diff --git a/doc/sampling.rst b/doc/sampling.rst
index 3914c4a..85b2aaf 100644
--- a/doc/sampling.rst
+++ b/doc/sampling.rst
@@ -50,3 +50,9 @@ Base classes
 
 .. autoclass:: sparse_ir.sampling.DecomposedMatrix
     :members:
+
+.. autoclass:: sparse_ir.sampling.SplitDecomposedMatrix
+    :members:
+
+.. autoclass:: sparse_ir.sampling.ConditioningWarning
+    :members:
diff --git a/src/sparse_ir/sampling.py b/src/sparse_ir/sampling.py
index e1fd569..fac169a 100644
--- a/src/sparse_ir/sampling.py
+++ b/src/sparse_ir/sampling.py
@@ -26,7 +26,12 @@ def evaluate(self, al, axis=None):
 
     def fit(self, ax, axis=None):
         """Fit basis coefficients from the sparse sampling points"""
-        return self.matrix.lstsq(ax, axis)
+        matrix = self.matrix
+        if self.basis.is_well_conditioned and not (matrix.cond <= 1e8):
+            warn(f"Sampling matrix is poorly conditioned "
+                 f"(kappa = {matrix.cond:.2g})", ConditioningWarning)
+
+        return matrix.lstsq(ax, axis)
 
     @property
     def cond(self):
@@ -68,9 +73,6 @@ def __init__(self, basis, sampling_points=None):
         self._sampling_points = sampling_points
         self._matrix = DecomposedMatrix(matrix)
 
-        if basis.is_well_conditioned and self._matrix.cond > 1e8:
-            warn(f"Sampling matrix is poorly conditioned "
-                 f"(kappa = {self._matrix.cond:.2g})", ConditioningWarning)
 
     @property
     def basis(self): return self._basis
@@ -125,10 +127,6 @@ def __init__(self, basis, sampling_points=None, *, positive_only=False):
         else:
             self._matrix = DecomposedMatrix(matrix)
 
-        if basis.is_well_conditioned and self._matrix.cond > 1e8:
-            warn(f"Sampling matrix is poorly conditioned "
-                 f"(kappa = {self._matrix.cond:.2g})", ConditioningWarning)
-
     @property
     def basis(self): return self._basis
 
@@ -314,6 +312,13 @@ def cond(self):
 
 
 class ConditioningWarning(RuntimeWarning):
+    """Warns about a poorly conditioned problem.
+
+    This warning is issued if the library detects a poorly conditioned fitting
+    problem.  This essentially means there is a high degree of ambiguity in how
+    to choose the solution.  One must therefore expect to lose significant
+    precision in the parameter values.
+    """
     pass