Enable aten::linalg_inv and aten::linalg_inv_ex (#1940)

This PR introduces the `inverse`, `linalg_inv` and `linalg_inv_ex`
operators for XPU.
Added skip entries for error and warning tests related to inverse
operations for all dtypes, due to a temporary regression in oneMKL.

Author: CuiYifeng

src/ATen/native/xpu/XPUFallback.template

@@ -201,7 +201,6 @@ TORCH_LIBRARY_IMPL(aten, XPU, m) {
     "_linalg_eigh.eigenvalues",
     "linalg_householder_product",
     "linalg_householder_product.out",
-    "linalg_inv_ex.inverse",
     "linalg_ldl_factor_ex.out",
     "linalg_ldl_solve.out",
     "linalg_lstsq.out",

test/xpu/skip_list_common.py

@@ -551,8 +551,6 @@
         "test_neg_view_linalg_eigh_xpu_float64",
         "test_neg_view_linalg_eigvalsh_xpu_float64",
         "test_neg_view_linalg_householder_product_xpu_float64",
-        "test_neg_view_linalg_inv_ex_xpu_float64",
-        "test_neg_view_linalg_inv_xpu_float64",
         "test_neg_view_linalg_ldl_factor_ex_xpu_float64",
         "test_neg_view_linalg_ldl_factor_xpu_float64",
         "test_neg_view_linalg_ldl_solve_xpu_float64",
@@ -1279,10 +1277,8 @@
         "test_invariance_error_spectral_decompositions_xpu_complex128",
         "test_inverse_many_batches_xpu_complex128",
         "test_inverse_many_batches_xpu_complex64",
-        "test_inverse_many_batches_xpu_float64",
         "test_inverse_xpu_complex128",
         "test_inverse_xpu_complex64",
-        "test_inverse_xpu_float64",
         "test_ldl_factor_xpu_complex128",
         "test_ldl_factor_xpu_complex64",
         "test_ldl_factor_xpu_float64",
@@ -1471,6 +1467,27 @@
         "test_scaled_gemm_offline_tunableop_xpu_float8_e5m2fnuz",
         # case need to port for xpu
         "test_gemm_bias_offline_tunableop_xpu_bfloat16",
+        # Exception is temporarily unavailable due to regression in oneMKL
+        "test_inv_errors_and_warnings_xpu_complex128",
+        "test_inv_errors_and_warnings_xpu_complex64",
+        "test_inv_errors_and_warnings_xpu_float32",
+        "test_inv_errors_and_warnings_xpu_float64",
+        "test_inverse_errors_large_xpu_complex128",
+        "test_inverse_errors_large_xpu_complex64",
+        "test_inverse_errors_large_xpu_float32",
+        "test_inverse_errors_large_xpu_float64",
+        "test_inverse_errors_xpu_complex128",
+        "test_inverse_errors_xpu_complex64",
+        "test_inverse_errors_xpu_float32",
+        "test_inverse_errors_xpu_float64",
+        "test_inv_ex_singular_xpu_complex128",
+        "test_inv_ex_singular_xpu_complex64",
+        "test_inv_ex_singular_xpu_float32",
+        "test_inv_ex_singular_xpu_float64",
+        "test_tensorinv_singular_input_xpu_complex128",
+        "test_tensorinv_singular_input_xpu_complex64",
+        "test_tensorinv_singular_input_xpu_float32",
+        "test_tensorinv_singular_input_xpu_float64",
     ),
     "test_ops_fwd_gradients_xpu.py": (
         # All of the followings are oneDNN issues
@@ -1520,9 +1537,7 @@
         "test_fn_fwgrad_bwgrad_linalg_householder_product_xpu_complex128",
         "test_fn_fwgrad_bwgrad_linalg_householder_product_xpu_float64",
         "test_fn_fwgrad_bwgrad_linalg_inv_ex_xpu_complex128",
-        "test_fn_fwgrad_bwgrad_linalg_inv_ex_xpu_float64",
         "test_fn_fwgrad_bwgrad_linalg_inv_xpu_complex128",
-        "test_fn_fwgrad_bwgrad_linalg_inv_xpu_float64",
         "test_fn_fwgrad_bwgrad_linalg_lstsq_grad_oriented_xpu_complex128",
         "test_fn_fwgrad_bwgrad_linalg_lstsq_grad_oriented_xpu_float64",
         "test_fn_fwgrad_bwgrad_linalg_lu_factor_ex_xpu_complex128",
@@ -1554,7 +1569,6 @@
         "test_fn_fwgrad_bwgrad_linalg_svdvals_xpu_complex128",
         "test_fn_fwgrad_bwgrad_linalg_svdvals_xpu_float64",
         "test_fn_fwgrad_bwgrad_linalg_tensorinv_xpu_complex128",
-        "test_fn_fwgrad_bwgrad_linalg_tensorinv_xpu_float64",
         "test_fn_fwgrad_bwgrad_linalg_tensorsolve_xpu_complex128",
         "test_fn_fwgrad_bwgrad_linalg_tensorsolve_xpu_float64",
         "test_fn_fwgrad_bwgrad_logdet_xpu_complex128",
@@ -1632,9 +1646,7 @@
         "test_forward_mode_AD_linalg_householder_product_xpu_complex128",
         "test_forward_mode_AD_linalg_householder_product_xpu_float64",
         "test_forward_mode_AD_linalg_inv_ex_xpu_complex128",
-        "test_forward_mode_AD_linalg_inv_ex_xpu_float64",
         "test_forward_mode_AD_linalg_inv_xpu_complex128",
-        "test_forward_mode_AD_linalg_inv_xpu_float64",
         "test_forward_mode_AD_linalg_lstsq_grad_oriented_xpu_complex128",
         "test_forward_mode_AD_linalg_lstsq_grad_oriented_xpu_float64",
         "test_forward_mode_AD_linalg_lu_factor_ex_xpu_complex128",
@@ -1667,7 +1679,6 @@
         "test_forward_mode_AD_linalg_svdvals_xpu_complex128",
         "test_forward_mode_AD_linalg_svdvals_xpu_float64",
         "test_forward_mode_AD_linalg_tensorinv_xpu_complex128",
-        "test_forward_mode_AD_linalg_tensorinv_xpu_float64",
         "test_forward_mode_AD_linalg_tensorsolve_xpu_complex128",
         "test_forward_mode_AD_linalg_tensorsolve_xpu_float64",
         "test_forward_mode_AD_logdet_xpu_complex128",
@@ -1858,9 +1869,7 @@
         "test_fn_grad_linalg_householder_product_xpu_complex128",
         "test_fn_grad_linalg_householder_product_xpu_float64",
         "test_fn_grad_linalg_inv_ex_xpu_complex128",
-        "test_fn_grad_linalg_inv_ex_xpu_float64",
         "test_fn_grad_linalg_inv_xpu_complex128",
-        "test_fn_grad_linalg_inv_xpu_float64",
         "test_fn_grad_linalg_lstsq_grad_oriented_xpu_complex128",
         "test_fn_grad_linalg_lstsq_grad_oriented_xpu_float64",
         "test_fn_grad_linalg_lu_factor_ex_xpu_complex128",
@@ -1893,7 +1902,6 @@
         "test_fn_grad_linalg_svdvals_xpu_complex128",
         "test_fn_grad_linalg_svdvals_xpu_float64",
         "test_fn_grad_linalg_tensorinv_xpu_complex128",
-        "test_fn_grad_linalg_tensorinv_xpu_float64",
         "test_fn_grad_linalg_tensorsolve_xpu_complex128",
         "test_fn_grad_linalg_tensorsolve_xpu_float64",
         "test_fn_grad_logdet_xpu_complex128",
@@ -1973,9 +1981,7 @@
         "test_fn_gradgrad_linalg_householder_product_xpu_complex128",
         "test_fn_gradgrad_linalg_householder_product_xpu_float64",
         "test_fn_gradgrad_linalg_inv_ex_xpu_complex128",
-        "test_fn_gradgrad_linalg_inv_ex_xpu_float64",
         "test_fn_gradgrad_linalg_inv_xpu_complex128",
-        "test_fn_gradgrad_linalg_inv_xpu_float64",
         "test_fn_gradgrad_linalg_lstsq_grad_oriented_xpu_complex128",
         "test_fn_gradgrad_linalg_lstsq_grad_oriented_xpu_float64",
         "test_fn_gradgrad_linalg_lu_factor_ex_xpu_complex128",
@@ -2006,7 +2012,6 @@
         "test_fn_gradgrad_linalg_svdvals_xpu_complex128",
         "test_fn_gradgrad_linalg_svdvals_xpu_float64",
         "test_fn_gradgrad_linalg_tensorinv_xpu_complex128",
-        "test_fn_gradgrad_linalg_tensorinv_xpu_float64",
         "test_fn_gradgrad_linalg_tensorsolve_xpu_complex128",
         "test_fn_gradgrad_linalg_tensorsolve_xpu_float64",
         "test_fn_gradgrad_logdet_xpu_complex128",
@@ -2334,9 +2339,7 @@
         "test_dispatch_meta_outplace_linalg_eigvalsh_xpu_complex",
         "test_dispatch_meta_outplace_linalg_eigvalsh_xpu_float64",
         "test_dispatch_meta_outplace_linalg_inv_ex_xpu_complex",
-        "test_dispatch_meta_outplace_linalg_inv_ex_xpu_float64",
         "test_dispatch_meta_outplace_linalg_inv_xpu_complex",
-        "test_dispatch_meta_outplace_linalg_inv_xpu_float64",
         "test_dispatch_meta_outplace_linalg_ldl_factor_ex_xpu_complex",
         "test_dispatch_meta_outplace_linalg_ldl_factor_ex_xpu_float64",
         "test_dispatch_meta_outplace_linalg_ldl_factor_xpu_complex",
@@ -2371,7 +2374,6 @@
         "test_dispatch_meta_outplace_linalg_svd_xpu_complex",
         "test_dispatch_meta_outplace_linalg_svd_xpu_float64",
         "test_dispatch_meta_outplace_linalg_tensorinv_xpu_complex",
-        "test_dispatch_meta_outplace_linalg_tensorinv_xpu_float64",
         "test_dispatch_meta_outplace_logdet_xpu_complex",
         "test_dispatch_meta_outplace_logdet_xpu_float64",
         "test_dispatch_meta_outplace_lu_solve_xpu_complex",
@@ -2454,9 +2456,7 @@
         "test_dispatch_symbolic_meta_outplace_linalg_eigvalsh_xpu_complex",
         "test_dispatch_symbolic_meta_outplace_linalg_eigvalsh_xpu_float64",
         "test_dispatch_symbolic_meta_outplace_linalg_inv_ex_xpu_complex",
-        "test_dispatch_symbolic_meta_outplace_linalg_inv_ex_xpu_float64",
         "test_dispatch_symbolic_meta_outplace_linalg_inv_xpu_complex",
-        "test_dispatch_symbolic_meta_outplace_linalg_inv_xpu_float64",
         "test_dispatch_symbolic_meta_outplace_linalg_ldl_factor_ex_xpu_complex",
         "test_dispatch_symbolic_meta_outplace_linalg_ldl_factor_ex_xpu_float64",
         "test_dispatch_symbolic_meta_outplace_linalg_ldl_factor_xpu_complex",
@@ -2491,7 +2491,6 @@
         "test_dispatch_symbolic_meta_outplace_linalg_svd_xpu_complex",
         "test_dispatch_symbolic_meta_outplace_linalg_svd_xpu_float64",
         "test_dispatch_symbolic_meta_outplace_linalg_tensorinv_xpu_complex",
-        "test_dispatch_symbolic_meta_outplace_linalg_tensorinv_xpu_float64",
         "test_dispatch_symbolic_meta_outplace_logdet_xpu_complex",
         "test_dispatch_symbolic_meta_outplace_logdet_xpu_float64",
         "test_dispatch_symbolic_meta_outplace_lu_solve_xpu_complex",
@@ -2574,9 +2573,7 @@
         "test_meta_outplace_linalg_eigvalsh_xpu_complex",
         "test_meta_outplace_linalg_eigvalsh_xpu_float64",
         "test_meta_outplace_linalg_inv_ex_xpu_complex",
-        "test_meta_outplace_linalg_inv_ex_xpu_float64",
         "test_meta_outplace_linalg_inv_xpu_complex",
-        "test_meta_outplace_linalg_inv_xpu_float64",
         "test_meta_outplace_linalg_ldl_factor_ex_xpu_complex",
         "test_meta_outplace_linalg_ldl_factor_ex_xpu_float64",
         "test_meta_outplace_linalg_ldl_factor_xpu_complex",
@@ -2611,7 +2608,6 @@
         "test_meta_outplace_linalg_svd_xpu_complex",
         "test_meta_outplace_linalg_svd_xpu_float64",
         "test_meta_outplace_linalg_tensorinv_xpu_complex",
-        "test_meta_outplace_linalg_tensorinv_xpu_float64",
         "test_meta_outplace_logdet_xpu_complex",
         "test_meta_outplace_logdet_xpu_float64",
         "test_meta_outplace_lu_solve_xpu_complex",

yaml/native/native_functions.yaml

@@ -9433,3 +9433,24 @@
 
 - func: linalg_solve(Tensor A, Tensor B, *, bool left=True) -> Tensor
   python_module: linalg
+
+- func: linalg_inv_ex(Tensor A, *, bool check_errors=False) -> (Tensor inverse, Tensor info)
+  python_module: linalg
+  structured_delegate: linalg_inv_ex.inverse
+
+- func: linalg_inv_ex.inverse(Tensor A, *, bool check_errors=False, Tensor(a!) inverse, Tensor(b!) info) -> (Tensor(a!) inverse, Tensor(b!) info)
+  python_module: linalg
+  structured: True
+  dispatch:
+    XPU: linalg_inv_ex_out
+
+- func: linalg_inv(Tensor A) -> Tensor
+  python_module: linalg
+
+- func: linalg_inv.out(Tensor A, *, Tensor(a!) out) -> Tensor(a!)
+  python_module: linalg
+
+- func: inverse(Tensor self) -> Tensor
+  variants: function, method
+
+- func: inverse.out(Tensor self, *, Tensor(a!) out) -> Tensor(a!)