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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