Specialize for Symmetric/Hermitian

Author: jishnub

src/symmetric.jl

@@ -414,6 +414,19 @@ function fillstored!(A::HermOrSym{T}, x) where T
     return A
 end
 
+function fillband!(A::HermOrSym, x, l, u)
+    if isa(A, Hermitian)
+        ishermitian(x) || throw(ArgumentError("cannot fill Hermitian matrix with a non-hermitian value"))
+    elseif isa(A, Symmetric)
+        issymmetric(x) || throw(ArgumentError("cannot fill Symmetric matrix with an asymmetric value"))
+    end
+    l == -u || throw(ArgumentError(lazy"lower and upper bands must be equal in magnitude and opposite in sign, got l=$(l), u=$(u)"))
+    lp = A.uplo == 'U' ? 0 : l
+    up = A.uplo == 'U' ? u : 0
+    applytri(A -> fillband!(A, x, lp, up), A)
+    return A
+end
+
 Base.isreal(A::HermOrSym{<:Real}) = true
 function Base.isreal(A::HermOrSym)
     n = size(A, 1)

test/symmetric.jl

@@ -1257,4 +1257,24 @@ end
     end
 end
 
+@testset "fillband!" begin
+    A = zeros(4,4)
+    @testset for T in (Symmetric, Hermitian), uplo in (:U, :L)
+        A .= 0
+        S = T(A, uplo)
+        LinearAlgebra.fillband!(S, 2, -2, 2)
+        @test all(all(==(2), diagview(S, k)) for k in -2:2)
+        @test iszero(diagview(S, -3))
+        @test iszero(diagview(S, 3))
+        LinearAlgebra.fillband!(S, 4, -1, 1)
+        @test all(all(==(4), diagview(S, k)) for k in -1:1)
+        @test all(==(2), diagview(S, -2))
+        @test all(==(2), diagview(S, 2))
+    end
+    msg = "cannot fill Hermitian matrix with a non-hermitian value"
+    @test_throws msg LinearAlgebra.fillband!(Hermitian(A), 2im, -3, 3)
+    msg = "lower and upper bands must be equal in magnitude and opposite in sign, got l=0, u=1"
+    @test_throws msg LinearAlgebra.fillband!(Symmetric(A), 2, 0, 1)
+end
+
 end # module TestSymmetric