diff --git a/native/dorghr.go b/native/dorghr.go
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--- /dev/null
+++ b/native/dorghr.go
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+// Copyright ©2016 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package native
+
+// Dorghr generates an n×n orthogonal matrix Q which is defined as the product
+// of ihi-ilo elementary reflectors:
+//  Q = H_{ilo} H_{ilo+1} ... H_{ihi-1}.
+/
+// a and lda represent an n×n matrix that contains the elementary reflectors, as
+// returned by Dgehrd. On return, a is overwritten by the n×n orthogonal matrix
+// Q. Q will be equal to the identity matrix except in the submatrix
+// Q[ilo+1:ihi+1,ilo+1:ihi+1].
+//
+// ilo and ihi must have the same values as in the previous call of Dgehrd. It
+// must hold that
+//  0 <= ilo <= ihi < n,  if n > 0,
+//  ilo = 0, ihi = -1,    if n == 0.
+//
+// tau contains the scalar factors of the elementary reflectors, as returned by
+// Dgehrd. tau must have length n-1.
+//
+// work must have length at least max(1,lwork) and lwork must be at least
+// ihi-ilo. For optimum performance lwork must be at least (ihi-ilo)*nb where nb
+// is the optimal blocksize. On return, work[0] will contain the optimal value
+// of lwork.
+//
+// If lwork == -1, instead of performing Dorghr, only the optimal value of lwork
+// will be stored into work[0].
+//
+// If any requirement on input sizes is not met, Dorghr will panic.
+//
+// Dorghr is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dorghr(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int) {
+	checkMatrix(n, n, a, lda)
+	nh := ihi - ilo
+	switch {
+	case ilo < 0 || max(1, n) <= ilo:
+		panic(badIlo)
+	case ihi < min(ilo, n-1) || n <= ihi:
+		panic(badIhi)
+	case lwork < max(1, nh) && lwork != -1:
+		panic(badWork)
+	case len(work) < max(1, lwork):
+		panic(shortWork)
+	}
+
+	lwkopt := max(1, nh) * impl.Ilaenv(1, "DORGQR", " ", nh, nh, nh, -1)
+	if lwork == -1 {
+		work[0] = float64(lwkopt)
+		return
+	}
+
+	// Quick return if possible.
+	if n == 0 {
+		work[0] = 1
+		return
+	}
+
+	// Shift the vectors which define the elementary reflectors one column
+	// to the right.
+	for i := ilo + 2; i < ihi+1; i++ {
+		copy(a[i*lda+ilo+1:i*lda+i], a[i*lda+ilo:i*lda+i-1])
+	}
+	// Set the first ilo+1 and the last n-ihi-1 rows and columns to those of
+	// the identity matrix.
+	for i := 0; i < ilo+1; i++ {
+		for j := 0; j < n; j++ {
+			a[i*lda+j] = 0
+		}
+		a[i*lda+i] = 1
+	}
+	for i := ilo + 1; i < ihi+1; i++ {
+		for j := 0; j <= ilo; j++ {
+			a[i*lda+j] = 0
+		}
+		for j := i; j < n; j++ {
+			a[i*lda+j] = 0
+		}
+	}
+	for i := ihi + 1; i < n; i++ {
+		for j := 0; j < n; j++ {
+			a[i*lda+j] = 0
+		}
+		a[i*lda+i] = 1
+	}
+	if nh > 0 {
+		// Generate Q[ilo+1:ihi+1,ilo+1:ihi+1].
+		impl.Dorgqr(nh, nh, nh, a[(ilo+1)*lda+ilo+1:], lda, tau[ilo:ihi], work, lwork)
+	}
+	work[0] = float64(lwkopt)
+}