Broadcasting

Broadcasting

Header: include/stratax/ops/Broadcasting.hpp.

Shape rules

Align dimensions from the right. A pair is compatible if its extents are equal or either is one; missing leading dimensions behave as ones. The output uses the non-singleton extent. In particular, zero paired with one produces zero, not one. Expanded axes always read coordinate zero from the source.

left:    (2, 3, 1)
right:      (1, 4)
result:  (2, 3, 4)

broadcastable(shape1, shape2) reports compatibility in O(r). broadcasted_shape(shape1, shape2) allocates the common shape or throws Exceptions::BroadcastError. These helpers inspect metadata only: Shape{} has no conflicting axes, but a rank-zero array has no scalar element to read. Array operations additionally reject an empty operand supplying a nonempty result. They can produce an empty result when the shapes are compatible.

Traversal and result selection

broadcasted_op(lhs, rhs, op) calls op in logical result order without changing its operands. Two numeric arrays infer a promoted result dtype. The explicit stratax::core::broadcasted_op<Result>(lhs, rhs, op) overload selects a dtype, also allowing Boolean results. Same-family arrays preserve their family; mixed families produce Tensor through PromoteArray.

Array-scalar and scalar-array forms preserve array shape and family and infer the dtype from both operands. Allocating forms require the owning result traits. The callable receives original element types, not values converted to the result dtype. Callable and allocation exceptions propagate.

Example

#include <stratax.h>
#include <cassert>
#include <functional>
 
int main() {
    stratax::container::Matrix<int> column{{1}, {2}};
    stratax::container::Vector<int> row{10, 20, 30};
    auto result = stratax::core::broadcasted_op(column, row, std::plus<>{});
    assert(result.shape() == stratax::core::Shape({2, 3}));
    assert(result(1, 2) == 32);
    auto mask = stratax::core::broadcasted_op<bool>(column, row, std::less<>{});
    assert(mask(0, 0));
    assert(broadcasted_shape(stratax::core::Shape{0, 3}, stratax::core::Shape{1, 3})
           == stratax::core::Shape({0, 3}));
}

Cost

With n output elements and maximum rank r, array-array traversal takes O((n + 1)r); scalar forms take O(n + r). Results allocate O(n + r) storage. Broadcasting is shared by arithmetic, comparison, bitwise, and binary math operations. Compound operators separately require the output shape to match the left operand exactly.

See Arithmetic, Comparison, Bitwise, and Math.