97 lines
2.5 KiB
Go
97 lines
2.5 KiB
Go
// 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)
|
||
}
|