from sklearn.discriminant_analysis import LinearDiscriminantAnalysis

n = ... # some int
X = [....] # q x r
Y = [....] # 1 x q, st. num_classes less than n

model = LinearDiscriminantAnalysis(n_components=n)
Xp = model.fit(X, Y).transform(X)

# Try to use Xp, and what!?!? Xp is of shape q x (num_classes - 1) not q x n as expected
raise ConfusionError()

import warnings
from .exceptions import ChangedBehaviorWarning
...

# https://github.com/scikit-learn/scikit-learn/blob/45dc891c96eebdb3b81bf14c2737d8f6540fabfe/sklearn/discriminant_analysis.py#L447
self._max_components = self.n_components
potential_components = len(self.classes_) - 1
if self._max_components is None:
     self._max_components = potential_components
elif self._max_components < potential_components:
     warnings.warn("Using a component size of %d due to invalid n_component" % potential_components, ChangedBehaviorWarning)
     self._max_components = potential_components