NAG C Library Function Document

nag_dgebak (f08njc)


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


#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)


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:




1:     order Nag_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 How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     job Nag_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:     side Nag_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:     n IntegerInput
On entry: n, the number of rows of the matrix of eigenvectors.
Constraint: n0.
5:     ilo IntegerInput
6:     ihi IntegerInput
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:     m IntegerInput
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:   pdv IntegerInput
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:   fail NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

Error Indicators and Warnings

Dynamic memory allocation failed.
See Section in How to Use the NAG Library and its Documentation for further information.
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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.


The errors are negligible.

Parallelism and Performance

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 x06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

Further Comments

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


See Section 10 in nag_dgebal (f08nhc).