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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,119 +1,173 @@ | ||
| @testset "aux" begin | ||
| # test Givens reflector corner cases | ||
| (c, s, ρ) = Krylov.sym_givens(0.0, 0.0) | ||
| @test (c == 1.0) && (s == 0.0) && (ρ == 0.0) | ||
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| a = 3.14 | ||
| (c, s, ρ) = Krylov.sym_givens(a, 0.0) | ||
| @test (c == 1.0) && (s == 0.0) && (ρ == a) | ||
| (c, s, ρ) = Krylov.sym_givens(-a, 0.0) | ||
| @test (c == -1.0) && (s == 0.0) && (ρ == a) | ||
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| b = 3.14 | ||
| (c, s, ρ) = Krylov.sym_givens(0.0, b) | ||
| @test (c == 0.0) && (s == 1.0) && (ρ == b) | ||
| (c, s, ρ) = Krylov.sym_givens(0.0, -b) | ||
| @test (c == 0.0) && (s == -1.0) && (ρ == b) | ||
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| (c, s, ρ) = Krylov.sym_givens(Complex(0.0), Complex(0.0)) | ||
| @test (c == 1.0) && (s == Complex(0.0)) && (ρ == Complex(0.0)) | ||
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| a = Complex(1.0, 1.0) | ||
| (c, s, ρ) = Krylov.sym_givens(a, Complex(0.0)) | ||
| @test (c == 1.0) && (s == Complex(0.0)) && (ρ == a) | ||
| (c, s, ρ) = Krylov.sym_givens(-a, Complex(0.0)) | ||
| @test (c == 1.0) && (s == Complex(0.0)) && (ρ == -a) | ||
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| b = Complex(1.0, 1.0) | ||
| (c, s, ρ) = Krylov.sym_givens(Complex(0.0), b) | ||
| @test (c == 0.0) && (s == Complex(1.0)) && (ρ == b) | ||
| (c, s, ρ) = Krylov.sym_givens(Complex(0.0), -b) | ||
| @test (c == 0.0) && (s == Complex(1.0)) && (ρ == -b) | ||
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| # test roots of a quadratic | ||
| roots = Krylov.roots_quadratic(0.0, 0.0, 0.0) | ||
| @test length(roots) == 1 | ||
| @test roots[1] == 0.0 | ||
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| roots = Krylov.roots_quadratic(0.0, 0.0, 1.0) | ||
| @test length(roots) == 0 | ||
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| roots = Krylov.roots_quadratic(0.0, 3.14, -1.0) | ||
| @test length(roots) == 1 | ||
| @test roots[1] == 1.0 / 3.14 | ||
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| roots = Krylov.roots_quadratic(1.0, 0.0, 1.0) | ||
| @test length(roots) == 0 | ||
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| roots = Krylov.roots_quadratic(1.0, 0.0, 0.0) | ||
| @test length(roots) == 2 | ||
| @test roots[1] == 0.0 | ||
| @test roots[2] == 0.0 | ||
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| roots = Krylov.roots_quadratic(1.0, 3.0, 2.0) | ||
| @test length(roots) == 2 | ||
| @test roots[1] ≈ -2.0 | ||
| @test roots[2] ≈ -1.0 | ||
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| roots = Krylov.roots_quadratic(1.0e+8, 1.0, 1.0) | ||
| @test length(roots) == 0 | ||
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| # ill-conditioned quadratic | ||
| roots = Krylov.roots_quadratic(-1.0e-8, 1.0e+5, 1.0, nitref=0) | ||
| @test length(roots) == 2 | ||
| @test roots[1] == 1.0e+13 | ||
| @test roots[2] == 0.0 | ||
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||
| # iterative refinement is crucial! | ||
| roots = Krylov.roots_quadratic(-1.0e-8, 1.0e+5, 1.0, nitref=1) | ||
| @test length(roots) == 2 | ||
| @test roots[1] == 1.0e+13 | ||
| @test roots[2] == -1.0e-05 | ||
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| # not ill-conditioned quadratic | ||
| roots = Krylov.roots_quadratic(-1.0e-7, 1.0, 1.0, nitref=0) | ||
| @test length(roots) == 2 | ||
| @test isapprox(roots[1], 1.0e+7, rtol=1.0e-6) | ||
| @test isapprox(roots[2], -1.0, rtol=1.0e-6) | ||
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| roots = Krylov.roots_quadratic(-1.0e-7, 1.0, 1.0, nitref=1) | ||
| @test length(roots) == 2 | ||
| @test isapprox(roots[1], 1.0e+7, rtol=1.0e-6) | ||
| @test isapprox(roots[2], -1.0, rtol=1.0e-6) | ||
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| # test trust-region boundary | ||
| x = ones(5) | ||
| d = ones(5); d[1:2:5] .= -1 | ||
| @test_throws ErrorException Krylov.to_boundary(x, d, -1.0) | ||
| @test_throws ErrorException Krylov.to_boundary(x, d, 0.5) | ||
| @test_throws ErrorException Krylov.to_boundary(x, zeros(5), 1.0) | ||
| @test maximum(Krylov.to_boundary(x, d, 5.0)) ≈ 2.209975124224178 | ||
| @test minimum(Krylov.to_boundary(x, d, 5.0)) ≈ -1.8099751242241782 | ||
| @test maximum(Krylov.to_boundary(x, d, 5.0, flip=true)) ≈ 1.8099751242241782 | ||
| @test minimum(Krylov.to_boundary(x, d, 5.0, flip=true)) ≈ -2.209975124224178 | ||
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| # test kzeros and kones | ||
| @test Krylov.kzeros(Vector{Float64}, 10) == zeros(10) | ||
| @test Krylov.kones(Vector{Float64}, 10) == ones(10) | ||
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| # test ktypeof | ||
| a = rand(Float32, 10) | ||
| b = view(a, 4:8) | ||
| @test Krylov.ktypeof(a) == Vector{Float32} | ||
| @test Krylov.ktypeof(b) == Vector{Float32} | ||
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| a = rand(Float64, 10) | ||
| b = view(a, 4:8) | ||
| @test Krylov.ktypeof(a) == Vector{Float64} | ||
| @test Krylov.ktypeof(b) == Vector{Float64} | ||
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| a = sprand(Float32, 10, 0.5) | ||
| b = view(a, 4:8) | ||
| @test Krylov.ktypeof(a) == Vector{Float32} | ||
| @test Krylov.ktypeof(b) == Vector{Float32} | ||
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| a = sprand(Float64, 10, 0.5) | ||
| b = view(a, 4:8) | ||
| @test Krylov.ktypeof(a) == Vector{Float64} | ||
| @test Krylov.ktypeof(b) == Vector{Float64} | ||
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| @testset "sym_givens" begin | ||
| # test Givens reflector corner cases | ||
| (c, s, ρ) = Krylov.sym_givens(0.0, 0.0) | ||
| @test (c == 1.0) && (s == 0.0) && (ρ == 0.0) | ||
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| a = 3.14 | ||
| (c, s, ρ) = Krylov.sym_givens(a, 0.0) | ||
| @test (c == 1.0) && (s == 0.0) && (ρ == a) | ||
| (c, s, ρ) = Krylov.sym_givens(-a, 0.0) | ||
| @test (c == -1.0) && (s == 0.0) && (ρ == a) | ||
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| b = 3.14 | ||
| (c, s, ρ) = Krylov.sym_givens(0.0, b) | ||
| @test (c == 0.0) && (s == 1.0) && (ρ == b) | ||
| (c, s, ρ) = Krylov.sym_givens(0.0, -b) | ||
| @test (c == 0.0) && (s == -1.0) && (ρ == b) | ||
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| (c, s, ρ) = Krylov.sym_givens(Complex(0.0), Complex(0.0)) | ||
| @test (c == 1.0) && (s == Complex(0.0)) && (ρ == Complex(0.0)) | ||
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| a = Complex(1.0, 1.0) | ||
| (c, s, ρ) = Krylov.sym_givens(a, Complex(0.0)) | ||
| @test (c == 1.0) && (s == Complex(0.0)) && (ρ == a) | ||
| (c, s, ρ) = Krylov.sym_givens(-a, Complex(0.0)) | ||
| @test (c == 1.0) && (s == Complex(0.0)) && (ρ == -a) | ||
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| b = Complex(1.0, 1.0) | ||
| (c, s, ρ) = Krylov.sym_givens(Complex(0.0), b) | ||
| @test (c == 0.0) && (s == Complex(1.0)) && (ρ == b) | ||
| (c, s, ρ) = Krylov.sym_givens(Complex(0.0), -b) | ||
| @test (c == 0.0) && (s == Complex(1.0)) && (ρ == -b) | ||
| end | ||
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| @testset "roots_quadratic" begin | ||
| # test roots of a quadratic | ||
| roots = Krylov.roots_quadratic(0.0, 0.0, 0.0) | ||
| @test length(roots) == 1 | ||
| @test roots[1] == 0.0 | ||
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| roots = Krylov.roots_quadratic(0.0, 0.0, 1.0) | ||
| @test length(roots) == 0 | ||
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| roots = Krylov.roots_quadratic(0.0, 3.14, -1.0) | ||
| @test length(roots) == 1 | ||
| @test roots[1] == 1.0 / 3.14 | ||
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| roots = Krylov.roots_quadratic(1.0, 0.0, 1.0) | ||
| @test length(roots) == 0 | ||
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| roots = Krylov.roots_quadratic(1.0, 0.0, 0.0) | ||
| @test length(roots) == 2 | ||
| @test roots[1] == 0.0 | ||
| @test roots[2] == 0.0 | ||
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| roots = Krylov.roots_quadratic(1.0, 3.0, 2.0) | ||
| @test length(roots) == 2 | ||
| @test roots[1] ≈ -2.0 | ||
| @test roots[2] ≈ -1.0 | ||
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| roots = Krylov.roots_quadratic(1.0e+8, 1.0, 1.0) | ||
| @test length(roots) == 0 | ||
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||
| # ill-conditioned quadratic | ||
| roots = Krylov.roots_quadratic(-1.0e-8, 1.0e+5, 1.0, nitref=0) | ||
| @test length(roots) == 2 | ||
| @test roots[1] == 1.0e+13 | ||
| @test roots[2] == 0.0 | ||
|
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||
| # iterative refinement is crucial! | ||
| roots = Krylov.roots_quadratic(-1.0e-8, 1.0e+5, 1.0, nitref=1) | ||
| @test length(roots) == 2 | ||
| @test roots[1] == 1.0e+13 | ||
| @test roots[2] == -1.0e-05 | ||
|
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| # not ill-conditioned quadratic | ||
| roots = Krylov.roots_quadratic(-1.0e-7, 1.0, 1.0, nitref=0) | ||
| @test length(roots) == 2 | ||
| @test isapprox(roots[1], 1.0e+7, rtol=1.0e-6) | ||
| @test isapprox(roots[2], -1.0, rtol=1.0e-6) | ||
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| roots = Krylov.roots_quadratic(-1.0e-7, 1.0, 1.0, nitref=1) | ||
| @test length(roots) == 2 | ||
| @test isapprox(roots[1], 1.0e+7, rtol=1.0e-6) | ||
| @test isapprox(roots[2], -1.0, rtol=1.0e-6) | ||
| end | ||
|
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| @testset "to_boundary" begin | ||
| # test trust-region boundary | ||
| x = ones(5) | ||
| d = ones(5); d[1:2:5] .= -1 | ||
| @test_throws ErrorException Krylov.to_boundary(x, d, -1.0) | ||
| @test_throws ErrorException Krylov.to_boundary(x, d, 0.5) | ||
| @test_throws ErrorException Krylov.to_boundary(x, zeros(5), 1.0) | ||
| @test maximum(Krylov.to_boundary(x, d, 5.0)) ≈ 2.209975124224178 | ||
| @test minimum(Krylov.to_boundary(x, d, 5.0)) ≈ -1.8099751242241782 | ||
| @test maximum(Krylov.to_boundary(x, d, 5.0, flip=true)) ≈ 1.8099751242241782 | ||
| @test minimum(Krylov.to_boundary(x, d, 5.0, flip=true)) ≈ -2.209975124224178 | ||
| end | ||
|
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| @testset "kzeros" begin | ||
| # test kzeros | ||
| @test Krylov.kzeros(Vector{Float64}, 10) == zeros(Float64, 10) | ||
| @test Krylov.kzeros(Vector{ComplexF32}, 10) == zeros(ComplexF32, 10) | ||
| end | ||
|
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| @testset "kones" begin | ||
| # test kones | ||
| @test Krylov.kones(Vector{Float64}, 10) == ones(Float64, 10) | ||
| @test Krylov.kones(Vector{ComplexF32}, 10) == ones(ComplexF32, 10) | ||
| end | ||
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| @testset "ktypeof" begin | ||
| # test ktypeof | ||
| a = rand(Float32, 10) | ||
| b = view(a, 4:8) | ||
| @test Krylov.ktypeof(a) == Vector{Float32} | ||
| @test Krylov.ktypeof(b) == Vector{Float32} | ||
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| a = rand(Float64, 10) | ||
| b = view(a, 4:8) | ||
| @test Krylov.ktypeof(a) == Vector{Float64} | ||
| @test Krylov.ktypeof(b) == Vector{Float64} | ||
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| a = sprand(Float32, 10, 0.5) | ||
| b = view(a, 4:8) | ||
| @test Krylov.ktypeof(a) == Vector{Float32} | ||
| @test Krylov.ktypeof(b) == Vector{Float32} | ||
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| a = sprand(Float64, 10, 0.5) | ||
| b = view(a, 4:8) | ||
| @test Krylov.ktypeof(a) == Vector{Float64} | ||
| @test Krylov.ktypeof(b) == Vector{Float64} | ||
| end | ||
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| @testset "macros" begin | ||
| # test macros | ||
| for FC ∈ (Float16, Float32, Float64, Complex{Float16}, Complex{Float32}, Complex{Float64}) | ||
| n = 10 | ||
| x = rand(FC, n) | ||
| y = rand(FC, n) | ||
| a = rand(FC) | ||
| b = rand(FC) | ||
| c = rand(FC) | ||
| s = rand(FC) | ||
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| T = real(FC) | ||
| a2 = rand(T) | ||
| b2 = rand(T) | ||
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| Krylov.@kdot(n, x, y) | ||
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| Krylov.@kdotr(n, x, y) | ||
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| Krylov.@knrm2(n, x) | ||
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| Krylov.@kaxpy!(n, a, x, y) | ||
| Krylov.@kaxpy!(n, a2, x, y) | ||
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| Krylov.@kaxpby!(n, a, x, b, y) | ||
| Krylov.@kaxpby!(n, a2, x, b, y) | ||
| Krylov.@kaxpby!(n, a, x, b2, y) | ||
| Krylov.@kaxpby!(n, a2, x, b2, y) | ||
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| Krylov.@kcopy!(n, x, y) | ||
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| Krylov.@kswap(x, y) | ||
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| Krylov.@kref!(n, x, y, c, s) | ||
| end | ||
| end | ||
| end |