import numpy as np
import scipy.sparse as sp
import scipy.sparse.linalg as spl

denseM = [[ 0.75,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0. ,
         0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.25,  0.5 ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,
         0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.5 , -0.25,  0.  ,  0.5 ,  0.  ,  0.  ,  0.  ,  0.  ,
         0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.25,  0.  ,  0.5 ,  0.  ,  0.  ,  0.  ,
         0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.  ,  0.5 ,  0.  , -0.25,  0.  ,  0.  ,  0.  ,  0.5 ,
         0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.5 ,  0.  , -0.75,  0.5 ,  0.  ,  0.  ,
         0.5 ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.5 , -0.25,  0.  ,  0.  ,
         0.  ,  0.5 ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.25,  0.  ,
         0.  ,  0.  ,  0.5 ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.5 ,  0.  ,  0.  ,  0.  ,  0.25,
         0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.5 ,  0.  ,  0.  ,  0.  ,
        -0.25,  0.5 ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.5 ,  0.  ,  0.  ,
         0.5 , -0.75,  0.  ,  0.5 ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.5 ,  0.  ,
         0.  ,  0.  , -0.25,  0.  ,  0.5 ,  0.  ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,
         0.  ,  0.5 ,  0.  ,  0.25,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,
         0.  ,  0.  ,  0.5 ,  0.  , -0.25,  0.5 ,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,
         0.  ,  0.  ,  0.  ,  0.  ,  0.5 ,  0.25,  0.  ],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,
         0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.75]]
denseM = np.array(denseM)

dense_vals = np.linalg.eigh(denseM)
sparseM = sp.csr_matrix(denseM)
sparse_vals = spl.eigs(sparseM, 1)

dense_eval, dense_evec = dense_vals[0][0], dense_vals[1][:, 0]
sparse_eval, sparse_evec = sparse_vals[0][0], sparse_vals[1].ravel()

# checks
if not denseM.dtype == sparseM.dtype == np.float64:
    print('wrong dtypes')
if not np.array_equal(denseM, denseM.T):
    print('not symmetric')
if np.isclose(*dense_vals[0][:2]):
    print('degenerate ground state')
if not (denseM == sparseM).all():
    print('dense != sparse')
if not np.allclose(denseM @ dense_evec - dense_eval * dense_evec, 0):
    print('not a dense eigenvector')
if not np.allclose(sparseM @ sparse_evec - sparse_eval * sparse_evec, 0):
    print('not a sparse eigenvector')
if not np.isclose(dense_eval, sparse_eval):
    print('not the same eigenvalues')
if not np.allclose(sparse_evec, dense_evec):
    print('not the same eigenvectors')