Shaped methods
Shaped values are rectangular rank-N component storage. They carry no matrix or mathematical-tensor meaning. Selectors and axis numbers are one-based.
Explicit shape construction and Matrix interpretation
grid := .Shaped.Generate({: 2, 3 }, index -> index[1] * 10 + index[2]);
grid.Map(value -> value + 1).Reshape({: 3, 2 }).Permute({: 2, 1 }).Get(1, 3) ##@ == 23;
a := {:2x2: /Matrix/ 1, 2; 3, 4};
b := [1, 0; 0, 1] ~!: :Matrix;
(a * b).Get(2, 1) ##@ == 3;
a.Hadamard(b).Get(1, 2) ##@ == 0;Bare rank-2 storage stays Shaped; * acts entrywise. Choose /Matrix/ or ~!: :Matrix explicitly for matrix algebra. Matrix-only methods diagnose this conversion when called on Shaped storage. Both operands must declare compatible scalar domains. .linalg and .optimize deliberately accept Shaped input data, validate dimensions and entries, and perform their own explicit Matrix conversion. These adapter contracts do not add implicit arithmetic conversion.
Mathematical vectors and tensors belong to named spaces with Frames. Their Components() operation exposes storage; storage methods alone do not supply those mathematical semantics.
Method reference
| Full syntax | Result | Meaning |
|---|---|---|
shaped.Shape() |
Tuple |
Return dimension sizes. |
shaped.Rank() |
Integer |
Return the number of axes. |
shaped.Size() |
Integer |
Return total cell count. |
shaped.ScalarDomain() |
String |
Return the declared scalar domain. |
shaped.WithScalarDomain(domain) |
Shaped |
Return a validated copy with the declared domain. |
shaped.SetScalarDomain!(domain) |
Shaped |
Validate and change the receiver’s declared domain. |
shaped.Get(selectors...) |
any \| ShapedView |
Read a cell or selection. A selector tuple is also accepted. |
shaped.Set(selectors..., value) |
Shaped |
Return a copy with selected cells assigned. |
shaped.Set!(selectors..., value) |
Shaped |
Mutate selected cells. |
shaped.Reshape(shapeTuple) |
Shaped |
Change shape without changing total size. |
shaped.Flatten() |
Shaped |
Return rank-1 storage in row-major order. |
shaped.Transpose() |
ShapedView |
Swap the axes of rank-2 storage. |
shaped.Permute(orderTuple) |
ShapedView |
Reorder rank-N axes. |
shaped.Map((value, indexTuple, shaped) -> result) |
Shaped |
Transform every cell. |
shaped.Fill!(value) |
Shaped |
Mutate every cell. |
shaped.Sum() |
number-like | Sum non-hole cells. |
shaped.Mean() |
number-like \| null |
Return arithmetic mean, or null when empty. |
shaped.Reduce((acc, value, indexTuple, shaped) -> next, initial?) |
any |
Fold cells; the default accumulator is hole-filled Shaped storage of the same shape. |
shaped.Iterator() |
Iterator |
Traverse cells in row-major order. |
shaped.CheckTraits() |
1 \| null |
Validate attached semantic traits. |
Shape, selection, and views
t := {:2x2: 1, 2; 3, 4 };
t.Shape().Get(1) ##@ == 2;
t.Rank() ##@ == 2;
t.Size() ##@ == 4;
t.Get(2, 1) ##@ == 3;
t.Get({: 1, 2 }) ##@ == 2;
t.Set(1, 2, 9).Get(1, 2) ##@ == 9;
t.Reshape({: 4 }).Shape().Get(1) ##@ == 4;
t.Flatten().Get(3) ##@ == 3;
t.Transpose().Get(1, 2) ##@ == 3;
t.Permute({: 2, 1 }).Get(2, 1) ##@ == 2;Mutation, arithmetic, callbacks, and traversal
t := {:2x2: 1, 2; 3, 4 }; t.Set!(1, 2, 9); t.Get(1, 2) ##@ == 9;
t := {:2x2: 1, 2; 3, 4 }; t.Fill!(5); t.Sum() ##@ == 20;
{:2x2: 1, 2; 3, 4 }.Sum() ##@ == 10;
{:2x2: 1, 2; 3, 4 }.Mean() ##@ == 5/2;
{:2x2: 1, 2; 3, 4 }.Map((value, index) -> value * index.Get(1)).Get(2, 2) ##@ == 8;
reduced := {:2x2: 1, 2; 3, 4 }.Reduce((acc, value, index) -> acc.Set!(index, value * 10));
reduced.Get(2, 1) ##@ == 30;
it := {:2x2: 1, 2; 3, 4 }.Iterator(); it.Next(3) ##@ == 3;
{:1: 1 }.CheckTraits() ##@ == 1;Transpose is currently rank-2 only. Permute accepts one occurrence of every axis number.