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Annotation of rpl/lapack/lapack/zla_gerpvgrw.f, revision 1.12

1.4       bertrand    1: *> \brief \b ZLA_GERPVGRW multiplies a square real matrix by a complex matrix.
1.1       bertrand    2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
1.9       bertrand    5: * Online html documentation available at
                      6: *            http://www.netlib.org/lapack/explore-html/
1.1       bertrand    7: *
                      8: *> \htmlonly
1.9       bertrand    9: *> Download ZLA_GERPVGRW + dependencies
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gerpvgrw.f">
                     11: *> [TGZ]</a>
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gerpvgrw.f">
                     13: *> [ZIP]</a>
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gerpvgrw.f">
1.1       bertrand   15: *> [TXT]</a>
1.9       bertrand   16: *> \endhtmlonly
1.1       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       DOUBLE PRECISION FUNCTION ZLA_GERPVGRW( N, NCOLS, A, LDA, AF,
1.12    ! bertrand   22: *                                               LDAF )
1.9       bertrand   23: *
1.1       bertrand   24: *       .. Scalar Arguments ..
                     25: *       INTEGER            N, NCOLS, LDA, LDAF
                     26: *       ..
                     27: *       .. Array Arguments ..
                     28: *       COMPLEX*16         A( LDA, * ), AF( LDAF, * )
                     29: *       ..
1.9       bertrand   30: *
1.1       bertrand   31: *
                     32: *> \par Purpose:
                     33: *  =============
                     34: *>
                     35: *> \verbatim
                     36: *>
1.9       bertrand   37: *>
1.1       bertrand   38: *> ZLA_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
1.7       bertrand   64: *>          A is COMPLEX*16 array, dimension (LDA,N)
1.1       bertrand   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
1.7       bertrand   76: *>          AF is COMPLEX*16 array, dimension (LDAF,N)
1.1       bertrand   77: *>     The factors L and U from the factorization
                     78: *>     A = P*L*U as computed by ZGETRF.
                     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: *
1.9       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: *
                     95: *> \ingroup complex16GEcomputational
                     96: *
                     97: *  =====================================================================
                     98:       DOUBLE PRECISION FUNCTION ZLA_GERPVGRW( N, NCOLS, A, LDA, AF,
1.12    ! bertrand   99:      $                                        LDAF )
1.1       bertrand  100: *
1.12    ! bertrand  101: *  -- LAPACK computational routine --
1.1       bertrand  102: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    103: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                    104: *
                    105: *     .. Scalar Arguments ..
                    106:       INTEGER            N, NCOLS, LDA, LDAF
                    107: *     ..
                    108: *     .. Array Arguments ..
                    109:       COMPLEX*16         A( LDA, * ), AF( LDAF, * )
                    110: *     ..
                    111: *
                    112: *  =====================================================================
                    113: *
                    114: *     .. Local Scalars ..
                    115:       INTEGER            I, J
                    116:       DOUBLE PRECISION   AMAX, UMAX, RPVGRW
                    117:       COMPLEX*16         ZDUM
                    118: *     ..
                    119: *     .. Intrinsic Functions ..
                    120:       INTRINSIC          MAX, MIN, ABS, REAL, DIMAG
                    121: *     ..
                    122: *     .. Statement Functions ..
                    123:       DOUBLE PRECISION   CABS1
                    124: *     ..
                    125: *     .. Statement Function Definitions ..
                    126:       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
                    127: *     ..
                    128: *     .. Executable Statements ..
                    129: *
                    130:       RPVGRW = 1.0D+0
                    131: 
                    132:       DO J = 1, NCOLS
                    133:          AMAX = 0.0D+0
                    134:          UMAX = 0.0D+0
                    135:          DO I = 1, N
                    136:             AMAX = MAX( CABS1( A( I, J ) ), AMAX )
                    137:          END DO
                    138:          DO I = 1, J
                    139:             UMAX = MAX( CABS1( AF( I, J ) ), UMAX )
                    140:          END DO
                    141:          IF ( UMAX /= 0.0D+0 ) THEN
                    142:             RPVGRW = MIN( AMAX / UMAX, RPVGRW )
                    143:          END IF
                    144:       END DO
                    145:       ZLA_GERPVGRW = RPVGRW
1.12    ! bertrand  146: *
        !           147: *     End of ZLA_GERPVGRW
        !           148: *
1.1       bertrand  149:       END