Visible to Intel only — GUID: GUID-C0F3193E-6FA3-4CD8-93E4-D0FAD17650E7
Visible to Intel only — GUID: GUID-C0F3193E-6FA3-4CD8-93E4-D0FAD17650E7
?laqhp
Scales a Hermitian matrix stored in packed form.
Syntax
call claqhp( uplo, n, ap, s, scond, amax, equed )
call zlaqhp( uplo, n, ap, s, scond, amax, equed )
Include Files
- mkl.fi
Description
The routine equilibrates a Hermitian matrix A using the scaling factors in the vector s.
Input Parameters
- uplo
-
CHARACTER*1.
Specifies whether to store the upper or lower part of the Hermitian matrix A.
If uplo = 'U', the upper triangular part of A;
if uplo = 'L', the lower triangular part of A.
- n
-
INTEGER. The order of the matrix A.
n≥ 0.
- ap
-
COMPLEX for claqhp
DOUBLE COMPLEX for zlaqhp
Array, DIMENSION (n*(n+1)/2). The Hermitian matrix A.
If uplo = 'U', the upper triangular part of the Hermitian matrix A is stored in the packed array ap as follows:
ap(i+(j-1)*j/2) = A(i,j) for 1 ≤ i ≤ j.
If uplo = 'L', the lower triangular part of Hermitian matrix A is stored in the packed array ap as follows:
ap(i+(j-1)*(2n-j)/2) = A(i,j) for j ≤ i ≤ n.
- s
-
REAL for claqhp
DOUBLE PRECISION for zlaqhp
Array, DIMENSION (n). The scale factors for A.
- scond
-
REAL for claqhp
DOUBLE PRECISION for zlaqhp
Ratio of the smallest s(i) to the largest s(i).
- amax
-
REAL for claqhp
DOUBLE PRECISION for zlaqhp
Absolute value of largest matrix entry.
Output Parameters
- a
-
If equed = 'Y', a contains the equilibrated matrix diag(s)*A*diag(s) in the same storage format as on input.
- 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If equed = 'Y': Equilibration was done, that is, A has been replaced by diag(s)*A*diag(s).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. The parameter thresh is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors. If scond < thresh, scaling is done.
The large and small parameters 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.