Man page - tgex2(3)

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Manual

tgex2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctgex2 (logical wantq, logical wantz, integer n, complex,dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b,integer ldb, complex, dimension( ldq, * ) q, integer ldq, complex,dimension( ldz, * ) z, integer ldz, integer j1, integer info)
subroutine dtgex2 (logical wantq, logical wantz, integer n, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( ldb, * ) b, integer ldb, double precision, dimension( ldq, *) q, integer ldq, double precision, dimension( ldz, * ) z, integer ldz,integer j1, integer n1, integer n2, double precision, dimension( * )work, integer lwork, integer info)
subroutine stgex2 (logical wantq, logical wantz, integer n, real,dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,integer ldb, real, dimension( ldq, * ) q, integer ldq, real, dimension(ldz, * ) z, integer ldz, integer j1, integer n1, integer n2, real,dimension( * ) work, integer lwork, integer info)
subroutine ztgex2 (logical wantq, logical wantz, integer n, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,integer ldb, complex*16, dimension( ldq, * ) q, integer ldq,complex*16, dimension( ldz, * ) z, integer ldz, integer j1, integerinfo)
Author

NAME

tgex2 - tgex2: reorder generalized Schur form

SYNOPSIS

Functions

subroutine ctgex2 (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, j1, info)
CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.
subroutine dtgex2 (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, j1, n1, n2, work, lwork, info)
DTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.
subroutine stgex2 (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, j1, n1, n2, work, lwork, info)
STGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.
subroutine ztgex2 (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, j1, info)
ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

Detailed Description

Function Documentation

subroutine ctgex2 (logical wantq, logical wantz, integer n, complex,dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b,integer ldb, complex, dimension( ldq, * ) q, integer ldq, complex,dimension( ldz, * ) z, integer ldz, integer j1, integer info)

CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

Purpose:

CTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
in an upper triangular matrix pair (A, B) by an unitary equivalence
transformation.

(A, B) must be in generalized Schur canonical form, that is, A and
B are both upper triangular.

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

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

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 COMPLEX array, dimension (LDA,N)
On entry, the matrix A in the pair (A, B).
On exit, the updated matrix A.

LDA

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

B

B is COMPLEX array, dimension (LDB,N)
On entry, the matrix B in the pair (A, B).
On exit, the updated matrix B.

LDB

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

Q

Q is COMPLEX array, dimension (LDQ,N)
If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,
the updated matrix Q.
Not referenced if WANTQ = .FALSE..

LDQ

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

Z

Z is COMPLEX array, dimension (LDZ,N)
If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit,
the updated matrix Z.
Not referenced if WANTZ = .FALSE..

LDZ

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

J1

J1 is INTEGER
The index to the first block (A11, B11).

INFO

INFO is INTEGER
=0: Successful exit.
=1: The transformed matrix pair (A, B) would be too far
from generalized Schur form; the problem is ill-
conditioned.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

In the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the internal logical parameter WANDS to .FALSE.. See ref. [2] for details.

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.
[2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified Eigenvalues of a Regular Matrix Pair (A, B) and Condition Estimation: Theory, Algorithms and Software, Report UMINF-94.04, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. To appear in Numerical Algorithms, 1996.

subroutine dtgex2 (logical wantq, logical wantz, integer n, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( ldb, * ) b, integer ldb, double precision, dimension( ldq, *) q, integer ldq, double precision, dimension( ldz, * ) z, integer ldz,integer j1, integer n1, integer n2, double precision, dimension( * )work, integer lwork, integer info)

DTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.

Purpose:

DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
(A, B) by an orthogonal equivalence transformation.

(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, dimensions (LDA,N)
On entry, the matrix A in the pair (A, B).
On exit, the updated matrix A.

LDA

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

B

B is DOUBLE PRECISION array, dimensions (LDB,N)
On entry, the matrix B in the pair (A, B).
On exit, the updated matrix 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.
Not referenced if WANTQ = .FALSE..

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.
Not referenced if WANTZ = .FALSE..

LDZ

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

J1

J1 is INTEGER
The index to the first block (A11, B11). 1 <= J1 <= N.

N1

N1 is INTEGER
The order of the first block (A11, B11). N1 = 0, 1 or 2.

N2

N2 is INTEGER
The order of the second block (A22, B22). N2 = 0, 1 or 2.

WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).

LWORK

LWORK is INTEGER
The dimension of the array WORK.
LWORK >= MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 )

INFO

INFO is INTEGER
=0: Successful exit
>0: If INFO = 1, the transformed matrix (A, B) would be
too far from generalized Schur form; the blocks are
not swapped and (A, B) and (Q, Z) are unchanged.
The problem of swapping is too ill-conditioned.
<0: If INFO = -16: LWORK is too small. Appropriate value
for LWORK is returned in WORK(1).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

In the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the internal logical parameter WANDS to .FALSE.. See ref. [2] for details.

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.

[2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
Eigenvalues of a Regular Matrix Pair (A, B) and Condition
Estimation: Theory, Algorithms and Software,
Report UMINF - 94.04, Department of Computing Science, Umea
University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working
Note 87. To appear in Numerical Algorithms, 1996.

subroutine stgex2 (logical wantq, logical wantz, integer n, real,dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,integer ldb, real, dimension( ldq, * ) q, integer ldq, real, dimension(ldz, * ) z, integer ldz, integer j1, integer n1, integer n2, real,dimension( * ) work, integer lwork, integer info)

STGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation.

Purpose:

STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
(A, B) by an orthogonal equivalence transformation.

(A, B) must be in generalized real Schur canonical form (as returned
by SGGES), 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 REAL array, dimension (LDA,N)
On entry, the matrix A in the pair (A, B).
On exit, the updated matrix A.

LDA

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

B

B is REAL array, dimension (LDB,N)
On entry, the matrix B in the pair (A, B).
On exit, the updated matrix B.

LDB

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

Q

Q is REAL array, dimension (LDQ,N)
On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
On exit, the updated matrix Q.
Not referenced if WANTQ = .FALSE..

LDQ

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

Z

Z is REAL array, dimension (LDZ,N)
On entry, if WANTZ =.TRUE., the orthogonal matrix Z.
On exit, the updated matrix Z.
Not referenced if WANTZ = .FALSE..

LDZ

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

J1

J1 is INTEGER
The index to the first block (A11, B11). 1 <= J1 <= N.

N1

N1 is INTEGER
The order of the first block (A11, B11). N1 = 0, 1 or 2.

N2

N2 is INTEGER
The order of the second block (A22, B22). N2 = 0, 1 or 2.

WORK

WORK is REAL array, dimension (MAX(1,LWORK)).

LWORK

LWORK is INTEGER
The dimension of the array WORK.
LWORK >= MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 )

INFO

INFO is INTEGER
=0: Successful exit
>0: If INFO = 1, the transformed matrix (A, B) would be
too far from generalized Schur form; the blocks are
not swapped and (A, B) and (Q, Z) are unchanged.
The problem of swapping is too ill-conditioned.
<0: If INFO = -16: LWORK is too small. Appropriate value
for LWORK is returned in WORK(1).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

In the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the internal logical parameter WANDS to .FALSE.. See ref. [2] for details.

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.

[2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
Eigenvalues of a Regular Matrix Pair (A, B) and Condition
Estimation: Theory, Algorithms and Software,
Report UMINF - 94.04, Department of Computing Science, Umea
University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working
Note 87. To appear in Numerical Algorithms, 1996.

subroutine ztgex2 (logical wantq, logical wantz, integer n, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,integer ldb, complex*16, dimension( ldq, * ) q, integer ldq,complex*16, dimension( ldz, * ) z, integer ldz, integer j1, integerinfo)

ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

Purpose:

ZTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
in an upper triangular matrix pair (A, B) by an unitary equivalence
transformation.

(A, B) must be in generalized Schur canonical form, that is, A and
B are both upper triangular.

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

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

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 COMPLEX*16 array, dimensions (LDA,N)
On entry, the matrix A in the pair (A, B).
On exit, the updated matrix A.

LDA

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

B

B is COMPLEX*16 array, dimensions (LDB,N)
On entry, the matrix B in the pair (A, B).
On exit, the updated matrix B.

LDB

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

Q

Q is COMPLEX*16 array, dimension (LDQ,N)
If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,
the updated matrix Q.
Not referenced if WANTQ = .FALSE..

LDQ

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

Z

Z is COMPLEX*16 array, dimension (LDZ,N)
If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit,
the updated matrix Z.
Not referenced if WANTZ = .FALSE..

LDZ

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

J1

J1 is INTEGER
The index to the first block (A11, B11).

INFO

INFO is INTEGER
=0: Successful exit.
=1: The transformed matrix pair (A, B) would be too far
from generalized Schur form; the problem is ill-
conditioned.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

In the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the internal logical parameter WANDS to .FALSE.. See ref. [2] for details.

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.
[2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified Eigenvalues of a Regular Matrix Pair (A, B) and Condition Estimation: Theory, Algorithms and Software, Report UMINF-94.04, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. To appear in Numerical Algorithms, 1996.

Author

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