+++ /dev/null
-// 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 gonum
-
-import "gonum.org/v1/gonum/blas"
-
-// Dorgtr generates a real orthogonal matrix Q which is defined as the product
-// of n-1 elementary reflectors of order n as returned by Dsytrd.
-//
-// The construction of Q depends on the value of uplo:
-// Q = H_{n-1} * ... * H_1 * H_0 if uplo == blas.Upper
-// Q = H_0 * H_1 * ... * H_{n-1} if uplo == blas.Lower
-// where H_i is constructed from the elementary reflectors as computed by Dsytrd.
-// See the documentation for Dsytrd for more information.
-//
-// tau must have length at least n-1, and Dorgtr will panic otherwise.
-//
-// work is temporary storage, and lwork specifies the usable memory length. At
-// minimum, lwork >= max(1,n-1), and Dorgtr will panic otherwise. The amount of blocking
-// is limited by the usable length.
-// If lwork == -1, instead of computing Dorgtr the optimal work length is stored
-// into work[0].
-//
-// Dorgtr is an internal routine. It is exported for testing purposes.
-func (impl Implementation) Dorgtr(uplo blas.Uplo, n int, a []float64, lda int, tau, work []float64, lwork int) {
- checkMatrix(n, n, a, lda)
- if len(tau) < n-1 {
- panic(badTau)
- }
- if len(work) < lwork {
- panic(badWork)
- }
- if lwork < n-1 && lwork != -1 {
- panic(badWork)
- }
- upper := uplo == blas.Upper
- if !upper && uplo != blas.Lower {
- panic(badUplo)
- }
-
- if n == 0 {
- work[0] = 1
- return
- }
-
- var nb int
- if upper {
- nb = impl.Ilaenv(1, "DORGQL", " ", n-1, n-1, n-1, -1)
- } else {
- nb = impl.Ilaenv(1, "DORGQR", " ", n-1, n-1, n-1, -1)
- }
- lworkopt := max(1, n-1) * nb
- if lwork == -1 {
- work[0] = float64(lworkopt)
- return
- }
-
- if upper {
- // Q was determined by a call to Dsytrd with uplo == blas.Upper.
- // Shift the vectors which define the elementary reflectors one column
- // to the left, and set the last row and column of Q to those of the unit
- // matrix.
- for j := 0; j < n-1; j++ {
- for i := 0; i < j; i++ {
- a[i*lda+j] = a[i*lda+j+1]
- }
- a[(n-1)*lda+j] = 0
- }
- for i := 0; i < n-1; i++ {
- a[i*lda+n-1] = 0
- }
- a[(n-1)*lda+n-1] = 1
-
- // Generate Q[0:n-1, 0:n-1].
- impl.Dorgql(n-1, n-1, n-1, a, lda, tau, work, lwork)
- } else {
- // Q was determined by a call to Dsytrd with uplo == blas.Upper.
- // Shift the vectors which define the elementary reflectors one column
- // to the right, and set the first row and column of Q to those of the unit
- // matrix.
- for j := n - 1; j > 0; j-- {
- a[j] = 0
- for i := j + 1; i < n; i++ {
- a[i*lda+j] = a[i*lda+j-1]
- }
- }
- a[0] = 1
- for i := 1; i < n; i++ {
- a[i*lda] = 0
- }
- if n > 1 {
- // Generate Q[1:n, 1:n].
- impl.Dorgqr(n-1, n-1, n-1, a[lda+1:], lda, tau, work, lwork)
- }
- }
- work[0] = float64(lworkopt)
-}