[SOLVED] numpy.linalg.eigh works with numpy array from sym.lambdify() but not from np.array()

numpy.linalg.eigh works with numpy array from sym.lambdify() but not from np.array()

Here's the code. 2a works but 2b does not, even though both matrices have the same shape and the same type. Can anybody explain?

import sympy as sym  
import numpy as np

x1, x2 = sym.symbols('x1 x2')  
f = 2*x1**2 - 2*x1*x2 + x2**2 + 2*x1 - 2*x2  
xk = np.array([[0 , 1]])  
print("xk shape = ", xk.shape)  
fmat = sym.Matrix([f])  
H = sym.hessian(fmat, (x1, x2))  
print("Symbolic H")  
sym.pprint(H)  

# 2a: Convert the SymPy Matrix to Numpy array using lambdify and then substitute values  
Hnp = sym.lambdify((x1, x2), H, 'numpy')  
Hknp = Hnp(xk[0][0], xk[0][1])  
print("Hknp")  
sym.pprint(Hknp)  
print("Hknp type:", type(Hknp))  
print("Hknp shape = ", Hknp.shape)  
v, Q = np.linalg.eigh(Hknp)  
print("v:", v)  
print("Q:")  
sym.pprint(Q)  

# 2b: Substitute values into SymPy Matrix then convert to Numpy array  
Hks = H.subs([(x1, xk[0][0]), (x2, xk[0][1])])  
Hk = np.array(Hks)  
print("Hk")  
sym.pprint(Hk)  
print("Hk type:", type(Hk))  
print("Hk shape = ", Hk.shape)  
v, Q = np.linalg.eigh(Hk)  
print("v:", v)  
print("Q:")  
sym.pprint(Q)

Solution

>>> Hk
array([[4, -2],
       [-2, 2]], dtype=object)


>>> Hknp.dtype
dtype('int64')

The solution is Hk = np.array(Hks, dtype=np.int64).