dot_op

→TensorImplPtr

int dot_op(const int & a, const int & b)

source edit

Python wrappers

pylucid.linalg.dotfunction

Compute the dot product of two vectors or the matrix product of two matrices, with autograd support for both cases.

Dispatches on rank:

1-D × 1-D — inner product $c = \sum_i a_i b_i$ $c = \sum_{i} a_{i} b_{i}$ producing a scalar (shape {}). Backed by Accelerate's cblas_*dot via the element-wise multiply and reduce_sum backend primitives. Backward node: Dot1DBackward (saves both operands).
- 2-D × 2-D — matrix product $C = A B$ . Backed by cblas_*gemm (Accelerate) on CPU, mlx::matmul on GPU. Backward node: Dot2DBackward (saves both operands).

Math

1-D case:

c = \sum_{i=0}^{N-1} a_i b_i, \qquad \frac{\partial L}{\partial a_i} = \frac{\partial L}{\partial c}\, b_i, \qquad \frac{\partial L}{\partial b_i} = \frac{\partial L}{\partial c}\, a_i

2-D case:

C = A B, \qquad \frac{\partial L}{\partial A} = \frac{\partial L}{\partial C}\, B^\top, \qquad \frac{\partial L}{\partial B} = A^\top\, \frac{\partial L}{\partial C}

Shape

1-D: a.shape[0] == b.shape[0]; output is rank-0.
2-D: a.shape[1] == b.shape[0]; output is $(M, N)$ .

References

NumPy numpy.dot semantics for the 1-D and 2-D cases.

See Also

matmul_op : N-D matmul with NumPy broadcasting on batch dims. inner_op : Last-axis contraction (NumPy inner). outer_op : 1-D × 1-D outer product.

Parameters

aTensorImplPtr

First operand. Must be 1-D or 2-D.

bTensorImplPtr

Second operand. Must have the same rank as a.

Returns

TensorImplPtr

1-D inputs → scalar tensor with shape {}. - 2-D inputs of shape $(M, K)$ and $(K, N)$ → matrix of shape $(M, N)$ .

Raises

ShapeMismatch

If the contracted dimensions disagree (1-D length mismatch, or 2-D a.shape[1] != b.shape[0]).

NotImplemented

If either input has rank other than 1 or 2.

Notes

Unlike matmul_op this entry point uses AmpPolicy::KeepInput — integer dot products are valid and must not be promoted silently.