Shrijesh Siwakoti Quiz 12

A = matrix(RDF,3,[2.3415, -1.6732,4.5620,-8.6532,0.2451,-3.2476,1.8935,-0.2315,7.5432])
print A

Q,R=A.QR()
A1 = R*Q
print "A1 ="
print A1
print "Q ="
print Q
print "R ="
print R

Aj = A1
for j in [2..80]:
    Q, R = Aj.QR()
    Aj = R*Q
    a = j%5
    b = 1
    if j % 5 == 0:
        print Aj.diagonal()

A = matrix(RDF,4,[4,2,-2,2,1,2,1,-1,0,0,3,0,1,1,-3,5])
print A

Q,R=A.QR()
A1 = R*Q
print "A1 ="
print A1
print "Q ="
print Q
print "R ="
print R

Aj = A1
for j in [2..25]:
    Q, R = Aj.QR()
    Aj = R*Q
    print Aj.diagonal()

A= matrix(QQ,4,[84,5,-5,5,1,0,1,-1,-1,1,0,1,3,5,-5,6])
print "A = "
print A
X0 = vector(RDF,[1,2,1,1]) 
print "X0="
print X0
temp = A*X0
X1 = (1/(temp.norm(Infinity)))*(temp)
L1 = ((A*X1).dot_product(X1))/(X1.dot_product(X1))
print "X1="
print X1 
print "λ1 ="
print L1

Xi = X1
temp2 = A * X1
for i in [2..10]: 
    temp3 = A*Xi
    Xi = (1/(temp3.norm(Infinity)))*(temp3)
    Li = (temp2.dot_product(Xi))/(Xi.dot_product(Xi))
    print Xi
    temp2 = A* Xi
    print " "
    print Li
    print "--------------------------------------- "

A= matrix(RDF,4,[4.5,5.5,-5.5,5.5,1.5,0.5,1.5,-1.5,-1,1,0,1,3,5,-6,7])
print "A = "
print A
X0 = vector(RDF,[1,2,1,1]) 
print "X0 ="
print X0
temp = A*X0
X1 = (1/(temp.norm(Infinity)))*(temp)
L1 = ((A*X1).dot_product(X1))/(X1.dot_product(X1))
print "X1 ="
print X1 
print "λ1 ="
print L1

Xi = X1
temp2 = A* X1
for i in [2..10]: 
    temp3 = A*Xi
    Xi = (1/(temp3.norm(Infinity)))*(temp3)
    Li = (temp2.dot_product(Xi))/(Xi.dot_product(Xi))
    print Xi
    temp2 = A*Xi
    print " "
    print Li
    print "--------------------------------------- "

A = matrix(CDF,4,[1,2,3,4,5,6,7,8])
print "A ="
print A
U,S,V = A.SVD()
print "U ="
print U
print "Σ ="
print S
print "V ="
print V