BUG: `DataFrame.equals` returns `True` when compared elements differ in being `np.array`s

[MaxGhenis]

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the master branch of pandas.

Reproducible Example

import pandas as pd
import numpy as np
# Create a minimal DataFrame.
df = pd.DataFrame(dict(x=["a"]))
df
#	x
# 0	a
# Change x to a numpy array.
df_np = df.copy()
df_np.x = [np.array(df.x)]
df_np  # Display that this differs from df.
# 	x
# 0	[a]
df_np.equals(df)
# True

Issue Description

When comparing two DataFrames, and some values are numpy arrays in one and not in another, equals returns True, despite them differing visibly.

Here's the above code in a notebook.

Possibly related: #43008

Expected Behavior

df_np.equals(df) should return False.

Installed Versions

/usr/local/lib/python3.7/dist-packages/psycopg2/init.py:144: UserWarning: The psycopg2 wheel package will be renamed from release 2.8; in order to keep installing from binary please use "pip install psycopg2-binary" instead. For details see: http://initd.org/psycopg/docs/install.html#binary-install-from-pypi.
""")

INSTALLED VERSIONS

commit : 73c6825
python : 3.7.12.final.0
python-bits : 64
OS : Linux
OS-release : 5.4.104+
Version : #1 SMP Sat Jun 5 09:50:34 PDT 2021
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.3.3
numpy : 1.19.5
pytz : 2018.9
dateutil : 2.8.2
pip : 21.1.3
setuptools : 57.4.0
Cython : 0.29.24
pytest : 3.6.4
hypothesis : None
sphinx : 1.8.5
blosc : None
feather : 0.4.1
xlsxwriter : None
lxml.etree : 4.2.6
html5lib : 1.0.1
pymysql : None
psycopg2 : 2.7.6.1 (dt dec pq3 ext lo64)
jinja2 : 2.11.3
IPython : 5.5.0
pandas_datareader: 0.9.0
bs4 : 4.6.3
bottleneck : 1.3.2
fsspec : None
fastparquet : None
gcsfs : None
matplotlib : 3.2.2
numexpr : 2.7.3
odfpy : None
openpyxl : 2.5.9
pandas_gbq : 0.13.3
pyarrow : 3.0.0
pyxlsb : None
s3fs : None
scipy : 1.4.1
sqlalchemy : 1.4.25
tables : 3.4.4
tabulate : 0.8.9
xarray : 0.18.2
xlrd : 1.1.0
xlwt : 1.3.0
numba : 0.51.2

[Nedwards0]

This is most likely being caused by how NumPy handles ==. It attempts to broadcast the shapes to the same see https://numpy.org/doc/stable/user/basics.broadcasting.html. This makes it seem like it actually is intended behavior since NumPy will say that 1==np.array([1]) is a true statement and this can be seen by code below.

print(np.shape(1))
print(np.shape([1]))
if(np.equal(1,[1])):
  print("Pass 1 Testing numpy equal between 1 and [1]")
else:
    print("Fail 1 Testing numpy equal between 1 and [1]")
if(1==[1]):
  print("Pass 2 Testing if 1 equals [1] base python")
else:
    print("Fail 2 Testing if 1 equals [1] base python")
if(1==np.array([1])):
  print("Pass 3 Testing if 1 equals np.array([1])")
else:
    print("Fail 3 Testing if 1 equals np.array([1])")
if(1==np.array([[[[[[[1]]]]]]])):
  print("Pass 4 Testing if 1 equals np.array([[[[[[[1]]]]]]]))")
else:
    print("Fail 4 Testing if 1 equals np.array([[[[[[[1]]]]]]]))")

Output

()
(1,)
Pass 1 Testing numpy equal between 1 and [1]
Fail 2 Testing if 1 equals [1] base python
Pass 3 Testing if 1 equals np.array([1])
Pass 4 Testing if 1 equals np.array([[[[[[[1]]]]]]]))