NAME

       sla_gbrpvgrw.f -

SYNOPSIS

   Functions/Subroutines
       real function sla_gbrpvgrw (N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)
           SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general
           banded matrix.

Function/Subroutine Documentation

   real function sla_gbrpvgrw (integerN, integerKL, integerKU, integerNCOLS, real, dimension(
       ldab, * )AB, integerLDAB, real, dimension( ldafb, * )AFB, integerLDAFB)
       SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general
       banded matrix.

       Purpose:

            SLA_GBRPVGRW computes the reciprocal pivot growth factor
            norm(A)/norm(U). The "max absolute element" norm is used. If this is
            much less than 1, the stability of the LU factorization of the
            (equilibrated) matrix A could be poor. This also means that the
            solution X, estimated condition numbers, and error bounds could be
            unreliable.

       Parameters:
           N

                     N is INTEGER
                The number of linear equations, i.e., the order 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.

           NCOLS

                     NCOLS is INTEGER
                The number of columns of the matrix A.  NCOLS >= 0.

           AB

                     AB is REAL 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 AB.  LDAB >= KL+KU+1.

           AFB

                     AFB is REAL array, dimension (LDAFB,N)
                Details of the LU factorization of the band matrix A, as
                computed by SGBTRF.  U is stored as an upper triangular
                band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
                and the multipliers used during the factorization are stored
                in rows KL+KU+2 to 2*KL+KU+1.

           LDAFB

                     LDAFB is INTEGER
                The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 117 of file sla_gbrpvgrw.f.

Author

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