'''equation solver using attributes and introspection''' from __future__ import division class Solver(object): '''takes a function, named arg value (opt.) and returns a Solver object''' def __init__(self,f,**args): self._f=f self._args={} # see important note on order of operations in __setattr__ below. for arg in f.func_code.co_varnames[0:f.func_code.co_argcount]: self._args[arg]=None self._setargs(**args) def __repr__(self): argstring=','.join(['%s=%s' % (arg,str(value)) for (arg,value) in self._args.items()]) if argstring: return 'Solver(%s,%s)' % (self._f.func_code.co_name, argstring) else: return 'Solver(%s)' % self._f.func_code.co_name def __getattr__(self,name): '''used to extract function argument values''' self._args[name] return self._solve_for(name) def __setattr__(self,name,value): '''sets function argument values''' # Note - once self._args is created, no new attributes can # be added to self.__dict__. This is a good thing as it throws # an exception if you try to assign to an arg which is inappropriate # for the function in the solver. if self.__dict__.has_key('_args'): if name in self._args: self._args[name]=value else: raise KeyError, name else: object.__setattr__(self,name,value) def _setargs(self,**args): '''sets values of function arguments''' for arg in args: self._args[arg] # raise exception if arg not in _args setattr(self,arg,args[arg]) def _solve_for(self,arg): '''Newton's method solver''' TOL=0.0000001 # tolerance ITERLIMIT=1000 # iteration limit CLOSE_RUNS=10 # after getting close, do more passes args=self._args if self._args[arg]: x0=self._args[arg] else: x0=1 if x0==0: x1=1 else: x1=x0*1.1 def f(x): '''function to solve''' args[arg]=x return self._f(**args) fx0=f(x0) n=0 while 1: # Newton's method loop here fx1 = f(x1) if fx1==0 or x1==x0: # managed to nail it exactly break if abs(fx1-fx0)ITERLIMIT: print "Failed to converge; exceeded iteration limit" break slope=(fx1-fx0)/(x1-x0) if slope==0: if close_flag: # we're close but have zero slope, finish break else: print 'Zero slope and not close enough to solution' break x2=x0-fx0/slope # New 'x1' fx0 = fx1 x0=x1 x1=x2 n+=1 self._args[arg]=x1 return x1 def tvm(pv,fv,pmt,n,i): '''equation for time value of money''' i=i/100 tmp=(1+i)**n return pv*tmp+pmt/i*(tmp-1)-fv