zlaqgb(3S)

NAME
     ZLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals
     and KU superdiagonals using the row and scaling factors in the vectors R
     and C

SYNOPSIS
     SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
                        EQUED )

         CHARACTER      EQUED

         INTEGER        KL, KU, LDAB, M, N

         DOUBLE         PRECISION AMAX, COLCND, ROWCND

         DOUBLE         PRECISION C( * ), R( * )

         COMPLEX*16     AB( LDAB, * )

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
     ZLAQGB equilibrates a general M by N band matrix A with KL subdiagonals
     and KU superdiagonals using the row and scaling factors in the vectors R
     and C.

ARGUMENTS
     M       (input) INTEGER
             The number of rows of the matrix A.  M >= 0.

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

     KL      (input) INTEGER
             The number of subdiagonals within the band of A.  KL >= 0.

     KU      (input) INTEGER
             The number of superdiagonals within the band of A.  KU >= 0.

     AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
             On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
             The j-th column of A is stored in the j-th column of the array AB
             as follows:  AB(ku+1+i-j,j) = A(i,j) for max(1,j-
             ku)<=i<=min(m,j+kl)

             On exit, the equilibrated matrix, in the same storage format as
             A.  See EQUED for the form of the equilibrated matrix.

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

     R       (output) DOUBLE PRECISION array, dimension (M)
             The row scale factors for A.

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

     ROWCND  (output) DOUBLE PRECISION
             Ratio of the smallest R(i) to the largest R(i).

     COLCND  (output) DOUBLE PRECISION
             Ratio of the smallest C(i) to the largest C(i).

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

     EQUED   (output) CHARACTER*1
             Specifies the form of equilibration that was done.  = 'N':  No
             equilibration
             = 'R':  Row equilibration, i.e., A has been premultiplied by
             diag(R).  = 'C':  Column equilibration, i.e., A has been
             postmultiplied by diag(C).  = 'B':  Both row and column
             equilibration, i.e., A has been replaced by diag(R) * A *
             diag(C).

PARAMETERS
     THRESH is a threshold value used to decide if row or column scaling
     should be done based on the ratio of the row or column scaling factors.
     If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column
     scaling is done.

     LARGE and SMALL are threshold values used to decide if row scaling should
     be done based on the absolute size of the largest matrix element.  If
     AMAX > LARGE or AMAX < SMALL, row scaling is done.

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

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