def test_simpson_integeration2D(x, y, test_f) :
i = 2
xx = []
yy = []
err = []
I1 = []
I2 = []
I = []
II = (der_f4_1(np.max(x))-der_f4_1(np.min(x)))*der_f4_2(y)
while i< 52:
xx.append(np.linspace(np.min(x),np.max(x), i))
yy.append(np.linspace(np.min(y),np.max(y), i))
I1.append(simpson_integration(xx[i-2], test_f4_1))
I2.append(simpson_integration(xx[i-2], test_f4_2))
I.append(I1[i-2]*I2[i-2])
err.append(LA.norm(np.array(I[0:i])-II, 2))
i += 1
fig4 = plt.figure
fig4.Figure()
ax41 = plt.pyplot.subplot(121)
ax42 = plt.pyplot.subplot(122)
ax41.plot(np.array(xx[-2]), I, 'r', np.array(xx[-2]), II*np.ones((i-2,)) , 'g')
ax41.legend(['num_integral','ana_integral'])
ax41.set_title('num and ana integeral of x*exp(-(x**2+y**2))')
plt.pyplot.savefig('num_and_ana_int_fun4.pdf',dpi=200)
ax42.plot(np.array(xx[-2]), err)
ax42.legend(['norm2'])
ax42.set_title('norm2 of integeral of x*exp(-(x**2+y**2))')
plt.pyplot.savefig('num_and_ana_int_fun4_error .pdf',dpi=200)
return err, I
def test_simpson_integeration2(x, test_f):
i = 2
xx = []
err = []
I = []
II = der_f2(np.max(x)) - der_f2(np.min(x))
while i < 52:
xx.append(np.linspace(np.min(x), np.max(x), i))
I.append(simpson_integration(xx[i - 2], test_f))
err.append(LA.norm(np.array(I[0:i]) - II, 2))
i += 1
fig2 = plt.figure
fig2.Figure()
ax21 = plt.pyplot.subplot(121)
ax22 = plt.pyplot.subplot(122)
ax21.plot(np.array(xx[-2]), I, 'r', np.array(xx[-2]),
II * np.ones((i - 2, )), 'g')
ax21.legend(['num_integral', 'ana_integral'])
ax21.set_title('num and ana integeral of sin(x)/x')
plt.pyplot.savefig('num_and_ana_int_fun2.pdf', dpi=200)
ax22.plot(np.array(xx[-2]), err)
ax22.legend(['norm2'])
ax22.set_title('norm2 of integeral of sin(x)/x')
plt.pyplot.savefig('num_and_ana_int_fun2_error.pdf', dpi=200)
return err, I
def test_simpson_integeration3(x, test_f) :
i = 2
xx = []
err = []
I = []
while i< 52:
xx.append(np.linspace(np.min(x),np.max(x), i))
I.append(simpson_integration(xx[i-2], test_f))
err.append(LA.norm(np.array(I[0:i])-der_f3(0), 2))
i += 1
fig3 = plt.figure
fig3.Figure()
ax31 = plt.pyplot.subplot(311)
ax32 = plt.pyplot.subplot(312)
ax33 = plt.pyplot.subplot(313)
cx1 =[x1.real for x1 in I]
cy1 =[y1.real for y1 in I]
ax31.plot(cx1, cy1)
ax31.legend(['num_integral'])
ax31.set_title('num integeral of exp(sin(x**3))')
plt.pyplot.savefig('num_int_fun3.pdf',dpi=200)
cnums = der_f3(0)*np.ones((i-2,))
cx =[x.real for x in cnums]
cy =[y.real for y in cnums]
ax32.plot(cx, cy, 'o')
ax32.legend(['ana_integral'])
ax32.set_title('ana integeral of exp(sin(x**3))')
plt.pyplot.savefig('ana_int_fun3.pdf',dpi=200)
cx2 =[x2.real for x2 in err]
cy2 =[y2.real for y2 in err]
ax33.plot(cx2, cy2)
ax33.legend(['norm2'])
ax33.set_title('norm2 of integeral of exp(sin(x**3))')
plt.pyplot.savefig('ana_num_int_fun3_error.pdf',dpi=200)
return err, I
def integrate_a3():
x = np.linspace(0, 5, 10000)
eval_integral = simpson_integration(x, f_a3)
print('Integral a3 =', eval_integral)
def integrate_a2():
x = np.linspace(0.001, 1,
10000) #Not from 0 to 1, because we divide through x
eval_integral = simpson_integration(x, f_a2)
print('Integral a2 =', eval_integral)
def integrate_a1():
x = np.linspace(0, 5 * 10**4,
100000) #Linspace defines the integration limits
eval_integral = simpson_integration(x, f_a1)
print('Integral a1 =', eval_integral)