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laqgb(3) LAPACK 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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