{"action":"created","comment":{"url":"https://api.github.com/repos/gonum/lapack/pulls/comments/62833063","id":62833063,"diff_hunk":"@@ -0,0 +1,609 @@\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 native\n+\n+import (\n+\t\"math\"\n+\n+\t\"github.com/gonum/blas\"\n+\t\"github.com/gonum/blas/blas64\"\n+)\n+\n+// Dlaqr5 performs a single small-bulge multi-shift QR sweep on an isolated\n+// block of a Hessenberg matrix.\n+//\n+// wantt and wantz determine whether the quasi-triangular Schur factor and the\n+// orthogonal Schur factor, respectively, will be computed.\n+//\n+// kacc22 specifies the computation mode of far-from-diagonal orthogonal\n+// updates. Permitted values are:\n+//  0: Dlaqr5 will not accumulate reflections and will not use matrix-matrix\n+//     multiply to update far-from-diagonal matrix entries.\n+//  1: Dlaqr5 will accumulate reflections and use matrix-matrix multiply to\n+//     update far-from-diagonal matrix entries.\n+//  2: Dlaqr5 will accumulate reflections, use matrix-matrix multiply to update\n+//     far-from-diagonal matrix entries, and take advantage of 2×2 block\n+//     structure during matrix multiplies.\n+// For other values of kacc2 Dlaqr5 will panic.\n+//\n+// n is the order of the Hessenberg matrix H.\n+//\n+// ktop and kbot are indices of the first and last row and column of an isolated\n+// diagonal block upon which the QR sweep will be applied. It must hold that\n+//  ktop == 0,   or 0 < ktop <= n-1 and H[ktop, ktop-1] == 0, and\n+//  kbot == n-1, or 0 <= kbot < n-1 and H[kbot+1, kbot] == 0,\n+// otherwise Dlaqr5 will panic.\n+//\n+// nshfts is the number of simultaneous shifts. It must be positive and even,\n+// otherwise Dlaqr5 will panic.\n+//\n+// sr and si contain the real and imaginary parts, respectively, of the shifts\n+// of origin that define the multi-shift QR sweep. On return both slices may be\n+// reordered by Dlaqr5. Their length must be equal to nshfts, otherwise Dlaqr5\n+// will panic.\n+//\n+// h and ldh represent the Hessenberg matrix H of size n×n. On return\n+// multi-shift QR sweep with shifts sr+i*si has been applied to the isolated\n+// diagonal block in rows and columns ktop through kbot, inclusive.\n+//\n+// iloz and ihiz specify the rows of Z to which transformations will be applied\n+// if wantz is true. It must hold that 0 <= iloz <= ihiz < n, otherwise Dlaqr5\n+// will panic.\n+//\n+// z and ldz represent the matrix Z of size n×n. If wantz is true, the QR sweep\n+// orthogonal similarity transformation is accumulated into\n+// z[iloz:ihiz,ilo:ihi] from the right, otherwise z not referenced.\n+//\n+// v and ldv represent an auxiliary matrix of size (nshfts/2)×3.\n+//\n+// u and ldv represent an auxiliary matrix of size (3*nshfts-3)×(3*nshfts-3).\n+//\n+// wh and ldwh represent an auxiliary matrix of size (3*nshfts-3)×nh.\n+//\n+// wv and ldwv represent an auxiliary matrix of size nv×(3*nshfts-3).\n+func (impl Implementation) Dlaqr5(wantt, wantz bool, kacc22 int, n, ktop, kbot, nshfts int, sr, si []float64, h []float64, ldh int, iloz, ihiz int, z []float64, ldz int, v []float64, ldv int, u []float64, ldu int, nh int, wh []float64, ldwh int, nv int, wv []float64, ldwv int) {\n+\tcheckMatrix(n, n, h, ldh)\n+\tif !(0 <= ktop && ktop < n) {\n+\t\tpanic(\"lapack: invalid value of ktop\")\n+\t}\n+\tif ktop > 0 && h[ktop*ldh+ktop-1] != 0 {\n+\t\tpanic(\"lapack: diagonal block is not isolated\")\n+\t}\n+\tif !(0 <= kbot && kbot < n) {\n+\t\tpanic(\"lapack: invalid value of kbot\")\n+\t}\n+\tif kbot < n-1 && h[(kbot+1)*ldh+kbot] != 0 {\n+\t\tpanic(\"lapack: diagonal block is not isolated\")\n+\t}\n+\tif nshfts < 0 || nshfts%2 != 0 {\n+\t\tpanic(\"lapack: invalid number of shifts\")\n+\t}\n+\tif len(sr) != nshfts || len(si) != nshfts {\n+\t\tpanic(badSlice) // TODO(vladimir-ch) Another message?\n+\t}\n+\tif wantz {\n+\t\tif !(0 <= iloz && iloz <= ihiz && ihiz < n) {\n+\t\t\tpanic(\"lapack: invalid value of iloz or ihiz\")\n+\t\t}\n+\t\tcheckMatrix(n, n, z, ldz)\n+\t}\n+\tcheckMatrix(nshfts/2, 3, v, ldv) // Transposed w.r.t. lapack.\n+\tcheckMatrix(3*nshfts-3, 3*nshfts-3, u, ldu)\n+\tcheckMatrix(3*nshfts-3, nh, wh, ldwh)\n+\tcheckMatrix(nv, 3*nshfts-3, wv, ldwv)\n+\tif kacc22 != 0 && kacc22 != 1 && kacc22 != 2 {\n+\t\tpanic(\"lapack: invalid value of kacc22\")\n+\t}\n+\n+\t// If there are no shifts, then there is nothing to do.\n+\tif nshfts < 2 {\n+\t\treturn\n+\t}\n+\t// If the active block is empty or 1×1, then there is nothing to do.\n+\tif ktop >= kbot {\n+\t\treturn\n+\t}\n+\n+\t// Shuffle shifts into pairs of real shifts and pairs of complex\n+\t// conjugate shifts assuming complex conjugate shifts are already\n+\t// adjacent to one another.\n+\tfor i := 0; i < nshfts-2; i += 2 {\n+\t\tif si[i] == -si[i+1] {\n+\t\t\tcontinue\n+\t\t}\n+\t\tswap := sr[i]\n+\t\tsr[i] = sr[i+1]\n+\t\tsr[i+1] = sr[i+2]\n+\t\tsr[i+2] = swap\n+\t\tswap = si[i]\n+\t\tsi[i] = si[i+1]\n+\t\tsi[i+1] = si[i+2]\n+\t\tsi[i+2] = swap\n+\t}\n+\n+\t// Note: lapack says that nshfts must be even but allows it to be odd\n+\t// anyway. At the moment, we panic above if nshfts is not even, so\n+\t// reducing it by one is unnecessary (it seems that Dlaqr0 and Dlaqr4\n+\t// indeed use only even nshfts).\n+\t//\n+\t// * NSHFTS is supposed to be even, but if it is odd,\n+\t// * then simply reduce it by one.  The shuffle above\n+\t// * ensures that the dropped shift is real and that\n+\t// * the remaining shifts are paired. ====\n+\t// NS = NSHFTS - MOD( NSHFTS, 2 )\n+\tns := nshfts\n+\n+\tsafmin := dlamchS\n+\tulp := dlamchP\n+\tsmlnum := safmin * float64(n) / ulp\n+\n+\t// Use accumulated reflections to update far-from-diagonal entries?\n+\taccum := kacc22 == 1 || kacc22 == 2\n+\t// If so, exploit the 2×2 block structure?\n+\tblk22 := ns > 2 && kacc22 == 2\n+\n+\t// Clear trash.\n+\tif ktop+2 <= kbot {\n+\t\th[(ktop+2)*ldh+ktop] = 0\n+\t}\n+\n+\t// nbmps = number of 2-shift bulges in the chain.\n+\tnbmps := ns / 2\n+\n+\t// kdu = width of slab.\n+\tkdu := 6*nbmps - 3\n+\n+\t// Create and chase chains of nbmps bulges.\n+\tfor incol := 3*(1-nbmps) + ktop - 1; incol <= kbot-2; incol += 3*nbmps - 2 {\n+\t\tndcol := incol + kdu\n+\t\tif accum {\n+\t\t\timpl.Dlaset(blas.All, kdu, kdu, 0, 1, u, ldu)\n+\t\t}\n+\n+\t\t// Near-the-diagonal bulge chase. The following loop performs\n+\t\t// the near-the-diagonal part of a small bulge multi-shift QR\n+\t\t// sweep. Each 6*nbmps-2 column diagonal chunk extends from\n+\t\t// column incol to column ndcol (including both column incol and\n+\t\t// column ndcol). The following loop chases a 3*nbmps column\n+\t\t// long chain of nbmps bulges 3*nbmps-2 columns to the right.\n+\t\t// (incol may be less than ktop and ndcol may be greater than\n+\t\t// kbot indicating phantom columns from which to chase bulges\n+\t\t// before they are actually introduced or to which to chase\n+\t\t// bulges beyond column kbot.)\n+\t\tfor krcol := incol; krcol <= min(incol+3*nbmps-3, kbot-2); krcol++ {\n+\t\t\t// Bulges number mtop to mbot are active double implicit\n+\t\t\t// shift bulges. There may or may not also be small 2×2\n+\t\t\t// bulge, if there is room. The inactive bulges (if any)\n+\t\t\t// must wait until the active bulges have moved down the\n+\t\t\t// diagonal to make room. The phantom matrix paradigm\n+\t\t\t// described above helps keep track.\n+\n+\t\t\tmtop := max(0, ((ktop-1)-krcol+2)/3)\n+\t\t\tmbot := min(nbmps, (kbot-krcol)/3) - 1\n+\t\t\tm22 := mbot + 1\n+\t\t\tbmp22 := (mbot < nbmps-1) && (krcol+3*m22 == kbot-2)\n+\n+\t\t\t// Generate reflections to chase the chain right one\n+\t\t\t// column. (The minimum value of k is ktop-1.)\n+\t\t\tfor m := mtop; m <= mbot; m++ {\n+\t\t\t\tk := krcol + 3*m\n+\t\t\t\tif k == ktop-1 {\n+\t\t\t\t\timpl.Dlaqr1(3, h[ktop*ldh+ktop:], ldh,\n+\t\t\t\t\t\tsr[2*m], si[2*m], sr[2*m+1], si[2*m+1],\n+\t\t\t\t\t\tv[m*ldv:m*ldv+3])\n+\t\t\t\t\talpha := v[m*ldv]\n+\t\t\t\t\t_, v[m*ldv] = impl.Dlarfg(3, alpha, v[m*ldv+1:m*ldv+3], 1)","path":"native/dlaqr5.go","position":197,"original_position":197,"commit_id":"7b10cfe296cd0777596c549d4cae6b1fa1db1f9e","original_commit_id":"093e59f88bf5dee260dc8d293d36f2185fed72e7","user":{"login":"kortschak","id":275221,"avatar_url":"https://avatars.githubusercontent.com/u/275221?v=3","gravatar_id":"","url":"https://api.github.com/users/kortschak","html_url":"https://github.com/kortschak","followers_url":"https://api.github.com/users/kortschak/followers","following_url":"https://api.github.com/users/kortschak/following{/other_user}","gists_url":"https://api.github.com/users/kortschak/gists{/gist_id}","starred_url":"https://api.github.com/users/kortschak/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/kortschak/subscriptions","organizations_url":"https://api.github.com/users/kortschak/orgs","repos_url":"https://api.github.com/users/kortschak/repos","events_url":"https://api.github.com/users/kortschak/events{/privacy}","received_events_url":"https://api.github.com/users/kortschak/received_events","type":"User","site_admin":false},"body":"Why is v sliced from 1 more here and in the next Dlarfg call than in the Dlaqr1 call above? They have the same index in the Fortran.","created_at":"2016-05-11T11:47:41Z","updated_at":"2016-05-11T11:47:41Z","html_url":"https://github.com/gonum/lapack/pull/129#discussion_r62833063","pull_request_url":"https://api.github.com/repos/gonum/lapack/pulls/129","_links":{"self":{"href":"https://api.github.com/repos/gonum/lapack/pulls/comments/62833063"},"html":{"href":"https://github.com/gonum/lapack/pull/129#discussion_r62833063"},"pull_request":{"href":"https://api.github.com/repos/gonum/lapack/pulls/129"}}},"pull_request":{"url":"https://api.github.com/repos/gonum/lapack/pulls/129","id":69630164,"html_url":"https://github.com/gonum/lapack/pull/129","diff_url":"https://github.com/gonum/lapack/pull/129.diff","patch_url":"https://github.com/gonum/lapack/pull/129.patch","issue_url":"https://api.github.com/repos/gonum/lapack/issues/129","number":129,"state":"open","locked":false,"title":"native: add Dlaqr5","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":"Dlaqr5 is a tough start for a lapack-porting beginner. Please review with great care.\r\n\r\nFor testing I went the way of comparing to generated data in `internal/testdata/dlaqr5test`. I use tip's cgo ability to deal with Fortran files, that's very convenient. I store one test case per text file and zip them together. I thought about generating a go file but it would be naturally bigger and I wanted to avoid that.\r\n\r\nI don't like much having duplicate copies of Lapack source files in the repository but I guess that's a future work.\r\n\r\nI tried to split the PR into narrowly focused commits so that some may be easily skipped (those that add generated data and fortran files).\r\n\r\nOh, and search me if there are any blatant mistakes.\r\n\r\nPTAL","created_at":"2016-05-11T08:05:25Z","updated_at":"2016-05-11T11:47:41Z","closed_at":null,"merged_at":null,"merge_commit_sha":"29091cd32ea179496bc98953d1e9cd015e095edd","assignee":null,"milestone":null,"commits_url":"https://api.github.com/repos/gonum/lapack/pulls/129/commits","review_comments_url":"https://api.github.com/repos/gonum/lapack/pulls/129/comments","review_comment_url":"https://api.github.com/repos/gonum/lapack/pulls/comments{/number}","comments_url":"https://api.github.com/repos/gonum/lapack/issues/129/comments","statuses_url":"https://api.github.com/repos/gonum/lapack/statuses/7b10cfe296cd0777596c549d4cae6b1fa1db1f9e","head":{"label":"gonum:dlaqr5","ref":"dlaqr5","sha":"7b10cfe296cd0777596c549d4cae6b1fa1db1f9e","user":{"login":"gonum","id":3771091,"avatar_url":"https://avatars.githubusercontent.com/u/3771091?v=3","gravatar_id":"","url":"https://api.github.com/users/gonum","html_url":"https://github.com/gonum","followers_url":"https://api.github.com/users/gonum/followers","following_url":"https://api.github.com/users/gonum/following{/other_user}","gists_url":"https://api.github.com/users/gonum/gists{/gist_id}","starred_url":"https://api.github.com/users/gonum/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/gonum/subscriptions","organizations_url":"https://api.github.com/users/gonum/orgs","repos_url":"https://api.github.com/users/gonum/repos","events_url":"https://api.github.com/users/gonum/events{/privacy}","received_events_url":"https://api.github.com/users/gonum/received_events","type":"Organization","site_admin":false},"repo":{"id":20473913,"name":"lapack","full_name":"gonum/lapack","owner":{"login":"gonum","id":3771091,"avatar_url":"https://avatars.githubusercontent.com/u/3771091?v=3","gravatar_id":"","url":"https://api.github.com/users/gonum","html_url":"https://github.com/gonum","followers_url":"https://api.github.com/users/gonum/followers","following_url":"https://api.github.com/users/gonum/following{/other_user}","gists_url":"https://api.github.com/users/gonum/gists{/gist_id}","starred_url":"https://api.github.com/users/gonum/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/gonum/subscriptions","organizations_url":"https://api.github.com/users/gonum/orgs","repos_url":"https://api.github.com/users/gonum/repos","events_url":"https://api.github.com/users/gonum/events{/privacy}","received_events_url":"https://api.github.com/users/gonum/received_events","type":"Organization","site_admin":false},"private":false,"html_url":"https://github.com/gonum/lapack","description":"A 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