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 (integerM, integerN, integerKL, integerKU, real, dimension( ldab, * )AB,
       integerLDAB, real, dimension( * )R, real, dimension( * )C, realROWCND, realCOLCND,
       realAMAX, integerINFO)
       SGBEQU

       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.

       Date:
           November 2011

       Definition at line 153 of file sgbequ.f.

Author

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