def method(fx,xi,xf,tol,iter,e = 000):
xi = float(xi)
xf = float(xf)
tol = float(tol)
yi = eval(fx,xi)
yf = eval(fx,xf)
xis = []
xfs = []
xms = []
yms = []
errors = []
if(yi*yf>0):
return {'status': "FAIL", 'message': "The interval is not valid"}
elif (yi==0):
return {'status': "FAIL", 'message': "The lower limit "+str(xi)+" is a root"}
elif (yf==0):
return {'status': "FAIL", 'message': "The lower limit "+str(xf)+" is a root"}
else:
error = tol*2
con = 1
ym = 1
xm = (xi+xf)/2
while(ym!=0 and error>tol and con<=int(iter)):
if(con>1):
xm = nxm
ym = float(eval(fx,xm))
xxi = xi
xxf = xf
if(ym*yi>0):
xi = xm
else:
xf = xm
nxm = float((xi+xf)/2)
if(e==1):
error = abs((nxm-xm)/nxm)
else:
error = abs(nxm-xm)
xis.append(xxi)
xfs.append(xxf)
xms.append(xm)
yms.append(ym)
errors.append(error)
con += 1
table = {'iter': con-1, 'xi' : xis, 'xf': xfs, 'ym':yms,'error':errors}
if(ym == 0):
return {'status': "SUCESS", 'message': str(xm)+" is a root with a error of " + str(error), 'xm' : xm,
'error':error,'table':table, 'stopBy':'xm'}
elif(error<tol):
return {'status': "SUCESS", 'message': str(xm)+" is a root with a error of " + str(error), 'xm' : xm,
'error':error, 'table':table, 'stopBy':'tol'}
else:
return {'status': "SUCESS", 'message': str(xm)+" is a possible root with a error of " + str(error), 'xm' : xm,
'error':error, 'table':table, 'stopBy':'iter'}
def method(tolerance,inferior_limit,superior_limit,iterations,function,e):
function_0=float(eval(function,inferior_limit))
function_1=float(eval(function,superior_limit))
if(function_0==0):
return {'status': "FAIL", 'message': "The lower limit "+str(inferior_limit)+" is a root"}
else:
counter=0
den=function_1-function_0
error=tolerance+1
errors=[]
xns = []
function1s = []
while error>tolerance and function_1!=0 and den!=0 and counter < iterations:
x_n= superior_limit-function_1*((superior_limit-inferior_limit)/den)
if(e==1):
error=abs((x_n-superior_limit)/x_n)
else:
error=abs(x_n-superior_limit)
inferior_limit=superior_limit
function_0=function_1
superior_limit=x_n
function_1=eval(function,superior_limit)
den=function_1-function_0
errors.append(error)
xns.append(x_n)
function1s.append(function_1)
counter=counter+1
table = {'iter': counter-1, 'xi' : inferior_limit, 'xf': superior_limit, 'xn':xns,'error':errors}
if (function_1 == 0):
return {'status': "SUCESS", 'message': str(superior_limit) + " is a root with a error of " + str(error),
'xn': x_n,
'error': error, 'table': table, 'stopBy': 'xm'}
elif (error < tolerance):
return {'status': "SUCESS", 'message': str(x_n) + " is a root with a error of " + str(error), 'xn': x_n,
'error': error, 'table': table, 'stopBy': 'tol'}
elif (den==0):
return {'status': "FAIL", 'message':'There is a possible multiple root',
'error':error,'table':table, 'stopBy':'derivate'}
else:
return {'status': "SUCESS", 'message': str(x_n) + " is a possible root with a error of " + str(error),
'x_n': x_n,
'error': error, 'table': table, 'stopBy': 'iter'}
def method(tolerance,xapproximate,iterations,function,derivative_function,e):
function_evaluated=float(eval(function,xapproximate))
derivative_evaluated= float(eval(derivative_function,xapproximate))
counter=0
error=tolerance+1
xns=[]
errors = []
fns = []
dfns = []
while error>tolerance and function_evaluated!=0 and derivative_function!=0 and counter<iterations:
x_n = xapproximate-(function_evaluated/derivative_evaluated)
f_n=float(eval(function,x_n))
d_f_n=float(eval(derivative_function,x_n))
function_evaluated=f_n
derivative_evaluated=d_f_n
if(e==1):
error=abs((x_n-xapproximate)/x_n)
else:
error=abs(x_n-xapproximate)
xapproximate=x_n
errors.append(error)
xns.append(x_n)
fns.append(f_n)
dfns.append(d_f_n)
counter=counter+1
table = {'iter': counter-1, 'xns' : xns, 'fns': fns, 'dfns':dfns,'error':errors}
if(function_evaluated == 0):
return {'status': "SUCESS", 'message': str(xapproximate)+" is a root with a error of " + str(error), 'xn' : xapproximate,
'error':error,'table':table, 'stopBy':'xm'}
elif(error<tolerance):
return {'status': "SUCESS", 'message': str(xapproximate)+" is a root with a error of " + str(error), 'xn' : xapproximate,
'error':error, 'table':table, 'stopBy':'tol'}
elif(derivative_evaluated==0):
return {'status': "FAIL", 'message': str(xapproximate)+" is a root with a possible multiple root", 'xn' : xapproximate,
'error':error,'table':table, 'stopBy':'derivate'}
else:
return {'status': "SUCESS", 'message': str(xapproximate)+" is a possible root with a error of " + str(error), 'xn' : xapproximate,
'error':error, 'table':table, 'stopBy':'iter'}
def method(fx,delta,xi):
yis = []
yyis = []
xi = float(xi)
delta = float(delta)
yi = eval(fx,xi)
yis.append(yi)
xxi = xi+ delta
yyi = eval(fx,xxi)
yyis.append(yyi)
c=0
while(int(yi*yyi)>0):
xi = xi+delta
yi = eval(fx,xi)
yis.append(yi)
xxi = xi+ delta
yyi = eval(fx,xxi)
yyis.append(yyi)
c += 1
if c<=10:
print str(xi) + "\n"
yis.append(yyis[len(yyis)-1])
return {'status': 'SUCCES', 'messaje':'There is a root in the interval ['+
str(xi)+ ' , '+str(xxi)+']', 'xi':str(xi), 'xf':str(xxi), 'list':yis }
