LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cla_gerpvgrw.f
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00001 *> \brief \b CLA_GERPVGRW
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLA_GERPVGRW + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL FUNCTION CLA_GERPVGRW( N, NCOLS, A, LDA, AF, LDAF )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       INTEGER            N, NCOLS, LDA, LDAF
00025 *       ..
00026 *       .. Array Arguments ..
00027 *       COMPLEX            A( LDA, * ), AF( LDAF, * )
00028 *       ..
00029 *  
00030 *
00031 *> \par Purpose:
00032 *  =============
00033 *>
00034 *> \verbatim
00035 *>
00036 *> 
00037 *> CLA_GERPVGRW computes the reciprocal pivot growth factor
00038 *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
00039 *> much less than 1, the stability of the LU factorization of the
00040 *> (equilibrated) matrix A could be poor. This also means that the
00041 *> solution X, estimated condition numbers, and error bounds could be
00042 *> unreliable.
00043 *> \endverbatim
00044 *
00045 *  Arguments:
00046 *  ==========
00047 *
00048 *> \param[in] N
00049 *> \verbatim
00050 *>          N is INTEGER
00051 *>     The number of linear equations, i.e., the order of the
00052 *>     matrix A.  N >= 0.
00053 *> \endverbatim
00054 *>
00055 *> \param[in] NCOLS
00056 *> \verbatim
00057 *>          NCOLS is INTEGER
00058 *>     The number of columns of the matrix A. NCOLS >= 0.
00059 *> \endverbatim
00060 *>
00061 *> \param[in] A
00062 *> \verbatim
00063 *>          A is COMPLEX array, dimension (LDA,N)
00064 *>     On entry, the N-by-N matrix A.
00065 *> \endverbatim
00066 *>
00067 *> \param[in] LDA
00068 *> \verbatim
00069 *>          LDA is INTEGER
00070 *>     The leading dimension of the array A.  LDA >= max(1,N).
00071 *> \endverbatim
00072 *>
00073 *> \param[in] AF
00074 *> \verbatim
00075 *>          AF is COMPLEX array, dimension (LDAF,N)
00076 *>     The factors L and U from the factorization
00077 *>     A = P*L*U as computed by CGETRF.
00078 *> \endverbatim
00079 *>
00080 *> \param[in] LDAF
00081 *> \verbatim
00082 *>          LDAF is INTEGER
00083 *>     The leading dimension of the array AF.  LDAF >= max(1,N).
00084 *> \endverbatim
00085 *
00086 *  Authors:
00087 *  ========
00088 *
00089 *> \author Univ. of Tennessee 
00090 *> \author Univ. of California Berkeley 
00091 *> \author Univ. of Colorado Denver 
00092 *> \author NAG Ltd. 
00093 *
00094 *> \date November 2011
00095 *
00096 *> \ingroup complexGEcomputational
00097 *
00098 *  =====================================================================
00099       REAL FUNCTION CLA_GERPVGRW( N, NCOLS, A, LDA, AF, LDAF )
00100 *
00101 *  -- LAPACK computational routine (version 3.4.0) --
00102 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00103 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00104 *     November 2011
00105 *
00106 *     .. Scalar Arguments ..
00107       INTEGER            N, NCOLS, LDA, LDAF
00108 *     ..
00109 *     .. Array Arguments ..
00110       COMPLEX            A( LDA, * ), AF( LDAF, * )
00111 *     ..
00112 *
00113 *  =====================================================================
00114 *
00115 *     .. Local Scalars ..
00116       INTEGER            I, J
00117       REAL               AMAX, UMAX, RPVGRW
00118       COMPLEX            ZDUM
00119 *     ..
00120 *     .. Intrinsic Functions ..
00121       INTRINSIC          MAX, MIN, ABS, REAL, AIMAG
00122 *     ..
00123 *     .. Statement Functions ..
00124       REAL               CABS1
00125 *     ..
00126 *     .. Statement Function Definitions ..
00127       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00128 *     ..
00129 *     .. Executable Statements ..
00130 *
00131       RPVGRW = 1.0
00132 
00133       DO J = 1, NCOLS
00134          AMAX = 0.0
00135          UMAX = 0.0
00136          DO I = 1, N
00137             AMAX = MAX( CABS1( A( I, J ) ), AMAX )
00138          END DO
00139          DO I = 1, J
00140             UMAX = MAX( CABS1( AF( I, J ) ), UMAX )
00141          END DO
00142          IF ( UMAX /= 0.0 ) THEN
00143             RPVGRW = MIN( AMAX / UMAX, RPVGRW )
00144          END IF
00145       END DO
00146       CLA_GERPVGRW = RPVGRW
00147       END
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