.TH "trexc" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
trexc \- trexc: reorder Schur form
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBctrexc\fP (compq, n, t, ldt, q, ldq, ifst, ilst, info)"
.br
.RI "\fBCTREXC\fP "
.ti -1c
.RI "subroutine \fBdtrexc\fP (compq, n, t, ldt, q, ldq, ifst, ilst, work, info)"
.br
.RI "\fBDTREXC\fP "
.ti -1c
.RI "subroutine \fBstrexc\fP (compq, n, t, ldt, q, ldq, ifst, ilst, work, info)"
.br
.RI "\fBSTREXC\fP "
.ti -1c
.RI "subroutine \fBztrexc\fP (compq, n, t, ldt, q, ldq, ifst, ilst, info)"
.br
.RI "\fBZTREXC\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine ctrexc (character compq, integer n, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, integer info)"

.PP
\fBCTREXC\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CTREXC reorders the Schur factorization of a complex matrix
!> A = Q*T*Q**H, so that the diagonal element of T with row index IFST
!> is moved to row ILST\&.
!>
!> The Schur form T is reordered by a unitary similarity transformation
!> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
!> postmultiplying it with Z\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fICOMPQ\fP 
.PP
.nf
!>          COMPQ is CHARACTER*1
!>          = 'V':  update the matrix Q of Schur vectors;
!>          = 'N':  do not update Q\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix T\&. N >= 0\&.
!>          If N == 0 arguments ILST and IFST may be any value\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is COMPLEX array, dimension (LDT,N)
!>          On entry, the upper triangular matrix T\&.
!>          On exit, the reordered upper triangular matrix\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&. LDT >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is COMPLEX array, dimension (LDQ,N)
!>          On entry, if COMPQ = 'V', the matrix Q of Schur vectors\&.
!>          On exit, if COMPQ = 'V', Q has been postmultiplied by the
!>          unitary transformation matrix Z which reorders T\&.
!>          If COMPQ = 'N', Q is not referenced\&.
!> 
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
!>          LDQ is INTEGER
!>          The leading dimension of the array Q\&.  LDQ >= 1, and if
!>          COMPQ = 'V', LDQ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIIFST\fP 
.PP
.nf
!>          IFST is INTEGER
!> 
.fi
.PP
.br
\fIILST\fP 
.PP
.nf
!>          ILST is INTEGER
!>
!>          Specify the reordering of the diagonal elements of T:
!>          The element with row index IFST is moved to row ILST by a
!>          sequence of transpositions between adjacent elements\&.
!>          1 <= IFST <= N; 1 <= ILST <= 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 \fB125\fP of file \fBctrexc\&.f\fP\&.
.SS "subroutine dtrexc (character compq, integer n, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, double precision, dimension( * ) work, integer info)"

.PP
\fBDTREXC\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DTREXC reorders the real Schur factorization of a real matrix
!> A = Q*T*Q**T, so that the diagonal block of T with row index IFST is
!> moved to row ILST\&.
!>
!> The real Schur form T is reordered by an orthogonal similarity
!> transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors
!> is updated by postmultiplying it with Z\&.
!>
!> T must be in Schur canonical form (as returned by DHSEQR), that is,
!> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
!> 2-by-2 diagonal block has its diagonal elements equal and its
!> off-diagonal elements of opposite sign\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fICOMPQ\fP 
.PP
.nf
!>          COMPQ is CHARACTER*1
!>          = 'V':  update the matrix Q of Schur vectors;
!>          = 'N':  do not update Q\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix T\&. N >= 0\&.
!>          If N == 0 arguments ILST and IFST may be any value\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is DOUBLE PRECISION array, dimension (LDT,N)
!>          On entry, the upper quasi-triangular matrix T, in Schur
!>          Schur canonical form\&.
!>          On exit, the reordered upper quasi-triangular matrix, again
!>          in Schur canonical form\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&. LDT >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
!>          On entry, if COMPQ = 'V', the matrix Q of Schur vectors\&.
!>          On exit, if COMPQ = 'V', Q has been postmultiplied by the
!>          orthogonal transformation matrix Z which reorders T\&.
!>          If COMPQ = 'N', Q is not referenced\&.
!> 
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
!>          LDQ is INTEGER
!>          The leading dimension of the array Q\&.  LDQ >= 1, and if
!>          COMPQ = 'V', LDQ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIIFST\fP 
.PP
.nf
!>          IFST is INTEGER
!> 
.fi
.PP
.br
\fIILST\fP 
.PP
.nf
!>          ILST is INTEGER
!>
!>          Specify the reordering of the diagonal blocks of T\&.
!>          The block with row index IFST is moved to row ILST, by a
!>          sequence of transpositions between adjacent blocks\&.
!>          On exit, if IFST pointed on entry to the second row of a
!>          2-by-2 block, it is changed to point to the first row; ILST
!>          always points to the first row of the block in its final
!>          position (which may differ from its input value by +1 or -1)\&.
!>          1 <= IFST <= N; 1 <= ILST <= N\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (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
!>          = 1:  two adjacent blocks were too close to swap (the problem
!>                is very ill-conditioned); T may have been partially
!>                reordered, and ILST points to the first row of the
!>                current position of the block being moved\&.
!> 
.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 \fB146\fP of file \fBdtrexc\&.f\fP\&.
.SS "subroutine strexc (character compq, integer n, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, real, dimension( * ) work, integer info)"

.PP
\fBSTREXC\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> STREXC reorders the real Schur factorization of a real matrix
!> A = Q*T*Q**T, so that the diagonal block of T with row index IFST is
!> moved to row ILST\&.
!>
!> The real Schur form T is reordered by an orthogonal similarity
!> transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors
!> is updated by postmultiplying it with Z\&.
!>
!> T must be in Schur canonical form (as returned by SHSEQR), that is,
!> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
!> 2-by-2 diagonal block has its diagonal elements equal and its
!> off-diagonal elements of opposite sign\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fICOMPQ\fP 
.PP
.nf
!>          COMPQ is CHARACTER*1
!>          = 'V':  update the matrix Q of Schur vectors;
!>          = 'N':  do not update Q\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix T\&. N >= 0\&.
!>          If N == 0 arguments ILST and IFST may be any value\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is REAL array, dimension (LDT,N)
!>          On entry, the upper quasi-triangular matrix T, in Schur
!>          Schur canonical form\&.
!>          On exit, the reordered upper quasi-triangular matrix, again
!>          in Schur canonical form\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&. LDT >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is REAL array, dimension (LDQ,N)
!>          On entry, if COMPQ = 'V', the matrix Q of Schur vectors\&.
!>          On exit, if COMPQ = 'V', Q has been postmultiplied by the
!>          orthogonal transformation matrix Z which reorders T\&.
!>          If COMPQ = 'N', Q is not referenced\&.
!> 
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
!>          LDQ is INTEGER
!>          The leading dimension of the array Q\&.  LDQ >= 1, and if
!>          COMPQ = 'V', LDQ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIIFST\fP 
.PP
.nf
!>          IFST is INTEGER
!> 
.fi
.PP
.br
\fIILST\fP 
.PP
.nf
!>          ILST is INTEGER
!>
!>          Specify the reordering of the diagonal blocks of T\&.
!>          The block with row index IFST is moved to row ILST, by a
!>          sequence of transpositions between adjacent blocks\&.
!>          On exit, if IFST pointed on entry to the second row of a
!>          2-by-2 block, it is changed to point to the first row; ILST
!>          always points to the first row of the block in its final
!>          position (which may differ from its input value by +1 or -1)\&.
!>          1 <= IFST <= N; 1 <= ILST <= N\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (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
!>          = 1:  two adjacent blocks were too close to swap (the problem
!>                is very ill-conditioned); T may have been partially
!>                reordered, and ILST points to the first row of the
!>                current position of the block being moved\&.
!> 
.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 \fB146\fP of file \fBstrexc\&.f\fP\&.
.SS "subroutine ztrexc (character compq, integer n, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, integer info)"

.PP
\fBZTREXC\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZTREXC reorders the Schur factorization of a complex matrix
!> A = Q*T*Q**H, so that the diagonal element of T with row index IFST
!> is moved to row ILST\&.
!>
!> The Schur form T is reordered by a unitary similarity transformation
!> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
!> postmultiplying it with Z\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fICOMPQ\fP 
.PP
.nf
!>          COMPQ is CHARACTER*1
!>          = 'V':  update the matrix Q of Schur vectors;
!>          = 'N':  do not update Q\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix T\&. N >= 0\&.
!>          If N == 0 arguments ILST and IFST may be any value\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is COMPLEX*16 array, dimension (LDT,N)
!>          On entry, the upper triangular matrix T\&.
!>          On exit, the reordered upper triangular matrix\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&. LDT >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
!>          Q is COMPLEX*16 array, dimension (LDQ,N)
!>          On entry, if COMPQ = 'V', the matrix Q of Schur vectors\&.
!>          On exit, if COMPQ = 'V', Q has been postmultiplied by the
!>          unitary transformation matrix Z which reorders T\&.
!>          If COMPQ = 'N', Q is not referenced\&.
!> 
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
!>          LDQ is INTEGER
!>          The leading dimension of the array Q\&.  LDQ >= 1, and if
!>          COMPQ = 'V', LDQ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIIFST\fP 
.PP
.nf
!>          IFST is INTEGER
!> 
.fi
.PP
.br
\fIILST\fP 
.PP
.nf
!>          ILST is INTEGER
!>
!>          Specify the reordering of the diagonal elements of T:
!>          The element with row index IFST is moved to row ILST by a
!>          sequence of transpositions between adjacent elements\&.
!>          1 <= IFST <= N; 1 <= ILST <= 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 \fB125\fP of file \fBztrexc\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.