the columns of A'A when A is sparse are just sparse linear combinations of 
columns of A. the coefficients being stored in the column-based sparse 
matrix representation (internally a vector of coefficients with pointers to 
new-column indices). so simply generating column by column with a for loop 
should be as-quick-as-it-gets without GPUing or some Fourier trickery.
did you already consider this? (i can try and make this description into 
code)

On Tuesday, November 17, 2015 at 10:26:21 PM UTC+2, Douglas Bates wrote:
>
> More careful reading of the spmatmul function in base/sparse/linalg.jl 
> provided a method directly downdates the dense square matrix C (i.e. does 
> not form a sparse A'A then downdate) but I still need to form a transpose. 
>  If anyone knows of a fast way of forming A'A without creating the 
> transpose I would be happy to hear of it.
>

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