github.com/gonum/lapack@v0.0.0-20181123203213-e4cdc5a0bff9/native/dgebak.go (about)

     1  // Copyright ©2016 The gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package native
     6  
     7  import (
     8  	"github.com/gonum/blas/blas64"
     9  	"github.com/gonum/lapack"
    10  )
    11  
    12  // Dgebak updates an n×m matrix V as
    13  //  V = P D V,        if side == lapack.RightEV,
    14  //  V = P D^{-1} V,   if side == lapack.LeftEV,
    15  // where P and D are n×n permutation and scaling matrices, respectively,
    16  // implicitly represented by job, scale, ilo and ihi as returned by Dgebal.
    17  //
    18  // Typically, columns of the matrix V contain the right or left (determined by
    19  // side) eigenvectors of the balanced matrix output by Dgebal, and Dgebak forms
    20  // the eigenvectors of the original matrix.
    21  //
    22  // Dgebak is an internal routine. It is exported for testing purposes.
    23  func (impl Implementation) Dgebak(job lapack.Job, side lapack.EVSide, n, ilo, ihi int, scale []float64, m int, v []float64, ldv int) {
    24  	switch job {
    25  	default:
    26  		panic(badJob)
    27  	case lapack.None, lapack.Permute, lapack.Scale, lapack.PermuteScale:
    28  	}
    29  	switch side {
    30  	default:
    31  		panic(badSide)
    32  	case lapack.LeftEV, lapack.RightEV:
    33  	}
    34  	checkMatrix(n, m, v, ldv)
    35  	switch {
    36  	case ilo < 0 || max(0, n-1) < ilo:
    37  		panic(badIlo)
    38  	case ihi < min(ilo, n-1) || n <= ihi:
    39  		panic(badIhi)
    40  	}
    41  
    42  	// Quick return if possible.
    43  	if n == 0 || m == 0 || job == lapack.None {
    44  		return
    45  	}
    46  
    47  	bi := blas64.Implementation()
    48  	if ilo != ihi && job != lapack.Permute {
    49  		// Backward balance.
    50  		if side == lapack.RightEV {
    51  			for i := ilo; i <= ihi; i++ {
    52  				bi.Dscal(m, scale[i], v[i*ldv:], 1)
    53  			}
    54  		} else {
    55  			for i := ilo; i <= ihi; i++ {
    56  				bi.Dscal(m, 1/scale[i], v[i*ldv:], 1)
    57  			}
    58  		}
    59  	}
    60  	if job == lapack.Scale {
    61  		return
    62  	}
    63  	// Backward permutation.
    64  	for i := ilo - 1; i >= 0; i-- {
    65  		k := int(scale[i])
    66  		if k == i {
    67  			continue
    68  		}
    69  		bi.Dswap(m, v[i*ldv:], 1, v[k*ldv:], 1)
    70  	}
    71  	for i := ihi + 1; i < n; i++ {
    72  		k := int(scale[i])
    73  		if k == i {
    74  			continue
    75  		}
    76  		bi.Dswap(m, v[i*ldv:], 1, v[k*ldv:], 1)
    77  	}
    78  }