Man page - gebal(3)

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Manual

gebal

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgebal (character job, integer n, complex, dimension( lda, * )a, integer lda, integer ilo, integer ihi, real, dimension( * ) scale,integer info)
subroutine dgebal (character job, integer n, double precision, dimension(lda, * ) a, integer lda, integer ilo, integer ihi, double precision,dimension( * ) scale, integer info)
subroutine sgebal (character job, integer n, real, dimension( lda, * ) a,integer lda, integer ilo, integer ihi, real, dimension( * ) scale,integer info)
subroutine zgebal (character job, integer n, complex*16, dimension( lda, *) a, integer lda, integer ilo, integer ihi, double precision,dimension( * ) scale, integer info)
Author

NAME

gebal - gebal: balance matrix

SYNOPSIS

Functions

subroutine cgebal (job, n, a, lda, ilo, ihi, scale, info)
CGEBAL
subroutine dgebal (job, n, a, lda, ilo, ihi, scale, info)
DGEBAL
subroutine sgebal (job, n, a, lda, ilo, ihi, scale, info)
SGEBAL
subroutine zgebal (job, n, a, lda, ilo, ihi, scale, info)
ZGEBAL

Detailed Description

Function Documentation

subroutine cgebal (character job, integer n, complex, dimension( lda, * )a, integer lda, integer ilo, integer ihi, real, dimension( * ) scale,integer info)

CGEBAL

Purpose:

CGEBAL balances a general complex matrix A. This involves, first,
permuting A by a similarity transformation 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 matrix, and improve the
accuracy of the computed eigenvalues and/or eigenvectors.

Parameters

JOB

JOB is CHARACTER*1
Specifies the operations to be performed on A:
= ’N’: none: simply set ILO = 1, IHI = N, SCALE(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 matrix A. 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.
See Further Details.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.
If JOB = ’N’ or ’S’, ILO = 1 and IHI = N.

SCALE

SCALE is REAL array, dimension (N)
Details of the permutations and scaling factors applied to
A. If P(j) is the index of the row and column interchanged
with row and column j and D(j) is the scaling factor
applied to row and column j, then
SCALE(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.

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:

The permutations consist of row and column interchanges which put
the matrix in the form

( T1 X Y )
P A P = ( 0 B Z )
( 0 0 T2 )

where T1 and T2 are upper triangular matrices whose eigenvalues lie
along the diagonal. The column indices ILO and IHI mark the starting
and ending columns of the submatrix B. Balancing consists of applying
a diagonal similarity transformation inv(D) * B * D to make the
1-norms of each row of B and its corresponding column nearly equal.
The output matrix is

( T1 X*D Y )
( 0 inv(D)*B*D inv(D)*Z ).
( 0 0 T2 )

Information about the permutations P and the diagonal matrix D is
returned in the vector SCALE.

This subroutine is based on the EISPACK routine CBAL.

Modified by Tzu-Yi Chen, Computer Science Division, University of
California at Berkeley, USA

Refactored by Evert Provoost, Department of Computer Science,
KU Leuven, Belgium

subroutine dgebal (character job, integer n, double precision, dimension(lda, * ) a, integer lda, integer ilo, integer ihi, double precision,dimension( * ) scale, integer info)

DGEBAL

Purpose:

DGEBAL balances a general real matrix A. This involves, first,
permuting A by a similarity transformation 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 matrix, and improve the
accuracy of the computed eigenvalues and/or eigenvectors.

Parameters

JOB

JOB is CHARACTER*1
Specifies the operations to be performed on A:
= ’N’: none: simply set ILO = 1, IHI = N, SCALE(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 matrix A. 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.
See Further Details.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.
If JOB = ’N’ or ’S’, ILO = 1 and IHI = N.

SCALE

SCALE is DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied to
A. If P(j) is the index of the row and column interchanged
with row and column j and D(j) is the scaling factor
applied to row and column j, then
SCALE(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.

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:

The permutations consist of row and column interchanges which put
the matrix in the form

( T1 X Y )
P A P = ( 0 B Z )
( 0 0 T2 )

where T1 and T2 are upper triangular matrices whose eigenvalues lie
along the diagonal. The column indices ILO and IHI mark the starting
and ending columns of the submatrix B. Balancing consists of applying
a diagonal similarity transformation inv(D) * B * D to make the
1-norms of each row of B and its corresponding column nearly equal.
The output matrix is

( T1 X*D Y )
( 0 inv(D)*B*D inv(D)*Z ).
( 0 0 T2 )

Information about the permutations P and the diagonal matrix D is
returned in the vector SCALE.

This subroutine is based on the EISPACK routine BALANC.

Modified by Tzu-Yi Chen, Computer Science Division, University of
California at Berkeley, USA

Refactored by Evert Provoost, Department of Computer Science,
KU Leuven, Belgium

subroutine sgebal (character job, integer n, real, dimension( lda, * ) a,integer lda, integer ilo, integer ihi, real, dimension( * ) scale,integer info)

SGEBAL

Purpose:

SGEBAL balances a general real matrix A. This involves, first,
permuting A by a similarity transformation 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 matrix, and improve the
accuracy of the computed eigenvalues and/or eigenvectors.

Parameters

JOB

JOB is CHARACTER*1
Specifies the operations to be performed on A:
= ’N’: none: simply set ILO = 1, IHI = N, SCALE(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 matrix A. 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.
See Further Details.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.
If JOB = ’N’ or ’S’, ILO = 1 and IHI = N.

SCALE

SCALE is REAL array, dimension (N)
Details of the permutations and scaling factors applied to
A. If P(j) is the index of the row and column interchanged
with row and column j and D(j) is the scaling factor
applied to row and column j, then
SCALE(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.

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:

The permutations consist of row and column interchanges which put
the matrix in the form

( T1 X Y )
P A P = ( 0 B Z )
( 0 0 T2 )

where T1 and T2 are upper triangular matrices whose eigenvalues lie
along the diagonal. The column indices ILO and IHI mark the starting
and ending columns of the submatrix B. Balancing consists of applying
a diagonal similarity transformation inv(D) * B * D to make the
1-norms of each row of B and its corresponding column nearly equal.
The output matrix is

( T1 X*D Y )
( 0 inv(D)*B*D inv(D)*Z ).
( 0 0 T2 )

Information about the permutations P and the diagonal matrix D is
returned in the vector SCALE.

This subroutine is based on the EISPACK routine BALANC.

Modified by Tzu-Yi Chen, Computer Science Division, University of
California at Berkeley, USA

Refactored by Evert Provoost, Department of Computer Science,
KU Leuven, Belgium

subroutine zgebal (character job, integer n, complex*16, dimension( lda, *) a, integer lda, integer ilo, integer ihi, double precision,dimension( * ) scale, integer info)

ZGEBAL

Purpose:

ZGEBAL balances a general complex matrix A. This involves, first,
permuting A by a similarity transformation 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 matrix, and improve the
accuracy of the computed eigenvalues and/or eigenvectors.

Parameters

JOB

JOB is CHARACTER*1
Specifies the operations to be performed on A:
= ’N’: none: simply set ILO = 1, IHI = N, SCALE(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 matrix A. 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.
See Further Details.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.
If JOB = ’N’ or ’S’, ILO = 1 and IHI = N.

SCALE

SCALE is DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied to
A. If P(j) is the index of the row and column interchanged
with row and column j and D(j) is the scaling factor
applied to row and column j, then
SCALE(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.

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:

The permutations consist of row and column interchanges which put
the matrix in the form

( T1 X Y )
P A P = ( 0 B Z )
( 0 0 T2 )

where T1 and T2 are upper triangular matrices whose eigenvalues lie
along the diagonal. The column indices ILO and IHI mark the starting
and ending columns of the submatrix B. Balancing consists of applying
a diagonal similarity transformation inv(D) * B * D to make the
1-norms of each row of B and its corresponding column nearly equal.
The output matrix is

( T1 X*D Y )
( 0 inv(D)*B*D inv(D)*Z ).
( 0 0 T2 )

Information about the permutations P and the diagonal matrix D is
returned in the vector SCALE.

This subroutine is based on the EISPACK routine CBAL.

Modified by Tzu-Yi Chen, Computer Science Division, University of
California at Berkeley, USA

Refactored by Evert Provoost, Department of Computer Science,
KU Leuven, Belgium

Author

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