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laqhe(3) LAPACK laqhe(3)

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



          N is INTEGER


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

A



          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



          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



          N is INTEGER


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

A



          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



          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



          N is INTEGER


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

A



          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



          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



          N is INTEGER


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

A



          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



          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



          N is INTEGER


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

A



          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



          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



          N is INTEGER


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

A



          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



          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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