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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"
)
// Dormqr multiplies an m×n matrix C by an orthogonal matrix Q as
// C = Q * C if side == blas.Left and trans == blas.NoTrans,
// C = Qᵀ * C if side == blas.Left and trans == blas.Trans,
// C = C * Q if side == blas.Right and trans == blas.NoTrans,
// C = C * Qᵀ if side == blas.Right and trans == blas.Trans,
// where Q is defined as the product of k elementary reflectors
// Q = H_0 * H_1 * ... * H_{k-1}.
//
// If side == blas.Left, A is an m×k matrix and 0 <= k <= m.
// If side == blas.Right, A is an n×k matrix and 0 <= k <= n.
// The ith column of A contains the vector which defines the elementary
// reflector H_i and tau[i] contains its scalar factor. tau must have length k
// and Dormqr will panic otherwise. Dgeqrf returns A and tau in the required
// form.
//
// work must have length at least max(1,lwork), and lwork must be at least n if
// side == blas.Left and at least m if side == blas.Right, otherwise Dormqr will
// panic.
//
// 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. Larger values of lwork
// will generally give better performance. On return, work[0] will contain the
// optimal value of lwork.
//
// If lwork is -1, instead of performing Dormqr, the optimal workspace size will
// be stored into work[0].
func (impl Implementation) Dormqr(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int) {
left := side == blas.Left
nq := n
nw := m
if left {
nq = m
nw = n
}
switch {
case !left && side != blas.Right:
panic(badSide)
case trans != blas.NoTrans && trans != blas.Trans:
panic(badTrans)
case m < 0:
panic(mLT0)
case n < 0:
panic(nLT0)
case k < 0:
panic(kLT0)
case left && k > m:
panic(kGTM)
case !left && k > n:
panic(kGTN)
case lda < max(1, k):
panic(badLdA)
case ldc < max(1, n):
panic(badLdC)
case lwork < max(1, nw) && lwork != -1:
panic(badLWork)
case len(work) < max(1, lwork):
panic(shortWork)
}
// Quick return if possible.
if m == 0 || n == 0 || k == 0 {
work[0] = 1
return
}
const (
nbmax = 64
ldt = nbmax
tsize = nbmax * ldt
)
opts := string(side) + string(trans)
nb := min(nbmax, impl.Ilaenv(1, "DORMQR", opts, m, n, k, -1))
lworkopt := max(1, nw)*nb + tsize
if lwork == -1 {
work[0] = float64(lworkopt)
return
}
switch {
case len(a) < (nq-1)*lda+k:
panic(shortA)
case len(tau) != k:
panic(badLenTau)
case len(c) < (m-1)*ldc+n:
panic(shortC)
}
nbmin := 2
if 1 < nb && nb < k {
if lwork < nw*nb+tsize {
nb = (lwork - tsize) / nw
nbmin = max(2, impl.Ilaenv(2, "DORMQR", opts, m, n, k, -1))
}
}
if nb < nbmin || k <= nb {
// Call unblocked code.
impl.Dorm2r(side, trans, m, n, k, a, lda, tau, c, ldc, work)
work[0] = float64(lworkopt)
return
}
var (
ldwork = nb
notrans = trans == blas.NoTrans
)
switch {
case left && notrans:
for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.ColumnWise, m-i, ib,
a[i*lda+i:], lda,
tau[i:],
work[:tsize], ldt)
impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m-i, n, ib,
a[i*lda+i:], lda,
work[:tsize], ldt,
c[i*ldc:], ldc,
work[tsize:], ldwork)
}
case left && !notrans:
for i := 0; i < k; i += nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.ColumnWise, m-i, ib,
a[i*lda+i:], lda,
tau[i:],
work[:tsize], ldt)
impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m-i, n, ib,
a[i*lda+i:], lda,
work[:tsize], ldt,
c[i*ldc:], ldc,
work[tsize:], ldwork)
}
case !left && notrans:
for i := 0; i < k; i += nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.ColumnWise, n-i, ib,
a[i*lda+i:], lda,
tau[i:],
work[:tsize], ldt)
impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m, n-i, ib,
a[i*lda+i:], lda,
work[:tsize], ldt,
c[i:], ldc,
work[tsize:], ldwork)
}
case !left && !notrans:
for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.ColumnWise, n-i, ib,
a[i*lda+i:], lda,
tau[i:],
work[:tsize], ldt)
impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m, n-i, ib,
a[i*lda+i:], lda,
work[:tsize], ldt,
c[i:], ldc,
work[tsize:], ldwork)
}
}
work[0] = float64(lworkopt)
}