用Python实现雅可比方法求解线性方程组

# Importing module for plotting and array
from pylab import *
from numpy import *

# Initial guess to start with
xg=0
yg=0
zg=0

# Setting error to move into the while loop
error=1

# Setting up iteration counter
count=0

while error>1.E-5:
   count+=1
    
   #Evaluating new values based on old guess
   x=(17-yg+2*zg)/20
   y=(zg-18-3*xg)/20
   z=(25-2*xg+3*yg)/20

   # Error evaluation and plotting
   error = abs(x-xg)+abs(y-yg)+abs(z-zg)
   figure(1,dpi=300)
   semilogy(count,error,'ko')
   xlabel('iterations')
   ylabel('error')

   # Updating the Guess for next iteration.
   xg=x
   yg=y
   zg=z

savefig('error_jacobi.jpg')
print(f'x={round(x,5)}, y={round(y,5)}, z={round(z,5)}')

# Importing module
from pylab import *
from numpy import *

#-----------------------------------------#
# Array of coefficients of x
a=array([[20,1,-2],[3,20,-1],[2,-3,20]])

# Array of RHS vector
b=array([17,-18,25])

# Number of rows and columns
n=len(b)
#-----------------------------------------#


# Setting up the initial guess array
xg=zeros(len(b))

# Starting error to enter in loop
error=1

# Setting iteration counter
count=0

# Generating array for new x
xn=empty(len(b)) 
#-----------------------------------------#


while error>1.E-5:
   count+=1
   for i in range(n):
      sum1=0
      for j in range(n):
         if i!=j:
            sum1=sum1+a[i,j]*xg[j]
      xn[i]=(-1/a[i,i])*(sum1-b[i])


   # Error evaluation and plotting
   error = sum(abs(xn-xg))
    
   figure(1,dpi=300)
   semilogy(count,error,'ko')
   xlabel('iterations')
   ylabel('error')

   # Substituting new value as the Guess for next iteration
   xg=xn.copy()
#-----------------------------------------#

savefig('error_jacobi.jpg')
print('x: ',xn)