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laqge(3) LAPACK laqge(3)

NAME

laqge - laqge: row/col scale matrix

SYNOPSIS

Functions


subroutine claqge (m, n, a, lda, r, c, rowcnd, colcnd, amax, equed)
CLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ. subroutine dlaqge (m, n, a, lda, r, c, rowcnd, colcnd, amax, equed)
DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ. subroutine slaqge (m, n, a, lda, r, c, rowcnd, colcnd, amax, equed)
SLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ. subroutine zlaqge (m, n, a, lda, r, c, rowcnd, colcnd, amax, equed)
ZLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

Detailed Description

Function Documentation

subroutine claqge (integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, character equed)

CLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

Purpose:

!>
!> CLAQGE equilibrates a general M by N matrix A using the row and
!> column 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.
!>

A

!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the M by N matrix A.
!>          On exit, the equilibrated matrix.  See EQUED for the form of
!>          the equilibrated matrix.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(M,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 dlaqge (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, character equed)

DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

Purpose:

!>
!> DLAQGE equilibrates a general M by N matrix A using the row and
!> column 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.
!>

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the M by N matrix A.
!>          On exit, the equilibrated matrix.  See EQUED for the form of
!>          the equilibrated matrix.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(M,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 slaqge (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, character equed)

SLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

Purpose:

!>
!> SLAQGE equilibrates a general M by N matrix A using the row and
!> column 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.
!>

A

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the M by N matrix A.
!>          On exit, the equilibrated matrix.  See EQUED for the form of
!>          the equilibrated matrix.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(M,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 zlaqge (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, character equed)

ZLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

Purpose:

!>
!> ZLAQGE equilibrates a general M by N matrix A using the row and
!> column 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.
!>

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the M by N matrix A.
!>          On exit, the equilibrated matrix.  See EQUED for the form of
!>          the equilibrated matrix.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(M,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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