addr

→Tensor

addr(input: Tensor, vec1: Tensor, vec2: Tensor, beta: _float = ..., alpha: _float = ...)

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Rank-1 update of a matrix by an outer product (BLAS-2 ger).

Computes $\beta \cdot \text{input} + \alpha \cdot (\text{vec1} \otimes \text{vec2})$ , i.e. updates the matrix input by adding the (scaled) outer product of two vectors. The classical BLAS ger routine.

Parameters

inputTensor

Accumulator matrix of shape (M, N).

vec1Tensor

First vector of length M.

vec2Tensor

Second vector of length N.

betafloat

Scalar multiplier on input. Defaults to 1.0.

alphafloat

Scalar multiplier on the outer product. Defaults to 1.0.

Returns

Tensor

Updated matrix of shape (M, N).

Notes

Element-wise:

\text{out}_{ij} = \beta \cdot \text{input}_{ij} + \alpha \cdot \text{vec1}_i \cdot \text{vec2}_j.

The outer product is a rank-1 matrix, so this update can be used to build rank-1 corrections in optimisation algorithms (Broyden / BFGS).

Examples

>>> import lucid
>>> M = lucid.zeros((2, 3))
>>> u = lucid.tensor([1., 2.])
>>> v = lucid.tensor([3., 4., 5.])
>>> lucid.addr(M, u, v)
Tensor([[ 3.,  4.,  5.],
        [ 6.,  8., 10.]])