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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"
)
// Dgelqf computes the LQ factorization of the m×n matrix A using a blocked
// algorithm. See the documentation for Dgelq2 for a description of the
// parameters at entry and exit.
//
// work is temporary storage, and lwork specifies the usable memory length.
// At minimum, lwork >= m, and this function will panic otherwise.
// Dgelqf is a blocked LQ factorization, but the block size is limited
// by the temporary space available. If lwork == -1, instead of performing Dgelqf,
// the optimal work length will be stored into work[0].
//
// tau must have length at least min(m,n), and this function will panic otherwise.
func (impl Implementation) Dgelqf(m, n int, a []float64, lda int, tau, work []float64, lwork int) {
switch {
case m < 0:
panic(mLT0)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
case lwork < max(1, m) && lwork != -1:
panic(badLWork)
case len(work) < max(1, lwork):
panic(shortWork)
}
k := min(m, n)
if k == 0 {
work[0] = 1
return
}
nb := impl.Ilaenv(1, "DGELQF", " ", m, n, -1, -1)
if lwork == -1 {
work[0] = float64(m * nb)
return
}
if len(a) < (m-1)*lda+n {
panic(shortA)
}
if len(tau) < k {
panic(shortTau)
}
// Find the optimal blocking size based on the size of available memory
// and optimal machine parameters.
nbmin := 2
var nx int
iws := m
if 1 < nb && nb < k {
nx = max(0, impl.Ilaenv(3, "DGELQF", " ", m, n, -1, -1))
if nx < k {
iws = m * nb
if lwork < iws {
nb = lwork / m
nbmin = max(2, impl.Ilaenv(2, "DGELQF", " ", m, n, -1, -1))
}
}
}
ldwork := nb
// Computed blocked LQ factorization.
var i int
if nbmin <= nb && nb < k && nx < k {
for i = 0; i < k-nx; i += nb {
ib := min(k-i, nb)
impl.Dgelq2(ib, n-i, a[i*lda+i:], lda, tau[i:], work)
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.NoTrans, 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)
}
}
}
// Perform unblocked LQ factorization on the remainder.
if i < k {
impl.Dgelq2(m-i, n-i, a[i*lda+i:], lda, tau[i:], work)
}
work[0] = float64(iws)
}