Updates in LinearOperators

[dpo]

I updated LinearOperators in JuliaSmoothOptimizers/LinearOperators.jl@6356eb3 for Julia 0.4 compatibility. The main change involved removing the use of Nothing to indicate missing operations. In order to play well with both 0.3 and 0.4, all that needs to be changed is:

1. require and import Compat
2. change constructs like

Alinop = LinearOperator(size(A,1), size(A,2), T, false, false,
                        v -> At_mul_B!(1.0,A,v,0.0,x),
                        nothing,
                        v -> At_mul_B!(1.0,A,v,0.0,x))

to

Alinop = LinearOperator(size(A,1), size(A,2), T, false, false,
                        v -> At_mul_B!(1.0,A,v,0.0,x),
                        Nullable{Function}(),
                        v -> At_mul_B!(1.0,A,v,0.0,x))

(e.g., in https://github.com/lruthotto/KrylovMethods.jl/blob/master/src/cg.jl#L7).

Note that there is a simplified constructor for real symmetric operators:

Alinop = LinearOperator(size(A,1), T, v -> At_mul_B!(1.0,A,v,0.0,x))

One of the symmetric and hermitian flags should probably be set to true in your CG. Something like

Alinop = LinearOperator(size(A,1), size(A,2), T, T <: Real, (T <: Complex) && !(T <: Real),
                        v -> At_mul_B!(1.0,A,v,0.0,x),
                        Nullable{Function}(),
                        v -> At_mul_B!(1.0,A,v,0.0,x))