{"action":"created","comment":{"url":"https://api.github.com/repos/gonum/lapack/pulls/comments/46915763","id":46915763,"diff_hunk":"@@ -0,0 +1,148 @@\n+// Copyright ©2015 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\"github.com/gonum/blas\"\n+\t\"github.com/gonum/blas/blas64\"\n+)\n+\n+// Dlabrd reduces the first NB rows and columns of a real general m×n matrix\n+// A to upper or lower bidiagonal form by an orthogonal transformation\n+//  Q**T * A * P\n+// If m >= n, A is reduced to upper bidiagonal form and upon exit the elements\n+// on and below the diagonal in the first nb columns represent the elementary\n+// reflectors, and the elements above the diagonal in the first nb rows represent\n+// the matrix P. If m < n, A is reduced to lower bidiagonal form and the elements\n+// P is instead stored above the diagonal.\n+//\n+// The reduction to bidiagonal form is stored in d and e, where d are the diagonal\n+// elements, and e are the off-diagonal elements.\n+//\n+// The matrices Q and P are products of elementary reflectors\n+//  Q = H_1 * H_2 * ... * H_nb\n+//  P = G_1 * G_2 * ... * G_nb\n+// where\n+//  H_i = I - tauQ[i] * v_i * v_i^T\n+//  G_i = I - tauP[i] * u_i * u_i^T\n+//\n+// As an example, on exit the entries of A when m = 6, n = 5, and nb = 2\n+//  (  1   1   u1  u1  u1 )\n+//  (  v1  1   1   u2  u2 )\n+//  (  v1  v2  a   a   a  )\n+//  (  v1  v2  a   a   a  )\n+//  (  v1  v2  a   a   a  )\n+//  (  v1  v2  a   a   a  )\n+// and when m = 5, n = 6, and nb = 2\n+//  (  1   u1  u1  u1  u1  u1 )\n+//  (  1   1   u2  u2  u2  u2 )\n+//  (  v1  1   a   a   a   a  )\n+//  (  v1  v2  a   a   a   a  )\n+//  (  v1  v2  a   a   a   a  )\n+//\n+// Dlabrd also returns the matrices X and Y which are used with U and V to\n+// apply the transformatino to the unreduced part of the matrix\n+//  A := A - V*Y^T - X*U^T\n+// and returns the matrices X and Y which are needed to apply the\n+// transformation to the unreduced part of A.\n+//\n+// X is an m×nb matrix, Y is an n×nb matrix. d, e, taup, and tauq must all have\n+// length at least nb. Dlabrd will panic if these size constraints are violated.\n+func (impl Implementation) Dlabrd(m, n, nb int, a []float64, lda int, d, e, tauQ, tauP, x []float64, ldx int, y []float64, ldy int) {\n+\tcheckMatrix(m, n, a, lda)\n+\tcheckMatrix(m, nb, x, ldx)\n+\tcheckMatrix(n, nb, y, ldy)\n+\tif len(d) < nb {\n+\t\tpanic(badD)\n+\t}\n+\tif len(e) < nb {\n+\t\tpanic(badE)\n+\t}\n+\tif len(tauQ) < nb {\n+\t\tpanic(badTauQ)\n+\t}\n+\tif len(tauP) < nb {\n+\t\tpanic(badTauP)\n+\t}\n+\tif m <= 0 || n <= 0 {\n+\t\treturn\n+\t}\n+\tbi := blas64.Implementation()\n+\tif m >= n {\n+\t\t// Reduce to upper bidiagonal form.\n+\t\tfor i := 0; i < nb; i++ {\n+\t\t\tbi.Dgemv(blas.NoTrans, m-i, i, -1, a[i*lda:], lda, y[i*ldy:], 1, 1, a[i*lda+i:], lda)\n+\t\t\tbi.Dgemv(blas.NoTrans, m-i, i, -1, x[i*ldx:], ldx, a[i:], lda, 1, a[i*lda+i:], lda)\n+\n+\t\t\ta[i*lda+i], tauQ[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], lda)\n+\t\t\td[i] = a[i*lda+i]\n+\t\t\tif i < n-1 {\n+\t\t\t\t// Compute Y[i+1:n, i].\n+\t\t\t\ta[i*lda+i] = 1\n+\t\t\t\tbi.Dgemv(blas.Trans, m-i, n-i-1, 1, a[i*lda+i+1:], lda, a[i*lda+i:], lda, 0, y[(i+1)*ldy+i:], ldy)\n+\t\t\t\tbi.Dgemv(blas.Trans, m-i, i, 1, a[i*lda:], lda, a[i*lda+i:], lda, 0, y[i:], ldy)\n+\t\t\t\tbi.Dgemv(blas.NoTrans, n-i-1, i, -1, y[(i+1)*ldy:], ldy, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)\n+\t\t\t\tbi.Dgemv(blas.Trans, m-i, i, 1, x[i*ldx:], ldx, a[i*lda+i:], lda, 0, y[i:], ldy)\n+\t\t\t\tbi.Dgemv(blas.Trans, i, n-i-1, -1, a[i+1:], lda, y[i:], ldy, 1, y[(i+1)*ldy+i:], ldy)\n+\t\t\t\tbi.Dscal(n-i-1, tauQ[i], y[(i+1)*ldy+i:], ldy)\n+\n+\t\t\t\t// Update A[i, i+1:n].\n+\t\t\t\tbi.Dgemv(blas.NoTrans, n-i-1, i+1, -1, y[(i+1)*ldy:], ldy, a[i*lda:], 1, 1, a[i*lda+i+1:], 1)\n+\t\t\t\tbi.Dgemv(blas.Trans, i, n-i-1, -1, a[i+1:], lda, x[i*ldx:], 1, 1, a[i*lda+i+1:], 1)\n+\n+\t\t\t\t// Generate reflection P[i] to annihilate A[i, i+2:n].\n+\t\t\t\ta[i*lda+i+1], tauP[i] = impl.Dlarfg(n-i-1, a[i*lda+i+1], a[i*lda+min(i+2, n-1):], 1)\n+\t\t\t\te[i] = a[i*lda+i+1]\n+\t\t\t\ta[i*lda+i+1] = 1\n+\n+\t\t\t\t// Compute X[i+1:m, i].\n+\t\t\t\tbi.Dgemv(blas.NoTrans, m-i-1, n-i-1, 1, a[(i+1)*lda+i+1:], lda, a[i*lda+i+1:], 1, 0, x[(i+1)*ldx+i:], ldx)\n+\t\t\t\tbi.Dgemv(blas.Trans, n-i-1, i+1, 1, y[(i+1)*ldy:], ldy, a[i*lda+i+1:], 1, 0, x[i:], ldx)\n+\t\t\t\tbi.Dgemv(blas.NoTrans, m-i-1, i+1, -1, a[(i+1)*lda:], lda, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)\n+\t\t\t\tbi.Dgemv(blas.NoTrans, i, n-i-1, 1, a[i+1:], lda, a[i*lda+i+1:], 1, 0, x[i:], ldx)\n+\t\t\t\tbi.Dgemv(blas.NoTrans, m-i-1, i, -1, x[(i+1)*ldx:], ldx, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)\n+\t\t\t\tbi.Dscal(m-i-1, tauP[i], x[(i+1)*ldx+i:], ldx)\n+\t\t\t}\n+\t\t}\n+\t\treturn\n+\t}\n+\t// Reduce to lower bidiagonal form.\n+\tfor i := 0; i < nb; i++ {\n+\t\t// Update A[i,i:n]\n+\t\tbi.Dgemv(blas.NoTrans, n-i, i, -1, y[i*ldy:], ldy, a[i*lda:], 1, 1, a[i*lda+i:], 1)\n+\t\tbi.Dgemv(blas.Trans, i, n-i, -1, a[i:], lda, x[i*ldx:], 1, 1, a[i*lda+i:], 1)\n+\n+\t\t// Generate reflection P[i] to annihilate A[i, i+1:n]\n+\t\ta[i*lda+i], tauP[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)\n+\t\td[i] = a[i*lda+i]\n+\t\tif i < m-1 {\n+\t\t\ta[i*lda+i] = 1\n+\t\t\t// Compute X[i+1:m, i].\n+\t\t\tbi.Dgemv(blas.NoTrans, m-i-1, n-i, 1, a[(i+1)*lda+i:], lda, a[i*lda+i:], 1, 0, x[(i+1)*ldx+i:], ldx)\n+\t\t\tbi.Dgemv(blas.Trans, n-i, i, 1, y[i*ldy:], ldy, a[i*lda+i:], 1, 0, x[i:], ldx)\n+\t\t\tbi.Dgemv(blas.NoTrans, m-i-1, i, -1, a[(i+1)*lda:], lda, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)\n+\t\t\tbi.Dgemv(blas.NoTrans, i, n-i, 1, a[i:], lda, a[i*lda+i:], 1, 0, x[i:], ldx)\n+\t\t\tbi.Dgemv(blas.NoTrans, m-i-1, i, -1, x[(i+1)*ldx:], ldx, x[i:], ldx, 1, x[(i+1)*ldx+i:], ldx)\n+\t\t\tbi.Dscal(m-i-1, tauP[i], x[(i+1)*ldx+i:], ldx)\n+\n+\t\t\t// Update A[i+1:m, i].\n+\t\t\tbi.Dgemv(blas.NoTrans, m-i-1, i, -1, a[(i+1)*lda:], lda, y[i*ldy:], 1, 1, a[(i+1)*lda+i:], lda)\n+\t\t\tbi.Dgemv(blas.NoTrans, m-i-1, i+1, -1, x[(i+1)*ldx:], ldx, a[i:], lda, 1, a[(i+1)*lda+i:], lda)\n+\n+\t\t\t// Generate reflection Q[i] to annihilate A[i+2:m, 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