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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZTPCON 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZTPCON + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztpcon.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztpcon.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztpcon.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, 00022 * INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER DIAG, NORM, UPLO 00026 * INTEGER INFO, N 00027 * DOUBLE PRECISION RCOND 00028 * .. 00029 * .. Array Arguments .. 00030 * DOUBLE PRECISION RWORK( * ) 00031 * COMPLEX*16 AP( * ), WORK( * ) 00032 * .. 00033 * 00034 * 00035 *> \par Purpose: 00036 * ============= 00037 *> 00038 *> \verbatim 00039 *> 00040 *> ZTPCON estimates the reciprocal of the condition number of a packed 00041 *> triangular matrix A, in either the 1-norm or the infinity-norm. 00042 *> 00043 *> The norm of A is computed and an estimate is obtained for 00044 *> norm(inv(A)), then the reciprocal of the condition number is 00045 *> 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] UPLO 00062 *> \verbatim 00063 *> UPLO is CHARACTER*1 00064 *> = 'U': A is upper triangular; 00065 *> = 'L': A is lower triangular. 00066 *> \endverbatim 00067 *> 00068 *> \param[in] DIAG 00069 *> \verbatim 00070 *> DIAG is CHARACTER*1 00071 *> = 'N': A is non-unit triangular; 00072 *> = 'U': A is unit triangular. 00073 *> \endverbatim 00074 *> 00075 *> \param[in] N 00076 *> \verbatim 00077 *> N is INTEGER 00078 *> The order of the matrix A. N >= 0. 00079 *> \endverbatim 00080 *> 00081 *> \param[in] AP 00082 *> \verbatim 00083 *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) 00084 *> The upper or lower triangular matrix A, packed columnwise in 00085 *> a linear array. The j-th column of A is stored in the array 00086 *> AP as follows: 00087 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00088 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00089 *> If DIAG = 'U', the diagonal elements of A are not referenced 00090 *> and are assumed to be 1. 00091 *> \endverbatim 00092 *> 00093 *> \param[out] RCOND 00094 *> \verbatim 00095 *> RCOND is DOUBLE PRECISION 00096 *> The reciprocal of the condition number of the matrix A, 00097 *> computed as RCOND = 1/(norm(A) * norm(inv(A))). 00098 *> \endverbatim 00099 *> 00100 *> \param[out] WORK 00101 *> \verbatim 00102 *> WORK is COMPLEX*16 array, dimension (2*N) 00103 *> \endverbatim 00104 *> 00105 *> \param[out] RWORK 00106 *> \verbatim 00107 *> RWORK is DOUBLE PRECISION array, dimension (N) 00108 *> \endverbatim 00109 *> 00110 *> \param[out] INFO 00111 *> \verbatim 00112 *> INFO is INTEGER 00113 *> = 0: successful exit 00114 *> < 0: if INFO = -i, the i-th argument had an illegal value 00115 *> \endverbatim 00116 * 00117 * Authors: 00118 * ======== 00119 * 00120 *> \author Univ. of Tennessee 00121 *> \author Univ. of California Berkeley 00122 *> \author Univ. of Colorado Denver 00123 *> \author NAG Ltd. 00124 * 00125 *> \date November 2011 00126 * 00127 *> \ingroup complex16OTHERcomputational 00128 * 00129 * ===================================================================== 00130 SUBROUTINE ZTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, 00131 $ INFO ) 00132 * 00133 * -- LAPACK computational routine (version 3.4.0) -- 00134 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00136 * November 2011 00137 * 00138 * .. Scalar Arguments .. 00139 CHARACTER DIAG, NORM, UPLO 00140 INTEGER INFO, N 00141 DOUBLE PRECISION RCOND 00142 * .. 00143 * .. Array Arguments .. 00144 DOUBLE PRECISION RWORK( * ) 00145 COMPLEX*16 AP( * ), WORK( * ) 00146 * .. 00147 * 00148 * ===================================================================== 00149 * 00150 * .. Parameters .. 00151 DOUBLE PRECISION ONE, ZERO 00152 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00153 * .. 00154 * .. Local Scalars .. 00155 LOGICAL NOUNIT, ONENRM, UPPER 00156 CHARACTER NORMIN 00157 INTEGER IX, KASE, KASE1 00158 DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM 00159 COMPLEX*16 ZDUM 00160 * .. 00161 * .. Local Arrays .. 00162 INTEGER ISAVE( 3 ) 00163 * .. 00164 * .. External Functions .. 00165 LOGICAL LSAME 00166 INTEGER IZAMAX 00167 DOUBLE PRECISION DLAMCH, ZLANTP 00168 EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANTP 00169 * .. 00170 * .. External Subroutines .. 00171 EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATPS 00172 * .. 00173 * .. Intrinsic Functions .. 00174 INTRINSIC ABS, DBLE, DIMAG, MAX 00175 * .. 00176 * .. Statement Functions .. 00177 DOUBLE PRECISION CABS1 00178 * .. 00179 * .. Statement Function definitions .. 00180 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00181 * .. 00182 * .. Executable Statements .. 00183 * 00184 * Test the input parameters. 00185 * 00186 INFO = 0 00187 UPPER = LSAME( UPLO, 'U' ) 00188 ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) 00189 NOUNIT = LSAME( DIAG, 'N' ) 00190 * 00191 IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN 00192 INFO = -1 00193 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00194 INFO = -2 00195 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN 00196 INFO = -3 00197 ELSE IF( N.LT.0 ) THEN 00198 INFO = -4 00199 END IF 00200 IF( INFO.NE.0 ) THEN 00201 CALL XERBLA( 'ZTPCON', -INFO ) 00202 RETURN 00203 END IF 00204 * 00205 * Quick return if possible 00206 * 00207 IF( N.EQ.0 ) THEN 00208 RCOND = ONE 00209 RETURN 00210 END IF 00211 * 00212 RCOND = ZERO 00213 SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) ) 00214 * 00215 * Compute the norm of the triangular matrix A. 00216 * 00217 ANORM = ZLANTP( NORM, UPLO, DIAG, N, AP, RWORK ) 00218 * 00219 * Continue only if ANORM > 0. 00220 * 00221 IF( ANORM.GT.ZERO ) THEN 00222 * 00223 * Estimate the norm of the inverse of A. 00224 * 00225 AINVNM = ZERO 00226 NORMIN = 'N' 00227 IF( ONENRM ) THEN 00228 KASE1 = 1 00229 ELSE 00230 KASE1 = 2 00231 END IF 00232 KASE = 0 00233 10 CONTINUE 00234 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00235 IF( KASE.NE.0 ) THEN 00236 IF( KASE.EQ.KASE1 ) THEN 00237 * 00238 * Multiply by inv(A). 00239 * 00240 CALL ZLATPS( UPLO, 'No transpose', DIAG, NORMIN, N, AP, 00241 $ WORK, SCALE, RWORK, INFO ) 00242 ELSE 00243 * 00244 * Multiply by inv(A**H). 00245 * 00246 CALL ZLATPS( UPLO, 'Conjugate transpose', DIAG, NORMIN, 00247 $ N, AP, WORK, SCALE, RWORK, INFO ) 00248 END IF 00249 NORMIN = 'Y' 00250 * 00251 * Multiply by 1/SCALE if doing so will not cause overflow. 00252 * 00253 IF( SCALE.NE.ONE ) THEN 00254 IX = IZAMAX( N, WORK, 1 ) 00255 XNORM = CABS1( WORK( IX ) ) 00256 IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO ) 00257 $ GO TO 20 00258 CALL ZDRSCL( N, SCALE, WORK, 1 ) 00259 END IF 00260 GO TO 10 00261 END IF 00262 * 00263 * Compute the estimate of the reciprocal condition number. 00264 * 00265 IF( AINVNM.NE.ZERO ) 00266 $ RCOND = ( ONE / ANORM ) / AINVNM 00267 END IF 00268 * 00269 20 CONTINUE 00270 RETURN 00271 * 00272 * End of ZTPCON 00273 * 00274 END