slaqgb.f(3)

NAME
slaqgb.f -

SYNOPSIS

  Functions/Subroutines

subroutine slaqgb (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED)
SLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Function/Subroutine Documentation

  subroutine slaqgb (integerM, integerN, integerKL, integerKU, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )R, real, dimension( * )C, realROWCND, realCOLCND, realAMAX, characterEQUED)

SLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Purpose:

     SLAQGB 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.

Parameters:
    M

              M is INTEGER
              The number of rows of the matrix A.  M >= 0.

    N

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

    KL

              KL is INTEGER
              The number of subdiagonals within the band of A.  KL >= 0.

    KU

              KU is INTEGER
              The number of superdiagonals within the band of A.  KU >= 0.

    AB

              AB is REAL 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

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

    R

              R is REAL array, dimension (M)
              The row scale factors for A.

    C

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

    ROWCND

              ROWCND is REAL
              Ratio of the smallest R(i) to the largest R(i).

    COLCND

              COLCND is REAL
              Ratio of the smallest C(i) to the largest C(i).

    AMAX

              AMAX is REAL
              Absolute value of largest matrix entry.

    EQUED

              EQUED is 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).

Internal 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.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

Definition at line 159 of file slaqgb.f.

Author

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