nag_dgebak (f08njc) (PDF version)
f08 Chapter Contents
f08 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_dgebak (f08njc)

+ Contents

    1  Purpose
    7  Accuracy
    10  Example

1  Purpose

nag_dgebak (f08njc) transforms eigenvectors of a balanced matrix to those of the original real nonsymmetric matrix.

2  Specification

#include <nag.h>
#include <nagf08.h>
void  nag_dgebak (Nag_OrderType order, Nag_JobType job, Nag_SideType side, Integer n, Integer ilo, Integer ihi, const double scale[], Integer m, double v[], Integer pdv, NagError *fail)

3  Description

nag_dgebak (f08njc) is intended to be used after a real nonsymmetric matrix A has been balanced by nag_dgebal (f08nhc), and eigenvectors of the balanced matrix A22 have subsequently been computed.
For a description of balancing, see the document for nag_dgebal (f08nhc). The balanced matrix A is obtained as A=DPAPTD-1, where P is a permutation matrix and D is a diagonal scaling matrix. This function transforms left or right eigenvectors as follows:

4  References


5  Arguments

1:     orderNag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     jobNag_JobTypeInput
On entry: this must be the same argument job as supplied to nag_dgebal (f08nhc).
Constraint: job=Nag_DoNothing, Nag_Permute, Nag_Scale or Nag_DoBoth.
3:     sideNag_SideTypeInput
On entry: indicates whether left or right eigenvectors are to be transformed.
The left eigenvectors are transformed.
The right eigenvectors are transformed.
Constraint: side=Nag_LeftSide or Nag_RightSide.
4:     nIntegerInput
On entry: n, the number of rows of the matrix of eigenvectors.
Constraint: n0.
5:     iloIntegerInput
6:     ihiIntegerInput
On entry: the values ilo and ihi, as returned by nag_dgebal (f08nhc).
  • if n>0, 1 ilo ihi n ;
  • if n=0, ilo=1 and ihi=0.
7:     scale[dim]const doubleInput
Note: the dimension, dim, of the array scale must be at least max1,n.
On entry: details of the permutations and/or the scaling factors used to balance the original real nonsymmetric matrix, as returned by nag_dgebal (f08nhc).
8:     mIntegerInput
On entry: m, the number of columns of the matrix of eigenvectors.
Constraint: m0.
9:     v[dim]doubleInput/Output
Note: the dimension, dim, of the array v must be at least
  • max1,pdv×m when order=Nag_ColMajor;
  • max1,n×pdv when order=Nag_RowMajor.
The i,jth element of the matrix V is stored in
  • v[j-1×pdv+i-1] when order=Nag_ColMajor;
  • v[i-1×pdv+j-1] when order=Nag_RowMajor.
On entry: the matrix of left or right eigenvectors to be transformed.
On exit: the transformed eigenvectors.
10:   pdvIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array v.
  • if order=Nag_ColMajor, pdv max1,n ;
  • if order=Nag_RowMajor, pdvmax1,m.
11:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
On entry, argument value had an illegal value.
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
On entry, pdv=value.
Constraint: pdv>0.
On entry, pdv=value and m=value.
Constraint: pdvmax1,m.
On entry, pdv=value and n=value.
Constraint: pdv max1,n .
On entry, n=value, ilo=value and ihi=value.
Constraint: if n>0, 1 ilo ihi n ;
if n=0, ilo=1 and ihi=0.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

7  Accuracy

The errors are negligible.

8  Parallelism and Performance

nag_dgebak (f08njc) is not threaded by NAG in any implementation.
nag_dgebak (f08njc) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the Users' Note for your implementation for any additional implementation-specific information.

9  Further Comments

The total number of floating-point operations is approximately proportional to nm.
The complex analogue of this function is nag_zgebak (f08nwc).

10  Example

See Section 10 in nag_dgebal (f08nhc).

nag_dgebak (f08njc) (PDF version)
f08 Chapter Contents
f08 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014