import pprint
import numpy
#funckja do tworzenia macierzy wstegowej z wykorzystaniem biblioteki numpy.
def tridiag(a, b, c, k1=-1, k2=0, k3=1):
    return numpy.diag(a, k1) + numpy.diag(b, k2) + numpy.diag(c, k3)

#ustawiamy wielkosc macierzy!!MOZNA MODYFIKOWAC DLA DOWOLNYCH n!!
n=7

#tworze macierz wstegowa o rozmiarze 7x7 i dodaje 1 w rogach
a = [1.0]*(n-1); b = [4.0]*n; c = [1.0]*(n-1)
A = tridiag(a, b, c)
A[6][0]=1
A[0][6]=1
print "A:"
pprint.pprint(A)
#zapelniam tablice L i U zerami
L=[];
L=[[0.0] * n for i in xrange(n)]
U=[[0.0] * n for i in xrange(n)]
uxv=[[0.0] * n for i in xrange(n)]
uxv[0][0]=1
uxv[0][n-1]=1
uxv[n-1][0]=1
uxv[n-1][n-1]=1
A=A-uxv
print "A1:"
pprint.pprint(A)
#ustawiam pierwsze wartosci macierzy L i U
U[0][0]=A[0][0]
U[0][1]=A[0][1]
L[0][0]=1.0;
#zapelniam
for n in range(0,(len(A)-1)):
    U[n][n+1]=A[n][n+1]
    L[n+1][n+1]=1.0;
    L[n+1][n]=(A[n+1][n]/U[n][n])
    U[n+1][n+1]=A[n+1][n+1]-L[n+1][n]*U[n][n+1]

print "L:"
pprint.pprint(L)

print "U:"
pprint.pprint(U)

n=len(A)
#inicjuje tablice b i v
b=[1.0,2.0,3.0,4.0,5.0,6.0,7.0]
u=[1.0,0.0,0.0,0.0,0.0,0.0,1.0]
#inicjuje tablice wynikow Z,Q,X i posrednich Z,Q
z=[0]*n
Z=[0]*n
q=[0]*n
Q=[0]*n
X=[0]*n
#wynik podstawowy
z[0]=b[0]
q[0]=u[0]
for n in range(1,(len(A))):
    z[n]=b[n]-((L[n][n-1])*(z[n-1]))
    q[n]=u[n]-((L[n][n-1])*(q[n-1]))

n=len(A)-1
Z[n]=z[n]/U[n][n]
Q[n]=q[n]/U[n][n]
for i in range((len(A))-2,-1,-1):
    Z[i]=(z[i]-((A[i][i+1])*(Z[i+1])))/U[i][i]
    Q[i]=(q[i]-((A[i][i+1])*(Q[i+1])))/U[i][i]
print "Z:"
pprint.pprint(Z)
print "Q:"
pprint.pprint(Q)

#obliczam iloczyny skalarne uZ i uQ
r=0.0
s=0.0
for i in range(7):
    r=r+u[i]*Z[i]
    s=s+u[i]*Q[i]
k=r/(1+s)

#wyznaczamy X
for i in range(7):
    X[i]=Z[i]-k*Q[i]

print "X:"
pprint.pprint(X)