From b2523ae48ee2eb32aac48f21379221ed91e21296 Mon Sep 17 00:00:00 2001
From: Sacha Verweij <sacha@stanford.edu>
Date: Thu, 28 Jul 2016 12:13:56 -0700
Subject: [PATCH] Make concatenations involving combinations of special
 matrices with special matrices, sparse matrices, or dense matrices/vectors
 yield sparse arrays.

---
 base/sparse/sparsematrix.jl | 14 +++++++++-----
 test/linalg/special.jl      | 38 +++++++++++++++++++++++++++++++++++++
 2 files changed, 47 insertions(+), 5 deletions(-)

diff --git a/base/sparse/sparsematrix.jl b/base/sparse/sparsematrix.jl
index 821e04d4d18da0..acabcf7a0d1b74 100644
--- a/base/sparse/sparsematrix.jl
+++ b/base/sparse/sparsematrix.jl
@@ -3229,19 +3229,23 @@ function hcat(X::SparseMatrixCSC...)
 end
 
 
-# Sparse/dense concatenation
+# Sparse/special/dense concatenation
 
-function hcat(Xin::Union{Vector, Matrix, SparseMatrixCSC}...)
+# TODO: A similar definition also exists in base/linalg/bidiag.jl. These definitions should
+# be consolidated in a more appropriate location, for example base/linalg/special.jl.
+SpecialArrays = Union{Diagonal, Bidiagonal, Tridiagonal, SymTridiagonal}
+
+function hcat(Xin::Union{Vector, Matrix, SparseMatrixCSC, SpecialArrays}...)
     X = SparseMatrixCSC[issparse(x) ? x : sparse(x) for x in Xin]
     hcat(X...)
 end
 
-function vcat(Xin::Union{Vector, Matrix, SparseMatrixCSC}...)
+function vcat(Xin::Union{Vector, Matrix, SparseMatrixCSC, SpecialArrays}...)
     X = SparseMatrixCSC[issparse(x) ? x : sparse(x) for x in Xin]
     vcat(X...)
 end
 
-function hvcat(rows::Tuple{Vararg{Int}}, X::Union{Vector, Matrix, SparseMatrixCSC}...)
+function hvcat(rows::Tuple{Vararg{Int}}, X::Union{Vector, Matrix, SparseMatrixCSC, SpecialArrays}...)
     nbr = length(rows)  # number of block rows
 
     tmp_rows = Array{SparseMatrixCSC}(nbr)
@@ -3253,7 +3257,7 @@ function hvcat(rows::Tuple{Vararg{Int}}, X::Union{Vector, Matrix, SparseMatrixCS
     vcat(tmp_rows...)
 end
 
-function cat(catdims, Xin::Union{Vector, Matrix, SparseMatrixCSC}...)
+function cat(catdims, Xin::Union{Vector, Matrix, SparseMatrixCSC, SpecialArrays}...)
     X = SparseMatrixCSC[issparse(x) ? x : sparse(x) for x in Xin]
     T = promote_eltype(Xin...)
     Base.cat_t(catdims, T, X...)
diff --git a/test/linalg/special.jl b/test/linalg/special.jl
index 89ddde5ee4b007..05105acd149a86 100644
--- a/test/linalg/special.jl
+++ b/test/linalg/special.jl
@@ -128,3 +128,41 @@ for typ in [UpperTriangular,LowerTriangular,Base.LinAlg.UnitUpperTriangular,Base
     @test Base.LinAlg.A_mul_Bc(atri,qrb[:Q]) ≈ full(atri) * qrb[:Q]'
     @test Base.LinAlg.A_mul_Bc!(copy(atri),qrb[:Q]) ≈ full(atri) * qrb[:Q]'
 end
+
+# Test that concatenations of combinations of special and other matrix types yield sparse arrays
+let
+    N = 4
+    # Test concatenating pairwise combinations of special matrices
+    diagmat = Diagonal(ones(N))
+    bidiagmat = Bidiagonal(ones(N), ones(N-1), true)
+    tridiagmat = Tridiagonal(ones(N-1), ones(N), ones(N-1))
+    symtridiagmat = SymTridiagonal(ones(N), ones(N-1))
+    specialmats = (diagmat, bidiagmat, tridiagmat, symtridiagmat)
+    for specialmata in specialmats, specialmatb in specialmats
+        @test issparse(hcat(specialmata, specialmatb))
+        @test issparse(vcat(specialmata, specialmatb))
+        @test issparse(hvcat((1,1), specialmata, specialmatb))
+        @test issparse(cat((1,2), specialmata, specialmatb))
+    end
+    # Test concatenating pairwise combinations of special matrices with sparse matrices,
+    # dense matrices, or dense vectors
+    densevec = ones(N)
+    densemat = diagm(ones(N))
+    spmat = spdiagm(ones(N))
+    for specialmat in specialmats
+        # --> Tests applicable only to pairs of matrices
+        for othermat in (spmat, densemat)
+            @test issparse(vcat(specialmat, othermat))
+            @test issparse(vcat(othermat, specialmat))
+        end
+        # --> Tests applicable also to pairs including vectors
+        for specialmat in specialmats, othermatorvec in (spmat, densemat, densevec)
+            @test issparse(hcat(specialmat, othermatorvec))
+            @test issparse(hcat(othermatorvec, specialmat))
+            @test issparse(hvcat((2,), specialmat, othermatorvec))
+            @test issparse(hvcat((2,), othermatorvec, specialmat))
+            @test issparse(cat((1,2), specialmat, othermatorvec))
+            @test issparse(cat((1,2), othermatorvec, specialmat))
+        end
+    end
+end