# zlaqsb.f - Man Page

SRC/zlaqsb.f

## Synopsis

### Functions/Subroutines

subroutine **zlaqsb** (uplo, n, kd, ab, ldab, s, scond, amax, equed)**ZLAQSB** scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

## Function/Subroutine Documentation

### subroutine zlaqsb (character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)

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

**Purpose:**

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

*KD*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*AB is COMPLEX*16 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*S is DOUBLE PRECISION array, dimension (N) The scale factors for A.

*SCOND*SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i).

*AMAX*AMAX is DOUBLE PRECISION 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).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.

Definition at line **140** of file **zlaqsb.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlaqsb(3) is an alias of zlaqsb.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK