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BUG: interpolate not respecting copy_on_write #51126

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@phofl

Description

@phofl

Pandas version checks

  • 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 main branch of pandas.

Reproducible Example

pd.options.mode.copy_on_write = True
df = DataFrame({"a": [1, np.nan, 3]})
view = df[:]
df.interpolate(inplace=True)

Issue Description

view should not get modified

     a
0  1.0
1  2.0
2  3.0

same problem for ffill, bfill, pad and backfill

Expected Behavior

     a
0  1.0
1  np.nan
2  3.0

Installed Versions

INSTALLED VERSIONS

commit : 948bf6d
python : 3.8.15.final.0
python-bits : 64
OS : Darwin
OS-release : 22.3.0
Version : Darwin Kernel Version 22.3.0: Thu Jan 5 20:50:21 PST 2023; root:xnu-8792.81.2~2/RELEASE_ARM64_T8112
machine : arm64
processor : arm
byteorder : little
LC_ALL : None
LANG : None
LOCALE : None.UTF-8

pandas : 2.0.0.dev0+1388.g948bf6d069
numpy : 1.23.5
pytz : 2022.7
dateutil : 2.8.2
setuptools : 65.6.3
pip : 22.3.1
Cython : 0.29.32
pytest : 7.2.0
hypothesis : 6.61.0
sphinx : 4.5.0
blosc : None
feather : None
xlsxwriter : 3.0.5
lxml.etree : 4.9.2
html5lib : 1.1
pymysql : 1.0.2
psycopg2 : 2.9.3
jinja2 : 3.1.2
IPython : 8.8.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : 1.3.5
brotli :
fastparquet : 2022.12.0
fsspec : 2022.11.0
gcsfs : 2022.11.0
matplotlib : 3.6.2
numba : 0.56.4
numexpr : 2.8.3
odfpy : None
openpyxl : 3.0.10
pandas_gbq : None
pyarrow : 10.0.1
pyreadstat : 1.2.0
pyxlsb : 1.0.10
s3fs : 2022.11.0
scipy : 1.9.3
snappy :
sqlalchemy : 1.4.46
tables : 3.7.0
tabulate : 0.9.0
xarray : 2022.12.0
xlrd : 2.0.1
zstandard : 0.19.0
tzdata : None
qtpy : None
pyqt5 : None
None

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