Visible to Intel only — GUID: GUID-7AFADF87-109F-47EC-B3B7-20ABBB07C2A1
Visible to Intel only — GUID: GUID-7AFADF87-109F-47EC-B3B7-20ABBB07C2A1
?laqsb
Scales a symmetric band matrix, using scaling factors computed by ?pbequ.
Syntax
call slaqsb( uplo, n, kd, ab, ldab, s, scond, amax, equed )
call dlaqsb( uplo, n, kd, ab, ldab, s, scond, amax, equed )
call claqsb( uplo, n, kd, ab, ldab, s, scond, amax, equed )
call zlaqsb( uplo, n, kd, ab, ldab, s, scond, amax, equed )
Include Files
- mkl.fi
Description
The routine equilibrates a symmetric 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 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.
- 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
-
REAL for slaqsb
DOUBLE PRECISION for dlaqsb
COMPLEX for claqsb
DOUBLE COMPLEX for zlaqsb
Array, DIMENSION (ldab,n). On entry, the upper or lower triangle of the symmetric 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.
- s
-
REAL for slaqsb/claqsb
DOUBLE PRECISION for dlaqsb/zlaqsb
Array, DIMENSION (n). The scale factors for A.
- scond
-
REAL for slaqsb/claqsb
DOUBLE PRECISION for dlaqsb/zlaqsb
Ratio of the smallest s(i) to the largest s(i).
- amax
-
REAL for slaqsb/claqsb
DOUBLE PRECISION for dlaqsb/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 of the band matrix A that can be A = UT*U or A = L*LT for real flavors and A = UH*U or A = L*LH for complex flavors, 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If equed = 'Y': Equilibration was done, that is, A has been replaced by diag(s)*A*diag(s).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.