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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"
)
// Dormbr applies a multiplicative update to the matrix C based on a
// decomposition computed by Dgebrd.
//
// Dormbr overwrites the m×n matrix C with
//
// Q * C if vect == lapack.ApplyQ, side == blas.Left, and trans == blas.NoTrans
// C * Q if vect == lapack.ApplyQ, side == blas.Right, and trans == blas.NoTrans
// Qᵀ * C if vect == lapack.ApplyQ, side == blas.Left, and trans == blas.Trans
// C * Qᵀ if vect == lapack.ApplyQ, side == blas.Right, and trans == blas.Trans
//
// P * C if vect == lapack.ApplyP, side == blas.Left, and trans == blas.NoTrans
// C * P if vect == lapack.ApplyP, side == blas.Right, and trans == blas.NoTrans
// Pᵀ * C if vect == lapack.ApplyP, side == blas.Left, and trans == blas.Trans
// C * Pᵀ if vect == lapack.ApplyP, side == blas.Right, and trans == blas.Trans
//
// where P and Q are the orthogonal matrices determined by Dgebrd when reducing
// a matrix A to bidiagonal form: A = Q * B * Pᵀ. See Dgebrd for the
// definitions of Q and P.
//
// If vect == lapack.ApplyQ, A is assumed to have been an nq×k matrix, while if
// vect == lapack.ApplyP, A is assumed to have been a k×nq matrix. nq = m if
// side == blas.Left, while nq = n if side == blas.Right.
//
// tau must have length min(nq,k), and Dormbr will panic otherwise. tau contains
// the elementary reflectors to construct Q or P depending on the value of
// vect.
//
// work must have length at least max(1,lwork), and lwork must be either -1 or
// at least max(1,n) if side == blas.Left, and at least max(1,m) if side ==
// blas.Right. For optimum performance lwork should be at least n*nb if side ==
// blas.Left, and at least m*nb if side == blas.Right, where nb is the optimal
// block size. On return, work[0] will contain the optimal value of lwork.
//
// If lwork == -1, the function only calculates the optimal value of lwork and
// returns it in work[0].
//
// Dormbr is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dormbr(vect lapack.ApplyOrtho, side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int) {
nq := n
nw := m
if side == blas.Left {
nq = m
nw = n
}
applyQ := vect == lapack.ApplyQ
switch {
case !applyQ && vect != lapack.ApplyP:
panic(badApplyOrtho)
case side != blas.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 applyQ && lda < max(1, min(nq, k)):
panic(badLdA)
case !applyQ && lda < max(1, nq):
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 {
work[0] = 1
return
}
// The current implementation does not use opts, but a future change may
// use these options so construct them.
var opts string
if side == blas.Left {
opts = "L"
} else {
opts = "R"
}
if trans == blas.Trans {
opts += "T"
} else {
opts += "N"
}
var nb int
if applyQ {
if side == blas.Left {
nb = impl.Ilaenv(1, "DORMQR", opts, m-1, n, m-1, -1)
} else {
nb = impl.Ilaenv(1, "DORMQR", opts, m, n-1, n-1, -1)
}
} else {
if side == blas.Left {
nb = impl.Ilaenv(1, "DORMLQ", opts, m-1, n, m-1, -1)
} else {
nb = impl.Ilaenv(1, "DORMLQ", opts, m, n-1, n-1, -1)
}
}
lworkopt := max(1, nw) * nb
if lwork == -1 {
work[0] = float64(lworkopt)
return
}
minnqk := min(nq, k)
switch {
case applyQ && len(a) < (nq-1)*lda+minnqk:
panic(shortA)
case !applyQ && len(a) < (minnqk-1)*lda+nq:
panic(shortA)
case len(tau) < minnqk:
panic(shortTau)
case len(c) < (m-1)*ldc+n:
panic(shortC)
}
if applyQ {
// Change the operation to get Q depending on the size of the initial
// matrix to Dgebrd. The size matters due to the storage location of
// the off-diagonal elements.
if nq >= k {
impl.Dormqr(side, trans, m, n, k, a, lda, tau[:k], c, ldc, work, lwork)
} else if nq > 1 {
mi := m
ni := n - 1
i1 := 0
i2 := 1
if side == blas.Left {
mi = m - 1
ni = n
i1 = 1
i2 = 0
}
impl.Dormqr(side, trans, mi, ni, nq-1, a[lda:], lda, tau[:nq-1], c[i1*ldc+i2:], ldc, work, lwork)
}
work[0] = float64(lworkopt)
return
}
transt := blas.Trans
if trans == blas.Trans {
transt = blas.NoTrans
}
// Change the operation to get P depending on the size of the initial
// matrix to Dgebrd. The size matters due to the storage location of
// the off-diagonal elements.
if nq > k {
impl.Dormlq(side, transt, m, n, k, a, lda, tau, c, ldc, work, lwork)
} else if nq > 1 {
mi := m
ni := n - 1
i1 := 0
i2 := 1
if side == blas.Left {
mi = m - 1
ni = n
i1 = 1
i2 = 0
}
impl.Dormlq(side, transt, mi, ni, nq-1, a[1:], lda, tau, c[i1*ldc+i2:], ldc, work, lwork)
}
work[0] = float64(lworkopt)
}
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