Refine column ranges in _isbanded_impl (#1267)

Fixes the column ranges, so that these correctly correspond to the
ranges over which there are top and bottom rows to consider beyond the
bands. The change is to the upper limit of the range.

(cherry picked from commit 95703b5)

Author: jishnub

src/generic.jl

@@ -1486,14 +1486,34 @@ 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

@@ -514,17 +514,17 @@ 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)
@@ -618,6 +618,17 @@ 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