?laqsp

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?laqsp

Scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by ?ppequ .

Syntax

call slaqsp(uplo, n, ap, s, scond, amax, equed)
call dlaqsp(uplo, n, ap, s, scond, amax, equed)
call claqsp(uplo, n, ap, s, scond, amax, equed)
call zlaqsp(uplo, n, ap, s, scond, amax, equed)

Include Files

mkl.fi

Description

The routine ?laqsp 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.

ap: REAL for slaqsp DOUBLE PRECISION for dlaqsp COMPLEX for claqsp DOUBLE COMPLEX for zlaqsp Array, DIMENSION ( n(n+1)/2 ). On entry, the upper or lower triangle of the symmetric matrix A , packed columnwise in a linear array. The j -th column of A is stored in the array ap as follows: if uplo = 'U' , ap(i + (j-1)j/2) = A(i,j) for 1 ≤ i ≤ j ; if uplo = 'L' , ap(i + (j-1)(2n-j)/2) = A(i,j) for j≤i≤n .
s: REAL for slaqsp / claqsp DOUBLE PRECISION for dlaqsp / zlaqsp Array, DIMENSION ( n ). The scale factors for A .
scond: REAL for slaqsp / claqsp DOUBLE PRECISION for dlaqsp / zlaqsp Ratio of the smallest s(i) to the largest s(i).
amax: REAL for slaqsp / claqsp DOUBLE PRECISION for dlaqsp / zlaqsp Absolute value of largest matrix entry.

Output Parameters

ap: On exit, the equilibrated matrix: diag(s)*A*diag(s) , in the same storage format as A .
equed: CHARACTER*1 . Specifies whether or not equilibration was done. If equed = 'N' : No equilibration. If equed = 'Y' : Equilibration was done, that is, A has been replaced by diag(s)*A*diag(s) .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

?laqsp

Syntax

Include Files

Description

Input Parameters

Output Parameters

Application Notes