docs: clarify broadcasting semantics and output shape in linalg.solve (#810)

PR-URL: #810

Author: asmeurer

src/array_api_stubs/_2022_12/linalg.py

@@ -594,12 +594,12 @@ def solve(x1: array, x2: array, /) -> array:
     x1: array
         coefficient array ``A`` having shape ``(..., M, M)`` and whose innermost two dimensions form square matrices. Must be of full rank (i.e., all rows or, equivalently, columns must be linearly independent). Should have a floating-point data type.
     x2: array
-        ordinate (or "dependent variable") array ``B``. If ``x2`` has shape ``(M,)``, ``x2`` is equivalent to an array having shape ``(..., M, 1)``. If ``x2`` has shape ``(..., M, K)``, each column ``k`` defines a set of ordinate values for which to compute a solution, and ``shape(x2)[:-1]`` must be compatible with ``shape(x1)[:-1]`` (see :ref:`broadcasting`). Should have a floating-point data type.
+        ordinate (or "dependent variable") array ``B``. If ``x2`` has shape ``(M,)``, ``x2`` is equivalent to an array having shape ``(..., M, 1)``. If ``x2`` has shape ``(..., M, K)``, each column ``k`` defines a set of ordinate values for which to compute a solution, and ``shape(x2)[:-2]`` must be compatible with ``shape(x1)[:-2]`` (see :ref:`broadcasting`). Should have a floating-point data type.
 
     Returns
     -------
     out: array
-        an array containing the solution to the system ``AX = B`` for each square matrix. The returned array must have the same shape as ``x2`` (i.e., the array corresponding to ``B``) and must have a floating-point data type determined by :ref:`type-promotion`.
+        an array containing the solution to the system ``AX = B`` for each square matrix. If ``x2`` has shape ``(M,)``, the returned array must have shape equal to ``shape(x1)[:-2] + shape(x2)[-1:]``. Otherwise, if ``x2`` has shape ``(..., M, K)```, the returned array must have shape equal to ``(..., M, K)``, where ``...`` refers to the result of broadcasting ``shape(x1)[:-2]`` and ``shape(x2)[:-2]``. The returned array must have a floating-point data type determined by :ref:`type-promotion`.
 
     Notes
     -----

src/array_api_stubs/_2023_12/linalg.py

@@ -623,12 +623,12 @@ def solve(x1: array, x2: array, /) -> array:
     x1: array
         coefficient array ``A`` having shape ``(..., M, M)`` and whose innermost two dimensions form square matrices. Must be of full rank (i.e., all rows or, equivalently, columns must be linearly independent). Should have a floating-point data type.
     x2: array
-        ordinate (or "dependent variable") array ``B``. If ``x2`` has shape ``(M,)``, ``x2`` is equivalent to an array having shape ``(..., M, 1)``. If ``x2`` has shape ``(..., M, K)``, each column ``k`` defines a set of ordinate values for which to compute a solution, and ``shape(x2)[:-1]`` must be compatible with ``shape(x1)[:-1]`` (see :ref:`broadcasting`). Should have a floating-point data type.
+        ordinate (or "dependent variable") array ``B``. If ``x2`` has shape ``(M,)``, ``x2`` is equivalent to an array having shape ``(..., M, 1)``. If ``x2`` has shape ``(..., M, K)``, each column ``k`` defines a set of ordinate values for which to compute a solution, and ``shape(x2)[:-2]`` must be compatible with ``shape(x1)[:-2]`` (see :ref:`broadcasting`). Should have a floating-point data type.
 
     Returns
     -------
     out: array
-        an array containing the solution to the system ``AX = B`` for each square matrix. The returned array must have the same shape as ``x2`` (i.e., the array corresponding to ``B``) and must have a floating-point data type determined by :ref:`type-promotion`.
+        an array containing the solution to the system ``AX = B`` for each square matrix. If ``x2`` has shape ``(M,)``, the returned array must have shape equal to ``shape(x1)[:-2] + shape(x2)[-1:]``. Otherwise, if ``x2`` has shape ``(..., M, K)```, the returned array must have shape equal to ``(..., M, K)``, where ``...`` refers to the result of broadcasting ``shape(x1)[:-2]`` and ``shape(x2)[:-2]``. The returned array must have a floating-point data type determined by :ref:`type-promotion`.
 
     Notes
     -----

src/array_api_stubs/_2023_12/manipulation_functions.py

@@ -347,7 +347,7 @@ def tile(x: array, repetitions: Tuple[int, ...], /) -> array:
 
 def unstack(x: array, /, *, axis: int = 0) -> Tuple[array, ...]:
     """
-    Splits an array in a sequence of arrays along the given axis.
+    Splits an array into a sequence of arrays along the given axis.
 
     Parameters
     ----------

src/array_api_stubs/_draft/linalg.py

@@ -623,12 +623,12 @@ def solve(x1: array, x2: array, /) -> array:
     x1: array
         coefficient array ``A`` having shape ``(..., M, M)`` and whose innermost two dimensions form square matrices. Must be of full rank (i.e., all rows or, equivalently, columns must be linearly independent). Should have a floating-point data type.
     x2: array
-        ordinate (or "dependent variable") array ``B``. If ``x2`` has shape ``(M,)``, ``x2`` is equivalent to an array having shape ``(..., M, 1)``. If ``x2`` has shape ``(..., M, K)``, each column ``k`` defines a set of ordinate values for which to compute a solution, and ``shape(x2)[:-1]`` must be compatible with ``shape(x1)[:-1]`` (see :ref:`broadcasting`). Should have a floating-point data type.
+        ordinate (or "dependent variable") array ``B``. If ``x2`` has shape ``(M,)``, ``x2`` is equivalent to an array having shape ``(..., M, 1)``. If ``x2`` has shape ``(..., M, K)``, each column ``k`` defines a set of ordinate values for which to compute a solution, and ``shape(x2)[:-2]`` must be compatible with ``shape(x1)[:-2]`` (see :ref:`broadcasting`). Should have a floating-point data type.
 
     Returns
     -------
     out: array
-        an array containing the solution to the system ``AX = B`` for each square matrix. The returned array must have the same shape as ``x2`` (i.e., the array corresponding to ``B``) and must have a floating-point data type determined by :ref:`type-promotion`.
+        an array containing the solution to the system ``AX = B`` for each square matrix. If ``x2`` has shape ``(M,)``, the returned array must have shape equal to ``shape(x1)[:-2] + shape(x2)[-1:]``. Otherwise, if ``x2`` has shape ``(..., M, K)```, the returned array must have shape equal to ``(..., M, K)``, where ``...`` refers to the result of broadcasting ``shape(x1)[:-2]`` and ``shape(x2)[:-2]``. The returned array must have a floating-point data type determined by :ref:`type-promotion`.
 
     Notes
     -----

src/array_api_stubs/_draft/manipulation_functions.py

@@ -347,7 +347,7 @@ def tile(x: array, repetitions: Tuple[int, ...], /) -> array:
 
 def unstack(x: array, /, *, axis: int = 0) -> Tuple[array, ...]:
     """
-    Splits an array in a sequence of arrays along the given axis.
+    Splits an array into a sequence of arrays along the given axis.
 
     Parameters
     ----------