Use explicit imports

Author: ChrisRackauckas

docs/src/advanced/custom.md

@@ -4,12 +4,13 @@ Julia users are building a wide variety of applications in the SciML ecosystem,
 often requiring problem-specific handling of their linear solves. As existing solvers in `LinearSolve.jl` may not
 be optimally suited for novel applications, it is essential for the linear solve
 interface to be easily extendable by users. To that end, the linear solve algorithm
-`LinearSolveFunction()` accepts a user-defined function for handling the solve. A
+`LS.LinearSolveFunction()` accepts a user-defined function for handling the solve. A
 user can pass in their custom linear solve function, say `my_linsolve`, to
-`LinearSolveFunction()`. A contrived example of solving a linear system with a custom solver is below.
+`LS.LinearSolveFunction()`. A contrived example of solving a linear system with a custom solver is below.
 
 ```@example advanced1
-using LinearSolve, LinearAlgebra
+import LinearSolve as LS
+import LinearAlgebra as LA
 
 function my_linsolve(A, b, u, p, newA, Pl, Pr, solverdata; verbose = true, kwargs...)
     if verbose == true
@@ -19,9 +20,9 @@ function my_linsolve(A, b, u, p, newA, Pl, Pr, solverdata; verbose = true, kwarg
     return u
 end
 
-prob = LinearProblem(Diagonal(rand(4)), rand(4))
-alg = LinearSolveFunction(my_linsolve)
-sol = solve(prob, alg)
+prob = LS.LinearProblem(LA.Diagonal(rand(4)), rand(4))
+alg = LS.LinearSolveFunction(my_linsolve)
+sol = LS.solve(prob, alg)
 sol.u
 ```
 
@@ -50,7 +51,7 @@ function my_linsolve!(A, b, u, p, newA, Pl, Pr, solverdata; verbose = true, kwar
     return u
 end
 
-alg = LinearSolveFunction(my_linsolve!)
-sol = solve(prob, alg)
+alg = LS.LinearSolveFunction(my_linsolve!)
+sol = LS.solve(prob, alg)
 sol.u
 ```

docs/src/basics/FAQ.md

@@ -57,10 +57,10 @@ A = rand(n, n)
 b = rand(n)
 
 weights = [1e-1, 1]
-precs = Returns((LinearSolve.InvPreconditioner(Diagonal(weights)), Diagonal(weights)))
+precs = Returns((LS.InvPreconditioner(LA.Diagonal(weights)), LA.Diagonal(weights)))
 
-prob = LinearProblem(A, b)
-sol = solve(prob, KrylovJL_GMRES(precs))
+prob = LS.LinearProblem(A, b)
+sol = LS.solve(prob, LS.KrylovJL_GMRES(precs))
 
 sol.u
 ```
@@ -70,18 +70,19 @@ can use `ComposePreconditioner` to apply the preconditioner after the applicatio
 of the weights like as follows:
 
 ```@example FAQ2
-using LinearSolve, LinearAlgebra
+import LinearSolve as LS
+import LinearAlgebra as LA
 
 n = 4
 A = rand(n, n)
 b = rand(n)
 
 weights = rand(n)
-realprec = lu(rand(n, n)) # some random preconditioner
-Pl = LinearSolve.ComposePreconditioner(LinearSolve.InvPreconditioner(Diagonal(weights)),
+realprec = LA.lu(rand(n, n)) # some random preconditioner
+Pl = LS.ComposePreconditioner(LS.InvPreconditioner(LA.Diagonal(weights)),
     realprec)
-Pr = Diagonal(weights)
+Pr = LA.Diagonal(weights)
 
-prob = LinearProblem(A, b)
-sol = solve(prob, KrylovJL_GMRES(precs = Returns((Pl, Pr))))
+prob = LS.LinearProblem(A, b)
+sol = LS.solve(prob, LS.KrylovJL_GMRES(precs = Returns((Pl, Pr))))
 ```

docs/src/basics/Preconditioners.md

@@ -38,16 +38,17 @@ the identity ``I``.
 In the following, we will use a left sided diagonal (Jacobi) preconditioner.
 
 ```@example precon1
-using LinearSolve, LinearAlgebra
+import LinearSolve as LS
+import LinearAlgebra as LA
 n = 4
 
 A = rand(n, n)
 b = rand(n)
 
-Pl = Diagonal(A)
+Pl = LA.Diagonal(A)
 
-prob = LinearProblem(A, b)
-sol = solve(prob, KrylovJL_GMRES(), Pl = Pl)
+prob = LS.LinearProblem(A, b)
+sol = LS.solve(prob, LS.KrylovJL_GMRES(), Pl = Pl)
 sol.u
 ```
 
@@ -56,14 +57,15 @@ an iterative solver specification. This argument shall deliver a factory method
 parameter `p` to a tuple `(Pl,Pr)` consisting a left and a right preconditioner.
 
 ```@example precon2
-using LinearSolve, LinearAlgebra
+import LinearSolve as LS
+import LinearAlgebra as LA
 n = 4
 
 A = rand(n, n)
 b = rand(n)
 
-prob = LinearProblem(A, b)
-sol = solve(prob, KrylovJL_GMRES(precs = (A, p) -> (Diagonal(A), I)))
+prob = LS.LinearProblem(A, b)
+sol = LS.solve(prob, LS.KrylovJL_GMRES(precs = (A, p) -> (LA.Diagonal(A), LA.I)))
 sol.u
 ```
 
@@ -73,26 +75,27 @@ and to  pass parameters to the constructor of the preconditioner instances. The
 to reuse the preconditioner once constructed for the subsequent solution of a modified problem.
 
 ```@example precon3
-using LinearSolve, LinearAlgebra
+import LinearSolve as LS
+import LinearAlgebra as LA
 
 Base.@kwdef struct WeightedDiagonalPreconBuilder
     w::Float64
 end
 
-(builder::WeightedDiagonalPreconBuilder)(A, p) = (builder.w * Diagonal(A), I)
+(builder::WeightedDiagonalPreconBuilder)(A, p) = (builder.w * LA.Diagonal(A), LA.I)
 
 n = 4
-A = n * I - rand(n, n)
+A = n * LA.I - rand(n, n)
 b = rand(n)
 
-prob = LinearProblem(A, b)
-sol = solve(prob, KrylovJL_GMRES(precs = WeightedDiagonalPreconBuilder(w = 0.9)))
+prob = LS.LinearProblem(A, b)
+sol = LS.solve(prob, LS.KrylovJL_GMRES(precs = WeightedDiagonalPreconBuilder(w = 0.9)))
 sol.u
 
 B = A .+ 0.1
 cache = sol.cache
-reinit!(cache, A = B, reuse_precs = true)
-sol = solve!(cache, KrylovJL_GMRES(precs = WeightedDiagonalPreconBuilder(w = 0.9)))
+LS.reinit!(cache, A = B, reuse_precs = true)
+sol = LS.solve!(cache, LS.KrylovJL_GMRES(precs = WeightedDiagonalPreconBuilder(w = 0.9)))
 sol.u
 ```
 

docs/src/solvers/solvers.md

@@ -1,6 +1,6 @@
 # [Linear System Solvers](@id linearsystemsolvers)
 
-`solve(prob::LinearProblem,alg;kwargs)`
+`LS.solve(prob::LS.LinearProblem,alg;kwargs)`
 
 Solves for ``Au=b`` in the problem defined by `prob` using the algorithm
 `alg`. If no algorithm is given, a default algorithm will be chosen.
@@ -11,7 +11,7 @@ Solves for ``Au=b`` in the problem defined by `prob` using the algorithm
 
 The default algorithm `nothing` is good for picking an algorithm that will work,
 but one may need to change this to receive more performance or precision. If
-more precision is necessary, `QRFactorization()` and `SVDFactorization()` are
+more precision is necessary, `LS.QRFactorization()` and `LS.SVDFactorization()` are
 the best choices, with SVD being the slowest but most precise.
 
 For efficiency, `RFLUFactorization` is the fastest for dense LU-factorizations until around
@@ -59,7 +59,7 @@ has, for example if positive definite then `Krylov_CG()`, but if no good propert
 use `Krylov_GMRES()`.
 
 Finally, a user can pass a custom function for handling the linear solve using
-`LinearSolveFunction()` if existing solvers are not optimally suited for their application.
+`LS.LinearSolveFunction()` if existing solvers are not optimally suited for their application.
 The interface is detailed [here](@ref custom).
 
 ### Lazy SciMLOperators

docs/src/tutorials/caching_interface.md

@@ -11,7 +11,7 @@ A \ b2
 then it would be more efficient to LU-factorize one time and reuse the factorization:
 
 ```julia
-lu!(A)
+LA.lu!(A)
 A \ b1
 A \ b2
 ```
@@ -21,21 +21,22 @@ means of solving and resolving linear systems. To do this with LinearSolve.jl,
 you simply `init` a cache, `solve`, replace `b`, and solve again. This looks like:
 
 ```@example linsys2
-using LinearSolve
+import LinearSolve as LS
+import LinearAlgebra as LA
 
 n = 4
 A = rand(n, n)
 b1 = rand(n);
 b2 = rand(n);
-prob = LinearProblem(A, b1)
+prob = LS.LinearProblem(A, b1)
 
-linsolve = init(prob)
-sol1 = solve!(linsolve)
+linsolve = LS.init(prob)
+sol1 = LS.solve!(linsolve)
 ```
 
 ```@example linsys2
 linsolve.b = b2
-sol2 = solve!(linsolve)
+sol2 = LS.solve!(linsolve)
 
 sol2.u
 ```
@@ -45,7 +46,7 @@ Then refactorization will occur when a new `A` is given:
 ```@example linsys2
 A2 = rand(n, n)
 linsolve.A = A2
-sol3 = solve!(linsolve)
+sol3 = LS.solve!(linsolve)
 
 sol3.u
 ```
@@ -54,7 +55,7 @@ The factorization occurs on the first solve, and it stores the factorization in
 the cache. You can retrieve this cache via `sol.cache`, which is the same object
 as the `init`, but updated to know not to re-solve the factorization.
 
-The advantage of course with using LinearSolve.jl in this form is that it is
+The advantage of course with import LinearSolve.jl in this form is that it is
 efficient while being agnostic to the linear solver. One can easily swap in
 iterative solvers, sparse solvers, etc. and it will do all the tricks like
 caching the symbolic factorization if the sparsity pattern is unchanged.

docs/src/tutorials/gpu.md

@@ -27,20 +27,20 @@ GPU offloading is simple as it's done simply by changing the solver algorithm. T
 example from the start of the documentation:
 
 ```julia
-using LinearSolve
+import LinearSolve as LS
 
 A = rand(4, 4)
 b = rand(4)
-prob = LinearProblem(A, b)
-sol = solve(prob)
+prob = LS.LinearProblem(A, b)
+sol = LS.solve(prob)
 sol.u
 ```
 
 This computation can be moved to the GPU by the following:
 
 ```julia
 using CUDA # Add the GPU library
-sol = solve(prob, CudaOffloadFactorization())
+sol = LS.solve(prob, LS.CudaOffloadFactorization())
 sol.u
 ```
 
@@ -56,8 +56,8 @@ using CUDA
 
 A = rand(4, 4) |> cu
 b = rand(4) |> cu
-prob = LinearProblem(A, b)
-sol = solve(prob)
+prob = LS.LinearProblem(A, b)
+sol = LS.solve(prob)
 sol.u
 ```
 
@@ -81,13 +81,13 @@ move things to CPU on command.
     However, this change in numerical precision needs to be accounted for in your mathematics
     as it could lead to instabilities. To disable this, use a constructor that is more
     specific about the bitsize, such as `CuArray{Float64}(A)`. Additionally, preferring more
-    stable factorization methods, such as `QRFactorization()`, can improve the numerics in
+    stable factorization methods, such as `LS.QRFactorization()`, can improve the numerics in
     such cases.
 
 Similarly to other use cases, you can choose the solver, for example:
 
 ```julia
-sol = solve(prob, QRFactorization())
+sol = LS.solve(prob, LS.QRFactorization())
 ```
 
 ## Sparse Matrices on GPUs
@@ -96,10 +96,12 @@ Currently, sparse matrix computations on GPUs are only supported for CUDA. This
 the `CUDA.CUSPARSE` sublibrary.
 
 ```julia
-using LinearAlgebra, CUDA.CUSPARSE
+import LinearAlgebra as LA
+import SparseArrays as SA
+import CUDA
 T = Float32
 n = 100
-A_cpu = sprand(T, n, n, 0.05) + I
+A_cpu = SA.sprand(T, n, n, 0.05) + LA.I
 x_cpu = zeros(T, n)
 b_cpu = rand(T, n)
 
@@ -112,7 +114,7 @@ In order to solve such problems using a direct method, you must add
 
 ```julia
 using CUDSS
-sol = solve(prob, LUFactorization())
+sol = LS.solve(prob, LS.LUFactorization())
 ```
 
 !!! note
@@ -122,13 +124,13 @@ sol = solve(prob, LUFactorization())
 Note that `KrylovJL` methods also work with sparse GPU arrays:
 
 ```julia
-sol = solve(prob, KrylovJL_GMRES())
+sol = LS.solve(prob, LS.KrylovJL_GMRES())
 ```
 
 Note that CUSPARSE also has some GPU-based preconditioners, such as a built-in `ilu`. However:
 
 ```julia
-sol = solve(prob, KrylovJL_GMRES(precs = (A, p) -> (CUDA.CUSPARSE.ilu02!(A, 'O'), I)))
+sol = LS.solve(prob, LS.KrylovJL_GMRES(precs = (A, p) -> (CUDA.CUSPARSE.ilu02!(A, 'O'), LA.I)))
 ```
 
 However, right now CUSPARSE is missing the right `ldiv!` implementation for this to work