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BUG: to_numpy_dtype_inference returns None when array is non-numeric and dtype isn't given #56991

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@derinwalters

Description

@derinwalters

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Reproducible Example

mport numpy as np
from pandas.core.arrays._utils import to_numpy_dtype_inference

# Issue 1: ArrayLike type of np.ndarray doesn't have atrribute .dtype.numpy_dtype
try:
    to_numpy_dtype_inference(np.array([1,2,3]), None, np.nan, False)
except Exception as e:
    print(e)

# Issue 2: If dtype isn't given and array is not a numeric dtype, returned dtype is None 
print(to_numpy_dtype_inference(np.array(['b','b','c']), None, np.nan, False))

Issue Description

Two places in utility method 'to_numpy_dtype_inference' have issues. The first is that the input array arg "arr" can be of type[ndarray] but ndarray doesn't have an attribute ".dtype.numpy_dtype". The second is that non-numeric array inputs without a given dtype will return None instead of np.dtype(np.object_)

def to_numpy_dtype_inference(
    arr: ArrayLike, dtype: npt.DTypeLike | None, na_value, hasna: bool
) -> tuple[npt.DTypeLike, Any]:
    if dtype is None and is_numeric_dtype(arr.dtype):
        dtype_given = False
        if hasna:
            if arr.dtype.kind == "b":
                dtype = np.dtype(np.object_)
            else:
                if arr.dtype.kind in "iu":
                    dtype = np.dtype(np.float64)
                else:
                    dtype = arr.dtype.numpy_dtype  # type: ignore[union-attr] # <-- Issue 1
                if na_value is lib.no_default:
                    na_value = np.nan
        else:
            dtype = arr.dtype.numpy_dtype  # type: ignore[union-attr]
    elif dtype is not None:
        dtype = np.dtype(dtype)
        dtype_given = True
    else:
        dtype_given = True # <-- Issue 2 [this should instead be "dtype = np.dtype(np.object_)"]

    if na_value is lib.no_default:
        na_value = arr.dtype.na_value

    if not dtype_given and hasna:
        try:
            np_can_hold_element(dtype, na_value)  # type: ignore[arg-type]
        except LossySetitemError:
            dtype = np.dtype(np.object_)
    return dtype, na_value

Expected Behavior

Issue 1: This case doesn't apply to me so I don't have any expectation other than Pandas shouldn't throw an exception.
Issue 2: return np.dtype(np.object_) when array is non-numeric and dtype is not provided

Installed Versions

INSTALLED VERSIONS

commit : f538741
python : 3.10.13.final.0
python-bits : 64
OS : Darwin
OS-release : 23.2.0
Version : Darwin Kernel Version 23.2.0: Wed Nov 15 21:53:34 PST 2023; root:xnu-10002.61.3~2/RELEASE_ARM64_T8103
machine : arm64
processor : arm
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.0
numpy : 1.26.3
pytz : 2023.3.post1
dateutil : 2.8.2
setuptools : 69.0.3
pip : 23.3.2
Cython : None
pytest : 7.4.4
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.3
IPython : None
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : 3.8.2
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 14.0.2
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : 1.11.4
sqlalchemy : None
tables : None
tabulate : None
xarray : 2024.1.0
xlrd : None
zstandard : 0.22.0
tzdata : 2023.4
qtpy : None
pyqt5 : None

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