NAG Library Routine Document
F08NJF (DGEBAK) transforms eigenvectors of a balanced matrix to those of the original real nonsymmetric matrix.
||N, ILO, IHI, M, LDV, INFO
The routine may be called by its
F08NJF (DGEBAK) is intended to be used after a real nonsymmetric matrix
has been balanced by F08NHF (DGEBAL)
, and eigenvectors of the balanced matrix
have subsequently been computed.
For a description of balancing, see the document for F08NHF (DGEBAL)
. The balanced matrix
is obtained as
is a permutation matrix and
is a diagonal scaling matrix. This routine transforms left or right eigenvectors as follows:
- if is a right eigenvector of , is a right eigenvector of ;
- if is a left eigenvector of , is a left eigenvector of .
- 1: – CHARACTER(1)Input
: this must
be the same argument JOB
as supplied to F08NHF (DGEBAL)
, , or .
- 2: – CHARACTER(1)Input
: indicates whether left or right eigenvectors are to be transformed.
- The left eigenvectors are transformed.
- The right eigenvectors are transformed.
- 3: – INTEGERInput
On entry: , the number of rows of the matrix of eigenvectors.
- 4: – INTEGERInput
- 5: – INTEGERInput
: the values
, as returned by F08NHF (DGEBAL)
- if , ;
- if , and .
- 6: – REAL (KIND=nag_wp) arrayInput
the dimension of the array SCALE
must be at least
: details of the permutations and/or the scaling factors used to balance the original real nonsymmetric matrix, as returned by F08NHF (DGEBAL)
- 7: – INTEGERInput
On entry: , the number of columns of the matrix of eigenvectors.
- 8: – REAL (KIND=nag_wp) arrayInput/Output
the second dimension of the array V
must be at least
On entry: the matrix of left or right eigenvectors to be transformed.
On exit: the transformed eigenvectors.
- 9: – INTEGERInput
: the first dimension of the array V
as declared in the (sub)program from which F08NJF (DGEBAK) is called.
- 10: – INTEGEROutput
unless the routine detects an error (see Section 6
6 Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
The errors are negligible.
8 Parallelism and Performance
F08NJF (DGEBAK) 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 routine. Please also consult the Users' Note
for your implementation for any additional implementation-specific information.
The total number of floating-point operations is approximately proportional to .
The complex analogue of this routine is F08NWF (ZGEBAK)
See Section 10
in F08NHF (DGEBAL).