dlaqsb(3S)

NAME
     DLAQSB - equilibrate a symmetric band matrix A using the scaling factors
     in the vector S

SYNOPSIS
     SUBROUTINE DLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )

         CHARACTER      EQUED, UPLO

         INTEGER        KD, LDAB, N

         DOUBLE         PRECISION AMAX, SCOND

         DOUBLE         PRECISION AB( LDAB, * ), S( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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

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

     N       (input) INTEGER
             The order of the matrix A.  N >= 0.

     KD      (input) 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      (input/output) DOUBLE PRECISION 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'*U or A = L*L' of the band matrix A,
             in the same storage format as A.

     LDAB    (input) INTEGER
             The leading dimension of the array AB.  LDAB >= KD+1.

     S       (output) DOUBLE PRECISION array, dimension (N)
             The scale factors for A.

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

     AMAX    (input) DOUBLE PRECISION
             Absolute value of largest matrix entry.

     EQUED   (output) 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).

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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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