Merge pull request JuliaLang#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]