Rectilinear (variable-length) chunk grid

chunk-grids/rectilinear/README.md

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+# Rectilinear chunk grid
+
+
+## Abstract
+
+This document defines a `chunk_grid` object to support rectilinear chunk grids. A rectilinear grid 
+is a grid parametrized by a sequence of elements per axis, where each sequence of elements may be 
+irregularly spaced. From a chunking perspective, a rectilinear grid is defined by a sequence of 
+(potentially) variable-length intervals, or chunk edge lengths, for each axis of an array.
+
+## Indexing
+
+The following diagram illustrates a rectilinear chunk grid. The chunk edge lengths are not to scale.
+
+```bash
+              24                  14
+   ┌───────────────────────┬──────────────┐
+   │                       │              │
+   │                       │              │
+   │ chunk (0,0)           │ chunk (0,1)  │
+16 │                       │              │
+   │                       │              │
+   │                       │              │
+   │                       │              │
+   ├───────────────────────┼──────────────┤
+   │                       │              │
+   │                       │              │
+10 │ chunk (1,0)           │ chunk (1,1)  │
+   │                       │              │
+   │                       │              │
+   └───────────────────────┴──────────────┘
+```
+
+Every array index resolves to a specific chunk, which can be identified by its index in the chunk 
+grid, and an index *within* that chunk, which we refer to here as the "chunk index".
+In this example, the chunk grid edge lengths are `[[16, 10], [24, 14]]` i.e., the chunk at chunk index `(0,0)` has shape `[16, 24]`, the chunk at chunk index `(0, 1)` has shape `[14, 16]`, etc.
+
+In this example, the array index `(20, 15)` resolves to the chunk grid index `(1, 0)` and the
+chunk index `(4, 15)`. 
+
+More generally, given a tuple of tuples of edge lengths `L` and an array index `idx`, the `nth` 
+element of `idx` (denoted `idx[n]`) maps to a chunk grid index by applying the following procedure: 
+compute the cumulative sum `C` of the edge lengths in `L[n]`, i.e. 
+`C := (L[n][0], L[n][0] + L[n][1], ...)`. The chunk grid index for 
+`idx[n]` is given by the index of the first element of `C` that exceeds `idx[n]`. 
+
+Once the chunk grid index `c` is resolved, the chunk index *within* that chunk can be determined by 
+subtracting `C[c-1]` from `idx[n]` if `c > 0`, or subtracting 0 otherwise.
+
+## Metadata
+
+| field | type | required |
+| - | - | - |
+| `name` | Literal `"rectilinear"` | yes | 
+| `configuration` | [Configuration](#configuration) | yes | 
+
+### Configuration
+
+| field | type | required | notes |
+| - | - | - | - |
+| `kind` | Literal `"inline"` | yes | see [kinds of encodings](#kinds-of-encodings) |
+| `chunk_shapes` | array of [Chunk edge lengths](#chunk-edge-lengths) | yes |  The length of `chunk_shapes` MUST match the number of dimensions of the array. 
+
+#### Kinds of encodings
+
+This specification defines a single permitted value for the `kind` field, namely the string 
+`"inline"`. Additions to this specification could define new permitted values for the `kind` field
+which could define new semantics for the `chunk_shapes` field.
+
+#### Chunk edge lengths
+
+All edge lengths MUST be positive integers (i.e., at least 1).
+
+The edge lengths of the chunks for an array axis with length `L` can be declared in two ways.
+
+- as an integer
+
+  A single integer defines the step size of a regular 1-dimensional grid.
+
+  To convert a single integer `m` into a sequence of explicit chunk edge lengths for an array axis 
+  with length `L`, repeat the integer `m` until it defines a sequence with a sum greater than or equal to `L`.
+
+  For example, if `L` is 10, and `m` is 3, the explicit list of chunk lengths is `[3, 3, 3, 3]`.
+
+- as an array that can contain two types of elements:
+    - an integer that explicitly denotes an edge length.
+    - an array that denotes a [run-length encoded](#run-length-encoding) sequence of integers, 
+    each of which denotes an edge length.
+
+The sum of the edge lengths MUST equal or exceed `L`. Overflowing `L` by multiple chunks is 
+permitted.
+
+#### Run-length encoding
+
+This specification defines a JSON representation for run-length encoded sequences.
+
+A run-length encoded sequence of `N` repetitions of some value `V` is denoted by the JSON array `[V, N]`. Both `V` and `N` MUST be positive integers (i.e., at least 1).
+
+For example, the sequence `[1, 1, 1, 1, 1]` becomes `[1, 5]` after applying this run-length encoding. 
+
+## Example
+
+This example demonstrates different ways of declaring the edge lengths for a rectilinear chunk grid 
+via the `chunk_shapes` field.
+
+```javascript
+{
+    ...
+    "shape": [6, 6, 6, 6, 6],
+    "chunk_grid": {
+        "name": "rectilinear",
+        "configuration": {
+            "kind": "inline",
+            "chunk_shapes": [
+                4, // integer. expands to [4, 4]
+                [1, 2, 3], // explicit list of edge lengths. expands to itself.
+                [[4, 2]], // run-length encoded. expands to [4, 4].
+                [[1, 3], 3], // run-length encoded and explicit list. expands to [1, 1, 1, 3]
+                [4, 4, 4] // explicit list with overflow chunks
+            ]
+        }
+    }
+}
+```
+
+## Compatibility with other chunk grids
+
+A rectilinear grid is a generalization of a regular grid (a grid of regularly-spaced elements). Any 
+[regular chunk grid ](https://zarr-specs.readthedocs.io/en/latest/v3/chunk-grids/regular-grid/index.html) 
+can be converted losslessly to a rectilinear chunk grid. 
+
+The simplest procedure is to copy the 
+`chunk_shape` field of the regular chunk grid and assign it to the `chunk_shapes` field of the 
+rectilinear chunk grid. 
+
+## Prior work
+
+A scheme for rectilinear chunking was proposed in a 
+Zarr extension proposal (ZEP) called [ZEP 0003](https://zarr.dev/zeps/draft/ZEP0003.html). 
+The specification presented here builds on the ZEP 0003 proposal and adapts it to the Zarr V3. 
+
+Key differences between this specification and ZEP 0003:
+- This specification adds run-length encoding for integer sequences
+- This specification uses the field name `"chunk_shapes"` in the `configuration` field, while ZEP 0003 uses the field name `"chunk_shape"`.
+
+## Change log
+No changes yet.
+
+## Current maintainers
+- Davis Bennett (@d-v-b)

chunk-grids/rectilinear/schema.json

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+{
+  "$schema": "https://json-schema.org/draft/2020-12/schema",
+  "title": "RectilinearChunkGridMetadata",
+  "type": "object",
+  "properties": {
+    "configuration": {
+      "$ref": "#/$defs/RectilinearChunkGridConfiguration"
+    },
+    "name": {
+      "$ref": "#/$defs/rectilinear"
+    }
+  },
+  "required": [
+    "name",
+    "configuration"
+  ],
+  "$defs": {
+    "ChunkEdgeLength": {
+      "anyOf": [
+        {
+          "type": "integer",
+          "format": "uint",
+          "minimum": 1
+        },
+        {
+          "type": "array",
+          "items": {
+            "$ref": "#/$defs/InnerChunkEdgeLength"
+          }
+        }
+      ]
+    },
+    "InnerChunkEdgeLength": {
+      "anyOf": [
+        {
+          "type": "array",
+          "maxItems": 2,
+          "minItems": 2,
+          "prefixItems": [
+            {
+              "type": "integer",
+              "format": "uint",
+              "minimum": 1
+            },
+            {
+              "type": "integer",
+              "format": "uint",
+              "minimum": 1
+            }
+          ]
+        },
+        {
+          "type": "integer",
+          "format": "uint",
+          "minimum": 1
+        }
+      ]
+    },
+    "RectilinearChunkGridConfiguration": {
+      "type": "object",
+      "properties": {
+        "chunk_shapes": {
+          "type": "array",
+          "items": {
+            "$ref": "#/$defs/ChunkEdgeLength"
+          }
+        },
+        "kind": {
+          "$ref": "#/$defs/inline"
+        }
+      },
+      "required": [
+        "kind",
+        "chunk_shapes"
+      ]
+    },
+    "inline": {
+      "const": "inline"
+    },
+    "rectilinear": {
+      "const": "rectilinear"
+    }
+  }
+}