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Tensor operations
Numeric type tensors implement elementwise addition and subtraction. Tensors with 2 dimensions also implement matrix multiplication.
§Multiplication
Matrix multiplication follows the standard definition based on matching dimension lengths. A Tensor of shape MxN can be multiplied with a tensor of shape NxL to yield a tensor of shape MxL. Only the length of the N dimensions needs to match, the dimension names along N in both tensors are discarded.
| Left Tensor shape | Right Tensor shape | Product Tensor shape |
|---|---|---|
[("rows", 2), ("columns", 3)] | [("rows", 3), ("columns", 2)] | [(rows", 2), ("columns", 2)] |
[("a", 3), ("b", 1)] | [("c", 1), ("d", 2)] | [("a", 3), ("d", 2)] |
[("rows", 2), ("columns", 3)] | [("columns", 3), ("rows", 2)] | not allowed - would attempt to be [(rows", 2), ("rows", 2)] |
§Addition and subtraction
Elementwise addition and subtraction requires that both dimension names and lengths match exactly.
| Left Tensor shape | Right Tensor shape | Sum Tensor shape |
|---|---|---|
[("rows", 2), ("columns", 3)] | [("rows", 2), ("columns", 3)] | [(rows", 2), ("columns", 3)] |
[("a", 3), ("b", 1)] | [("b", 1), ("a", 3)] | not allowed - reshape one first |
[("a", 2), ("b", 2)] | [("a", 2), ("c", 2)] | not allowed - rename the shape of one first |
Left hand side assigning addition (+=) and subtraction (-=) are also implemented and
require both dimension names and lengths to match exactly.
§Implementations
When doing numeric operations with tensors you should be careful to not consume a tensor by accidentally using it by value. All the operations are also defined on references to tensors so you should favor &x + &y style notation for tensors you intend to continue using.
These implementations are written here but Rust docs will display them on their implemented types. All 16 combinations of owned and referenced Tensor and TensorView operations and all 8 combinations for assigning operations are implemented.
Operations on tensors of the wrong sizes or mismatched dimension names will result in a panic. No broadcasting is performed, ie you cannot multiply a (NxM) ‘matrix’ tensor by a (Nx1) ‘column vector’ tensor, you must manipulate the shapes of at least one of the arguments so that the operation is valid.
Traits§
- Similar
- Similarity comparisons. This is a looser comparison than PartialEq, but anything which returns true for PartialEq::eq will also return true for Similar::similar.