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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"
"gonum.org/v1/gonum/lapack"
)
// Dorgql generates the m×n matrix Q with orthonormal columns defined as the
// last n columns of a product of k elementary reflectors of order m
//
// Q = H_{k-1} * ... * H_1 * H_0.
//
// It must hold that
//
// 0 <= k <= n <= m,
//
// and Dorgql will panic otherwise.
//
// On entry, the (n-k+i)-th column of A must contain the vector which defines
// the elementary reflector H_i, for i=0,...,k-1, and tau[i] must contain its
// scalar factor. On return, a contains the m×n matrix Q.
//
// tau must have length at least k, and Dorgql will panic otherwise.
//
// work must have length at least max(1,lwork), and lwork must be at least
// max(1,n), otherwise Dorgql will panic. For optimum performance lwork must
// be a sufficiently large multiple of n.
//
// If lwork == -1, instead of computing Dorgql the optimal work length is stored
// into work[0].
//
// Dorgql is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dorgql(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):
panic(badLdA)
case lwork < max(1, n) && lwork != -1:
panic(badLWork)
case len(work) < max(1, lwork):
panic(shortWork)
}
// Quick return if possible.
if n == 0 {
work[0] = 1
return
}
nb := impl.Ilaenv(1, "DORGQL", " ", m, n, k, -1)
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
var nx, ldwork int
iws := n
if 1 < nb && nb < k {
// Determine when to cross over from blocked to unblocked code.
nx = max(0, impl.Ilaenv(3, "DORGQL", " ", m, n, k, -1))
if nx < k {
// Determine if workspace is large enough for blocked code.
iws = n * nb
if lwork < iws {
// Not enough workspace to use optimal nb: reduce nb and determine
// the minimum value of nb.
nb = lwork / n
nbmin = max(2, impl.Ilaenv(2, "DORGQL", " ", m, n, k, -1))
}
ldwork = nb
}
}
var kk int
if nbmin <= nb && nb < k && nx < k {
// Use blocked code after the first block. The last kk columns are handled
// by the block method.
kk = min(k, ((k-nx+nb-1)/nb)*nb)
// Set A(m-kk:m, 0:n-kk) to zero.
for i := m - kk; i < m; i++ {
for j := 0; j < n-kk; j++ {
a[i*lda+j] = 0
}
}
}
// Use unblocked code for the first or only block.
impl.Dorg2l(m-kk, n-kk, k-kk, a, lda, tau, work)
if kk > 0 {
// Use blocked code.
for i := k - kk; i < k; i += nb {
ib := min(nb, k-i)
if n-k+i > 0 {
// Form the triangular factor of the block reflector
// H = H_{i+ib-1} * ... * H_{i+1} * H_i.
impl.Dlarft(lapack.Backward, lapack.ColumnWise, m-k+i+ib, ib,
a[n-k+i:], lda, tau[i:], work, ldwork)
// Apply H to A[0:m-k+i+ib, 0:n-k+i] from the left.
impl.Dlarfb(blas.Left, blas.NoTrans, lapack.Backward, lapack.ColumnWise,
m-k+i+ib, n-k+i, ib, a[n-k+i:], lda, work, ldwork,
a, lda, work[ib*ldwork:], ldwork)
}
// Apply H to rows 0:m-k+i+ib of current block.
impl.Dorg2l(m-k+i+ib, ib, ib, a[n-k+i:], lda, tau[i:], work)
// Set rows m-k+i+ib:m of current block to zero.
for j := n - k + i; j < n-k+i+ib; j++ {
for l := m - k + i + ib; l < m; l++ {
a[l*lda+j] = 0
}
}
}
}
work[0] = float64(iws)
}
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