.TH "ggbak" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME ggbak \- ggbak: back-transform eigvec .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcggbak\fP (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)" .br .RI "\fBCGGBAK\fP " .ti -1c .RI "subroutine \fBdggbak\fP (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)" .br .RI "\fBDGGBAK\fP " .ti -1c .RI "subroutine \fBsggbak\fP (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)" .br .RI "\fBSGGBAK\fP " .ti -1c .RI "subroutine \fBzggbak\fP (job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)" .br .RI "\fBZGGBAK\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cggbak (character job, character side, integer n, integer ilo, integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale, integer m, complex, dimension( ldv, * ) v, integer ldv, integer info)" .PP \fBCGGBAK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CGGBAK forms the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by CGGBAL\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOB\fP .PP .nf JOB is CHARACTER*1 Specifies the type of backward transformation required: = 'N': do nothing, return immediately; = 'P': do backward transformation for permutation only; = 'S': do backward transformation for scaling only; = 'B': do backward transformations for both permutation and scaling\&. JOB must be the same as the argument JOB supplied to CGGBAL\&. .fi .PP .br \fISIDE\fP .PP .nf SIDE is CHARACTER*1 = 'R': V contains right eigenvectors; = 'L': V contains left eigenvectors\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of rows of the matrix V\&. N >= 0\&. .fi .PP .br \fIILO\fP .PP .nf ILO is INTEGER .fi .PP .br \fIIHI\fP .PP .nf IHI is INTEGER The integers ILO and IHI determined by CGGBAL\&. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0\&. .fi .PP .br \fILSCALE\fP .PP .nf LSCALE is REAL array, dimension (N) Details of the permutations and/or scaling factors applied to the left side of A and B, as returned by CGGBAL\&. .fi .PP .br \fIRSCALE\fP .PP .nf RSCALE is REAL array, dimension (N) Details of the permutations and/or scaling factors applied to the right side of A and B, as returned by CGGBAL\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of columns of the matrix V\&. M >= 0\&. .fi .PP .br \fIV\fP .PP .nf V is COMPLEX array, dimension (LDV,M) On entry, the matrix of right or left eigenvectors to be transformed, as returned by CTGEVC\&. On exit, V is overwritten by the transformed eigenvectors\&. .fi .PP .br \fILDV\fP .PP .nf LDV is INTEGER The leading dimension of the matrix V\&. LDV >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit\&. < 0: if INFO = -i, the i-th argument had an illegal value\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf See R\&.C\&. Ward, Balancing the generalized eigenvalue problem, SIAM J\&. Sci\&. Stat\&. Comp\&. 2 (1981), 141-152\&. .fi .PP .RE .PP .SS "subroutine dggbak (character job, character side, integer n, integer ilo, integer ihi, double precision, dimension( * ) lscale, double precision, dimension( * ) rscale, integer m, double precision, dimension( ldv, * ) v, integer ldv, integer info)" .PP \fBDGGBAK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DGGBAK forms the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOB\fP .PP .nf JOB is CHARACTER*1 Specifies the type of backward transformation required: = 'N': do nothing, return immediately; = 'P': do backward transformation for permutation only; = 'S': do backward transformation for scaling only; = 'B': do backward transformations for both permutation and scaling\&. JOB must be the same as the argument JOB supplied to DGGBAL\&. .fi .PP .br \fISIDE\fP .PP .nf SIDE is CHARACTER*1 = 'R': V contains right eigenvectors; = 'L': V contains left eigenvectors\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of rows of the matrix V\&. N >= 0\&. .fi .PP .br \fIILO\fP .PP .nf ILO is INTEGER .fi .PP .br \fIIHI\fP .PP .nf IHI is INTEGER The integers ILO and IHI determined by DGGBAL\&. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0\&. .fi .PP .br \fILSCALE\fP .PP .nf LSCALE is DOUBLE PRECISION array, dimension (N) Details of the permutations and/or scaling factors applied to the left side of A and B, as returned by DGGBAL\&. .fi .PP .br \fIRSCALE\fP .PP .nf RSCALE is DOUBLE PRECISION array, dimension (N) Details of the permutations and/or scaling factors applied to the right side of A and B, as returned by DGGBAL\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of columns of the matrix V\&. M >= 0\&. .fi .PP .br \fIV\fP .PP .nf V is DOUBLE PRECISION array, dimension (LDV,M) On entry, the matrix of right or left eigenvectors to be transformed, as returned by DTGEVC\&. On exit, V is overwritten by the transformed eigenvectors\&. .fi .PP .br \fILDV\fP .PP .nf LDV is INTEGER The leading dimension of the matrix V\&. LDV >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit\&. < 0: if INFO = -i, the i-th argument had an illegal value\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf See R\&.C\&. Ward, Balancing the generalized eigenvalue problem, SIAM J\&. Sci\&. Stat\&. Comp\&. 2 (1981), 141-152\&. .fi .PP .RE .PP .SS "subroutine sggbak (character job, character side, integer n, integer ilo, integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale, integer m, real, dimension( ldv, * ) v, integer ldv, integer info)" .PP \fBSGGBAK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SGGBAK forms the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOB\fP .PP .nf JOB is CHARACTER*1 Specifies the type of backward transformation required: = 'N': do nothing, return immediately; = 'P': do backward transformation for permutation only; = 'S': do backward transformation for scaling only; = 'B': do backward transformations for both permutation and scaling\&. JOB must be the same as the argument JOB supplied to SGGBAL\&. .fi .PP .br \fISIDE\fP .PP .nf SIDE is CHARACTER*1 = 'R': V contains right eigenvectors; = 'L': V contains left eigenvectors\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of rows of the matrix V\&. N >= 0\&. .fi .PP .br \fIILO\fP .PP .nf ILO is INTEGER .fi .PP .br \fIIHI\fP .PP .nf IHI is INTEGER The integers ILO and IHI determined by SGGBAL\&. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0\&. .fi .PP .br \fILSCALE\fP .PP .nf LSCALE is REAL array, dimension (N) Details of the permutations and/or scaling factors applied to the left side of A and B, as returned by SGGBAL\&. .fi .PP .br \fIRSCALE\fP .PP .nf RSCALE is REAL array, dimension (N) Details of the permutations and/or scaling factors applied to the right side of A and B, as returned by SGGBAL\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of columns of the matrix V\&. M >= 0\&. .fi .PP .br \fIV\fP .PP .nf V is REAL array, dimension (LDV,M) On entry, the matrix of right or left eigenvectors to be transformed, as returned by STGEVC\&. On exit, V is overwritten by the transformed eigenvectors\&. .fi .PP .br \fILDV\fP .PP .nf LDV is INTEGER The leading dimension of the matrix V\&. LDV >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit\&. < 0: if INFO = -i, the i-th argument had an illegal value\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf See R\&.C\&. Ward, Balancing the generalized eigenvalue problem, SIAM J\&. Sci\&. Stat\&. Comp\&. 2 (1981), 141-152\&. .fi .PP .RE .PP .SS "subroutine zggbak (character job, character side, integer n, integer ilo, integer ihi, double precision, dimension( * ) lscale, double precision, dimension( * ) rscale, integer m, complex*16, dimension( ldv, * ) v, integer ldv, integer info)" .PP \fBZGGBAK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZGGBAK forms the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ZGGBAL\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOB\fP .PP .nf JOB is CHARACTER*1 Specifies the type of backward transformation required: = 'N': do nothing, return immediately; = 'P': do backward transformation for permutation only; = 'S': do backward transformation for scaling only; = 'B': do backward transformations for both permutation and scaling\&. JOB must be the same as the argument JOB supplied to ZGGBAL\&. .fi .PP .br \fISIDE\fP .PP .nf SIDE is CHARACTER*1 = 'R': V contains right eigenvectors; = 'L': V contains left eigenvectors\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of rows of the matrix V\&. N >= 0\&. .fi .PP .br \fIILO\fP .PP .nf ILO is INTEGER .fi .PP .br \fIIHI\fP .PP .nf IHI is INTEGER The integers ILO and IHI determined by ZGGBAL\&. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0\&. .fi .PP .br \fILSCALE\fP .PP .nf LSCALE is DOUBLE PRECISION array, dimension (N) Details of the permutations and/or scaling factors applied to the left side of A and B, as returned by ZGGBAL\&. .fi .PP .br \fIRSCALE\fP .PP .nf RSCALE is DOUBLE PRECISION array, dimension (N) Details of the permutations and/or scaling factors applied to the right side of A and B, as returned by ZGGBAL\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of columns of the matrix V\&. M >= 0\&. .fi .PP .br \fIV\fP .PP .nf V is COMPLEX*16 array, dimension (LDV,M) On entry, the matrix of right or left eigenvectors to be transformed, as returned by ZTGEVC\&. On exit, V is overwritten by the transformed eigenvectors\&. .fi .PP .br \fILDV\fP .PP .nf LDV is INTEGER The leading dimension of the matrix V\&. LDV >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit\&. < 0: if INFO = -i, the i-th argument had an illegal value\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf See R\&.C\&. Ward, Balancing the generalized eigenvalue problem, SIAM J\&. Sci\&. Stat\&. Comp\&. 2 (1981), 141-152\&. .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.