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Diffstat (limited to 'spec')
| -rw-r--r-- | spec/primitive.md | 4 | ||||
| -rw-r--r-- | spec/reference.bqn | 4 |
2 files changed, 4 insertions, 4 deletions
diff --git a/spec/primitive.md b/spec/primitive.md index 26a05aa7..360c8629 100644 --- a/spec/primitive.md +++ b/spec/primitive.md @@ -147,7 +147,7 @@ A left argument for any of the three reduction-based modifiers indicates an init **Join To** (`∾`) combines its two arguments along an existing initial axis, unless both arguments are units, in which case it creates an axis and is identical to Couple (`≍`). The arguments must differ in rank by at most 1, and the result rank is equal to the maximum of 1 and the higher argument rank. Each argument with rank less than the result, and each major cell of an argument with rank equal to it, becomes a major cell of the result, with cells from the left argument placed before those from the right. **Join** (`∾`) generalizes the equal-rank subset of this behavior to an array of values instead of just two. The argument must be an array (unlike Merge), and its elements must all the same rank, which is at least the argument rank. Atom elements are treated as unit arrays. Then "outer" argument axes are matched up with leading "inner" element axes, and elements are joined along these axes. In order to allow this, the length of an element along a particular axis must depend only on the position along the corresponding axis in the argument. An empty argument to Join is return unchanged, as though the element rank is equal to the argument rank. -**Deshape** (`⥊`) differs from the provided function (which returns the element list of an array) only in that it accepts an atom, returning a one-element list containing it. **Reshape** (`⥊`) is extended in numerous ways. It accepts any list of natural numbers (including as a unit array or atom) for the left argument and any right argument; `𝕩` is deshaped first so that it is treated as a list of elements. These elements are repeated cyclically to fill the result array in ravel order. If `𝕩` is empty but the result is not, then the result consists of fill elements for `𝕩`. Furthermore, at most one element of `𝕨` can be a "length code": one of the primitives `∘⌊⌽↑`. In this case, a target length is computed from the number of elements in `𝕩` divided by the product of the other elements of `𝕨` (which must not be zero). If the target length is an integer then it is used directly for the length code. Otherwise, an error is given if the length code is `∘`, and the target length is rounded down if the code is `⌊` and up if it's `⌽` or `↑`. With code `⌽`, elements are repeated cyclically as usual, but with code `↑`, the extra elements after each argument element is used are fill values for `𝕩`. +**Deshape** (`⥊`) differs from the provided function (which returns the element list of an array) only in that it accepts an atom, returning a one-element list containing it. **Reshape** (`⥊`) is extended in numerous ways. It accepts any list of natural numbers (including as a unit array or atom) for the left argument and any right argument; `𝕩` is deshaped first so that it is treated as a list of elements. These elements are repeated cyclically to fill the result array in ravel order. If `𝕩` is empty then a non-empty requested result shape causes an error. Furthermore, at most one element of `𝕨` can be a "length code": one of the primitives `∘⌊⌽↑`. In this case, a target length is computed from the number of elements in `𝕩` divided by the product of the other elements of `𝕨` (which must not be zero). If the target length is an integer then it is used directly for the length code. Otherwise, an error is given if the length code is `∘`, and the target length is rounded down if the code is `⌊` and up if it's `⌽` or `↑`. With code `⌽`, elements are repeated cyclically as usual, but with code `↑`, the extra elements after each argument element is used are fill values for `𝕩`. **Transpose** (`⍉`) reorders axes of its argument to place the first axis last; if the argument has one or fewer axes then it's enclosed if it's an atom and otherwise returned unchanged. **Reorder Axes** (`⍉`) requires the left argument to be a list or unit of natural numbers, with length at most the rank of the right argument. This list is extended to match the right argument rank exactly by repeatedly appending the least unused natural number (for example, given `1‿3‿0‿0`, `2` is appended). After extension, it specifies a result axis for each axis of the right argument. There must be no gaps in the list: that is, with the result rank equal to one plus the greatest value present, every result axis must appear at least once. Now each argument axis is "sent to" the specified result axis: in terms of indices, `i⊑𝕨⍉𝕩` is `(𝕨⊏i)⊑𝕩` if `𝕨` is complete. If multiple argument axes correspond to the same result axis, then a diagonal is taken, and it's as long as the shortest of those argument axes. Like Transpose, Reorder Axes encloses `𝕩` if it's an atom, so that its result is always an array. @@ -159,7 +159,7 @@ Each element in an array `s⥊e` is associated with an *index*, which is a list **Pick** (`⊑`) is extended to array left arguments. In this case, it requires every depth-1 array in the nested structure of `𝕨` to be a valid index list for `𝕩`, and every atom to be contained in one of these lists. The result is `𝕨` with each index list replaced by the element of `𝕩` at that index. In the simple case where `𝕨` itself is an index list, the result is the element of `𝕩` at index `𝕨`. -**First** (`⊑`) simply takes the first element of its argument in index order, or the fill element if `𝕩` is empty. +**First** (`⊑`) simply takes the first element of its argument in index order, with an error if `𝕩` is empty. For **Select** (`⊏`), `𝕨` is an array of natural numbers, or a list of such arrays; if it's an empty list, it's interpreted as the former. The given arrays are matched with leading axes of `𝕩` and used to select from those axes. Their shape is retained, so that the final shape is the combined shapes of each array of natural numbers in `𝕨` in order, followed by the trailing (unmatched) shape of `𝕩`. This means that a single axis in `𝕩` can correspond to any number of axes in `𝕨⊏𝕩`, depending on the rank of that portion of `𝕨`. More precisely, the value of the result at an index `j` is obtained by splitting `j` into one index into each array of `𝕨` followed by a partial index into `𝕩`. An index `i` for `𝕩` comes from selecting from each array of `𝕨` and appending the results to the partial index from `j`, and the value `i⊑𝕩` is `j⊑𝕨⊏𝕩`. diff --git a/spec/reference.bqn b/spec/reference.bqn index f8130f2e..1d841a71 100644 --- a/spec/reference.bqn +++ b/spec/reference.bqn @@ -157,7 +157,7 @@ Reshape←{ s↩p⊣◶⊢‿a¨s {d∾↩(Fill d)⌜↕𝕩-n⋄n↩𝕩}⍟(n⊸<)⍟(3=t)lp×a } s - s⥊(↕l)(0<n)◶⟨<∘Fill⊸(⊣¨)⋄{⊑⟜𝕩¨n|𝕨}⟩⍟(l≠n)d + s⥊(↕l){!0<n⋄⊑⟜𝕩¨n|𝕨}⍟(l≠n)d } Range←{ @@ -176,7 +176,7 @@ Pick1←{ } Pickd←(∨´∘⥊IsArray¨∘⊣)◶Pick1‿{Pickd⟜𝕩¨𝕨} Pick←IsArray◶⥊‿⊢⊸Pickd -First←(0<≠)◶⟨Fill,0⊸⊑⟩∘Deshape +First←(0<≠)◶⟨!∘0,0⊸⊑⟩∘Deshape match←{¬∘(0⊑𝕨)◶(1⊑𝕨)‿𝕩}´⟨ ⟨≠○IsArray , 0⟩ |