SRC/zgbequb.f(3)

NAME
SRC/zgbequb.f

SYNOPSIS

  Functions/Subroutines
subroutine zgbequb (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
ZGBEQUB

Function/Subroutine Documentation

  subroutine zgbequb (integer m, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)

ZGBEQUB

Purpose:

    !>
    !> ZGBEQUB computes row and column scalings intended to equilibrate an
    !> M-by-N 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 an absolute value of at most
    !> the radix.
    !>
    !> R(i) and C(j) are restricted to be a power of the radix 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.
    !>
    !> This routine differs from ZGEEQU by restricting the scaling factors
    !> to a power of the radix.  Barring over- and underflow, scaling by
    !> these factors introduces no additional rounding errors.  However, the
    !> scaled entries' magnitudes are no longer approximately 1 but lie
    !> between sqrt(radix) and 1/sqrt(radix).
    !>

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 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(N,j+kl)
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array A.  LDAB >= max(1,M).
    !>

    R

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

    C

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

    ROWCND

    !>          ROWCND is DOUBLE PRECISION
    !>          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 DOUBLE PRECISION
    !>          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 DOUBLE PRECISION
    !>          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 159 of file zgbequb.f.

Author

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