HW 3-1: power method - Naguib

1903 days ago by bigdata2016

I have used power method to find the dominant Eigen value and corresponding normalized Eigen vector of the 7x7 matrix I used in HW1

A=matrix(7,7,[[5,4,6,2,7,1,5],[5,2,1,6,2,9,5],[3,4,2,7,7,8,8],[9,1,4,6,2,5,8],[4,1,8,5,4,4,6],[1,9,0,5,6,4,4],[8,10,0,3,8,3,8]]) X= matrix(7,1,[1,1,1,1,1,1,1]) print "A =" show(A) print "X(0) =", X.transpose() 
       
A =

X(0) = [1 1 1 1 1 1 1]
A =

X(0) = [1 1 1 1 1 1 1]
for i in range(15): Y=A*X C=max(max(Y)) X=Y/C print "Iteration number", i+1 print "Y(%d)=AX(%d)"%(i+1,i) print "C = max(Y(%d)) = %f"%(i+1,C) #show(("X = ", X)) print "X(%d) ="%(i+1) , X.transpose().change_ring(RDF) show(" ") 
       
Iteration number 1
Y(1)=AX(0)
C = max(Y(1)) = 14.621602
X(1) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 2
Y(2)=AX(1)
C = max(Y(2)) = 33.548327
X(2) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 3
Y(3)=AX(2)
C = max(Y(3)) = 33.548327
X(3) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 4
Y(4)=AX(3)
C = max(Y(4)) = 33.548327
X(4) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 5
Y(5)=AX(4)
C = max(Y(5)) = 33.548327
X(5) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 6
Y(6)=AX(5)
C = max(Y(6)) = 33.548327
X(6) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 7
Y(7)=AX(6)
C = max(Y(7)) = 33.548327
X(7) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 8
Y(8)=AX(7)
C = max(Y(8)) = 33.548327
X(8) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 9
Y(9)=AX(8)
C = max(Y(9)) = 33.548327
X(9) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 10
Y(10)=AX(9)
C = max(Y(10)) = 33.548327
X(10) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 11
Y(11)=AX(10)
C = max(Y(11)) = 33.548327
X(11) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 12
Y(12)=AX(11)
C = max(Y(12)) = 33.548327
X(12) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 13
Y(13)=AX(12)
C = max(Y(13)) = 33.548327
X(13) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 14
Y(14)=AX(13)
C = max(Y(14)) = 33.548327
X(14) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]

Iteration number 15
Y(15)=AX(14)
C = max(Y(15)) = 33.548327
X(15) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118
0.857309457529 0.718543042413            1.0]
Iteration number 1
Y(1)=AX(0)
C = max(Y(1)) = 14.621602
X(1) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 2
Y(2)=AX(1)
C = max(Y(2)) = 33.548327
X(2) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 3
Y(3)=AX(2)
C = max(Y(3)) = 33.548327
X(3) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 4
Y(4)=AX(3)
C = max(Y(4)) = 33.548327
X(4) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 5
Y(5)=AX(4)
C = max(Y(5)) = 33.548327
X(5) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 6
Y(6)=AX(5)
C = max(Y(6)) = 33.548327
X(6) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 7
Y(7)=AX(6)
C = max(Y(7)) = 33.548327
X(7) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 8
Y(8)=AX(7)
C = max(Y(8)) = 33.548327
X(8) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 9
Y(9)=AX(8)
C = max(Y(9)) = 33.548327
X(9) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 10
Y(10)=AX(9)
C = max(Y(10)) = 33.548327
X(10) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 11
Y(11)=AX(10)
C = max(Y(11)) = 33.548327
X(11) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 12
Y(12)=AX(11)
C = max(Y(12)) = 33.548327
X(12) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 13
Y(13)=AX(12)
C = max(Y(13)) = 33.548327
X(13) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 14
Y(14)=AX(13)
C = max(Y(14)) = 33.548327
X(14) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]

Iteration number 15
Y(15)=AX(14)
C = max(Y(15)) = 33.548327
X(15) = [0.789168496853 0.748183211852 0.998495031712 0.913014192118 0.857309457529 0.718543042413            1.0]
X=X/norm(X) print "Dominant Eigen Value =", RDF(C) print "Normalized corresponding Eigen Vector is:" show(X.change_ring(RDF)) print "X^T . A . X =", (X.transpose() * A * X).change_ring(RDF) 
       
__main__:2: DeprecationWarning: The default norm will be changing from
p='frob' to p=2.  Use p='frob' explicitly to continue calculating the
Frobenius norm.
See http://trac.sagemath.org/13643 for details.
Dominant Eigen Value = 33.5483274572
Normalized corresponding Eigen Vector is:

X^T . A . X = [33.5483274572]
__main__:2: DeprecationWarning: The default norm will be changing from p='frob' to p=2.  Use p='frob' explicitly to continue calculating the Frobenius norm.
See http://trac.sagemath.org/13643 for details.
Dominant Eigen Value = 33.5483274572
Normalized corresponding Eigen Vector is:

X^T . A . X = [33.5483274572]