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79 lines
2.0 KiB
Go
79 lines
2.0 KiB
Go
// Copyright ©2016 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package native
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import (
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"gonum.org/v1/gonum/blas/blas64"
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"gonum.org/v1/gonum/lapack"
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)
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// Dgebak updates an n×m matrix V as
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// V = P D V, if side == lapack.RightEV,
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// V = P D^{-1} V, if side == lapack.LeftEV,
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// where P and D are n×n permutation and scaling matrices, respectively,
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// implicitly represented by job, scale, ilo and ihi as returned by Dgebal.
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//
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// Typically, columns of the matrix V contain the right or left (determined by
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// side) eigenvectors of the balanced matrix output by Dgebal, and Dgebak forms
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// the eigenvectors of the original matrix.
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//
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// Dgebak is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dgebak(job lapack.Job, side lapack.EVSide, n, ilo, ihi int, scale []float64, m int, v []float64, ldv int) {
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switch job {
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default:
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panic(badJob)
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case lapack.None, lapack.Permute, lapack.Scale, lapack.PermuteScale:
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}
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switch side {
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default:
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panic(badSide)
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case lapack.LeftEV, lapack.RightEV:
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}
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checkMatrix(n, m, v, ldv)
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switch {
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case ilo < 0 || max(0, n-1) < ilo:
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panic(badIlo)
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case ihi < min(ilo, n-1) || n <= ihi:
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panic(badIhi)
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}
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// Quick return if possible.
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if n == 0 || m == 0 || job == lapack.None {
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return
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}
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bi := blas64.Implementation()
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if ilo != ihi && job != lapack.Permute {
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// Backward balance.
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if side == lapack.RightEV {
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for i := ilo; i <= ihi; i++ {
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bi.Dscal(m, scale[i], v[i*ldv:], 1)
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}
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} else {
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for i := ilo; i <= ihi; i++ {
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bi.Dscal(m, 1/scale[i], v[i*ldv:], 1)
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}
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}
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}
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if job == lapack.Scale {
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return
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}
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// Backward permutation.
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for i := ilo - 1; i >= 0; i-- {
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k := int(scale[i])
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if k == i {
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continue
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}
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bi.Dswap(m, v[i*ldv:], 1, v[k*ldv:], 1)
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}
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for i := ihi + 1; i < n; i++ {
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k := int(scale[i])
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if k == i {
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continue
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}
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bi.Dswap(m, v[i*ldv:], 1, v[k*ldv:], 1)
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}
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}
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