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 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.



          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 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 141 of file claqge.f.

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 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.



          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 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 140 of file dlaqge.f.

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 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.



          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 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 140 of file slaqge.f.

subroutine zlaqge (integer m, integer n, complex16, 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 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.



          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 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 141 of file zlaqge.f.

Author

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