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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DSPCON 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DSPCON + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspcon.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspcon.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspcon.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK, 00022 * INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER UPLO 00026 * INTEGER INFO, N 00027 * DOUBLE PRECISION ANORM, RCOND 00028 * .. 00029 * .. Array Arguments .. 00030 * INTEGER IPIV( * ), IWORK( * ) 00031 * DOUBLE PRECISION AP( * ), WORK( * ) 00032 * .. 00033 * 00034 * 00035 *> \par Purpose: 00036 * ============= 00037 *> 00038 *> \verbatim 00039 *> 00040 *> DSPCON estimates the reciprocal of the condition number (in the 00041 *> 1-norm) of a real symmetric packed matrix A using the factorization 00042 *> A = U*D*U**T or A = L*D*L**T computed by DSPTRF. 00043 *> 00044 *> An estimate is obtained for norm(inv(A)), and the reciprocal of the 00045 *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). 00046 *> \endverbatim 00047 * 00048 * Arguments: 00049 * ========== 00050 * 00051 *> \param[in] UPLO 00052 *> \verbatim 00053 *> UPLO is CHARACTER*1 00054 *> Specifies whether the details of the factorization are stored 00055 *> as an upper or lower triangular matrix. 00056 *> = 'U': Upper triangular, form is A = U*D*U**T; 00057 *> = 'L': Lower triangular, form is A = L*D*L**T. 00058 *> \endverbatim 00059 *> 00060 *> \param[in] N 00061 *> \verbatim 00062 *> N is INTEGER 00063 *> The order of the matrix A. N >= 0. 00064 *> \endverbatim 00065 *> 00066 *> \param[in] AP 00067 *> \verbatim 00068 *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) 00069 *> The block diagonal matrix D and the multipliers used to 00070 *> obtain the factor U or L as computed by DSPTRF, stored as a 00071 *> packed triangular matrix. 00072 *> \endverbatim 00073 *> 00074 *> \param[in] IPIV 00075 *> \verbatim 00076 *> IPIV is INTEGER array, dimension (N) 00077 *> Details of the interchanges and the block structure of D 00078 *> as determined by DSPTRF. 00079 *> \endverbatim 00080 *> 00081 *> \param[in] ANORM 00082 *> \verbatim 00083 *> ANORM is DOUBLE PRECISION 00084 *> The 1-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/(ANORM * AINVNM), where AINVNM is an 00092 *> estimate of the 1-norm of inv(A) computed in this routine. 00093 *> \endverbatim 00094 *> 00095 *> \param[out] WORK 00096 *> \verbatim 00097 *> WORK is DOUBLE PRECISION array, dimension (2*N) 00098 *> \endverbatim 00099 *> 00100 *> \param[out] IWORK 00101 *> \verbatim 00102 *> IWORK is INTEGER array, dimension (N) 00103 *> \endverbatim 00104 *> 00105 *> \param[out] INFO 00106 *> \verbatim 00107 *> INFO is INTEGER 00108 *> = 0: successful exit 00109 *> < 0: if INFO = -i, the i-th argument had an illegal value 00110 *> \endverbatim 00111 * 00112 * Authors: 00113 * ======== 00114 * 00115 *> \author Univ. of Tennessee 00116 *> \author Univ. of California Berkeley 00117 *> \author Univ. of Colorado Denver 00118 *> \author NAG Ltd. 00119 * 00120 *> \date November 2011 00121 * 00122 *> \ingroup doubleOTHERcomputational 00123 * 00124 * ===================================================================== 00125 SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK, 00126 $ INFO ) 00127 * 00128 * -- LAPACK computational routine (version 3.4.0) -- 00129 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00131 * November 2011 00132 * 00133 * .. Scalar Arguments .. 00134 CHARACTER UPLO 00135 INTEGER INFO, N 00136 DOUBLE PRECISION ANORM, RCOND 00137 * .. 00138 * .. Array Arguments .. 00139 INTEGER IPIV( * ), IWORK( * ) 00140 DOUBLE PRECISION AP( * ), WORK( * ) 00141 * .. 00142 * 00143 * ===================================================================== 00144 * 00145 * .. Parameters .. 00146 DOUBLE PRECISION ONE, ZERO 00147 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00148 * .. 00149 * .. Local Scalars .. 00150 LOGICAL UPPER 00151 INTEGER I, IP, KASE 00152 DOUBLE PRECISION AINVNM 00153 * .. 00154 * .. Local Arrays .. 00155 INTEGER ISAVE( 3 ) 00156 * .. 00157 * .. External Functions .. 00158 LOGICAL LSAME 00159 EXTERNAL LSAME 00160 * .. 00161 * .. External Subroutines .. 00162 EXTERNAL DLACN2, DSPTRS, XERBLA 00163 * .. 00164 * .. Executable Statements .. 00165 * 00166 * Test the input parameters. 00167 * 00168 INFO = 0 00169 UPPER = LSAME( UPLO, 'U' ) 00170 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00171 INFO = -1 00172 ELSE IF( N.LT.0 ) THEN 00173 INFO = -2 00174 ELSE IF( ANORM.LT.ZERO ) THEN 00175 INFO = -5 00176 END IF 00177 IF( INFO.NE.0 ) THEN 00178 CALL XERBLA( 'DSPCON', -INFO ) 00179 RETURN 00180 END IF 00181 * 00182 * Quick return if possible 00183 * 00184 RCOND = ZERO 00185 IF( N.EQ.0 ) THEN 00186 RCOND = ONE 00187 RETURN 00188 ELSE IF( ANORM.LE.ZERO ) THEN 00189 RETURN 00190 END IF 00191 * 00192 * Check that the diagonal matrix D is nonsingular. 00193 * 00194 IF( UPPER ) THEN 00195 * 00196 * Upper triangular storage: examine D from bottom to top 00197 * 00198 IP = N*( N+1 ) / 2 00199 DO 10 I = N, 1, -1 00200 IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO ) 00201 $ RETURN 00202 IP = IP - I 00203 10 CONTINUE 00204 ELSE 00205 * 00206 * Lower triangular storage: examine D from top to bottom. 00207 * 00208 IP = 1 00209 DO 20 I = 1, N 00210 IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO ) 00211 $ RETURN 00212 IP = IP + N - I + 1 00213 20 CONTINUE 00214 END IF 00215 * 00216 * Estimate the 1-norm of the inverse. 00217 * 00218 KASE = 0 00219 30 CONTINUE 00220 CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) 00221 IF( KASE.NE.0 ) THEN 00222 * 00223 * Multiply by inv(L*D*L**T) or inv(U*D*U**T). 00224 * 00225 CALL DSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO ) 00226 GO TO 30 00227 END IF 00228 * 00229 * Compute the estimate of the reciprocal condition number. 00230 * 00231 IF( AINVNM.NE.ZERO ) 00232 $ RCOND = ( ONE / AINVNM ) / ANORM 00233 * 00234 RETURN 00235 * 00236 * End of DSPCON 00237 * 00238 END