{"action":"created","comment":{"url":"https://api.github.com/repos/gonum/lapack/pulls/comments/81743078","pull_request_review_id":2699356,"id":81743078,"diff_hunk":"@@ -0,0 +1,693 @@\n+// Copyright ©2016 The gonum Authors. All rights reserved.\n+// Use of this source code is governed by a BSD-style\n+// license that can be found in the LICENSE file.\n+\n+package testlapack\n+\n+import (\n+\t\"fmt\"\n+\t\"math\"\n+\t\"math/cmplx\"\n+\t\"math/rand\"\n+\t\"strconv\"\n+\t\"testing\"\n+\n+\t\"github.com/gonum/blas/blas64\"\n+\t\"github.com/gonum/floats\"\n+\t\"github.com/gonum/lapack\"\n+)\n+\n+type Dgeever interface {\n+\tDgeev(jobvl lapack.JobLeftEV, jobvr lapack.JobRightEV, n int, a []float64, lda int,\n+\t\twr, wi []float64, vl []float64, ldvl int, vr []float64, ldvr int, work []float64, lwork int) int\n+}\n+\n+type dgeevTest struct {\n+\ta      blas64.General\n+\tevWant []complex128 // If nil, the eigenvalues are not known.\n+\ttol    float64\n+}\n+\n+func DgeevTest(t *testing.T, impl Dgeever) {\n+\trnd := rand.New(rand.NewSource(1))\n+\n+\tfor i, test := range []dgeevTest{\n+\t\t{\n+\t\t\ta:      A123{}.Matrix(),\n+\t\t\tevWant: A123{}.Eigenvalues(),\n+\t\t},\n+\n+\t\tdgeevTestForAntisymRandom(10, rnd),\n+\t\tdgeevTestForAntisymRandom(11, rnd),\n+\t\tdgeevTestForAntisymRandom(50, rnd),\n+\t\tdgeevTestForAntisymRandom(51, rnd),\n+\t\tdgeevTestForAntisymRandom(100, rnd),\n+\t\tdgeevTestForAntisymRandom(101, rnd),\n+\n+\t\t{\n+\t\t\ta:      Circulant(2).Matrix(),\n+\t\t\tevWant: Circulant(2).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Circulant(3).Matrix(),\n+\t\t\tevWant: Circulant(3).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Circulant(4).Matrix(),\n+\t\t\tevWant: Circulant(4).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Circulant(5).Matrix(),\n+\t\t\tevWant: Circulant(5).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Circulant(10).Matrix(),\n+\t\t\tevWant: Circulant(10).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Circulant(15).Matrix(),\n+\t\t\tevWant: Circulant(15).Eigenvalues(),\n+\t\t\ttol:    1e-12,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Circulant(30).Matrix(),\n+\t\t\tevWant: Circulant(30).Eigenvalues(),\n+\t\t\ttol:    1e-11,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Circulant(50).Matrix(),\n+\t\t\tevWant: Circulant(50).Eigenvalues(),\n+\t\t\ttol:    1e-11,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Circulant(101).Matrix(),\n+\t\t\tevWant: Circulant(101).Eigenvalues(),\n+\t\t\ttol:    1e-10,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Circulant(150).Matrix(),\n+\t\t\tevWant: Circulant(150).Eigenvalues(),\n+\t\t\ttol:    1e-9,\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Clement(2).Matrix(),\n+\t\t\tevWant: Clement(2).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Clement(3).Matrix(),\n+\t\t\tevWant: Clement(3).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Clement(4).Matrix(),\n+\t\t\tevWant: Clement(4).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Clement(5).Matrix(),\n+\t\t\tevWant: Clement(5).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Clement(10).Matrix(),\n+\t\t\tevWant: Clement(10).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Clement(15).Matrix(),\n+\t\t\tevWant: Clement(15).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Clement(30).Matrix(),\n+\t\t\tevWant: Clement(30).Eigenvalues(),\n+\t\t\ttol:    1e-11,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Clement(50).Matrix(),\n+\t\t\tevWant: Clement(50).Eigenvalues(),\n+\t\t\ttol:    1e-7,\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Creation(2).Matrix(),\n+\t\t\tevWant: Creation(2).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Creation(3).Matrix(),\n+\t\t\tevWant: Creation(3).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Creation(4).Matrix(),\n+\t\t\tevWant: Creation(4).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Creation(5).Matrix(),\n+\t\t\tevWant: Creation(5).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Creation(10).Matrix(),\n+\t\t\tevWant: Creation(10).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Creation(15).Matrix(),\n+\t\t\tevWant: Creation(15).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Creation(30).Matrix(),\n+\t\t\tevWant: Creation(30).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Creation(50).Matrix(),\n+\t\t\tevWant: Creation(50).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Creation(101).Matrix(),\n+\t\t\tevWant: Creation(101).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Creation(150).Matrix(),\n+\t\t\tevWant: Creation(150).Eigenvalues(),\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Diagonal(0).Matrix(),\n+\t\t\tevWant: Diagonal(0).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Diagonal(10).Matrix(),\n+\t\t\tevWant: Diagonal(10).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Diagonal(50).Matrix(),\n+\t\t\tevWant: Diagonal(50).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Diagonal(151).Matrix(),\n+\t\t\tevWant: Diagonal(151).Eigenvalues(),\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Downshift(2).Matrix(),\n+\t\t\tevWant: Downshift(2).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Downshift(3).Matrix(),\n+\t\t\tevWant: Downshift(3).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Downshift(4).Matrix(),\n+\t\t\tevWant: Downshift(4).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Downshift(5).Matrix(),\n+\t\t\tevWant: Downshift(5).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Downshift(10).Matrix(),\n+\t\t\tevWant: Downshift(10).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Downshift(15).Matrix(),\n+\t\t\tevWant: Downshift(15).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Downshift(30).Matrix(),\n+\t\t\tevWant: Downshift(30).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Downshift(50).Matrix(),\n+\t\t\tevWant: Downshift(50).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Downshift(101).Matrix(),\n+\t\t\tevWant: Downshift(101).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Downshift(150).Matrix(),\n+\t\t\tevWant: Downshift(150).Eigenvalues(),\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Fibonacci(2).Matrix(),\n+\t\t\tevWant: Fibonacci(2).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Fibonacci(3).Matrix(),\n+\t\t\tevWant: Fibonacci(3).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Fibonacci(4).Matrix(),\n+\t\t\tevWant: Fibonacci(4).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Fibonacci(5).Matrix(),\n+\t\t\tevWant: Fibonacci(5).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Fibonacci(10).Matrix(),\n+\t\t\tevWant: Fibonacci(10).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Fibonacci(15).Matrix(),\n+\t\t\tevWant: Fibonacci(15).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Fibonacci(30).Matrix(),\n+\t\t\tevWant: Fibonacci(30).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Fibonacci(50).Matrix(),\n+\t\t\tevWant: Fibonacci(50).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Fibonacci(101).Matrix(),\n+\t\t\tevWant: Fibonacci(101).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Fibonacci(150).Matrix(),\n+\t\t\tevWant: Fibonacci(150).Eigenvalues(),\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Gear(2).Matrix(),\n+\t\t\tevWant: Gear(2).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Gear(3).Matrix(),\n+\t\t\tevWant: Gear(3).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Gear(4).Matrix(),\n+\t\t\tevWant: Gear(4).Eigenvalues(),\n+\t\t\ttol:    1e-7,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Gear(5).Matrix(),\n+\t\t\tevWant: Gear(5).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Gear(10).Matrix(),\n+\t\t\tevWant: Gear(10).Eigenvalues(),\n+\t\t\ttol:    1e-8,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Gear(15).Matrix(),\n+\t\t\tevWant: Gear(15).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Gear(30).Matrix(),\n+\t\t\tevWant: Gear(30).Eigenvalues(),\n+\t\t\ttol:    1e-8,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Gear(50).Matrix(),\n+\t\t\tevWant: Gear(50).Eigenvalues(),\n+\t\t\ttol:    1e-8,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Gear(101).Matrix(),\n+\t\t\tevWant: Gear(101).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Gear(150).Matrix(),\n+\t\t\tevWant: Gear(150).Eigenvalues(),\n+\t\t\ttol:    1e-8,\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Grcar{N: 10, K: 3}.Matrix(),\n+\t\t\tevWant: Grcar{N: 10, K: 3}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Grcar{N: 10, K: 7}.Matrix(),\n+\t\t\tevWant: Grcar{N: 10, K: 7}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Grcar{N: 11, K: 7}.Matrix(),\n+\t\t\tevWant: Grcar{N: 11, K: 7}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Grcar{N: 50, K: 3}.Matrix(),\n+\t\t\tevWant: Grcar{N: 50, K: 3}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Grcar{N: 51, K: 3}.Matrix(),\n+\t\t\tevWant: Grcar{N: 51, K: 3}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Grcar{N: 50, K: 10}.Matrix(),\n+\t\t\tevWant: Grcar{N: 50, K: 10}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Grcar{N: 51, K: 10}.Matrix(),\n+\t\t\tevWant: Grcar{N: 51, K: 10}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Grcar{N: 50, K: 30}.Matrix(),\n+\t\t\tevWant: Grcar{N: 50, K: 30}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Grcar{N: 150, K: 2}.Matrix(),\n+\t\t\tevWant: Grcar{N: 150, K: 2}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Grcar{N: 150, K: 148}.Matrix(),\n+\t\t\tevWant: Grcar{N: 150, K: 148}.Eigenvalues(),\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Hanowa{N: 6, Alpha: 17}.Matrix(),\n+\t\t\tevWant: Hanowa{N: 6, Alpha: 17}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Hanowa{N: 50, Alpha: -1}.Matrix(),\n+\t\t\tevWant: Hanowa{N: 50, Alpha: -1}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Hanowa{N: 100, Alpha: -1}.Matrix(),\n+\t\t\tevWant: Hanowa{N: 100, Alpha: -1}.Eigenvalues(),\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Lesp(2).Matrix(),\n+\t\t\tevWant: Lesp(2).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Lesp(3).Matrix(),\n+\t\t\tevWant: Lesp(3).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Lesp(4).Matrix(),\n+\t\t\tevWant: Lesp(4).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Lesp(5).Matrix(),\n+\t\t\tevWant: Lesp(5).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Lesp(10).Matrix(),\n+\t\t\tevWant: Lesp(10).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Lesp(15).Matrix(),\n+\t\t\tevWant: Lesp(15).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Lesp(30).Matrix(),\n+\t\t\tevWant: Lesp(30).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Lesp(50).Matrix(),\n+\t\t\tevWant: Lesp(50).Eigenvalues(),\n+\t\t\ttol:    1e-12,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Lesp(101).Matrix(),\n+\t\t\tevWant: Lesp(101).Eigenvalues(),\n+\t\t\ttol:    1e-12,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Lesp(150).Matrix(),\n+\t\t\tevWant: Lesp(150).Eigenvalues(),\n+\t\t\ttol:    1e-12,\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Rutis{}.Matrix(),\n+\t\t\tevWant: Rutis{}.Eigenvalues(),\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Tris{N: 74, X: 1, Y: -2, Z: 1}.Matrix(),\n+\t\t\tevWant: Tris{N: 74, X: 1, Y: -2, Z: 1}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Tris{N: 74, X: 1, Y: 2, Z: -3}.Matrix(),\n+\t\t\tevWant: Tris{N: 74, X: 1, Y: 2, Z: -3}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Tris{N: 75, X: 1, Y: 2, Z: -3}.Matrix(),\n+\t\t\tevWant: Tris{N: 75, X: 1, Y: 2, Z: -3}.Eigenvalues(),\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Wilk4{}.Matrix(),\n+\t\t\tevWant: Wilk4{}.Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Wilk12{}.Matrix(),\n+\t\t\tevWant: Wilk12{}.Eigenvalues(),\n+\t\t\ttol:    1e-8,\n+\t\t},\n+\t\t{\n+\t\t\ta:      Wilk20(0).Matrix(),\n+\t\t\tevWant: Wilk20(0).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Wilk20(1e-10).Matrix(),\n+\t\t\tevWant: Wilk20(1e-10).Eigenvalues(),\n+\t\t\ttol:    1e-12,\n+\t\t},\n+\n+\t\t{\n+\t\t\ta:      Zero(1).Matrix(),\n+\t\t\tevWant: Zero(1).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Zero(10).Matrix(),\n+\t\t\tevWant: Zero(10).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Zero(50).Matrix(),\n+\t\t\tevWant: Zero(50).Eigenvalues(),\n+\t\t},\n+\t\t{\n+\t\t\ta:      Zero(100).Matrix(),\n+\t\t\tevWant: Zero(100).Eigenvalues(),\n+\t\t},\n+\t} {\n+\t\tfor _, jobvl := range []lapack.JobLeftEV{lapack.ComputeLeftEV, lapack.None} {\n+\t\t\tfor _, jobvr := range []lapack.JobRightEV{lapack.ComputeRightEV, lapack.None} {\n+\t\t\t\tfor _, extra := range []int{0, 11} {\n+\t\t\t\t\tfor _, optwork := range []bool{false, true} {\n+\t\t\t\t\t\ttestDgeev(t, impl, strconv.Itoa(i), test, jobvl, jobvr, extra, optwork)\n+\t\t\t\t\t}\n+\t\t\t\t}\n+\t\t\t}\n+\t\t}\n+\t}\n+\n+\t// for _, n := range []int{10, 30, 50} {","path":"testlapack/dgeev.go","position":null,"original_position":477,"commit_id":"2de253cf6bcbf750f4b17952dc510b6145ef065a","original_commit_id":"5a24ce5115477b43579f35dedee178d69e117109","user":{"login":"vladimir-ch","id":1837502,"avatar_url":"https://avatars.githubusercontent.com/u/1837502?v=3","gravatar_id":"","url":"https://api.github.com/users/vladimir-ch","html_url":"https://github.com/vladimir-ch","followers_url":"https://api.github.com/users/vladimir-ch/followers","following_url":"https://api.github.com/users/vladimir-ch/following{/other_user}","gists_url":"https://api.github.com/users/vladimir-ch/gists{/gist_id}","starred_url":"https://api.github.com/users/vladimir-ch/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/vladimir-ch/subscriptions","organizations_url":"https://api.github.com/users/vladimir-ch/orgs","repos_url":"https://api.github.com/users/vladimir-ch/repos","events_url":"https://api.github.com/users/vladimir-ch/events{/privacy}","received_events_url":"https://api.github.com/users/vladimir-ch/received_events","type":"User","site_admin":false},"body":"I've tried using the Jordan canonical form with the same result. I've also tried replacing `reflector` and `applyReflector` with generating a random orthogonal matrix and passing it through `Dgeqrf` and `Dorgqr` with the same result. Also, `cgo` behaves identically. All this kind of confirms my initial suspicion that `Q T Q^T` simply has slightly different eigenvalues from those of `T`  due to the matrix multiplication . Without known eigenvalues this test becomes worthless so I suggest removing it. @btracey ?","created_at":"2016-10-04T12:19:48Z","updated_at":"2016-10-04T12:19:48Z","html_url":"https://github.com/gonum/lapack/pull/191#discussion_r81743078","pull_request_url":"https://api.github.com/repos/gonum/lapack/pulls/191","_links":{"self":{"href":"https://api.github.com/repos/gonum/lapack/pulls/comments/81743078"},"html":{"href":"https://github.com/gonum/lapack/pull/191#discussion_r81743078"},"pull_request":{"href":"https://api.github.com/repos/gonum/lapack/pulls/191"}}},"pull_request":{"url":"https://api.github.com/repos/gonum/lapack/pulls/191","id":87433311,"html_url":"https://github.com/gonum/lapack/pull/191","diff_url":"https://github.com/gonum/lapack/pull/191.diff","patch_url":"https://github.com/gonum/lapack/pull/191.patch","issue_url":"https://api.github.com/repos/gonum/lapack/issues/191","number":191,"state":"open","locked":false,"title":"native,cgo: add Dgeev","user":{"login":"vladimir-ch","id":1837502,"avatar_url":"https://avatars.githubusercontent.com/u/1837502?v=3","gravatar_id":"","url":"https://api.github.com/users/vladimir-ch","html_url":"https://github.com/vladimir-ch","followers_url":"https://api.github.com/users/vladimir-ch/followers","following_url":"https://api.github.com/users/vladimir-ch/following{/other_user}","gists_url":"https://api.github.com/users/vladimir-ch/gists{/gist_id}","starred_url":"https://api.github.com/users/vladimir-ch/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/vladimir-ch/subscriptions","organizations_url":"https://api.github.com/users/vladimir-ch/orgs","repos_url":"https://api.github.com/users/vladimir-ch/repos","events_url":"https://api.github.com/users/vladimir-ch/events{/privacy}","received_events_url":"https://api.github.com/users/vladimir-ch/received_events","type":"User","site_admin":false},"body":"I still want to extend the testing a bit but you can start looking at this, especially the 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