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Annotation of rpl/lapack/lapack/dla_gerpvgrw.f, revision 1.8

1.1       bertrand    1: *> \brief \b DLA_GERPVGRW
                      2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
1.7       bertrand    5: * Online html documentation available at
                      6: *            http://www.netlib.org/lapack/explore-html/
1.1       bertrand    7: *
                      8: *> \htmlonly
1.7       bertrand    9: *> Download DLA_GERPVGRW + dependencies
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gerpvgrw.f">
                     11: *> [TGZ]</a>
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gerpvgrw.f">
                     13: *> [ZIP]</a>
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gerpvgrw.f">
1.1       bertrand   15: *> [TXT]</a>
1.7       bertrand   16: *> \endhtmlonly
1.1       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       DOUBLE PRECISION FUNCTION DLA_GERPVGRW( N, NCOLS, A, LDA, AF,
                     22: *                LDAF )
1.7       bertrand   23: *
1.1       bertrand   24: *       .. Scalar Arguments ..
                     25: *       INTEGER            N, NCOLS, LDA, LDAF
                     26: *       ..
                     27: *       .. Array Arguments ..
                     28: *       DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * )
                     29: *       ..
1.7       bertrand   30: *
1.1       bertrand   31: *
                     32: *> \par Purpose:
                     33: *  =============
                     34: *>
                     35: *> \verbatim
                     36: *>
1.7       bertrand   37: *>
1.1       bertrand   38: *> DLA_GERPVGRW computes the reciprocal pivot growth factor
                     39: *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
                     40: *> much less than 1, the stability of the LU factorization of the
                     41: *> (equilibrated) matrix A could be poor. This also means that the
                     42: *> solution X, estimated condition numbers, and error bounds could be
                     43: *> unreliable.
                     44: *> \endverbatim
                     45: *
                     46: *  Arguments:
                     47: *  ==========
                     48: *
                     49: *> \param[in] N
                     50: *> \verbatim
                     51: *>          N is INTEGER
                     52: *>     The number of linear equations, i.e., the order of the
                     53: *>     matrix A.  N >= 0.
                     54: *> \endverbatim
                     55: *>
                     56: *> \param[in] NCOLS
                     57: *> \verbatim
                     58: *>          NCOLS is INTEGER
                     59: *>     The number of columns of the matrix A. NCOLS >= 0.
                     60: *> \endverbatim
                     61: *>
                     62: *> \param[in] A
                     63: *> \verbatim
                     64: *>          A is DOUBLE PRECISION array, dimension (LDA,N)
                     65: *>     On entry, the N-by-N matrix A.
                     66: *> \endverbatim
                     67: *>
                     68: *> \param[in] LDA
                     69: *> \verbatim
                     70: *>          LDA is INTEGER
                     71: *>     The leading dimension of the array A.  LDA >= max(1,N).
                     72: *> \endverbatim
                     73: *>
                     74: *> \param[in] AF
                     75: *> \verbatim
                     76: *>          AF is DOUBLE PRECISION array, dimension (LDAF,N)
                     77: *>     The factors L and U from the factorization
                     78: *>     A = P*L*U as computed by DGETRF.
                     79: *> \endverbatim
                     80: *>
                     81: *> \param[in] LDAF
                     82: *> \verbatim
                     83: *>          LDAF is INTEGER
                     84: *>     The leading dimension of the array AF.  LDAF >= max(1,N).
                     85: *> \endverbatim
                     86: *
                     87: *  Authors:
                     88: *  ========
                     89: *
1.7       bertrand   90: *> \author Univ. of Tennessee
                     91: *> \author Univ. of California Berkeley
                     92: *> \author Univ. of Colorado Denver
                     93: *> \author NAG Ltd.
1.1       bertrand   94: *
1.7       bertrand   95: *> \date December 2016
1.1       bertrand   96: *
                     97: *> \ingroup doubleGEcomputational
                     98: *
                     99: *  =====================================================================
                    100:       DOUBLE PRECISION FUNCTION DLA_GERPVGRW( N, NCOLS, A, LDA, AF,
                    101:      $         LDAF )
                    102: *
1.7       bertrand  103: *  -- LAPACK computational routine (version 3.7.0) --
1.1       bertrand  104: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    105: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7       bertrand  106: *     December 2016
1.1       bertrand  107: *
                    108: *     .. Scalar Arguments ..
                    109:       INTEGER            N, NCOLS, LDA, LDAF
                    110: *     ..
                    111: *     .. Array Arguments ..
                    112:       DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * )
                    113: *     ..
                    114: *
                    115: *  =====================================================================
                    116: *
                    117: *     .. Local Scalars ..
                    118:       INTEGER            I, J
                    119:       DOUBLE PRECISION   AMAX, UMAX, RPVGRW
                    120: *     ..
                    121: *     .. Intrinsic Functions ..
                    122:       INTRINSIC          ABS, MAX, MIN
                    123: *     ..
                    124: *     .. Executable Statements ..
                    125: *
                    126:       RPVGRW = 1.0D+0
                    127: 
                    128:       DO J = 1, NCOLS
                    129:          AMAX = 0.0D+0
                    130:          UMAX = 0.0D+0
                    131:          DO I = 1, N
                    132:             AMAX = MAX( ABS( A( I, J ) ), AMAX )
                    133:          END DO
                    134:          DO I = 1, J
                    135:             UMAX = MAX( ABS( AF( I, J ) ), UMAX )
                    136:          END DO
                    137:          IF ( UMAX /= 0.0D+0 ) THEN
                    138:             RPVGRW = MIN( AMAX / UMAX, RPVGRW )
                    139:          END IF
                    140:       END DO
                    141:       DLA_GERPVGRW = RPVGRW
                    142:       END