Why do I keep getting ValueError: solve: Input operand 1 has a mismatch in its core dimension 0?

Question

我正在尝试为 Python 中的非线性系统的牛顿法编写代码。我的 g 函数是一个 5x1 矩阵，它的雅可比矩阵（导数矩阵）是一个 5x5 矩阵。初始 y 值 (y0) 的向量也是 5x1。我一直收到错误

ValueError: solve: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (m,m),(m,n)->(m,n) (size 1 is different from 5)

我尝试手动解决我的问题，但是当我运行我的代码时，我得到了答案。我怀疑这个错误是我忽略的愚蠢的事情。但我终其一生都无法弄清楚问题出在哪里。下面是我的代码：


def newton_prob(y0, g, jac, tol):
    
    max_iteration = 100
    tol = 1e-6
    
    y_value = y0
    
    for k in range(max_iteration):
        
        J = np.array(jac(y_value))
        G = np.array(g(y_value))
        
        diff = np.linalg.solve(J, -G)
        y_value = y_value + diff
        stopcrit = np.linalg.norm(y_value - y0, 2) / np.linalg.norm(y0, 2)
        
        if stopcrit < tol:
            
            print('Convergence, nre iter:' , k)
            break
        
    else:
        
        
        return y_value
        
        
#Test  
     
y0 = np.array([[17],
               [17],
               [17],
               [17],
               [17]])     
g = lambda y: np.array([[-9*y[1] + 18*y[0] - 9*(17) - (3/16)*y[0]*y[1] + (3/16)*y[0]*(17) + (124/27)], 
                         [-9*y[2] + 18*y[1] -9*y[0] -(3/16)*y[1]*y[2] + (3/16)*y[0]*y[1] +(557/108)],
                         [-9*y[3] + 18*y[2] -9*y[1] + (3/16)*y[1]*y[2] - (3/16)*y[2]*y[3] + 6],
                         [-9*y[4] + 9*y[3] -9*y[2] - (3/16)*y[3]*y[4] + (3/16)*y[2]*y[3] + (775/108)],
                         [-9*(43/3) +18*y[4] -9*y[3] + (3/16)*y[3]*y[4] - (3/16)*y[4]*(43/3) + (236/27)]])
jac = lambda y: np.array([[18 -(3/16)*y[1] + (3/16)*(17), -9 -(3/16)*y[0], 0, 0, 0],
                           [-9 + (3/16)*y[1], 18 - (3/16)*y[2] + (3/16)*y[0], -9 - (3/16)*y[1], 0, 0],
                           [0, -9 + (3/16)*y[2], 18 + (3/16)*y[1] - (3/16)*y[3], -9 - (3/16)*y[2], 0],
                           [0, 0, -9 + (3/16)*y[3], 9 - (3/16)*y[3] + (3/16)*y[2], -9 - (3/16)*y[3]],
                           [0, 0, 0, -9 + (3/16)*y[4], 18 + (3/16)*y[3] - (3/16)*(43/3)]])

tol = 1e-6

print(newton_prob(y0, g, jac, tol))

如果可能请帮忙

Answer 1

y0 和 g 的尺寸似乎有误。将它们缩小一维：

y0 = np.array([17,
               17,
               17,
               17,
               17])     
g = lambda y: np.array([-9*y[1] + 18*y[0] - 9*(17) - (3/16)*y[0]*y[1] + (3/16)*y[0]*(17) + (124/27), 
                         -9*y[2] + 18*y[1] -9*y[0] -(3/16)*y[1]*y[2] + (3/16)*y[0]*y[1] +(557/108),
                         -9*y[3] + 18*y[2] -9*y[1] + (3/16)*y[1]*y[2] - (3/16)*y[2]*y[3] + 6,
                         -9*y[4] + 9*y[3] -9*y[2] - (3/16)*y[3]*y[4] + (3/16)*y[2]*y[3] + (775/108),
                         -9*(43/3) +18*y[4] -9*y[3] + (3/16)*y[3]*y[4] - (3/16)*y[4]*(43/3) + (236/27)])

输出：

[ 1.90727371e-01 -1.59772226e+01 -4.74196657e+01 -5.16165838e+03  4.86453399e+01]

Why do I keep getting ValueError: solve: Input operand 1 has a mismatch in its core dimension 0?

Why do I keep getting ValueError: solve: Input operand 1 has a mismatch in its core dimension 0?

python

numpy

function

numeric