How to build the Jacobi method in Python?

原文地址

Jacobi method

from pprint import pprint
from numpy import array, zeros, diag, diagflat, dot

def jacobi(A,b,N=25,x=None):
    """Solves the equation Ax=b via the Jacobi iterative method."""
    # Create an initial guess if needed                                                                                                                                                            
    if x is None:
        x = zeros(len(A[0]))

    # Create a vector of the diagonal elements of A                                                                                                                                                
    # and subtract them from A                                                                                                                                                                     
    D = diag(A)
    R = A - diagflat(D)

    # Iterate for N times                                                                                                                                                                          
    for i in range(N):
        x = (b - dot(R,x)) / D
    return x

A = array([[2.0,1.0],[5.0,7.0]])
b = array([11.0,13.0])
guess = array([1.0,1.0])

sol = jacobi(A,b,N=25,x=guess)

print "A:"
pprint(A)

print "b:"
pprint(b)

print "x:"
pprint(sol)

输出结果

A:
array([[ 2.,  1.],
       [ 5.,  7.]])
b:
array([ 11.,  13.])
x:
array([ 7.11110202, -3.22220342])