Remove FactCheck, use Base.test and simplify tests (#150)

* Make sure CG gets the correct types

* Use Base.Test in bicgstab

* Use Base.Test in cg

* Simplify cg

* Chebyshev to base.test and simplified tests

* Remove LinearMaps tests (basically verifying LinearMaps internals) and move to Base.Test

* Simplify GMRES tests and move partially to Base.Test

* Use new API for LinearMap

* Move factorization to Base.Test

* Use Base.Test in Hessenberg test

* Simplify tests and use Base.Test

* Indentation and move initialization to the start of the test

* Use Base.Test in lsmr

* Use Base.Test in orthogonalization tests

* Use Base.Test in rlinalg

* Use Base.Test in rsvd and use broadcasting

* Use Base.Test in rsvd_fnkz

* Use Base.Test in simple eigensolvers and update the API for LinearMaps

* Simplify stationary solvers tests and use Base.Test

* Update the Lanczos test

* Remove FastCheck related things

* Remove FactCheck dependency

* Simplify ls__ tests

* Surpress broadcast warning

* Use broadcasting properly

* Use Base.Test in minres

* Remove empty tests in history smoke test

* Move matrix stuff to benchmark folder

* Reduce dependencies in test REQUIRE file

* Test preconditioners with UmfpackLU on Julia 0.6+ only, since Julia 0.5 does not have support for A_ldiv_B!(::UmfpackLU, ::SubArray)

* Fix builds on Julia nightly by escaping strings properly

* Support 0.5

* Escape even more strings

* Remove LinearMaps where it isn't used

* Remove checking for 0.5

* Use latest API of LinearMaps

* Use I over (sp)eye

* Actually run the orthogonalization test

* Simplify orth. test

* Fix one() in CG

Author: haampie

test/matrixcollection.jl renamed to benchmark/matrixcollection.jl

@@ -118,17 +118,15 @@ function cg_iterator!(x, A, b, Pl = Identity();
         reltol = norm(b) * tol
     end
 
-    # Stopping criterion
-    ρ = one(residual)
-
     # Return the iterable
     if isa(Pl, Identity)
         return CGIterable(A, x, b,
             r, c, u,
-            reltol, residual, ρ,
+            reltol, residual, one(residual),
             maxiter, mv_products
         )
     else
+        ρ = one(eltype(r))
         return PCGIterable(Pl, A, x, b,
             r, c, u,
             reltol, residual, ρ,

test/matrixmarket.jl renamed to benchmark/matrixmarket.jl

@@ -12,7 +12,7 @@ and `P` computed by `idfact()`. See the documentation of `idfact()` for details.
 
 # References
 
-\cite{Cheng2005, Liberty2007}
+\\cite{Cheng2005, Liberty2007}
 """
 immutable Interpolative{T} <: Factorization{T}
     B :: AbstractMatrix{T}
@@ -43,13 +43,13 @@ Where:
 
 # Implementation note
 
-This is a hacky version of the algorithms described in \cite{Liberty2007}
-and \cite{Cheng2005}. The former refers to the factorization (3.1) of the
+This is a hacky version of the algorithms described in \\cite{Liberty2007}
+and \\cite{Cheng2005}. The former refers to the factorization (3.1) of the
 latter.  However, it is not actually necessary to compute this
 factorization in its entirely to compute an interpolative decomposition.
 
 Instead, it suffices to find some permutation of the first k columns of Y =
-R * A, extract the subset of A into B, then compute the P matrix as B\A
+R * A, extract the subset of A into B, then compute the P matrix as B\\A
 which will automatically compute P using a suitable least-squares
 algorithm.
 
@@ -59,7 +59,7 @@ pivoted QR process.
 
 # References
 
-\cite[Algorithm I]{Liberty2007}
+\\cite[Algorithm I]{Liberty2007}
 
 ```bibtex
 @article{Cheng2005,

src/cg.jl

@@ -86,7 +86,7 @@ see [`rnorms`](@ref) for a different estimator that uses premultiplying by both
 
 # References
 
-\cite[Lemma 4.1]{Halko2011}
+\\cite[Lemma 4.1]{Halko2011}
 """
 function rnorm(A, r::Int, p::Real=0.05)
     @assert 0<p≤1
@@ -113,7 +113,7 @@ bound on the true norm by a factor
 
 	ρ ≤ α ‖A‖
 
-with probability greater than `1 - p`, where `p = 4\sqrt(n/(iters-1)) α^(-2iters)`.
+with probability greater than `1 - p`, where `p = 4\\sqrt(n/(iters-1)) α^(-2iters)`.
 
 # Arguments
 
@@ -138,7 +138,7 @@ premultiplying by `A'`
 
 # References
 
-Appendix of \cite{Liberty2007}.
+Appendix of \\cite{Liberty2007}.
 
 ```bibtex
 @article{Liberty2007,
@@ -175,7 +175,7 @@ Estimate matrix condition number randomly.
 # Arguments
 
 `A`: matrix whose condition number to estimate. Must be square and
-support premultiply (`A*⋅`) and solve (`A\⋅`).
+support premultiply (`A*⋅`) and solve (`A\\⋅`).
 
 `iters::Int = 1`: number of power iterations to run.
 
@@ -189,7 +189,7 @@ Interval `(x, y)` which contains `κ(A)` with probability `1 - p`.
 
 # Implementation note
 
-\cite{Dixon1983} originally describes this as a computation that
+\\cite{Dixon1983} originally describes this as a computation that
 can be done by computing the necessary number of power iterations given p
 and the desired accuracy parameter `θ=y/x`. However, these bounds were only
 derived under the assumptions of exact arithmetic. Empirically, `iters≥4` has
@@ -200,7 +200,7 @@ parameter and hence the interval containing `κ(A)`.
 
 # References
 
-\cite[Theorem 2]{Dixon1983}
+\\cite[Theorem 2]{Dixon1983}
 
 ```bibtex
 @article{Dixon1983,
@@ -256,7 +256,7 @@ probability `1 - p`.
 
 # References
 
-\cite[Corollary of Theorem 1]{Dixon1983}.
+\\cite[Corollary of Theorem 1]{Dixon1983}.
 """
 function reigmax(A, k::Int=1, p::Real=0.05)
     @assert 0<p≤1
@@ -294,7 +294,7 @@ probability `1 - p`.
 
 # References
 
-\cite[Corollary of Theorem 1]{Dixon1983}.
+\\cite[Corollary of Theorem 1]{Dixon1983}.
 """
 function reigmin(A, k::Int=1, p::Real=0.05)
     @assert 0<p≤1
@@ -345,7 +345,7 @@ Apply a subsampled random Fourier transform to the columns of `A`.
 
 # References
 
-\[Equation 4.6]{Halko2011}
+\\[Equation 4.6]{Halko2011}
 """
 #Define two methods here to avoid method ambiguity with f::Function*b::Any
 *(A::Function, Ω::srft) = function *(A, Ω::srft)

src/factorization.jl

@@ -40,9 +40,9 @@ largest.
 
 This function calls `rrange`, which uses naive randomized rangefinding to
 compute a basis for a subspace of dimension `n` (Algorithm 4.1 of
-\cite{Halko2011}), followed by `svdfact_restricted()`, which computes the
+\\cite{Halko2011}), followed by `svdfact_restricted()`, which computes the
 exact SVD factorization on the restriction of `A` to this randomly selected
-subspace (Algorithm 5.1 of \cite{Halko2011}).
+subspace (Algorithm 5.1 of \\cite{Halko2011}).
 
 Alternatively, you can mix and match your own randomized algorithm using
 any of the randomized range finding algorithms to find a suitable subspace
@@ -100,9 +100,9 @@ largest.
 
 This function calls `rrange`, which uses naive randomized rangefinding to
 compute a basis for a subspace of dimension `n` (Algorithm 4.1 of
-\cite{Halko2011}), followed by `svdfact_restricted()`, which computes the
+\\cite{Halko2011}), followed by `svdfact_restricted()`, which computes the
 exact SVD factorization on the restriction of `A` to this randomly selected
-subspace (Algorithm 5.1 of \cite{Halko2011}).
+subspace (Algorithm 5.1 of \\cite{Halko2011}).
 
 Alternatively, you can mix and match your own randomized algorithm using
 any of the randomized range finding algorithms to find a suitable subspace
@@ -153,7 +153,7 @@ The Reference explicitly discourages using this algorithm.
 
 # Implementation note
 
-Whereas \cite{Halko2011} recommends classical Gram-Schmidt with double
+Whereas \\cite{Halko2011} recommends classical Gram-Schmidt with double
 reorthogonalization, we instead compute the basis with `qrfact()`, which
 for dense `A` computes the QR factorization using Householder reflectors.
 """
@@ -198,7 +198,7 @@ vectors of the computed subspace of `A`.
 
 # References
 
-Algorithm 4.2 of \cite{Halko2011}
+Algorithm 4.2 of \\cite{Halko2011}
 """
 function rrange_adaptive(A, r::Integer, ϵ::Real=eps(); maxiter::Int=10)
     m, n = size(A)
@@ -265,7 +265,7 @@ for dense A computes the QR factorization using Householder reflectors.
 
 # References
 
-Algorithm 4.4 of \cite{Halko2011}
+Algorithm 4.4 of \\cite{Halko2011}
 """
 function rrange_si(A, l::Int; At=A', q::Int=0)
     basis=x->full(qrfact(x)[:Q])
@@ -312,7 +312,7 @@ for dense `A` computes the QR factorization using Householder reflectors.
 
 # References
 
-Algorithm 4.5 of \cite{Halko2011}
+Algorithm 4.5 of \\cite{Halko2011}
 """
 function rrange_f(A, l::Int)
     n = size(A, 2)
@@ -340,7 +340,7 @@ desired.
 
 # References
 
-Algorithm 5.1 of \cite{Halko2011}
+Algorithm 5.1 of \\cite{Halko2011}
 """
 function svdfact_restricted(A, Q, n::Int)
     B=Q'A
@@ -367,7 +367,7 @@ desired.
 
 # References
 
-Algorithm 5.1 of \cite{Halko2011}
+Algorithm 5.1 of \\cite{Halko2011}
 """
 function svdvals_restricted(A, Q, n::Int)
     B=Q'A
@@ -380,7 +380,7 @@ end
 Compute the SVD factorization of `A` restricted to the subspace spanned by `Q`
 using row extraction.
 
-*Note:* \cite[Remark 5.2]{Halko2011} recommends input of `Q` of the form `Q=A*Ω`
+*Note:* \\cite[Remark 5.2]{Halko2011} recommends input of `Q` of the form `Q=A*Ω`
 where `Ω` is a sample computed by `randn(n,l)` or even `srft(l)`.
 
 # Arguments
@@ -401,7 +401,7 @@ interpolative decomposition `idfact`.
 
 # References
 
-Algorithm 5.2 of \cite{Halko2011}
+Algorithm 5.2 of \\cite{Halko2011}
 """
 function svdfact_re(A, Q)
     F = idfact(Q)
@@ -431,7 +431,7 @@ restriction to is desired.
 
 # References
 
-Algorithm 5.3 of \cite{Halko2011}
+Algorithm 5.3 of \\cite{Halko2011}
 """
 function eigfact_restricted(A::Hermitian, Q)
     B = Q'A*Q
@@ -445,7 +445,7 @@ end
 Compute the spectral (`Eigen`) factorization of `A` restricted to the subspace
 spanned by `Q` using row extraction.
 
-*Note:* \cite[Remark 5.2]{Halko2011} recommends input of `Q` of the form `Q=A*Ω`
+*Note:* \\cite[Remark 5.2]{Halko2011} recommends input of `Q` of the form `Q=A*Ω`
 where `Ω` is a sample computed by `randn(n,l)` or even `srft(l)`.
 
 # Arguments
@@ -466,7 +466,7 @@ interpolative decomposition `idfact()`.
 
 # References
 
-Algorithm 5.4 of \cite{Halko2011}
+Algorithm 5.4 of \\cite{Halko2011}
 """
 function eigfact_re(A::Hermitian, Q)
     X, J = idfact(Q)
@@ -501,7 +501,7 @@ that can be Cholesky decomposed.
 
 # References
 
-Algorithm 5.5 of \cite{Halko2011}
+Algorithm 5.5 of \\cite{Halko2011}
 """
 function eigfact_nystrom(A, Q)
     B₁=A*Q
@@ -534,7 +534,7 @@ product involving `A`.
 
 # References
 
-Algorithm 5.6 of \cite{Halko2011}
+Algorithm 5.6 of \\cite{Halko2011}
 """
 function eigfact_onepass(A::Hermitian, Ω)
     Y=A*Ω; Q = full(qrfact!(Y)[:Q])

src/rlinalg.jl

@@ -75,7 +75,7 @@ function rsvd_fnkz(A, k::Int;
         A[π, :]
     end
     X, RRR = qr(B₀)
-    X = X[:, abs(diag(RRR)) .> ϵ] #Remove linear dependent columns
+    X = X[:, abs.(diag(RRR)) .> ϵ] #Remove linear dependent columns
     B = tallandskinny ? X ⊗ A'X : X ⊗ X'A
 
     oldnrmB = 0.0
@@ -86,7 +86,7 @@ function rsvd_fnkz(A, k::Int;
         π = randperm(k)[1:l]
         #Update B using Theorem 2.4
         X, RRR = qr([B.X A[:, π]]) #We are doing more work than needed here
-        X = X[:, abs(diag(RRR)) .> ϵ] #Remove linearly dependent columns
+        X = X[:, abs.(diag(RRR)) .> ϵ] #Remove linearly dependent columns
         Y = A'X
         if dosvd
             S = svdfact!(Y)
@@ -111,5 +111,5 @@ function rsvd_fnkz(A, k::Int;
     for i=1:size(B.Y, 2)
         scale!(view(B.Y, :, i), 1/√Λ[i])
     end
-    Base.LinAlg.SVD(B.X, √Λ, B.Y')
+    Base.LinAlg.SVD(B.X, sqrt.(Λ), B.Y')
 end

src/rsvd.jl

@@ -83,7 +83,7 @@ end
     svdl(A)
 
 Compute some singular values (and optionally vectors) using Golub-Kahan-Lanczos
-bidiagonalization \cite{Golub1965} with thick restarting \cite{Wu2000}.
+bidiagonalization \\cite{Golub1965} with thick restarting \\cite{Wu2000}.
 
 If `log` is set to `true` is given, method will output a tuple `X, L, ch`. Where
 `ch` is a `ConvergenceHistory` object. Otherwise it will only return `X, L`.
@@ -346,7 +346,7 @@ function isconverged(L::PartialFactorization, F::Base.LinAlg.SVD, k::Int, tol::R
     @assert tol ≥ 0
 
     σ = F[:S][1:k]
-    Δσ= L.β*abs(F[:U][end, 1:k])
+    Δσ= L.β * abs.(F[:U][end, 1 : k])
 
     #Best available eigenvalue bounds
     δσ = copy(Δσ)
@@ -577,7 +577,7 @@ which case it will be necessary to orthogonalize both sets of vectors. See
 
 ```bibtex
 @book{Bjorck2015,
-    author = {Bj{\"{o}}rck, {\AA}ke},
+    author = {Bj{\\"{o}}rck, {\\AA}ke},
     doi = {10.1007/978-3-319-05089-8},
     publisher = {Springer},
     series = {Texts in Applied Mathematics},

src/rsvd_fnkz.jl

@@ -1,7 +1,3 @@
-FactCheck
-MAT
-MatrixMarket
 Plots
 UnicodePlots
 LinearMaps
-JLD