#!/usr/bin/python -Wall

# ================================================================
# John Kerl
# kerl.john.r@gmail.com
# 2008-02-08
# ================================================================

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

# ----------------------------------------------------------------
# Wikipedia:
#
# Approximation to
#   dy/dt = f(t,y) with y(t_0) = y_0.
# is
#   y_{n+1} = y_n + h/6(k1 + 2 k2 + 2 k3 + k4)
#   t_{n+1} = t_n + h
# where
#   k1 = f(t_n,       y_n)
#   k2 = f(t_n + h/2, y_n + k1 h/2)
#   k3 = f(t_n + h/2, y_n + k2 h/2)
#   k4 = f(t_n + h,   y_n + k3 h)



# ----------------------------------------------------------------
# 3rd attempt:
#   x'' + a x' + b x = g(t)
# Converting to a system of 1st-order ODEs:
#   y1 = x
#   y2 = x'
# Then
#   y1' =    y2
#   y2' = -a y2 - b y1 - g(t)
#
# ----------------------------------------------------------------

# ----------------------------------------------------------------
def f(t, y):
	return [y[1], -a*y[1] - b*y[0] - sin(c*t)]

# ----------------------------------------------------------------
a  = 2
b  = 3
c  = 4

h  = 0.01
t0 = 0.0

y0 = [1.0, 0.0]

niter = 800

eulery = copy.copy(y0)
rk4y   = copy.copy(y0)
t      = t0

for iter in range(0, niter):

	print "%11.7f  %11.7f %11.7f" % (t, rk4y[0], rk4y[1])

	k1 = f(t,     rk4y)
	k2 = f(t+h/2, vecadd(rk4y, vecsmul(k1, h/2)))
	k3 = f(t+h/2, vecadd(rk4y, vecsmul(k2, h/2)))
	k4 = f(t+h,   vecadd(rk4y, vecsmul(k3, h)))

	rk4y[0] += h/6 * (k1[0] + 2*k2[0] + 2*k3[0] + k4[0])
	rk4y[1] += h/6 * (k1[1] + 2*k2[1] + 2*k3[1] + k4[1])

	t += h