dtgexc (3) - Linux Manuals

NAME

dtgexc.f -

SYNOPSIS

Functions/Subroutines

subroutine dtgexc (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, WORK, LWORK, INFO)
DTGEXC

Function/Subroutine Documentation

subroutine dtgexc (logicalWANTQ, logicalWANTZ, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldq, * )Q, integerLDQ, double precision, dimension( ldz, * )Z, integerLDZ, integerIFST, integerILST, double precision, dimension( * )WORK, integerLWORK, integerINFO)

DTGEXC

Purpose:

 DTGEXC reorders the generalized real Schur decomposition of a real
 matrix pair (A,B) using an orthogonal equivalence transformation

                (A, B) = Q * (A, B) * Z**T,

 so that the diagonal block of (A, B) with row index IFST is moved
 to row ILST.

 (A, B) must be in generalized real Schur canonical form (as returned
 by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
 diagonal blocks. B is upper triangular.

 Optionally, the matrices Q and Z of generalized Schur vectors are
 updated.

        Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
        Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T

 

Parameters:

WANTQ

          WANTQ is LOGICAL
          .TRUE. : update the left transformation matrix Q;
          .FALSE.: do not update Q.

WANTZ

          WANTZ is LOGICAL
          .TRUE. : update the right transformation matrix Z;
          .FALSE.: do not update Z.

N

          N is INTEGER
          The order of the matrices A and B. N >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the matrix A in generalized real Schur canonical
          form.
          On exit, the updated matrix A, again in generalized
          real Schur canonical form.

LDA

          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,N).

B

          B is DOUBLE PRECISION array, dimension (LDB,N)
          On entry, the matrix B in generalized real Schur canonical
          form (A,B).
          On exit, the updated matrix B, again in generalized
          real Schur canonical form (A,B).

LDB

          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).

Q

          Q is DOUBLE PRECISION array, dimension (LDQ,N)
          On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
          On exit, the updated matrix Q.
          If WANTQ = .FALSE., Q is not referenced.

LDQ

          LDQ is INTEGER
          The leading dimension of the array Q. LDQ >= 1.
          If WANTQ = .TRUE., LDQ >= N.

Z

          Z is DOUBLE PRECISION array, dimension (LDZ,N)
          On entry, if WANTZ = .TRUE., the orthogonal matrix Z.
          On exit, the updated matrix Z.
          If WANTZ = .FALSE., Z is not referenced.

LDZ

          LDZ is INTEGER
          The leading dimension of the array Z. LDZ >= 1.
          If WANTZ = .TRUE., LDZ >= N.

IFST

          IFST is INTEGER

ILST

          ILST is INTEGER
          Specify the reordering of the diagonal blocks of (A, B).
          The block with row index IFST is moved to row ILST, by a
          sequence of swapping 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, ILST <= N.

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

          INFO is INTEGER
           =0:  successful exit.
           <0:  if INFO = -i, the i-th argument had an illegal value.
           =1:  The transformed matrix pair (A, B) would be too far
                from generalized Schur form; the problem is ill-
                conditioned. (A, B) may have been partially reordered,
                and ILST points to the first row of the current
                position of the block being moved.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Contributors:

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

References:

  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
      M.S. Moonen et al (eds), Linear Algebra for Large Scale and
      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.

 

Definition at line 220 of file dtgexc.f.

Author

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