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laqhb(3) LAPACK laqhb(3)

NAME

laqhb - laqhb: row/col scale matrix

SYNOPSIS

Functions


subroutine claqhb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ. subroutine claqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. subroutine dlaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. subroutine slaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. subroutine zlaqhb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ. subroutine zlaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed)
ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Detailed Description

Function Documentation

subroutine claqhb (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real amax, character equed)

CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.

Purpose:

!>
!> CLAQHB equilibrates an Hermitian band 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.
!>

KD

!>          KD is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
!>

AB

!>          AB is COMPLEX array, dimension (LDAB,N)
!>          On entry, the upper or lower triangle of the symmetric band
!>          matrix A, stored in the first KD+1 rows of the array.  The
!>          j-th column of A is stored in the j-th column of the array AB
!>          as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
!>          On exit, if INFO = 0, the triangular factor U or L from the
!>          Cholesky factorization A = U**H *U or A = L*L**H of the band
!>          matrix A, in the same storage format as A.
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+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 claqsb (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real amax, character equed)

CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:

!>
!> CLAQSB equilibrates a symmetric band 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.
!>

KD

!>          KD is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
!>

AB

!>          AB is COMPLEX array, dimension (LDAB,N)
!>          On entry, the upper or lower triangle of the symmetric band
!>          matrix A, stored in the first KD+1 rows of the array.  The
!>          j-th column of A is stored in the j-th column of the array AB
!>          as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
!>          On exit, if INFO = 0, the triangular factor U or L from the
!>          Cholesky factorization A = U**H *U or A = L*L**H of the band
!>          matrix A, in the same storage format as A.
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+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 dlaqsb (character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:

!>
!> DLAQSB equilibrates a symmetric band 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.
!>

KD

!>          KD is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
!>

AB

!>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
!>          On entry, the upper or lower triangle of the symmetric band
!>          matrix A, stored in the first KD+1 rows of the array.  The
!>          j-th column of A is stored in the j-th column of the array AB
!>          as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
!>          On exit, if INFO = 0, the triangular factor U or L from the
!>          Cholesky factorization A = U**T*U or A = L*L**T of the band
!>          matrix A, in the same storage format as A.
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+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 slaqsb (character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real amax, character equed)

SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:

!>
!> SLAQSB equilibrates a symmetric band 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.
!>

KD

!>          KD is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
!>

AB

!>          AB is REAL array, dimension (LDAB,N)
!>          On entry, the upper or lower triangle of the symmetric band
!>          matrix A, stored in the first KD+1 rows of the array.  The
!>          j-th column of A is stored in the j-th column of the array AB
!>          as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
!>          On exit, if INFO = 0, the triangular factor U or L from the
!>          Cholesky factorization A = U**T*U or A = L*L**T of the band
!>          matrix A, in the same storage format as A.
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+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 zlaqhb (character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.

Purpose:

!>
!> ZLAQHB equilibrates a Hermitian band 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.
!>

KD

!>          KD is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
!>

AB

!>          AB is COMPLEX*16 array, dimension (LDAB,N)
!>          On entry, the upper or lower triangle of the symmetric band
!>          matrix A, stored in the first KD+1 rows of the array.  The
!>          j-th column of A is stored in the j-th column of the array AB
!>          as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
!>          On exit, if INFO = 0, the triangular factor U or L from the
!>          Cholesky factorization A = U**H *U or A = L*L**H of the band
!>          matrix A, in the same storage format as A.
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+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 zlaqsb (character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

ZLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:

!>
!> ZLAQSB equilibrates a symmetric band 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.
!>

KD

!>          KD is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
!>

AB

!>          AB is COMPLEX*16 array, dimension (LDAB,N)
!>          On entry, the upper or lower triangle of the symmetric band
!>          matrix A, stored in the first KD+1 rows of the array.  The
!>          j-th column of A is stored in the j-th column of the array AB
!>          as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
!>          On exit, if INFO = 0, the triangular factor U or L from the
!>          Cholesky factorization A = U**H *U or A = L*L**H of the band
!>          matrix A, in the same storage format as A.
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+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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