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// 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) {
switch {
case m < 0:
panic(mLT0)
case n < 0:
panic(nLT0)
case n > m:
panic(nGTM)
case k < 0:
panic(kLT0)
case k > n:
panic(kGTN)
case lda < max(1, n) && lwork != -1:
// Normally, we follow the reference and require the leading
// dimension to be always valid, even in case of workspace
// queries. However, if a caller provided a placeholder value
// for lda (and a) when doing a workspace query that didn't
// fulfill the condition here, it would cause a panic. This is
// exactly what Dgesvd does.
panic(badLdA)
case lwork < max(1, n) && lwork != -1:
panic(badLWork)
case len(work) < max(1, lwork):
panic(shortWork)
}
if n == 0 {
work[0] = 1
return
}
nb := impl.Ilaenv(1, "DORGQR", " ", m, n, k, -1)
// work is treated as an n×nb matrix
if lwork == -1 {
work[0] = float64(n * nb)
return
}
switch {
case len(a) < (m-1)*lda+n:
panic(shortA)
case len(tau) < k:
panic(shortTau)
}
nbmin := 2 // Minimum block size
var nx int // Crossover size from blocked to unbloked code
iws := n // Length of work needed
var ldwork int
if 1 < nb && 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 nbmin <= nb && nb < k && nx < k {
// The first kk columns are handled by the blocked method.
ki = ((k - nx - 1) / nb) * nb
kk = min(k, ki+nb)
for i := 0; i < kk; i++ {
for j := kk; j < n; j++ {
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 {
// 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
}
}
}
}
work[0] = float64(iws)
}