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givens.jl
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givens.jl
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# This file is a part of Julia. License is MIT: http:https://julialang.org/license
let
debug = false
# Test givens rotations
for elty in (Float32, Float64, Complex64, Complex128)
debug && println("elty is $elty")
if elty <: Real
A = convert(Matrix{elty}, randn(10,10))
else
A = convert(Matrix{elty}, complex(randn(10,10),randn(10,10)))
end
Ac = copy(A)
R = Base.LinAlg.Rotation(Base.LinAlg.Givens{elty}[])
for j = 1:8
for i = j+2:10
G, _ = givens(A, j+1, i, j)
A_mul_B!(G, A)
A_mul_Bc!(A, G)
A_mul_B!(G, R)
# test transposes
@test_approx_eq ctranspose(G)*G*eye(10) eye(elty, 10)
@test_approx_eq ctranspose(R)*(R*eye(10)) eye(elty, 10)
@test_throws ErrorException transpose(G)
@test_throws ErrorException transpose(R)
end
end
@test_throws ArgumentError givens(A, 3, 2, 2)
@test_throws ArgumentError givens(one(elty),zero(elty),3,2)
G, _ = givens(one(elty),zero(elty),11,12)
@test_throws DimensionMismatch A_mul_B!(G, A)
@test_throws DimensionMismatch A_mul_Bc!(A,G)
@test_approx_eq abs(A) abs(hessfact(Ac)[:H])
@test_approx_eq norm(R*eye(elty, 10)) one(elty)
G, _ = givens(one(elty),zero(elty),9,10)
@test_approx_eq ctranspose(G*eye(elty,10))*(G*eye(elty,10)) eye(elty, 10)
K, _ = givens(zero(elty),one(elty),9,10)
@test_approx_eq ctranspose(K*eye(elty,10))*(K*eye(elty,10)) eye(elty, 10)
end
end #let