NAME

       sla_gbrcond.f -

SYNOPSIS

   Functions/Subroutines
       real function sla_gbrcond (TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, CMODE, C, INFO,
           WORK, IWORK)
           SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

Function/Subroutine Documentation

   real function sla_gbrcond (characterTRANS, integerN, integerKL, integerKU, real, dimension(
       ldab, * )AB, integerLDAB, real, dimension( ldafb, * )AFB, integerLDAFB, integer,
       dimension( * )IPIV, integerCMODE, real, dimension( * )C, integerINFO, real, dimension( *
       )WORK, integer, dimension( * )IWORK)
       SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

       Purpose:

               SLA_GBRCOND Estimates the Skeel condition number of  op(A) * op2(C)
               where op2 is determined by CMODE as follows
               CMODE =  1    op2(C) = C
               CMODE =  0    op2(C) = I
               CMODE = -1    op2(C) = inv(C)
               The Skeel condition number  cond(A) = norminf( |inv(A)||A| )
               is computed by computing scaling factors R such that
               diag(R)*A*op2(C) is row equilibrated and computing the standard
               infinity-norm condition number.

       Parameters:
           TRANS

                     TRANS is CHARACTER*1
                Specifies the form of the system of equations:
                  = 'N':  A * X = B     (No transpose)
                  = 'T':  A**T * X = B  (Transpose)
                  = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)

           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.

           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.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                The pivot indices from the factorization A = P*L*U
                as computed by SGBTRF; row i of the matrix was interchanged
                with row IPIV(i).

           CMODE

                     CMODE is INTEGER
                Determines op2(C) in the formula op(A) * op2(C) as follows:
                CMODE =  1    op2(C) = C
                CMODE =  0    op2(C) = I
                CMODE = -1    op2(C) = inv(C)

           C

                     C is REAL array, dimension (N)
                The vector C in the formula op(A) * op2(C).

           INFO

                     INFO is INTEGER
                  = 0:  Successful exit.
                i > 0:  The ith argument is invalid.

           WORK

                     WORK is REAL array, dimension (5*N).
                Workspace.

           IWORK

                     IWORK is INTEGER array, dimension (N).
                Workspace.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 168 of file sla_gbrcond.f.

Author

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