Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  - computes row and column scalings intended to equilibrate an M-by-N band matrix
       A and reduce its condition number

SYNOPSIS

       SUBROUTINE ZGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO )

           INTEGER        INFO, KL, KU, LDAB, M, N

           DOUBLE         PRECISION AMAX, COLCND, ROWCND

           DOUBLE         PRECISION C( * ), R( * )

           COMPLEX*16     AB( LDAB, * )

PURPOSE

       ZGBEQU 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.

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) COMPLEX*16 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    (input) INTEGER
                The leading dimension of the array AB.  LDAB >= KL+KU+1.

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

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

        ROWCND  (output) 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  (output) 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    (output) 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    (output) 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

 LAPACK routine (version 3.2)               April 2011                            ZGBEQU(3lapack)