Specialize istriu/istril/isdiag using bandwidths (#358)

* specialize istriu/istril/isdiag using bandwidths

* bump version to v0.17.23

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "BandedMatrices"
 uuid = "aae01518-5342-5314-be14-df237901396f"
-version = "0.17.22"
+version = "0.17.23"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"

src/BandedMatrices.jl

@@ -19,7 +19,7 @@ import LinearAlgebra: axpy!, _chol!, rot180, dot, cholcopy, _apply_ipiv_rows!,
             _apply_inverse_ipiv_rows!, diag, eigvals!, eigvals, eigen!, eigen,
             qr, qr!, ldiv!, mul!, lu, lu!, ldlt, ldlt!,
             kron, lmul!, rmul!, factorize, logabsdet,
-            svdvals, svdvals!, tril!, triu!, diagzero
+            svdvals, svdvals!, tril!, triu!, diagzero, istriu, istril, isdiag
 
 using LinearAlgebra.LAPACK
 using LinearAlgebra.LAPACK: chkuplo, chktrans

src/generic/AbstractBandedMatrix.jl

@@ -139,6 +139,19 @@ function triu!(A::AbstractBandedMatrix{T}, k::Integer) where T
     A
 end
 
+function isdiag(B::AbstractBandedMatrix)
+    l, u = bandwidths(B)
+    l + u < 0 || (iszero(l) && iszero(u))
+end
+function istriu(B::AbstractBandedMatrix, k::Integer)
+    l, u = bandwidths(B)
+    l + u < 0 || min(l, size(B,1)-1) <= -k
+end
+function istril(B::AbstractBandedMatrix, k::Integer)
+    l, u = bandwidths(B)
+    l + u < 0 || min(u, size(B,2)-1) <= k
+end
+
 
 ## @inbands
 

test/test_linalg.jl

@@ -360,5 +360,71 @@ import BandedMatrices: BandedColumns, _BandedMatrix
             end
         end
     end
+
+    @testset "isdiag/istril/istriu" begin
+        @testset "no bands" begin
+            B = brand(3,2,-2,1)
+            for k in -5:5
+                @test istriu(B, k)
+                @test istril(B, k)
+                @test isdiag(B)
+            end
+        end
+
+        @testset "one band" begin
+            B = brand(3,3,-1,1)
+            A = Array(B)
+            @test !isdiag(B)
+            @test all(k -> istril(B,k), 1:5)
+            @test all(k -> !istril(B,k), -5:0)
+            @test all(k -> istriu(B,k), -5:1)
+            @test all(k -> !istriu(B,k), 2:5)
+            @test all(k -> istriu(A,k) == istriu(B,k), -5:5)
+            @test all(k -> istril(A,k) == istril(B,k), -5:5)
+
+            B = brand(3,3,1,-1)
+            A = Array(B)
+            @test !isdiag(B)
+            @test all(k -> istril(B,k), -1:5)
+            @test all(k -> !istril(B,k), -5:-2)
+            @test all(k -> istriu(B,k), -5:-1)
+            @test all(k -> !istriu(B,k), 0:5)
+            @test all(k -> istriu(A,k) == istriu(B,k), -5:5)
+            @test all(k -> istril(A,k) == istril(B,k), -5:5)
+
+            B = brand(3,3,0,0)
+            A = Array(B)
+            @test isdiag(B)
+            @test all(k -> istril(B,k), 0:5)
+            @test all(k -> !istril(B,k), -5:-1)
+            @test all(k -> istriu(B,k), -5:0)
+            @test all(k -> !istriu(B,k), 1:5)
+            @test all(k -> istriu(A,k) == istriu(B,k), -5:5)
+            @test all(k -> istril(A,k) == istril(B,k), -5:5)
+        end
+
+        @testset "multiple bands" begin
+            B = brand(3,6,1,2)
+            A = Array(B)
+            @test !isdiag(B)
+            @test all(k -> istril(B,k), 2:5)
+            @test all(k -> !istril(B,k), -5:1)
+            @test all(k -> istriu(B,k), -5:-1)
+            @test all(k -> !istriu(B,k), 0:-5)
+            @test all(k -> istriu(A,k) == istriu(B,k), -5:5)
+            @test all(k -> istril(A,k) == istril(B,k), -5:5)
+
+            for B in (brand(3,3,3,3), brand(3,3,2,2), brand(3,3,4,4))
+                A = Array(B)
+                @test !isdiag(B)
+                @test all(k -> istril(B,k), 2:5)
+                @test all(k -> !istril(B,k), -5:1)
+                @test all(k -> istriu(B,k), -5:-2)
+                @test all(k -> !istriu(B,k), -1:-5)
+                @test all(k -> istriu(A,k) == istriu(B,k), -5:5)
+                @test all(k -> istril(A,k) == istril(B,k), -5:5)
+            end
+        end
+    end
 end