() - bestFeasiblePoint.f())) *contol/ fTol
# assert self.f() >= bestFeasiblePoint.f()
# assert point2compare.f() >= bestFeasiblePoint.f()
# mr += (self.f() - bestFeasiblePoint.f()) / fTol
# point2compareResidual += (point2compare.f() - bestFeasiblePoint.f()) / fTol
criticalResidualValue = max((contol, point2compareResidual))
self_nNaNs, point2compare_nNaNs = self.nNaNs(), point2compare.nNaNs()
if point2compare_nNaNs > self_nNaNs: return True
elif point2compare_nNaNs < self_nNaNs: return False
# TODO: check me
if self_nNaNs == 0:
if mr > self.p.contol and mr > point2compareResidual: return False
elif point2compareResidual > self.p.contol and point2compareResidual > mr: return True
else: # got here means self_nNaNs = point2compare_nNaNs but not equal to 0
if mr == 0 and point2compareResidual == 0:
if not self.p.solver.__name__.startswith('interalg'):
self.p.err('you should provide at least one active constraint in each point from R^n where some constraints are undefined')
return mr < point2compareResidual
point2compareF_is_NaN = isnan(point2compare.f())
selfF_is_NaN = isnan(self.f())
if isPyPy:
if type(point2compareF_is_NaN) == ndarray: point2compareF_is_NaN = asscalar(point2compareF_is_NaN)
if type(selfF_is_NaN) == ndarray: selfF_is_NaN = asscalar(selfF_is_NaN)
if not point2compareF_is_NaN: # f(point2compare) is not NaN
if not selfF_is_NaN: # f(newPoint) is not NaN
return self.f() < point2compare.f()
else: # f(newPoint) is NaN
return False
else: # f(point2compare) is NaN
if selfF_is_NaN: # f(newPoint) is NaN
return mr < point2compareResidual
else: # f(newPoint) is not NaN
return True
def isFeas(self, altLinInEq):
if not all(isfinite(self.f())): return False
if self.p.isUC: return True
if self.nNaNs() != 0: return False
contol = self.p.contol
if altLinInEq:
if self.mr_alt() > contol: return False
else:
if hasattr(self, '_mr'):
if self._mr > contol: return False
else:
#TODO: simplify it!
#for fn in residuals: (...)
if any(self.lb() > contol): return False
if any(self.ub() > contol): return False
if any(abs(self.lin_eq()) > contol): return False
if any(self.lin_ineq() > contol): return False
if any(abs(self.h()) > contol): return False
if any(self.c() > contol): return False
return True
def nNaNs(self):
# returns number of nans in constraints
if self.p._baseClassName != 'NonLin': return 0
r = 0
c, h = self.c(), self.h()
r += len(where(isnan(c))[0])
r += len(where(isnan(h))[0])
return r
def linePoint(self, alp, point2, ls=None):
# returns alp * point1 + (1-alp) * point2
# where point1 is self, alp is real number
assert isscalar(alp)
p = self.p
r = p.point(self.x * (1-alp) + point2.x * alp)
#lin_eqs = self.lin_eq()*alp + point2.lin_eq() * (1-alp)
#print '!>>, ', p.norm(lin_eqs), p.norm(lin_eqs - r.lin_eq())
# TODO: optimize it, take ls into account!
#if ls is not None and
if not (p.iter % 16):
lin_ineq_predict = self.lin_ineq()*(1-alp) + point2.lin_ineq() * alp
#if 1 or p.debug: print('!>>', p.norm(lin_ineq_predict-r.lin_ineq()))
r._lin_ineq = lin_ineq_predict
r._lin_eq = self.lin_eq()*(1-alp) + point2.lin_eq() * alp
# don't calculate c for inside points
if 0<alp<1:
c1, c2 = self.c(), point2.c()
ind1 = logical_or(c1 > 0, isnan(c1))
ind2 = logical_or(c2 > 0, isnan(c2))
# prev
# ind = where(ind1 | ind2)[0]
#
# _c = zeros(p.nc)
# if ind.size != 0:
# _c[ind] = p.c(r.x, ind)
# new, temporary walkaround for PyPy
ind = logical_or(ind1, ind2)
_c = zeros(p.nc)
if any(ind):
_c[ind] = p.c(r.x, where(ind)[0])
r._c = _c
# TODO: mb same for h?
return r
def all_lin(self): # TODO: rename it wrt lin_eq that are present here
if not hasattr(self, '_all_lin'):
lb, ub, lin_ineq = self.lb(), self.ub(), self.lin_ineq()
r = 0.0
# TODO: CHECK IT - when 0 (if some nans), when contol
# if all(isfinite(self.f())): threshold = self.p.contol
# else: 0.0 = 0
lin_eq = self.lin_eq()
ind_lb, ind_ub = lb>0.0, ub>0.0
ind_lin_ineq = lin_ineq>0.0
ind_lin_eq = abs(lin_eq)>0.0
USE_SQUARES = 1
if USE_SQUARES:
if any(ind_lb):
r += sum(lb[ind_lb] ** 2)
if any(ind_ub):
r += sum(ub[ind_ub] ** 2)
# if ind_lb.size != 0:
# r += sum(lb[ind_lb])
# if ind_ub.size != 0:
# r += sum(ub[ind_ub])
if any(ind_lin_ineq):
r += sum(lin_ineq[ind_lin_ineq] ** 2)
if any(ind_lin_eq):
r += sum(lin_eq[ind_lin_eq] ** 2)
self._all_lin = r / self.p.contol
# self._all_lin = r
else:
if any(ind_lb):
r += sum(lb[ind_lb])
if any(ind_ub):
r += sum(ub[ind_ub])
if any(ind_lin_ineq):
r += sum(lin_ineq[ind_lin_ineq])
if any(ind_lin_eq):
r += sum(abs(lin_eq[ind_lin_eq]))
self._all_lin = r
return copy(self._all_lin)
def all_lin_gradient(self):
if not hasattr(self, '_all_lin_gradient'):
p = self.p
n = p.n
d = zeros(n)
lb, ub = self.lb(), self.ub()
lin_ineq = self.lin_ineq()
lin_eq = self.lin_eq()
ind_lb, ind_ub = lb > 0.0, ub > 0.0
ind_lin_ineq = lin_ineq > 0.0
ind_lin_eq = abs(lin_eq) != 0.0
USE_SQUARES = 1
if USE_SQUARES:
if any(ind_lb):
d[ind_lb] -= lb[ind_lb]# d/dx((x-lb)^2) for violated constraints
if any(ind_ub):
d[ind_ub] += ub[ind_ub]# d/dx((x-ub)^2) for violated constraints
if any(ind_lin_ineq):
# d/dx((Ax-b)^2)
b = p.b[ind_lin_ineq]
if hasattr(p, '_A'):
a = p._A[ind_lin_ineq]
tmp = a._mul_sparse_matrix(csr_matrix((self.x, (arange(n), zeros(n))), shape=(n, 1))).toarray().flatten() - b
#tmp = a._mul_sparse_matrix(csr_matrix((self.x, reshape(p.n, 1))).toarray().flatten() - b
d += a.T._mul_sparse_matrix(tmp.reshape(tmp.size, 1)).A.flatten()
#d += dot(a.T, dot(a, self.x) - b)
else:
if isPyPy:
a = array([p.A[j] for j in where(ind_lin_ineq)[0]])
else:
a = p.A[ind_lin_ineq]
d += dot(a.T, dot(a, self.x) - b) # d/dx((Ax-b)^2)
if any(ind_lin_eq):
if isspmatrix(p.Aeq):
p.err('this solver is not ajusted to handle sparse Aeq matrices yet')
#self.p.err('nonzero threshold is not ajusted with lin eq yet')
aeq = p.Aeq#[ind_lin_eq]
beq = p.beq#[ind_lin_eq]
d += dot(aeq.T, dot(aeq, self.x) - beq) # d/dx((Aeq x - beq)^2)
# self._all_lin_gradient = 2.0 * d
self._all_lin_gradient = 2.0 * d / p.contol
else:
if any(ind_lb):
d[ind_lb] -= 1# d/dx(lb-x) for violated constraints
if any(ind_ub):
d[ind_ub] += 1# d/dx(x-ub) for violated constraints
if any(ind_lin_ineq):
# d/dx(Ax-b)
b = p.b[ind_lin_ineq]
if hasattr(p, '_A'):
d += (p._A[ind_lin_ineq]).sum(0).A.flatten()
else:
d += (p.A[ind_lin_ineq]).sum(0).flatten()
if any(ind_lin_eq):
# currently for ralg it should be handled in dilation matrix
p.err('not implemented yet, if you see it inform OpenOpt developers')
# beq = p.beq[ind_lin_eq]
# if hasattr(p, '_Aeq'):
# tmp = p._Aeq[ind_lin_eq]
# ind_change = where()
# tmp
# d += ().sum(0).A.flatten()
# else:
# #d += (p.Aeq[ind_lin_eq]).sum(0).flatten()
# aeq = p.Aeq[ind_lin_eq]
# beq = p.beq[ind_lin_eq]
# d += dot(aeq.T, dot(aeq, self.x) - beq) # 0.5*d/dx((Aeq x - beq)^2)
self._all_lin_gradient = d
return copy(self._all_lin_gradient)
def sum_of_all_active_constraints_gradient(self):
if not hasattr(self, '_sum_of_all_active_constraints_gradient'):
p = self.p
contol = p.contol
x = self.x
direction = self.all_lin_gradient()
if p.solver.__name__ == 'ralg':
new = 1
elif p.solver.__name__ == 'gsubg':
new = 0
else:
p.err('unhandled case in Point._getDirection')
if p.userProvided.c:
th = 0.0
#th = contol / 2.0
C = p.c(x)
Ind = C>th
ind = where(Ind)[0]
activeC = asarray(C[Ind])# asarray and Ind for PyPy compatibility
if len(ind) > 0:
tmp = p.dc(x, ind)
if new:
if tmp.ndim == 1 or min(tmp.shape) == 1:
if hasattr(tmp, 'toarray'):
tmp = tmp.toarray()#.flatten()
if activeC.size == prod(tmp.shape):
activeC = activeC.reshape(tmp.shape)
tmp *= (activeC-th*(1.0-1e-15))/norm(tmp)
else:
if hasattr(tmp, 'toarray'):
tmp = tmp.toarray()
tmp *= ((activeC - th*(1.0-1e-15))/sqrt((tmp**2).sum(1))).reshape(-1, 1)
if tmp.ndim > 1:
tmp = tmp.sum(0)
direction += (tmp.A if type(tmp) != ndarray else tmp).flatten()
if p.userProvided.h:
#th = 0.0
th = contol / 2.0
H = p.h(x)
Ind1 = H>th
ind1 = where(Ind1)[0]
H1 = asarray(H[Ind1])# asarray and Ind1 for PyPy compatibility
if len(ind1) > 0:
tmp = p.dh(x, ind1)
if new:
if tmp.ndim == 1 or min(tmp.shape) == 1:
if hasattr(tmp, 'toarray'):
tmp = tmp.toarray()#.flatten()
if H1.size == prod(tmp.shape):
H1 = H1.reshape(tmp.shape)
tmp *= (H1-th*(1.0-1e-15))/norm(tmp)
else:
if hasattr(tmp, 'toarray'):
tmp = tmp.toarray()
tmp *= ((H1 - th*(1.0-1e-15))/sqrt((tmp**2).sum(1))).reshape(-1, 1)
if tmp.ndim > 1:
tmp = tmp.sum(0)
direction += (tmp.A if isspmatrix(tmp) or hasattr(tmp, 'toarray') else tmp).flatten()
ind2 = where(H<-th)[0]
H2 = H[ind2]
if len(ind2) > 0:
tmp = p.dh(x, ind2)
if new:
if tmp.ndim == 1 or min(tmp.shape) == 1:
if hasattr(tmp, 'toarray'):
tmp = tmp.toarray()#.flatten()
if H2.size == prod(tmp.shape):
H2 = H2.reshape(tmp.shape)
tmp *= (-H2-th*(1.0-1e-15))/norm(tmp)
else:
if hasattr(tmp, 'toarray'):
tmp = tmp.toarray()
tmp *= ((-H2 - th*(1.0-1e-15))/sqrt((tmp**2).sum(1))).reshape(-1, 1)
if tmp.ndim > 1:
tmp = tmp.sum(0)
direction -= (tmp.A if isspmatrix(tmp) or isinstance(tmp, matrix) else tmp).flatten()
self._sum_of_all_active_constraints_gradient = direction
return Copy(self._sum_of_all_active_constraints_gradient)
def _getDirection(self, approach, currBestFeasPoint = None):
if self.isFeas(altLinInEq=True):
self.direction, self.dType = self.df(),'f'
if type(self.direction) != ndarray: self.direction = self.direction.A.flatten()
return self.direction.copy()
else:
if approach == 'all active':
self.dType = 'all active'
self.direction = self.sum_of_all_active_constraints_gradient()
else:
maxRes, fname, ind = self.mr_alt(1, bestFeasiblePoint = currBestFeasPoint)
if fname == 'all_lin':
d = self.all_lin_gradient()
self.dType = 'all_lin'
elif fname == 'lin_eq':
self.p.err("kernel error, inform openopt developers")
#d = self.dmr()
#self.dType = 'lin_eq'
elif fname == 'c':
d = self.dmr()
#if p.debug: assert array_equal(self.dc(ind).flatten(), self.dmr())
self.dType = 'c'
elif fname == 'h':
d = self.dmr()#sign(self.h(ind))*self.dh(ind)
#if p.debug: assert array_equal(self.dh(ind).flatten(), self.dmr())
self.dType = 'h'
else:
p.err('error in getRalgDirection (unknown residual type ' + fname + ' ), you should report the bug')
self.direction = d.flatten()
if type(self.direction) != ndarray: self.direction = self.direction.A.flatten()
# print 'currBestFeasPoint is not None:', (currBestFeasPoint is not None), 'self.f() > currBestFeasPoint.f():', self.f() > currBestFeasPoint.f()
contol, fTol = self.p.contol, self.p.fTol
# print self.f(), currBestFeasPoint.f(), self.f() - fTol == currBestFeasPoint.f()
if currBestFeasPoint is not None and self.f() + 0.25*fTol > currBestFeasPoint.f():
#self.direction += ((self.f()-currBestFeasPoint.f()) * p.contol / nDF / fTol) * DF
# self.direction += self.df() * (contol/fTol)
pass
return self.direction.copy() # it may be modified in ralg when some constraints coords are NaN
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