Repository: google/jax
Issue: jax.numpy.meshgrid arg check for "indexing" fails

Hi,
I just noticed `meshgrid` function failed to throw error if  there is typo for arg `indexing`, this cause me a lot time for debugging.

```python
import jax.numpy as jnp
import numpy as np

if __name__ == "__main__":
    jm = jnp.arange(2)
    jn = jnp.arange(2)
    # here is a typo "index" which should be "indexing"
    # but there is no error, and the output is just as if
    # it was indexing="xy"
    jmm, jnn = jnp.meshgrid(jm, jn, index="ij")
    print("jax: typo index, but no error,xy ordered output")
    print(jmm)
    print(jnn)
    print("jax: no typo, correct ij ordered output")
    # here is the right args
    jmm, jnn = jnp.meshgrid(jm, jn, indexing="ij")
    print(jmm)
    print(jnn)

    m = np.arange(2)
    n = np.arange(2)
    mm, nn = np.meshgrid(m, n, indexing="ij")
    print("numpy correct ij ordered output")
    print(mm)
    print(nn)

    # below typo of index for numpy code will error
    mm, nn = np.meshgrid(m, n, index="ij")

```
output:
```python
jax: typo index, but no error,xy ordered output
[[0 1]
 [0 1]]
[[0 0]
 [1 1]]
jax: no typo, correct ij ordered output
[[0 0]
 [1 1]]
[[0 1]
 [0 1]]
numpy correct ij ordered output
[[0 0]
 [1 1]]
[[0 1]
 [0 1]]
Traceback (most recent call last):
  File "6.py", line 28, in <module>
    mm, nn = np.meshgrid(m, n, index="ij")
  File "<__array_function__ internals>", line 4, in meshgrid
TypeError: _meshgrid_dispatcher() got an unexpected keyword argument 'index'
```


Changed files:
jax/_src/numpy/lax_numpy.py

diff --git a/jax/_src/numpy/lax_numpy.py b/jax/_src/numpy/lax_numpy.py
index 16aeeffc5..73dba24bc 100644
--- a/jax/_src/numpy/lax_numpy.py
+++ b/jax/_src/numpy/lax_numpy.py
@@ -3870,41 +3870,23 @@ def _geomspace(start, stop, num=50, endpoint=True, dtype=None, axis: int = 0):
 
 
 @_wraps(np.meshgrid, lax_description=_ARRAY_VIEW_DOC)
-def meshgrid(*args, **kwargs):
-  _check_arraylike("meshgrid", *args)
-  indexing = kwargs.get("indexing", "xy")
-  sparse = kwargs.get("sparse", False)
-  copy = kwargs.get("copy", True)
+def meshgrid(*xi, copy=True, sparse=False, indexing='xy'):
+  _check_arraylike("meshgrid", *xi)
+  args = [asarray(x) for x in xi]
   if not copy:
     raise ValueError("jax.numpy.meshgrid only supports copy=True")
-
-  args = list(args)
-  if indexing == "xy":
-    if len(args) >= 2:
-      args[0], args[1] = args[1], args[0]
-  elif indexing != "ij":
-    raise ValueError("Valid values for indexing are 'xy' and 'ij', got {}"
-                     .format(indexing))
-
-  shape = []
-  for i, a in enumerate(args):
-    args[i] = a = asarray(a)
-    if len(a.shape) != 1:
-      msg = "Arguments to jax.numpy.meshgrid must be 1D, got shape {}"
-      raise ValueError(msg.format(a.shape))
-    shape.append(1 if sparse else a.shape[0])
-
-  output = []
-  for i, a in enumerate(args):
-    s = shape
-    if sparse:
-      s = list(s)
-      s[i] = _shape(a)[0]
-    output.append(lax.broadcast_in_dim(a, s, (i,)))
-
+  if indexing not in ["xy", "ij"]:
+    raise ValueError(f"Valid values for indexing are 'xy' and 'ij', got {indexing}")
+  if _any(a.ndim != 1 for a in args):
+    raise ValueError("Arguments to jax.numpy.meshgrid must be 1D, got shapes "
+                     f"{[a.shape for a in args]}")
+  if indexing == "xy" and len(args) >= 2:
+    args[0], args[1] = args[1], args[0]
+  shape = [1 if sparse else a.shape[0] for a in args]
+  _a_shape = lambda i, a: [*shape[:i], a.shape[0], *shape[i + 1:]] if sparse else shape
+  output = [lax.broadcast_in_dim(a, _a_shape(i, a), (i,)) for i, a, in enumerate(args)]
   if indexing == "xy" and len(args) >= 2:
     output[0], output[1] = output[1], output[0]
-
   return output