promote integer types for LAPACK routines

[StefanKarpinski]

@HomerReid wrote:

eig() fails for integer matrices:

 julia> eig([1 2; 2 1])
 no method eig(Array{Int32,2},)
 in method_missing, boot.j:250
 in run_repl, /home/homer/hacking/julia/j/client.j:23
 in _start, /home/homer/hacking/julia/j/client.j:153

The solution is to add promotions for Real types in the lapack macros.

[ViralBShah]

But, we'd have to change each BLAS/LAPACK/ARPACK macro and such. Isn't there a simpler way?

[StefanKarpinski]

See the discussion in #133.

[ViralBShah]

Let's say we have a promotion rule from Array{Int32} to Array{Float32}, and foo(Array{Float32}).

If I now call foo(Array{Int32}), will julia automatically do the promotion and then call foo on the promoted value?

[StefanKarpinski]

No, that's not how our promotions work. Promotions are only for combinations of operands; things like +(Int64, Float64), in which situation both operands get converted to the smallest common supertype — in this case, Float64. For "promoting" array arguments, we would just define the following method:

foo{T<:Real}(x::Array{T}) = foo(float(x))

That's it. That method will get called for any real-valued array that doesn't have a specific implementation already defined, and first convert x to an array of floats (assuming proper vectorization of the float function, which isn't there yet, but should be), and then calls the core foo implementation for floats on it.