Project function for Arrays

[Rajath Shashidhara]

Hi,

I would like to propose the addition of this function to Julia.

Given a matrix/vector, the function should return the projection along that direction.

for e.g - 

A = [1,2,3,4,5] ; proj(A, 2) = [0,2,0,0,0]

A = 1   2   3   4  5

      6   7   8   9  10

      11 12 13 14 15

proj(A, 4, 2) = 0 0 0 0 0

                     0 0 0 9 0

                     0 0 0 0 0

proj(A, 4) =  0 0 0 4  0

                  0 0 0 9  0

                  0 0 0 14 0

Thank you,

Rajath Shashidhara

[Jiahao Chen]

You can do almost exactly what you want with this simple function:

julia> function proj(A, i...)

           B = zeros(A)

           B[i...] = A[i...]

           B

       end

proj (generic function with 1 method)

julia> proj(reshape(1:15, 5, 3), 4, 2)

5x3 Array{Int64,2}:

 0  0  0

 0  0  0

 0  0  0

 0  9  0

 0  0  0

What use cases would merit including a function like this in Base? (I don't see any compelling uses of this function.)

Thanks,

Jiahao Chen

Research Scientist

MIT CSAIL

[Rajath Shashidhara]

I agree that the implementation is quite easy. But, I believe that this function is quite useful in vector and relational algebra.

For example, the function below calculates the finite difference gradient of a given function in n-dimensional space - 

function finitedifferencegradient{T<:FloatingPoint}(operator::Function, point::Array{T,1}, step::Array{T,1})

    dim = length(point)

    grad = zeros(Complex{T}, dim)

    for i=1:dim

        k = zeros(step)

        k[i] = step[i]/2.0

        grad[i] = (operator((point+k)...) - operator((point-k)...))/(step[i])

    end

    grad, norm(grad)

end

It would be nicer to write it this way:

grad = [(operator(point+proj(step,i))-operator(point-proj(step,i)))/step[i] for i=1:length(point)]

It is not really a big thing, but I think it will be useful in certain situations. 

Thank you,

Rajath Shashidhara 

[John Myles White]

I think a good rule of thumb is that Base is never allowed to grow, only shrink. Obviously unrealistic when applied universally, but it's a good heuristic for answering the question: "what should go in Base?"

 -- John