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// 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) {
switch {
case uplo != blas.Upper && uplo != blas.Lower:
panic(badUplo)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
case lwork < max(1, n-1) && lwork != -1:
panic(badLWork)
case len(work) < max(1, lwork):
panic(shortWork)
}
if n == 0 {
work[0] = 1
return
}
var nb int
if uplo == blas.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
}
switch {
case len(a) < (n-1)*lda+n:
panic(shortA)
case len(tau) < n-1:
panic(shortTau)
}
if uplo == blas.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)
}