Refine column ranges in _isbanded_impl

src/generic.jl

@@ -1493,14 +1493,34 @@ function _isbanded_impl(A, kl, ku)
     beyond ku, where the elements should all be zero. The reason we separate this from the
     third group is that we may loop over all the rows using A[:, col] instead of A[rowrange, col],
     which is usually faster.
+
+    E.g., in the following 6x10 matrix with (kl,ku) = (-1,1):
+     1  1  0  0  0  0  0  0  0  0
+     1  2  2  0  0  0  0  0  0  0
+     0  2  3  3  0  0  0  0  0  0
+     0  0  3  4  4  0  0  0  0  0
+     0  0  0  4  5  5  0  0  0  0
+     0  0  0  0  5  6  6  0  0  0
+
+    last_col_nonzeroblocks: 7, as every column beyond this is entirely zero
+    last_col_emptytoprows: 2, as there are zeros above the stored bands beyond this column
+    last_col_nonemptybottomrows: 4, as there are no zeros below the stored bands beyond this column
+    colrange_onlybottomrows: 1:2, as these columns only have zeros below the stored bands
+    colrange_topbottomrows: 3:4, as these columns have zeros both above and below the stored bands
+    colrange_onlytoprows_nonzero: 5:7, as these columns only have zeros above the stored bands
+    colrange_zero_block: 8:10, as every column in this range is filled with zeros
+
+    These are used to determine which rows to check for zeros in each column.
     =#
 
     last_col_nonzeroblocks = size(A,1) + ku # fully zero rectangular block beyond this column
     last_col_emptytoprows = ku + 1 # empty top rows before this column
     last_col_nonemptybottomrows = size(A,1) + kl - 1 # empty bottom rows after this column
 
     colrange_onlybottomrows = firstindex(A,2):min(last_col_nonemptybottomrows, last_col_emptytoprows)
-    colrange_topbottomrows = max(last_col_emptytoprows, last(colrange_onlybottomrows))+1:last_col_nonzeroblocks
+    col_topbotrows_start = max(last_col_emptytoprows, last(colrange_onlybottomrows))+1
+    col_topbotrows_end = min(last_col_nonemptybottomrows, last_col_nonzeroblocks)
+    colrange_topbottomrows = col_topbotrows_start:col_topbotrows_end
     colrange_onlytoprows_nonzero = last(colrange_topbottomrows)+1:last_col_nonzeroblocks
     colrange_zero_block = last_col_nonzeroblocks+1:lastindex(A,2)
 

test/generic.jl

@@ -534,17 +534,17 @@ end
 
 @testset "generic functions for checking whether matrices have banded structure" begin
     pentadiag = [1 2 3; 4 5 6; 7 8 9]
-    tridiag   = [1 2 0; 4 5 6; 0 8 9]
-    tridiagG  = GenericArray([1 2 0; 4 5 6; 0 8 9])
+    tridiag   = diagm(-1=>1:6, 1=>1:6)
+    tridiagG  = GenericArray(tridiag)
     Tridiag   = Tridiagonal(tridiag)
     ubidiag   = [1 2 0; 0 5 6; 0 0 9]
-    ubidiagG  = GenericArray([1 2 0; 0 5 6; 0 0 9])
+    ubidiagG  = GenericArray(ubidiag)
     uBidiag   = Bidiagonal(ubidiag, :U)
     lbidiag   = [1 0 0; 4 5 0; 0 8 9]
-    lbidiagG  = GenericArray([1 0 0; 4 5 0; 0 8 9])
+    lbidiagG  = GenericArray(lbidiag)
     lBidiag   = Bidiagonal(lbidiag, :L)
     adiag     = [1 0 0; 0 5 0; 0 0 9]
-    adiagG    = GenericArray([1 0 0; 0 5 0; 0 0 9])
+    adiagG    = GenericArray(adiag)
     aDiag     = Diagonal(adiag)
     @testset "istriu" begin
         @test !istriu(pentadiag)
@@ -638,6 +638,17 @@ end
             end
         end
     end
+
+    tridiag   = diagm(-1=>1:6, 1=>1:6)
+    A = [tridiag zeros(size(tridiag,1), 2)]
+    G = GenericArray(A)
+    @testset for (kl,ku) in Iterators.product(-10:10, -10:10)
+        @test isbanded(A, kl, ku) == isbanded(G, kl, ku)
+    end
+    @testset for k in -10:10
+        @test istriu(A,k) == istriu(G,k)
+        @test istril(A,k) == istril(G,k)
+    end
 end
 
 @testset "missing values" begin