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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"
// Dormr2 multiplies a general matrix C by an orthogonal matrix from a RQ factorization
// determined by Dgerqf.
//
// 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
//
// If side == blas.Left, a is a matrix of size k×m, and if side == blas.Right
// a is of size k×n.
//
// tau contains the Householder factors and is of length at least k and this function
// will panic otherwise.
//
// work is temporary storage of length at least n if side == blas.Left
// and at least m if side == blas.Right and this function will panic otherwise.
//
// Dormr2 is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dormr2(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64) {
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, nq):
panic(badLdA)
case ldc < max(1, n):
panic(badLdC)
}
// Quick return if possible.
if m == 0 || n == 0 || k == 0 {
return
}
switch {
case len(a) < (k-1)*lda+nq:
panic(shortA)
case len(tau) < k:
panic(shortTau)
case len(c) < (m-1)*ldc+n:
panic(shortC)
case len(work) < nw:
panic(shortWork)
}
if left {
if trans == blas.NoTrans {
for i := k - 1; i >= 0; i-- {
aii := a[i*lda+(m-k+i)]
a[i*lda+(m-k+i)] = 1
impl.Dlarf(side, m-k+i+1, n, a[i*lda:], 1, tau[i], c, ldc, work)
a[i*lda+(m-k+i)] = aii
}
return
}
for i := 0; i < k; i++ {
aii := a[i*lda+(m-k+i)]
a[i*lda+(m-k+i)] = 1
impl.Dlarf(side, m-k+i+1, n, a[i*lda:], 1, tau[i], c, ldc, work)
a[i*lda+(m-k+i)] = aii
}
return
}
if trans == blas.NoTrans {
for i := 0; i < k; i++ {
aii := a[i*lda+(n-k+i)]
a[i*lda+(n-k+i)] = 1
impl.Dlarf(side, m, n-k+i+1, a[i*lda:], 1, tau[i], c, ldc, work)
a[i*lda+(n-k+i)] = aii
}
return
}
for i := k - 1; i >= 0; i-- {
aii := a[i*lda+(n-k+i)]
a[i*lda+(n-k+i)] = 1
impl.Dlarf(side, m, n-k+i+1, a[i*lda:], 1, tau[i], c, ldc, work)
a[i*lda+(n-k+i)] = aii
}
}
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