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#! /usr/bin/python
import os
import sys
import re
from Numeric import *
from LinearAlgebra import *
nampat = re.compile("([A-Z][a-z]?[+=-][A-Z][a-z]?[+=-][A-Z][a-z]?)\.1\.log")
thetapat = re.compile(" INPUT CARD\> *theta *= *([\d\.-]+)")
engpat = re.compile(" FINAL U-B3LYP ENERGY IS +([\d\.-]+)")
hobond = re.compile("[A-Z+=]+\.")
Hartree = 4.3597482 # attoJoules
Bohr = 0.5291772083 # Angstroms
def fexist(fname):
try: os.stat(fname)
except OSError: return False
return True
def findnext(f,pat):
while 1:
card = f.readline()
if not card: return None
m = pat.match(card)
if m: return m
def ending(nam,suf):
if suf==nam[-len(suf):]: return nam
else: return nam+suf
def readangle(name):
b=zeros((0,2),Float)
for num in "123456789":
fn='angles/'+name+'.'+num+'.log'
if not fexist(fn): continue
f=open(fn)
theta = 2*(180-float(findnext(f,thetapat).group(1)))*pi/180.0
try: e = float(findnext(f,engpat).group(1))*Hartree
except AttributeError:
# print '# bad energy in',name+'.'+num
e=0.0
if e != 0.0: b=concatenate((b,array(((theta,e),))),axis=0)
return b
# return a function that evals a polynomial
def poly(c):
def ep(x):
b=0.0
for q in c:
b = q+x*b
return b
return ep
# The derivative of a polynomial
def dif(p):
a=arange(len(p))[::-1]
return (a*p)[:-1]
def newton(f,df,g):
fg=f(g)
while abs(fg)>1e-8:
dfg=df(g)
g=g-fg/dfg
fg=f(g)
return g
def quadmin(a,fa,b,fb,c,fc):
num = (b-a)**2 * (fb-fc) - (b-c)**2 * (fb-fa)
den = (b-a) * (fb-fc) - (b-c) * (fb-fa)
if den == 0.0: return b
return b - num / (2*den)
def golden(f,a,fa,b,fb,c,fc, tol=1e-2):
if c-a<tol: return quadmin(a,fa,b,fb,c,fc)
if c-b > b-a:
new = b+0.38197*(c-b)
fnew = f(new)
if fnew < fb: return golden(f, b,fb, new,fnew, c,fc)
else: return golden(f, a,fa, b,fb, new, fnew)
else:
new = a+0.61803*(b-a)
fnew = f(new)
if fnew < fb: return golden(f, a, fa, new,fnew, b,fb)
else: return golden(f, new, fnew, b,fb, c,fc)
def ak(m):
# find lowest point
lo=m[0][1]
ix=0
for i in range(shape(m)[0]):
if m[i][1] < lo:
lo=m[i][1]
ix=i
# take it and its neighbors for parabolic interpolation
a = m[ix-1][0]
fa= m[ix-1][1]
b = m[ix][0]
fb= m[ix][1]
c = m[ix+1][0]
fc= m[ix+1][1]
# the lowest point on the parabola
th0 = quadmin(a,fa,b,fb,c,fc)
# its value via Lagrange's formula
eth0 = (fa*((th0-b)*(th0-c))/((a-b)*(a-c)) +
fb*((th0-a)*(th0-c))/((b-a)*(b-c)) +
fc*((th0-a)*(th0-b))/((c-a)*(c-b)))
# adjust points to min of 0
m=m-array([0.0,eth0])
fa= m[ix-1][1]
fb= m[ix][1]
fc= m[ix+1][1]
# stiffness, interpolated between two triples of points
# this assumes equally spaced abcissas
num = (b - a)*fc + (a - c)*fb + (c - b)*fa
den = (b - a)* c**2 + (a**2 - b**2 )*c + a*b**2 - a**2 * b
Kth1 = 200.0 * num / den
ob = b
if th0>b: ix += 1
else: ix -= 1
a = m[ix-1][0]
fa= m[ix-1][1]
b = m[ix][0]
fb= m[ix][1]
c = m[ix+1][0]
fc= m[ix+1][1]
num = (b - a)*fc + (a - c)*fb + (c - b)*fa
den = (b - a)* c**2 + (a**2 - b**2 )*c + a*b**2 - a**2 * b
Kth2 = 200.0 * num / den
Kth = Kth1 + (Kth2-Kth1)*(th0-ob)/(b-ob)
return th0, Kth
for fn in os.listdir('angles'):
m=nampat.match(fn)
if not m: continue
name=m.group(1)
m=readangle(name)
## x=m[:,0]
## xn=1.0
## a=zeros((shape(m)[0],5),Float)
## for i in range(5):
## a[:,4-i]=xn
## xn=x*xn
## b=m[:,1]
## coef, sosr, rank, svs = linear_least_squares(a,b)
## d2f=poly(dif(dif(coef)))
## nx = newton(poly(dif(coef)), d2f, 1.5)
## print name, 'theta0=', nx, 'Ktheta=', d2f(nx)
# find lowest point
lo=m[0][1]
ix=0
for i in range(shape(m)[0]):
if m[i][1] < lo:
lo=m[i][1]
ix=i
# take it and its neighbors for parabolic interpolation
if ix==0: ix=1
if ix>len(m)-2: ix=len(m)-2
m2=m[ix-1:ix+2]
x=m2[:,0]
xn=1.0
a=zeros((3,3),Float)
for i in [2,1,0]:
a[:,i]=xn
xn=x*xn
b=m2[:,1]
coef, sosr, rank, svs = linear_least_squares(a,b)
d2f=poly(dif(dif(coef)))
nx = newton(poly(dif(coef)), d2f, m2[1,0])
print name, 'theta0=', nx, 'Ktheta=', d2f(nx)
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