dtrexc (l) - Linux Manuals

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

NAME

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

SYNOPSIS

SUBROUTINE DTREXC(
COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO )

    
CHARACTER COMPQ

    
INTEGER IFST, ILST, INFO, LDQ, LDT, N

    
DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * )

PURPOSE

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.

ARGUMENTS

COMPQ (input) CHARACTER*1
= aqVaq: update the matrix Q of Schur vectors;
= aqNaq: do not update Q.
N (input) INTEGER
The order of the matrix T. N >= 0.
T (input/output) 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.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= max(1,N).
Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
On entry, if COMPQ = aqVaq, the matrix Q of Schur vectors. On exit, if COMPQ = aqVaq, Q has been postmultiplied by the orthogonal transformation matrix Z which reorders T. If COMPQ = aqNaq, Q is not referenced.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
IFST (input/output) INTEGER
ILST (input/output) 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.
WORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) 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.

Pages related to dtrexc

  • dtrexc (3)
  • dtrevc (l) - computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
  • dtrcon (l) - estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
  • dtrmm (l) - performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ),
  • dtrmv (l) - performs one of the matrix-vector operations x := A*x, or x := Aaq*x,
  • dtrrfs (l) - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
  • dtrsen (l) - reorders the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T,
  • dtrsm (l) - solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,