Visible to Intel only — GUID: GUID-99CE2EAC-0CDB-4030-88DA-5B94FF07088C
Visible to Intel only — GUID: GUID-99CE2EAC-0CDB-4030-88DA-5B94FF07088C
?laqhb
Scales a Hermetian band matrix, using scaling factors computed by ?pbequ.
Syntax
call claqhb( uplo, n, kd, ab, ldab, s, scond, amax, equed )
call zlaqhb( uplo, n, kd, ab, ldab, s, scond, amax, equed )
Include Files
- mkl.fi
Description
The routine equilibrates a Hermetian band 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 band matrix A is stored.
If uplo = 'U': upper triangular.
If uplo = 'L': lower triangular.
- n
-
INTEGER. The order of the matrix A.
n≥ 0.
- kd
-
INTEGER. The number of super-diagonals of the matrix A if uplo = 'U', or the number of sub-diagonals if uplo = 'L'.
kd≥ 0.
- ab
-
COMPLEX for claqhb
DOUBLE COMPLEX for zlaqhb
Array, DIMENSION (ldab,n). On entry, the upper or lower triangle of the band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array ab as follows:
if uplo = 'U', ab(kd+1+i-j,j) = A(i,j) for max(1,j-kd) ≤ i ≤ j;
if uplo = 'L', ab(1+i-j,j) = A(i,j) for j ≤ i ≤ min(n,j+kd).
- ldab
-
INTEGER. The leading dimension of the array ab.
ldab≥kd+1.
- scond
-
REAL for claqsb
DOUBLE PRECISION for zlaqsb
Ratio of the smallest s(i) to the largest s(i).
- amax
-
REAL for claqsb
DOUBLE PRECISION for zlaqsb
Absolute value of largest matrix entry.
Output Parameters
- ab
-
On exit, if info = 0, the triangular factor U or L from the Cholesky factorization A = UH*U or A = L*LH of the band matrix A, in the same storage format as A.
- s
-
REAL for claqsb
DOUBLE PRECISION for zlaqsb
Array, DIMENSION (n). The scale factors for 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If equed = 'Y': Equilibration was done, that is, A has been replaced by diag(s)*A*diag(s).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.
The values 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.