Chapter 7 Computations with Matrices

Ex:7.4.1 Pg: 238

from __future__ import division
from numpy import mat,transpose,zeros
A=mat([[2 ,-1],[-1, 2]])
S=mat([[2, 0],[0, 2]])
T=mat([[0, 1],[1, 0]])
p=S**-1*T
b=transpose(mat([2 ,2]))
x=zeros([2,1])
print 'intial v & w:\n',x,'\n'
x_1=zeros([1,2])
for k in range(0,26):
    x_1=p*x+(S**-1)*b
    x=x_1
    print 'k=',k
    print 'v(k+1) & w(k+1)=',x_1,'\n'

intial v & w:
[[ 0.]
 [ 0.]] 

k= 0
v(k+1) & w(k+1)= [[ 1.]
 [ 1.]] 

k= 1
v(k+1) & w(k+1)= [[ 1.5]
 [ 1.5]] 

k= 2
v(k+1) & w(k+1)= [[ 1.75]
 [ 1.75]] 

k= 3
v(k+1) & w(k+1)= [[ 1.875]
 [ 1.875]] 

k= 4
v(k+1) & w(k+1)= [[ 1.9375]
 [ 1.9375]] 

k= 5
v(k+1) & w(k+1)= [[ 1.96875]
 [ 1.96875]] 

k= 6
v(k+1) & w(k+1)= [[ 1.984375]
 [ 1.984375]] 

k= 7
v(k+1) & w(k+1)= [[ 1.9921875]
 [ 1.9921875]] 

k= 8
v(k+1) & w(k+1)= [[ 1.99609375]
 [ 1.99609375]] 

k= 9
v(k+1) & w(k+1)= [[ 1.99804688]
 [ 1.99804688]] 

k= 10
v(k+1) & w(k+1)= [[ 1.99902344]
 [ 1.99902344]] 

k= 11
v(k+1) & w(k+1)= [[ 1.99951172]
 [ 1.99951172]] 

k= 12
v(k+1) & w(k+1)= [[ 1.99975586]
 [ 1.99975586]] 

k= 13
v(k+1) & w(k+1)= [[ 1.99987793]
 [ 1.99987793]] 

k= 14
v(k+1) & w(k+1)= [[ 1.99993896]
 [ 1.99993896]] 

k= 15
v(k+1) & w(k+1)= [[ 1.99996948]
 [ 1.99996948]] 

k= 16
v(k+1) & w(k+1)= [[ 1.99998474]
 [ 1.99998474]] 

k= 17
v(k+1) & w(k+1)= [[ 1.99999237]
 [ 1.99999237]] 

k= 18
v(k+1) & w(k+1)= [[ 1.99999619]
 [ 1.99999619]] 

k= 19
v(k+1) & w(k+1)= [[ 1.99999809]
 [ 1.99999809]] 

k= 20
v(k+1) & w(k+1)= [[ 1.99999905]
 [ 1.99999905]] 

k= 21
v(k+1) & w(k+1)= [[ 1.99999952]
 [ 1.99999952]] 

k= 22
v(k+1) & w(k+1)= [[ 1.99999976]
 [ 1.99999976]] 

k= 23
v(k+1) & w(k+1)= [[ 1.99999988]
 [ 1.99999988]] 

k= 24
v(k+1) & w(k+1)= [[ 1.99999994]
 [ 1.99999994]] 

k= 25
v(k+1) & w(k+1)= [[ 1.99999997]
 [ 1.99999997]] 

Ex:7.4.2 Pg: 238

from __future__ import division
from numpy import mat,transpose,zeros
from numpy.random import rand
from numpy.linalg import inv
A=mat([[2, -1],[-1, 2]])
S=mat([[2, 0],[-1, 2]])
T=mat([[0, 1],[0, 0]])
b=rand(2,1)
p=inv(S)*T
x=zeros([2,1])
print 'intial v & w:',x
x_1=zeros([1,2])
for k in range(0,26):
    x_1=p*x+inv(S)*b
    x=x_1
    print 'k=\n',k
    print 'v(k+1) & w(k+1)=\n',x_1

intial v & w: [[ 0.]
 [ 0.]]
k=
0
v(k+1) & w(k+1)=
[[ 0.10887353]
 [ 0.53877511]]
k=
1
v(k+1) & w(k+1)=
[[ 0.37826108]
 [ 0.67346888]]
k=
2
v(k+1) & w(k+1)=
[[ 0.44560797]
 [ 0.70714233]]
k=
3
v(k+1) & w(k+1)=
[[ 0.46244469]
 [ 0.71556069]]
k=
4
v(k+1) & w(k+1)=
[[ 0.46665387]
 [ 0.71766528]]
k=
5
v(k+1) & w(k+1)=
[[ 0.46770617]
 [ 0.71819143]]
k=
6
v(k+1) & w(k+1)=
[[ 0.46796924]
 [ 0.71832296]]
k=
7
v(k+1) & w(k+1)=
[[ 0.46803501]
 [ 0.71835585]]
k=
8
v(k+1) & w(k+1)=
[[ 0.46805145]
 [ 0.71836407]]
k=
9
v(k+1) & w(k+1)=
[[ 0.46805556]
 [ 0.71836612]]
k=
10
v(k+1) & w(k+1)=
[[ 0.46805659]
 [ 0.71836664]]
k=
11
v(k+1) & w(k+1)=
[[ 0.46805685]
 [ 0.71836676]]
k=
12
v(k+1) & w(k+1)=
[[ 0.46805691]
 [ 0.7183668 ]]
k=
13
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
14
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
15
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
16
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
17
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
18
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
19
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
20
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
21
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
22
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
23
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
24
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]
k=
25
v(k+1) & w(k+1)=
[[ 0.46805693]
 [ 0.71836681]]