How to convert an array of array into a matrix?

Question

Suppose I want to apply a vector-valued function phi to a vector x:

phi(x, d) = [x.^i for i=0:d]    # vector-valued function x = rand(7)                     # vector y = phi(x, 3)                   # should be matrix, but isn't 

Now y should be a matrix, but it is an 4-element Array{Array{Float64,1},1}, i.e. an array of arrays. Actually, I want y to be a matrix. Is the implementation of phi wrong? Or how do I convert it?

Thanks!

Answer 1

As you noted, you can concatenate an array of arrays x using hcat(x...), but it's usually better to create a matrix to begin with instead. Two ways that you can do it in this case:

1. Using broadcasting:

   phi(x, d) = x.^((0:d)') 

   As long as x is a vector, it will broadcast against the row matrix (0:d)'.

   You can get the transpose result by transposing x instead of the range 0:d.

2. Using a two-dimensional array comprehension:

   phi(x, d) = [xi.^di for xi in x, di in 0:d] 

   This will work as long as x is iterable. If x is an n-d array, it will be interpreted as if it were flattened first.

   You can transpose the result by switching the order of the comprehension variables:

   phi(x, d) = [xi.^di for di in 0:d, xi in x]