How to plot integration equation using Python?
I have a few of integration equations and need to convert it into Python. The problem is when I tried to plot a graph according to the equation, some of the plot is not same with the original one.
The first equation is the error probability of authentication in normal operation:
The second equation is the error probability of authentication under MIM attack:
The error probability can be calculated by:
It is noted that:
Supposedly, the graph (original) will be shown like this:
Pe^normal = blue lines
Pe^MIM = red lines
Differences between two error probabilities = green lines
I tried to code it into Python and this is my full codes:
import matplotlib.pyplot as plt
import math
import numpy as np
from scipy.special import iv,modstruve
x=np.arange(0.1,21,1)
x = np.array(x)
t = 0.9
y = (np.exp(t*x/2)*(iv(0, t*x/2) - modstruve(0,t*x/2))-1)/(np.exp(t*x)-1)
z = (np.exp((1-t**2)*x/2)*(iv(0, (1-t**2)*x/2) - modstruve(0,(1-t**2)*x/2))-1)/(np.exp((1-t**2)*x)-1)
z2= y+z
plt.plot(x, y,'o', color='red',label='Normal')
plt.plot(x, z2, '-', color='black', label='MIM')
plt.plot(x, z, marker='s', linestyle='--', color='g', label='DIFF')
plt.xlabel('Mean photon number N')
plt.ylabel('Error probabiity')
plt.scatter(x,y)
plt.text(10, 0.4, 't=0.9', size=12, ha='center', va='center')
plt.ylim([0, 0.5])
plt.xlim([0, 20])
plt.legend()
plt.show()
The graph produce from the code is:
It looks like that my plot is not same with the original one in terms N=0 of Pe^MIM (red line) and differences between two error probabilities (green line).
I hope that anyone may help me to solve this problem.
Thank you.
python integral
asked Dec 28 '18 at 8:34
Afir Afir
10611
add a comment |
I have a few of integration equations and need to convert it into Python. The problem is when I tried to plot a graph according to the equation, some of the plot is not same with the original one.
The first equation is the error probability of authentication in normal operation:
The second equation is the error probability of authentication under MIM attack:
The error probability can be calculated by:
It is noted that:
Supposedly, the graph (original) will be shown like this:
Pe^normal = blue lines
Pe^MIM = red lines
Differences between two error probabilities = green lines
I tried to code it into Python and this is my full codes:
import matplotlib.pyplot as plt
import math
import numpy as np
from scipy.special import iv,modstruve
x=np.arange(0.1,21,1)
x = np.array(x)
t = 0.9
y = (np.exp(t*x/2)*(iv(0, t*x/2) - modstruve(0,t*x/2))-1)/(np.exp(t*x)-1)
z = (np.exp((1-t**2)*x/2)*(iv(0, (1-t**2)*x/2) - modstruve(0,(1-t**2)*x/2))-1)/(np.exp((1-t**2)*x)-1)
z2= y+z
plt.plot(x, y,'o', color='red',label='Normal')
plt.plot(x, z2, '-', color='black', label='MIM')
plt.plot(x, z, marker='s', linestyle='--', color='g', label='DIFF')
plt.xlabel('Mean photon number N')
plt.ylabel('Error probabiity')
plt.scatter(x,y)
plt.text(10, 0.4, 't=0.9', size=12, ha='center', va='center')
plt.ylim([0, 0.5])
plt.xlim([0, 20])
plt.legend()
plt.show()
The graph produce from the code is:
It looks like that my plot is not same with the original one in terms N=0 of Pe^MIM (red line) and differences between two error probabilities (green line).
I hope that anyone may help me to solve this problem.
Thank you.
python integral
asked Dec 28 '18 at 8:34
Afir Afir
10611
Looks like a math issue. You did not show us a formula forP^{Auth, MIM}, also I note that you calculate thedifffirst and then getP^{Auth, MIM}from the diff. Is that a supposed method?
– Konstantin Sekeresh
Dec 28 '18 at 9:00
@ Konstantin Sekeresh.P^{Auth, MIM}was not given in this calculation. For thediff, I just try & error to calculate it using theP^{Auth, MIM}, and I know maybe my calculation is wrong. Thus, I need clarification from others about this calculation.
– Afir
Dec 28 '18 at 13:34
@ Konstantin Sekeresh.It can be noted that the difference isP^{Auth, MIM}-P^{Auth, normal}.
– Afir
Dec 29 '18 at 4:38
add a comment |
I have a few of integration equations and need to convert it into Python. The problem is when I tried to plot a graph according to the equation, some of the plot is not same with the original one.
The first equation is the error probability of authentication in normal operation:
The second equation is the error probability of authentication under MIM attack:
The error probability can be calculated by:
It is noted that:
Supposedly, the graph (original) will be shown like this:
Pe^normal = blue lines
Pe^MIM = red lines
Differences between two error probabilities = green lines
I tried to code it into Python and this is my full codes:
import matplotlib.pyplot as plt
import math
import numpy as np
from scipy.special import iv,modstruve
x=np.arange(0.1,21,1)
x = np.array(x)
t = 0.9
y = (np.exp(t*x/2)*(iv(0, t*x/2) - modstruve(0,t*x/2))-1)/(np.exp(t*x)-1)
z = (np.exp((1-t**2)*x/2)*(iv(0, (1-t**2)*x/2) - modstruve(0,(1-t**2)*x/2))-1)/(np.exp((1-t**2)*x)-1)
z2= y+z
plt.plot(x, y,'o', color='red',label='Normal')
plt.plot(x, z2, '-', color='black', label='MIM')
plt.plot(x, z, marker='s', linestyle='--', color='g', label='DIFF')
plt.xlabel('Mean photon number N')
plt.ylabel('Error probabiity')
plt.scatter(x,y)
plt.text(10, 0.4, 't=0.9', size=12, ha='center', va='center')
plt.ylim([0, 0.5])
plt.xlim([0, 20])
plt.legend()
plt.show()
The graph produce from the code is:
It looks like that my plot is not same with the original one in terms N=0 of Pe^MIM (red line) and differences between two error probabilities (green line).
I hope that anyone may help me to solve this problem.
Thank you.
python integral
asked Dec 28 '18 at 8:34
Afir Afir
10611
I have a few of integration equations and need to convert it into Python. The problem is when I tried to plot a graph according to the equation, some of the plot is not same with the original one.
The first equation is the error probability of authentication in normal operation:
The second equation is the error probability of authentication under MIM attack:
The error probability can be calculated by:
It is noted that:
Supposedly, the graph (original) will be shown like this:
Pe^normal = blue lines
Pe^MIM = red lines
Differences between two error probabilities = green lines
I tried to code it into Python and this is my full codes:
import matplotlib.pyplot as plt
import math
import numpy as np
from scipy.special import iv,modstruve
x=np.arange(0.1,21,1)
x = np.array(x)
t = 0.9
y = (np.exp(t*x/2)*(iv(0, t*x/2) - modstruve(0,t*x/2))-1)/(np.exp(t*x)-1)
z = (np.exp((1-t**2)*x/2)*(iv(0, (1-t**2)*x/2) - modstruve(0,(1-t**2)*x/2))-1)/(np.exp((1-t**2)*x)-1)
z2= y+z
plt.plot(x, y,'o', color='red',label='Normal')
plt.plot(x, z2, '-', color='black', label='MIM')
plt.plot(x, z, marker='s', linestyle='--', color='g', label='DIFF')
plt.xlabel('Mean photon number N')
plt.ylabel('Error probabiity')
plt.scatter(x,y)
plt.text(10, 0.4, 't=0.9', size=12, ha='center', va='center')
plt.ylim([0, 0.5])
plt.xlim([0, 20])
plt.legend()
plt.show()
The graph produce from the code is:
It looks like that my plot is not same with the original one in terms N=0 of Pe^MIM (red line) and differences between two error probabilities (green line).
I hope that anyone may help me to solve this problem.
Thank you.
python integral
python integral
asked Dec 28 '18 at 8:34
Afir Afir
10611
asked Dec 28 '18 at 8:34
Afir Afir
10611
edited Dec 29 '18 at 4:40
Afir
asked Dec 28 '18 at 8:34
Afir Afir
10611
asked Dec 28 '18 at 8:34
Afir Afir
10611
asked Dec 28 '18 at 8:34
Afir Afir
10611
10611
Looks like a math issue. You did not show us a formula forP^{Auth, MIM}, also I note that you calculate thedifffirst and then getP^{Auth, MIM}from the diff. Is that a supposed method?
– Konstantin Sekeresh
Dec 28 '18 at 9:00
@ Konstantin Sekeresh.P^{Auth, MIM}was not given in this calculation. For thediff, I just try & error to calculate it using theP^{Auth, MIM}, and I know maybe my calculation is wrong. Thus, I need clarification from others about this calculation.
– Afir
Dec 28 '18 at 13:34
@ Konstantin Sekeresh.It can be noted that the difference isP^{Auth, MIM}-P^{Auth, normal}.
– Afir
Dec 29 '18 at 4:38
add a comment |
Looks like a math issue. You did not show us a formula forP^{Auth, MIM}, also I note that you calculate thedifffirst and then getP^{Auth, MIM}from the diff. Is that a supposed method?
– Konstantin Sekeresh
Dec 28 '18 at 9:00
@ Konstantin Sekeresh.P^{Auth, MIM}was not given in this calculation. For thediff, I just try & error to calculate it using theP^{Auth, MIM}, and I know maybe my calculation is wrong. Thus, I need clarification from others about this calculation.
– Afir
Dec 28 '18 at 13:34
@ Konstantin Sekeresh.It can be noted that the difference isP^{Auth, MIM}-P^{Auth, normal}.
– Afir
Dec 29 '18 at 4:38
Looks like a math issue. You did not show us a formula for
P^{Auth, MIM}, also I note that you calculate the diff first and then get P^{Auth, MIM} from the diff. Is that a supposed method?– Konstantin Sekeresh
Dec 28 '18 at 9:00
Looks like a math issue. You did not show us a formula for
P^{Auth, MIM}, also I note that you calculate the diff first and then get P^{Auth, MIM} from the diff. Is that a supposed method?– Konstantin Sekeresh
Dec 28 '18 at 9:00
@ Konstantin Sekeresh.
P^{Auth, MIM} was not given in this calculation. For the diff, I just try & error to calculate it using the P^{Auth, MIM}, and I know maybe my calculation is wrong. Thus, I need clarification from others about this calculation.– Afir
Dec 28 '18 at 13:34
@ Konstantin Sekeresh.
P^{Auth, MIM} was not given in this calculation. For the diff, I just try & error to calculate it using the P^{Auth, MIM}, and I know maybe my calculation is wrong. Thus, I need clarification from others about this calculation.– Afir
Dec 28 '18 at 13:34
@ Konstantin Sekeresh.It can be noted that the difference is
P^{Auth, MIM}- P^{Auth, normal}.– Afir
Dec 29 '18 at 4:38
@ Konstantin Sekeresh.It can be noted that the difference is
P^{Auth, MIM}- P^{Auth, normal}.– Afir
Dec 29 '18 at 4:38
add a comment |
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Looks like a math issue. You did not show us a formula for
P^{Auth, MIM}, also I note that you calculate thedifffirst and then getP^{Auth, MIM}from the diff. Is that a supposed method?– Konstantin Sekeresh
Dec 28 '18 at 9:00
@ Konstantin Sekeresh.
P^{Auth, MIM}was not given in this calculation. For thediff, I just try & error to calculate it using theP^{Auth, MIM}, and I know maybe my calculation is wrong. Thus, I need clarification from others about this calculation.– Afir
Dec 28 '18 at 13:34
@ Konstantin Sekeresh.It can be noted that the difference is
P^{Auth, MIM}-P^{Auth, normal}.– Afir
Dec 29 '18 at 4:38