#!/usr/bin/python

# ================================================================
# This program displays Taylor-polynomial approximations and their
# errors.
#
# John Kerl
# kerl.john.r@gmail.com
# 2007-03-16
# ================================================================
# This software is released under the terms of the GNU GPL.
# Please see LICENSE.txt in the same directory as this file.
# ================================================================

from __future__ import division # 1/2 = 0.5, not 0.
from math import *

# For frange() and fact():
from kerl_common import *

# ----------------------------------------------------------------
#def f(x):
#   return atan(x)
#def pa(x):
#   return x
#def pb(x):
#   return x - x**3/3
#def pc(x):
#   return x - x**3/3 + x**5/5
#def pd(x):
#   return x - x**3/3 + x**5/5 - x**7/7

def f(x):
    return sin(x)
def pa(x):
    return x
def pb(x):
    return x - x**3/fact(3)
def pc(x):
    return x - x**3/fact(3) + x**5/fact(5)
def pd(x):
    return x - x**3/fact(3) + x**5/fact(5) - x**7/fact(7)

# ----------------------------------------------------------------
xlo = -1.0
xhi =  1.0
nx  = 200
dx  = (xhi - xlo) / nx

for x in mfrange(xlo, dx, xhi):
    y = f(x)
    ya = pa(x)
    yb = pb(x)
    yc = pc(x)
    yd = pd(x)

    print "%9.4f %9.4f %9.4f %9.4f %9.4f %9.4f %9.2e %9.2e %9.2e %9.2e" \
        % (x, y, ya, yb, yc, yd, y-ya, y-yb, y-yc, y-yd)