MAINT: Fix computation of numpy.array_api.linalg.vector_norm (#21084)

* Fix computation of numpy.array_api.linalg.vector_norm

Various pieces were incorrect due to a lack of complete coverage of this
function in the array API test suite.

* Fix the output dtype nonstandard vector norm()

Previously it would always give float64 because an internal calculation
involved a NumPy scalar and a Python float. The fix is to use a 0-D array
instead of a NumPy scalar so that it type promotes with the float correctly.

Fixes #21083

I don't have a test for this yet because I'm unclear how exactly to test it.

* Clean up the numpy.array_api.linalg.vector_norm code a little bit

Original NumPy Commit: 70026c4dde47d89d6a7a4916bfac045e714a5b4f

Author: asmeurer

array_api_strict/linalg.py

@@ -1,8 +1,11 @@
 from __future__ import annotations
 
 from ._dtypes import _floating_dtypes, _numeric_dtypes
+from ._manipulation_functions import reshape
 from ._array_object import Array
 
+from numpy.core.numeric import normalize_axis_tuple
+
 from typing import TYPE_CHECKING
 if TYPE_CHECKING:
     from ._typing import Literal, Optional, Sequence, Tuple, Union
@@ -395,18 +398,38 @@ def vector_norm(x: Array, /, *, axis: Optional[Union[int, Tuple[int, ...]]] = No
     if x.dtype not in _floating_dtypes:
         raise TypeError('Only floating-point dtypes are allowed in norm')
 
+    # np.linalg.norm tries to do a matrix norm whenever axis is a 2-tuple or
+    # when axis=None and the input is 2-D, so to force a vector norm, we make
+    # it so the input is 1-D (for axis=None), or reshape so that norm is done
+    # on a single dimension.
     a = x._array
     if axis is None:
-        a = a.flatten()
-        axis = 0
+        # Note: np.linalg.norm() doesn't handle 0-D arrays
+        a = a.ravel()
+        _axis = 0
     elif isinstance(axis, tuple):
-        # Note: The axis argument supports any number of axes, whereas norm()
-        # only supports a single axis for vector norm.
-        rest = tuple(i for i in range(a.ndim) if i not in axis)
+        # Note: The axis argument supports any number of axes, whereas
+        # np.linalg.norm() only supports a single axis for vector norm.
+        normalized_axis = normalize_axis_tuple(axis, x.ndim)
+        rest = tuple(i for i in range(a.ndim) if i not in normalized_axis)
         newshape = axis + rest
-        a = np.transpose(a, newshape).reshape((np.prod([a.shape[i] for i in axis]), *[a.shape[i] for i in rest]))
-        axis = 0
-    return Array._new(np.linalg.norm(a, axis=axis, keepdims=keepdims, ord=ord))
+        a = np.transpose(a, newshape).reshape(
+            (np.prod([a.shape[i] for i in axis], dtype=int), *[a.shape[i] for i in rest]))
+        _axis = 0
+    else:
+        _axis = axis
+
+    res = Array._new(np.linalg.norm(a, axis=_axis, ord=ord))
+
+    if keepdims:
+        # We can't reuse np.linalg.norm(keepdims) because of the reshape hacks
+        # above to avoid matrix norm logic.
+        shape = list(x.shape)
+        _axis = normalize_axis_tuple(range(x.ndim) if axis is None else axis, x.ndim)
+        for i in _axis:
+            shape[i] = 1
+        res = reshape(res, tuple(shape))
 
+    return res
 
 __all__ = ['cholesky', 'cross', 'det', 'diagonal', 'eigh', 'eigvalsh', 'inv', 'matmul', 'matrix_norm', 'matrix_power', 'matrix_rank', 'matrix_transpose', 'outer', 'pinv', 'qr', 'slogdet', 'solve', 'svd', 'svdvals', 'tensordot', 'trace', 'vecdot', 'vector_norm']