--- /dev/null
+// Copyright ©2017 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 gonum
+
+import (
+ "gonum.org/v1/gonum/blas"
+ "gonum.org/v1/gonum/lapack"
+)
+
+// Dgerqf computes an RQ factorization of the m×n matrix A,
+// A = R * Q.
+// On exit, if m <= n, the upper triangle of the subarray
+// A[0:m, n-m:n] contains the m×m upper triangular matrix R.
+// If m >= n, the elements on and above the (m-n)-th subdiagonal
+// contain the m×n upper trapezoidal matrix R.
+// The remaining elements, with tau, represent the
+// orthogonal matrix Q as a product of min(m,n) elementary
+// reflectors.
+//
+// The matrix Q is represented as a product of elementary reflectors
+// Q = H_0 H_1 . . . H_{min(m,n)-1}.
+// Each H(i) has the form
+// H_i = I - tau_i * v * v^T
+// where v is a vector with v[0:n-k+i-1] stored in A[m-k+i, 0:n-k+i-1],
+// v[n-k+i:n] = 0 and v[n-k+i] = 1.
+//
+// tau must have length min(m,n), work must have length max(1, lwork),
+// and lwork must be -1 or at least max(1, m), otherwise Dgerqf will panic.
+// On exit, work[0] will contain the optimal length for work.
+//
+// Dgerqf is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int) {
+ checkMatrix(m, n, a, lda)
+
+ if len(work) < max(1, lwork) {
+ panic(shortWork)
+ }
+ if lwork != -1 && lwork < max(1, m) {
+ panic(badWork)
+ }
+
+ k := min(m, n)
+ if len(tau) != k {
+ panic(badTau)
+ }
+
+ var nb, lwkopt int
+ if k == 0 {
+ lwkopt = 1
+ } else {
+ nb = impl.Ilaenv(1, "DGERQF", " ", m, n, -1, -1)
+ lwkopt = m * nb
+ }
+ work[0] = float64(lwkopt)
+
+ if lwork == -1 {
+ return
+ }
+
+ // Return quickly if possible.
+ if k == 0 {
+ return
+ }
+
+ nbmin := 2
+ nx := 1
+ iws := m
+ var ldwork int
+ if 1 < nb && nb < k {
+ // Determine when to cross over from blocked to unblocked code.
+ nx = max(0, impl.Ilaenv(3, "DGERQF", " ", m, n, -1, -1))
+ if nx < k {
+ // Determine whether workspace is large enough for blocked code.
+ iws = m * nb
+ if lwork < iws {
+ // Not enough workspace to use optimal nb. Reduce
+ // nb and determine the minimum value of nb.
+ nb = lwork / m
+ nbmin = max(2, impl.Ilaenv(2, "DGERQF", " ", m, n, -1, -1))
+ }
+ ldwork = nb
+ }
+ }
+
+ var mu, nu int
+ if nbmin <= nb && nb < k && nx < k {
+ // Use blocked code initially.
+ // The last kk rows are handled by the block method.
+ ki := ((k - nx - 1) / nb) * nb
+ kk := min(k, ki+nb)
+
+ var i int
+ for i = k - kk + ki; i >= k-kk; i -= nb {
+ ib := min(k-i, nb)
+
+ // Compute the RQ factorization of the current block
+ // A[m-k+i:m-k+i+ib-1, 0:n-k+i+ib-1].
+ impl.Dgerq2(ib, n-k+i+ib, a[(m-k+i)*lda:], lda, tau[i:], work)
+ if m-k+i > 0 {
+ // Form the triangular factor of the block reflector
+ // H = H_{i+ib-1} . . . H_{i+1} H_i.
+ impl.Dlarft(lapack.Backward, lapack.RowWise,
+ n-k+i+ib, ib, a[(m-k+i)*lda:], lda, tau[i:],
+ work, ldwork)
+
+ // Apply H to A[0:m-k+i-1, 0:n-k+i+ib-1] from the right.
+ impl.Dlarfb(blas.Right, blas.NoTrans, lapack.Backward, lapack.RowWise,
+ m-k+i, n-k+i+ib, ib, a[(m-k+i)*lda:], lda,
+ work, ldwork,
+ a, lda,
+ work[ib*ldwork:], ldwork)
+ }
+ }
+ mu = m - k + i + nb
+ nu = n - k + i + nb
+ } else {
+ mu = m
+ nu = n
+ }
+
+ // Use unblocked code to factor the last or only block.
+ if mu > 0 && nu > 0 {
+ impl.Dgerq2(mu, nu, a, lda, tau, work)
+ }
+ work[0] = float64(iws)
+}
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