Ubuntu Manpage: laqhe - laqhe: row/col scale matrix

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NAME

       laqhe - laqhe: row/col scale matrix

SYNOPSIS

   Functions
       subroutine claqhe (uplo, n, a, lda, s, scond, amax, equed)
           CLAQHE scales a Hermitian matrix.
       subroutine claqsy (uplo, n, a, lda, s, scond, amax, equed)
           CLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
       subroutine dlaqsy (uplo, n, a, lda, s, scond, amax, equed)
           DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
       subroutine slaqsy (uplo, n, a, lda, s, scond, amax, equed)
           SLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
       subroutine zlaqhe (uplo, n, a, lda, s, scond, amax, equed)
           ZLAQHE scales a Hermitian matrix.
       subroutine zlaqsy (uplo, n, a, lda, s, scond, amax, equed)
           ZLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

Detailed Description

Function Documentation

subroutine claqhe (character uplo, integer n, complex, dimension( lda, * ) a, integer lda,
real, dimension( * ) s, real scond, real amax, character equed)
CLAQHE scales a Hermitian matrix.

Purpose:

CLAQHE equilibrates a Hermitian matrix A using the scaling factors
in the vector S.

Parameters
UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular

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

A is COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
n by n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading n by n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix:
diag(S) * A * diag(S).

LDA

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

S is REAL array, dimension (N)
The scale factors for A.

SCOND

SCOND is REAL
Ratio of the smallest S(i) to the largest S(i).

AMAX

AMAX is REAL
Absolute value of largest matrix entry.

EQUED

EQUED is CHARACTER*1
Specifies whether or not equilibration was done.
= 'N': No equilibration.
= 'Y': Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).

Internal Parameters:

THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors. If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.

Author
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine claqsy (character uplo, integer n, complex, dimension( lda, * ) a, integer lda,
real, dimension( * ) s, real scond, real amax, character equed)
CLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

Purpose:

CLAQSY equilibrates a symmetric matrix A using the scaling factors
in the vector S.

Parameters
UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular

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

A is COMPLEX array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
n by n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading n by n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix:
diag(S) * A * diag(S).

LDA

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

S is REAL array, dimension (N)
The scale factors for A.

SCOND

SCOND is REAL
Ratio of the smallest S(i) to the largest S(i).

AMAX

AMAX is REAL
Absolute value of largest matrix entry.

EQUED

EQUED is CHARACTER*1
Specifies whether or not equilibration was done.
= 'N': No equilibration.
= 'Y': Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).

Internal Parameters:

THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors. If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.

Author
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dlaqsy (character uplo, integer n, double precision, dimension( lda, * ) a, integer
lda, double precision, dimension( * ) s, double precision scond, double precision amax,
character equed)
DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

Purpose:

DLAQSY equilibrates a symmetric matrix A using the scaling factors
in the vector S.

Parameters
UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular

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

A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
n by n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading n by n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix:
diag(S) * A * diag(S).

LDA

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

S is DOUBLE PRECISION array, dimension (N)
The scale factors for A.

SCOND

SCOND is DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).

AMAX

AMAX is DOUBLE PRECISION
Absolute value of largest matrix entry.

EQUED

EQUED is CHARACTER*1
Specifies whether or not equilibration was done.
= 'N': No equilibration.
= 'Y': Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).

Internal Parameters:

THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors. If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.

Author
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine slaqsy (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real,
dimension( * ) s, real scond, real amax, character equed)
SLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

Purpose:

SLAQSY equilibrates a symmetric matrix A using the scaling factors
in the vector S.

Parameters
UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular

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

A is REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
n by n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading n by n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix:
diag(S) * A * diag(S).

LDA

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

S is REAL array, dimension (N)
The scale factors for A.

SCOND

SCOND is REAL
Ratio of the smallest S(i) to the largest S(i).

AMAX

AMAX is REAL
Absolute value of largest matrix entry.

EQUED

EQUED is CHARACTER*1
Specifies whether or not equilibration was done.
= 'N': No equilibration.
= 'Y': Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).

Internal Parameters:

THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors. If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.

Author
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zlaqhe (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda,
double precision, dimension( * ) s, double precision scond, double precision amax,
character equed)
ZLAQHE scales a Hermitian matrix.

Purpose:

ZLAQHE equilibrates a Hermitian matrix A using the scaling factors
in the vector S.

Parameters
UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular

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

A is COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
n by n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading n by n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix:
diag(S) * A * diag(S).

LDA

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

S is DOUBLE PRECISION array, dimension (N)
The scale factors for A.

SCOND

SCOND is DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).

AMAX

AMAX is DOUBLE PRECISION
Absolute value of largest matrix entry.

EQUED

EQUED is CHARACTER*1
Specifies whether or not equilibration was done.
= 'N': No equilibration.
= 'Y': Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).

Internal Parameters:

THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors. If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.

Author
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zlaqsy (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda,
double precision, dimension( * ) s, double precision scond, double precision amax,
character equed)
ZLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

Purpose:

ZLAQSY equilibrates a symmetric matrix A using the scaling factors
in the vector S.

Parameters
UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular

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

A is COMPLEX*16 array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
n by n upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading n by n lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.

On exit, if EQUED = 'Y', the equilibrated matrix:
diag(S) * A * diag(S).

LDA

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

S is DOUBLE PRECISION array, dimension (N)
The scale factors for A.

SCOND

SCOND is DOUBLE PRECISION
Ratio of the smallest S(i) to the largest S(i).

AMAX

AMAX is DOUBLE PRECISION
Absolute value of largest matrix entry.

EQUED

EQUED is CHARACTER*1
Specifies whether or not equilibration was done.
= 'N': No equilibration.
= 'Y': Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).

Internal Parameters:

THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors. If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.

Author
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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