Don't mask out zero elements on the diagonal of the matrix when inver…

…ting triangular matrices.

The intent of this code seems to have been to mask out zeros that were part of padding on the diagonal. However, this isn't correct: if there is a zero on the diagonal, we very much want to get an inf or nan! We also appear to now pad with the identity matrix.

Fixes #3589
Fixes #15429

PiperOrigin-RevId: 653562611

CHANGELOG.md

@@ -42,6 +42,8 @@ Remember to align the itemized text with the first line of an item within a list
 * Bug fixes
   * Fixed a bug that meant that negative static_argnums to a jit were mishandled
     by the jit dispatch fast path.
+  * Fixed a bug that meant triangular solves of batches of singular matrices
+    produce nonsensical finite values, instead of inf or nan (#3589, #15429).
 
 ## jax 0.4.30 (June 18, 2024)
 

tests/linalg_test.py

@@ -16,6 +16,7 @@
 
 from functools import partial
 import itertools
+import unittest
 
 import numpy as np
 import scipy
@@ -33,6 +34,7 @@
 from jax._src.lax import linalg as lax_linalg
 from jax._src import test_util as jtu
 from jax._src import xla_bridge
+from jax._src.lib import xla_extension_version
 from jax._src.numpy.util import promote_dtypes_inexact
 
 config.parse_flags_with_absl()
@@ -1623,6 +1625,15 @@ def testTriangularSolveGradPrecision(self):
         (a, b),
         (a, b))
 
+  @unittest.skipIf(xla_extension_version < 277, "Requires jaxlib > 0.4.30")
+  def testTriangularSolveSingularBatched(self):
+    x = jnp.array([[1, 1], [0, 0]], dtype=np.float32)
+    y = jnp.array([[1], [1.]], dtype=np.float32)
+    out = jax.lax.linalg.triangular_solve(x[None], y[None], left_side=True)
+    # x is singular. The triangular solve may contain either nans or infs, but
+    # it should not consist of only finite values.
+    self.assertFalse(np.all(np.isfinite(out)))
+
   @jtu.sample_product(
     n=[1, 4, 5, 20, 50, 100],
     batch_size=[(), (2,), (3, 4)] if scipy_version >= (1, 9, 0) else [()],