NAG CL Interface
f08nwc (zgebak)

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1 Purpose

f08nwc transforms eigenvectors of a balanced matrix to those of the original complex general matrix.

2 Specification

#include <nag.h>
void  f08nwc (Nag_OrderType order, Nag_JobType job, Nag_SideType side, Integer n, Integer ilo, Integer ihi, const double scale[], Integer m, Complex v[], Integer pdv, NagError *fail)
The function may be called by the names: f08nwc, nag_lapackeig_zgebak or nag_zgebak.

3 Description

f08nwc is intended to be used after a complex general matrix A has been balanced by f08nvc, and eigenvectors of the balanced matrix A22 have subsequently been computed.
For a description of balancing, see the document for f08nvc. 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: order Nag_OrderType Input
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 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2: job Nag_JobType Input
On entry: this must be the same argument job as supplied to f08nvc.
Constraint: job=Nag_DoNothing, Nag_Permute, Nag_Scale or Nag_DoBoth.
3: side Nag_SideType Input
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 Integer Input
On entry: n, the number of rows of the matrix of eigenvectors.
Constraint: n0.
5: ilo Integer Input
6: ihi Integer Input
On entry: the values ilo and ihi, as returned by f08nvc.
  • if n>0, 1 ilo ihi n ;
  • if n=0, ilo=1 and ihi=0.
7: scale[dim] const double Input
Note: the dimension, dim, of the array scale must be at least max(1,n).
On entry: details of the permutations and/or the scaling factors used to balance the original complex general matrix, as returned by f08nvc.
8: m Integer Input
On entry: m, the number of columns of the matrix of eigenvectors.
Constraint: m0.
9: v[dim] Complex Input/Output
Note: the dimension, dim, of the array v must be at least
  • max(1,pdv×m) when order=Nag_ColMajor;
  • max(1,n×pdv) when order=Nag_RowMajor.
The (i,j)th 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 Integer Input
On entry: the stride separating row or column elements (depending on the value of order) in the array v.
  • if order=Nag_ColMajor, pdv max(1,n) ;
  • if order=Nag_RowMajor, pdvmax(1,m).
11: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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: pdvmax(1,m).
On entry, pdv=value and n=value.
Constraint: pdv max(1,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 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

The errors are negligible.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f08nwc 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.

9 Further Comments

The total number of real floating-point operations is approximately proportional to nm.
The real analogue of this function is f08njc.

10 Example

See f08nvc.