def test_taylor_approx_x():
x = np.array([3,4,5,6,7,8])
f = tp.tanh(x)
trial = tp.taylor(x,f,0,100)[0]
actual = x
print("Trial: ", trial)
print("Actual: ", actual)
np.testing.assert_equal(actual, trial)
x = np.array([3,4,5,6,7,8])
func = np.vectorize(tp.inverse)
f = func(x)
trial = tp.taylor(x,f,0,100)[0]
actual = x
print("Trial: ", trial)
print("Actual: ", actual)
np.testing.assert_equal(actual, trial)
x = np.array([3,4,5,6,7,8])
func = np.vectorize(tp.f)
f = func(x)
trial = tp.taylor(x,f,0,100)[0]
actual = x
print("Trial: ", trial)
print("Actual: ", actual)
np.testing.assert_equal(actual, trial)
def test_taylor_approx_acc():
x = np.array([3,4,5,6,7,8])
f = tp.tanh(x)
trial = tp.taylor(x,f,0,100)[1] #returns 2 arrays, takes the second entry
actual = tp.tanh(3)
print("Trial: ", trial[0])
print("Actual: ", actual)
nose.tools.assert_almost_equal(actual, trial[0], 2)
x = np.array([3,4,5,6,7,8])
func = np.vectorize(tp.inverse)
f = func(x)
trial = tp.taylor(x,f,0,100)[1]
actual = tp.inverse(3)
print("Trial: ", trial[0])
print("Actual: ", actual)
nose.tools.assert_almost_equal(actual, trial[0], 2)
x = np.array([3,4,5,6,7,8])
func = np.vectorize(tp.f)
f = func(x)
trial = tp.taylor(x,f,0,100)[1]
actual = tp.f(3)
print("Trial: ", trial[0])
print("Actual: ", actual)
nose.tools.assert_almost_equal(actual, trial[0], 2)
def make_plots(x, i):
for f, s in (
(np.sin(x), "sin(x)"), (np.tanh(x), "tanh(x)"),
(my_functions.poly(x), "poly(x)"), (my_functions.denom(x), "denom(x)"),
(my_functions.theta(x), "theta(x)")
): #ensures all functions are being plotted, including the sin(x) test function.
for n in range(
0, 6): #range enables 0-5th order approximations to be plotted
out_X, out_fapprox = taylor_approx.taylor(x, f, i,
n) #plots approximations
plt.figure(figsize=(3, 3))
plt.ylabel('y') #y-axis label
plt.xlabel('x') #x-axis label
font = {'size': 16} #font size
title = n #enables the title to be each function's name
plt.title(title)
plt.plot(out_X, out_fapprox, label=s + "approx", color="green"
) #green plot demonstrates the ordered approximation
plt.plot(x, f, label=s,
color="blue") #blue plot demonstrates the actual function
plt.legend(loc='upper left', frameon=False)
plt.plot(
x[500], f[500], 'r*'
) #marks the specific point which function is being approximated around
plt.show()
def test_taylor_5():
"""test_taylor_5()
Tests for the accuracy of the Taylor formula approximation at point x[50] by calling sin(x) and taylor; fifth order derivative approximation
"""
a = -5
b = 5
numberOfPoints = 101
x = np.linspace(a, b, numberOfPoints)
f = my_functions.sin(x)
i = 50
out_X, out_fapprox = taylor_approx.taylor(
x, f, i - 10, n=5) #approximating x[50] at x[40], described as i-10
desired = -0.0005
np.testing.assert_almost_equal(out_fapprox[i], desired, 1)
def test_taylor_approx():
"""Tests our function taylor(x,f,i,n) to approximate the Gaussian function around
some point arbitrarily chosen."""
a, b, n = 0, 3, 1000
t = np.linspace(a, b, n)
desired = ac.g(a, b, n)
# Values obtained from taylor approximation
actual = ta.taylor(t, desired, 501, 10)
# Debug message
print("We expected this: ", desired[500:503], " but got this: ",
actual[1][500:503])
# Testing accuracy
for k in range(500, 502):
nose.tools.assert_almost_equal(desired[k], actual[1][k], 4)