?laqsp

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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

slaqsp dlaqsp claqsp zlaqsp

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 . The order of the matrix A . n≥ 0 .
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 If equed = 'Y' : Equilibration was done, that is, A has been replaced by diag(s)*A*diag(s) .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