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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLA_PORPVGRW 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZLA_PORPVGRW + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_porpvgrw.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_porpvgrw.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_porpvgrw.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION ZLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF, 00022 * LDAF, WORK ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER*1 UPLO 00026 * INTEGER NCOLS, LDA, LDAF 00027 * .. 00028 * .. Array Arguments .. 00029 * COMPLEX*16 A( LDA, * ), AF( LDAF, * ) 00030 * DOUBLE PRECISION WORK( * ) 00031 * .. 00032 * 00033 * 00034 *> \par Purpose: 00035 * ============= 00036 *> 00037 *> \verbatim 00038 *> 00039 *> 00040 *> ZLA_PORPVGRW computes the reciprocal pivot growth factor 00041 *> norm(A)/norm(U). The "max absolute element" norm is used. If this is 00042 *> much less than 1, the stability of the LU factorization of the 00043 *> (equilibrated) matrix A could be poor. This also means that the 00044 *> solution X, estimated condition numbers, and error bounds could be 00045 *> unreliable. 00046 *> \endverbatim 00047 * 00048 * Arguments: 00049 * ========== 00050 * 00051 *> \param[in] UPLO 00052 *> \verbatim 00053 *> UPLO is CHARACTER*1 00054 *> = 'U': Upper triangle of A is stored; 00055 *> = 'L': Lower triangle of A is stored. 00056 *> \endverbatim 00057 *> 00058 *> \param[in] NCOLS 00059 *> \verbatim 00060 *> NCOLS is INTEGER 00061 *> The number of columns of the matrix A. NCOLS >= 0. 00062 *> \endverbatim 00063 *> 00064 *> \param[in] A 00065 *> \verbatim 00066 *> A is COMPLEX*16 array, dimension (LDA,N) 00067 *> On entry, the N-by-N matrix A. 00068 *> \endverbatim 00069 *> 00070 *> \param[in] LDA 00071 *> \verbatim 00072 *> LDA is INTEGER 00073 *> The leading dimension of the array A. LDA >= max(1,N). 00074 *> \endverbatim 00075 *> 00076 *> \param[in] AF 00077 *> \verbatim 00078 *> AF is COMPLEX*16 array, dimension (LDAF,N) 00079 *> The triangular factor U or L from the Cholesky factorization 00080 *> A = U**T*U or A = L*L**T, as computed by ZPOTRF. 00081 *> \endverbatim 00082 *> 00083 *> \param[in] LDAF 00084 *> \verbatim 00085 *> LDAF is INTEGER 00086 *> The leading dimension of the array AF. LDAF >= max(1,N). 00087 *> \endverbatim 00088 *> 00089 *> \param[in] WORK 00090 *> \verbatim 00091 *> WORK is COMPLEX*16 array, dimension (2*N) 00092 *> \endverbatim 00093 * 00094 * Authors: 00095 * ======== 00096 * 00097 *> \author Univ. of Tennessee 00098 *> \author Univ. of California Berkeley 00099 *> \author Univ. of Colorado Denver 00100 *> \author NAG Ltd. 00101 * 00102 *> \date November 2011 00103 * 00104 *> \ingroup complex16POcomputational 00105 * 00106 * ===================================================================== 00107 DOUBLE PRECISION FUNCTION ZLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF, 00108 $ LDAF, WORK ) 00109 * 00110 * -- LAPACK computational routine (version 3.4.0) -- 00111 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00113 * November 2011 00114 * 00115 * .. Scalar Arguments .. 00116 CHARACTER*1 UPLO 00117 INTEGER NCOLS, LDA, LDAF 00118 * .. 00119 * .. Array Arguments .. 00120 COMPLEX*16 A( LDA, * ), AF( LDAF, * ) 00121 DOUBLE PRECISION WORK( * ) 00122 * .. 00123 * 00124 * ===================================================================== 00125 * 00126 * .. Local Scalars .. 00127 INTEGER I, J 00128 DOUBLE PRECISION AMAX, UMAX, RPVGRW 00129 LOGICAL UPPER 00130 COMPLEX*16 ZDUM 00131 * .. 00132 * .. External Functions .. 00133 EXTERNAL LSAME, ZLASET 00134 LOGICAL LSAME 00135 * .. 00136 * .. Intrinsic Functions .. 00137 INTRINSIC ABS, MAX, MIN, REAL, DIMAG 00138 * .. 00139 * .. Statement Functions .. 00140 DOUBLE PRECISION CABS1 00141 * .. 00142 * .. Statement Function Definitions .. 00143 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00144 * .. 00145 * .. Executable Statements .. 00146 UPPER = LSAME( 'Upper', UPLO ) 00147 * 00148 * DPOTRF will have factored only the NCOLSxNCOLS leading minor, so 00149 * we restrict the growth search to that minor and use only the first 00150 * 2*NCOLS workspace entries. 00151 * 00152 RPVGRW = 1.0D+0 00153 DO I = 1, 2*NCOLS 00154 WORK( I ) = 0.0D+0 00155 END DO 00156 * 00157 * Find the max magnitude entry of each column. 00158 * 00159 IF ( UPPER ) THEN 00160 DO J = 1, NCOLS 00161 DO I = 1, J 00162 WORK( NCOLS+J ) = 00163 $ MAX( CABS1( A( I, J ) ), WORK( NCOLS+J ) ) 00164 END DO 00165 END DO 00166 ELSE 00167 DO J = 1, NCOLS 00168 DO I = J, NCOLS 00169 WORK( NCOLS+J ) = 00170 $ MAX( CABS1( A( I, J ) ), WORK( NCOLS+J ) ) 00171 END DO 00172 END DO 00173 END IF 00174 * 00175 * Now find the max magnitude entry of each column of the factor in 00176 * AF. No pivoting, so no permutations. 00177 * 00178 IF ( LSAME( 'Upper', UPLO ) ) THEN 00179 DO J = 1, NCOLS 00180 DO I = 1, J 00181 WORK( J ) = MAX( CABS1( AF( I, J ) ), WORK( J ) ) 00182 END DO 00183 END DO 00184 ELSE 00185 DO J = 1, NCOLS 00186 DO I = J, NCOLS 00187 WORK( J ) = MAX( CABS1( AF( I, J ) ), WORK( J ) ) 00188 END DO 00189 END DO 00190 END IF 00191 * 00192 * Compute the *inverse* of the max element growth factor. Dividing 00193 * by zero would imply the largest entry of the factor's column is 00194 * zero. Than can happen when either the column of A is zero or 00195 * massive pivots made the factor underflow to zero. Neither counts 00196 * as growth in itself, so simply ignore terms with zero 00197 * denominators. 00198 * 00199 IF ( LSAME( 'Upper', UPLO ) ) THEN 00200 DO I = 1, NCOLS 00201 UMAX = WORK( I ) 00202 AMAX = WORK( NCOLS+I ) 00203 IF ( UMAX /= 0.0D+0 ) THEN 00204 RPVGRW = MIN( AMAX / UMAX, RPVGRW ) 00205 END IF 00206 END DO 00207 ELSE 00208 DO I = 1, NCOLS 00209 UMAX = WORK( I ) 00210 AMAX = WORK( NCOLS+I ) 00211 IF ( UMAX /= 0.0D+0 ) THEN 00212 RPVGRW = MIN( AMAX / UMAX, RPVGRW ) 00213 END IF 00214 END DO 00215 END IF 00216 00217 ZLA_PORPVGRW = RPVGRW 00218 END