def order_conditions(self,p):
"""
Generate a list of order conditions up to order p
"""
forest=rt.list_trees(0)
for i in range(1,p+1): forest+=rt.list_trees(i)
oc={rt.RootedTree(''):''}
for tree in forest[1:]:
oc[tree]=self.elementary_weight(tree)-rt.Emap(tree)
return oc
def TSRKOrderConditions(p, ind='all'):
from nodepy.rooted_trees import Emap_str
forest = rt.list_trees(p)
code = []
for tree in forest:
code.append(tsrk_elementary_weight_str(tree) + '-' + Emap_str(tree))
code[-1] = code[-1].replace('--', '')
code[-1] = code[-1].replace('1 ', 'e ')
code[-1] = code[-1].replace('1)', 'e)')
return code
def TSRKOrderConditions(p,ind='all'):
from nodepy.rooted_trees import Emap_str
forest=rt.list_trees(p)
code=[]
for tree in forest:
code.append(tsrk_elementary_weight_str(tree)+'-'+Emap_str(tree))
code[-1]=code[-1].replace('--','')
code[-1]=code[-1].replace('1 ','e ')
code[-1]=code[-1].replace('1)','e)')
return code
#Make matlab script to evaluate error coefficient
#for RK methods
from nodepy import rooted_trees as rt
from nodepy import runge_kutta_method as rk
p=10
f=open('oc_butcher.m','w')
ioc=1
for ip in range(2,p):
f.write("if p>="+str(ip))
f.write("\n % order "+str(ip)+" conditions:\n")
forest = rt.list_trees(ip)
for tree in forest:
oc=rk.elementary_weight_str(tree,style='matlab')
rhs =str(rt.Emap(tree))
f.write(" coneq("+str(ioc)+")="+oc+"-"+rhs+";\n")
ioc+=1
f.write("end\n\n")
f.close()
#for RK methods
from nodepy import rooted_trees as rt
from nodepy import runge_kutta_method as rk
p_max=15
f=open('oc_butcher.py','w')
f.write("def order(rk,tol=1.e-13):\n")
f.write(" from numpy import dot,zeros,all,sum,abs\n")
f.write(" coneq = zeros((1000))\n")
f.write(" A=rk.A\n b=rk.b\n c=rk.c\n")
f.write(" coneq[0]=sum(b)-1.\n")
f.write(" if any(abs(coneq)>tol):\n")
f.write(" return 0")
for ip in range(2,p_max):
print 'Generating order '+str(ip)+' conditions...'
ioc=0
f.write("\n # order "+str(ip)+" conditions:\n")
forest = rt.list_trees(ip)
for tree in forest:
oc=rk.elementary_weight_str(tree,style='python')
rhs =str(rt.Emap(tree))
f.write(" coneq["+str(ioc)+"]="+oc+"-"+rhs+".\n")
ioc+=1
f.write(" if any(abs(coneq)>tol):\n")
f.write(" return "+str(ip-1))
f.close()