ztrexc (l) - Linux Manuals

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

NAME

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

SYNOPSIS

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

    
CHARACTER COMPQ

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

    
COMPLEX*16 Q( LDQ, * ), T( LDT, * )

PURPOSE

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 postmultplying it with Z.

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) COMPLEX*16 array, dimension (LDT,N)
On entry, the upper triangular matrix T. On exit, the reordered upper triangular matrix.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= max(1,N).
Q (input/output) COMPLEX*16 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 unitary 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) INTEGER
ILST (input) 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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Pages related to ztrexc

  • ztrexc (3)
  • ztrevc (l) - computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
  • ztrcon (l) - estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
  • ztrmm (l) - performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = Aaq or op( A ) = conjg( Aaq )
  • ztrmv (l) - performs one of the matrix-vector operations x := A*x, or x := Aaq*x, or x := conjg( Aaq )*x,
  • ztrrfs (l) - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
  • ztrsen (l) - reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace
  • ztrsm (l) - solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,