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// Copyright ©2016 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/blas64"
"gonum.org/v1/gonum/lapack"
)
// Dgebak updates an n×m matrix V as
// V = P D V if side == lapack.EVRight,
// V = P D^{-1} V if side == lapack.EVLeft,
// where P and D are n×n permutation and scaling matrices, respectively,
// implicitly represented by job, scale, ilo and ihi as returned by Dgebal.
//
// Typically, columns of the matrix V contain the right or left (determined by
// side) eigenvectors of the balanced matrix output by Dgebal, and Dgebak forms
// the eigenvectors of the original matrix.
//
// Dgebak is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dgebak(job lapack.BalanceJob, side lapack.EVSide, n, ilo, ihi int, scale []float64, m int, v []float64, ldv int) {
switch {
case job != lapack.BalanceNone && job != lapack.Permute && job != lapack.Scale && job != lapack.PermuteScale:
panic(badBalanceJob)
case side != lapack.EVLeft && side != lapack.EVRight:
panic(badEVSide)
case n < 0:
panic(nLT0)
case ilo < 0 || max(0, n-1) < ilo:
panic(badIlo)
case ihi < min(ilo, n-1) || n <= ihi:
panic(badIhi)
case m < 0:
panic(mLT0)
case ldv < max(1, m):
panic(badLdV)
}
// Quick return if possible.
if n == 0 || m == 0 {
return
}
if len(scale) < n {
panic(shortScale)
}
if len(v) < (n-1)*ldv+m {
panic(shortV)
}
// Quick return if possible.
if job == lapack.BalanceNone {
return
}
bi := blas64.Implementation()
if ilo != ihi && job != lapack.Permute {
// Backward balance.
if side == lapack.EVRight {
for i := ilo; i <= ihi; i++ {
bi.Dscal(m, scale[i], v[i*ldv:], 1)
}
} else {
for i := ilo; i <= ihi; i++ {
bi.Dscal(m, 1/scale[i], v[i*ldv:], 1)
}
}
}
if job == lapack.Scale {
return
}
// Backward permutation.
for i := ilo - 1; i >= 0; i-- {
k := int(scale[i])
if k == i {
continue
}
bi.Dswap(m, v[i*ldv:], 1, v[k*ldv:], 1)
}
for i := ihi + 1; i < n; i++ {
k := int(scale[i])
if k == i {
continue
}
bi.Dswap(m, v[i*ldv:], 1, v[k*ldv:], 1)
}
}