Man page - tgsy2(3)

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Manual

tgsy2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctgsy2 (character trans, integer ijob, integer m, integer n,complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, *) b, integer ldb, complex, dimension( ldc, * ) c, integer ldc, complex,dimension( ldd, * ) d, integer ldd, complex, dimension( lde, * ) e,integer lde, complex, dimension( ldf, * ) f, integer ldf, real scale,real rdsum, real rdscal, integer info)
subroutine dtgsy2 (character trans, integer ijob, integer m, integer n,double precision, dimension( lda, * ) a, integer lda, double precision,dimension( ldb, * ) b, integer ldb, double precision, dimension( ldc, *) c, integer ldc, double precision, dimension( ldd, * ) d, integer ldd,double precision, dimension( lde, * ) e, integer lde, double precision,dimension( ldf, * ) f, integer ldf, double precision scale, doubleprecision rdsum, double precision rdscal, integer, dimension( * )iwork, integer pq, integer info)
subroutine stgsy2 (character trans, integer ijob, integer m, integer n,real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,integer ldb, real, dimension( ldc, * ) c, integer ldc, real, dimension(ldd, * ) d, integer ldd, real, dimension( lde, * ) e, integer lde,real, dimension( ldf, * ) f, integer ldf, real scale, real rdsum, realrdscal, integer, dimension( * ) iwork, integer pq, integer info)
subroutine ztgsy2 (character trans, integer ijob, integer m, integer n,complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(ldb, * ) b, integer ldb, complex*16, dimension( ldc, * ) c, integerldc, complex*16, dimension( ldd, * ) d, integer ldd, complex*16,dimension( lde, * ) e, integer lde, complex*16, dimension( ldf, * ) f,integer ldf, double precision scale, double precision rdsum, doubleprecision rdscal, integer info)
Author

NAME

tgsy2 - tgsy2: Sylvester equation panel (?)

SYNOPSIS

Functions

subroutine ctgsy2 (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, rdsum, rdscal, info)
CTGSY2 solves the generalized Sylvester equation (unblocked algorithm).
subroutine dtgsy2 (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, rdsum, rdscal, iwork, pq, info)
DTGSY2 solves the generalized Sylvester equation (unblocked algorithm).
subroutine stgsy2 (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, rdsum, rdscal, iwork, pq, info)
STGSY2 solves the generalized Sylvester equation (unblocked algorithm).
subroutine ztgsy2 (trans, ijob, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, scale, rdsum, rdscal, info)
ZTGSY2 solves the generalized Sylvester equation (unblocked algorithm).

Detailed Description

Function Documentation

subroutine ctgsy2 (character trans, integer ijob, integer m, integer n,complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, *) b, integer ldb, complex, dimension( ldc, * ) c, integer ldc, complex,dimension( ldd, * ) d, integer ldd, complex, dimension( lde, * ) e,integer lde, complex, dimension( ldf, * ) f, integer ldf, real scale,real rdsum, real rdscal, integer info)

CTGSY2 solves the generalized Sylvester equation (unblocked algorithm).

Purpose:

CTGSY2 solves the generalized Sylvester equation

A * R - L * B = scale * C (1)
D * R - L * E = scale * F

using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices,
(A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M,
N-by-N and M-by-N, respectively. A, B, D and E are upper triangular
(i.e., (A,D) and (B,E) in generalized Schur form).

The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output
scaling factor chosen to avoid overflow.

In matrix notation solving equation (1) corresponds to solve
Zx = scale * b, where Z is defined as

Z = [ kron(In, A) -kron(B**H, Im) ] (2)
[ kron(In, D) -kron(E**H, Im) ],

Ik is the identity matrix of size k and X**H is the transpose of X.
kron(X, Y) is the Kronecker product between the matrices X and Y.

If TRANS = ’C’, y in the conjugate transposed system Z**H*y = scale*b
is solved for, which is equivalent to solve for R and L in

A**H * R + D**H * L = scale * C (3)
R * B**H + L * E**H = scale * -F

This case is used to compute an estimate of Dif[(A, D), (B, E)] =
= sigma_min(Z) using reverse communication with CLACON.

CTGSY2 also (IJOB >= 1) contributes to the computation in CTGSYL
of an upper bound on the separation between to matrix pairs. Then
the input (A, D), (B, E) are sub-pencils of two matrix pairs in
CTGSYL.

Parameters

TRANS

TRANS is CHARACTER*1
= ’N’: solve the generalized Sylvester equation (1).
= ’T’: solve the ’transposed’ system (3).

IJOB

IJOB is INTEGER
Specifies what kind of functionality to be performed.
= 0: solve (1) only.
= 1: A contribution from this subsystem to a Frobenius
norm-based estimate of the separation between two matrix
pairs is computed. (look ahead strategy is used).
= 2: A contribution from this subsystem to a Frobenius
norm-based estimate of the separation between two matrix
pairs is computed. (SGECON on sub-systems is used.)
Not referenced if TRANS = ’T’.

M

M is INTEGER
On entry, M specifies the order of A and D, and the row
dimension of C, F, R and L.

N

N is INTEGER
On entry, N specifies the order of B and E, and the column
dimension of C, F, R and L.

A

A is COMPLEX array, dimension (LDA, M)
On entry, A contains an upper triangular matrix.

LDA

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

B

B is COMPLEX array, dimension (LDB, N)
On entry, B contains an upper triangular matrix.

LDB

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

C

C is COMPLEX array, dimension (LDC, N)
On entry, C contains the right-hand-side of the first matrix
equation in (1).
On exit, if IJOB = 0, C has been overwritten by the solution
R.

LDC

LDC is INTEGER
The leading dimension of the matrix C. LDC >= max(1, M).

D

D is COMPLEX array, dimension (LDD, M)
On entry, D contains an upper triangular matrix.

LDD

LDD is INTEGER
The leading dimension of the matrix D. LDD >= max(1, M).

E

E is COMPLEX array, dimension (LDE, N)
On entry, E contains an upper triangular matrix.

LDE

LDE is INTEGER
The leading dimension of the matrix E. LDE >= max(1, N).

F

F is COMPLEX array, dimension (LDF, N)
On entry, F contains the right-hand-side of the second matrix
equation in (1).
On exit, if IJOB = 0, F has been overwritten by the solution
L.

LDF

LDF is INTEGER
The leading dimension of the matrix F. LDF >= max(1, M).

SCALE

SCALE is REAL
On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions
R and L (C and F on entry) will hold the solutions to a
slightly perturbed system but the input matrices A, B, D and
E have not been changed. If SCALE = 0, R and L will hold the
solutions to the homogeneous system with C = F = 0.
Normally, SCALE = 1.

RDSUM

RDSUM is REAL
On entry, the sum of squares of computed contributions to
the Dif-estimate under computation by CTGSYL, where the
scaling factor RDSCAL (see below) has been factored out.
On exit, the corresponding sum of squares updated with the
contributions from the current sub-system.
If TRANS = ’T’ RDSUM is not touched.
NOTE: RDSUM only makes sense when CTGSY2 is called by
CTGSYL.

RDSCAL

RDSCAL is REAL
On entry, scaling factor used to prevent overflow in RDSUM.
On exit, RDSCAL is updated w.r.t. the current contributions
in RDSUM.
If TRANS = ’T’, RDSCAL is not touched.
NOTE: RDSCAL only makes sense when CTGSY2 is called by
CTGSYL.

INFO

INFO is INTEGER
On exit, if INFO is set to
=0: Successful exit
<0: If INFO = -i, input argument number i is illegal.
>0: The matrix pairs (A, D) and (B, E) have common or very
close eigenvalues.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

subroutine dtgsy2 (character trans, integer ijob, integer m, integer n,double precision, dimension( lda, * ) a, integer lda, double precision,dimension( ldb, * ) b, integer ldb, double precision, dimension( ldc, *) c, integer ldc, double precision, dimension( ldd, * ) d, integer ldd,double precision, dimension( lde, * ) e, integer lde, double precision,dimension( ldf, * ) f, integer ldf, double precision scale, doubleprecision rdsum, double precision rdscal, integer, dimension( * )iwork, integer pq, integer info)

DTGSY2 solves the generalized Sylvester equation (unblocked algorithm).

Purpose:

DTGSY2 solves the generalized Sylvester equation:

A * R - L * B = scale * C (1)
D * R - L * E = scale * F,

using Level 1 and 2 BLAS. where R and L are unknown M-by-N matrices,
(A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M,
N-by-N and M-by-N, respectively, with real entries. (A, D) and (B, E)
must be in generalized Schur canonical form, i.e. A, B are upper
quasi triangular and D, E are upper triangular. The solution (R, L)
overwrites (C, F). 0 <= SCALE <= 1 is an output scaling factor
chosen to avoid overflow.

In matrix notation solving equation (1) corresponds to solve
Z*x = scale*b, where Z is defined as

Z = [ kron(In, A) -kron(B**T, Im) ] (2)
[ kron(In, D) -kron(E**T, Im) ],

Ik is the identity matrix of size k and X**T is the transpose of X.
kron(X, Y) is the Kronecker product between the matrices X and Y.
In the process of solving (1), we solve a number of such systems
where Dim(In), Dim(In) = 1 or 2.

If TRANS = ’T’, solve the transposed system Z**T*y = scale*b for y,
which is equivalent to solve for R and L in

A**T * R + D**T * L = scale * C (3)
R * B**T + L * E**T = scale * -F

This case is used to compute an estimate of Dif[(A, D), (B, E)] =
sigma_min(Z) using reverse communication with DLACON.

DTGSY2 also (IJOB >= 1) contributes to the computation in DTGSYL
of an upper bound on the separation between to matrix pairs. Then
the input (A, D), (B, E) are sub-pencils of the matrix pair in
DTGSYL. See DTGSYL for details.

Parameters

TRANS

TRANS is CHARACTER*1
= ’N’: solve the generalized Sylvester equation (1).
= ’T’: solve the ’transposed’ system (3).

IJOB

IJOB is INTEGER
Specifies what kind of functionality to be performed.
= 0: solve (1) only.
= 1: A contribution from this subsystem to a Frobenius
norm-based estimate of the separation between two matrix
pairs is computed. (look ahead strategy is used).
= 2: A contribution from this subsystem to a Frobenius
norm-based estimate of the separation between two matrix
pairs is computed. (DGECON on sub-systems is used.)
Not referenced if TRANS = ’T’.

M

M is INTEGER
On entry, M specifies the order of A and D, and the row
dimension of C, F, R and L.

N

N is INTEGER
On entry, N specifies the order of B and E, and the column
dimension of C, F, R and L.

A

A is DOUBLE PRECISION array, dimension (LDA, M)
On entry, A contains an upper quasi triangular matrix.

LDA

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

B

B is DOUBLE PRECISION array, dimension (LDB, N)
On entry, B contains an upper quasi triangular matrix.

LDB

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

C

C is DOUBLE PRECISION array, dimension (LDC, N)
On entry, C contains the right-hand-side of the first matrix
equation in (1).
On exit, if IJOB = 0, C has been overwritten by the
solution R.

LDC

LDC is INTEGER
The leading dimension of the matrix C. LDC >= max(1, M).

D

D is DOUBLE PRECISION array, dimension (LDD, M)
On entry, D contains an upper triangular matrix.

LDD

LDD is INTEGER
The leading dimension of the matrix D. LDD >= max(1, M).

E

E is DOUBLE PRECISION array, dimension (LDE, N)
On entry, E contains an upper triangular matrix.

LDE

LDE is INTEGER
The leading dimension of the matrix E. LDE >= max(1, N).

F

F is DOUBLE PRECISION array, dimension (LDF, N)
On entry, F contains the right-hand-side of the second matrix
equation in (1).
On exit, if IJOB = 0, F has been overwritten by the
solution L.

LDF

LDF is INTEGER
The leading dimension of the matrix F. LDF >= max(1, M).

SCALE

SCALE is DOUBLE PRECISION
On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions
R and L (C and F on entry) will hold the solutions to a
slightly perturbed system but the input matrices A, B, D and
E have not been changed. If SCALE = 0, R and L will hold the
solutions to the homogeneous system with C = F = 0. Normally,
SCALE = 1.

RDSUM

RDSUM is DOUBLE PRECISION
On entry, the sum of squares of computed contributions to
the Dif-estimate under computation by DTGSYL, where the
scaling factor RDSCAL (see below) has been factored out.
On exit, the corresponding sum of squares updated with the
contributions from the current sub-system.
If TRANS = ’T’ RDSUM is not touched.
NOTE: RDSUM only makes sense when DTGSY2 is called by DTGSYL.

RDSCAL

RDSCAL is DOUBLE PRECISION
On entry, scaling factor used to prevent overflow in RDSUM.
On exit, RDSCAL is updated w.r.t. the current contributions
in RDSUM.
If TRANS = ’T’, RDSCAL is not touched.
NOTE: RDSCAL only makes sense when DTGSY2 is called by
DTGSYL.

IWORK

IWORK is INTEGER array, dimension (M+N+2)

PQ

PQ is INTEGER
On exit, the number of subsystems (of size 2-by-2, 4-by-4 and
8-by-8) solved by this routine.

INFO

INFO is INTEGER
On exit, if INFO is set to
=0: Successful exit
<0: If INFO = -i, the i-th argument had an illegal value.
>0: The matrix pairs (A, D) and (B, E) have common or very
close eigenvalues.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

subroutine stgsy2 (character trans, integer ijob, integer m, integer n,real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,integer ldb, real, dimension( ldc, * ) c, integer ldc, real, dimension(ldd, * ) d, integer ldd, real, dimension( lde, * ) e, integer lde,real, dimension( ldf, * ) f, integer ldf, real scale, real rdsum, realrdscal, integer, dimension( * ) iwork, integer pq, integer info)

STGSY2 solves the generalized Sylvester equation (unblocked algorithm).

Purpose:

STGSY2 solves the generalized Sylvester equation:

A * R - L * B = scale * C (1)
D * R - L * E = scale * F,

using Level 1 and 2 BLAS. where R and L are unknown M-by-N matrices,
(A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M,
N-by-N and M-by-N, respectively, with real entries. (A, D) and (B, E)
must be in generalized Schur canonical form, i.e. A, B are upper
quasi triangular and D, E are upper triangular. The solution (R, L)
overwrites (C, F). 0 <= SCALE <= 1 is an output scaling factor
chosen to avoid overflow.

In matrix notation solving equation (1) corresponds to solve
Z*x = scale*b, where Z is defined as

Z = [ kron(In, A) -kron(B**T, Im) ] (2)
[ kron(In, D) -kron(E**T, Im) ],

Ik is the identity matrix of size k and X**T is the transpose of X.
kron(X, Y) is the Kronecker product between the matrices X and Y.
In the process of solving (1), we solve a number of such systems
where Dim(In), Dim(In) = 1 or 2.

If TRANS = ’T’, solve the transposed system Z**T*y = scale*b for y,
which is equivalent to solve for R and L in

A**T * R + D**T * L = scale * C (3)
R * B**T + L * E**T = scale * -F

This case is used to compute an estimate of Dif[(A, D), (B, E)] =
sigma_min(Z) using reverse communication with SLACON.

STGSY2 also (IJOB >= 1) contributes to the computation in STGSYL
of an upper bound on the separation between to matrix pairs. Then
the input (A, D), (B, E) are sub-pencils of the matrix pair in
STGSYL. See STGSYL for details.

Parameters

TRANS

TRANS is CHARACTER*1
= ’N’: solve the generalized Sylvester equation (1).
= ’T’: solve the ’transposed’ system (3).

IJOB

IJOB is INTEGER
Specifies what kind of functionality to be performed.
= 0: solve (1) only.
= 1: A contribution from this subsystem to a Frobenius
norm-based estimate of the separation between two matrix
pairs is computed. (look ahead strategy is used).
= 2: A contribution from this subsystem to a Frobenius
norm-based estimate of the separation between two matrix
pairs is computed. (SGECON on sub-systems is used.)
Not referenced if TRANS = ’T’.

M

M is INTEGER
On entry, M specifies the order of A and D, and the row
dimension of C, F, R and L.

N

N is INTEGER
On entry, N specifies the order of B and E, and the column
dimension of C, F, R and L.

A

A is REAL array, dimension (LDA, M)
On entry, A contains an upper quasi triangular matrix.

LDA

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

B

B is REAL array, dimension (LDB, N)
On entry, B contains an upper quasi triangular matrix.

LDB

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

C

C is REAL array, dimension (LDC, N)
On entry, C contains the right-hand-side of the first matrix
equation in (1).
On exit, if IJOB = 0, C has been overwritten by the
solution R.

LDC

LDC is INTEGER
The leading dimension of the matrix C. LDC >= max(1, M).

D

D is REAL array, dimension (LDD, M)
On entry, D contains an upper triangular matrix.

LDD

LDD is INTEGER
The leading dimension of the matrix D. LDD >= max(1, M).

E

E is REAL array, dimension (LDE, N)
On entry, E contains an upper triangular matrix.

LDE

LDE is INTEGER
The leading dimension of the matrix E. LDE >= max(1, N).

F

F is REAL array, dimension (LDF, N)
On entry, F contains the right-hand-side of the second matrix
equation in (1).
On exit, if IJOB = 0, F has been overwritten by the
solution L.

LDF

LDF is INTEGER
The leading dimension of the matrix F. LDF >= max(1, M).

SCALE

SCALE is REAL
On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions
R and L (C and F on entry) will hold the solutions to a
slightly perturbed system but the input matrices A, B, D and
E have not been changed. If SCALE = 0, R and L will hold the
solutions to the homogeneous system with C = F = 0. Normally,
SCALE = 1.

RDSUM

RDSUM is REAL
On entry, the sum of squares of computed contributions to
the Dif-estimate under computation by STGSYL, where the
scaling factor RDSCAL (see below) has been factored out.
On exit, the corresponding sum of squares updated with the
contributions from the current sub-system.
If TRANS = ’T’ RDSUM is not touched.
NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL.

RDSCAL

RDSCAL is REAL
On entry, scaling factor used to prevent overflow in RDSUM.
On exit, RDSCAL is updated w.r.t. the current contributions
in RDSUM.
If TRANS = ’T’, RDSCAL is not touched.
NOTE: RDSCAL only makes sense when STGSY2 is called by
STGSYL.

IWORK

IWORK is INTEGER array, dimension (M+N+2)

PQ

PQ is INTEGER
On exit, the number of subsystems (of size 2-by-2, 4-by-4 and
8-by-8) solved by this routine.

INFO

INFO is INTEGER
On exit, if INFO is set to
=0: Successful exit
<0: If INFO = -i, the i-th argument had an illegal value.
>0: The matrix pairs (A, D) and (B, E) have common or very
close eigenvalues.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

subroutine ztgsy2 (character trans, integer ijob, integer m, integer n,complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(ldb, * ) b, integer ldb, complex*16, dimension( ldc, * ) c, integerldc, complex*16, dimension( ldd, * ) d, integer ldd, complex*16,dimension( lde, * ) e, integer lde, complex*16, dimension( ldf, * ) f,integer ldf, double precision scale, double precision rdsum, doubleprecision rdscal, integer info)

ZTGSY2 solves the generalized Sylvester equation (unblocked algorithm).

Purpose:

ZTGSY2 solves the generalized Sylvester equation

A * R - L * B = scale * C (1)
D * R - L * E = scale * F

using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices,
(A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M,
N-by-N and M-by-N, respectively. A, B, D and E are upper triangular
(i.e., (A,D) and (B,E) in generalized Schur form).

The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output
scaling factor chosen to avoid overflow.

In matrix notation solving equation (1) corresponds to solve
Zx = scale * b, where Z is defined as

Z = [ kron(In, A) -kron(B**H, Im) ] (2)
[ kron(In, D) -kron(E**H, Im) ],

Ik is the identity matrix of size k and X**H is the conjugate transpose of X.
kron(X, Y) is the Kronecker product between the matrices X and Y.

If TRANS = ’C’, y in the conjugate transposed system Z**H*y = scale*b
is solved for, which is equivalent to solve for R and L in

A**H * R + D**H * L = scale * C (3)
R * B**H + L * E**H = scale * -F

This case is used to compute an estimate of Dif[(A, D), (B, E)] =
= sigma_min(Z) using reverse communication with ZLACON.

ZTGSY2 also (IJOB >= 1) contributes to the computation in ZTGSYL
of an upper bound on the separation between to matrix pairs. Then
the input (A, D), (B, E) are sub-pencils of two matrix pairs in
ZTGSYL.

Parameters

TRANS

TRANS is CHARACTER*1
= ’N’: solve the generalized Sylvester equation (1).
= ’T’: solve the ’transposed’ system (3).

IJOB

IJOB is INTEGER
Specifies what kind of functionality to be performed.
=0: solve (1) only.
=1: A contribution from this subsystem to a Frobenius
norm-based estimate of the separation between two matrix
pairs is computed. (look ahead strategy is used).
=2: A contribution from this subsystem to a Frobenius
norm-based estimate of the separation between two matrix
pairs is computed. (DGECON on sub-systems is used.)
Not referenced if TRANS = ’T’.

M

M is INTEGER
On entry, M specifies the order of A and D, and the row
dimension of C, F, R and L.

N

N is INTEGER
On entry, N specifies the order of B and E, and the column
dimension of C, F, R and L.

A

A is COMPLEX*16 array, dimension (LDA, M)
On entry, A contains an upper triangular matrix.

LDA

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

B

B is COMPLEX*16 array, dimension (LDB, N)
On entry, B contains an upper triangular matrix.

LDB

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

C

C is COMPLEX*16 array, dimension (LDC, N)
On entry, C contains the right-hand-side of the first matrix
equation in (1).
On exit, if IJOB = 0, C has been overwritten by the solution
R.

LDC

LDC is INTEGER
The leading dimension of the matrix C. LDC >= max(1, M).

D

D is COMPLEX*16 array, dimension (LDD, M)
On entry, D contains an upper triangular matrix.

LDD

LDD is INTEGER
The leading dimension of the matrix D. LDD >= max(1, M).

E

E is COMPLEX*16 array, dimension (LDE, N)
On entry, E contains an upper triangular matrix.

LDE

LDE is INTEGER
The leading dimension of the matrix E. LDE >= max(1, N).

F

F is COMPLEX*16 array, dimension (LDF, N)
On entry, F contains the right-hand-side of the second matrix
equation in (1).
On exit, if IJOB = 0, F has been overwritten by the solution
L.

LDF

LDF is INTEGER
The leading dimension of the matrix F. LDF >= max(1, M).

SCALE

SCALE is DOUBLE PRECISION
On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions
R and L (C and F on entry) will hold the solutions to a
slightly perturbed system but the input matrices A, B, D and
E have not been changed. If SCALE = 0, R and L will hold the
solutions to the homogeneous system with C = F = 0.
Normally, SCALE = 1.

RDSUM

RDSUM is DOUBLE PRECISION
On entry, the sum of squares of computed contributions to
the Dif-estimate under computation by ZTGSYL, where the
scaling factor RDSCAL (see below) has been factored out.
On exit, the corresponding sum of squares updated with the
contributions from the current sub-system.
If TRANS = ’T’ RDSUM is not touched.
NOTE: RDSUM only makes sense when ZTGSY2 is called by
ZTGSYL.

RDSCAL

RDSCAL is DOUBLE PRECISION
On entry, scaling factor used to prevent overflow in RDSUM.
On exit, RDSCAL is updated w.r.t. the current contributions
in RDSUM.
If TRANS = ’T’, RDSCAL is not touched.
NOTE: RDSCAL only makes sense when ZTGSY2 is called by
ZTGSYL.

INFO

INFO is INTEGER
On exit, if INFO is set to
=0: Successful exit
<0: If INFO = -i, input argument number i is illegal.
>0: The matrix pairs (A, D) and (B, E) have common or very
close eigenvalues.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

Author

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