Merge pull request #11989 from JuliaLang/anj/fixqr

Fix \ for underdetermined systems of integers

base/linalg/dense.jl

@@ -389,18 +389,16 @@ end
 
 (\)(a::Vector, B::StridedVecOrMat) = (\)(reshape(a, length(a), 1), B)
 
-for (T1,PIVOT) in ((BlasFloat,Val{true}),(Any,Val{false}))
-    @eval function (\){T<:$T1}(A::StridedMatrix{T}, B::StridedVecOrMat)
-        m, n = size(A)
-        if m == n
-            if istril(A)
-                return istriu(A) ? \(Diagonal(A),B) : \(LowerTriangular(A),B)
-            end
-            istriu(A) && return \(UpperTriangular(A),B)
-            return \(lufact(A),B)
+function (\)(A::StridedMatrix, B::StridedVecOrMat)
+    m, n = size(A)
+    if m == n
+        if istril(A)
+            return istriu(A) ? \(Diagonal(A),B) : \(LowerTriangular(A),B)
         end
-        return qrfact(A,$PIVOT)\B
+        istriu(A) && return \(UpperTriangular(A),B)
+        return \(lufact(A),B)
     end
+    return qrfact(A,Val{true})\B
 end
 
 ## Moore-Penrose pseudoinverse

test/choosetests.jl

@@ -62,7 +62,7 @@ function choosetests(choices = [])
 
     linalgtests = ["linalg1", "linalg2", "linalg3", "linalg4",
                    "linalg/lapack", "linalg/triangular", "linalg/tridiag",
-                   "linalg/bidiag", "linalg/diagonal",
+                   "linalg/bidiag", "linalg/diagonal", "linalg/dense",
                    "linalg/pinv", "linalg/givens", "linalg/cholesky",
                    "linalg/lu", "linalg/symmetric", "linalg/generic"]
     if Base.USE_GPL_LIBS

test/linalg/bidiag.jl

@@ -66,7 +66,9 @@ for relty in (Float32, Float64, BigFloat), elty in (relty, Complex{relty})
         debug && println("Generic Mat-vec ops")
         @test_approx_eq T*dv Tfull*dv
         @test_approx_eq T'*dv Tfull'*dv
-        @test_approx_eq T/dv' Tfull/dv'
+        if relty != BigFloat # not supported by pivoted QR
+            @test_approx_eq T/dv' Tfull/dv'
+        end
 
         debug && println("Diagonals")
         @test diag(T,2) == zeros(elty, n-2)

test/linalg/dense.jl

@@ -0,0 +1,4 @@
+using Base.Test
+
+# Check that non-floats are correctly promoted
+@test_approx_eq [1 0 0; 0 1 0]\[1,1] [1;1;0]