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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