sgbequ.f(3)

NAME
sgbequ.f

SYNOPSIS

  Functions/Subroutines
subroutine sgbequ (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO)
SGBEQU

Function/Subroutine Documentation

  subroutine sgbequ (integer M, integer N, integer KL, integer KU, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) R, real, dimension( * ) C, real ROWCND, real COLCND, real AMAX, integer INFO)

Purpose:

     SGBEQU computes row and column scalings intended to equilibrate an
     M-by-N band matrix A and reduce its condition number.  R returns the
     row scale factors and C the column scale factors, chosen to try to
     make the largest element in each row and column of the matrix B with
     elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
     R(i) and C(j) are restricted to be between SMLNUM = smallest safe
     number and BIGNUM = largest safe number.  Use of these scaling
     factors is not guaranteed to reduce the condition number of A but
     works well in practice.

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)
              The band matrix A, stored 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).

    LDAB

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

    R

              R is REAL array, dimension (M)
              If INFO = 0, or INFO > M, R contains the row scale factors
              for A.

    C

              C is REAL array, dimension (N)
              If INFO = 0, C contains the column scale factors for A.

    ROWCND

              ROWCND is REAL
              If INFO = 0 or INFO > M, ROWCND contains the ratio of the
              smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
              AMAX is neither too large nor too small, it is not worth
              scaling by R.

    COLCND

              COLCND is REAL
              If INFO = 0, COLCND contains the ratio of the smallest
              C(i) to the largest C(i).  If COLCND >= 0.1, it is not
              worth scaling by C.

    AMAX

              AMAX is REAL
              Absolute value of largest matrix element.  If AMAX is very
              close to overflow or very close to underflow, the matrix
              should be scaled.

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value
              > 0:  if INFO = i, and i is
                    <= M:  the i-th row of A is exactly zero
                    >  M:  the (i-M)-th column of A is exactly zero

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 151 of file sgbequ.f.

Author

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