#!/usr/bin/python -Wall

# ================================================================
# Generates an n x n discrete-Laplacian matrix for the periodic case.
#
# bash$ disclap 6
# -2  1  0  0  0  1
#  1 -2  1  0  0  0
#  0  1 -2  1  0  0
#  0  0  1 -2  1  0
#  0  0  0  1 -2  1
#  1  0  0  0  1 -2
#
# John Kerl
# kerl.john.r@gmail.com
# 2008-02-11
# ================================================================
# 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.
import sys

argc = len(sys.argv)
if (argc != 2):
	print >> sys.stderr, "Usage: %s {n}" % (sys.argv[0])
	sys.exit(1)

n = int(sys.argv[1])

for i in range(0, n):
	for j in range(0, n):
		if (i == j):
			print "%2d" % (-2),
		elif (i == j-1):
			print "%2d" % (1),
		elif (i == j+1):
			print "%2d" % (1),
		elif ((i == n-1) and (j == 0)):
			print "%2d" % (1),
		elif ((i == 0) and (j == n-1)):
			print "%2d" % (1),
		else:
			print "%2d" % (0),
	print