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@willow-ahrens
willow-ahrens committed May 13, 2024
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143 changes: 72 additions & 71 deletions spec/latest/index.bs
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Expand Up @@ -305,7 +305,7 @@ and tensors. For example, a dense vector of sparse vectors is equivalent to the
CSR matrix format, and a sparse vector of sparse vectors is equivalent to the
hypersparse DCSR matrix format.

When defining a custom format, the outermost `subformat` key is defined as the
When defining a custom format, the outermost `level` key is defined as the
root level descriptor (a level which will only hold one array). If a level holds
many different arrays, we refer to the `p`th array as the array in position `p`.

Expand All @@ -316,24 +316,25 @@ to represent is `A` and the tensor described by the format descriptor is `B`,
then `A[i_1, ..., i_n] = B[i_(transpose[1]), ..., i_(transpose[n])]`. `transpose` must
be a permutation.

If the format key is a dictionary, the `level` key must be present and shall
describe the storage format of the level used to represent the sparse array.
If the `custom` key is present, it holds a dictionary for custom formats. The
root level is stored under the `level` key. Each level mush have a `level_desc`
attribute which describe the storage format of the level.

The level descriptors are dictionaries defined as follows:

#### Element #### {#element_level}

If the level key is "element", the level represents zero or more scalars.
If the level descriptor is "element", the level represents zero or more scalars.

: values
:: Array of size `number_of_positions` whose `p`th element holds the value of the scalar at position `p`.

#### Dense #### {#dense_level}

If the level key is "dense", the `subformat` key must be present. The `rank`
If the level descriptor is "dense", the `level` key must be present. The `rank`
key must be present, and set to an integer `r` greater than or equal to 1. The
dense level represents zero or more r-dimensional dense arrays whose elements
are themselves arrays specified by `subformat`. For example, a dense level
are themselves arrays specified by `level`. For example, a dense level
of
rank 2 represents a collection of dense matrices of subarrays.

Expand All @@ -350,10 +351,10 @@ of the sublevel.

#### Sparse #### {#sparse_level}

If the level key is "sparse", the `subformat` key must be present. The
If the level descriptor is "sparse", the `level` key must be present. The
`rank` key must be present, and set to an integer `r` greater than or equal to
`1`. The sparse level represents zero or more `r`-dimensional sparse arrays
whose non-implicit elements are themselves arrays specified by `subformat`. For
whose non-implicit elements are themselves arrays specified by `level`. For
example, a sparse level of rank 1 represents a collection of sparse vectors of
subarrays.

Expand All @@ -374,17 +375,17 @@ length of any of the `indices` arrays in this level.

### Equivalent Formats ### {#equivalent_formats}

The following formats are equivalent
The following formats are equivalent. Parsers which support custom formats should also write `format` aliases when appropriate.

#### DVEC #### {#dvec_format_equiv}

```json
"format": {
"subformat": {
"level": "dense",
"custom": {
"level": {
"level_desc": "dense",
"rank": 1,
"subformat": {
"level": "element",
"level": {
"level_desc": "element",
}
}
}
Expand All @@ -393,15 +394,15 @@ The following formats are equivalent
#### DMATR #### {#dmatr_format_equiv}

```json
"format": {
"subformat": {
"level": "dense",
"custom": {
"level": {
"level_desc": "dense",
"rank": 1,
"subformat": {
"level": "dense",
"level": {
"level_desc": "dense",
"rank": 1,
"subformat": {
"level": "element",
"level": {
"level_desc": "element",
}
}
}
Expand All @@ -411,16 +412,16 @@ The following formats are equivalent
#### DMATC #### {#dmatr_format_equiv}

```json
"format": {
"custom": {
"transpose": [1, 0],
"subformat": {
"level": "dense",
"level": {
"level_desc": "dense",
"rank": 1,
"subformat": {
"level": "dense",
"level": {
"level_desc": "dense",
"rank": 1,
"subformat": {
"level": "element",
"level": {
"level_desc": "element",
}
}
}
Expand All @@ -430,12 +431,12 @@ The following formats are equivalent
#### CVEC #### {#cvec_format_equiv}

```json
"format": {
"subformat": {
"level": "sparse",
"custom": {
"level": {
"level_desc": "sparse",
"rank": 1,
"subformat": {
"level": "element",
"level": {
"level_desc": "element",
}
}
}
Expand All @@ -444,15 +445,15 @@ The following formats are equivalent
#### CSR #### {#csr_format_equiv}

```json
"format": {
"subformat": {
"level": "dense",
"custom": {
"level": {
"level_desc": "dense",
"rank": 1,
"subformat": {
"level": "sparse",
"level": {
"level_desc": "sparse",
"rank": 1,
"subformat": {
"level": "element",
"level": {
"level_desc": "element",
}
}
}
Expand All @@ -462,16 +463,16 @@ The following formats are equivalent
#### CSC #### {#csc_format_equiv}

```json
"format": {
"custom": {
"transpose": [1, 0],
"subformat": {
"level": "dense",
"level": {
"level_desc": "dense",
"rank": 1,
"subformat": {
"level": "sparse",
"level": {
"level_desc": "sparse",
"rank": 1,
"subformat": {
"level": "element",
"level": {
"level_desc": "element",
}
}
}
Expand All @@ -481,15 +482,15 @@ The following formats are equivalent
#### DCSR #### {#dcsr_format_equiv}

```json
"format": {
"subformat": {
"level": "sparse",
"custom": {
"level": {
"level_desc": "sparse",
"rank": 1,
"subformat": {
"level": "sparse",
"level": {
"level_desc": "sparse",
"rank": 1,
"subformat": {
"level": "element",
"level": {
"level_desc": "element",
}
}
}
Expand All @@ -499,16 +500,16 @@ The following formats are equivalent
#### DCSC #### {#dcsc_format_equiv}

```json
"format": {
"custom": {
"transpose": [1, 0],
"subformat": {
"level": "sparse",
"level": {
"level_desc": "sparse",
"rank": 1,
"subformat": {
"level": "sparse",
"level": {
"level_desc": "sparse",
"rank": 1,
"subformat": {
"level": "element",
"level": {
"level_desc": "element",
}
}
}
Expand All @@ -518,12 +519,12 @@ The following formats are equivalent
#### COOR #### {#coor_format_equiv}

```json
"format": {
"subformat": {
"level": "sparse",
"custom": {
"level": {
"level_desc": "sparse",
"rank": 2,
"subformat": {
"level": "element",
"level": {
"level_desc": "element",
}
}
}
Expand All @@ -534,13 +535,13 @@ The following formats are equivalent
Column-wise Coordinate format

```json
"format": {
"custom": {
"transpose": [1, 0],
"subformat": {
"level": "sparse",
"level": {
"level_desc": "sparse",
"rank": 2,
"subformat": {
"level": "element",
"level": {
"level_desc": "element",
}
}
}
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