雅可比迭代法解线性方程组

import os
os.getcwd()

'D:\\#Python\\jupter'

import numpy as np
def jacobi(a,b,c=0.0001,d=30):
    x1=np.zeros(a.shape[1])
    x2=np.zeros(a.shape[1])
    k=0
    while k<d:
        k=k+1
        print('k=',k)
        for i in range(a.shape[1]):
            x2[i]=(-a[i].dot(x1)+b[i]+a[i,i]*x1[i])/a[i,i]
        if np.max(np.abs(x2-x1))<=c:
            print("x%d=" % k,x2)
            print(np.max(np.abs(x2-x1)))
            break
        print("x%d=" % k,x2)
        x1=x2.copy()
    return x2

a=np.array([[1,0,0,0,0,0,0],
             [-0.9,1,0,0,0,0,0],
             [0,0.54,-1,0,0.36,0,0],
             [0.18,0,0.72,-1,0,0,0],
             [0,0,0.36,0.36,-1,0.18,0],
             [0,0,0,0.45,0,-1,0.45],
             [0,0,0,0,0,0.09,-0.19]]
             )
b=np.array([0,10,2,2,-1,2,1])
jacobi(a,b)

k= 1
x1= [ 0.         10.         -2.         -2.          1.         -2.
 -5.26315789]
k= 2
x2= [ 0.         10.          3.76       -3.44       -0.8        -5.26842105
 -6.21052632]
k= 3
x3= [ 0.         10.          3.112       0.7072      0.16688421 -6.34273684
 -7.75872576]
k= 4
x4= [ 0.         10.          3.46007832  0.24064     1.23321937 -5.17318659
 -8.26761219]
k= 5
x5= [ 0.         10.          3.84395897  0.49125639  1.40108501 -5.61213748
 -7.7136147 ]
k= 6
x6= [ 0.         10.          3.9043906   0.76765046  1.55049278 -5.25006124
 -7.92153881]
k= 7
x7= [ 0.         10.          3.9581774   0.81116123  1.73692376 -5.21924976
 -7.75002901]
k= 8
x8= [ 0.         10.          4.02529255  0.84988773  1.77749695 -5.1224905
 -7.7354341 ]
k= 9
x9= [ 0.         10.          4.0398989   0.89821064  1.83301661 -5.09849586
 -7.68960076]
k= 10
x10= [ 0.         10.          4.05988598  0.90872721  1.85999018 -5.05612556
 -7.67823488]
k= 11
x11= [ 0.         10.          4.06959646  0.92311791  1.87859815 -5.04627845
 -7.65816474]
k= 12
x12= [ 0.         10.          4.07629533  0.93010945  1.88904705 -5.03077107
 -7.65350032]
k= 13
x13= [ 0.         10.          4.08005694  0.93493264  1.89676693 -5.02552589
 -7.64615472]
k= 14
x14= [ 0.         10.          4.08283609  0.937641    1.90080159 -5.02004994
 -7.64367016]
k= 15
x15= [ 0.         10.          4.08428857  0.93964199  1.90376276 -5.01771312
 -7.64107629]
k= 16
x16= [ 0.         10.          4.0853546   0.94068777  1.90542664 -5.01564543
 -7.63996937]
k= 17
x17= [ 0.         10.          4.08595359  0.94145531  1.90655907 -5.01467672
 -7.63898994]
k= 18
x18= [ 0.         10.          4.08636127  0.94188658  1.90722539 -5.01389059
 -7.63853108]
k= 19
x19= [ 0.         10.          4.08660114  0.94218011  1.90766892 -5.01349002
 -7.6381587 ]
k= 20
x20= [ 0.         10.          4.08676081  0.94235282  1.90793305 -5.01319036
 -7.63796896]
k= 21
x21= [ 0.         10.          4.0868559   0.94246778  1.90810664 -5.01302726
 -7.63782701]
k= 22
x22= [ 0.         10.          4.08691839  0.94253625  1.90821162 -5.01291165
 -7.63774976]
k= 23
x23= [ 0.         10.          4.08695618  0.94258124  1.90827957 -5.01284608
 -7.63769499]
6.795344688015348e-05





array([ 0.        , 10.        ,  4.08695618,  0.94258124,  1.90827957,
       -5.01284608, -7.63769499])