?laqge

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?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 )

Include Files

mkl.fi

Description

slaqge dlaqge claqge zlaqge

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 If equed = 'B' : Both row and column equilibration, that is, A has been replaced by diag(r)*A*diag(c) .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

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?laqge

Syntax

Include Files

Description

Input Parameters

Output Parameters

Application Notes