#!/usr/bin/python -Wall

# ================================================================
# John Kerl
# kerl at math dot arizona dot edu
# 2008-05-12
# ================================================================

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

# ----------------------------------------------------------------
def usage():
	print >> sys.stderr, "Usage: %s [options]" % (sys.argv[0])
	print >> sys.stderr, "Options:"
	print >> sys.stderr, "  T=[number]"
	print >> sys.stderr, "  nt=[number]"
	print >> sys.stderr, "  nX=[number]"
	sys.exit(1)

# ----------------------------------------------------------------
# Brownian bridges using B_t - t B_1.

T  = 1
nt = 1000
nX = 20

argc = len(sys.argv)
for argi in range(1, argc):
	if   re.match(r'^T=',  sys.argv[argi]): T  = float(sys.argv[argi][2:])
	elif re.match(r'^nt=', sys.argv[argi]): nt = int  (sys.argv[argi][3:])
	elif re.match(r'^nX=', sys.argv[argi]): nX = int  (sys.argv[argi][3:])
	else: usage()

X0 = 0.0
t  = 0
dt = T/nt
Bt     = [0.0] * nX
sqrtdt = sqrt(dt)
I      = [0.0] * nX

ts = []
bridges = []

# First pass to find B(1)
while (t < T):
	for j in range(0, nX):
		dB  = random.gauss(0, sqrtdt)
		Bt[j] += dB
	ts.append(t)
	bridges.append(copy.copy(Bt))
	t  += dt

# Second pass to subtract off t*B1
numt = len(bridges)
for i in range(0, numt):
	t = ts[i]
	print "%11.7f" % (t),
	for j in range(0, nX):
		Bt = bridges[i][j]
		B1 = bridges[-1][j]
		Xt = Bt - t*B1
		print "%11.7f" % (Xt),
	print