`sc.pp.neighbors` uses the default value of `n_comps` in `sc.pp.pca` instead of `n_pcs` in `sc.pp.neighbors` when `X_pca ` is not precomputed

• [yes] I have checked that this issue has not already been reported.
• [yes] I have confirmed this bug exists on the latest version of scanpy.
• [yes] I have confirmed this bug exists on the master branch of scanpy.

Suggested fix: change line 44 in scanpy/scanpy/tools/_utils.py

https://github.com/theislab/scanpy/blob/83f90141fd18943a1795772d3d39f4e9eefd65c3/scanpy/tools/_utils.py#L44

from X = pca(adata.X) to X = pca(adata.X)[:, :n_pcs].

Note: Please read this guide detailing how to provide the necessary information for us to reproduce your bug.

Minimal code sample (that we can copy&paste without having any data)

# Minimal code 
import scanpy as sc
import anndata
import numpy as np
print('scanpy=', sc.__version__)
print('anndata=', anndata.__version__)
print('numpy=', np.__version__)

np.random.seed(0)
adata_raw = anndata.AnnData(np.random.randn(20,200))
print('adata shape', adata.shape)

# neighbors without precomputed pca
adata = adata_raw.copy()
sc.pp.neighbors(adata, n_neighbors=10, n_pcs=15)
mat_neighbor10_pc15_without_pca = adata.obsp["connectivities"].copy()

adata = adata_raw.copy()
sc.pp.pca(adata, n_comps=15)
sc.pp.neighbors(adata, n_neighbors=10, n_pcs=15)
mat_neighbor10_pc15_with_pca = adata.obsp["connectivities"].copy()

adata = adata_raw.copy()
sc.pp.pca(adata, n_comps=19) # max n_comps for 30 cells
sc.pp.neighbors(adata, n_neighbors=10, n_pcs=19)
mat_neighbor10_pc19_with_pca = adata.obsp["connectivities"].copy()

print('\nResults for `sc.pp.neighbors(adata, n_neighbors=10, n_pcs=15)` '
      'with and without precomputed pca are different:')
print(np.allclose(mat_neighbor10_pc15_without_pca.toarray(), mat_neighbor10_pc15_with_pca.toarray()))
print('\nResults of `sc.pp.neighbors(adata, n_neighbors=10, n_pcs=15)` without precomputed pca is same as '
      'results of `sc.pp.neighbors(adata, n_neighbors=10, n_pcs=19)` (19 is default `n_comps` for sc.pp.pca)'
      ' with precomputed pca')
print(np.allclose(mat_neighbor10_pc15_without_pca.toarray(), mat_neighbor10_pc19_with_pca.toarray()))

scanpy= 1.6.0
anndata= 0.7.4
numpy= 1.19.0
adata shape (20, 200)
WARNING: You’re trying to run this on 200 dimensions of `.X`, if you really want this, set `use_rep='X'`.
         Falling back to preprocessing with `sc.pp.pca` and default params.

Results for `sc.pp.neighbors(adata, n_neighbors=10, n_pcs=15)` with and without precomputed pca are different
False

Results of `sc.pp.neighbors(adata, n_neighbors=10, n_pcs=15)` without precomputed pca is same as results of `sc.pp.neighbors(adata, n_neighbors=10, n_pcs=19)` (19 is default `n_comps` for sc.pp.pca) with precomputed pca
True

Versions

Start at scanpy/scanpy/tools/_utils.py line 44 and reproduce the behavior with the minimal Python example using sc.pp.neighbors and sc.pp.pca. Update the fallback PCA path so the requested n_pcs is respected, then verify that neighbor results match the precomputed-PCA case in the supplied comparisons.