Visible to Intel only — GUID: GUID-62ECE47D-696A-4EA0-A46C-6BC3158F5EF7
Visible to Intel only — GUID: GUID-62ECE47D-696A-4EA0-A46C-6BC3158F5EF7
?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. 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If equed = 'Y': Equilibration was done, that is, A has been replaced by diag(s)*A*diag(s).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.