#  Demonstration code for Scientific Computing class,
#  http://www.math.nyu.edu/faculty/goodman/teaching/SciComp2022/
#  IntegrationDemo.py
#  Demonstrate a software package, with IntegrandClass.py
#  and IntegrationPackage.py

import IntegrationPackage as ip      #  Code to do numerical integration
import IntegrandClass     as ic      #  How the integrand is defined
import numpy              as np      #  to use numpy arrays

# use the package to integrate a polynomial

d = 2               # a quadratic polynomial
c = np.zeros(d+1)   # an array for the coefficients in f(x)
c[0] = 1.           # f(x) = 1+2x+3x^3
c[1] = 2.
c[2] = 3.

poly = ic.Integrand(d, c)     # a polynomial class instance with these coefficients

x = 0.
outString = "Integrand: f(x) with x ={x:6.2f} is f ={f:6.2f}"
outString = outString.format(x = x, f = poly.f(x) )
print(outString)

x = 2.
outString = "Integrand: f(x) with x ={x:6.2f} is f ={f:6.2f}"
outString = outString.format(x = x, f = poly.f(x) )
print(outString)

n = 1000
ans = ip.Integrate( poly, -1., 1., n)
outString = "Approximate integral using {n:5d} points is {ans:8.4f}"
outString = outString.format(n = n, ans = ans)
print(outString)

n = 10000
ans = ip.Integrate( poly, -1., 1., n)
outString = "Approximate integral using {n:5d} points is {ans:8.4f}"
outString = outString.format(n = n, ans = ans)
print(outString)