?laqsy

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?laqsy

Scales a symmetric/Hermitian matrix, using scaling factors computed by ?syequ , ?syequb , ?poequ , or ?poequb .

Syntax

call slaqsy ( uplo , n , a , lda , s , scond , amax , equed )

call dlaqsy ( uplo , n , a , lda , s , scond , amax , equed )

call claqsy ( uplo , n , a , lda , s , scond , amax , equed )

call zlaqsy ( uplo , n , a , lda , s , scond , amax , equed )

Include Files

mkl.fi

Description

slaqsy dlaqsy claqsy zlaqsy

The routine equilibrates a symmetric matrix A using the scaling factors in the vector s .

Input Parameters

uplo: CHARACTER*1 . Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. If uplo = 'U' : upper triangular. If uplo = 'L' : lower triangular.
n: INTEGER . The order of the matrix A . n≥ 0 .
a: REAL for slaqsy DOUBLE PRECISION for dlaqsy COMPLEX for claqsy DOUBLE COMPLEX for zlaqsy Array, DIMENSION ( lda , n ). On entry, the symmetric matrix A . If uplo = 'U' , the leading n -by- n upper triangular part of a contains the upper triangular part of the matrix A , and the strictly lower triangular part of a is not referenced. If uplo = 'L' , the leading n -by- n lower triangular part of a contains the lower triangular part of the matrix A , and the strictly upper triangular part of a is not referenced.
lda: INTEGER . The leading dimension of the array a . lda≥ max(n,1) .
s: REAL for slaqsy / claqsy DOUBLE PRECISION for dlaqsy / zlaqsy Array, DIMENSION ( n ). The scale factors for A .
scond: REAL for slaqsy / claqsy DOUBLE PRECISION for dlaqsy / zlaqsy Ratio of the smallest s(i) to the largest s(i).
amax: REAL for slaqsy / claqsy DOUBLE PRECISION for dlaqsy / zlaqsy Absolute value of largest matrix entry.

Output Parameters

a: On exit, if equed = 'Y' , the equilibrated matrix: diag(s)*A*diag(s) .
equed: CHARACTER*1 . Specifies whether or not equilibration was done. If equed = 'N' : No equilibration. If equed = 'Y' : Equilibration was done, i.e., A has been replaced by diag(s)*A*diag(s) .

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 scaling should be based on the ratio of the scaling factors. If scond < thresh , scaling is done. large and small are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element. If amax > large or amax < small , scaling is done.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?laqsy

Syntax

Include Files

Description

Input Parameters

Output Parameters

Application Notes