May-27-2024, 10:20 AM
(This post was last modified: May-27-2024, 10:20 AM by Safinazsalem.)
I try to triple integrate the following function but it gives many errors:
I mean in
Here is the code I use:
IntegrationWarning: The integral is probably divergent, or slowly convergent.
IntegrationWarning: The maximum number of subdivisions (50) has been achieved. If increasing the limit yields no improvement it is advised to analyze the integrand in order to determine the difficulties.
IntegrationWarning: The algorithm does not converge. Roundoff error is detected in the extrapolation table. It is assumed that the requested tolerance cannot be achieved, and that the returned result (if full_output = 1) is the best which can be obtained.The function is
f(t1,t2,m)
(-(50*t1**2*(-16*(16 + 20*t1 + 6*t1**2 + 4*t1**3 + 3*t1**4) + (1 + t1)**2*(448 + 1568*t1 + 2400*t1**2 + 1920*t1**3 + 864*t1**4 + 240*t1**5 + 72*t1**6 + 42*t1**7 + 18*t1**8 + 3*t1**9)*math.exp((4*(1 + t1))/(2 + t1))) + m*(1 + t1)*(-128 + 1536*t1**2*math.exp((4*(1 + t1))/(2 + t1)) + 2112*t1**4*math.exp((4*(1 + t1))/(2 + t1)) + 1008*t1**5*math.exp((4*(1 + t1))/(2 + t1)) + 312*t1**6*math.exp((4*(1 + t1))/(2 + t1)) + 114*t1**7*math.exp((4*(1 + t1))/(2 + t1)) + 60*t1**8*math.exp((4*(1 + t1))/(2 + t1)) + 21*t1**9*math.exp((4*(1 + t1))/(2 + t1)) + 3*t1**10*math.exp((4*(1 + t1))/(2 + t1)) + 64*t1*(-1 + 6*math.exp((4*(1 + t1))/(2 + t1))) + 32*t1**3*(-1 + 78*math.exp((4*(1 + t1))/(2 + t1)))))/(4.*(1 + t1)*(2 + t1)*(-48 - 96*t1 + 8*(-3 + 2*m**2)*t1**2 + 8*(3 + 2*m**2)*t1**3 + (6 + 4*m**2)*t1**4 + 6*t1**5 + 3*t1**6))) * ((50 * t1**2) +5* (-(50*t1**2*(-16*(16 + 20*t1 + 6*t1**2 + 4*t1**3 + 3*t1**4) + (1 + t1)**2*(448 + 1568*t1 + 2400*t1**2 + 1920*t1**3 + 864*t1**4 + 240*t1**5 + 72*t1**6 + 42*t1**7 + 18*t1**8 + 3*t1**9)*math.exp((4*(1 + t1))/(2 + t1))) + (k - m)*(1 + t1)*(-128 + 1536*t1**2*math.exp((4*(1 + t1))/(2 + t1)) + 2112*t1**4*math.exp((4*(1 + t1))/(2 + t1)) + 1008*t1**5*math.exp((4*(1 + t1))/(2 + t1)) + 312*t1**6*math.exp((4*(1 + t1))/(2 + t1)) + 114*t1**7*math.exp((4*(1 + t1))/(2 + t1)) + 60*t1**8*math.exp((4*(1 + t1))/(2 + t1)) + 21*t1**9*math.exp((4*(1 + t1))/(2 + t1)) + 3*t1**10*math.exp((4*(1 + t1))/(2 + t1)) + 64*t1*(-1 + 6*math.exp((4*(1 + t1))/(2 + t1))) + 32*t1**3*(-1 + 78*math.exp((4*(1 + t1))/(2 + t1)))))/(4.*(1 + t1)*(2 + t1)*(-48 - 96*t1 + 8*(-3 + 2*(k - m)**2)*t1**2 + 8*(3 + 2*(k - m)**2)*t1**3 + (6 + 4*(k - m)**2)*t1**4 + 6*t1**5 + 3*t1**6))))I wonder is there a way to make python integrate this function smoothly.
I mean in
quad
one can pass various parameters to integrate.quad
to change the absolute tolerance by epsrel
or epsabs
. Or one can discard the singularity points by points=
. But in triple integral how to do so by tplquad
or nquad
. Also may be using if: else
will be helpful with this function, but I wonder how ?Here is the code I use:
from scipy import integrate import math import scipy k=3;a=0.1;nab=10**-9;n=0.94;kz= 0.002; # Define the function to be integrated def f(m,t1,t2): return (-(50*t1**2*(-16*(16 + 20*t1 + 6*t1**2 + 4*t1**3 + 3*t1**4) + (1 + t1)**2*(448 + 1568*t1 + 2400*t1**2 + 1920*t1**3 + 864*t1**4 + 240*t1**5 + 72*t1**6 + 42*t1**7 + 18*t1**8 + 3*t1**9)*math.exp((4*(1 + t1))/(2 + t1))) + m*(1 + t1)*(-128 + 1536*t1**2*math.exp((4*(1 + t1))/(2 + t1)) + 2112*t1**4*math.exp((4*(1 + t1))/(2 + t1)) + 1008*t1**5*math.exp((4*(1 + t1))/(2 + t1)) + 312*t1**6*math.exp((4*(1 + t1))/(2 + t1)) + 114*t1**7*math.exp((4*(1 + t1))/(2 + t1)) + 60*t1**8*math.exp((4*(1 + t1))/(2 + t1)) + 21*t1**9*math.exp((4*(1 + t1))/(2 + t1)) + 3*t1**10*math.exp((4*(1 + t1))/(2 + t1)) + 64*t1*(-1 + 6*math.exp((4*(1 + t1))/(2 + t1))) + 32*t1**3*(-1 + 78*math.exp((4*(1 + t1))/(2 + t1)))))/(4.*(1 + t1)*(2 + t1)*(-48 - 96*t1 + 8*(-3 + 2*m**2)*t1**2 + 8*(3 + 2*m**2)*t1**3 + (6 + 4*m**2)*t1**4 + 6*t1**5 + 3*t1**6))) * ((50 * t1**2) +5* (-(50*t1**2*(-16*(16 + 20*t1 + 6*t1**2 + 4*t1**3 + 3*t1**4) + (1 + t1)**2*(448 + 1568*t1 + 2400*t1**2 + 1920*t1**3 + 864*t1**4 + 240*t1**5 + 72*t1**6 + 42*t1**7 + 18*t1**8 + 3*t1**9)*math.exp((4*(1 + t1))/(2 + t1))) + (k - m)*(1 + t1)*(-128 + 1536*t1**2*math.exp((4*(1 + t1))/(2 + t1)) + 2112*t1**4*math.exp((4*(1 + t1))/(2 + t1)) + 1008*t1**5*math.exp((4*(1 + t1))/(2 + t1)) + 312*t1**6*math.exp((4*(1 + t1))/(2 + t1)) + 114*t1**7*math.exp((4*(1 + t1))/(2 + t1)) + 60*t1**8*math.exp((4*(1 + t1))/(2 + t1)) + 21*t1**9*math.exp((4*(1 + t1))/(2 + t1)) + 3*t1**10*math.exp((4*(1 + t1))/(2 + t1)) + 64*t1*(-1 + 6*math.exp((4*(1 + t1))/(2 + t1))) + 32*t1**3*(-1 + 78*math.exp((4*(1 + t1))/(2 + t1)))))/(4.*(1 + t1)*(2 + t1)*(-48 - 96*t1 + 8*(-3 + 2*(k - m)**2)*t1**2 + 8*(3 + 2*(k - m)**2)*t1**3 + (6 + 4*(k - m)**2)*t1**4 + 6*t1**5 + 3*t1**6)))) # Define the limits of integration a = 0.1 b = 5 # Perform the integration result, error = integrate.tplquad(f, 0.1, 2, lambda x: 0.1, lambda x: 2, lambda x,y: 0.1, lambda x,y: 2 ) print("result:", result)Any help is appreciated!