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.

Definition at line 133 of file claqhe.f.

  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.

Definition at line 133 of file claqsy.f.

  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.

Definition at line 132 of file dlaqsy.f.

  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.

Definition at line 132 of file slaqsy.f.

  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.

Definition at line 133 of file zlaqhe.f.

  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.

Definition at line 133 of file zlaqsy.f.

Author

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