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April24_numerical_integration.py
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April24_numerical_integration.py
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# In this file I have numerical integration methods
# In particular, I have trapezoidal and Riemann sum methods
# import tools
import math
import numpy as np
from scipy.linalg import solve_banded
from numpy.linalg import norm
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d
# composite, nonuniform, trapezoidal rule
def trap_nonuni(f_vals, x_vals):
num = len(x_vals)
# define the mesh spacing
h_vals = []
for i in range(1, num):
h = x_vals[i][0] - x_vals[i-1][0]
h_vals.append(h)
# trapezoidal sum
sum_trap = 0
for i in range(1, num):
val = ((f_vals[i][0] + f_vals[i-1][0]) / 2) * h_vals[i-1]
sum_trap += val
return sum_trap
# A 'Riemann Integral'
# SUM(i) f(xi) * hi
def int_constant(f_vals, x_vals):
num = len(f_vals)
# define the mesh spacing
h_vals = []
for i in range(1, num):
h = x_vals[i][0] - x_vals[i-1][0]
h_vals.append(h)
int_final = 0
for i in range(1, num):
val = f_vals[i][0] * h_vals[i-1]
int_final += val
return int_final