?ggbak

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?ggbak

Forms the right or left eigenvectors of a generalized eigenvalue problem.

Syntax

lapack_int LAPACKE_sggbak(int matrix_layout, char job, char side, lapack_int n,
                          lapack_int ilo, lapack_int ihi, const float *lscale,
                          const float *rscale, lapack_int m, float *v, lapack_int ldv);

lapack_int LAPACKE_dggbak(int matrix_layout, char job, char side, lapack_int n,
                          lapack_int ilo, lapack_int ihi, const double *lscale,
                          const double *rscale, lapack_int m, double *v, lapack_int ldv);

lapack_int LAPACKE_cggbak(int matrix_layout, char job, char side, lapack_int n,
                          lapack_int ilo, lapack_int ihi, const float *lscale,
                          const float *rscale, lapack_int m, lapack_complex_float *v,
                          lapack_int ldv);

lapack_int LAPACKE_zggbak(int matrix_layout, char job, char side, lapack_int n,
                          lapack_int ilo, lapack_int ihi, const double *lscale,
                          const double *rscale, lapack_int m, lapack_complex_double *v,
                          lapack_int ldv);

Include Files

mkl.h

Description

The routine forms the right or left eigenvectors of a real/complex generalized eigenvalue problem

A*x = λ*B*x

by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ggbal .

Input Parameters

matrix_layout: Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).

job

Specifies the type of backward transformation required. Must be ‘N’ , ‘P’ , ‘S’ , or ‘B’ .

If job = 'N' , then no operations are done; return. If job = 'P' , then do backward transformation for permutation only. If job = 'S' , then do backward transformation for scaling only. If job = 'B' , then do backward transformation for both permutation and scaling. This argument must be the same as the argument job supplied to ?ggbal .

side

Must be ‘L’ or ‘R’ .

If side = 'L' , then v contains left eigenvectors. If side = 'R' , then v contains right eigenvectors.

n

The number of rows of the matrix V ( n ≥ 0).

ilo , ihi

The integers ilo and ihi determined by ?gebal . Constraint:

If n > 0 , then 1 ≤ ilo ≤ ihi ≤ n ; if n = 0 , then ilo = 1 and ihi = 0 .

lscale , rscale: REAL for single precision flavors DOUBLE PRECISION for double precision flavors. Arrays, size at least max(1, n ). The array lscale contains details of the permutations and/or scaling factors applied to the left side of A and B , as returned by ?ggbal . The array rscale contains details of the permutations and/or scaling factors applied to the right side of A and B , as returned by ?ggbal .

m

The number of columns of the matrix V

( m ≥ 0).

v

REAL for sggbak DOUBLE PRECISION for dggbak COMPLEX for cggbak DOUBLE COMPLEX for zggbak .

Array v (size max(1, ldv * m ) for column major layout and max(1, ldv * n ) for row major layout) . Contains the matrix of right or left eigenvectors to be transformed, as returned by tgevc .

The second dimension of v must be at least max(1, m ).

ldv

The leading dimension of v ; at least max(1, n ) for column major layout and at least max(1, m ) for row major layout .

Output Parameters

v: Overwritten by the transformed eigenvectors

Return Values

This function returns a value info .

If info=0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?ggbak

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes