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Strong zero in Diagonal triple multiplication #55927

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Oct 1, 2024
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Strong zero in Diagonal triple multiplication #55927

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2 changes: 2 additions & 0 deletions stdlib/LinearAlgebra/src/special.jl
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Expand Up @@ -112,6 +112,8 @@ for op in (:+, :-)
end
end

(*)(Da::Diagonal, A::BandedMatrix, Db::Diagonal) = _tri_matmul(Da, A, Db)

# disambiguation between triangular and banded matrices, banded ones "dominate"
_mul!(C::AbstractMatrix, A::AbstractTriangular, B::BandedMatrix, alpha::Number, beta::Number) =
@stable_muladdmul _mul!(C, A, B, MulAddMul(alpha, beta))
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11 changes: 11 additions & 0 deletions stdlib/LinearAlgebra/test/diagonal.jl
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Expand Up @@ -1265,6 +1265,17 @@ end
@test *(Diagonal(ones(n)), Diagonal(1:n), Diagonal(ones(n)), Diagonal(1:n)) isa Diagonal
end

@testset "triple multiplication with a sandwiched BandedMatrix" begin
D = Diagonal(StepRangeLen(NaN, 0, 4));
B = Bidiagonal(1:4, 1:3, :U)
C = D * B * D
@test iszero(diag(C, 2))
# test associativity
C1 = (D * B) * D
C2 = D * (B * D)
@test diag(C,2) == diag(C1,2) == diag(C2,2)
end

@testset "diagind" begin
D = Diagonal(1:4)
M = Matrix(D)
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