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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZHPCON 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZHPCON + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpcon.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpcon.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpcon.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, N 00026 * DOUBLE PRECISION ANORM, RCOND 00027 * .. 00028 * .. Array Arguments .. 00029 * INTEGER IPIV( * ) 00030 * COMPLEX*16 AP( * ), WORK( * ) 00031 * .. 00032 * 00033 * 00034 *> \par Purpose: 00035 * ============= 00036 *> 00037 *> \verbatim 00038 *> 00039 *> ZHPCON estimates the reciprocal of the condition number of a complex 00040 *> Hermitian packed matrix A using the factorization A = U*D*U**H or 00041 *> A = L*D*L**H computed by ZHPTRF. 00042 *> 00043 *> An estimate is obtained for norm(inv(A)), and the reciprocal of the 00044 *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). 00045 *> \endverbatim 00046 * 00047 * Arguments: 00048 * ========== 00049 * 00050 *> \param[in] UPLO 00051 *> \verbatim 00052 *> UPLO is CHARACTER*1 00053 *> Specifies whether the details of the factorization are stored 00054 *> as an upper or lower triangular matrix. 00055 *> = 'U': Upper triangular, form is A = U*D*U**H; 00056 *> = 'L': Lower triangular, form is A = L*D*L**H. 00057 *> \endverbatim 00058 *> 00059 *> \param[in] N 00060 *> \verbatim 00061 *> N is INTEGER 00062 *> The order of the matrix A. N >= 0. 00063 *> \endverbatim 00064 *> 00065 *> \param[in] AP 00066 *> \verbatim 00067 *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) 00068 *> The block diagonal matrix D and the multipliers used to 00069 *> obtain the factor U or L as computed by ZHPTRF, stored as a 00070 *> packed triangular matrix. 00071 *> \endverbatim 00072 *> 00073 *> \param[in] IPIV 00074 *> \verbatim 00075 *> IPIV is INTEGER array, dimension (N) 00076 *> Details of the interchanges and the block structure of D 00077 *> as determined by ZHPTRF. 00078 *> \endverbatim 00079 *> 00080 *> \param[in] ANORM 00081 *> \verbatim 00082 *> ANORM is DOUBLE PRECISION 00083 *> The 1-norm of the original matrix A. 00084 *> \endverbatim 00085 *> 00086 *> \param[out] RCOND 00087 *> \verbatim 00088 *> RCOND is DOUBLE PRECISION 00089 *> The reciprocal of the condition number of the matrix A, 00090 *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an 00091 *> estimate of the 1-norm of inv(A) computed in this routine. 00092 *> \endverbatim 00093 *> 00094 *> \param[out] WORK 00095 *> \verbatim 00096 *> WORK is COMPLEX*16 array, dimension (2*N) 00097 *> \endverbatim 00098 *> 00099 *> \param[out] INFO 00100 *> \verbatim 00101 *> INFO is INTEGER 00102 *> = 0: successful exit 00103 *> < 0: if INFO = -i, the i-th argument had an illegal value 00104 *> \endverbatim 00105 * 00106 * Authors: 00107 * ======== 00108 * 00109 *> \author Univ. of Tennessee 00110 *> \author Univ. of California Berkeley 00111 *> \author Univ. of Colorado Denver 00112 *> \author NAG Ltd. 00113 * 00114 *> \date November 2011 00115 * 00116 *> \ingroup complex16OTHERcomputational 00117 * 00118 * ===================================================================== 00119 SUBROUTINE ZHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO ) 00120 * 00121 * -- LAPACK computational routine (version 3.4.0) -- 00122 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00123 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00124 * November 2011 00125 * 00126 * .. Scalar Arguments .. 00127 CHARACTER UPLO 00128 INTEGER INFO, N 00129 DOUBLE PRECISION ANORM, RCOND 00130 * .. 00131 * .. Array Arguments .. 00132 INTEGER IPIV( * ) 00133 COMPLEX*16 AP( * ), WORK( * ) 00134 * .. 00135 * 00136 * ===================================================================== 00137 * 00138 * .. Parameters .. 00139 DOUBLE PRECISION ONE, ZERO 00140 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00141 * .. 00142 * .. Local Scalars .. 00143 LOGICAL UPPER 00144 INTEGER I, IP, KASE 00145 DOUBLE PRECISION AINVNM 00146 * .. 00147 * .. Local Arrays .. 00148 INTEGER ISAVE( 3 ) 00149 * .. 00150 * .. External Functions .. 00151 LOGICAL LSAME 00152 EXTERNAL LSAME 00153 * .. 00154 * .. External Subroutines .. 00155 EXTERNAL XERBLA, ZHPTRS, ZLACN2 00156 * .. 00157 * .. Executable Statements .. 00158 * 00159 * Test the input parameters. 00160 * 00161 INFO = 0 00162 UPPER = LSAME( UPLO, 'U' ) 00163 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00164 INFO = -1 00165 ELSE IF( N.LT.0 ) THEN 00166 INFO = -2 00167 ELSE IF( ANORM.LT.ZERO ) THEN 00168 INFO = -5 00169 END IF 00170 IF( INFO.NE.0 ) THEN 00171 CALL XERBLA( 'ZHPCON', -INFO ) 00172 RETURN 00173 END IF 00174 * 00175 * Quick return if possible 00176 * 00177 RCOND = ZERO 00178 IF( N.EQ.0 ) THEN 00179 RCOND = ONE 00180 RETURN 00181 ELSE IF( ANORM.LE.ZERO ) THEN 00182 RETURN 00183 END IF 00184 * 00185 * Check that the diagonal matrix D is nonsingular. 00186 * 00187 IF( UPPER ) THEN 00188 * 00189 * Upper triangular storage: examine D from bottom to top 00190 * 00191 IP = N*( N+1 ) / 2 00192 DO 10 I = N, 1, -1 00193 IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO ) 00194 $ RETURN 00195 IP = IP - I 00196 10 CONTINUE 00197 ELSE 00198 * 00199 * Lower triangular storage: examine D from top to bottom. 00200 * 00201 IP = 1 00202 DO 20 I = 1, N 00203 IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO ) 00204 $ RETURN 00205 IP = IP + N - I + 1 00206 20 CONTINUE 00207 END IF 00208 * 00209 * Estimate the 1-norm of the inverse. 00210 * 00211 KASE = 0 00212 30 CONTINUE 00213 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00214 IF( KASE.NE.0 ) THEN 00215 * 00216 * Multiply by inv(L*D*L**H) or inv(U*D*U**H). 00217 * 00218 CALL ZHPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO ) 00219 GO TO 30 00220 END IF 00221 * 00222 * Compute the estimate of the reciprocal condition number. 00223 * 00224 IF( AINVNM.NE.ZERO ) 00225 $ RCOND = ( ONE / AINVNM ) / ANORM 00226 * 00227 RETURN 00228 * 00229 * End of ZHPCON 00230 * 00231 END