Remove KrylovSubspace type (#149)

* Remove KrylovSubspace type

* Fix docs

Author: haampie

docs/src/library/internal.md

@@ -34,19 +34,6 @@ IterativeSolvers.setconv
 IterativeSolvers.showplot
 ```
 
-## KrylovSubspace Internals
-
-**`Functions`**
-
-```@docs
-IterativeSolvers.lastvec
-IterativeSolvers.nextvec
-IterativeSolvers.init!
-IterativeSolvers.initrand!(::KrylovSubspace)
-IterativeSolvers.appendunit!
-IterativeSolvers.orthogonalize
-```
-
 ## Other Functions
 
 

docs/src/library/public.md

@@ -21,12 +21,6 @@ Pages = ["public.md"]
 ConvergenceHistory
 ```
 
-### `KrylovSubspace`
-
-```@docs
-KrylovSubspace
-```
-
 ## Linear Solvers
 
 ### `Jacobi`

docs/src/user_manual.md

@@ -18,19 +18,21 @@ julia> Pkg.checkout("IterativeSolvers")
 ## Interface
 
 All linear-algebraic routines will take as input a linear operator `A` that maps
-vectors to vectors. `A` is not explicitly typed, but must either be a
-[`KrylovSubspace`](@ref) or support multiplication `*` or function composition (apply)
-that behave as necessary to produce the correct mapping on the vector space.
+vectors to vectors. Typically `A` is a `Matrix` or a `SparseMatrixCSC`, but since
+`A` is not explicitly typed, any linear operator that supports matrix operations
+can be used as well. This makes it possible to apply solvers *matrix-free*. In 
+IterativeSolvers.jl we strongly recommend [LinearMaps.jl](https://github.com/Jutho/LinearMaps.jl) 
+for non-matrix types of `A`.
 
-A custom type for `A` may be specified. The following interface is expected to
-be defined on `A`:
+For matrix-free types of `A` the following interface is expected to be defined:
 
-`A*v` is defined and computes the matrix-vector product on a `v::Vector`.
+`A*v` computes the matrix-vector product on a `v::AbstractVector`.
 
-`eltype(A)` is defined and returns the element type implicit in the equivalent
-matrix representation of `A`.
+`A_mul_B!(y, A, v)` computes the matrix-vector product on a `v::AbstractVector` in-place.
 
-`size(A, d)` is defined and returns the nominal dimensions along the dth axis
+`eltype(A)` returns the element type implicit in the equivalent matrix representation of `A`.
+
+`size(A, d)` is defined and returns the nominal dimensions along the `d`th axis
 in the equivalent matrix representation of `A`.
 
 ### Solvers
@@ -158,109 +160,3 @@ plot(ch, :resnorm, sep = :blue)
 *Plot additional keywords*
 
 `sep::Symbol = :white`: color of the line separator in restarted methods.
-
-## KrylovSubspace
-
-When [`KrylovSubspace`](@ref) is supported by the method, `A` can be replaced
-by an instance `K` of it. To check if a certain function supports it use  
-`methods` or `?` to find out, if there is a `K` in the argument list then it does.
-
-```julia
-julia> ?cg!
-
-    cg!(x, A, b)
-    cg!(x, K, b)
-
-    ...
-```
-
-`KrylovSubspace` is only allowed on functions that accept `x` as an argument,
-that's why `cg` doesn't allow it. This is also true when `x` is a keyword as
-is the case of `powm`.
-
-```julia
-julia> ?cg!
-
-    powm(A)
-    powm(K)
-
-    ...
-```
-
-The `KrylovSubspace` type collects information on the Krylov subspace generated
-over the course of an iterative Krylov solver.
-
-Recall that the Krylov subspace of order r given a starting vector `b` and a
-linear operator `A` is spanned by the vectors `[b, A*b, A^2*b,... A^(r-1)*b]`.
-Many modern iterative solvers work on Krylov spaces which expand until they span
-enough of the range of `A` for the solution vector to converge. Most practical
-algorithms, however, will truncate the order of the Krylov subspace to save
-memory and control the accumulation of roundoff errors. Additionally, they do
-not work directly with the raw iterates `A^n*b`, but will orthogonalize
-subsequent vectors as they are computed so as to improve numerical stability.
-`KrylovSubspace`s provide a natural framework to express operations such as a
-(possibly non-orthonormalized) basis for the Krylov subspace, retrieving the
-next vector in the subspace, and orthogonalizing an arbitrary vector against
-(part or all of) the subspace.
-
-The implementation of `KrylovSubspace` in this package differs from standard
-textbook presentations of iterative solvers. First, the `KrylovSubspace` type
-shows clearly the relationship between the linear operator A and the sequence of
-basis vectors for the Krylov subspace that is generated by each new iteration.
-Second, the grouping together of basis vectors also makes the orthogonalization
-steps in each iteration routine clearer. Third, unlike in other languages, the
-powerful type system of Julia allows for a simplified notation for iterative
-algorithms without compromising on performance, and enhances code reuse across
-multiple solvers.
-
-### Constructors
-
-A [`KrylovSubspace`](@ref) can be initialized by three constructors, depending on the type
-of the linear operator:
-
-```
-KrylovSubspace{T}(A::AbstractMatrix{T}, [order::Int, v::Vector{Vector{T}}])
-
-KrylovSubspace{T}(A::KrylovSubspace{T}, [order::Int, v::Vector{Vector{T}}])
-
-KrylovSubspace(A, n::Int, [order::Int, v::Vector{Vector{T}}])
-```
-
-`A`: The linear operator associated with the `KrylovSubspace`.
-
-`order`: the order of the `KrylovSubspace`, i.e. the maximal number of Krylov
-vectors to remember.
-
-`n`: the dimensionality of the underlying vector space `T^n`.
-
-`v`: the iterable collection of Krylov vectors (of maximal length order).
-
-The dimensionality of the underlying vector space is automatically inferred where
-possible, i.e. when the linear operator is an `AbstractMatrix` or `KrylovSubspace`.
-
-*`Note:`* second constructor destroys the old `KrylovSubspace`.
-
-### Orthogonalization
-
-Orthogonalizing the basis vectors for a `KrylovSubspace` is crucial for numerical
-stability, and is a core low-level operation for many iterative solvers.
-
-```
-orthogonalize{T}(v::Vector{T}, K::KrylovSubspace{T}, [p::Int]; [method::Symbol], [normalize::Bool])
-```
-
-`v`: vector to orthogonalize.
-
-`K`: `KrylovSubspace` to orthogonalize against.
-
-`p`: number of Krylov vectors to orthogonalize against. (Default is all available)
-
-`method`: Orthogonalization method. Currently supported methods are:
-
-* `:GramSchmidt`
-* `:ModifiedGramSchmidt` (default)
-* `:Householder`.
-
-## Define function as matrix
-
-This package supports the use of [LinearMaps.jl](https://github.com/Jutho/LinearMaps.jl) for creating matrices using custom functions.

src/IterativeSolvers.jl

@@ -11,7 +11,6 @@ using Compat
 
 include("common.jl")
 include("orthogonalize.jl")
-include("krylov.jl")
 include("history.jl")
 
 #Specialized factorizations