Fix pinv jax test and support hermitian flag

pytensor/link/jax/dispatch/nlinalg.py

@@ -89,7 +89,7 @@ def dot(x, y):
 @jax_funcify.register(MatrixPinv)
 def jax_funcify_Pinv(op, **kwargs):
     def pinv(x):
-        return jnp.linalg.pinv(x)
+        return jnp.linalg.pinv(x, hermitian=op.hermitian)
 
     return pinv
 

tests/link/jax/test_nlinalg.py

@@ -141,5 +141,36 @@ def test_pinv():
     x_inv = at_nlinalg.pinv(x)
 
     fgraph = FunctionGraph([x], [x_inv])
-    x_np = np.array([[1.0, 2.0], [3.0, 4.0]])
+    x_np = np.array([[1.0, 2.0], [3.0, 4.0]], dtype=config.floatX)
     compare_jax_and_py(fgraph, [x_np])
+
+
+def test_pinv_hermitian():
+    A = matrix("A", dtype="complex128")
+    A_h_test = np.c_[[3, 3 + 2j], [3 - 2j, 2]]
+    A_not_h_test = A_h_test + 0 + 1j
+
+    A_inv = at_nlinalg.pinv(A, hermitian=False)
+    jax_fn = function([A], A_inv, mode="JAX")
+
+    assert np.allclose(jax_fn(A_h_test), np.linalg.pinv(A_h_test, hermitian=False))
+    assert np.allclose(jax_fn(A_h_test), np.linalg.pinv(A_h_test, hermitian=True))
+    assert np.allclose(
+        jax_fn(A_not_h_test), np.linalg.pinv(A_not_h_test, hermitian=False)
+    )
+    assert not np.allclose(
+        jax_fn(A_not_h_test), np.linalg.pinv(A_not_h_test, hermitian=True)
+    )
+
+    A_inv = at_nlinalg.pinv(A, hermitian=True)
+    jax_fn = function([A], A_inv, mode="JAX")
+
+    assert np.allclose(jax_fn(A_h_test), np.linalg.pinv(A_h_test, hermitian=False))
+    assert np.allclose(jax_fn(A_h_test), np.linalg.pinv(A_h_test, hermitian=True))
+    assert not np.allclose(
+        jax_fn(A_not_h_test), np.linalg.pinv(A_not_h_test, hermitian=False)
+    )
+    # Numpy fails differently than JAX when hermitian assumption is violated
+    assert not np.allclose(
+        jax_fn(A_not_h_test), np.linalg.pinv(A_not_h_test, hermitian=True)
+    )