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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