zgbequb.f(3)

NAME
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 (integerM, integerN, integerKL, integerKU, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )R, double precision, dimension( * )C, double precisionROWCND, double precisionCOLCND, double precisionAMAX, integerINFO)

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.  Baring over- and underflow, scaling by
     these factors introduces no additional rounding errors.  However, the
     scaled entries' magnitured 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 DOUBLE PRECISION 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.

Date:
    November 2011

Definition at line 161 of file zgbequb.f.

Author

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