Mgrid

https://numpy.org/doc/2.1/reference/generated/numpy.mgrid.html

TensorLib/Basic.lean

@@ -11,3 +11,4 @@ import TensorLib.Broadcast
 import TensorLib.Slice
 import TensorLib.Tensor
 import TensorLib.Index
+import TensorLib.Mgrid

TensorLib/Mgrid.lean

@@ -0,0 +1,135 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Jean-Baptiste Tristan, Paul Govereau, Sean McLaughlin
+-/
+
+import Mathlib
+import TensorLib.Common
+import TensorLib.Tensor
+import TensorLib.Slice
+import TensorLib.Index
+
+namespace TensorLib
+
+/-
+Shape of the resulting tensor is |slices| :: slices.map(fun x => x.shape)
+
+Slices are treated differently in NumPy when used in mgrid vs indexing. In particular,
+since we don't know what the stopping point should be from the context, it can use the `start`
+value as a `stop` instead.  For example,
+
+  # np.arange(10)[5:]
+  [5, 6, 7, 8, 9]
+
+  # np.mgrid[5:]
+  [0, 1, 2, 3, 4]
+
+However, things work normally when there is a stopping point
+
+  # np.mgrid[5:10]
+  [5, 6, 7, 8, 9]
+
+Since this is imo surprising, we just fail if the start or stopping point are absent.
+Moreover, we require more than one slice, since `mgrid[slice] == arange(slice)`, and a single
+slice behaves differently from all other quantities.
+
+All mgrid ints are stored as 64-bit, little-endian ints by convention. In Numpy they are stored with
+native byte order, as the architecture word size.
+
+For eample,
+
+# np.mgrid[2:4:, 4:7:]
+array([[[2, 2, 2],
+        [3, 3, 3]],
+
+       [[4, 5, 6],
+        [4, 5, 6]]])
+
+We have an iterator that will give us the indices [0, 0], [0, 1], [0, 2], [1, 0], ..., [1, 2]
+and an interator that will give us the values [2, 4], [2, 5], [2, 6], ... , [3, 6]
+These are the same length, so we can combine them to get the mgrid;
+- [0, 0] of the first element gits 2,
+- [0, 0] of the second element gets 4
+- [0, 1] of the first gets 2
+- [0, 1] of the second gets 5
+- ...
+-/
+def mgrid (slices : List Slice) : Err Tensor := do
+  let sliceCount := slices.length
+  if sliceCount < 2 then .error "mgrid requires at least two slices"
+  let arbitrary : Nat := 10  -- Slice.size does not use the second argument if both start and stop are specified
+  let sliceSize (slice : Slice) : Nat := slice.size arbitrary
+  let mut slicesShape := []
+  for slice in slices.reverse do
+    match slice.start, slice.stop with
+    | .none, _ => .error "Slices need an upper bound in mgrid"
+    | _, .none => .error "Slices need a lower bound in mgrid"
+    | _, _ =>
+      let sz := sliceSize slice
+      slicesShape := sz :: slicesShape
+  let shape := sliceCount :: slicesShape
+  let dtype := Dtype.uint64
+  let mut arr := Tensor.zeros dtype shape
+  let basic := slices.map fun s => .slice (Slice.Iter.make s arbitrary)
+  let mut sliceIter <- Index.BasicIter.make slicesShape basic
+  let indexIter := DimsIter.make slicesShape
+  if sliceIter.size != indexIter.size then .error "Invariant failure: iterator size mismatch at start"
+  for index in indexIter do
+    match sliceIter.next with
+    | .none => .error "Invariant failure: iterator size mismatch during iteration"
+    | .some (values, sliceIter') =>
+      sliceIter := sliceIter'
+      if values.length != sliceCount then .error "Invariant failure: value length mismatch"
+      for (i, v) in (List.range sliceCount).zip values do
+        let value := BV64.ofNat v
+        arr <- Tensor.Element.setDimIndex arr (i :: index) value
+  return arr
+
+section Test
+
+open TensorLib.Tensor.Format
+open Tree
+
+#guard (get! (mgrid [Slice.ofStartStop 2 4, Slice.ofStartStop 4 7])).toTree BV64 == .ok (
+  .node [
+    .node [
+      .root [2, 2, 2], .root [3, 3, 3]
+    ],
+    .node [
+      .root [4, 5, 6], .root [4, 5, 6]
+    ]
+  ]
+)
+
+#guard (get! (mgrid [Slice.ofStartStop 2 4, Slice.ofStartStop 4 7, Slice.ofStop 2])).toTree BV64 == .ok (
+  .node [
+    .node [
+      .node [
+        .root [2, 2], .root [2, 2], .root [2, 2]
+      ],
+      .node [
+        .root [3, 3], .root [3, 3], .root [3, 3]
+      ],
+    ],
+    .node [
+      .node [
+        .root [4, 4], .root [5, 5], .root [6, 6]
+      ],
+      .node [
+        .root [4, 4], .root [5, 5], .root [6, 6]
+      ]
+    ],
+    .node [
+      .node [
+        .root [0, 1], .root [0, 1], .root [0, 1]
+      ],
+      .node [
+        .root [0, 1], .root [0, 1], .root [0, 1]
+      ]
+    ]
+  ]
+)
+
+end Test
+end TensorLib