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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"
)
// Dgeqrf computes the QR factorization of the m×n matrix A using a blocked
// algorithm. See the documentation for Dgeqr2 for a description of the
// parameters at entry and exit.
//
// work is temporary storage, and lwork specifies the usable memory length.
// The length of work must be at least max(1, lwork) and lwork must be -1
// or at least n, otherwise this function will panic.
// Dgeqrf is a blocked QR factorization, but the block size is limited
// by the temporary space available. If lwork == -1, instead of performing Dgeqrf,
// 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) Dgeqrf(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, n) && lwork != -1:
panic(badLWork)
case len(work) < max(1, lwork):
panic(shortWork)
}
// Quick return if possible.
k := min(m, n)
if k == 0 {
work[0] = 1
return
}
// nb is the optimal blocksize, i.e. the number of columns transformed at a time.
nb := impl.Ilaenv(1, "DGEQRF", " ", m, n, -1, -1)
if lwork == -1 {
work[0] = float64(n * nb)
return
}
if len(a) < (m-1)*lda+n {
panic(shortA)
}
if len(tau) < k {
panic(shortTau)
}
nbmin := 2 // Minimal block size.
var nx int // Use unblocked (unless changed in the next for loop)
iws := n
// Only consider blocked if the suggested block size is > 1 and the
// number of rows or columns is sufficiently large.
if 1 < nb && nb < k {
// nx is the block size at which the code switches from blocked
// to unblocked.
nx = max(0, impl.Ilaenv(3, "DGEQRF", " ", m, n, -1, -1))
if k > nx {
iws = n * nb
if lwork < iws {
// Not enough workspace to use the optimal block
// size. Get the minimum block size instead.
nb = lwork / n
nbmin = max(2, impl.Ilaenv(2, "DGEQRF", " ", m, n, -1, -1))
}
}
}
// Compute QR using a blocked algorithm.
var i int
if nbmin <= nb && nb < k && nx < k {
ldwork := nb
for i = 0; i < k-nx; i += nb {
ib := min(k-i, nb)
// Compute the QR factorization of the current block.
impl.Dgeqr2(m-i, ib, a[i*lda+i:], lda, tau[i:], work)
if i+ib < n {
// Form the triangular factor of the block reflector and apply Hᵀ
// In Dlarft, work becomes the T matrix.
impl.Dlarft(lapack.Forward, lapack.ColumnWise, m-i, ib,
a[i*lda+i:], lda,
tau[i:],
work, ldwork)
impl.Dlarfb(blas.Left, blas.Trans, 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)
}
}
}
// Call unblocked code on the remaining columns.
if i < k {
impl.Dgeqr2(m-i, n-i, a[i*lda+i:], lda, tau[i:], work)
}
work[0] = float64(iws)
}