claqsb-f(3)

claqsb.f –

Synopsis

Functions/Subroutines

subroutine claqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Function/Subroutine Documentation

subroutine claqsb (characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )S, realSCOND, realAMAX, characterEQUED)

CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:

 CLAQSB equilibrates a symmetric band matrix A using the scaling
 factors in the vector S.

Parameters:

UPLO

 UPLO is CHARACTER*1
 Specifies whether the upper or lower triangular part of the
 symmetric matrix A is stored.
 = 'U': Upper triangular
 = 'L': Lower triangular

 N is INTEGER
 The order of the matrix A. N >= 0.

 KD is 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 is COMPLEX 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).
 On exit, if INFO = 0, the triangular factor U or L from the
 Cholesky factorization A = U**H *U or A = L*L**H of the band
 matrix A, in the same storage format as A.

LDAB

 LDAB is INTEGER
 The leading dimension of the array AB. LDAB >= KD+1.

 S is REAL array, dimension (N)
 The scale factors for A.

SCOND

 SCOND is REAL
 Ratio of the smallest S(i) to the largest S(i).

AMAX

 AMAX is REAL
 Absolute value of largest matrix entry.

EQUED

 EQUED is CHARACTER*1
 Specifies whether or not equilibration was done.
 = 'N': No equilibration.
 = 'Y': Equilibration was done, i.e., A has been replaced by
 diag(S) * A * diag(S).

Internal Parameters:

 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.
 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 142 of file claqsb.f.

Author

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