?laqge

Scales a general rectangular matrix, using row and column scaling factors computed by ?geequ.

Syntax

call slaqge( m, n, a, lda, r, c, rowcnd, colcnd, amax, equed )

call dlaqge( m, n, a, lda, r, c, rowcnd, colcnd, amax, equed )

call claqge( m, n, a, lda, r, c, rowcnd, colcnd, amax, equed )

call zlaqge( m, n, a, lda, r, c, rowcnd, colcnd, amax, equed )

• mkl.fi

Description

The routine equilibrates a general m-by-n matrix A using the row and column scaling factors in the vectors r and c.

Input Parameters

m

INTEGER. The number of rows of the matrix A.

m 0.

n

INTEGER. The number of columns of the matrix A.

n 0.

a

REAL for slaqge

DOUBLE PRECISION for dlaqge

COMPLEX for claqge

DOUBLE COMPLEX for zlaqge

Array, DIMENSION (lda,n). On entry, the m-by-n matrix A.

lda

INTEGER. The leading dimension of the array a.

lda max(m,1).

r

REAL for slanqge/claqge

DOUBLE PRECISION for dlaqge/zlaqge

Array, DIMENSION (m). The row scale factors for A.

c

REAL for slanqge/claqge

DOUBLE PRECISION for dlaqge/zlaqge

Array, DIMENSION (n). The column scale factors for A.

rowcnd

REAL for slanqge/claqge

DOUBLE PRECISION for dlaqge/zlaqge

Ratio of the smallest r(i) to the largest r(i).

colcnd

REAL for slanqge/claqge

DOUBLE PRECISION for dlaqge/zlaqge

Ratio of the smallest c(i) to the largest c(i).

amax

REAL for slanqge/claqge

DOUBLE PRECISION for dlaqge/zlaqge

Absolute value of largest matrix entry.

Output Parameters

a

On exit, the equilibrated matrix.

See equed for the form of the equilibrated matrix.

equed

CHARACTER*1.

Specifies the form of equilibration that was done.

If equed = 'N': No equilibration

If equed = 'R': Row equilibration, that is, A has been premultiplied by diag(r).

If equed = 'C': Column equilibration, that is, A has been postmultiplied by diag(c).

If equed = 'B': Both row and column equilibration, that is, A has been replaced by diag(r)*A*diag(c).

Application Notes

The routine uses internal parameters thresh, large, and small, which have the following meaning. 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.

For more complete information about compiler optimizations, see our Optimization Notice.