Integrating Doxygen in comments

1 files changed, 365 insertions, 241 deletions

diff --git a/SRC/zgbsvx.f b/SRC/zgbsvx.f
index 54d10518..2fbcd31f 100644
--- a/SRC/zgbsvx.f
+++ b/SRC/zgbsvx.f
@@ -1,11 +1,374 @@
+*> \brief <b> ZGBSVX 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 ZGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
+*                          LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
+*                          RCOND, FERR, BERR, WORK, RWORK, INFO )
+* 
+*       .. Scalar Arguments ..
+*       CHARACTER          EQUED, FACT, TRANS
+*       INTEGER            INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
+*       DOUBLE PRECISION   RCOND
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       DOUBLE PRECISION   BERR( * ), C( * ), FERR( * ), R( * ),
+*      $                   RWORK( * )
+*       COMPLEX*16         AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ),
+*      $                   WORK( * ), X( LDX, * )
+*       ..
+*  
+*  Purpose
+*  =======
+*
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> ZGBSVX uses the LU factorization to compute the solution to a complex
+*> system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
+*> where A is a band matrix of order N with KL subdiagonals and KU
+*> superdiagonals, and X and B are N-by-NRHS matrices.
+*>
+*> Error bounds on the solution and a condition estimate are also
+*> provided.
+*>
+*> Description
+*> ===========
+*>
+*> The following steps are performed by this subroutine:
+*>
+*> 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 = L * U,
+*>    where L is a product of permutation and unit lower triangular
+*>    matrices with KL subdiagonals, and U is upper triangular with
+*>    KL+KU superdiagonals.
+*>
+*> 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.  If the
+*>    reciprocal of the condition number is less than machine precision,
+*>    INFO = N+1 is returned as a warning, but 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. Iterative refinement is applied to improve the computed solution
+*>    matrix and calculate error bounds and backward error estimates
+*>    for it.
+*>
+*> 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
+*  =========
+*
+*> \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, AFB 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.
+*>                  AB, AFB, and IPIV are not modified.
+*>          = 'N':  The matrix A will be copied to AFB and factored.
+*>          = 'E':  The matrix A will be equilibrated if necessary, then
+*>                  copied to AFB 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)
+*> \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 COMPLEX*16 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 A 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) COMPLEX*16 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 ZGBTRF.  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 AFB is an output argument and on exit
+*>          returns details of the LU factorization of A.
+*> \endverbatim
+*> \verbatim
+*>          If FACT = 'E', then AFB is an output argument and on exit
+*>          returns details of the LU factorization of the equilibrated
+*>          matrix A (see the description of AB 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 = L*U
+*>          as computed by ZGBTRF; 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 = 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 = 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) 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.  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.
+*> \endverbatim
+*>
+*> \param[in,out] C
+*> \verbatim
+*>          C is or output) 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.  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.
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is COMPLEX*16 array, dimension (LDB,NRHS)
+*>          On entry, the 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 COMPLEX*16 array, dimension (LDX,NRHS)
+*>          If INFO = 0 or INFO = N+1, 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 DOUBLE PRECISION
+*>          The estimate of the reciprocal condition number of the matrix
+*>          A after equilibration (if done).  If RCOND is less than the
+*>          machine precision (in particular, if RCOND = 0), the matrix
+*>          is singular to working precision.  This condition is
+*>          indicated by a return code of INFO > 0.
+*> \endverbatim
+*>
+*> \param[out] FERR
+*> \verbatim
+*>          FERR is DOUBLE PRECISION array, dimension (NRHS)
+*>          The estimated forward error bound for each solution vector
+*>          X(j) (the j-th column of the solution matrix X).
+*>          If XTRUE is the true solution corresponding to X(j), FERR(j)
+*>          is an estimated upper bound for the magnitude of the largest
+*>          element in (X(j) - XTRUE) divided by the magnitude of the
+*>          largest element in X(j).  The estimate is as reliable as
+*>          the estimate for RCOND, and is almost always a slight
+*>          overestimate of the true error.
+*> \endverbatim
+*>
+*> \param[out] BERR
+*> \verbatim
+*>          BERR is DOUBLE PRECISION array, dimension (NRHS)
+*>          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[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX*16 array, dimension (2*N)
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*>          RWORK is DOUBLE PRECISION array, dimension (N)
+*>          On exit, RWORK(1) contains the reciprocal pivot growth
+*>          factor norm(A)/norm(U). The "max absolute element" norm is
+*>          used. If RWORK(1) 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, condition
+*>          estimator RCOND, and forward error bound FERR could be
+*>          unreliable. If factorization fails with 0<INFO<=N, then
+*>          RWORK(1) contains the reciprocal pivot growth factor for the
+*>          leading INFO columns of A.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          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
+*>                <= N:  U(i,i) 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+1: U is nonsingular, but RCOND is less than machine
+*>                       precision, meaning that the matrix is singular
+*>                       to working precision.  Nevertheless, the
+*>                       solution and error bounds are computed because
+*>                       there are a number of situations where the
+*>                       computed solution can be more accurate than the
+*>                       value of RCOND would suggest.
+*> \endverbatim
+*>
+*
+*  Authors
+*  =======
+*
+*> \author Univ. of Tennessee 
+*> \author Univ. of California Berkeley 
+*> \author Univ. of Colorado Denver 
+*> \author NAG Ltd. 
+*
+*> \date November 2011
+*
+*> \ingroup complex16GBsolve
+*
+*  =====================================================================
       SUBROUTINE ZGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
      $                   LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
      $                   RCOND, FERR, BERR, WORK, RWORK, INFO )
 *
-*  -- LAPACK driver routine (version 3.2) --
+*  -- 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 2006
+*     November 2011
 *
 *     .. Scalar Arguments ..
       CHARACTER          EQUED, FACT, TRANS
@@ -20,245 +383,6 @@
      $                   WORK( * ), X( LDX, * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  ZGBSVX uses the LU factorization to compute the solution to a complex
-*  system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
-*  where A is a band matrix of order N with KL subdiagonals and KU
-*  superdiagonals, and X and B are N-by-NRHS matrices.
-*
-*  Error bounds on the solution and a condition estimate are also
-*  provided.
-*
-*  Description
-*  ===========
-*
-*  The following steps are performed by this subroutine:
-*
-*  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 = L * U,
-*     where L is a product of permutation and unit lower triangular
-*     matrices with KL subdiagonals, and U is upper triangular with
-*     KL+KU superdiagonals.
-*
-*  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.  If the
-*     reciprocal of the condition number is less than machine precision,
-*     INFO = N+1 is returned as a warning, but 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. Iterative refinement is applied to improve the computed solution
-*     matrix and calculate error bounds and backward error estimates
-*     for it.
-*
-*  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
-*  =========
-*
-*  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, AFB 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.
-*                  AB, AFB, and IPIV are not modified.
-*          = 'N':  The matrix A will be copied to AFB and factored.
-*          = 'E':  The matrix A will be equilibrated if necessary, then
-*                  copied to AFB 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)
-*
-*  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) COMPLEX*16 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 A 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) COMPLEX*16 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 ZGBTRF.  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 AFB is an output argument and on exit
-*          returns details of the LU factorization of A.
-*
-*          If FACT = 'E', then AFB is an output argument and on exit
-*          returns details of the LU factorization of the equilibrated
-*          matrix A (see the description of AB 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 = L*U
-*          as computed by ZGBTRF; 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 = 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 = 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) 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.  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.
-*
-*  C       (input or output) 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.  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.
-*
-*  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
-*          On entry, the 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) COMPLEX*16 array, dimension (LDX,NRHS)
-*          If INFO = 0 or INFO = N+1, 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) DOUBLE PRECISION
-*          The estimate of the reciprocal condition number of the matrix
-*          A after equilibration (if done).  If RCOND is less than the
-*          machine precision (in particular, if RCOND = 0), the matrix
-*          is singular to working precision.  This condition is
-*          indicated by a return code of INFO > 0.
-*
-*  FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
-*          The estimated forward error bound for each solution vector
-*          X(j) (the j-th column of the solution matrix X).
-*          If XTRUE is the true solution corresponding to X(j), FERR(j)
-*          is an estimated upper bound for the magnitude of the largest
-*          element in (X(j) - XTRUE) divided by the magnitude of the
-*          largest element in X(j).  The estimate is as reliable as
-*          the estimate for RCOND, and is almost always a slight
-*          overestimate of the true error.
-*
-*  BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
-*          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).
-*
-*  WORK    (workspace) COMPLEX*16 array, dimension (2*N)
-*
-*  RWORK   (workspace/output) DOUBLE PRECISION array, dimension (N)
-*          On exit, RWORK(1) contains the reciprocal pivot growth
-*          factor norm(A)/norm(U). The "max absolute element" norm is
-*          used. If RWORK(1) 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, condition
-*          estimator RCOND, and forward error bound FERR could be
-*          unreliable. If factorization fails with 0<INFO<=N, then
-*          RWORK(1) contains the reciprocal pivot growth factor for the
-*          leading INFO columns of A.
-*
-*  INFO    (output) INTEGER
-*          = 0:  successful exit
-*          < 0:  if INFO = -i, the i-th argument had an illegal value
-*          > 0:  if INFO = i, and i is
-*                <= N:  U(i,i) 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+1: U is nonsingular, but RCOND is less than machine
-*                       precision, meaning that the matrix is singular
-*                       to working precision.  Nevertheless, the
-*                       solution and error bounds are computed because
-*                       there are a number of situations where the
-*                       computed solution can be more accurate than the
-*                       value of RCOND would suggest.
-*
 *  =====================================================================
 *  Moved setting of INFO = N+1 so INFO does not subsequently get
 *  overwritten.  Sven, 17 Mar 05.