+++ /dev/null
-// Copyright ©2015 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"
-)
-
-// Dgeqrf computes the QR factorization of the m×n matrix A using a blocked
-// algorithm. See the documentation for Dgeqr2 for a description of the
-// parameters at entry and exit.
-//
-// work is temporary storage, and lwork specifies the usable memory length.
-// The length of work must be at least max(1, lwork) and lwork must be -1
-// or at least n, otherwise this function will panic.
-// Dgeqrf is a blocked QR factorization, but the block size is limited
-// by the temporary space available. If lwork == -1, instead of performing Dgeqrf,
-// the optimal work length will be stored into work[0].
-//
-// tau must have length at least min(m,n), and this function will panic otherwise.
-func (impl Implementation) Dgeqrf(m, n int, a []float64, lda int, tau, work []float64, lwork int) {
- if len(work) < max(1, lwork) {
- panic(shortWork)
- }
- // nb is the optimal blocksize, i.e. the number of columns transformed at a time.
- nb := impl.Ilaenv(1, "DGEQRF", " ", m, n, -1, -1)
- lworkopt := n * max(nb, 1)
- lworkopt = max(n, lworkopt)
- if lwork == -1 {
- work[0] = float64(lworkopt)
- return
- }
- checkMatrix(m, n, a, lda)
- if lwork < n {
- panic(badWork)
- }
- k := min(m, n)
- if len(tau) < k {
- panic(badTau)
- }
- if k == 0 {
- work[0] = float64(lworkopt)
- return
- }
- nbmin := 2 // Minimal block size.
- var nx int // Use unblocked (unless changed in the next for loop)
- iws := n
- ldwork := nb
- // Only consider blocked if the suggested block size is > 1 and the
- // number of rows or columns is sufficiently large.
- if 1 < nb && nb < k {
- // nx is the block size at which the code switches from blocked
- // to unblocked.
- nx = max(0, impl.Ilaenv(3, "DGEQRF", " ", m, n, -1, -1))
- if k > nx {
- iws = ldwork * n
- if lwork < iws {
- // Not enough workspace to use the optimal block
- // size. Get the minimum block size instead.
- nb = lwork / n
- nbmin = max(2, impl.Ilaenv(2, "DGEQRF", " ", m, n, -1, -1))
- }
- }
- }
- for i := range work {
- work[i] = 0
- }
- // Compute QR using a blocked algorithm.
- var i int
- if nbmin <= nb && nb < k && nx < k {
- for i = 0; i < k-nx; i += nb {
- ib := min(k-i, nb)
- // Compute the QR factorization of the current block.
- impl.Dgeqr2(m-i, ib, a[i*lda+i:], lda, tau[i:], work)
- if i+ib < n {
- // Form the triangular factor of the block reflector and apply H^T
- // In Dlarft, work becomes the T matrix.
- impl.Dlarft(lapack.Forward, lapack.ColumnWise, m-i, ib,
- a[i*lda+i:], lda,
- tau[i:],
- work, ldwork)
- impl.Dlarfb(blas.Left, blas.Trans, lapack.Forward, lapack.ColumnWise,
- m-i, n-i-ib, ib,
- a[i*lda+i:], lda,
- work, ldwork,
- a[i*lda+i+ib:], lda,
- work[ib*ldwork:], ldwork)
- }
- }
- }
- // Call unblocked code on the remaining columns.
- if i < k {
- impl.Dgeqr2(m-i, n-i, a[i*lda+i:], lda, tau[i:], work)
- }
- work[0] = float64(lworkopt)
-}
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