From 788e01ecf83bbb50d62dcd27d8a1f49ed186a50d Mon Sep 17 00:00:00 2001
From: Sacha Verweij <sacha@stanford.edu>
Date: Thu, 28 Jul 2016 14:03:12 -0700
Subject: [PATCH] Make general concatenations (`cat`) of combinations of sparse
 matrices with sparse matrices or dense matrices/vectors yield sparse arrays
 (fixes #17680).

---
 base/abstractarray.jl       |  2 +-
 base/array.jl               |  3 +++
 base/sparse/sparse.jl       |  4 ++--
 base/sparse/sparsematrix.jl |  6 ++++++
 test/sparsedir/sparse.jl    | 32 ++++++++++++++++++++++++--------
 5 files changed, 36 insertions(+), 11 deletions(-)

diff --git a/base/abstractarray.jl b/base/abstractarray.jl
index ca46ba05d13c1..067cdd0093174 100644
--- a/base/abstractarray.jl
+++ b/base/abstractarray.jl
@@ -998,7 +998,7 @@ function cat_t(catdims, typeC::Type, X...)
         end
     end
 
-    C = similar(isa(X[1],AbstractArray) ? full(X[1]) : [X[1]], typeC, tuple(dimsC...))
+    C = similar(isa(X[1],AbstractArray) ? X[1] : [X[1]], typeC, tuple(dimsC...))
     if length(catdims)>1
         fill!(C,0)
     end
diff --git a/base/array.jl b/base/array.jl
index 19e548054e338..4fc67b12ba356 100644
--- a/base/array.jl
+++ b/base/array.jl
@@ -699,6 +699,9 @@ hvcat{T}(rows::Tuple{Vararg{Int}}, xs::Vector{T}...) = typed_hvcat(T, rows, xs..
 hvcat(rows::Tuple{Vararg{Int}}, xs::Matrix...) = typed_hvcat(promote_eltype(xs...), rows, xs...)
 hvcat{T}(rows::Tuple{Vararg{Int}}, xs::Matrix{T}...) = typed_hvcat(T, rows, xs...)
 
+cat(catdims, xs::Union{Matrix,Vector}...) = Base.cat_t(catdims, promote_eltype(xs...), xs...)
+cat{T}(catdims, xs::Union{Matrix{T},Vector{T}}...) = Base.cat_t(catdims, T, xs...)
+
 ## find ##
 
 # returns the index of the next non-zero element, or 0 if all zeros
diff --git a/base/sparse/sparse.jl b/base/sparse/sparse.jl
index e303c0e0b8969..189a8562814df 100644
--- a/base/sparse/sparse.jl
+++ b/base/sparse/sparse.jl
@@ -21,10 +21,10 @@ import Base: @get!, acos, acosd, acot, acotd, acsch, asech, asin, asind, asinh,
     tand, tanh, trace, transpose!, tril!, triu!, trunc, vecnorm, abs, abs2,
     broadcast, ceil, complex, cond, conj, convert, copy, copy!, ctranspose, diagm,
     exp, expm1, factorize, find, findmax, findmin, findnz, float, full, getindex,
-    hcat, hvcat, imag, indmax, ishermitian, kron, length, log, log1p, max, min,
+    vcat, hcat, hvcat, cat, imag, indmax, ishermitian, kron, length, log, log1p, max, min,
     maximum, minimum, norm, one, promote_eltype, real, reinterpret, reshape, rot180,
     rotl90, rotr90, round, scale!, setindex!, similar, size, transpose, tril,
-    triu, vcat, vec, permute!
+    triu, vec, permute!
 
 import Base.Broadcast: broadcast_shape
 
diff --git a/base/sparse/sparsematrix.jl b/base/sparse/sparsematrix.jl
index 876f1e74b0cae..821e04d4d18da 100644
--- a/base/sparse/sparsematrix.jl
+++ b/base/sparse/sparsematrix.jl
@@ -3253,6 +3253,12 @@ function hvcat(rows::Tuple{Vararg{Int}}, X::Union{Vector, Matrix, SparseMatrixCS
     vcat(tmp_rows...)
 end
 
+function cat(catdims, Xin::Union{Vector, Matrix, SparseMatrixCSC}...)
+    X = SparseMatrixCSC[issparse(x) ? x : sparse(x) for x in Xin]
+    T = promote_eltype(Xin...)
+    Base.cat_t(catdims, T, X...)
+end
+
 """
     blkdiag(A...)
 
diff --git a/test/sparsedir/sparse.jl b/test/sparsedir/sparse.jl
index fbe6e18f9a3b4..e6d4e9767e2b1 100644
--- a/test/sparsedir/sparse.jl
+++ b/test/sparsedir/sparse.jl
@@ -1554,14 +1554,30 @@ end
 @inferred sprand(1, 1, 1.0, rand, Float64)
 @inferred sprand(1, 1, 1.0, x->round(Int,rand(x)*100))
 
-# dense sparse concatenation -> sparse return type
-@test issparse([sprand(10,10,.1) rand(10,10)])
-@test issparse([sprand(10,10,.1); rand(10,10)])
-@test issparse([sprand(10,10,.1) rand(10,10); rand(10,10) rand(10,10)])
-# ---
-@test !issparse([rand(10,10)  rand(10,10)])
-@test !issparse([rand(10,10); rand(10,10)])
-@test !issparse([rand(10,10)  rand(10,10); rand(10,10) rand(10,10)])
+# Test that concatenations of combinations of sparse matrices with sparse matrices or dense
+# matrices/vectors yield sparse arrays
+let
+    N = 4
+    densevec = ones(N)
+    densemat = diagm(ones(N))
+    spmat = spdiagm(ones(N))
+    # Test that concatenations of pairs of sparse matrices yield sparse arrays
+    @test issparse(vcat(spmat, spmat))
+    @test issparse(hcat(spmat, spmat))
+    @test issparse(hvcat((2,), spmat, spmat))
+    @test issparse(cat((1,2), spmat, spmat))
+    # Test that concatenations of a sparse matrice with a dense matrix/vector yield sparse arrays
+    @test issparse(vcat(spmat, densemat))
+    @test issparse(vcat(densemat, spmat))
+    for densearg in (densevec, densemat)
+        @test issparse(hcat(spmat, densearg))
+        @test issparse(hcat(densearg, spmat))
+        @test issparse(hvcat((2,), spmat, densearg))
+        @test issparse(hvcat((2,), densearg, spmat))
+        @test issparse(cat((1,2), spmat, densearg))
+        @test issparse(cat((1,2), densearg, spmat))
+    end
+end
 
 # issue #14816
 let m = 5