View a scalar as a vector/array

Is there is any built-in mechanism in Julia to “view” a scalar quantity, like a number, as an array? I am thinking something like as follows, given that the shape of b and c could be broadcast against A.

A = ones(3, 3)
b = 1
c = ones(3)

A .+ b == A .+ c  # works, since b and c can each be broadcast to the shape of A
B = broadcast_to(b, (3,3))
C = broadcast_to(c, (3,3))
A + B == a .+ B  # true
A + C == a .+ C  # true

I think numpy has a function broadcast_to like I am illustrating here. This could be useful if, e.g., you were solving a matrix equation with a constant vector on the right-hand side.

A = ones(3, 3)
b = broadcast_to(1, (3,))
x = A \ b
x == A .\ ones(3)

Note that, consistent with other broadcast functions, doing A .\ b broadcasts b=1 to a 3x3 matrix of 1s, so A .\ b == A \ ones(3,3).

Sounds like you want GitHub - JuliaArrays/FillArrays.jl: Julia package for lazily representing matrices filled with a single entry

3 Likes

What? Unless I misunderstand, this is wrong:

jl> A = rand(3,3);

jl> A .\ ones(3, 3)
3×3 Matrix{Float64}:
 4.47187  475.907    4.43528
 1.494      2.97416  6.40232
 2.93817    1.11483  3.30267

jl> A \ ones(3, 3)
3×3 Matrix{Float64}:
  0.872241   0.872241   0.872241
 -0.422581  -0.422581  -0.422581
  3.57412    3.57412    3.57412

It doesn’t just broadcast the shapes, but also does elementwise operations.

Yes you are right and thanks for pointing that out – beginner mistake for me thinking about broadcasting backwards.

julia> A = rand(3, 3)
3×3 Matrix{Float64}:
 0.96678   0.876051  0.849013
 0.966259  0.257086  0.658442
 0.818418  0.825752  0.210322

julia> A .\ ones(3,3) == A .\ ones(3) == A .\ 1  # All elementwise inverse of each element of A
true

A \ ones(3,3) == A .\ 1
false

Indeed. Thanks for your reply.