def secante(xn, fn, error):
errorTemp = 1000000
maxIt = 100
cont = 0
h = error / 10
xAnt = xn
prs = Parse()
prs.setEc(fn)
historial = []
historial.append([xn, 0.0])
while (errorTemp > error and maxIt > cont):
prs.addVariable("x", xAnt)
resfn = prs.evaluate()
prs.addVariable("x", xAnt + h)
resfxh = prs.evaluate()
prs.addVariable("x", xAnt - h)
resfx_h = prs.evaluate()
if ((resfxh - resfx_h) == 0):
print("division entre zero")
break
x = xAnt - ((2 * h * resfn) / (resfxh - resfx_h))
errorTemp = abs(xAnt - x)
historial.append([xAnt, errorTemp])
xAnt = x
if (errorTemp < error):
break
cont += 1
return x, historial
def bolzano(fn, a, b):
prs = Parse()
prs.setEc(fn)
prs.addVariable("x", a)
evA = prs.evaluate()
prs.addVariable("x", b)
evB = prs.evaluate()
print("bolzano val", evA, evB)
if ((evA * evB) < 0):
return True
return False
def trapecio(a, b, fn, n):
h = (b - a) / n
prs = Parse()
prs.setEc(fn)
i = a + h
sum = 0
while (i < b):
prs.addVariable("x", i)
sum += prs.evaluate()
i += h
prs.addVariable("x", a)
fa = prs.evaluate()
prs.addVariable("x", b)
fb = prs.evaluate()
resp = h * (((fa + fb) / 2) + sum)
return resp
def imagenNR(LFn, Lx):
tparse = Parse()
LFxn = []
for i in range(len(LFn)):
tparse.setEc(LFn[i])
tparse.addVarFromList(Lx)
LFxn.append(tparse.evaluate())
return LFxn
def getY(formula, x):
prs = Parse()
y = []
prs.setEc(formula)
for i in x:
prs.addVariable("x", i)
yT = prs.evaluate()
#print(yT)
y.append(yT)
return y
def simpson(a, b, fn, n):
h = (b - a) / (2 * n)
prs = Parse()
prs.setEc(fn)
parSum = 0
imparSum = 0
i = a + h
xi = np.arange(i, b, h)
for index in range(len(xi)):
prs.addVariable("x", xi[index])
if (index % 2 == 0):
imparSum += prs.evaluate()
else:
parSum += prs.evaluate()
prs.addVariable("x", a)
fa = prs.evaluate()
prs.addVariable("x", b)
fb = prs.evaluate()
resp = (h / 3) * (fa + fb + (2 * parSum) + (4 * imparSum))
return resp
def jacobiana(LFn, Lx, err):
tparse = Parse()
Jmatrix = []
h = err / 10
TLx = []
for i in range(len(LFn)):
mTemp = []
for j in range(len(Lx)):
TLx = list(Lx)
TLx[j] = Lx[j] + h
tparse.setEc(LFn[i])
tparse.addVarFromList(TLx)
rH = tparse.evaluate()
TLx = list(Lx)
TLx[j] = Lx[j] - h
tparse.addVarFromList(TLx)
r_H = tparse.evaluate()
DR = (rH - r_H) / (2 * (h * 100))
mTemp.append(DR)
Jmatrix.append(mTemp)
result = Jmatrix
return result
def eulerSimple(df, xn, yn, h, xf):
prs = Parse()
prs.setEc(df)
h = float(h)
xt = xn
yt = yn
while (xt < xf):
prs.addVariable("x", xt)
prs.addVariable("y", yt)
yt = yt + h * (prs.evaluate())
print(yt)
xt = round(xt + h, 15)
return yt
def puntofijo(xn, fn, error):
maxIt = 100
historial = []
xr = xn
prs = Parse()
fn = fn + "+x"
prs.setEc(fn)
historial.append([xn, 0])
for i in range(maxIt):
xAnt = xr
prs.addVariable("x", xr)
xr = prs.evaluate()
print("xr", xr)
errorTemp = abs(xAnt - xr)
historial.append([xr, errorTemp])
if (errorTemp < error):
break
return xr, historial
