Integrating Doxygen in comments

1 files changed, 426 insertions, 286 deletions

diff --git a/SRC/dgerfsx.f b/SRC/dgerfsx.f
index a33c5bfa..37b66716 100644
--- a/SRC/dgerfsx.f
+++ b/SRC/dgerfsx.f
@@ -1,18 +1,435 @@
+*> \brief \b DGERFSX
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at 
+*            http://www.netlib.org/lapack/explore-html/ 
+*
+*  Definition
+*  ==========
+*
+*       SUBROUTINE DGERFSX( TRANS, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
+*                           R, C, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
+*                           ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
+*                           WORK, IWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          TRANS, EQUED
+*       INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
+*      $                   N_ERR_BNDS
+*       DOUBLE PRECISION   RCOND
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * ), IWORK( * )
+*       DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
+*      $                   X( LDX , * ), WORK( * )
+*       DOUBLE PRECISION   R( * ), C( * ), PARAMS( * ), BERR( * ),
+*      $                   ERR_BNDS_NORM( NRHS, * ),
+*      $                   ERR_BNDS_COMP( NRHS, * )
+*       ..
+*  
+*  Purpose
+*  =======
+*
+*>\details \b Purpose:
+*>\verbatim
+*> Purpose
+*>    =======
+*>
+*>    DGERFSX improves the computed solution to a system of linear
+*>    equations and provides error bounds and backward error estimates
+*>    for the solution.  In addition to normwise error bound, the code
+*>    provides maximum componentwise error bound if possible.  See
+*>    comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
+*>    error bounds.
+*>
+*>    The original system of linear equations may have been equilibrated
+*>    before calling this routine, as described by arguments EQUED, R
+*>    and C below. In this case, the solution and error bounds returned
+*>    are for the original unequilibrated system.
+*>
+*>\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] 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] EQUED
+*> \verbatim
+*>          EQUED is CHARACTER*1
+*>     Specifies the form of equilibration that was done to A
+*>     before calling this routine. This is needed to compute
+*>     the solution and error bounds correctly.
+*>       = 'N':  No equilibration
+*>       = '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).
+*>               The right hand side B has been changed accordingly.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>     The order of the matrix A.  N >= 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] A
+*> \verbatim
+*>          A is DOUBLE PRECISION array, dimension (LDA,N)
+*>     The original N-by-N matrix A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>     The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] AF
+*> \verbatim
+*>          AF is DOUBLE PRECISION array, dimension (LDAF,N)
+*>     The factors L and U from the factorization A = P*L*U
+*>     as computed by DGETRF.
+*> \endverbatim
+*>
+*> \param[in] LDAF
+*> \verbatim
+*>          LDAF is INTEGER
+*>     The leading dimension of the array AF.  LDAF >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>     The pivot indices from DGETRF; for 1<=i<=N, row i of the
+*>     matrix was interchanged with row IPIV(i).
+*> \endverbatim
+*>
+*> \param[in] R
+*> \verbatim
+*>          R is DOUBLE PRECISION 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.  
+*>     If R is accessed, 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] C
+*> \verbatim
+*>          C is DOUBLE PRECISION 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. 
+*>     If C is accessed, 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] B
+*> \verbatim
+*>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
+*>     The right hand side matrix B.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>     The leading dimension of the array B.  LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] X
+*> \verbatim
+*>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
+*>     On entry, the solution matrix X, as computed by DGETRS.
+*>     On exit, the improved solution matrix X.
+*> \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 DOUBLE PRECISION
+*>     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] BERR
+*> \verbatim
+*>          BERR is DOUBLE PRECISION 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 DOUBLE PRECISION 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) * dlamch('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) * dlamch('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) * dlamch('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 DOUBLE PRECISION 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) * dlamch('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) * dlamch('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) * dlamch('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) DOUBLE PRECISION 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: 1.0D+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 DOUBLE PRECISION 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 doubleGEcomputational
+*
+*  =====================================================================
       SUBROUTINE DGERFSX( TRANS, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
      $                    R, C, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
      $                    ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
      $                    WORK, IWORK, INFO )
 *
-*     -- LAPACK routine (version 3.2.2)                                 --
-*     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
-*     -- Jason Riedy of Univ. of California Berkeley.                 --
-*     -- June 2010                                                    --
-*
-*     -- LAPACK is a software package provided by Univ. of Tennessee, --
-*     -- Univ. of California Berkeley and NAG Ltd.                    --
+*  -- LAPACK computational routine (version 3.2.2) --
+*  -- 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          TRANS, EQUED
       INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
@@ -28,283 +445,6 @@
      $                   ERR_BNDS_COMP( NRHS, * )
 *     ..
 *
-*  Purpose
-*     =======
-*
-*     DGERFSX improves the computed solution to a system of linear
-*     equations and provides error bounds and backward error estimates
-*     for the solution.  In addition to normwise error bound, the code
-*     provides maximum componentwise error bound if possible.  See
-*     comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
-*     error bounds.
-*
-*     The original system of linear equations may have been equilibrated
-*     before calling this routine, as described by arguments EQUED, R
-*     and C below. In this case, the solution and error bounds returned
-*     are for the original unequilibrated system.
-*
-*  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.
-*
-*     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)
-*
-*     EQUED   (input) CHARACTER*1
-*     Specifies the form of equilibration that was done to A
-*     before calling this routine. This is needed to compute
-*     the solution and error bounds correctly.
-*       = 'N':  No equilibration
-*       = '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).
-*               The right hand side B has been changed accordingly.
-*
-*     N       (input) INTEGER
-*     The order of the matrix A.  N >= 0.
-*
-*     NRHS    (input) INTEGER
-*     The number of right hand sides, i.e., the number of columns
-*     of the matrices B and X.  NRHS >= 0.
-*
-*     A       (input) DOUBLE PRECISION array, dimension (LDA,N)
-*     The original N-by-N matrix A.
-*
-*     LDA     (input) INTEGER
-*     The leading dimension of the array A.  LDA >= max(1,N).
-*
-*     AF      (input) DOUBLE PRECISION array, dimension (LDAF,N)
-*     The factors L and U from the factorization A = P*L*U
-*     as computed by DGETRF.
-*
-*     LDAF    (input) INTEGER
-*     The leading dimension of the array AF.  LDAF >= max(1,N).
-*
-*     IPIV    (input) INTEGER array, dimension (N)
-*     The pivot indices from DGETRF; for 1<=i<=N, row i of the
-*     matrix was interchanged with row IPIV(i).
-*
-*     R       (input) DOUBLE PRECISION 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.  
-*     If R is accessed, 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) DOUBLE PRECISION 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. 
-*     If C is accessed, 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) DOUBLE PRECISION array, dimension (LDB,NRHS)
-*     The right hand side matrix B.
-*
-*     LDB     (input) INTEGER
-*     The leading dimension of the array B.  LDB >= max(1,N).
-*
-*     X       (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
-*     On entry, the solution matrix X, as computed by DGETRS.
-*     On exit, the improved solution matrix X.
-*
-*     LDX     (input) INTEGER
-*     The leading dimension of the array X.  LDX >= max(1,N).
-*
-*     RCOND   (output) DOUBLE PRECISION
-*     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.
-*
-*     BERR    (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) * dlamch('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) * dlamch('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) * dlamch('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) DOUBLE PRECISION 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) * dlamch('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) * dlamch('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) * dlamch('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) DOUBLE PRECISION 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: 1.0D+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) DOUBLE PRECISION 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 ..