Add: julia-0.6.2

Former-commit-id: ccc667cf67d569f3fb3df39aa57c2134755a7551
2018-02-10 10:27:19 -07:00
parent 94220957d7
commit 019f8e3064
723 changed files with 276164 additions and 0 deletions
--- a/julia-0.6.2/share/julia/test/linalg/bunchkaufman.jl
+++ b/julia-0.6.2/share/julia/test/linalg/bunchkaufman.jl
@@ -0,0 +1,126 @@
+# This file is a part of Julia. License is MIT: https://julialang.org/license
+
+using Base.Test
+
+using Base.LinAlg: BlasComplex, BlasFloat, BlasReal, QRPivoted
+
+n = 10
+
+# Split n into 2 parts for tests needing two matrices
+n1 = div(n, 2)
+n2 = 2*n1
+
+srand(1234321)
+
+areal = randn(n,n)/2
+aimg  = randn(n,n)/2
+a2real = randn(n,n)/2
+a2img  = randn(n,n)/2
+breal = randn(n,2)/2
+bimg  = randn(n,2)/2
+
+@testset for eltya in (Float32, Float64, Complex64, Complex128, Int)
+    a = eltya == Int ? rand(1:7, n, n) : convert(Matrix{eltya}, eltya <: Complex ? complex.(areal, aimg) : areal)
+    a2 = eltya == Int ? rand(1:7, n, n) : convert(Matrix{eltya}, eltya <: Complex ? complex.(a2real, a2img) : a2real)
+    @testset for atype in ("Array", "SubArray")
+        asym = a'+a                  # symmetric indefinite
+        apd  = a'*a                 # symmetric positive-definite
+        if atype == "Array"
+            a = a
+            a2 = a2
+        else
+            a = view(a, 1:n, 1:n)
+            a2 = view(a2, 1:n, 1:n)
+            asym = view(asym, 1:n, 1:n)
+            apd = view(apd, 1:n, 1:n)
+        end
+        ε = εa = eps(abs(float(one(eltya))))
+
+        @testset for eltyb in (Float32, Float64, Complex64, Complex128, Int)
+            b = eltyb == Int ? rand(1:5, n, 2) : convert(Matrix{eltyb}, eltyb <: Complex ? complex.(breal, bimg) : breal)
+            @testset for btype in ("Array", "SubArray")
+                if btype == "Array"
+                    b = b
+                else
+                    b = view(b, 1:n, 1:2)
+                end
+
+                εb = eps(abs(float(one(eltyb))))
+                ε = max(εa,εb)
+
+                @testset "(Automatic) Bunch-Kaufman factor of indefinite matrix" begin
+                    bc1 = factorize(asym)
+                    @test logabsdet(bc1)[1] ≈ log(abs(det(bc1)))
+                    if eltya <: Real
+                        @test logabsdet(bc1)[2] == sign(det(bc1))
+                    else
+                        @test logabsdet(bc1)[2] ≈ sign(det(bc1))
+                    end
+                    @test inv(bc1)*asym ≈ eye(n)
+                    @test asym*(bc1\b) ≈ b atol=1000ε
+                    @testset for rook in (false, true)
+                        @test inv(bkfact(a.'+a, :U, true, rook))*(a.'+a) ≈ eye(n)
+                        @test size(bc1) == size(bc1.LD)
+                        @test size(bc1,1) == size(bc1.LD,1)
+                        @test size(bc1,2) == size(bc1.LD,2)
+                        if eltya <: BlasReal
+                            @test_throws ArgumentError bkfact(a)
+                        end
+                    end
+                end
+
+                @testset "Bunch-Kaufman factors of a pos-def matrix" begin
+                    @testset for rook in (false, true)
+                        bc2 = bkfact(apd, :U, issymmetric(apd), rook)
+                        @test logdet(bc2) ≈ log(det(bc2))
+                        @test logabsdet(bc2)[1] ≈ log(abs(det(bc2)))
+                        @test logabsdet(bc2)[2] == sign(det(bc2))
+                        @test inv(bc2)*apd ≈ eye(n)
+                        @test apd*(bc2\b) ≈ b atol=150000ε
+                        @test ishermitian(bc2) == !issymmetric(bc2)
+                    end
+                end
+            end
+        end
+    end
+end
+
+
+@testset "Bunch-Kaufman factors of a singular matrix" begin
+    let As1 = ones(n, n)
+        As2 = complex(ones(n, n))
+        As3 = complex(ones(n, n))
+        As3[end, 1] += im
+        As3[1, end] -= im
+
+        for As = (As1, As2, As3)
+            @testset for Astype in ("Array", "SubArray")
+                if Astype == "Array"
+                    As = As
+                else
+                    As = view(As, 1:n, 1:n)
+                end
+
+                @testset for rook in (false, true)
+                    F = bkfact(As, :U, issymmetric(As), rook)
+                    @test det(F) == 0
+                    @test_throws LinAlg.SingularException inv(F)
+                    @test_throws LinAlg.SingularException F \ ones(size(As, 1))
+                end
+            end
+        end
+    end
+end
+
+
+# test example due to @timholy in PR 15354
+let
+    A = rand(6,5); A = complex(A'*A) # to avoid calling the real-lhs-complex-rhs method
+    F = cholfact(A);
+    v6 = rand(Complex128, 6)
+    v5 = view(v6, 1:5)
+    @test F\v5 == F\v6[1:5]
+end
+
+@test_throws DomainError logdet(bkfact([-1 -1; -1 1]))
+@test logabsdet(bkfact([8 4; 4 2]))[1] == -Inf