Man page - heequb(3)

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Manual

heequb

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cheequb (character uplo, integer n, complex, dimension( lda, * )a, integer lda, real, dimension( * ) s, real scond, real amax, complex,dimension( * ) work, integer info)
subroutine csyequb (character uplo, integer n, complex, dimension( lda, * )a, integer lda, real, dimension( * ) s, real scond, real amax, complex,dimension( * ) work, integer info)
subroutine dsyequb (character uplo, integer n, double precision, dimension(lda, * ) a, integer lda, double precision, dimension( * ) s, doubleprecision scond, double precision amax, double precision, dimension( *) work, integer info)
subroutine ssyequb (character uplo, integer n, real, dimension( lda, * ) a,integer lda, real, dimension( * ) s, real scond, real amax, real,dimension( * ) work, integer info)
subroutine zheequb (character uplo, integer n, complex*16, dimension( lda,* ) a, integer lda, double precision, dimension( * ) s, doubleprecision scond, double precision amax, complex*16, dimension( * )work, integer info)
subroutine zsyequb (character uplo, integer n, complex*16, dimension( lda,* ) a, integer lda, double precision, dimension( * ) s, doubleprecision scond, double precision amax, complex*16, dimension( * )work, integer info)
Author

NAME

heequb - {he,sy}equb: equilibration, power of 2

SYNOPSIS

Functions

subroutine cheequb (uplo, n, a, lda, s, scond, amax, work, info)
CHEEQUB
subroutine csyequb (uplo, n, a, lda, s, scond, amax, work, info)
CSYEQUB
subroutine dsyequb (uplo, n, a, lda, s, scond, amax, work, info)
DSYEQUB
subroutine ssyequb (uplo, n, a, lda, s, scond, amax, work, info)
SSYEQUB
subroutine zheequb (uplo, n, a, lda, s, scond, amax, work, info)
ZHEEQUB
subroutine zsyequb (uplo, n, a, lda, s, scond, amax, work, info)
ZSYEQUB

Detailed Description

Function Documentation

subroutine cheequb (character uplo, integer n, complex, dimension( lda, * )a, integer lda, real, dimension( * ) s, real scond, real amax, complex,dimension( * ) work, integer info)

CHEEQUB

Purpose:

CHEEQUB computes row and column scalings intended to equilibrate a
Hermitian matrix A (with respect to the Euclidean norm) and reduce
its condition number. The scale factors S are computed by the BIN
algorithm (see references) so that the scaled matrix B with elements
B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
the smallest possible condition number over all possible diagonal
scalings.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX array, dimension (LDA,N)
The N-by-N Hermitian matrix whose scaling factors are to be
computed.

LDA

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

S

S is REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

SCOND is REAL
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.

AMAX

AMAX is REAL
Largest absolute value of any matrix element. If AMAX is
very close to overflow or very close to underflow, the
matrix should be scaled.

WORK

WORK is COMPLEX array, dimension (2*N)

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

References:

Livne, O.E. and Golub, G.H., ā€™Scaling by Binormalizationā€™,
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

subroutine csyequb (character uplo, integer n, complex, dimension( lda, * )a, integer lda, real, dimension( * ) s, real scond, real amax, complex,dimension( * ) work, integer info)

CSYEQUB

Purpose:

CSYEQUB computes row and column scalings intended to equilibrate a
symmetric matrix A (with respect to the Euclidean norm) and reduce
its condition number. The scale factors S are computed by the BIN
algorithm (see references) so that the scaled matrix B with elements
B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
the smallest possible condition number over all possible diagonal
scalings.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX array, dimension (LDA,N)
The N-by-N symmetric matrix whose scaling factors are to be
computed.

LDA

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

S

S is REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

SCOND is REAL
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.

AMAX

AMAX is REAL
Largest absolute value of any matrix element. If AMAX is
very close to overflow or very close to underflow, the
matrix should be scaled.

WORK

WORK is COMPLEX array, dimension (2*N)

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

References:

Livne, O.E. and Golub, G.H., ā€™Scaling by Binormalizationā€™,
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

subroutine dsyequb (character uplo, integer n, double precision, dimension(lda, * ) a, integer lda, double precision, dimension( * ) s, doubleprecision scond, double precision amax, double precision, dimension( *) work, integer info)

DSYEQUB

Purpose:

DSYEQUB computes row and column scalings intended to equilibrate a
symmetric matrix A (with respect to the Euclidean norm) and reduce
its condition number. The scale factors S are computed by the BIN
algorithm (see references) so that the scaled matrix B with elements
B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
the smallest possible condition number over all possible diagonal
scalings.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is DOUBLE PRECISION array, dimension (LDA,N)
The N-by-N symmetric matrix whose scaling factors are to be
computed.

LDA

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

S

S is DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

SCOND is DOUBLE PRECISION
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.

AMAX

AMAX is DOUBLE PRECISION
Largest absolute value of any matrix element. If AMAX is
very close to overflow or very close to underflow, the
matrix should be scaled.

WORK

WORK is DOUBLE PRECISION array, dimension (2*N)

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

References:

Livne, O.E. and Golub, G.H., ā€™Scaling by Binormalizationā€™,
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

subroutine ssyequb (character uplo, integer n, real, dimension( lda, * ) a,integer lda, real, dimension( * ) s, real scond, real amax, real,dimension( * ) work, integer info)

SSYEQUB

Purpose:

SSYEQUB computes row and column scalings intended to equilibrate a
symmetric matrix A (with respect to the Euclidean norm) and reduce
its condition number. The scale factors S are computed by the BIN
algorithm (see references) so that the scaled matrix B with elements
B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
the smallest possible condition number over all possible diagonal
scalings.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is REAL array, dimension (LDA,N)
The N-by-N symmetric matrix whose scaling factors are to be
computed.

LDA

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

S

S is REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

SCOND is REAL
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.

AMAX

AMAX is REAL
Largest absolute value of any matrix element. If AMAX is
very close to overflow or very close to underflow, the
matrix should be scaled.

WORK

WORK is REAL array, dimension (2*N)

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

References:

Livne, O.E. and Golub, G.H., ā€™Scaling by Binormalizationā€™,
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

subroutine zheequb (character uplo, integer n, complex*16, dimension( lda,* ) a, integer lda, double precision, dimension( * ) s, doubleprecision scond, double precision amax, complex*16, dimension( * )work, integer info)

ZHEEQUB

Purpose:

ZHEEQUB computes row and column scalings intended to equilibrate a
Hermitian matrix A (with respect to the Euclidean norm) and reduce
its condition number. The scale factors S are computed by the BIN
algorithm (see references) so that the scaled matrix B with elements
B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
the smallest possible condition number over all possible diagonal
scalings.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N)
The N-by-N Hermitian matrix whose scaling factors are to be
computed.

LDA

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

S

S is DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

SCOND is DOUBLE PRECISION
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.

AMAX

AMAX is DOUBLE PRECISION
Largest absolute value of any matrix element. If AMAX is
very close to overflow or very close to underflow, the
matrix should be scaled.

WORK

WORK is COMPLEX*16 array, dimension (2*N)

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

References:

Livne, O.E. and Golub, G.H., ā€™Scaling by Binormalizationā€™,
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

subroutine zsyequb (character uplo, integer n, complex*16, dimension( lda,* ) a, integer lda, double precision, dimension( * ) s, doubleprecision scond, double precision amax, complex*16, dimension( * )work, integer info)

ZSYEQUB

Purpose:

ZSYEQUB computes row and column scalings intended to equilibrate a
symmetric matrix A (with respect to the Euclidean norm) and reduce
its condition number. The scale factors S are computed by the BIN
algorithm (see references) so that the scaled matrix B with elements
B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
the smallest possible condition number over all possible diagonal
scalings.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N)
The N-by-N symmetric matrix whose scaling factors are to be
computed.

LDA

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

S

S is DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

SCOND is DOUBLE PRECISION
If INFO = 0, S contains the ratio of the smallest S(i) to
the largest S(i). If SCOND >= 0.1 and AMAX is neither too
large nor too small, it is not worth scaling by S.

AMAX

AMAX is DOUBLE PRECISION
Largest absolute value of any matrix element. If AMAX is
very close to overflow or very close to underflow, the
matrix should be scaled.

WORK

WORK is COMPLEX*16 array, dimension (2*N)

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

References:

Livne, O.E. and Golub, G.H., ā€™Scaling by Binormalizationā€™,
Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
DOI 10.1023/B:NUMA.0000016606.32820.69
Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

Author

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