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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DPPCON 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DPPCON + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dppcon.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dppcon.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dppcon.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, N 00026 * DOUBLE PRECISION ANORM, RCOND 00027 * .. 00028 * .. Array Arguments .. 00029 * INTEGER IWORK( * ) 00030 * DOUBLE PRECISION AP( * ), WORK( * ) 00031 * .. 00032 * 00033 * 00034 *> \par Purpose: 00035 * ============= 00036 *> 00037 *> \verbatim 00038 *> 00039 *> DPPCON estimates the reciprocal of the condition number (in the 00040 *> 1-norm) of a real symmetric positive definite packed matrix using 00041 *> the Cholesky factorization A = U**T*U or A = L*L**T computed by 00042 *> DPPTRF. 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 *> = 'U': Upper triangle of A is stored; 00055 *> = 'L': Lower triangle of A is stored. 00056 *> \endverbatim 00057 *> 00058 *> \param[in] N 00059 *> \verbatim 00060 *> N is INTEGER 00061 *> The order of the matrix A. N >= 0. 00062 *> \endverbatim 00063 *> 00064 *> \param[in] AP 00065 *> \verbatim 00066 *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) 00067 *> The triangular factor U or L from the Cholesky factorization 00068 *> A = U**T*U or A = L*L**T, packed columnwise in a linear 00069 *> array. The j-th column of U or L is stored in the array AP 00070 *> as follows: 00071 *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; 00072 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. 00073 *> \endverbatim 00074 *> 00075 *> \param[in] ANORM 00076 *> \verbatim 00077 *> ANORM is DOUBLE PRECISION 00078 *> The 1-norm (or infinity-norm) of the symmetric matrix A. 00079 *> \endverbatim 00080 *> 00081 *> \param[out] RCOND 00082 *> \verbatim 00083 *> RCOND is DOUBLE PRECISION 00084 *> The reciprocal of the condition number of the matrix A, 00085 *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an 00086 *> estimate of the 1-norm of inv(A) computed in this routine. 00087 *> \endverbatim 00088 *> 00089 *> \param[out] WORK 00090 *> \verbatim 00091 *> WORK is DOUBLE PRECISION array, dimension (3*N) 00092 *> \endverbatim 00093 *> 00094 *> \param[out] IWORK 00095 *> \verbatim 00096 *> IWORK is INTEGER array, dimension (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 doubleOTHERcomputational 00117 * 00118 * ===================================================================== 00119 SUBROUTINE DPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, 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 IWORK( * ) 00133 DOUBLE PRECISION 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 CHARACTER NORMIN 00145 INTEGER IX, KASE 00146 DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM 00147 * .. 00148 * .. Local Arrays .. 00149 INTEGER ISAVE( 3 ) 00150 * .. 00151 * .. External Functions .. 00152 LOGICAL LSAME 00153 INTEGER IDAMAX 00154 DOUBLE PRECISION DLAMCH 00155 EXTERNAL LSAME, IDAMAX, DLAMCH 00156 * .. 00157 * .. External Subroutines .. 00158 EXTERNAL DLACN2, DLATPS, DRSCL, XERBLA 00159 * .. 00160 * .. Intrinsic Functions .. 00161 INTRINSIC ABS 00162 * .. 00163 * .. Executable Statements .. 00164 * 00165 * Test the input parameters. 00166 * 00167 INFO = 0 00168 UPPER = LSAME( UPLO, 'U' ) 00169 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00170 INFO = -1 00171 ELSE IF( N.LT.0 ) THEN 00172 INFO = -2 00173 ELSE IF( ANORM.LT.ZERO ) THEN 00174 INFO = -4 00175 END IF 00176 IF( INFO.NE.0 ) THEN 00177 CALL XERBLA( 'DPPCON', -INFO ) 00178 RETURN 00179 END IF 00180 * 00181 * Quick return if possible 00182 * 00183 RCOND = ZERO 00184 IF( N.EQ.0 ) THEN 00185 RCOND = ONE 00186 RETURN 00187 ELSE IF( ANORM.EQ.ZERO ) THEN 00188 RETURN 00189 END IF 00190 * 00191 SMLNUM = DLAMCH( 'Safe minimum' ) 00192 * 00193 * Estimate the 1-norm of the inverse. 00194 * 00195 KASE = 0 00196 NORMIN = 'N' 00197 10 CONTINUE 00198 CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) 00199 IF( KASE.NE.0 ) THEN 00200 IF( UPPER ) THEN 00201 * 00202 * Multiply by inv(U**T). 00203 * 00204 CALL DLATPS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, 00205 $ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO ) 00206 NORMIN = 'Y' 00207 * 00208 * Multiply by inv(U). 00209 * 00210 CALL DLATPS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, 00211 $ AP, WORK, SCALEU, WORK( 2*N+1 ), INFO ) 00212 ELSE 00213 * 00214 * Multiply by inv(L). 00215 * 00216 CALL DLATPS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N, 00217 $ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO ) 00218 NORMIN = 'Y' 00219 * 00220 * Multiply by inv(L**T). 00221 * 00222 CALL DLATPS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, 00223 $ AP, WORK, SCALEU, WORK( 2*N+1 ), INFO ) 00224 END IF 00225 * 00226 * Multiply by 1/SCALE if doing so will not cause overflow. 00227 * 00228 SCALE = SCALEL*SCALEU 00229 IF( SCALE.NE.ONE ) THEN 00230 IX = IDAMAX( N, WORK, 1 ) 00231 IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) 00232 $ GO TO 20 00233 CALL DRSCL( N, SCALE, WORK, 1 ) 00234 END IF 00235 GO TO 10 00236 END IF 00237 * 00238 * Compute the estimate of the reciprocal condition number. 00239 * 00240 IF( AINVNM.NE.ZERO ) 00241 $ RCOND = ( ONE / AINVNM ) / ANORM 00242 * 00243 20 CONTINUE 00244 RETURN 00245 * 00246 * End of DPPCON 00247 * 00248 END