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Copy pathSP3_limit_integer.py
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SP3_limit_integer.py
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### Michael Jarrett
### 3D SP3 Limit
### To calculate SP3 limit of 2D/1D method with anisotropic TL
#########################################
# This code performs algebra to determine the theoretical limit of
# accuracy for a 2D/1D method with linear axial and radial TL moments.
# There are 4 linear moments. Equations for each
# in terms of the others are determined by hand, and hardcoded into
# this script. The script then solves the 10x10 system algebraically
# to determine each moment in terms of derivatives of the isotropic moment.
#########################################
import numpy as np
import math
import sys
import time
from subprocess import call
###################
### Code design ###
###################
# The system of equations is defined hierarchically.
# Each TL component has an expression. e.g.,
# dEzz/dz = [ 1/3 Lz + 1/5 Lz^2 + 1/7 Lz^3 + ...] [ F - dJ/dz ]
# Each expression is a sum of several terms.
# Each term consists of several subterms, and a variable.
# Each subterm consists of a coefficient, and an order for the radial and axial operator (0-3),
# and a component. (e.g., 1/3 Lz)
# If the sum of the order of the operators is greater than (3), the subterm is dropped.
# Two terms can be multiplied. Coefficients and operator orders are multiplied accordingly.
# An expression can be simplified by combining like terms (i.e., terms with the same variable).
# An expression can be solved if there are terms with the same variable as the self-variable.
# A component will have a method to substitute another component in for the variable in one of the terms.
# The component definitions will be hardcorded. The solution order will also be hardcorded.
class ComponentList:
def __init__(self, component_list):
self.component_list = component_list
def __del__(self):
self.component_list = []
def ncomponents(self):
return len(self.component_list)
def add_component(self,thatComponent):
ic = 0
while(ic < self.ncomponents()):
if(self.component_list[ic].CID == thatComponent.CID):
del self.component_list[ic]
else:
ic += 1
self.component_list.append(thatComponent)
def find_component(self,thatID):
for myComponent in self.component_list:
if(myComponent.CID == thatID):
return myComponent
class Component:
def __init__(self, term_list, myTL_ID):
self.term_list = term_list
self.CID = myTL_ID
self.LHS = Term([Subterm(1.0,0,0)], myTL_ID)
#self.LHS = Term([Subterm([],[],0,0)], myTL_ID)
def __del__(self):
self.term_list = []
self.CID = 0
@property
def CID(self):
return self.CID
@CID.setter
def CID(self,ID):
self.CID = ID
def nterms(self):
return len(self.term_list)
def substitute_component(self,thatComponent):
# substitute the expression for that Component
# where it appears in this Component
#print "that Component ID = %i" % thatComponent.CID
itx = 0
newTermList = []
#print "thatComponenet.CID = %i" % thatComponent.CID
while(itx < self.nterms()):
tmpTerm = self.term_list[itx]
#print "tmpTerm.TID = %i" % tmpTerm.TID
if(tmpTerm.TID == thatComponent.CID):
#print "Match at ID = %i" % tmpTerm.TID
# calculate new terms by distributing
for thatTerm in thatComponent.term_list:
newTerm = term_mult(thatTerm,tmpTerm)
newTermList.append(newTerm)
#delete the old term
del self.term_list[itx]
else:
itx += 1
# add new term list to Component expression
self.term_list.extend(newTermList)
# combine any like terms that result from substitution
self.combine_terms()
def combine_terms(self):
itx = 0
while (itx < self.nterms()):
tmpTerm1 = self.term_list[itx]
x = itx+1
while (x < self.nterms()):
tmpTerm2 = self.term_list[x]
if(tmpTerm1.match_ID(tmpTerm2)):
tmpTerm1.term_add(tmpTerm2)
del self.term_list[x]
else:
x += 1
itx += 1
def remove_high_order(self):
for myterm in self.term_list:
myterm.remove_high_order()
# solve component if the term appears on left and right sides of the equation
def solve(self):
# first, ensure the component is "clean" for solving
self.remove_high_order()
self.combine_terms()
### move self terms to the LHS
itx = 0
while(itx < self.nterms()):
myTerm = self.term_list[itx]
newSubTermList = []
if(myTerm.TID == self.CID):
for mySubTerm in myTerm.subterm_list:
newSubTerm = copy_subterm(mySubTerm)
newSubTerm.sign = -1*mySubTerm.sign
newSubTermList.append(newSubTerm)
self.LHS.subterm_list.extend(newSubTermList)
del self.term_list[itx]
itx += 1
### invert the operator on the LHS and apply to the RHS
### (1 - x)^-1 = 1 + x + x^2 + x^3 + ...
### calc extra term x, then calculate x^2, x^3, etc.
extraTerm = Term([],0)
if(self.LHS.subterm_list[0].isIdentity):
for mySubTerm in self.LHS.subterm_list[1:]:
extraTerm.subterm_list.append(mySubTerm)
else:
### TODO: if the first subterm is not I, then adjust the whole term
print "*********************************************************."
print "We've run into a non-identity! Have to code for this case."
print "*********************************************************."
### negate each subterm
for mySubTerm in extraTerm.subterm_list:
mySubTerm.sign = -1*mySubTerm.sign
### calculate x^2, x^3
extraTerm_squared = term_mult(extraTerm,extraTerm)
extraTerm_cubed = term_mult(extraTerm,extraTerm_squared)
extraTerm.term_add(extraTerm_squared)
extraTerm.term_add(extraTerm_cubed)
extraTerm.subterm_list.insert(0,Subterm(1.0,0,0))
#extraTerm.subterm_list.insert(0,Subterm([],[],0,0))
### now, extra term = I + x + x^2 + x^3
print "Extra term is:"
extraTerm.print_info()
### next, multiply each term in the component by the new extraTerm
newTermList = []
for myTerm in self.term_list:
tmpTerm = term_mult(myTerm,extraTerm)
newTermList.append(tmpTerm)
self.term_list = newTermList
self.reset_LHS()
# perform final solution for expression F = [ ... ] \phi
# requires that the component be an expression in the form \phi = [ ... ] F
def solve_F(self):
self.remove_high_order()
self.combine_terms()
if(self.nterms() == 1 and
self.term_list[0].TID == SOURCE_3D and
self.CID == SCALAR_FLUX):
extraTerm = Term([],SCALAR_FLUX)
FTerm = self.term_list[0]
if(FTerm.subterm_list[0].isIdentity):
for mySubTerm in FTerm.subterm_list[1:]:
newSubTerm = copy_subterm(mySubTerm)
#newSubTerm.sign = -1*mySubTerm.sign
extraTerm.subterm_list.append(newSubTerm)
else:
### TODO: if the first subterm is not I, then adjust the whole term
print "*********************************************************."
print "We've run into a non-identity! Have to code for this case."
print "*********************************************************."
else:
print "called solve_F but the component is not ready!"
self.print_component()
### negate each subterm
for mySubTerm in extraTerm.subterm_list:
#mySubTerm.coeff = -1.0*mySubTerm.coeff
#mySubTerm.numerator.insert(0,[-1])
mySubTerm.sign = -1*mySubTerm.sign
### calculate x^2, x^3
print "extraTerm subterms:"
extraTerm.print_term()
print "calculating extraTerm_squared. subterms:"
extraTerm_squared = term_mult(extraTerm,extraTerm)
extraTerm_squared.print_term()
print "calculating extraTerm_cubed. subterms:"
extraTerm_cubed = term_mult(extraTerm,extraTerm_squared)
extraTerm_cubed.print_term()
extraTerm.term_add(extraTerm_squared)
extraTerm.term_add(extraTerm_cubed)
extraTerm.subterm_list.insert(0,Subterm(1.0,0,0))
#extraTerm.subterm_list.insert(0,Subterm([],[],0,0))
### now, extra term = I + x + x^2 + x^3
### combine subterms
extraTerm.combine_subterms()
### sort subterms
extraTerm.sort_subterms()
print "Extra term is:"
extraTerm.print_info()
newComponent = Component([extraTerm],SOURCE_3D)
print "The solution is:"
newComponent.print_component()
newComponent.write_latex_equation()
### multiplies entire component by halfLZ
def mult_halfLZ(self):
halfLZterm = Term([Subterm(1.0,0,0.5)],0)
#halfLZterm = Term([Subterm([],[],0,0.5)],0)
newTermList = []
for myTerm in self.term_list:
tmpTerm = term_mult(myTerm,halfLZterm)
newTermList.append(tmpTerm)
self.term_list = newTermList
def reset_LHS(self):
self.LHS.subterm_list = []
self.LHS = Term([Subterm(1.0,0,0)],0)
#self.LHS = Term([Subterm([],[],0,0)],0)
def print_info(self):
print "My component terms: ID = %i (%s)" % (self.CID,variable_names[self.CID])
for myterm in self.term_list:
myterm.print_info()
def print_component(self):
print "My component terms: ID = %i (%s)" % (self.CID,variable_names[self.CID])
for myterm in self.term_list:
myterm.print_term()
def write_latex_equation(self):
texfile = open(texname,"a")
texstr = "\\begin{alignat}{2} \n"
texfile.write(texstr)
texstr = "\\label{eq:%s_%i} \n" % (equation_labels[self.CID],equation_counter.get_index(self.CID))
texfile.write(texstr)
#texstr = "%s = & \\nonumber \\\\ \n" % (latex_expressions[self.CID])
texstr = "& %s = \\\\ \n" % (latex_expressions[self.CID])
texfile.write(texstr)
for myTerm in self.term_list:
print "nsubterms = %i" % myTerm.nsubterms()
print "Printing term info:"
myTerm.print_info()
print "done printing term info:"
texstr = myTerm.write_term_latex()
texfile.write(texstr)
texstr = "\\end{alignat} \n"
texfile.write(texstr)
texstr = "\n"
texfile.write(texstr)
texfile.write(texstr)
class Term:
def __init__(self, subterm_list, variable_ID):
self.subterm_list = subterm_list
self.TID = variable_ID
#self.max_order = 3
def __del__(self):
self.subterm_list = []
self.TID = 0
@property
def TID(self):
return self.TID
@TID.setter
def TID(self,ID):
self.TID = ID
#@property
#def max_order(self):
# return self.max_order
#@max_order.setter
#def max_order(self,number):
# self.max_order = number
def nsubterms(self):
return len(self.subterm_list)
def term_add(self, otherTerm):
if(self.TID == otherTerm.TID):
self.subterm_list.extend(otherTerm.subterm_list)
self.combine_subterms()
else:
print "These terms don't add! myTermID = %i, otherTermID = %i" % (self.TID,otherTerm.TID)
del otherTerm
# combine subterms with the same r_order and z_order
def combine_subterms(self):
ist = 0
while (ist < self.nsubterms()):
#print "ist = %i, self.nsubterms = %i" % (ist,self.nsubterms())
tmpSubTerm1 = self.subterm_list[ist]
x = ist+1
while (x < self.nsubterms()):
#print "x = %i, self.nsubterms = %i" % (x,self.nsubterms())
tmpSubTerm2 = self.subterm_list[x]
if(tmpSubTerm1.match_order(tmpSubTerm2)):
tmpSubTerm1.subterm_add(tmpSubTerm2)
del self.subterm_list[x]
else:
x += 1
ist += 1
self.remove_zero()
def remove_zero(self):
ist = 0
while (ist < self.nsubterms()):
tmpSubTerm = self.subterm_list[ist]
if(abs(tmpSubTerm.coeff_float()) < THRESHOLD):
del self.subterm_list[ist]
else:
ist += 1
# remove terms with total order higher than max_order (3)
def remove_high_order(self):
ist = 0
while (ist < self.nsubterms()):
tmpSubTerm1 = self.subterm_list[ist]
if(tmpSubTerm1.total_order() > MAX_ORDER):
del self.subterm_list[ist]
else:
ist += 1
# check that this term's component TL ID matches another term's
def match_ID(self,thatTerm):
if(self.TID == thatTerm.TID):
return True
else:
return False
def print_info(self):
print "Term variable ID: %i (%s)" % (self.TID,variable_names[self.TID])
for mySubTerm in self.subterm_list:
mySubTerm.print_info()
def print_term(self):
print "Term variable ID: %i (%s)" % (self.TID,variable_names[self.TID])
print "( ",
for mySubTerm in self.subterm_list:
#if(mySubTerm.coeff_float() > 0.0):
if(mySubTerm.sign == 1):
print "+ ",
else:
print "- ",
#print "%7.5f" % (mySubTerm.coeff_float()),
print "%i/%i" % (mySubTerm.get_numerator(),mySubTerm.get_denominator()),
if(mySubTerm.r_order > 0):
if(mySubTerm.r_order == 1):
print "Lr",
else:
print "Lr^%i" % mySubTerm.r_order,
if(mySubTerm.z_order > 0):
if(mySubTerm.z_order == 1):
print "Lz",
else:
print "Lz^%i" % mySubTerm.z_order,
print ") "
def write_term_latex(self):
tmpstr = []
### determine if whole term is negative
allneg = True
for mySubTerm in self.subterm_list:
if(mySubTerm.sign == 1):
allneg = False
if(allneg):
tmpstr.append('& -')
else:
tmpstr.append('& +')
tmpstr.append(' \\l[ ')
firstTerm = True
for mySubTerm in self.subterm_list:
if(firstTerm):
if(mySubTerm.coeff_float() < 0.0 and allneg == False):
mystr = "- "
else:
mystr = ""
tmpstr.append(mystr)
if(mySubTerm.sign == 1 or allneg):
if(not firstTerm):
tmpstr.append('+ ')
else:
if(not firstTerm):
tmpstr.append('- ')
if(not (abs(mySubTerm.coeff_float()) == 1.0)):
mystr = '\\frac{%i}{%i} ' % (mySubTerm.get_numerator(),mySubTerm.get_denominator())
tmpstr.append(mystr)
if(mySubTerm.r_order > 0):
if(mySubTerm.r_order == 1):
tmpstr.append('\\opL_r ')
else:
mystr = '\\opL_r^{%i} ' % mySubTerm.r_order
tmpstr.append(mystr)
intzorder = int(mySubTerm.z_order)
if(intzorder > 0):
if(intzorder == 1):
tmpstr.append('\\opL_z ')
else:
mystr = '\\opL_z^{%i} ' % intzorder
tmpstr.append(mystr)
if(mySubTerm.r_order == 0 and intzorder == 0):
mystr = "I "
tmpstr.append(mystr)
firstTerm = False
tmpstr.append(' \\r] ')
if((2*self.subterm_list[0].z_order)%2 == 1): # half LZ is present
tmpstr.append('\halfLZ ')
tmpstr.append(latex_expressions[self.TID])
tmpstr.append(' \\nonumber \\\\ \n')
#print tmpstr
nospace = ''
#str_return = nospace.join(['\\l[','\\r]'])
return nospace.join(tmpstr)
def sort_subterms(self):
# first, ensure higher order terms are removed
self.remove_high_order()
# and like terms are combined
self.combine_subterms()
ist = 0
st_order = []
while(ist < self.nsubterms()):
thisSubTerm = self.subterm_list[ist]
st_order.append(thisSubTerm.r_order + thisSubTerm.z_order)
ist += 1
# st_order is a list of the order of each subterm
# sorted_order is a list of the old subterm indices
# in the order they should be placed
sorted_order = [0] * self.nsubterms()
sorted_operator_order = [0] * self.nsubterms()
x = 0
# go up by 1/2, orders can be non-zero
tot_order = 0.0
while(tot_order <= MAX_ORDER):
for ist in range(0,self.nsubterms()):
if(st_order[ist] == tot_order):
sorted_order[x] = ist
sorted_operator_order[x] = st_order[ist]
x += 1
tot_order += 0.5
### pass 10 times to get it right
for i in range(0,10):
for x in range(0,self.nsubterms()-1):
### sort within a group of similar order
if(sorted_operator_order[x] == sorted_operator_order[x+1]):
ist = sorted_order[x]
istp = sorted_order[x+1]
### put non-cross terms first
if((self.subterm_list[ist].r_order > 0.0 and self.subterm_list[ist].z_order > 0.0) and
(self.subterm_list[istp].r_order == 0.0 or self.subterm_list[istp].z_order == 0.0)):
tmp = sorted_order[x]
sorted_order[x] = sorted_order[x+1]
sorted_order[x+1] = tmp
### put higher r_order first
elif((self.subterm_list[ist].z_order > self.subterm_list[ist].r_order) and
(self.subterm_list[istp].r_order > self.subterm_list[istp].z_order)):
tmp = sorted_order[x]
sorted_order[x] = sorted_order[x+1]
sorted_order[x+1] = tmp
### generate new subterm list in the correct order
newSubTermList = []
for x in range(0,self.nsubterms()):
tmpSubTerm = copy_subterm(self.subterm_list[sorted_order[x]])
newSubTermList.append(tmpSubTerm)
self.subterm_list = newSubTermList
class Subterm:
#def __init__(self, numerator, denominator, r_order, z_order):
def __init__(self, coeff, r_order, z_order):
if(coeff < 0.0):
self.sign = -1
else:
self.sign = 1
i = compare_fraction(coeff)
if(i >= 0):
myPair = common_fractions[i]
self.numerator = compute_prime_factors(myPair[0])
self.denominator = compute_prime_factors(myPair[1])
self.r_order = r_order
self.z_order = z_order
#print "Found the fraction! value = %8.6f (%i/%i)" % (self.coeff_float(),myPair[0],myPair[1])
else:
print "Did not find the fraction! value = %8.6f" % coeff
self.numerator = []
self.denominator = []
self.r_order = 0
self.z_order = 0
def __del__(self):
#self.coeff = 0.0
self.numerator = []
self.denominator = []
self.r_order = 0
self.z_order = 0
self.sign = 1
@property
def r_order(self):
return self.r_order
@r_order.setter
def r_order(self,number):
self.r_order = number
@property
def z_order(self):
return self.z_order
@z_order.setter
def z_order(self,number):
self.z_order = number
@property
def sign(self):
return self.sign
@z_order.setter
def sign(self,sign):
self.sign = sign
def nnumer(self):
return len(self.numerator)
def ndenom(self):
return len(self.denominator)
def coeff_float(self):
numval = self.get_numerator()
denomval = self.get_denominator()
return float(self.sign)*float(numval)/float(denomval)
def get_numerator(self):
numval = 1
for val in self.numerator:
numval *= val
return numval
def get_denominator(self):
denomval = 1
for val in self.denominator:
denomval *= val
return denomval
def reduce_fraction(self):
self.sort_num_denom()
ival = 0
while(ival < self.nnumer()):
jval = 0
while(jval < self.ndenom() and ival < self.nnumer()):
#print "ival = %i, nnum = %i, jval = %i, ndenom = %i" % (ival,self.nnumer(),jval,self.ndenom())
if(self.numerator[ival] == self.denominator[jval]):
### common multiple, eliminate this term
del self.numerator[ival]
del self.denominator[jval]
else:
jval += 1
ival += 1
def sort_num_denom(self):
self.numerator.sort()
self.denominator.sort()
def add_r_order(self,number):
self.r_order += number
def add_z_order(self,z_order):
self.z_order += number
def total_order(self):
return self.r_order + self.z_order
# add two subterms
def subterm_add(self,thatSubTerm):
if(self.match_order(thatSubTerm)):
tmpStore = Subterm(1.0,0,0)
tmpStore.numerator = list(self.denominator)
tmpStore.denominator = list(thatSubTerm.denominator)
### reduce fractions
common_factors = tmpStore.find_common_factors()
#tmpStore.reduce_fraction()
### compute sum of the two fractions
numeratorA = self.get_numerator() * tmpStore.get_denominator()
numeratorB = tmpStore.get_numerator() * thatSubTerm.get_numerator()
tmpNum = self.sign*numeratorA + thatSubTerm.sign*numeratorB
if(tmpNum >= 0.0):
self.sign = 1
else:
self.sign = -1
#tmpSubTerm1.denominator.extend(tmpSubTerm2.denominator)
tmpStore.denominator.extend(tmpStore.numerator)
tmpStore.denominator.extend(common_factors)
self.denominator = tmpStore.denominator
### old way
#print "Adding two terms: term1 = %i/%i, term2 = %i/%i" % (self.get_numerator(),
# self.get_denominator(),thatSubTerm.get_numerator(),thatSubTerm.get_denominator())
### calculate numerator
#numeratorA = self.get_numerator() * thatSubTerm.get_denominator()
#numeratorB = self.get_denominator() * thatSubTerm.get_numerator()
#print "numeratorA = %6.1f, numeratorB = %6.1f" % (numeratorA,numeratorB)
#tmpNum = self.sign*numeratorA + thatSubTerm.sign*numeratorB
#tmpDenom = self.get_denominator() * thatSubTerm.get_denominator()
#self.denominator.extend(thatSubTerm.denominator)
#print "tmpnum = %i, tmpDenom = %i" % (tmpNum, tmpDenom)
self.numerator = compute_prime_factors(int(abs(tmpNum)))
#self.denominator = compute_prime_factors(tmpDenom)
self.reduce_fraction()
else:
print "These terms don't add! my (r,z) = (%i,%i), their (r,z) = (%i,%i) " % (
(self.r_order,self.z_order,thatSubTerm.r_order,thatSubTerm.z_order) )
def find_common_factors(self):
# find common factors between numerator and denominator
# this is used for adding two fractions
common_factors = []
ifac = 0
while(ifac < self.nnumer()):
jfac = 0
while(jfac < self.ndenom() and ifac < self.nnumer()):
if(self.numerator[ifac] == self.denominator[jfac]):
common_factors.append(int(self.numerator[ifac]))
del self.numerator[ifac]
del self.denominator[jfac]
else:
jfac += 1
ifac += 1
return common_factors
# determine if r_order and z_order matches that of another subterm
def match_order(self,thatSubTerm):
if(self.r_order == thatSubTerm.r_order and
self.z_order == thatSubTerm.z_order):
return True
else:
return False
def isIdentity(self):
if(self.coeff_float() == 1.0 and self.r_order == 0 and self.z_order == 0):
return True
else:
return False
def print_info(self):
#print "Subterm: coeff = %.5f, Lr = %i, Lz = %i" % (self.coeff,self.r_order,self.z_order)
print "Subterm: coeff = %.5f, (%i/%i), Lr = %i, Lz = %i" % (self.coeff_float(),
self.get_numerator(),self.get_denominator(),self.r_order,self.z_order)
class Counter:
def __init__(self,nvalues):
self.nvalues = nvalues
self.count_list = [0] * (nvalues+1)
def __del__(self):
self.nvalues = 0
self.count_list = []
def get_index(self,ID):
index = self.count_list[ID]
self.count_list[ID] += 1
return index
# multiply two terms
# retain TL component ID from first term
def term_mult(myTerm, thatTerm):
### this function multiplies two terms
### each term has an associated TL component ID.
### when multiplying, the ID of the self is retained. Only the
### subterms of otherTerm are retained.
#print "Multiplying myTerm: "
#myTerm.print_term()
#print "by thatTerm: "
#thatTerm.print_term()
newSubTermList = []
for mySubTerm in myTerm.subterm_list:
for thatSubTerm in thatTerm.subterm_list:
newSubTerm = subterm_mult(mySubTerm,thatSubTerm)
newSubTermList.append(newSubTerm)
newTerm = Term(newSubTermList,myTerm.TID)
newTerm.remove_high_order()
### combining subterms
newTerm.print_info()
newTerm.sort_subterms()
return newTerm
# multiply two subterms
def subterm_mult(mySubTerm,thatSubTerm):
newSubTerm = copy_subterm(mySubTerm)
thatCopy = copy_subterm(thatSubTerm)
newSubTerm.numerator.extend(thatCopy.numerator)
newSubTerm.denominator.extend(thatCopy.denominator)
newSubTerm.reduce_fraction()
newSubTerm.sign = mySubTerm.sign*thatSubTerm.sign
newSubTerm.r_order = mySubTerm.r_order + thatSubTerm.r_order
newSubTerm.z_order = mySubTerm.z_order + thatSubTerm.z_order
#print "Subterm mult result:"
#print newSubTerm.numerator,newSubTerm.denominator
return newSubTerm
def copy_subterm_list(thatSubTermList):
newSubTermList = []
for mySubTerm in thatSubTermList:
newSubTermList.append(copy_subterm(mySubTerm))
return newSubTermList
def copy_subterm(thatSubTerm):
newSubTermCopy = Subterm(1.0,thatSubTerm.r_order,thatSubTerm.z_order)
newSubTermCopy.numerator = list(thatSubTerm.numerator)
newSubTermCopy.denominator = list(thatSubTerm.denominator)
newSubTermCopy.sign = thatSubTerm.sign
return newSubTermCopy
def compare_fraction(thatFloat):
for i in range(0,nfrac):
myPair = common_fractions[i]
myFloat = float(myPair[0])/float(myPair[1])
if(abs(myFloat - abs(thatFloat)) < THRESHOLD*abs(thatFloat)): # this is a match
return i
return -1
def compare_fraction_sum(thatFloat):
for i in range(0,nfrac):
for j in range(0,nfrac):
myPair1 = common_fractions[i]
myPair2 = common_fractions[j]
myFloat1 = float(myPair1[0])/float(myPair1[1])
myFloat2 = float(myPair2[0])/float(myPair2[1])
if(abs(myFloat1 + myFloat2 - abs(thatFloat)) < THRESHOLD*abs(thatFloat)): # this is a match
return [i,j]
return [-1,-1]
def compute_prime_factors(myInt):
factor_list = []
i = 2
while(myInt > 1):
if(myInt%i == 0):
### i is a factor of myInt. is it prime? it should be.
myInt = myInt/i
factor_list.append(i)
else:
i += 1
#if(is_prime(i)):
return factor_list
#def is_prime(n):
# if(n == 2 or n == 3): return True
# if(n < 2 or n%2 == 0): return False
# if(n < 9): return True
# if(n%3 == 0): return False
# r = int(n**0.5)
# f = 5
# while(f <= r):
# if(n%f == 0): return False
# if(n%(f+2) == 0): return False
# f +=6
# return True
### indexing for each TL component
### linear TL terms
LIN_AX_POL = 1
LIN_AX_AZI = 2
LIN_RAD_POL = 3
LIN_RAD_AZI = 4
### quadratic TL terms
QUAD_AX_POL = 5
QUAD_AX_AZI = 6
QUAD_AX_XXX = 7
QUAD_RAD_POL = 8
QUAD_RAD_AZI = 9
QUAD_RAD_XXX = 10
### isotropic TL terms
ISO_AX_TL = 11 # dJ/dz
ISO_RAD_TL = 12 # (dJ/dx + dJ/dy)
### isotropic source terms
SOURCE_2D = 13 # F - dJ/dz
SOURCE_1D = 14 # F - (dJ/dx + dJ/dy)
### flux
SCALAR_FLUX = 15
### F: 3D source (this is the component we ultimately need to solve for)
SOURCE_3D = 16
nID = 16
MAX_ORDER = 3
THRESHOLD = 1.0E-6
if(int(sys.argv[1]) == 1):
texname = "equations_output_integer_linear.tex"
if(int(sys.argv[1]) == 2):
texname = "equations_output_integer.tex"
equation_counter = Counter(nID)
# names for each TL component variable
variable_names = ['null',
'Linear polar axial TL',
'Linear azimuthal axial TL',
'Linear polar radial TL',
'Linear azimuthal radial TL',
'Quadratic polar axial TL',
'Quadratic azimuthal axial TL',
'Quadratic cross moment axial TL',
'Quadratic polar radial TL',
'Quadratic azimuthal radial TL',
'Quadratic cross moment radial TL',
'Isotropic axial TL',
'Isotropic radial TL',
'Isotropic 2D MOC source',
'Isotropic 1D axial source',
'Scalar Flux',
'Source (F)']
latex_expressions = ['',
'\\axpolTL',
'\\axaziTL',
'\\radpolTL',
'\\radaziTL',
'\\quadaxpolTL',
'\\quadaxaziTL',
'\\quadaxcrossTL',
'\\quadradpolTL',
'\\quadradaziTL',
'\\quadradcrossTL',
'\\ATL',
'\\RTL',
'\\l[ F - \ATL \\r]',
'\\l[ F - \RTL \\r]',
'\phi',
'F']
equation_labels = ['',
'linaxpolTL',
'linaxaziTL',
'linradpolTL',
'linradaziTL',
'quadaxpolTL',
'quadaxaziTL',
'quadaxcrossTL',
'quadradpolTL',
'quadradaziTL',
'quadradcrossTL',
'isoATL',
'isoRTL',
'transport2D',
'transport1D',
'scalarFlux',
'transport3D']
##### commonly encountered fractions for LaTeX output
common_fractions = [(1, 1),
(1, 3),
(1, 5),
(1, 7),
(1, 9),
(1, 11),
(1, 15),
(1, 21),
(1, 25),
(1, 35),
(1, 63),
(1, 99),
(1,105),
(1,126),
(3, 3),
(3, 5),
(3, 7),
(3, 9),
(3, 11),
(3, 15),
(3, 21),
(3, 35),
(3, 63),
(3, 99),
(3,105),
(3,126),
(5, 3),
(5, 5),
(5, 7),
(5, 9),
(5, 11),
(5, 15),
(5, 21),
(5, 33),
(5, 35),
(5, 63),
(5, 99),
(5,105),
(5,126),
(7, 3),
(7, 5),
(7, 7),
(7, 9),
(7, 11),
(7, 15),
(7, 21),
(7, 35),
(7, 63),
(7, 99),
(7,105),
(7,126)]
nfrac = len(common_fractions)