Annotate a few types to improve type inference and thus allocation

Necessary for Krylov.

docs/src/tutorial.md

@@ -64,28 +64,21 @@ op = LinearOperator(Float64, 10, 10, false, false,
                     nothing,
                     w -> [w[1]; w[1] + w[2]])
 ```
-Notice, however, that type is not enforced, which can cause unintended consequences
+Make sure that the type passed to `LinearOperator` is correct, otherwise errors may occur.
 ```@example ex1
+using LinearOperators, FFTW # hide
 dft = LinearOperator(Float64, 10, 10, false, false,
                      v -> fft(v),
                      nothing,
                      w -> ifft(w))
 v = rand(10)
-println("eltype(dft)     = $(eltype(dft))")
-println("eltype(v)       = $(eltype(v))")
-println("eltype(dft * v) = $(eltype(dft * v))")
-```
-or even errors
-```jldoctest
-using LinearOperators
-A = [im 1.0; 0.0 1.0]
-op = LinearOperator(Float64, 2, 2, false, false,
-                     v -> A * v, u -> transpose(A) * u, w -> A' * w)
-Matrix(op) # Tries to create Float64 matrix with contents of A
-# output
-ERROR: InexactError: Float64(0.0 + 1.0im)
-[...]
-```
+println("eltype(dft)         = $(eltype(dft))")
+println("eltype(v)           = $(eltype(v))")
+println("eltype(dft.prod(v)) = $(eltype(dft.prod(v)))")
+# dft * v     # ERROR: expected Vector{Float64}
+# Matrix(dft) # ERROR: tried to create a Matrix of Float64
+``` 
+
 ## Limited memory BFGS and SR1
 
 Two other useful operators are the Limited-Memory BFGS in forward and inverse form.

src/LinearOperators.jl

@@ -239,10 +239,10 @@ end
 
 
 # Apply an operator to a vector.
-function *(op :: AbstractLinearOperator, v :: AbstractVector)
+function *(op :: AbstractLinearOperator{T}, v :: AbstractVector{S}) where {T,S}
   size(v, 1) == size(op, 2) || throw(LinearOperatorException("shape mismatch"))
   increase_nprod(op)
-  op.prod(v)
+  op.prod(v)::Vector{promote_type(T,S)}
 end
 
 
@@ -251,14 +251,14 @@ end
 
 Materialize an operator as a dense array using `op.ncol` products.
 """
-function Base.Matrix(op :: AbstractLinearOperator)
+function Base.Matrix(op :: AbstractLinearOperator{T}) where T
   (m, n) = size(op)
-  A = Array{eltype(op)}(undef, m, n)
-  ei = zeros(eltype(op), n)
+  A = Array{T}(undef, m, n)
+  ei = zeros(T, n)
   for i = 1 : n
-    ei[i] = 1
+    ei[i] = one(T)
     A[:, i] = op * ei
-    ei[i] = 0
+    ei[i] = zero(T)
   end
   return A
 end
@@ -531,8 +531,8 @@ Zero operator of size `nrow`-by-`ncol` and of data type `T` (defaults to
 `Float64`).
 """
 function opZeros(T :: DataType, nrow :: Int, ncol :: Int)
-  prod = @closure v -> zeros(T, nrow)
-  tprod = @closure u -> zeros(T, ncol)
+  prod = @closure v -> zeros(promote_type(T,eltype(v)), nrow)
+  tprod = @closure u -> zeros(promote_type(T,eltype(u)), ncol)
   LinearOperator{T}(nrow, ncol, nrow == ncol, nrow == ncol, prod, tprod, tprod)
 end
 

src/adjtrans.jl

@@ -71,13 +71,13 @@ function show(io :: IO, op :: ConjugateLinearOperator)
   show(io, op.parent)
 end
 
-function *(op :: AdjointLinearOperator, v :: AbstractVector)
-  length(v) == size(op.parent, 1) || throw(LinearOperatorException("shape mismatch"))
-  p = op.parent
+function *(op :: AdjointLinearOperator{T}, v :: AbstractVector{S}) where {T,S}
+  p = op.parent::AbstractLinearOperator{T}
+  length(v) == size(p, 1) || throw(LinearOperatorException("shape mismatch"))
   ishermitian(p) && return p * v
   if p.ctprod !== nothing
     increase_nctprod(p)
-    return p.ctprod(v)
+    return p.ctprod(v)::Vector{promote_type(T,S)}
   end
   tprod = p.tprod
   increment_tprod = true
@@ -94,16 +94,16 @@ function *(op :: AdjointLinearOperator, v :: AbstractVector)
   else
     increase_nprod(p)
   end
-  return conj.(tprod(conj.(v)))
+  return conj.(tprod(conj.(v)))::Vector{promote_type(T,S)}
 end
 
-function *(op :: TransposeLinearOperator, v :: AbstractVector)
-  length(v) == size(op.parent, 1) || throw(LinearOperatorException("shape mismatch"))
-  p = op.parent
+function *(op :: TransposeLinearOperator{T}, v :: AbstractVector{S}) where {T,S}
+  p = op.parent::AbstractLinearOperator{T}
+  length(v) == size(p, 1) || throw(LinearOperatorException("shape mismatch"))
   issymmetric(p) && return p * v
   if p.tprod !== nothing
     increase_ntprod(p)
-    return p.tprod(v)
+    return p.tprod(v)::Vector{promote_type(T,S)}
   end
   increment_ctprod = true
   ctprod = p.ctprod
@@ -120,12 +120,12 @@ function *(op :: TransposeLinearOperator, v :: AbstractVector)
   else
     increase_nprod(p)
   end
-  return conj.(ctprod(conj.(v)))
+  return conj.(ctprod(conj.(v)))::Vector{promote_type(T,S)}
 end
 
-function *(op :: ConjugateLinearOperator, v :: AbstractVector)
+function *(op :: ConjugateLinearOperator{T}, v :: AbstractVector{S}) where {T,S}
   p = op.parent
-  return conj.(p * conj.(v))
+  return conj.(p * conj.(v))::Vector{promote_type(T,S)}
 end
 
 -(op :: AdjointLinearOperator)   = adjoint(-op.parent)

test/test_linop.jl

@@ -502,7 +502,7 @@ function test_linop()
     @test A == Matrix(opC)
     opF = LinearOperator(Float64, 2, 2, false, false, prod, tprod, ctprod) # The type is a lie
     @test eltype(opF) == Float64
-    @test_throws InexactError Matrix(opF)
+    @test_throws TypeError Matrix(opF)
   end
 
   # Issue #80