.TH "gebak" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME gebak \- gebak: back-transform eigvec .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcgebak\fP (job, side, n, ilo, ihi, scale, m, v, ldv, info)" .br .RI "\fBCGEBAK\fP " .ti -1c .RI "subroutine \fBdgebak\fP (job, side, n, ilo, ihi, scale, m, v, ldv, info)" .br .RI "\fBDGEBAK\fP " .ti -1c .RI "subroutine \fBsgebak\fP (job, side, n, ilo, ihi, scale, m, v, ldv, info)" .br .RI "\fBSGEBAK\fP " .ti -1c .RI "subroutine \fBzgebak\fP (job, side, n, ilo, ihi, scale, m, v, ldv, info)" .br .RI "\fBZGEBAK\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cgebak (character job, character side, integer n, integer ilo, integer ihi, real, dimension( * ) scale, integer m, complex, dimension( ldv, * ) v, integer ldv, integer info)" .PP \fBCGEBAK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CGEBAK forms the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by CGEBAL\&. .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 CGEBAL\&. .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 CGEBAL\&. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0\&. .fi .PP .br \fISCALE\fP .PP .nf SCALE is REAL array, dimension (N) Details of the permutation and scaling factors, as returned by CGEBAL\&. .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 CHSEIN or CTREVC\&. On exit, V is overwritten by the transformed eigenvectors\&. .fi .PP .br \fILDV\fP .PP .nf LDV is INTEGER The leading dimension of the array 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 .SS "subroutine dgebak (character job, character side, integer n, integer ilo, integer ihi, double precision, dimension( * ) scale, integer m, double precision, dimension( ldv, * ) v, integer ldv, integer info)" .PP \fBDGEBAK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DGEBAK forms the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL\&. .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 DGEBAL\&. .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 DGEBAL\&. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0\&. .fi .PP .br \fISCALE\fP .PP .nf SCALE is DOUBLE PRECISION array, dimension (N) Details of the permutation and scaling factors, as returned by DGEBAL\&. .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 DHSEIN or DTREVC\&. On exit, V is overwritten by the transformed eigenvectors\&. .fi .PP .br \fILDV\fP .PP .nf LDV is INTEGER The leading dimension of the array 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 .SS "subroutine sgebak (character job, character side, integer n, integer ilo, integer ihi, real, dimension( * ) scale, integer m, real, dimension( ldv, * ) v, integer ldv, integer info)" .PP \fBSGEBAK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SGEBAK forms the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by SGEBAL\&. .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 SGEBAL\&. .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 SGEBAL\&. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0\&. .fi .PP .br \fISCALE\fP .PP .nf SCALE is REAL array, dimension (N) Details of the permutation and scaling factors, as returned by SGEBAL\&. .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 SHSEIN or STREVC\&. On exit, V is overwritten by the transformed eigenvectors\&. .fi .PP .br \fILDV\fP .PP .nf LDV is INTEGER The leading dimension of the array 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 .SS "subroutine zgebak (character job, character side, integer n, integer ilo, integer ihi, double precision, dimension( * ) scale, integer m, complex*16, dimension( ldv, * ) v, integer ldv, integer info)" .PP \fBZGEBAK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZGEBAK forms the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL\&. .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 ZGEBAL\&. .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 ZGEBAL\&. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0\&. .fi .PP .br \fISCALE\fP .PP .nf SCALE is DOUBLE PRECISION array, dimension (N) Details of the permutation and scaling factors, as returned by ZGEBAL\&. .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 ZHSEIN or ZTREVC\&. On exit, V is overwritten by the transformed eigenvectors\&. .fi .PP .br \fILDV\fP .PP .nf LDV is INTEGER The leading dimension of the array 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 .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.