laqgb(3)

NAME
laqgb - laqgb: row/col scale matrix

SYNOPSIS

  Functions

subroutine claqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)
CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
subroutine dlaqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)
DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
subroutine slaqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)
SLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
subroutine zlaqgb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, equed)
ZLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Detailed Description

Function Documentation

  subroutine claqgb (integer m, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, character equed)

CLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Purpose:

    !>
    !> CLAQGB equilibrates a general M by N band matrix A with KL
    !> subdiagonals and KU superdiagonals using the row and scaling factors
    !> in the vectors R and C.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is COMPLEX array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, the equilibrated matrix, in the same storage format
    !>          as A.  See EQUED for the form of the equilibrated matrix.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDA >= KL+KU+1.
    !>

    R

    !>          R is REAL array, dimension (M)
    !>          The row scale factors for A.
    !>

    C

    !>          C is REAL array, dimension (N)
    !>          The column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is REAL
    !>          Ratio of the smallest R(i) to the largest R(i).
    !>

    COLCND

    !>          COLCND is REAL
    !>          Ratio of the smallest C(i) to the largest C(i).
    !>

    AMAX

    !>          AMAX is REAL
    !>          Absolute value of largest matrix entry.
    !>

    EQUED

    !>          EQUED is CHARACTER*1
    !>          Specifies the form of equilibration that was done.
    !>          = 'N':  No equilibration
    !>          = 'R':  Row equilibration, i.e., A has been premultiplied by
    !>                  diag(R).
    !>          = 'C':  Column equilibration, i.e., A has been postmultiplied
    !>                  by diag(C).
    !>          = 'B':  Both row and column equilibration, i.e., A has been
    !>                  replaced by diag(R) * A * diag(C).
    !>

Internal Parameters:

    !>  THRESH is a threshold value used to decide if row or column scaling
    !>  should be done based on the ratio of the row or column scaling
    !>  factors.  If ROWCND < THRESH, row scaling is done, and if
    !>  COLCND < THRESH, column scaling is done.
    !>
    !>  LARGE and SMALL are threshold values used to decide if row scaling
    !>  should be done based on the absolute size of the largest matrix
    !>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dlaqgb (integer m, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, character equed)

DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Purpose:

    !>
    !> DLAQGB equilibrates a general M by N band matrix A with KL
    !> subdiagonals and KU superdiagonals using the row and scaling factors
    !> in the vectors R and C.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, the equilibrated matrix, in the same storage format
    !>          as A.  See EQUED for the form of the equilibrated matrix.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDA >= KL+KU+1.
    !>

    R

    !>          R is DOUBLE PRECISION array, dimension (M)
    !>          The row scale factors for A.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (N)
    !>          The column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is DOUBLE PRECISION
    !>          Ratio of the smallest R(i) to the largest R(i).
    !>

    COLCND

    !>          COLCND is DOUBLE PRECISION
    !>          Ratio of the smallest C(i) to the largest C(i).
    !>

    AMAX

    !>          AMAX is DOUBLE PRECISION
    !>          Absolute value of largest matrix entry.
    !>

    EQUED

    !>          EQUED is CHARACTER*1
    !>          Specifies the form of equilibration that was done.
    !>          = 'N':  No equilibration
    !>          = 'R':  Row equilibration, i.e., A has been premultiplied by
    !>                  diag(R).
    !>          = 'C':  Column equilibration, i.e., A has been postmultiplied
    !>                  by diag(C).
    !>          = 'B':  Both row and column equilibration, i.e., A has been
    !>                  replaced by diag(R) * A * diag(C).
    !>

Internal Parameters:

    !>  THRESH is a threshold value used to decide if row or column scaling
    !>  should be done based on the ratio of the row or column scaling
    !>  factors.  If ROWCND < THRESH, row scaling is done, and if
    !>  COLCND < THRESH, column scaling is done.
    !>
    !>  LARGE and SMALL are threshold values used to decide if row scaling
    !>  should be done based on the absolute size of the largest matrix
    !>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine slaqgb (integer m, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, character equed)

SLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Purpose:

    !>
    !> SLAQGB equilibrates a general M by N band matrix A with KL
    !> subdiagonals and KU superdiagonals using the row and scaling factors
    !> in the vectors R and C.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is REAL array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, the equilibrated matrix, in the same storage format
    !>          as A.  See EQUED for the form of the equilibrated matrix.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDA >= KL+KU+1.
    !>

    R

    !>          R is REAL array, dimension (M)
    !>          The row scale factors for A.
    !>

    C

    !>          C is REAL array, dimension (N)
    !>          The column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is REAL
    !>          Ratio of the smallest R(i) to the largest R(i).
    !>

    COLCND

    !>          COLCND is REAL
    !>          Ratio of the smallest C(i) to the largest C(i).
    !>

    AMAX

    !>          AMAX is REAL
    !>          Absolute value of largest matrix entry.
    !>

    EQUED

    !>          EQUED is CHARACTER*1
    !>          Specifies the form of equilibration that was done.
    !>          = 'N':  No equilibration
    !>          = 'R':  Row equilibration, i.e., A has been premultiplied by
    !>                  diag(R).
    !>          = 'C':  Column equilibration, i.e., A has been postmultiplied
    !>                  by diag(C).
    !>          = 'B':  Both row and column equilibration, i.e., A has been
    !>                  replaced by diag(R) * A * diag(C).
    !>

Internal Parameters:

    !>  THRESH is a threshold value used to decide if row or column scaling
    !>  should be done based on the ratio of the row or column scaling
    !>  factors.  If ROWCND < THRESH, row scaling is done, and if
    !>  COLCND < THRESH, column scaling is done.
    !>
    !>  LARGE and SMALL are threshold values used to decide if row scaling
    !>  should be done based on the absolute size of the largest matrix
    !>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zlaqgb (integer m, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, character equed)

ZLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Purpose:

    !>
    !> ZLAQGB equilibrates a general M by N band matrix A with KL
    !> subdiagonals and KU superdiagonals using the row and scaling factors
    !> in the vectors R and C.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    AB

    !>          AB is COMPLEX*16 array, dimension (LDAB,N)
    !>          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
    !>          The j-th column of A is stored in the j-th column of the
    !>          array AB as follows:
    !>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
    !>
    !>          On exit, the equilibrated matrix, in the same storage format
    !>          as A.  See EQUED for the form of the equilibrated matrix.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDA >= KL+KU+1.
    !>

    R

    !>          R is DOUBLE PRECISION array, dimension (M)
    !>          The row scale factors for A.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (N)
    !>          The column scale factors for A.
    !>

    ROWCND

    !>          ROWCND is DOUBLE PRECISION
    !>          Ratio of the smallest R(i) to the largest R(i).
    !>

    COLCND

    !>          COLCND is DOUBLE PRECISION
    !>          Ratio of the smallest C(i) to the largest C(i).
    !>

    AMAX

    !>          AMAX is DOUBLE PRECISION
    !>          Absolute value of largest matrix entry.
    !>

    EQUED

    !>          EQUED is CHARACTER*1
    !>          Specifies the form of equilibration that was done.
    !>          = 'N':  No equilibration
    !>          = 'R':  Row equilibration, i.e., A has been premultiplied by
    !>                  diag(R).
    !>          = 'C':  Column equilibration, i.e., A has been postmultiplied
    !>                  by diag(C).
    !>          = 'B':  Both row and column equilibration, i.e., A has been
    !>                  replaced by diag(R) * A * diag(C).
    !>

Internal Parameters:

    !>  THRESH is a threshold value used to decide if row or column scaling
    !>  should be done based on the ratio of the row or column scaling
    !>  factors.  If ROWCND < THRESH, row scaling is done, and if
    !>  COLCND < THRESH, column scaling is done.
    !>
    !>  LARGE and SMALL are threshold values used to decide if row scaling
    !>  should be done based on the absolute size of the largest matrix
    !>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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