nag_zggbak (f08wwc) (PDF version)
f08 Chapter Contents
f08 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_zggbak (f08wwc)

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

nag_zggbak (f08wwc) forms the right or left eigenvectors of the real generalized eigenvalue problem Ax=λBx, by backward transformation on the computed eigenvectors given by nag_ztgevc (f08yxc). It is necessary to call this function only if the optional balancing function nag_zggbal (f08wvc) was previously called to balance the matrix pair A,B.

2  Specification

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

3  Description

If the matrix pair has been previously balanced using the function nag_zggbal (f08wvc) then nag_zggbak (f08wwc) backtransforms the eigenvector solution given by nag_ztgevc (f08yxc). This is usually the sixth and last step in the solution of the generalized eigenvalue problem.
For a description of balancing, see the document for nag_zggbal (f08wvc).

4  References

Ward R C (1981) Balancing the generalized eigenvalue problem SIAM J. Sci. Stat. Comp. 2 141–152

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: specifies the backtransformation step required.
job=Nag_DoNothing
No transformations are done.
job=Nag_Permute
Only do backward transformations based on permutations.
job=Nag_Scale
Only do backward transformations based on scaling.
job=Nag_DoBoth
Do backward transformations for both permutations and scaling.
Note:  this must be identical to the argument job as supplied to nag_zggbal (f08wvc).
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 order of the matrices A and B of the generalized eigenvalue problem.
Constraint: n0.
5:     iloIntegerInput
6:     ihiIntegerInput
On entry: ilo and ihi as determined by a previous call to nag_zggbal (f08wvc).
Constraints:
  • if n>0, 1 ilo ihi n ;
  • if n=0, ilo=1 and ihi=0.
7:     lscale[dim]const doubleInput
Note: the dimension, dim, of the array lscale must be at least max1,n.
On entry: details of the permutations and scaling factors applied to the left side of the matrices A and B, as returned by a previous call to nag_zggbal (f08wvc).
8:     rscale[dim]const doubleInput
Note: the dimension, dim, of the array rscale must be at least max1,n.
On entry: details of the permutations and scaling factors applied to the right side of the matrices A and B, as returned by a previous call to nag_zggbal (f08wvc).
9:     mIntegerInput
On entry: m, the required number of left or right eigenvectors.
Constraint: 0mn.
10:   v[dim]ComplexInput/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 right or left eigenvectors, as returned by nag_zggbal (f08wvc).
On exit: the transformed right or left eigenvectors.
11:   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.
12:   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, n=value.
Constraint: n0.
On entry, pdv=value.
Constraint: pdv>0.
NE_INT_2
On entry, m=value and n=value.
Constraint: 0mn.
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 number of operations is proportional to n2.
The real analogue of this function is nag_dggbak (f08wjc).

9  Example

See Section 9 in nag_zhgeqz (f08xsc) and nag_ztgevc (f08yxc).

nag_zggbak (f08wwc) (PDF version)
f08 Chapter Contents
f08 Chapter Introduction
NAG C Library Manual

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