Man page - ggbal(3)

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Manual

ggbal

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cggbal (character job, integer n, complex, dimension( lda, * )a, integer lda, complex, dimension( ldb, * ) b, integer ldb, integerilo, integer ihi, real, dimension( * ) lscale, real, dimension( * )rscale, real, dimension( * ) work, integer info)
subroutine dggbal (character job, integer n, double precision, dimension(lda, * ) a, integer lda, double precision, dimension( ldb, * ) b,integer ldb, integer ilo, integer ihi, double precision, dimension( * )lscale, double precision, dimension( * ) rscale, double precision,dimension( * ) work, integer info)
subroutine sggbal (character job, integer n, real, dimension( lda, * ) a,integer lda, real, dimension( ldb, * ) b, integer ldb, integer ilo,integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale,real, dimension( * ) work, integer info)
subroutine zggbal (character job, integer n, complex*16, dimension( lda, *) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb,integer ilo, integer ihi, double precision, dimension( * ) lscale,double precision, dimension( * ) rscale, double precision, dimension( *) work, integer info)
Author

NAME

ggbal - ggbal: balance matrix

SYNOPSIS

Functions

subroutine cggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
CGGBAL
subroutine dggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
DGGBAL
subroutine sggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
SGGBAL
subroutine zggbal (job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
ZGGBAL

Detailed Description

Function Documentation

subroutine cggbal (character job, integer n, complex, dimension( lda, * )a, integer lda, complex, dimension( ldb, * ) b, integer ldb, integerilo, integer ihi, real, dimension( * ) lscale, real, dimension( * )rscale, real, dimension( * ) work, integer info)

CGGBAL

Purpose:

CGGBAL balances a pair of general complex matrices (A,B). This
involves, first, permuting A and B by similarity transformations to
isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N
elements on the diagonal; and second, applying a diagonal similarity
transformation to rows and columns ILO to IHI to make the rows
and columns as close in norm as possible. Both steps are optional.

Balancing may reduce the 1-norm of the matrices, and improve the
accuracy of the computed eigenvalues and/or eigenvectors in the
generalized eigenvalue problem A*x = lambda*B*x.

Parameters

JOB

JOB is CHARACTER*1
Specifies the operations to be performed on A and B:
= ’N’: none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
and RSCALE(I) = 1.0 for i=1,...,N;
= ’P’: permute only;
= ’S’: scale only;
= ’B’: both permute and scale.

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 input matrix A.
On exit, A is overwritten by the balanced matrix.
If JOB = ’N’, A is not referenced.

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 input matrix B.
On exit, B is overwritten by the balanced matrix.
If JOB = ’N’, B is not referenced.

LDB

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

ILO

ILO is INTEGER

IHI

IHI is INTEGER
ILO and IHI are set to integers such that on exit
A(i,j) = 0 and B(i,j) = 0 if i > j and
j = 1,...,ILO-1 or i = IHI+1,...,N.
If JOB = ’N’ or ’S’, ILO = 1 and IHI = N.

LSCALE

LSCALE is REAL array, dimension (N)
Details of the permutations and scaling factors applied
to the left side of A and B. If P(j) is the index of the
row interchanged with row j, and D(j) is the scaling factor
applied to row j, then
LSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.

RSCALE

RSCALE is REAL array, dimension (N)
Details of the permutations and scaling factors applied
to the right side of A and B. If P(j) is the index of the
column interchanged with column j, and D(j) is the scaling
factor applied to column j, then
RSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.

WORK

WORK is REAL array, dimension (lwork)
lwork must be at least max(1,6*N) when JOB = ’S’ or ’B’, and
at least 1 when JOB = ’N’ or ’P’.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

See R.C. WARD, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

subroutine dggbal (character job, integer n, double precision, dimension(lda, * ) a, integer lda, double precision, dimension( ldb, * ) b,integer ldb, integer ilo, integer ihi, double precision, dimension( * )lscale, double precision, dimension( * ) rscale, double precision,dimension( * ) work, integer info)

DGGBAL

Purpose:

DGGBAL balances a pair of general real matrices (A,B). This
involves, first, permuting A and B by similarity transformations to
isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N
elements on the diagonal; and second, applying a diagonal similarity
transformation to rows and columns ILO to IHI to make the rows
and columns as close in norm as possible. Both steps are optional.

Balancing may reduce the 1-norm of the matrices, and improve the
accuracy of the computed eigenvalues and/or eigenvectors in the
generalized eigenvalue problem A*x = lambda*B*x.

Parameters

JOB

JOB is CHARACTER*1
Specifies the operations to be performed on A and B:
= ’N’: none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
and RSCALE(I) = 1.0 for i = 1,...,N.
= ’P’: permute only;
= ’S’: scale only;
= ’B’: both permute and scale.

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 input matrix A.
On exit, A is overwritten by the balanced matrix.
If JOB = ’N’, A is not referenced.

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 input matrix B.
On exit, B is overwritten by the balanced matrix.
If JOB = ’N’, B is not referenced.

LDB

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

ILO

ILO is INTEGER

IHI

IHI is INTEGER
ILO and IHI are set to integers such that on exit
A(i,j) = 0 and B(i,j) = 0 if i > j and
j = 1,...,ILO-1 or i = IHI+1,...,N.
If JOB = ’N’ or ’S’, ILO = 1 and IHI = N.

LSCALE

LSCALE is DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied
to the left side of A and B. If P(j) is the index of the
row interchanged with row j, and D(j)
is the scaling factor applied to row j, then
LSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.

RSCALE

RSCALE is DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied
to the right side of A and B. If P(j) is the index of the
column interchanged with column j, and D(j)
is the scaling factor applied to column j, then
LSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.

WORK

WORK is DOUBLE PRECISION array, dimension (lwork)
lwork must be at least max(1,6*N) when JOB = ’S’ or ’B’, and
at least 1 when JOB = ’N’ or ’P’.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

See R.C. WARD, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

subroutine sggbal (character job, integer n, real, dimension( lda, * ) a,integer lda, real, dimension( ldb, * ) b, integer ldb, integer ilo,integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale,real, dimension( * ) work, integer info)

SGGBAL

Purpose:

SGGBAL balances a pair of general real matrices (A,B). This
involves, first, permuting A and B by similarity transformations to
isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N
elements on the diagonal; and second, applying a diagonal similarity
transformation to rows and columns ILO to IHI to make the rows
and columns as close in norm as possible. Both steps are optional.

Balancing may reduce the 1-norm of the matrices, and improve the
accuracy of the computed eigenvalues and/or eigenvectors in the
generalized eigenvalue problem A*x = lambda*B*x.

Parameters

JOB

JOB is CHARACTER*1
Specifies the operations to be performed on A and B:
= ’N’: none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
and RSCALE(I) = 1.0 for i = 1,...,N.
= ’P’: permute only;
= ’S’: scale only;
= ’B’: both permute and scale.

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 input matrix A.
On exit, A is overwritten by the balanced matrix.
If JOB = ’N’, A is not referenced.

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 input matrix B.
On exit, B is overwritten by the balanced matrix.
If JOB = ’N’, B is not referenced.

LDB

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

ILO

ILO is INTEGER

IHI

IHI is INTEGER
ILO and IHI are set to integers such that on exit
A(i,j) = 0 and B(i,j) = 0 if i > j and
j = 1,...,ILO-1 or i = IHI+1,...,N.
If JOB = ’N’ or ’S’, ILO = 1 and IHI = N.

LSCALE

LSCALE is REAL array, dimension (N)
Details of the permutations and scaling factors applied
to the left side of A and B. If P(j) is the index of the
row interchanged with row j, and D(j)
is the scaling factor applied to row j, then
LSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.

RSCALE

RSCALE is REAL array, dimension (N)
Details of the permutations and scaling factors applied
to the right side of A and B. If P(j) is the index of the
column interchanged with column j, and D(j)
is the scaling factor applied to column j, then
LSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.

WORK

WORK is REAL array, dimension (lwork)
lwork must be at least max(1,6*N) when JOB = ’S’ or ’B’, and
at least 1 when JOB = ’N’ or ’P’.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

See R.C. WARD, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

subroutine zggbal (character job, integer n, complex*16, dimension( lda, *) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb,integer ilo, integer ihi, double precision, dimension( * ) lscale,double precision, dimension( * ) rscale, double precision, dimension( *) work, integer info)

ZGGBAL

Purpose:

ZGGBAL balances a pair of general complex matrices (A,B). This
involves, first, permuting A and B by similarity transformations to
isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N
elements on the diagonal; and second, applying a diagonal similarity
transformation to rows and columns ILO to IHI to make the rows
and columns as close in norm as possible. Both steps are optional.

Balancing may reduce the 1-norm of the matrices, and improve the
accuracy of the computed eigenvalues and/or eigenvectors in the
generalized eigenvalue problem A*x = lambda*B*x.

Parameters

JOB

JOB is CHARACTER*1
Specifies the operations to be performed on A and B:
= ’N’: none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
and RSCALE(I) = 1.0 for i=1,...,N;
= ’P’: permute only;
= ’S’: scale only;
= ’B’: both permute and scale.

N

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

A

A is COMPLEX*16 array, dimension (LDA,N)
On entry, the input matrix A.
On exit, A is overwritten by the balanced matrix.
If JOB = ’N’, A is not referenced.

LDA

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

B

B is COMPLEX*16 array, dimension (LDB,N)
On entry, the input matrix B.
On exit, B is overwritten by the balanced matrix.
If JOB = ’N’, B is not referenced.

LDB

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

ILO

ILO is INTEGER

IHI

IHI is INTEGER
ILO and IHI are set to integers such that on exit
A(i,j) = 0 and B(i,j) = 0 if i > j and
j = 1,...,ILO-1 or i = IHI+1,...,N.
If JOB = ’N’ or ’S’, ILO = 1 and IHI = N.

LSCALE

LSCALE is DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied
to the left side of A and B. If P(j) is the index of the
row interchanged with row j, and D(j) is the scaling factor
applied to row j, then
LSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.

RSCALE

RSCALE is DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied
to the right side of A and B. If P(j) is the index of the
column interchanged with column j, and D(j) is the scaling
factor applied to column j, then
RSCALE(j) = P(j) for J = 1,...,ILO-1
= D(j) for J = ILO,...,IHI
= P(j) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.

WORK

WORK is DOUBLE PRECISION array, dimension (lwork)
lwork must be at least max(1,6*N) when JOB = ’S’ or ’B’, and
at least 1 when JOB = ’N’ or ’P’.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

See R.C. WARD, Balancing the generalized eigenvalue problem,
SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.

Author

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