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