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