def newtoninterpolate(alpha_data, phi_data, old_alpha, old_phi):
# Interpolates using a polynomial of increasing order
# The coefficients of the interpolated polynomial are found using the Newton method
if very_old_alpha is None:
return quadinterpolate(alpha_lo, alpha_hi, old_alpha, old_phi)
if old_alpha in alpha_data:
return quadinterpolate(alpha_lo, alpha_hi, old_alpha, old_phi)
alpha_data.append(old_alpha)
phi_data.append(old_phi)
coefs = newton_poly(alpha_data, phi_data)
alpha, ii = newtonroot(coefs, alpha_data, old_alpha)
if alpha < alpha_lo or alpha > alpha_hi: # Root is outside the domain
if getMPIRankWorld() == 0:
zoomlogger.debug(
"NOTE: Newton interpolation converged on a root outside of [alpha_lo,alpha_hi]. Falling back on cubic interpolation"
)
return cubicinterpolate(alpha_lo, alpha_hi, old_alpha, old_phi,
very_old_alpha, very_old_phi)
if np.abs(alpha - old_alpha) < tol_df or np.abs(
alpha) < tol_sm * np.abs(old_alpha):
alpha = 0.5 * old_alpha
if abs(alpha) <= 0:
if getMPIRankWorld() == 0:
zoomlogger.debug(
"NOTE: Newton interpolation returned alpha <= 0. Falling back on cubic interpolation"
)
return cubicinterpolate(alpha_lo, alpha_hi, old_alpha, old_phi,
very_old_alpha, very_old_phi)
return alpha, len(alpha_data)
def getMeshHandler(self):
"""
Returns a handle to a mesh meshing the design. In the current
implementation a mesh file name in Triangle format is returned.
"""
args = self.getCommandString().split()
args[-1]=args[-1]%self.getScriptFileName()
if getMPIRankWorld() == 0:
import subprocess
open(self.getScriptFileName(),"w").write(self.getScriptString())
ret = subprocess.call(args) / 256
else:
ret=0
ret=getMPIWorldMax(ret)
if ret > 0:
raise RuntimeError("Could not build mesh: %s"%" ".join(args))
else:
# <hack> so that users can set the mesh filename they want.
name=self.getScriptFileName()
if (".poly" in name) or (".ele" in name) or (".node" in name):
s=name.split(".")[:-1]
name=s[0]
if len(s) > 1: name+=".%s"*(len(s)-1)%tuple(s[1:])
files=glob.glob("%s.1.*"%name)
for f in files:
sufx=f.split(".")[-1]
mshName=self.getMeshFileName()+"."+sufx
os.rename(f,mshName)
# </hack>
return self.getMeshFileName()
def getScriptHandler(self):
"""
Returns a handler to the script file to generate the geometry.
In the current implementation a script file name is returned.
"""
if getMPIRankWorld() == 0:
open(self.getScriptFileName(),"w").write(self.getScriptString())
return self.getScriptFileName()
def newtonroot(coefs, alpha_data, startingGuess):
# Solves for the root of a polynomial using the newton method
dfcoefs = list(range(1, len(coefs)))
for i in range(0, len(coefs) - 1):
dfcoefs[i] *= coefs[i + 1]
tol = 1e-6
error = 100
maxiterations = 100
point = startingGuess
counter = 0
for i in range(0, maxiterations):
counter += 1
product = 1
numer = coefs[0]
denom = dfcoefs[0]
for i in range(1, len(coefs)):
product *= (point - alpha_data[i - 1])
numer += product * coefs[i]
if i < len(coefs) - 1:
denom += product * dfcoefs[i]
if denom == 0:
if getMPIRankWorld() == 0:
zoomlogger.debug(
"NOTE: The Newton solver failed (denom==0). Falling back on cubic interpolation"
)
return cubicinterpolate(alpha_lo, alpha_hi, old_alpha, old_phi,
very_old_alpha, very_old_phi)
newpoint = float(point - numer / denom)
error = abs(newpoint - point)
if error < tol:
if getMPIRankWorld() == 0:
zoomlogger.debug(
"Newton interpolation converged in %d iterations. Got alpha = %f"
% (counter, newpoint))
return newpoint, counter
else:
point = newpoint
# zoomlogger.debug("NOTE: Newton interpolation failed to converge (exceeded max iterations). Falling back on cubic interpolation" % error)
return cubicinterpolate(alpha_lo, alpha_hi, old_alpha, old_phi,
very_old_alpha, very_old_phi)