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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"
)
// Dorglq generates an m×n matrix Q with orthonormal rows defined as the first m
// rows of a product of k elementary reflectors of order n
//
// Q = H_{k-1} * ... * H_0
//
// as returned by Dgelqf.
//
// On entry, tau and the first k rows of A must contain the scalar factors and
// the vectors, respectively, which define the elementary reflectors H_i,
// i=0,...,k-1, as returned by Dgelqf. On return, A contains the matrix Q.
//
// tau must have length at least k, work must have length at least lwork and
// lwork must be at least max(1,m). On return, optimal value of lwork will be
// stored in work[0]. It must also hold that 0 <= k <= m <= n, otherwise Dorglq
// will panic.
//
// If lwork == -1, instead of performing Dorglq, the function only calculates
// the optimal value of lwork and stores it into work[0].
func (impl Implementation) Dorglq(m, n, k int, a []float64, lda int, tau, work []float64, lwork int) {
switch {
case m < 0:
panic(mLT0)
case n < m:
panic(nLTM)
case k < 0:
panic(kLT0)
case k > m:
panic(kGTM)
case lda < max(1, n):
panic(badLdA)
case lwork < max(1, m) && lwork != -1:
panic(badLWork)
case len(work) < max(1, lwork):
panic(shortWork)
}
if m == 0 {
work[0] = 1
return
}
nb := impl.Ilaenv(1, "DORGLQ", " ", m, n, k, -1)
if lwork == -1 {
work[0] = float64(m * 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 unblocked code
iws := m // Length of work needed
var ldwork int
if 1 < nb && nb < k {
nx = max(0, impl.Ilaenv(3, "DORGLQ", " ", m, n, k, -1))
if nx < k {
ldwork = nb
iws = m * ldwork
if lwork < iws {
nb = lwork / m
ldwork = nb
nbmin = max(2, impl.Ilaenv(2, "DORGLQ", " ", m, n, k, -1))
}
}
}
var ki, kk int
if nbmin <= nb && nb < k && nx < k {
// The first kk rows are handled by the blocked method.
ki = ((k - nx - 1) / nb) * nb
kk = min(k, ki+nb)
for i := kk; i < m; i++ {
for j := 0; j < kk; j++ {
a[i*lda+j] = 0
}
}
}
if kk < m {
// Perform the operation on columns kk to the end.
impl.Dorgl2(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 < m {
impl.Dlarft(lapack.Forward, lapack.RowWise,
n-i, ib,
a[i*lda+i:], lda,
tau[i:],
work, ldwork)
impl.Dlarfb(blas.Right, blas.Trans, lapack.Forward, lapack.RowWise,
m-i-ib, n-i, ib,
a[i*lda+i:], lda,
work, ldwork,
a[(i+ib)*lda+i:], lda,
work[ib*ldwork:], ldwork)
}
impl.Dorgl2(ib, n-i, ib, a[i*lda+i:], lda, tau[i:], work)
for l := i; l < i+ib; l++ {
for j := 0; j < i; j++ {
a[l*lda+j] = 0
}
}
}
}
work[0] = float64(iws)
}
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