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laqhp(3) Library Functions Manual 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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