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

NAG Library Function Document

nag_dgebak (f08njc)

+ Contents

    1  Purpose
    7  Accuracy
    9  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

None.

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 3.2.1.3 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.
side=Nag_LeftSide
The left eigenvectors are transformed.
side=Nag_RightSide
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).
Constraints:
  • 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.
Constraints:
  • 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

NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
On entry, pdv=value.
Constraint: pdv>0.
NE_INT_2
On entry, pdv=value and m=value.
Constraint: pdvmax1,m.
On entry, pdv=value and n=value.
Constraint: pdv max1,n .
NE_INT_3
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.
NE_INTERNAL_ERROR
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  Further Comments

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

9  Example

See Section 9 in nag_dgebal (f08nhc).

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

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012