diff --git a/tests/qdwh_test.py b/tests/qdwh_test.py
index e6d299ae9..67a081e41 100644
--- a/tests/qdwh_test.py
+++ b/tests/qdwh_test.py
@@ -64,12 +64,18 @@ class QdwhTest(jtu.JaxTestCase):
     self._testUnitary(u, tol)
     self._testHermitian(h, tol)
 
-  def _testQdwh(self, a, is_hermitian=False):
+  def _testQdwh(self, a, is_hermitian=False, dynamic_shape=None):
     """Computes the polar decomposition and tests its basic properties."""
     eps = jnp.finfo(a.dtype).eps
-
-    u, h, iters, conv = qdwh.qdwh(a, is_hermitian=is_hermitian)
+    u, h, iters, conv = qdwh.qdwh(
+        a, is_hermitian=is_hermitian, dynamic_shape=dynamic_shape
+    )
     tol = 10 * eps
+    if dynamic_shape is not None:
+      m, n = dynamic_shape
+      a = a[:m, :n]
+      u = u[:m, :n]
+      h = h[:n, :n]
     self._testPolarDecomposition(a, u, h, tol=tol)
 
   @jtu.sample_product(
@@ -83,6 +89,40 @@ class QdwhTest(jtu.JaxTestCase):
     a = jnp.triu(jnp.ones((m, n))).astype(dtype)
     self._testQdwh(a)
 
+  @jtu.sample_product(
+      shape=[(2, 2), (5, 5), (8, 5), (10, 10)],
+      is_hermitian=[True, False],
+      dtype=float_types + complex_types,
+  )
+  def testQdwhWithDynamicShape(self, shape, is_hermitian, dtype):
+    """Tests qdwh with dynamic shapes."""
+    if is_hermitian & (shape[0] != shape[1]):
+      self.skipTest('Invalid combination')
+    rng = jtu.rand_uniform(self.rng())
+    a = rng((10, 10), dtype)
+
+    if is_hermitian:
+      a = (a + a.conj().T) / 2
+    self._testQdwh(a, is_hermitian=is_hermitian, dynamic_shape=shape)
+
+  @jtu.sample_product(
+      shape=[(8, 6), (5, 5), (10, 10), (20, 18), (300, 300)],
+      log_cond=np.linspace(0, 1, 4),
+      hermitian=[True, False],
+      dtype=float_types + complex_types,
+  )
+  def testQdwhWithRandomMatrix0(self, shape, log_cond, hermitian, dtype):
+    """Tests qdwh with upper triangular input of all ones."""
+    m, n = shape
+    rng = jtu.rand_uniform(self.rng())
+    a = rng((m, n), dtype)
+
+    # Generates input matrix with prescribed condition number.
+    hermitian = hermitian & (m == n)
+    if hermitian:
+      a = (a + a.conj().T) / 2
+    self._testQdwh(a, is_hermitian=hermitian)
+
   @jtu.sample_product(
       shape=[(8, 6), (10, 10), (20, 18), (300, 300)],
       log_cond=np.linspace(0, 1, 4),