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.

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

    !>          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.

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

    !>          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.

Definition at line 140 of file slaqge.f.

  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.

Definition at line 141 of file zlaqge.f.

Author

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