+++ /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"
-)
-
-// Dorgqr generates an m×n matrix Q with orthonormal columns defined by the
-// product of elementary reflectors
-// Q = H_0 * H_1 * ... * H_{k-1}
-// as computed by Dgeqrf.
-// Dorgqr is the blocked version of Dorg2r that makes greater use of level-3 BLAS
-// routines.
-//
-// The length of tau must be at least k, and the length of work must be at least n.
-// It also must be that 0 <= k <= n and 0 <= n <= m.
-//
-// work is temporary storage, and lwork specifies the usable memory length. At
-// minimum, lwork >= n, and the amount of blocking is limited by the usable
-// length. If lwork == -1, instead of computing Dorgqr the optimal work length
-// is stored into work[0].
-//
-// Dorgqr will panic if the conditions on input values are not met.
-//
-// Dorgqr is an internal routine. It is exported for testing purposes.
-func (impl Implementation) Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int) {
- nb := impl.Ilaenv(1, "DORGQR", " ", m, n, k, -1)
- // work is treated as an n×nb matrix
- if lwork == -1 {
- work[0] = float64(max(1, n) * nb)
- return
- }
- checkMatrix(m, n, a, lda)
- if k < 0 {
- panic(kLT0)
- }
- if k > n {
- panic(kGTN)
- }
- if n > m {
- panic(mLTN)
- }
- if len(tau) < k {
- panic(badTau)
- }
- if len(work) < lwork {
- panic(shortWork)
- }
- if lwork < n {
- panic(badWork)
- }
- if n == 0 {
- return
- }
- nbmin := 2 // Minimum number of blocks
- var nx int // Minimum number of rows
- iws := n // Length of work needed
- var ldwork int
- if nb > 1 && nb < k {
- nx = max(0, impl.Ilaenv(3, "DORGQR", " ", m, n, k, -1))
- if nx < k {
- ldwork = nb
- iws = n * ldwork
- if lwork < iws {
- nb = lwork / n
- ldwork = nb
- nbmin = max(2, impl.Ilaenv(2, "DORGQR", " ", m, n, k, -1))
- }
- }
- }
- var ki, kk int
- if nb >= nbmin && nb < k && nx < k {
- // The first kk columns are handled by the blocked method.
- // Note: lapack has nx here, but this means the last nx rows are handled
- // serially which could be quite different than nb.
- ki = ((k - nb - 1) / nb) * nb
- kk = min(k, ki+nb)
- for j := kk; j < n; j++ {
- for i := 0; i < kk; i++ {
- a[i*lda+j] = 0
- }
- }
- }
- if kk < n {
- // Perform the operation on colums kk to the end.
- impl.Dorg2r(m-kk, n-kk, k-kk, a[kk*lda+kk:], lda, tau[kk:], work)
- }
- if kk == 0 {
- return
- }
- // Perform the operation on column-blocks
- for i := ki; i >= 0; i -= nb {
- ib := min(nb, k-i)
- if i+ib < n {
- impl.Dlarft(lapack.Forward, lapack.ColumnWise,
- m-i, ib,
- a[i*lda+i:], lda,
- tau[i:],
- work, ldwork)
-
- impl.Dlarfb(blas.Left, blas.NoTrans, 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)
- }
- impl.Dorg2r(m-i, ib, ib, a[i*lda+i:], lda, tau[i:], work)
- // Set rows 0:i-1 of current block to zero
- for j := i; j < i+ib; j++ {
- for l := 0; l < i; l++ {
- a[l*lda+j] = 0
- }
- }
- }
-}
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