import math as mt
import copy
class SquareMatrix():
def __init__(self,a):
self.A = self.ori = a
self.n = len(a)
self.trans = []
self.Q = [[0]*self.n for i in range(self.n)]
for i in range(self.n):
self.Q[i][i] = 1
def get_max(self):
max = -1e9
maxx = 0
maxy = 0
for i in range(self.n):
for j in range(self.n):
if i==j:
continue
if abs(self.A[i][j])>max:
maxx = i
maxy= j
max = abs(self.A[i][j])
return (max,maxx,maxy)
def Jacobi_eigen(self,eps,iterN):
_A = self.A
count = 0
while True:
pos = self.get_max()
if pos[0]iterN:
break
Givens_trans_eliminate(self.A,pos[1],pos[2],self.Q)
count +=1
# print(self.A)
# print(count)
list = []
for i in range(self.n):
list.append(self.A[i][i])
list.sort()
for i in range(self.n ):
print("%.2f"%list[i],end=" ")
def Givens_trans_eliminate(a,i,j,Q):
b = (a[i][i]-a[j][j])/(2*a[i][j])
t = 1/(abs(b)+mt.sqrt(1+b**2))
if b<0:
t = -t
cos = 1/(mt.sqrt(1+t**2))
sin = t/(mt.sqrt(1+t**2))
olda = copy.deepcopy(a)
for s in range(len(a)):
if s!=i and s!=j:
a[s][i] = a[i][s] = olda[s][i]*cos+olda[s][j]*sin
a[s][j] = a[j][s] = -olda[s][i]*sin+olda[s][j]*cos
a[i][i] = olda[i][i]*cos*cos +2*olda[i][j]*cos*sin+olda[j][j]*sin*sin
a[j][j] = olda[i][i]*sin*sin-2*olda[i][j]*cos*sin+olda[j][j]*cos*cos
a[i][j] = a[j][i] = 0
oldq = copy.deepcopy(Q)
for s in range(len(a)):
# Q[s][i] = Q[s][i]*cos+Q[s][j]*sin
# Q[s][j] = -Q[s][i]*sin+Q[s][j]*cos
Q[s][i] = oldq[s][i] * cos + oldq[s][j] * sin
Q[s][j] = -oldq[s][i] * sin + oldq[s][j] * cos
def _getMatrix():
matrix = []
row = []
for i in range(3):
inp = input().split(' ')
row = [float(inp[num]) for num in range(len(inp)) ]
matrix.append(row)
return matrix
a = _getMatrix()
s = SquareMatrix(a)
inp = input().split(' ')
eps = float(inp[1])
itern = float(inp[0])
s.Jacobi_eigen(eps,itern)
