.TH "gebak" 3 "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

.PP
Definition at line \fB129\fP of file \fBcgebak\&.f\fP\&.
.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

.PP
Definition at line \fB128\fP of file \fBdgebak\&.f\fP\&.
.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

.PP
Definition at line \fB128\fP of file \fBsgebak\&.f\fP\&.
.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

.PP
Definition at line \fB129\fP of file \fBzgebak\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.