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+*> \brief <b> SGBSVXX computes the solution to system of linear equations A * X = B for GB matrices</b>
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition
+*  ==========
+*
+*       SUBROUTINE SGBSVXX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
+*                           LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
+*                           RCOND, RPVGRW, BERR, N_ERR_BNDS,
+*                           ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
+*                           WORK, IWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          EQUED, FACT, TRANS
+*       INTEGER            INFO, LDAB, LDAFB, LDB, LDX, N, NRHS, NPARAMS,
+*      $                   N_ERR_BNDS
+*       REAL               RCOND, RPVGRW
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * ), IWORK( * )
+*       REAL               AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ),
+*      $                   X( LDX , * ),WORK( * )
+*       REAL               R( * ), C( * ), PARAMS( * ), BERR( * ),
+*      $                   ERR_BNDS_NORM( NRHS, * ),
+*      $                   ERR_BNDS_COMP( NRHS, * )
+*       ..
+*  
+*  Purpose
+*  =======
+*
+*>\details \b Purpose:
+*>\verbatim
+*> Purpose
+*>    =======
+*>
+*>    SGBSVXX uses the LU factorization to compute the solution to a
+*>    real system of linear equations  A * X = B,  where A is an
+*>    N-by-N matrix and X and B are N-by-NRHS matrices.
+*>
+*>    If requested, both normwise and maximum componentwise error bounds
+*>    are returned. SGBSVXX will return a solution with a tiny
+*>    guaranteed error (O(eps) where eps is the working machine
+*>    precision) unless the matrix is very ill-conditioned, in which
+*>    case a warning is returned. Relevant condition numbers also are
+*>    calculated and returned.
+*>
+*>    SGBSVXX accepts user-provided factorizations and equilibration
+*>    factors; see the definitions of the FACT and EQUED options.
+*>    Solving with refinement and using a factorization from a previous
+*>    SGBSVXX call will also produce a solution with either O(eps)
+*>    errors or warnings, but we cannot make that claim for general
+*>    user-provided factorizations and equilibration factors if they
+*>    differ from what SGBSVXX would itself produce.
+*>
+*> Description
+*> ===========
+*>
+*>    The following steps are performed:
+*>
+*>    1. If FACT = 'E', real scaling factors are computed to equilibrate
+*>    the system:
+*>
+*>      TRANS = 'N':  diag(R)*A*diag(C)     *inv(diag(C))*X = diag(R)*B
+*>      TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
+*>      TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
+*>
+*>    Whether or not the system will be equilibrated depends on the
+*>    scaling of the matrix A, but if equilibration is used, A is
+*>    overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
+*>    or diag(C)*B (if TRANS = 'T' or 'C').
+*>
+*>    2. If FACT = 'N' or 'E', the LU decomposition is used to factor
+*>    the matrix A (after equilibration if FACT = 'E') as
+*>
+*>      A = P * L * U,
+*>
+*>    where P is a permutation matrix, L is a unit lower triangular
+*>    matrix, and U is upper triangular.
+*>
+*>    3. If some U(i,i)=0, so that U is exactly singular, then the
+*>    routine returns with INFO = i. Otherwise, the factored form of A
+*>    is used to estimate the condition number of the matrix A (see
+*>    argument RCOND). If the reciprocal of the condition number is less
+*>    than machine precision, the routine still goes on to solve for X
+*>    and compute error bounds as described below.
+*>
+*>    4. The system of equations is solved for X using the factored form
+*>    of A.
+*>
+*>    5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
+*>    the routine will use iterative refinement to try to get a small
+*>    error and error bounds.  Refinement calculates the residual to at
+*>    least twice the working precision.
+*>
+*>    6. If equilibration was used, the matrix X is premultiplied by
+*>    diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
+*>    that it solves the original system before equilibration.
+*>
+*>\endverbatim
+*
+*  Arguments
+*  =========
+*
+*> \verbatim
+*>     Some optional parameters are bundled in the PARAMS array.  These
+*>     settings determine how refinement is performed, but often the
+*>     defaults are acceptable.  If the defaults are acceptable, users
+*>     can pass NPARAMS = 0 which prevents the source code from accessing
+*>     the PARAMS argument.
+*> \endverbatim
+*>
+*> \param[in] FACT
+*> \verbatim
+*>          FACT is CHARACTER*1
+*>     Specifies whether or not the factored form of the matrix A is
+*>     supplied on entry, and if not, whether the matrix A should be
+*>     equilibrated before it is factored.
+*>       = 'F':  On entry, AF and IPIV contain the factored form of A.
+*>               If EQUED is not 'N', the matrix A has been
+*>               equilibrated with scaling factors given by R and C.
+*>               A, AF, and IPIV are not modified.
+*>       = 'N':  The matrix A will be copied to AF and factored.
+*>       = 'E':  The matrix A will be equilibrated if necessary, then
+*>               copied to AF and factored.
+*> \endverbatim
+*>
+*> \param[in] TRANS
+*> \verbatim
+*>          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)
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>     The number of linear equations, i.e., the order of the
+*>     matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] KL
+*> \verbatim
+*>          KL is INTEGER
+*>     The number of subdiagonals within the band of A.  KL >= 0.
+*> \endverbatim
+*>
+*> \param[in] KU
+*> \verbatim
+*>          KU is INTEGER
+*>     The number of superdiagonals within the band of A.  KU >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*>          NRHS is INTEGER
+*>     The number of right hand sides, i.e., the number of columns
+*>     of the matrices B and X.  NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] AB
+*> \verbatim
+*>          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)
+*> \endverbatim
+*> \verbatim
+*>     If FACT = 'F' and EQUED is not 'N', then AB must have been
+*>     equilibrated by the scaling factors in R and/or C.  AB is not
+*>     modified if FACT = 'F' or 'N', or if FACT = 'E' and
+*>     EQUED = 'N' on exit.
+*> \endverbatim
+*> \verbatim
+*>     On exit, if EQUED .ne. 'N', A is scaled as follows:
+*>     EQUED = 'R':  A := diag(R) * A
+*>     EQUED = 'C':  A := A * diag(C)
+*>     EQUED = 'B':  A := diag(R) * A * diag(C).
+*> \endverbatim
+*>
+*> \param[in] LDAB
+*> \verbatim
+*>          LDAB is INTEGER
+*>     The leading dimension of the array AB.  LDAB >= KL+KU+1.
+*> \endverbatim
+*>
+*> \param[in,out] AFB
+*> \verbatim
+*>          AFB is or output) REAL array, dimension (LDAFB,N)
+*>     If FACT = 'F', then AFB is an input argument and on entry
+*>     contains 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.  If EQUED .ne. 'N', then AFB is
+*>     the factored form of the equilibrated matrix A.
+*> \endverbatim
+*> \verbatim
+*>     If FACT = 'N', then AF is an output argument and on exit
+*>     returns the factors L and U from the factorization A = P*L*U
+*>     of the original matrix A.
+*> \endverbatim
+*> \verbatim
+*>     If FACT = 'E', then AF is an output argument and on exit
+*>     returns the factors L and U from the factorization A = P*L*U
+*>     of the equilibrated matrix A (see the description of A for
+*>     the form of the equilibrated matrix).
+*> \endverbatim
+*>
+*> \param[in] LDAFB
+*> \verbatim
+*>          LDAFB is INTEGER
+*>     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
+*> \endverbatim
+*>
+*> \param[in,out] IPIV
+*> \verbatim
+*>          IPIV is or output) INTEGER array, dimension (N)
+*>     If FACT = 'F', then IPIV is an input argument and on entry
+*>     contains the pivot indices from the factorization A = P*L*U
+*>     as computed by SGETRF; row i of the matrix was interchanged
+*>     with row IPIV(i).
+*> \endverbatim
+*> \verbatim
+*>     If FACT = 'N', then IPIV is an output argument and on exit
+*>     contains the pivot indices from the factorization A = P*L*U
+*>     of the original matrix A.
+*> \endverbatim
+*> \verbatim
+*>     If FACT = 'E', then IPIV is an output argument and on exit
+*>     contains the pivot indices from the factorization A = P*L*U
+*>     of the equilibrated matrix A.
+*> \endverbatim
+*>
+*> \param[in,out] EQUED
+*> \verbatim
+*>          EQUED is or output) CHARACTER*1
+*>     Specifies the form of equilibration that was done.
+*>       = 'N':  No equilibration (always true if FACT = 'N').
+*>       = 'R':  Row equilibration, i.e., A has been premultiplied by
+*>               diag(R).
+*>       = 'C':  Column equilibration, i.e., A has been postmultiplied
+*>               by diag(C).
+*>       = 'B':  Both row and column equilibration, i.e., A has been
+*>               replaced by diag(R) * A * diag(C).
+*>     EQUED is an input argument if FACT = 'F'; otherwise, it is an
+*>     output argument.
+*> \endverbatim
+*>
+*> \param[in,out] R
+*> \verbatim
+*>          R is or output) REAL array, dimension (N)
+*>     The row scale factors for A.  If EQUED = 'R' or 'B', A is
+*>     multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
+*>     is not accessed.  R is an input argument if FACT = 'F';
+*>     otherwise, R is an output argument.  If FACT = 'F' and
+*>     EQUED = 'R' or 'B', each element of R must be positive.
+*>     If R is output, each element of R is a power of the radix.
+*>     If R is input, each element of R should be a power of the radix
+*>     to ensure a reliable solution and error estimates. Scaling by
+*>     powers of the radix does not cause rounding errors unless the
+*>     result underflows or overflows. Rounding errors during scaling
+*>     lead to refining with a matrix that is not equivalent to the
+*>     input matrix, producing error estimates that may not be
+*>     reliable.
+*> \endverbatim
+*>
+*> \param[in,out] C
+*> \verbatim
+*>          C is or output) REAL array, dimension (N)
+*>     The column scale factors for A.  If EQUED = 'C' or 'B', A is
+*>     multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
+*>     is not accessed.  C is an input argument if FACT = 'F';
+*>     otherwise, C is an output argument.  If FACT = 'F' and
+*>     EQUED = 'C' or 'B', each element of C must be positive.
+*>     If C is output, each element of C is a power of the radix.
+*>     If C is input, each element of C should be a power of the radix
+*>     to ensure a reliable solution and error estimates. Scaling by
+*>     powers of the radix does not cause rounding errors unless the
+*>     result underflows or overflows. Rounding errors during scaling
+*>     lead to refining with a matrix that is not equivalent to the
+*>     input matrix, producing error estimates that may not be
+*>     reliable.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is REAL array, dimension (LDB,NRHS)
+*>     On entry, the N-by-NRHS right hand side matrix B.
+*>     On exit,
+*>     if EQUED = 'N', B is not modified;
+*>     if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by
+*>        diag(R)*B;
+*>     if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is
+*>        overwritten by diag(C)*B.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>     The leading dimension of the array B.  LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] X
+*> \verbatim
+*>          X is REAL array, dimension (LDX,NRHS)
+*>     If INFO = 0, the N-by-NRHS solution matrix X to the original
+*>     system of equations.  Note that A and B are modified on exit
+*>     if EQUED .ne. 'N', and the solution to the equilibrated system is
+*>     inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or
+*>     inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'.
+*> \endverbatim
+*>
+*> \param[in] LDX
+*> \verbatim
+*>          LDX is INTEGER
+*>     The leading dimension of the array X.  LDX >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] RCOND
+*> \verbatim
+*>          RCOND is REAL
+*>     Reciprocal scaled condition number.  This is an estimate of the
+*>     reciprocal Skeel condition number of the matrix A after
+*>     equilibration (if done).  If this is less than the machine
+*>     precision (in particular, if it is zero), the matrix is singular
+*>     to working precision.  Note that the error may still be small even
+*>     if this number is very small and the matrix appears ill-
+*>     conditioned.
+*> \endverbatim
+*>
+*> \param[out] RPVGRW
+*> \verbatim
+*>          RPVGRW is REAL
+*>     Reciprocal pivot growth.  On exit, this contains the reciprocal
+*>     pivot growth factor norm(A)/norm(U). The "max absolute element"
+*>     norm is used.  If this is much less than 1, then 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. If factorization fails with
+*>     0<INFO<=N, then this contains the reciprocal pivot growth factor
+*>     for the leading INFO columns of A.  In SGESVX, this quantity is
+*>     returned in WORK(1).
+*> \endverbatim
+*>
+*> \param[out] BERR
+*> \verbatim
+*>          BERR is REAL array, dimension (NRHS)
+*>     Componentwise relative backward error.  This is the
+*>     componentwise relative backward error of each solution vector X(j)
+*>     (i.e., the smallest relative change in any element of A or B that
+*>     makes X(j) an exact solution).
+*> \endverbatim
+*>
+*> \param[in] N_ERR_BNDS
+*> \verbatim
+*>          N_ERR_BNDS is INTEGER
+*>     Number of error bounds to return for each right hand side
+*>     and each type (normwise or componentwise).  See ERR_BNDS_NORM and
+*>     ERR_BNDS_COMP below.
+*> \endverbatim
+*>
+*> \param[out] ERR_BNDS_NORM
+*> \verbatim
+*>          ERR_BNDS_NORM is REAL array, dimension (NRHS, N_ERR_BNDS)
+*>     For each right-hand side, this array contains information about
+*>     various error bounds and condition numbers corresponding to the
+*>     normwise relative error, which is defined as follows:
+*> \endverbatim
+*> \verbatim
+*>     Normwise relative error in the ith solution vector:
+*>             max_j (abs(XTRUE(j,i) - X(j,i)))
+*>            ------------------------------
+*>                  max_j abs(X(j,i))
+*> \endverbatim
+*> \verbatim
+*>     The array is indexed by the type of error information as described
+*>     below. There currently are up to three pieces of information
+*>     returned.
+*> \endverbatim
+*> \verbatim
+*>     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
+*>     right-hand side.
+*> \endverbatim
+*> \verbatim
+*>     The second index in ERR_BNDS_NORM(:,err) contains the following
+*>     three fields:
+*>     err = 1 "Trust/don't trust" boolean. Trust the answer if the
+*>              reciprocal condition number is less than the threshold
+*>              sqrt(n) * slamch('Epsilon').
+*> \endverbatim
+*> \verbatim
+*>     err = 2 "Guaranteed" error bound: The estimated forward error,
+*>              almost certainly within a factor of 10 of the true error
+*>              so long as the next entry is greater than the threshold
+*>              sqrt(n) * slamch('Epsilon'). This error bound should only
+*>              be trusted if the previous boolean is true.
+*> \endverbatim
+*> \verbatim
+*>     err = 3  Reciprocal condition number: Estimated normwise
+*>              reciprocal condition number.  Compared with the threshold
+*>              sqrt(n) * slamch('Epsilon') to determine if the error
+*>              estimate is "guaranteed". These reciprocal condition
+*>              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
+*>              appropriately scaled matrix Z.
+*>              Let Z = S*A, where S scales each row by a power of the
+*>              radix so all absolute row sums of Z are approximately 1.
+*> \endverbatim
+*> \verbatim
+*>     See Lapack Working Note 165 for further details and extra
+*>     cautions.
+*> \endverbatim
+*>
+*> \param[out] ERR_BNDS_COMP
+*> \verbatim
+*>          ERR_BNDS_COMP is REAL array, dimension (NRHS, N_ERR_BNDS)
+*>     For each right-hand side, this array contains information about
+*>     various error bounds and condition numbers corresponding to the
+*>     componentwise relative error, which is defined as follows:
+*> \endverbatim
+*> \verbatim
+*>     Componentwise relative error in the ith solution vector:
+*>                    abs(XTRUE(j,i) - X(j,i))
+*>             max_j ----------------------
+*>                         abs(X(j,i))
+*> \endverbatim
+*> \verbatim
+*>     The array is indexed by the right-hand side i (on which the
+*>     componentwise relative error depends), and the type of error
+*>     information as described below. There currently are up to three
+*>     pieces of information returned for each right-hand side. If
+*>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     the first (:,N_ERR_BNDS) entries are returned.
+*> \endverbatim
+*> \verbatim
+*>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
+*>     right-hand side.
+*> \endverbatim
+*> \verbatim
+*>     The second index in ERR_BNDS_COMP(:,err) contains the following
+*>     three fields:
+*>     err = 1 "Trust/don't trust" boolean. Trust the answer if the
+*>              reciprocal condition number is less than the threshold
+*>              sqrt(n) * slamch('Epsilon').
+*> \endverbatim
+*> \verbatim
+*>     err = 2 "Guaranteed" error bound: The estimated forward error,
+*>              almost certainly within a factor of 10 of the true error
+*>              so long as the next entry is greater than the threshold
+*>              sqrt(n) * slamch('Epsilon'). This error bound should only
+*>              be trusted if the previous boolean is true.
+*> \endverbatim
+*> \verbatim
+*>     err = 3  Reciprocal condition number: Estimated componentwise
+*>              reciprocal condition number.  Compared with the threshold
+*>              sqrt(n) * slamch('Epsilon') to determine if the error
+*>              estimate is "guaranteed". These reciprocal condition
+*>              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
+*>              appropriately scaled matrix Z.
+*>              Let Z = S*(A*diag(x)), where x is the solution for the
+*>              current right-hand side and S scales each row of
+*>              A*diag(x) by a power of the radix so all absolute row
+*>              sums of Z are approximately 1.
+*> \endverbatim
+*> \verbatim
+*>     See Lapack Working Note 165 for further details and extra
+*>     cautions.
+*> \endverbatim
+*>
+*> \param[in] NPARAMS
+*> \verbatim
+*>          NPARAMS is INTEGER
+*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     PARAMS array is never referenced and default values are used.
+*> \endverbatim
+*>
+*> \param[in,out] PARAMS
+*> \verbatim
+*>          PARAMS is / output) REAL array, dimension NPARAMS
+*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     that entry will be filled with default value used for that
+*>     parameter.  Only positions up to NPARAMS are accessed; defaults
+*>     are used for higher-numbered parameters.
+*> \endverbatim
+*> \verbatim
+*>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
+*>            refinement or not.
+*>         Default: 1.0
+*>            = 0.0 : No refinement is performed, and no error bounds are
+*>                    computed.
+*>            = 1.0 : Use the double-precision refinement algorithm,
+*>                    possibly with doubled-single computations if the
+*>                    compilation environment does not support DOUBLE
+*>                    PRECISION.
+*>              (other values are reserved for future use)
+*> \endverbatim
+*> \verbatim
+*>       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
+*>            computations allowed for refinement.
+*>         Default: 10
+*>         Aggressive: Set to 100 to permit convergence using approximate
+*>                     factorizations or factorizations other than LU. If
+*>                     the factorization uses a technique other than
+*>                     Gaussian elimination, the guarantees in
+*>                     err_bnds_norm and err_bnds_comp may no longer be
+*>                     trustworthy.
+*> \endverbatim
+*> \verbatim
+*>       PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
+*>            will attempt to find a solution with small componentwise
+*>            relative error in the double-precision algorithm.  Positive
+*>            is true, 0.0 is false.
+*>         Default: 1.0 (attempt componentwise convergence)
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is REAL array, dimension (4*N)
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*>          IWORK is INTEGER array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>       = 0:  Successful exit. The solution to every right-hand side is
+*>         guaranteed.
+*>       < 0:  If INFO = -i, the i-th argument had an illegal value
+*>       > 0 and <= N:  U(INFO,INFO) is exactly zero.  The factorization
+*>         has been completed, but the factor U is exactly singular, so
+*>         the solution and error bounds could not be computed. RCOND = 0
+*>         is returned.
+*>       = N+J: The solution corresponding to the Jth right-hand side is
+*>         not guaranteed. The solutions corresponding to other right-
+*>         hand sides K with K > J may not be guaranteed as well, but
+*>         only the first such right-hand side is reported. If a small
+*>         componentwise error is not requested (PARAMS(3) = 0.0) then
+*>         the Jth right-hand side is the first with a normwise error
+*>         bound that is not guaranteed (the smallest J such
+*>         that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
+*>         the Jth right-hand side is the first with either a normwise or
+*>         componentwise error bound that is not guaranteed (the smallest
+*>         J such that either ERR_BNDS_NORM(J,1) = 0.0 or
+*>         ERR_BNDS_COMP(J,1) = 0.0). See the definition of
+*>         ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
+*>         about all of the right-hand sides check ERR_BNDS_NORM or
+*>         ERR_BNDS_COMP.
+*> \endverbatim
+*>
+*
+*  Authors
+*  =======
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup realGBsolve
+*
+*  =====================================================================
       SUBROUTINE SGBSVXX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
      $                    LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
      $                    RCOND, RPVGRW, BERR, N_ERR_BNDS,
      $                    ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
      $                    WORK, IWORK, INFO )
 *
-*     -- LAPACK driver routine (version 3.2)                          --
-*     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
-*     -- Jason Riedy of Univ. of California Berkeley.                 --
-*     -- November 2008                                                --
-*
-*     -- LAPACK is a software package provided by Univ. of Tennessee, --
-*     -- Univ. of California Berkeley and NAG Ltd.                    --
+*  -- LAPACK solve routine (version 3.2) --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
+*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2011
 *
-      IMPLICIT NONE
-*     ..
 *     .. Scalar Arguments ..
       CHARACTER          EQUED, FACT, TRANS
       INTEGER            INFO, LDAB, LDAFB, LDB, LDX, N, NRHS, NPARAMS,
@@ -29,415 +597,6 @@
      $                   ERR_BNDS_COMP( NRHS, * )
 *     ..
 *
-*  Purpose
-*     =======
-*
-*     SGBSVXX uses the LU factorization to compute the solution to a
-*     real system of linear equations  A * X = B,  where A is an
-*     N-by-N matrix and X and B are N-by-NRHS matrices.
-*
-*     If requested, both normwise and maximum componentwise error bounds
-*     are returned. SGBSVXX will return a solution with a tiny
-*     guaranteed error (O(eps) where eps is the working machine
-*     precision) unless the matrix is very ill-conditioned, in which
-*     case a warning is returned. Relevant condition numbers also are
-*     calculated and returned.
-*
-*     SGBSVXX accepts user-provided factorizations and equilibration
-*     factors; see the definitions of the FACT and EQUED options.
-*     Solving with refinement and using a factorization from a previous
-*     SGBSVXX call will also produce a solution with either O(eps)
-*     errors or warnings, but we cannot make that claim for general
-*     user-provided factorizations and equilibration factors if they
-*     differ from what SGBSVXX would itself produce.
-*
-*  Description
-*  ===========
-*
-*     The following steps are performed:
-*
-*     1. If FACT = 'E', real scaling factors are computed to equilibrate
-*     the system:
-*
-*       TRANS = 'N':  diag(R)*A*diag(C)     *inv(diag(C))*X = diag(R)*B
-*       TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
-*       TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
-*
-*     Whether or not the system will be equilibrated depends on the
-*     scaling of the matrix A, but if equilibration is used, A is
-*     overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
-*     or diag(C)*B (if TRANS = 'T' or 'C').
-*
-*     2. If FACT = 'N' or 'E', the LU decomposition is used to factor
-*     the matrix A (after equilibration if FACT = 'E') as
-*
-*       A = P * L * U,
-*
-*     where P is a permutation matrix, L is a unit lower triangular
-*     matrix, and U is upper triangular.
-*
-*     3. If some U(i,i)=0, so that U is exactly singular, then the
-*     routine returns with INFO = i. Otherwise, the factored form of A
-*     is used to estimate the condition number of the matrix A (see
-*     argument RCOND). If the reciprocal of the condition number is less
-*     than machine precision, the routine still goes on to solve for X
-*     and compute error bounds as described below.
-*
-*     4. The system of equations is solved for X using the factored form
-*     of A.
-*
-*     5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
-*     the routine will use iterative refinement to try to get a small
-*     error and error bounds.  Refinement calculates the residual to at
-*     least twice the working precision.
-*
-*     6. If equilibration was used, the matrix X is premultiplied by
-*     diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
-*     that it solves the original system before equilibration.
-*
-*  Arguments
-*  =========
-*
-*     Some optional parameters are bundled in the PARAMS array.  These
-*     settings determine how refinement is performed, but often the
-*     defaults are acceptable.  If the defaults are acceptable, users
-*     can pass NPARAMS = 0 which prevents the source code from accessing
-*     the PARAMS argument.
-*
-*     FACT    (input) CHARACTER*1
-*     Specifies whether or not the factored form of the matrix A is
-*     supplied on entry, and if not, whether the matrix A should be
-*     equilibrated before it is factored.
-*       = 'F':  On entry, AF and IPIV contain the factored form of A.
-*               If EQUED is not 'N', the matrix A has been
-*               equilibrated with scaling factors given by R and C.
-*               A, AF, and IPIV are not modified.
-*       = 'N':  The matrix A will be copied to AF and factored.
-*       = 'E':  The matrix A will be equilibrated if necessary, then
-*               copied to AF and factored.
-*
-*     TRANS   (input) 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       (input) INTEGER
-*     The number of linear equations, i.e., the order 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.
-*
-*     NRHS    (input) INTEGER
-*     The number of right hand sides, i.e., the number of columns
-*     of the matrices B and X.  NRHS >= 0.
-*
-*     AB      (input/output) 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)
-*
-*     If FACT = 'F' and EQUED is not 'N', then AB must have been
-*     equilibrated by the scaling factors in R and/or C.  AB is not
-*     modified if FACT = 'F' or 'N', or if FACT = 'E' and
-*     EQUED = 'N' on exit.
-*
-*     On exit, if EQUED .ne. 'N', A is scaled as follows:
-*     EQUED = 'R':  A := diag(R) * A
-*     EQUED = 'C':  A := A * diag(C)
-*     EQUED = 'B':  A := diag(R) * A * diag(C).
-*
-*     LDAB    (input) INTEGER
-*     The leading dimension of the array AB.  LDAB >= KL+KU+1.
-*
-*     AFB     (input or output) REAL array, dimension (LDAFB,N)
-*     If FACT = 'F', then AFB is an input argument and on entry
-*     contains 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.  If EQUED .ne. 'N', then AFB is
-*     the factored form of the equilibrated matrix A.
-*
-*     If FACT = 'N', then AF is an output argument and on exit
-*     returns the factors L and U from the factorization A = P*L*U
-*     of the original matrix A.
-*
-*     If FACT = 'E', then AF is an output argument and on exit
-*     returns the factors L and U from the factorization A = P*L*U
-*     of the equilibrated matrix A (see the description of A for
-*     the form of the equilibrated matrix).
-*
-*     LDAFB   (input) INTEGER
-*     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
-*
-*     IPIV    (input or output) INTEGER array, dimension (N)
-*     If FACT = 'F', then IPIV is an input argument and on entry
-*     contains the pivot indices from the factorization A = P*L*U
-*     as computed by SGETRF; row i of the matrix was interchanged
-*     with row IPIV(i).
-*
-*     If FACT = 'N', then IPIV is an output argument and on exit
-*     contains the pivot indices from the factorization A = P*L*U
-*     of the original matrix A.
-*
-*     If FACT = 'E', then IPIV is an output argument and on exit
-*     contains the pivot indices from the factorization A = P*L*U
-*     of the equilibrated matrix A.
-*
-*     EQUED   (input or output) CHARACTER*1
-*     Specifies the form of equilibration that was done.
-*       = 'N':  No equilibration (always true if FACT = 'N').
-*       = 'R':  Row equilibration, i.e., A has been premultiplied by
-*               diag(R).
-*       = 'C':  Column equilibration, i.e., A has been postmultiplied
-*               by diag(C).
-*       = 'B':  Both row and column equilibration, i.e., A has been
-*               replaced by diag(R) * A * diag(C).
-*     EQUED is an input argument if FACT = 'F'; otherwise, it is an
-*     output argument.
-*
-*     R       (input or output) REAL array, dimension (N)
-*     The row scale factors for A.  If EQUED = 'R' or 'B', A is
-*     multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
-*     is not accessed.  R is an input argument if FACT = 'F';
-*     otherwise, R is an output argument.  If FACT = 'F' and
-*     EQUED = 'R' or 'B', each element of R must be positive.
-*     If R is output, each element of R is a power of the radix.
-*     If R is input, each element of R should be a power of the radix
-*     to ensure a reliable solution and error estimates. Scaling by
-*     powers of the radix does not cause rounding errors unless the
-*     result underflows or overflows. Rounding errors during scaling
-*     lead to refining with a matrix that is not equivalent to the
-*     input matrix, producing error estimates that may not be
-*     reliable.
-*
-*     C       (input or output) REAL array, dimension (N)
-*     The column scale factors for A.  If EQUED = 'C' or 'B', A is
-*     multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
-*     is not accessed.  C is an input argument if FACT = 'F';
-*     otherwise, C is an output argument.  If FACT = 'F' and
-*     EQUED = 'C' or 'B', each element of C must be positive.
-*     If C is output, each element of C is a power of the radix.
-*     If C is input, each element of C should be a power of the radix
-*     to ensure a reliable solution and error estimates. Scaling by
-*     powers of the radix does not cause rounding errors unless the
-*     result underflows or overflows. Rounding errors during scaling
-*     lead to refining with a matrix that is not equivalent to the
-*     input matrix, producing error estimates that may not be
-*     reliable.
-*
-*     B       (input/output) REAL array, dimension (LDB,NRHS)
-*     On entry, the N-by-NRHS right hand side matrix B.
-*     On exit,
-*     if EQUED = 'N', B is not modified;
-*     if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by
-*        diag(R)*B;
-*     if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is
-*        overwritten by diag(C)*B.
-*
-*     LDB     (input) INTEGER
-*     The leading dimension of the array B.  LDB >= max(1,N).
-*
-*     X       (output) REAL array, dimension (LDX,NRHS)
-*     If INFO = 0, the N-by-NRHS solution matrix X to the original
-*     system of equations.  Note that A and B are modified on exit
-*     if EQUED .ne. 'N', and the solution to the equilibrated system is
-*     inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or
-*     inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'.
-*
-*     LDX     (input) INTEGER
-*     The leading dimension of the array X.  LDX >= max(1,N).
-*
-*     RCOND   (output) REAL
-*     Reciprocal scaled condition number.  This is an estimate of the
-*     reciprocal Skeel condition number of the matrix A after
-*     equilibration (if done).  If this is less than the machine
-*     precision (in particular, if it is zero), the matrix is singular
-*     to working precision.  Note that the error may still be small even
-*     if this number is very small and the matrix appears ill-
-*     conditioned.
-*
-*     RPVGRW  (output) REAL
-*     Reciprocal pivot growth.  On exit, this contains the reciprocal
-*     pivot growth factor norm(A)/norm(U). The "max absolute element"
-*     norm is used.  If this is much less than 1, then 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. If factorization fails with
-*     0<INFO<=N, then this contains the reciprocal pivot growth factor
-*     for the leading INFO columns of A.  In SGESVX, this quantity is
-*     returned in WORK(1).
-*
-*     BERR    (output) REAL array, dimension (NRHS)
-*     Componentwise relative backward error.  This is the
-*     componentwise relative backward error of each solution vector X(j)
-*     (i.e., the smallest relative change in any element of A or B that
-*     makes X(j) an exact solution).
-*
-*     N_ERR_BNDS (input) INTEGER
-*     Number of error bounds to return for each right hand side
-*     and each type (normwise or componentwise).  See ERR_BNDS_NORM and
-*     ERR_BNDS_COMP below.
-*
-*     ERR_BNDS_NORM  (output) REAL array, dimension (NRHS, N_ERR_BNDS)
-*     For each right-hand side, this array contains information about
-*     various error bounds and condition numbers corresponding to the
-*     normwise relative error, which is defined as follows:
-*
-*     Normwise relative error in the ith solution vector:
-*             max_j (abs(XTRUE(j,i) - X(j,i)))
-*            ------------------------------
-*                  max_j abs(X(j,i))
-*
-*     The array is indexed by the type of error information as described
-*     below. There currently are up to three pieces of information
-*     returned.
-*
-*     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
-*     right-hand side.
-*
-*     The second index in ERR_BNDS_NORM(:,err) contains the following
-*     three fields:
-*     err = 1 "Trust/don't trust" boolean. Trust the answer if the
-*              reciprocal condition number is less than the threshold
-*              sqrt(n) * slamch('Epsilon').
-*
-*     err = 2 "Guaranteed" error bound: The estimated forward error,
-*              almost certainly within a factor of 10 of the true error
-*              so long as the next entry is greater than the threshold
-*              sqrt(n) * slamch('Epsilon'). This error bound should only
-*              be trusted if the previous boolean is true.
-*
-*     err = 3  Reciprocal condition number: Estimated normwise
-*              reciprocal condition number.  Compared with the threshold
-*              sqrt(n) * slamch('Epsilon') to determine if the error
-*              estimate is "guaranteed". These reciprocal condition
-*              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
-*              appropriately scaled matrix Z.
-*              Let Z = S*A, where S scales each row by a power of the
-*              radix so all absolute row sums of Z are approximately 1.
-*
-*     See Lapack Working Note 165 for further details and extra
-*     cautions.
-*
-*     ERR_BNDS_COMP  (output) REAL array, dimension (NRHS, N_ERR_BNDS)
-*     For each right-hand side, this array contains information about
-*     various error bounds and condition numbers corresponding to the
-*     componentwise relative error, which is defined as follows:
-*
-*     Componentwise relative error in the ith solution vector:
-*                    abs(XTRUE(j,i) - X(j,i))
-*             max_j ----------------------
-*                         abs(X(j,i))
-*
-*     The array is indexed by the right-hand side i (on which the
-*     componentwise relative error depends), and the type of error
-*     information as described below. There currently are up to three
-*     pieces of information returned for each right-hand side. If
-*     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
-*     the first (:,N_ERR_BNDS) entries are returned.
-*
-*     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
-*     right-hand side.
-*
-*     The second index in ERR_BNDS_COMP(:,err) contains the following
-*     three fields:
-*     err = 1 "Trust/don't trust" boolean. Trust the answer if the
-*              reciprocal condition number is less than the threshold
-*              sqrt(n) * slamch('Epsilon').
-*
-*     err = 2 "Guaranteed" error bound: The estimated forward error,
-*              almost certainly within a factor of 10 of the true error
-*              so long as the next entry is greater than the threshold
-*              sqrt(n) * slamch('Epsilon'). This error bound should only
-*              be trusted if the previous boolean is true.
-*
-*     err = 3  Reciprocal condition number: Estimated componentwise
-*              reciprocal condition number.  Compared with the threshold
-*              sqrt(n) * slamch('Epsilon') to determine if the error
-*              estimate is "guaranteed". These reciprocal condition
-*              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
-*              appropriately scaled matrix Z.
-*              Let Z = S*(A*diag(x)), where x is the solution for the
-*              current right-hand side and S scales each row of
-*              A*diag(x) by a power of the radix so all absolute row
-*              sums of Z are approximately 1.
-*
-*     See Lapack Working Note 165 for further details and extra
-*     cautions.
-*
-*     NPARAMS (input) INTEGER
-*     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
-*     PARAMS array is never referenced and default values are used.
-*
-*     PARAMS  (input / output) REAL array, dimension NPARAMS
-*     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
-*     that entry will be filled with default value used for that
-*     parameter.  Only positions up to NPARAMS are accessed; defaults
-*     are used for higher-numbered parameters.
-*
-*       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
-*            refinement or not.
-*         Default: 1.0
-*            = 0.0 : No refinement is performed, and no error bounds are
-*                    computed.
-*            = 1.0 : Use the double-precision refinement algorithm,
-*                    possibly with doubled-single computations if the
-*                    compilation environment does not support DOUBLE
-*                    PRECISION.
-*              (other values are reserved for future use)
-*
-*       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
-*            computations allowed for refinement.
-*         Default: 10
-*         Aggressive: Set to 100 to permit convergence using approximate
-*                     factorizations or factorizations other than LU. If
-*                     the factorization uses a technique other than
-*                     Gaussian elimination, the guarantees in
-*                     err_bnds_norm and err_bnds_comp may no longer be
-*                     trustworthy.
-*
-*       PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
-*            will attempt to find a solution with small componentwise
-*            relative error in the double-precision algorithm.  Positive
-*            is true, 0.0 is false.
-*         Default: 1.0 (attempt componentwise convergence)
-*
-*     WORK    (workspace) REAL array, dimension (4*N)
-*
-*     IWORK   (workspace) INTEGER array, dimension (N)
-*
-*     INFO    (output) INTEGER
-*       = 0:  Successful exit. The solution to every right-hand side is
-*         guaranteed.
-*       < 0:  If INFO = -i, the i-th argument had an illegal value
-*       > 0 and <= N:  U(INFO,INFO) is exactly zero.  The factorization
-*         has been completed, but the factor U is exactly singular, so
-*         the solution and error bounds could not be computed. RCOND = 0
-*         is returned.
-*       = N+J: The solution corresponding to the Jth right-hand side is
-*         not guaranteed. The solutions corresponding to other right-
-*         hand sides K with K > J may not be guaranteed as well, but
-*         only the first such right-hand side is reported. If a small
-*         componentwise error is not requested (PARAMS(3) = 0.0) then
-*         the Jth right-hand side is the first with a normwise error
-*         bound that is not guaranteed (the smallest J such
-*         that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
-*         the Jth right-hand side is the first with either a normwise or
-*         componentwise error bound that is not guaranteed (the smallest
-*         J such that either ERR_BNDS_NORM(J,1) = 0.0 or
-*         ERR_BNDS_COMP(J,1) = 0.0). See the definition of
-*         ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
-*         about all of the right-hand sides check ERR_BNDS_NORM or
-*         ERR_BNDS_COMP.
-*
 *  ==================================================================
 *
 *     .. Parameters ..