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 matrix A and
       reduce its condition number

SYNOPSIS

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

           IMPLICIT        NONE

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

           REAL            AMAX, COLCND, ROWCND

           REAL            AB( LDAB, * ), C( * ), R( * )

PURPOSE

       SGBEQUB 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 SGEEQU 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).

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

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

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

        ROWCND  (output) 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  (output) 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    (output) 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    (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                           SGBEQUB(3lapack)