Allocate a *similar* vector in zerox s.t. GPUArrays work out of the box

Author: haampie

docs/src/linear_systems/cg.md

@@ -9,6 +9,24 @@ cg
 cg!
 ```
 
+## On the GPU
+
+The method should work fine on the GPU. As a minimal working example, consider:
+
+```julia
+using LinearAlgebra, CuArrays, IterativeSolvers
+
+n = 100
+A = cu(rand(n, n))
+A = A + A' + 2*n*I
+b = cu(rand(n))
+x = cg(A, b)
+```
+
+!!! note
+    Make sure that all state vectors are stored on the GPU. CG will *not* copy the right-hand side to the GPU if the provided initial guess `x` is stored on the GPU.
+
+
 ## Implementation details
 
 The current implementation follows a rather standard approach. Note that preconditioned CG (or PCG) is slightly different from ordinary CG, because the former must compute the residual explicitly, while it is available as byproduct in the latter. Our implementation of CG ensures the minimal number of vector operations.

src/common.jl

@@ -12,9 +12,15 @@ Adivtype(A, b) = typeof(one(eltype(b))/one(eltype(A)))
 
 """
     zerox(A, b)
-Build a zeros vector `Vector{T}`, where `T` is `Adivtype(A,b)`.
+
+Build a zeros vector similar to `b` of eltype `Adivtype(A,b)`.
 """
-zerox(A, b) = zeros(Adivtype(A, b), size(A, 2))
+function zerox(A, b)
+    T = Adivtype(A, b)
+    x = similar(b, T, size(A, 2))
+    fill!(x, zero(T))
+    return x
+end
 
 """
 No-op preconditioner