Optimize _batched_lu_factor for dpnp.linalg.det/slogdet (#2572)

This PR suggests optimizing and simplifying `_batched_lu_factor` logic
by replacing per-iteration allocations with a single preallocated buffer
and batch-axis views which improves performance in `dpnp.linalg.det` and
`dpnp.linalg.slogdet`

Author: vlad-perevezentsev

CHANGELOG.md

@@ -42,6 +42,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 * Improved performance of `dpnp.isclose` function by implementing a dedicated kernel for scalar `rtol` and `atol` arguments [#2540](https://github.com/IntelPython/dpnp/pull/2540)
 * Extended `dpnp.pad` to support `pad_width` keyword as a dictionary [#2535](https://github.com/IntelPython/dpnp/pull/2535)
 * Redesigned `dpnp.erf` function through pybind11 extension of OneMKL call or dedicated kernel in `ufunc` namespace [#2551](https://github.com/IntelPython/dpnp/pull/2551)
+* Improved performance of batched implementation of `dpnp.linalg.det` and `dpnp.linalg.slogdet` [#2572](https://github.com/IntelPython/dpnp/pull/2572)
 
 ### Deprecated
 

dpnp/linalg/dpnp_utils_linalg.py

@@ -297,26 +297,27 @@ def _batched_lu_factor(a, res_type):
     batch_size = a.shape[0]
     a_usm_arr = dpnp.get_usm_ndarray(a)
 
+    # `a` must be copied because getrf/getrf_batch destroys the input matrix
+    a_h = dpnp.empty_like(a, order="C", dtype=res_type)
+    ht_ev, copy_ev = ti._copy_usm_ndarray_into_usm_ndarray(
+        src=a_usm_arr,
+        dst=a_h.get_array(),
+        sycl_queue=a_sycl_queue,
+        depends=_manager.submitted_events,
+    )
+    _manager.add_event_pair(ht_ev, copy_ev)
+
+    ipiv_h = dpnp.empty(
+        (batch_size, n),
+        dtype=dpnp.int64,
+        order="C",
+        usm_type=a_usm_type,
+        sycl_queue=a_sycl_queue,
+    )
+
     if use_batch:
-        # `a` must be copied because getrf_batch destroys the input matrix
-        a_h = dpnp.empty_like(a, order="C", dtype=res_type)
-        ipiv_h = dpnp.empty(
-            (batch_size, n),
-            dtype=dpnp.int64,
-            order="C",
-            usm_type=a_usm_type,
-            sycl_queue=a_sycl_queue,
-        )
         dev_info_h = [0] * batch_size
 
-        ht_ev, copy_ev = ti._copy_usm_ndarray_into_usm_ndarray(
-            src=a_usm_arr,
-            dst=a_h.get_array(),
-            sycl_queue=a_sycl_queue,
-            depends=_manager.submitted_events,
-        )
-        _manager.add_event_pair(ht_ev, copy_ev)
-
         ipiv_stride = n
         a_stride = a_h.strides[0]
 
@@ -336,63 +337,25 @@ def _batched_lu_factor(a, res_type):
         )
         _manager.add_event_pair(ht_ev, getrf_ev)
 
-        dev_info_array = dpnp.array(
-            dev_info_h, usm_type=a_usm_type, sycl_queue=a_sycl_queue
-        )
-
-        # Reshape the results back to their original shape
-        a_h = a_h.reshape(orig_shape)
-        ipiv_h = ipiv_h.reshape(orig_shape[:-1])
-        dev_info_array = dev_info_array.reshape(orig_shape[:-2])
-
-        return (a_h, ipiv_h, dev_info_array)
-
-    # Initialize lists for storing arrays and events for each batch
-    a_vecs = [None] * batch_size
-    ipiv_vecs = [None] * batch_size
-    dev_info_vecs = [None] * batch_size
-
-    dep_evs = _manager.submitted_events
-
-    # Process each batch
-    for i in range(batch_size):
-        # Copy each 2D slice to a new array because getrf will destroy
-        # the input matrix
-        a_vecs[i] = dpnp.empty_like(a[i], order="C", dtype=res_type)
-
-        ht_ev, copy_ev = ti._copy_usm_ndarray_into_usm_ndarray(
-            src=a_usm_arr[i],
-            dst=a_vecs[i].get_array(),
-            sycl_queue=a_sycl_queue,
-            depends=dep_evs,
-        )
-        _manager.add_event_pair(ht_ev, copy_ev)
-
-        ipiv_vecs[i] = dpnp.empty(
-            (n,),
-            dtype=dpnp.int64,
-            order="C",
-            usm_type=a_usm_type,
-            sycl_queue=a_sycl_queue,
-        )
-        dev_info_vecs[i] = [0]
+    else:
+        dev_info_h = [[0] for _ in range(batch_size)]
 
-        # Call the LAPACK extension function _getrf
-        # to perform LU decomposition on each batch in 'a_vecs[i]'
-        ht_ev, getrf_ev = li._getrf(
-            a_sycl_queue,
-            a_vecs[i].get_array(),
-            ipiv_vecs[i].get_array(),
-            dev_info_vecs[i],
-            depends=[copy_ev],
-        )
-        _manager.add_event_pair(ht_ev, getrf_ev)
+        # Sequential LU factorization using getrf per slice
+        for i in range(batch_size):
+            ht_ev, getrf_ev = li._getrf(
+                a_sycl_queue,
+                a_h[i].get_array(),
+                ipiv_h[i].get_array(),
+                dev_info_h[i],
+                depends=[copy_ev],
+            )
+            _manager.add_event_pair(ht_ev, getrf_ev)
 
     # Reshape the results back to their original shape
-    out_a = dpnp.array(a_vecs, order="C").reshape(orig_shape)
-    out_ipiv = dpnp.array(ipiv_vecs).reshape(orig_shape[:-1])
+    out_a = a_h.reshape(orig_shape)
+    out_ipiv = ipiv_h.reshape(orig_shape[:-1])
     out_dev_info = dpnp.array(
-        dev_info_vecs, usm_type=a_usm_type, sycl_queue=a_sycl_queue
+        dev_info_h, usm_type=a_usm_type, sycl_queue=a_sycl_queue
     ).reshape(orig_shape[:-2])
 
     return (out_a, out_ipiv, out_dev_info)