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mohamed82008
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Add more tests
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‎test/lobpcg.jl

Lines changed: 172 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -2,8 +2,16 @@ using IterativeSolvers
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using LinearMaps
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using Base.Test
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import Base.A_ldiv_B!
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include("laplace_matrix.jl")
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struct JacobiPrec{TD}
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diagonal::TD
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end
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A_ldiv_B!(y, P::JacobiPrec, x) = y .= x ./ P.diagonal
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function max_err(R)
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r = zeros(real(eltype(R)), size(R, 2))
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for j in 1:length(r)
@@ -18,8 +26,8 @@ end
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@testset "Locally Optimal Block Preconditioned Conjugate Gradient" begin
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srand(1234321)
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@testset "Single eigenvalue" begin
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n = 10
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@testset "Small full system" begin
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n = 10
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@testset "Simple eigenvalue problem" begin
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@testset "Matrix{$T}" for T in (Float32, Float64, Complex64, Complex128)
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@testset "largest = $largest" for largest in (true, false)
@@ -59,7 +67,6 @@ end
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end
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end
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end
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@testset "Sparse Laplacian" begin
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A = laplace_matrix(Float64, 20, 2)
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rhs = randn(size(A, 2), 1)
@@ -74,6 +81,168 @@ end
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end
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end
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end
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@testset "Zero initial solution" begin
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@testset "Simple eigenvalue problem" begin
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@testset "Matrix{$T}" for T in (Float32, Float64, Complex64, Complex128)
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@testset "largest = $largest" for largest in (true, false)
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A = rand(T, n, n)
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A = A' * A + I
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b = zeros(T, n, 1)
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tol = √eps(real(T))
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r = lobpcg(A, largest, b; tol=tol, maxiter=Inf, log=false)
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λ, X = r.λ, r.X
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@test norm(A*X - X*λ) ≤ tol
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end
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end
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end
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@testset "Generalized eigenvalue problem" begin
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@testset "Matrix{$T}" for T in (Float32, Float64, Complex64, Complex128)
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@testset "largest = $largest" for largest in (true, false)
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A = rand(T, n, n)
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A = A' * A + I
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B = rand(T, n, n)
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B = B' * B + I
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b = zeros(T, n, 1)
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tol = √eps(real(T))
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109+
r = lobpcg(A, B, largest, b; tol=tol, maxiter=Inf, log=true)
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λ, X = r.λ, r.X
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@test max_err(A*X - B*X*λ) ≤ tol
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end
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end
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end
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end
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@testset "No initial solution" begin
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@testset "Simple eigenvalue problem" begin
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@testset "Matrix{$T}" for T in (Float32, Float64, Complex64, Complex128)
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@testset "largest = $largest" for largest in (true, false)
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A = rand(T, n, n)
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A = A' * A + I
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tol = √eps(real(T))
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r = lobpcg(A, largest, 1; tol=tol, maxiter=Inf, log=false)
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λ, X = r.λ, r.X
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@test norm(A*X - X*λ) ≤ tol
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end
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end
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end
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@testset "Generalized eigenvalue problem" begin
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@testset "Matrix{$T}" for T in (Float32, Float64, Complex64, Complex128)
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@testset "largest = $largest" for largest in (true, false)
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A = rand(T, n, n)
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A = A' * A + I
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B = rand(T, n, n)
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B = B' * B + I
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tol = √eps(real(T))
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r = lobpcg(A, B, largest, 1; tol=tol, maxiter=Inf, log=true)
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λ, X = r.λ, r.X
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@test max_err(A*X - B*X*λ) ≤ tol
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end
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end
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end
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end
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@testset "Inplace" begin
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@testset "Simple eigenvalue problem" begin
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@testset "Matrix{$T}" for T in (Float32, Float64, Complex64, Complex128)
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@testset "largest = $largest" for largest in (true, false)
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A = rand(T, n, n)
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A = A' * A + I
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tol = √eps(real(T))
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b = rand(T, n, 1)
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itr = LOBPCGIterator(A, b, largest)
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156+
r = lobpcg!(itr; tol=tol, maxiter=Inf, log=false)
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λ, X = r.λ, r.X
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@test norm(A*X - X*λ) ≤ tol
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end
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end
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end
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@testset "Generalized eigenvalue problem" begin
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@testset "Matrix{$T}" for T in (Float32, Float64, Complex64, Complex128)
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@testset "largest = $largest" for largest in (true, false)
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A = rand(T, n, n)
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A = A' * A + I
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B = rand(T, n, n)
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B = B' * B + I
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b = rand(T, n, 1)
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tol = √eps(real(T))
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itr = LOBPCGIterator(A, B, b, largest)
172+
173+
r = lobpcg!(itr; tol=tol, maxiter=Inf, log=true)
174+
λ, X = r.λ, r.X
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@test max_err(A*X - B*X*λ) ≤ tol
176+
end
177+
end
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end
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end
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@testset "Jacobi preconditioner" begin
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@testset "Simple eigenvalue problem" begin
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@testset "Matrix{$T}" for T in (Float32, Float64, Complex64, Complex128)
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@testset "largest = $largest" for largest in (true, false)
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A = rand(T, n, n)
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A = A' * A + I
186+
tol = √eps(real(T))
187+
P = JacobiPrec(diag(A))
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r = lobpcg(A, largest, 1; P=P, tol=tol, maxiter=Inf, log=false)
189+
λ, X = r.λ, r.X
190+
@test norm(A*X - X*λ) ≤ tol
191+
end
192+
end
193+
end
194+
@testset "Generalized eigenvalue problem" begin
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@testset "Matrix{$T}" for T in (Float32, Float64, Complex64, Complex128)
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@testset "largest = $largest" for largest in (true, false)
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A = rand(T, n, n)
198+
A = A' * A + I
199+
P = JacobiPrec(diag(A))
200+
B = rand(T, n, n)
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B = B' * B + I
202+
tol = √eps(real(T))
203+
204+
r = lobpcg(A, B, largest, 1; P=P, tol=tol, maxiter=Inf, log=true)
205+
λ, X = r.λ, r.X
206+
@test max_err(A*X - B*X*λ) ≤ tol
207+
end
208+
end
209+
end
210+
end
211+
212+
@testset "Constraint" begin
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@testset "Simple eigenvalue problem" begin
214+
@testset "Matrix{$T}" for T in (Float32, Float64, Complex64, Complex128)
215+
@testset "largest = $largest" for largest in (true, false)
216+
A = rand(T, n, n)
217+
A = A' * A + I
218+
tol = √eps(real(T))
219+
r = lobpcg(A, largest, 1; tol=tol, maxiter=Inf, log=false)
220+
λ1, X1 = r.λ, r.X
221+
r = lobpcg(A, largest, 1; C=copy(r.X), tol=tol, maxiter=Inf, log=false)
222+
λ2, X2 = r.λ, r.X
223+
@test norm(A*X2 - X2*λ2) ≤ tol
224+
@test isapprox(real(Ac_mul_B(X1, X2)[1,1]), 0, atol=n*tol)
225+
end
226+
end
227+
end
228+
@testset "Generalized eigenvalue problem" begin
229+
@testset "Matrix{$T}" for T in (Float32, Float64, Complex64, Complex128)
230+
@testset "largest = $largest" for largest in (true, false)
231+
A = rand(T, n, n)
232+
A = A' * A + I
233+
B = rand(T, n, n)
234+
B = B' * B + I
235+
tol = √eps(real(T))
236+
r = lobpcg(A, B, largest, 1; tol=tol, maxiter=Inf, log=false)
237+
λ1, X1 = r.λ, r.X
238+
r = lobpcg(A, B, largest, 1; C=copy(r.X), tol=tol, maxiter=Inf, log=false)
239+
λ2, X2 = r.λ, r.X
240+
@test norm(A*X2 - B*X2*λ2) ≤ tol
241+
@test isapprox(real(Ac_mul_B(X1, B*X2)[1,1]), 0, atol=n*tol)
242+
end
243+
end
244+
end
245+
end
77246
end
78247
@testset "Two eigenvalues" begin
79248
@testset "Small full system" begin
@@ -104,8 +273,7 @@ end
104273
B = rand(T, n, n)
105274
B = B' * B + I
106275
b = rand(T, n, 2)
107-
tol = √eps(real(T))
108-
276+
tol = eps(real(T))^(real(T)(4/10))
109277
r = lobpcg(A, B, largest, b; tol=tol, maxiter=Inf, log=true)
110278
λ, X = r.λ, r.X
111279
@test max_err(A*X - B*X*diagm(λ)) ≤ tol

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