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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLA_GERPVGRW 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZLA_GERPVGRW + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gerpvgrw.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gerpvgrw.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gerpvgrw.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION ZLA_GERPVGRW( N, NCOLS, A, LDA, AF, 00022 * LDAF ) 00023 * 00024 * .. Scalar Arguments .. 00025 * INTEGER N, NCOLS, LDA, LDAF 00026 * .. 00027 * .. Array Arguments .. 00028 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> 00038 *> ZLA_GERPVGRW computes the reciprocal pivot growth factor 00039 *> norm(A)/norm(U). The "max absolute element" norm is used. If this is 00040 *> much less than 1, the stability of the LU factorization of the 00041 *> (equilibrated) matrix A could be poor. This also means that the 00042 *> solution X, estimated condition numbers, and error bounds could be 00043 *> unreliable. 00044 *> \endverbatim 00045 * 00046 * Arguments: 00047 * ========== 00048 * 00049 *> \param[in] N 00050 *> \verbatim 00051 *> N is INTEGER 00052 *> The number of linear equations, i.e., the order of the 00053 *> matrix A. N >= 0. 00054 *> \endverbatim 00055 *> 00056 *> \param[in] NCOLS 00057 *> \verbatim 00058 *> NCOLS is INTEGER 00059 *> The number of columns of the matrix A. NCOLS >= 0. 00060 *> \endverbatim 00061 *> 00062 *> \param[in] A 00063 *> \verbatim 00064 *> A is DOUBLE PRECISION array, dimension (LDA,N) 00065 *> On entry, the N-by-N matrix A. 00066 *> \endverbatim 00067 *> 00068 *> \param[in] LDA 00069 *> \verbatim 00070 *> LDA is INTEGER 00071 *> The leading dimension of the array A. LDA >= max(1,N). 00072 *> \endverbatim 00073 *> 00074 *> \param[in] AF 00075 *> \verbatim 00076 *> AF is DOUBLE PRECISION array, dimension (LDAF,N) 00077 *> The factors L and U from the factorization 00078 *> A = P*L*U as computed by ZGETRF. 00079 *> \endverbatim 00080 *> 00081 *> \param[in] LDAF 00082 *> \verbatim 00083 *> LDAF is INTEGER 00084 *> The leading dimension of the array AF. LDAF >= max(1,N). 00085 *> \endverbatim 00086 * 00087 * Authors: 00088 * ======== 00089 * 00090 *> \author Univ. of Tennessee 00091 *> \author Univ. of California Berkeley 00092 *> \author Univ. of Colorado Denver 00093 *> \author NAG Ltd. 00094 * 00095 *> \date November 2011 00096 * 00097 *> \ingroup complex16GEcomputational 00098 * 00099 * ===================================================================== 00100 DOUBLE PRECISION FUNCTION ZLA_GERPVGRW( N, NCOLS, A, LDA, AF, 00101 $ LDAF ) 00102 * 00103 * -- LAPACK computational routine (version 3.4.0) -- 00104 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00105 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00106 * November 2011 00107 * 00108 * .. Scalar Arguments .. 00109 INTEGER N, NCOLS, LDA, LDAF 00110 * .. 00111 * .. Array Arguments .. 00112 COMPLEX*16 A( LDA, * ), AF( LDAF, * ) 00113 * .. 00114 * 00115 * ===================================================================== 00116 * 00117 * .. Local Scalars .. 00118 INTEGER I, J 00119 DOUBLE PRECISION AMAX, UMAX, RPVGRW 00120 COMPLEX*16 ZDUM 00121 * .. 00122 * .. Intrinsic Functions .. 00123 INTRINSIC MAX, MIN, ABS, REAL, DIMAG 00124 * .. 00125 * .. Statement Functions .. 00126 DOUBLE PRECISION CABS1 00127 * .. 00128 * .. Statement Function Definitions .. 00129 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00130 * .. 00131 * .. Executable Statements .. 00132 * 00133 RPVGRW = 1.0D+0 00134 00135 DO J = 1, NCOLS 00136 AMAX = 0.0D+0 00137 UMAX = 0.0D+0 00138 DO I = 1, N 00139 AMAX = MAX( CABS1( A( I, J ) ), AMAX ) 00140 END DO 00141 DO I = 1, J 00142 UMAX = MAX( CABS1( AF( I, J ) ), UMAX ) 00143 END DO 00144 IF ( UMAX /= 0.0D+0 ) THEN 00145 RPVGRW = MIN( AMAX / UMAX, RPVGRW ) 00146 END IF 00147 END DO 00148 ZLA_GERPVGRW = RPVGRW 00149 END