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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DGECON 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DGECON + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgecon.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgecon.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgecon.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, 00022 * INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER NORM 00026 * INTEGER INFO, LDA, N 00027 * DOUBLE PRECISION ANORM, RCOND 00028 * .. 00029 * .. Array Arguments .. 00030 * INTEGER IWORK( * ) 00031 * DOUBLE PRECISION A( LDA, * ), WORK( * ) 00032 * .. 00033 * 00034 * 00035 *> \par Purpose: 00036 * ============= 00037 *> 00038 *> \verbatim 00039 *> 00040 *> DGECON estimates the reciprocal of the condition number of a general 00041 *> real matrix A, in either the 1-norm or the infinity-norm, using 00042 *> the LU factorization computed by DGETRF. 00043 *> 00044 *> An estimate is obtained for norm(inv(A)), and the reciprocal of the 00045 *> condition number is computed as 00046 *> RCOND = 1 / ( norm(A) * norm(inv(A)) ). 00047 *> \endverbatim 00048 * 00049 * Arguments: 00050 * ========== 00051 * 00052 *> \param[in] NORM 00053 *> \verbatim 00054 *> NORM is CHARACTER*1 00055 *> Specifies whether the 1-norm condition number or the 00056 *> infinity-norm condition number is required: 00057 *> = '1' or 'O': 1-norm; 00058 *> = 'I': Infinity-norm. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] N 00062 *> \verbatim 00063 *> N is INTEGER 00064 *> The order of the matrix A. N >= 0. 00065 *> \endverbatim 00066 *> 00067 *> \param[in] A 00068 *> \verbatim 00069 *> A is DOUBLE PRECISION array, dimension (LDA,N) 00070 *> The factors L and U from the factorization A = P*L*U 00071 *> as computed by DGETRF. 00072 *> \endverbatim 00073 *> 00074 *> \param[in] LDA 00075 *> \verbatim 00076 *> LDA is INTEGER 00077 *> The leading dimension of the array A. LDA >= max(1,N). 00078 *> \endverbatim 00079 *> 00080 *> \param[in] ANORM 00081 *> \verbatim 00082 *> ANORM is DOUBLE PRECISION 00083 *> If NORM = '1' or 'O', the 1-norm of the original matrix A. 00084 *> If NORM = 'I', the infinity-norm of the original matrix A. 00085 *> \endverbatim 00086 *> 00087 *> \param[out] RCOND 00088 *> \verbatim 00089 *> RCOND is DOUBLE PRECISION 00090 *> The reciprocal of the condition number of the matrix A, 00091 *> computed as RCOND = 1/(norm(A) * norm(inv(A))). 00092 *> \endverbatim 00093 *> 00094 *> \param[out] WORK 00095 *> \verbatim 00096 *> WORK is DOUBLE PRECISION array, dimension (4*N) 00097 *> \endverbatim 00098 *> 00099 *> \param[out] IWORK 00100 *> \verbatim 00101 *> IWORK is INTEGER array, dimension (N) 00102 *> \endverbatim 00103 *> 00104 *> \param[out] INFO 00105 *> \verbatim 00106 *> INFO is INTEGER 00107 *> = 0: successful exit 00108 *> < 0: if INFO = -i, the i-th argument had an illegal value 00109 *> \endverbatim 00110 * 00111 * Authors: 00112 * ======== 00113 * 00114 *> \author Univ. of Tennessee 00115 *> \author Univ. of California Berkeley 00116 *> \author Univ. of Colorado Denver 00117 *> \author NAG Ltd. 00118 * 00119 *> \date November 2011 00120 * 00121 *> \ingroup doubleGEcomputational 00122 * 00123 * ===================================================================== 00124 SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, 00125 $ INFO ) 00126 * 00127 * -- LAPACK computational routine (version 3.4.0) -- 00128 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00130 * November 2011 00131 * 00132 * .. Scalar Arguments .. 00133 CHARACTER NORM 00134 INTEGER INFO, LDA, N 00135 DOUBLE PRECISION ANORM, RCOND 00136 * .. 00137 * .. Array Arguments .. 00138 INTEGER IWORK( * ) 00139 DOUBLE PRECISION A( LDA, * ), WORK( * ) 00140 * .. 00141 * 00142 * ===================================================================== 00143 * 00144 * .. Parameters .. 00145 DOUBLE PRECISION ONE, ZERO 00146 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00147 * .. 00148 * .. Local Scalars .. 00149 LOGICAL ONENRM 00150 CHARACTER NORMIN 00151 INTEGER IX, KASE, KASE1 00152 DOUBLE PRECISION AINVNM, SCALE, SL, SMLNUM, SU 00153 * .. 00154 * .. Local Arrays .. 00155 INTEGER ISAVE( 3 ) 00156 * .. 00157 * .. External Functions .. 00158 LOGICAL LSAME 00159 INTEGER IDAMAX 00160 DOUBLE PRECISION DLAMCH 00161 EXTERNAL LSAME, IDAMAX, DLAMCH 00162 * .. 00163 * .. External Subroutines .. 00164 EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA 00165 * .. 00166 * .. Intrinsic Functions .. 00167 INTRINSIC ABS, MAX 00168 * .. 00169 * .. Executable Statements .. 00170 * 00171 * Test the input parameters. 00172 * 00173 INFO = 0 00174 ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) 00175 IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN 00176 INFO = -1 00177 ELSE IF( N.LT.0 ) THEN 00178 INFO = -2 00179 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00180 INFO = -4 00181 ELSE IF( ANORM.LT.ZERO ) THEN 00182 INFO = -5 00183 END IF 00184 IF( INFO.NE.0 ) THEN 00185 CALL XERBLA( 'DGECON', -INFO ) 00186 RETURN 00187 END IF 00188 * 00189 * Quick return if possible 00190 * 00191 RCOND = ZERO 00192 IF( N.EQ.0 ) THEN 00193 RCOND = ONE 00194 RETURN 00195 ELSE IF( ANORM.EQ.ZERO ) THEN 00196 RETURN 00197 END IF 00198 * 00199 SMLNUM = DLAMCH( 'Safe minimum' ) 00200 * 00201 * Estimate the norm of inv(A). 00202 * 00203 AINVNM = ZERO 00204 NORMIN = 'N' 00205 IF( ONENRM ) THEN 00206 KASE1 = 1 00207 ELSE 00208 KASE1 = 2 00209 END IF 00210 KASE = 0 00211 10 CONTINUE 00212 CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) 00213 IF( KASE.NE.0 ) THEN 00214 IF( KASE.EQ.KASE1 ) THEN 00215 * 00216 * Multiply by inv(L). 00217 * 00218 CALL DLATRS( 'Lower', 'No transpose', 'Unit', NORMIN, N, A, 00219 $ LDA, WORK, SL, WORK( 2*N+1 ), INFO ) 00220 * 00221 * Multiply by inv(U). 00222 * 00223 CALL DLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, 00224 $ A, LDA, WORK, SU, WORK( 3*N+1 ), INFO ) 00225 ELSE 00226 * 00227 * Multiply by inv(U**T). 00228 * 00229 CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A, 00230 $ LDA, WORK, SU, WORK( 3*N+1 ), INFO ) 00231 * 00232 * Multiply by inv(L**T). 00233 * 00234 CALL DLATRS( 'Lower', 'Transpose', 'Unit', NORMIN, N, A, 00235 $ LDA, WORK, SL, WORK( 2*N+1 ), INFO ) 00236 END IF 00237 * 00238 * Divide X by 1/(SL*SU) if doing so will not cause overflow. 00239 * 00240 SCALE = SL*SU 00241 NORMIN = 'Y' 00242 IF( SCALE.NE.ONE ) THEN 00243 IX = IDAMAX( N, WORK, 1 ) 00244 IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) 00245 $ GO TO 20 00246 CALL DRSCL( N, SCALE, WORK, 1 ) 00247 END IF 00248 GO TO 10 00249 END IF 00250 * 00251 * Compute the estimate of the reciprocal condition number. 00252 * 00253 IF( AINVNM.NE.ZERO ) 00254 $ RCOND = ( ONE / AINVNM ) / ANORM 00255 * 00256 20 CONTINUE 00257 RETURN 00258 * 00259 * End of DGECON 00260 * 00261 END