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 is INTEGER


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



          N is INTEGER


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



          KL is INTEGER


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



          KU is INTEGER


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



          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 is REAL array, dimension (M)


          The row scale factors for A.



          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.

Definition at line 158 of file claqgb.f.

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 is INTEGER


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



          N is INTEGER


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



          KL is INTEGER


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



          KU is INTEGER


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



          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 is DOUBLE PRECISION array, dimension (M)


          The row scale factors for A.



          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.

Definition at line 157 of file dlaqgb.f.

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 is INTEGER


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



          N is INTEGER


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



          KL is INTEGER


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



          KU is INTEGER


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



          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 is REAL array, dimension (M)


          The row scale factors for A.



          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.

Definition at line 157 of file slaqgb.f.

subroutine zlaqgb (integer m, integer n, integer kl, integer ku, complex16, 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 is INTEGER


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



          N is INTEGER


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



          KL is INTEGER


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



          KU is INTEGER


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



          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 is DOUBLE PRECISION array, dimension (M)


          The row scale factors for A.



          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.

Definition at line 158 of file zlaqgb.f.

Author

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