Python library for Gauss-Seidel Iterative Solver?

Question

Is there a linear algebra library that implements iterative Gauss-Seidel to solve linear systems? Or maybe a preconditioned gradient solver?

Thanks

EDIT: In the end I used a kind of crude but correct way to solve it. As i had to create the matrix A (for Ax=b) anyway, I partitioned the matrix as

A = M - N

with

 M = (D + L) and N = -U

where D is the diagonal, L is the lower triangular section, and U the upper triangular section. Then

Pinv = scipy.linalg.inv(M)
x_k_1 = np.dot(Pinv,np.dot(N,x_k)) + np.dot(Pinv,b)

Also did some convergence tests. It works.

Answer 1

I know this is old but, I haven't found any pre existing library in python for gauss - seidel. Instead I created my own little function that with the help of a permutation matrix as seen in another answer of mine permutation matrix will produce the solution (x vector) for any square matrix, including those with zeros on the diagonal.

def gauss_seidel(A, b, tolerance, max_iterations, x):
    #x is the initial condition
    iter1 = 0
    #Iterate
    for k in range(max_iterations):
        iter1 = iter1 + 1
        print ("The solution vector in iteration", iter1, "is:", x)    
        x_old  = x.copy()
        
        #Loop over rows
        for i in range(A.shape[0]):
            x[i] = (b[i] - np.dot(A[i,:i], x[:i]) - np.dot(A[i,(i+1):], x_old[(i+1):])) / A[i ,i]
            
        #Stop condition 
        #LnormInf corresponds to the absolute value of the greatest element of the vector.
        
        LnormInf = max(abs((x - x_old)))/max(abs(x_old))   
        print ("The L infinity norm in iteration", iter1,"is:", LnormInf)
        if  LnormInf < tolerance:
            break
    
           
    return x

After re searching I have found the following that could be used as a ready to go package, but haven't used it myself numerica PyPI