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version 1.5, 2011/07/22 07:38:06 version 1.6, 2011/11/21 20:42:53
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   *> \brief \b DLA_GBRCOND
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLA_GBRCOND + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbrcond.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gbrcond.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gbrcond.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       DOUBLE PRECISION FUNCTION DLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB,
   *                                              AFB, LDAFB, IPIV, CMODE, C,
   *                                              INFO, WORK, IWORK )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          TRANS
   *       INTEGER            N, LDAB, LDAFB, INFO, KL, KU, CMODE
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IWORK( * ), IPIV( * )
   *       DOUBLE PRECISION   AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
   *      $                   C( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *>    DLA_GBRCOND Estimates the Skeel condition number of  op(A) * op2(C)
   *>    where op2 is determined by CMODE as follows
   *>    CMODE =  1    op2(C) = C
   *>    CMODE =  0    op2(C) = I
   *>    CMODE = -1    op2(C) = inv(C)
   *>    The Skeel condition number  cond(A) = norminf( |inv(A)||A| )
   *>    is computed by computing scaling factors R such that
   *>    diag(R)*A*op2(C) is row equilibrated and computing the standard
   *>    infinity-norm condition number.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \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] AB
   *> \verbatim
   *>          AB is DOUBLE PRECISION 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
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>     The leading dimension of the array AB.  LDAB >= KL+KU+1.
   *> \endverbatim
   *>
   *> \param[in] AFB
   *> \verbatim
   *>          AFB is DOUBLE PRECISION array, dimension (LDAFB,N)
   *>     Details of the LU factorization of the band matrix A, as
   *>     computed by DGBTRF.  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.
   *> \endverbatim
   *>
   *> \param[in] LDAFB
   *> \verbatim
   *>          LDAFB is INTEGER
   *>     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
   *> \endverbatim
   *>
   *> \param[in] IPIV
   *> \verbatim
   *>          IPIV is INTEGER array, dimension (N)
   *>     The pivot indices from the factorization A = P*L*U
   *>     as computed by DGBTRF; row i of the matrix was interchanged
   *>     with row IPIV(i).
   *> \endverbatim
   *>
   *> \param[in] CMODE
   *> \verbatim
   *>          CMODE is INTEGER
   *>     Determines op2(C) in the formula op(A) * op2(C) as follows:
   *>     CMODE =  1    op2(C) = C
   *>     CMODE =  0    op2(C) = I
   *>     CMODE = -1    op2(C) = inv(C)
   *> \endverbatim
   *>
   *> \param[in] C
   *> \verbatim
   *>          C is DOUBLE PRECISION array, dimension (N)
   *>     The vector C in the formula op(A) * op2(C).
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>       = 0:  Successful exit.
   *>     i > 0:  The ith argument is invalid.
   *> \endverbatim
   *>
   *> \param[in] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (5*N).
   *>     Workspace.
   *> \endverbatim
   *>
   *> \param[in] IWORK
   *> \verbatim
   *>          IWORK is INTEGER array, dimension (N).
   *>     Workspace.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleGBcomputational
   *
   *  =====================================================================
       DOUBLE PRECISION FUNCTION DLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB,        DOUBLE PRECISION FUNCTION DLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB,
      $                                       AFB, LDAFB, IPIV, CMODE, C,       $                                       AFB, LDAFB, IPIV, CMODE, C,
      $                                       INFO, WORK, IWORK )       $                                       INFO, WORK, IWORK )
 *  *
 *     -- LAPACK routine (version 3.2.2)                               --  *  -- LAPACK computational routine (version 3.4.0) --
 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *     -- Jason Riedy of Univ. of California Berkeley.                 --  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     -- June 2010                                                    --  *     November 2011
 *  *
 *     -- LAPACK is a software package provided by Univ. of Tennessee, --  
 *     -- Univ. of California Berkeley and NAG Ltd.                    --  
 *  
       IMPLICIT NONE  
 *     ..  
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          TRANS        CHARACTER          TRANS
       INTEGER            N, LDAB, LDAFB, INFO, KL, KU, CMODE        INTEGER            N, LDAB, LDAFB, INFO, KL, KU, CMODE
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      $                   C( * )       $                   C( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *     DLA_GBRCOND Estimates the Skeel condition number of  op(A) * op2(C)  
 *     where op2 is determined by CMODE as follows  
 *     CMODE =  1    op2(C) = C  
 *     CMODE =  0    op2(C) = I  
 *     CMODE = -1    op2(C) = inv(C)  
 *     The Skeel condition number  cond(A) = norminf( |inv(A)||A| )  
 *     is computed by computing scaling factors R such that  
 *     diag(R)*A*op2(C) is row equilibrated and computing the standard  
 *     infinity-norm condition number.  
 *  
 *  Arguments  
 *  =========  
 *  
 *     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.  
 *  
 *     AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)  
 *     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.  
 *     The j-th column of A is stored in the j-th column of the  
 *     array AB as follows:  
 *     AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)  
 *  
 *     LDAB    (input) INTEGER  
 *     The leading dimension of the array AB.  LDAB >= KL+KU+1.  
 *  
 *     AFB     (input) DOUBLE PRECISION array, dimension (LDAFB,N)  
 *     Details of the LU factorization of the band matrix A, as  
 *     computed by DGBTRF.  U is stored as an upper triangular  
 *     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,  
 *     and the multipliers used during the factorization are stored  
 *     in rows KL+KU+2 to 2*KL+KU+1.  
 *  
 *     LDAFB   (input) INTEGER  
 *     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.  
 *  
 *     IPIV    (input) INTEGER array, dimension (N)  
 *     The pivot indices from the factorization A = P*L*U  
 *     as computed by DGBTRF; row i of the matrix was interchanged  
 *     with row IPIV(i).  
 *  
 *     CMODE   (input) INTEGER  
 *     Determines op2(C) in the formula op(A) * op2(C) as follows:  
 *     CMODE =  1    op2(C) = C  
 *     CMODE =  0    op2(C) = I  
 *     CMODE = -1    op2(C) = inv(C)  
 *  
 *     C       (input) DOUBLE PRECISION array, dimension (N)  
 *     The vector C in the formula op(A) * op2(C).  
 *  
 *     INFO    (output) INTEGER  
 *       = 0:  Successful exit.  
 *     i > 0:  The ith argument is invalid.  
 *  
 *     WORK    (input) DOUBLE PRECISION array, dimension (5*N).  
 *     Workspace.  
 *  
 *     IWORK   (input) INTEGER array, dimension (N).  
 *     Workspace.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
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  Added in v.1.6

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