#!/usr/bin/python -Wall

# ================================================================
# John Kerl
# kerl.john.r@gmail.com
# 2008-02-06
# ================================================================
# 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
from sackmat_m import *

# ----------------------------------------------------------------
argc = len(sys.argv)
if (argc == 1):
	A = sackmat([
		[ -2,  1,  0,  0,  0,  0,  0,  1],
		[  1, -2,  1,  0,  0,  0,  0,  0],
		[  0,  1, -2,  1,  0,  0,  0,  0],
		[  0,  0,  1, -2,  1,  0,  0,  0],
		[  0,  0,  0,  1, -2,  1,  0,  0],
		[  0,  0,  0,  0,  1, -2,  1,  0],
		[  0,  0,  0,  0,  0,  1, -2,  1],
		[  1,  0,  0,  0,  0,  0,  1, -2]])
elif (argc == 2):
	file_name = sys.argv[1]
	A = read_matrix(float, file_name)
else:
	print >> sys.stderr, "Usage: %s [file name].\n" % (sys.argv[0])
	print >> sys.stderr, "Use \"-\" as file name if input is stdin."
	sys.exit(1)

# ----------------------------------------------------------------
nr = A.square_dim()

[L, V] = rs_eigensystem(A)

for j in range(0, nr):
	ell  = L[j]
	v    = V.get_column(j)
	Av   = A*v
	ellv = vecsmul(v, ell)
	diff = vecsub(Av, ellv)

	print "ell:   ",; print_row_vector([ell])
	print "v:     ",; print_row_vector(v)
	print "A v:   ",; print_row_vector(Av)
	print "ell v: ",; print_row_vector(ellv)
	print "Diff:  ",; print_row_vector(diff)
	print