From b7f0c03e49d54a686c5f5766d84f0b2674c60aac Mon Sep 17 00:00:00 2001
From: Jim Garrison <jim@garrison.cc>
Date: Thu, 23 Apr 2015 20:44:41 -0700
Subject: [PATCH] Fix #10739, implement `isdiag` method

---
 base/exports.jl           |  1 +
 base/linalg.jl            |  1 +
 base/linalg/generic.jl    |  3 +++
 doc/stdlib/linalg.rst     |  4 ++++
 test/arrayops.jl          | 11 +++++++++++
 test/linalg/bidiag.jl     |  4 ++--
 test/linalg/triangular.jl |  6 +++++-
 7 files changed, 27 insertions(+), 3 deletions(-)

diff --git a/base/exports.jl b/base/exports.jl
index 98d358a445aec..73d9ed60eeec2 100644
--- a/base/exports.jl
+++ b/base/exports.jl
@@ -634,6 +634,7 @@ export
     givens,
     hessfact!,
     hessfact,
+    isdiag,
     ishermitian,
     isposdef!,
     isposdef,
diff --git a/base/linalg.jl b/base/linalg.jl
index 54c9ca18c10f6..69b370a61a234 100644
--- a/base/linalg.jl
+++ b/base/linalg.jl
@@ -69,6 +69,7 @@ export
     gradient,
     hessfact,
     hessfact!,
+    isdiag,
     ishermitian,
     isposdef,
     isposdef!,
diff --git a/base/linalg/generic.jl b/base/linalg/generic.jl
index cf8ab0ecd9c24..31b09a13d7749 100644
--- a/base/linalg/generic.jl
+++ b/base/linalg/generic.jl
@@ -308,8 +308,11 @@ function istril(A::AbstractMatrix)
     return true
 end
 
+isdiag(A::AbstractMatrix) = istril(A) && istriu(A)
+
 istriu(x::Number) = true
 istril(x::Number) = true
+isdiag(x::Number) = true
 
 linreg{T<:Number}(X::StridedVecOrMat{T}, y::Vector{T}) = [ones(T, size(X,1)) X] \ y
 
diff --git a/doc/stdlib/linalg.rst b/doc/stdlib/linalg.rst
index 667b049048232..4a981534c233f 100644
--- a/doc/stdlib/linalg.rst
+++ b/doc/stdlib/linalg.rst
@@ -630,6 +630,10 @@ Linear algebra functions in Julia are largely implemented by calling functions f
 
    Test whether a matrix is upper triangular.
 
+.. function:: isdiag(A) -> Bool
+
+   Test whether a matrix is diagonal.
+
 .. function:: ishermitian(A) -> Bool
 
    Test whether a matrix is Hermitian.
diff --git a/test/arrayops.jl b/test/arrayops.jl
index 3beab3105d8cd..e6a9dfce6ed93 100644
--- a/test/arrayops.jl
+++ b/test/arrayops.jl
@@ -806,6 +806,17 @@ end
 @test_throws ArgumentError flipdim(1:10, -1)
 @test isequal(flipdim(Array(Int,0,0),1), Array(Int,0,0))  # issue #5872
 
+# isdiag, istril, istriu
+@test isdiag(3)
+@test istril(4)
+@test istriu(5)
+@test !isdiag([1 2; 3 4])
+@test !istril([1 2; 3 4])
+@test !istriu([1 2; 3 4])
+@test isdiag([1 0; 0 4])
+@test istril([1 0; 3 4])
+@test istriu([1 2; 0 4])
+
 # issue 4228
 A = [[i i; i i] for i=1:2]
 @test cumsum(A) == Any[[1 1; 1 1], [3 3; 3 3]]
diff --git a/test/linalg/bidiag.jl b/test/linalg/bidiag.jl
index d1854805a9310..57e884c350481 100644
--- a/test/linalg/bidiag.jl
+++ b/test/linalg/bidiag.jl
@@ -78,8 +78,8 @@ for relty in (Float32, Float64, BigFloat), elty in (relty, Complex{relty})
     end
 end
 
-#Issue 10742
+# Issue 10742 and similar
 let A = Bidiagonal([1,2,3], [0,0], true)
     @test istril(A)
+    @test isdiag(A)
 end
-
diff --git a/test/linalg/triangular.jl b/test/linalg/triangular.jl
index cd5fffdaf5cc6..5ead78671e276 100644
--- a/test/linalg/triangular.jl
+++ b/test/linalg/triangular.jl
@@ -275,6 +275,10 @@ for eltya in (Float32, Float64, Complex64, Complex128, BigFloat, Int)
     end
 end
 
-# Issue 10742
+# Issue 10742 and similar
 @test istril(UpperTriangular(diagm([1,2,3,4])))
 @test istriu(LowerTriangular(diagm([1,2,3,4])))
+@test isdiag(UpperTriangular(diagm([1,2,3,4])))
+@test isdiag(LowerTriangular(diagm([1,2,3,4])))
+@test !isdiag(UpperTriangular(rand(4, 4)))
+@test !isdiag(LowerTriangular(rand(4, 4)))