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dormlq.go
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dormlq.go
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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 native
import (
"github.com/gonum/blas"
"github.com/gonum/lapack"
)
// Dormlq multiplies the matrix c by the othogonal matrix q defined by the
// slices a and tau. A and tau are as returned from Dgelqf.
// C = Q * C if side == blas.Left and trans == blas.NoTrans
// C = Q^T * C if side == blas.Left and trans == blas.Trans
// C = C * Q if side == blas.Right and trans == blas.NoTrans
// C = C * Q^T if side == blas.Right and trans == blas.Trans
// If side == blas.Left, a is a matrix of side k×m, and if side == blas.Right
// a is of size k×n. This uses a blocked algorithm.
//
// Work is temporary storage, and lwork specifies the usable memory length.
// At minimum, lwork >= m if side == blas.Left and lwork >= n if side == blas.Right,
// and this function will panic otherwise.
// Dormlq uses a block algorithm, but the block size is limited
// by the temporary space available. If lwork == -1, instead of performing Dormlq,
// the optimal work length will be stored into work[0].
//
// Tau contains the householder scales and must have length at least k, and
// this function will panic otherwise.
func (impl Implementation) Dormlq(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int) {
if side != blas.Left && side != blas.Right {
panic(badSide)
}
if trans != blas.Trans && trans != blas.NoTrans {
panic(badTrans)
}
left := side == blas.Left
notran := trans == blas.NoTrans
if left {
checkMatrix(k, m, a, lda)
} else {
checkMatrix(k, n, a, lda)
}
checkMatrix(m, n, c, ldc)
if len(tau) < k {
panic(badTau)
}
const nbmax = 64
nw := n
if !left {
nw = m
}
opts := string(side) + string(trans)
nb := min(nbmax, impl.Ilaenv(1, "DORMLQ", opts, m, n, k, -1))
lworkopt := max(1, nw) * nb
if lwork == -1 {
work[0] = float64(lworkopt)
return
}
if left {
if lwork < n {
panic(badWork)
}
} else {
if lwork < m {
panic(badWork)
}
}
if m == 0 || n == 0 || k == 0 {
return
}
nbmin := 2
ldwork := nb
if nb > 1 && nb < k {
iws := nw * nb
if lwork < iws {
nb = lwork / nw
nbmin = max(2, impl.Ilaenv(2, "DORMLQ", opts, m, n, k, -1))
}
}
if nb < nbmin || nb >= k {
// Call unblocked code
impl.Dorml2(side, trans, m, n, k, a, lda, tau, c, ldc, work)
return
}
ldt := nb
t := make([]float64, nb*ldt)
transt := blas.NoTrans
if notran {
transt = blas.Trans
}
switch {
case left && notran:
for i := 0; i < k; i += nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.RowWise, m-i, ib,
a[i*lda+i:], lda,
tau[i:],
t, ldt)
impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m-i, n, ib,
a[i*lda+i:], lda,
t, ldt,
c[i*ldc:], ldc,
work, ldwork)
}
return
case left && !notran:
for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.RowWise, m-i, ib,
a[i*lda+i:], lda,
tau[i:],
t, ldt)
impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m-i, n, ib,
a[i*lda+i:], lda,
t, ldt,
c[i*ldc:], ldc,
work, ldwork)
}
return
case !left && notran:
for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.RowWise, n-i, ib,
a[i*lda+i:], lda,
tau[i:],
t, ldt)
impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m, n-i, ib,
a[i*lda+i:], lda,
t, ldt,
c[i:], ldc,
work, ldwork)
}
return
case !left && !notran:
for i := 0; i < k; i += nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.RowWise, n-i, ib,
a[i*lda+i:], lda,
tau[i:],
t, ldt)
impl.Dlarfb(side, transt, lapack.Forward, lapack.RowWise, m, n-i, ib,
a[i*lda+i:], lda,
t, ldt,
c[i:], ldc,
work, ldwork)
}
return
}
}