?laqsy

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

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

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. Specifies the order of the matrix A. The value of n must be at least zero.

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 If equed = 'Y' : Equilibration was done, i.e., A has been replaced by diag(s)*A*diag(s) .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