Use computation dtype in dpnp.linalg.pinv for default tolerance and empty input

CHANGELOG.md

@@ -56,6 +56,7 @@ This release is compatible with NumPy 2.5.
 * Updated the implementation of `dpnp.putmask` by adding dedicated contiguous and strided SYCL kernels [#3014](https://github.com/IntelPython/dpnp/pull/3014)
 * Changed `dpnp.sort`, `dpnp.argsort`, and their `dpnp.ndarray`/`dpnp.tensor` counterparts to place `NaN` values last instead of first when sorting in descending order [#3066](https://github.com/IntelPython/dpnp/pull/3066)
 * Documented and made explicit support for `copy=None` ("copy only if needed") in `dpnp.nan_to_num` [#3083](https://github.com/IntelPython/dpnp/pull/3083)
+* Changed `dpnp.linalg.pinv` to compute the default tolerance from the machine epsilon of the data type used for the computation, and to return a floating-point result for an empty integer or boolean array [#3090](https://github.com/IntelPython/dpnp/pull/3090)
 
 ### Deprecated
 

dpnp/linalg/dpnp_utils_linalg.py

@@ -2402,10 +2402,12 @@ def dpnp_pinv(a, rcond=None, hermitian=False, rtol=None):
 
     """
 
+    # dtype the SVD is computed in
+    res_type = _common_type(a)
+
     if rcond is None:
         if rtol is None:
-            dtype = dpnp.result_type(a.dtype, dpnp.default_float_type(a.device))
-            rcond = max(a.shape[-2:]) * dpnp.finfo(dtype).eps
+            rcond = max(a.shape[-2:]) * dpnp.finfo(res_type).eps
         else:
             rcond = rtol
     elif rtol is not None:
@@ -2414,7 +2416,7 @@ def dpnp_pinv(a, rcond=None, hermitian=False, rtol=None):
     if _is_empty_2d(a):
         m, n = a.shape[-2:]
         sh = a.shape[:-2] + (n, m)
-        return dpnp.empty_like(a, shape=sh)
+        return dpnp.empty_like(a, shape=sh, dtype=res_type)
 
     if dpnp.is_supported_array_type(rcond):
         # Check that `a` and `rcond` are allocated on the same device

dpnp/tests/test_linalg.py

@@ -20,6 +20,7 @@
     generate_random_numpy_array,
     get_all_dtypes,
     get_float_complex_dtypes,
+    get_integer_dtypes,
     get_integer_float_dtypes,
     has_support_aspect64,
     numpy_version,
@@ -4370,7 +4371,29 @@ def test_pinv_rtol(self):
         result = dpnp.linalg.pinv(a_dp, rtol=1e-15)
         assert_dtype_allclose(result, expected)
 
-    @pytest.mark.parametrize("dtype", get_all_dtypes(no_bool=True))
+    @testing.with_requires("numpy>=2.0")
+    @pytest.mark.parametrize("dtype", get_float_complex_dtypes())
+    def test_pinv_rtol_none(self, dtype):
+        # singular value 1e-9 is cut off for single precision only
+        a = numpy.diag([1.0, 1e-9]).astype(dtype)
+        a_dp = dpnp.array(a)
+
+        expected = numpy.linalg.pinv(a, rtol=None)
+        result = dpnp.linalg.pinv(a_dp, rtol=None)
+        assert_dtype_allclose(result, expected)
+
+    @testing.with_requires("numpy>=2.0")
+    @pytest.mark.parametrize("dtype", get_integer_dtypes() + [dpnp.bool])
+    def test_pinv_rtol_none_non_inexact(self, dtype):
+        a = numpy.array([[1, 2, 3], [4, 1, 1], [2, 3, 1]]).astype(dtype)
+        a_dp = dpnp.array(a)
+
+        # NumPy < 2.6.0 raises ValueError for non-inexact input
+        expected = numpy.linalg.pinv(a.astype(numpy.float64), rtol=None)
+        result = dpnp.linalg.pinv(a_dp, rtol=None)
+        assert_dtype_allclose(result, expected)
+
+    @pytest.mark.parametrize("dtype", get_all_dtypes())
     @pytest.mark.parametrize(
         "shape",
         [(0, 0), (0, 2), (2, 0), (2, 0, 3), (2, 3, 0), (0, 2, 3)],
@@ -4388,6 +4411,9 @@ def test_pinv_empty(self, dtype, shape):
         a_dp = dpnp.array(a)
 
         B = numpy.linalg.pinv(a)
+        if numpy_version() < "2.6.0" and a.dtype.kind in "biu":
+            # NumPy < 2.6.0 returns the input dtype for empty int/bool input
+            B = B.astype(numpy.float64)
         B_dp = dpnp.linalg.pinv(a_dp)
 
         assert_dtype_allclose(B_dp, B)

dpnp/tests/third_party/cupy/linalg_tests/test_solve.py

@@ -7,6 +7,7 @@
 from dpnp.tests.helper import (
     assert_dtype_allclose,
     has_support_aspect64,
+    numpy_version,
 )
 from dpnp.tests.third_party.cupy import testing
 from dpnp.tests.third_party.cupy.testing import _condition
@@ -247,6 +248,9 @@ def check_x(self, a_shape, rcond, dtype):
         if not isinstance(rcond, float):
             rcond = numpy.asarray(rcond)
         result_cpu = numpy.linalg.pinv(a_cpu, rcond=rcond)
+        if numpy_version() < "2.6.0" and a_cpu.dtype.kind in "biu":
+            # NumPy < 2.6.0 returns the input dtype for empty int/bool input
+            result_cpu = result_cpu.astype(numpy.float64)
         if not isinstance(rcond, float):
             rcond = cupy.asarray(rcond)
         result_gpu = cupy.linalg.pinv(a_gpu, rcond=rcond)