dtgexc.f (3) Linux Manual Page

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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