laqhp(3)

NAME
laqhp - laqhp: row/col scale matrix

SYNOPSIS

  Functions
subroutine claqhp (uplo, n, ap, s, scond, amax, equed)
CLAQHP scales a Hermitian matrix stored in packed form.
subroutine claqsp (uplo, n, ap, s, scond, amax, equed)
CLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
subroutine dlaqsp (uplo, n, ap, s, scond, amax, equed)
DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
subroutine slaqsp (uplo, n, ap, s, scond, amax, equed)
SLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
subroutine zlaqhp (uplo, n, ap, s, scond, amax, equed)
ZLAQHP scales a Hermitian matrix stored in packed form.
subroutine zlaqsp (uplo, n, ap, s, scond, amax, equed)
ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

Detailed Description

Function Documentation

  subroutine claqhp (character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed)

CLAQHP scales a Hermitian matrix stored in packed form.

Purpose:

    !>
    !> CLAQHP 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.
    !>

    AP

    !>          AP is COMPLEX array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the Hermitian matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>
    !>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
    !>          the same storage format as A.
    !>

    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 125 of file claqhp.f.

  subroutine claqsp (character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed)

CLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

Purpose:

    !>
    !> CLAQSP 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.
    !>

    AP

    !>          AP is COMPLEX array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the symmetric matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>
    !>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
    !>          the same storage format as A.
    !>

    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 125 of file claqsp.f.

  subroutine dlaqsp (character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

Purpose:

    !>
    !> DLAQSP 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.
    !>

    AP

    !>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the symmetric matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>
    !>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
    !>          the same storage format as A.
    !>

    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 124 of file dlaqsp.f.

  subroutine slaqsp (character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed)

SLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

Purpose:

    !>
    !> SLAQSP 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.
    !>

    AP

    !>          AP is REAL array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the symmetric matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>
    !>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
    !>          the same storage format as A.
    !>

    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 124 of file slaqsp.f.

  subroutine zlaqhp (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

ZLAQHP scales a Hermitian matrix stored in packed form.

Purpose:

    !>
    !> ZLAQHP 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.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the Hermitian matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>
    !>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
    !>          the same storage format as A.
    !>

    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 125 of file zlaqhp.f.

  subroutine zlaqsp (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

ZLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

Purpose:

    !>
    !> ZLAQSP 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.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the symmetric matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>
    !>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
    !>          the same storage format as A.
    !>

    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 125 of file zlaqsp.f.

Author

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