genTable.py

## Begin file genTable.py
## Created by Gregory Croisdale March 2017
## CreatePT for Computer Science Principles

## library importation and constant defintion for user use
from math import sin, cos, tan, exp, sqrt
pi = 3.14159265359
e = 2.71828182846

## initial variable declaration
fVal = [] ## y values of f(x)
gVal = [] ## y values of g(x)
xVal = [] ## x values of f(x) and g(x)
iVal = [] ## y values of intersection between f(x) and g(x)
xiVal = [] ## x values of intersection
t = 0 ## trapezoidal approximation of area
v = 0 ## volume of trapezoidal washer

## UI:
## user inputs python code to be used as function
f = eval("lambda x: {0}".format(input("f(x): ")))
g = eval("lambda x: {0}".format(input("g(x): ")))
## user defines bounds and delta
x = xmin = float(input("x min: "))
xmax = float(input("x max: "))
delx = float(input("delta x: "))
## delta for derivative calculation
delta = .000001

## Newton's method:
## function which subtracts user inputted equations for newton's method
def cfunc(x):
    return (f(x) - g(x))
## finds derivative with previously defined delta
def cderiv(x):
    return (cfunc(x+delta)-cfunc(x)) / delta
## newton's method, finds intersect of two equations
def rt(guess=2, trials=12, func=cfunc, deriv=cderiv):
    for i in range(0, trials):
        guess = guess - (func(guess)/deriv(guess))
    return guess

## coordinate generation:
## defines two intersects
int1 = rt(guess=xmin, trials=20)
int2 = rt(guess=xmax, trials=20)
## finds y values when functions are not yet intersecting
while x <= xmax:
   if x <= int1 or x >= int2:
       fVal += [f(x)]
       gVal += [g(x)]
       xVal += [x]
   x += delx
## finds y values of intersection
x = int1
while x < int2:
    iVal += [f(x)]
    xiVal += [x]
    iVal += [g(x)]
    xiVal += [x]
    x += delx
## adds final coordinate to f and g lists
fVal += [f(int1), f(int2)]
gVal += [g(int1), g(int2)]
xVal += [int1, int2]

## integral estimation
## calculates volume of intersect solid
i = 0
while i <= len(iVal) / 2 - 1:
    t += (abs(iVal[i] - iVal[i + 1]) + abs(iVal[i + 2] - iVal[i + 3])) / 2 * (xiVal[i + 2] - xiVal[i]) ## generates trapezoid
    v += (pi * (max(iVal[i], iVal[i + 1]) ** 2 - min(iVal[i], iVal[i + 1]) ** 2)) * delx ## generates left riemman washer
    i += 1

## output:
print("f(x) and g(x) intersect at (%s, %s) and (%s, %s)." % (int1, f(int1), int2, f(int2)))
print("The area of the intersection is %s units^2." % t)
print("The volume of the intersection revolved around the x axis is %s units^3." % v)
## exports data
open('f.coord','w').write(str(fVal).replace("[","").replace("]",""))
open('g.coord','w').write(str(gVal).replace("[","").replace("]",""))
open('x.coord','w').write(str(xVal).replace("[","").replace("]",""))
open('i.coord','w').write(str(iVal).replace("[","").replace("]",""))
open('xi.coord','w').write(str(xiVal).replace("[","").replace("]",""))
## End file genTable.py