def __call__(self,
x0=None,
**kwargs): ## > runs cg with/without preconditioner
"""
Runs the conjugate gradient minimization.
Parameters
----------
x0 : field, *optional*
Starting guess for the minimization.
tol : scalar, *optional*
Tolerance specifying convergence; measured by current relative
residual (default: 1E-4).
clevel : integer, *optional*
Number of times the tolerance should be undershot before
exiting (default: 1).
limii : integer, *optional*
Maximum number of iterations performed (default: 10 * b.dim()).
Returns
-------
x : field
Latest `x` of the minimization.
convergence : integer
Latest convergence level indicating whether the minimization
has converged or not.
"""
self.x = field(self.b.domain, val=x0, target=self.b.target)
if (self.W is None):
return self._calc_without(**kwargs)
else:
return self._calc_with(**kwargs)
def __call__(self,x0=None,**kwargs): ## > runs cg with/without preconditioner
"""
Runs the conjugate gradient minimization.
Parameters
----------
x0 : field, *optional*
Starting guess for the minimization.
tol : scalar, *optional*
Tolerance specifying convergence; measured by current relative
residual (default: 1E-4).
clevel : integer, *optional*
Number of times the tolerance should be undershot before
exiting (default: 1).
limii : integer, *optional*
Maximum number of iterations performed (default: 10 * b.dim()).
Returns
-------
x : field
Latest `x` of the minimization.
convergence : integer
Latest convergence level indicating whether the minimization
has converged or not.
"""
self.x = field(self.b.domain,val=x0,target=self.b.target)
if(self.W is None):
return self._calc_without(**kwargs)
else:
return self._calc_with(**kwargs)
def _briefing(self, x): ## > prepares x for `multiply`
## inspect x
if (not isinstance(x, field)):
return field(self.domain, val=x, target=None), False
## check x.domain
elif (x.domain == self.domain):
return x, False
elif (x.domain == self.codomain):
return x, True
## transform
else:
return x.transform(target=self.codomain, overwrite=False), True
def _briefing(self,x): ## > prepares x for `multiply`
## inspect x
if(not isinstance(x,field)):
return field(self.domain,val=x,target=None),False
## check x.domain
elif(x.domain==self.domain):
return x,False
elif(x.domain==self.codomain):
return x,True
## transform
else:
return x.transform(target=self.codomain,overwrite=False),True
def _calc_without(self,
tol=1E-4,
clevel=1,
limii=None): ## > runs cg without preconditioner
clevel = int(clevel)
if (limii is None):
limii = 10 * self.b.domain.dim(split=False)
else:
limii = int(limii)
r = self.b - self.A(self.x)
d = field(self.b.domain, val=np.copy(r.val), target=self.b.target)
gamma = r.dot(d)
if (gamma == 0):
return self.x, clevel + 1
delta_ = np.absolute(gamma)**(-0.5)
convergence = 0
ii = 1
while (True):
q = self.A(d)
alpha = gamma / d.dot(q) ## positive definite
if (not np.isfinite(alpha)):
self.note.cprint(
"\niteration : %08u alpha = NAN\n... dead." % ii)
return self.x, 0
self.x += alpha * d
if (np.signbit(np.real(alpha))):
about.warnings.cprint(
"WARNING: positive definiteness of A violated.")
r = self.b - self.A(self.x)
elif (ii % self.reset == 0):
r = self.b - self.A(self.x)
else:
r -= alpha * q
gamma_ = gamma
gamma = r.dot(r)
beta = max(0, gamma / gamma_) ## positive definite
d = r + beta * d
delta = delta_ * np.absolute(gamma)**0.5
self.note.cflush(
"\niteration : %08u alpha = %3.1E beta = %3.1E delta = %3.1E"
% (ii, np.real(alpha), np.real(beta), np.real(delta)))
if (gamma == 0):
convergence = clevel + 1
self.note.cprint(" convergence level : INF\n... done.")
break
elif (np.absolute(delta) < tol):
convergence += 1
self.note.cflush(" convergence level : %u" % convergence)
if (convergence == clevel):
self.note.cprint("\n... done.")
break
else:
convergence = max(0, convergence - 1)
if (ii == limii):
self.note.cprint("\n... quit.")
break
if (self.spam is not None):
self.spam(self.x, ii)
ii += 1
if (self.spam is not None):
self.spam(self.x, ii)
return self.x, convergence
def _calc_without(self,tol=1E-4,clevel=1,limii=None): ## > runs cg without preconditioner
clevel = int(clevel)
if(limii is None):
limii = 10*self.b.domain.dim(split=False)
else:
limii = int(limii)
r = self.b-self.A(self.x)
d = field(self.b.domain,val=np.copy(r.val),target=self.b.target)
gamma = r.dot(d)
if(gamma==0):
return self.x,clevel+1
delta_ = np.absolute(gamma)**(-0.5)
convergence = 0
ii = 1
while(True):
q = self.A(d)
alpha = gamma/d.dot(q) ## positive definite
if(not np.isfinite(alpha)):
self.note.cprint("\niteration : %08u alpha = NAN\n... dead."%ii)
return self.x,0
self.x += alpha*d
if(np.signbit(np.real(alpha))):
about.warnings.cprint("WARNING: positive definiteness of A violated.")
r = self.b-self.A(self.x)
elif(ii%self.reset==0):
r = self.b-self.A(self.x)
else:
r -= alpha*q
gamma_ = gamma
gamma = r.dot(r)
beta = max(0,gamma/gamma_) ## positive definite
d = r+beta*d
delta = delta_*np.absolute(gamma)**0.5
self.note.cflush("\niteration : %08u alpha = %3.1E beta = %3.1E delta = %3.1E"%(ii,np.real(alpha),np.real(beta),np.real(delta)))
if(gamma==0):
convergence = clevel+1
self.note.cprint(" convergence level : INF\n... done.")
break
elif(np.absolute(delta)<tol):
convergence += 1
self.note.cflush(" convergence level : %u"%convergence)
if(convergence==clevel):
self.note.cprint("\n... done.")
break
else:
convergence = max(0,convergence-1)
if(ii==limii):
self.note.cprint("\n... quit.")
break
if(self.spam is not None):
self.spam(self.x,ii)
ii += 1
if(self.spam is not None):
self.spam(self.x,ii)
return self.x,convergence
