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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZTBCON 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZTBCON + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztbcon.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztbcon.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztbcon.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, 00022 * RWORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER DIAG, NORM, UPLO 00026 * INTEGER INFO, KD, LDAB, N 00027 * DOUBLE PRECISION RCOND 00028 * .. 00029 * .. Array Arguments .. 00030 * DOUBLE PRECISION RWORK( * ) 00031 * COMPLEX*16 AB( LDAB, * ), WORK( * ) 00032 * .. 00033 * 00034 * 00035 *> \par Purpose: 00036 * ============= 00037 *> 00038 *> \verbatim 00039 *> 00040 *> ZTBCON estimates the reciprocal of the condition number of a 00041 *> triangular band 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] KD 00082 *> \verbatim 00083 *> KD is INTEGER 00084 *> The number of superdiagonals or subdiagonals of the 00085 *> triangular band matrix A. KD >= 0. 00086 *> \endverbatim 00087 *> 00088 *> \param[in] AB 00089 *> \verbatim 00090 *> AB is COMPLEX*16 array, dimension (LDAB,N) 00091 *> The upper or lower triangular band matrix A, stored in the 00092 *> first kd+1 rows of the array. The j-th column of A is stored 00093 *> in the j-th column of the array AB as follows: 00094 *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; 00095 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). 00096 *> If DIAG = 'U', the diagonal elements of A are not referenced 00097 *> and are assumed to be 1. 00098 *> \endverbatim 00099 *> 00100 *> \param[in] LDAB 00101 *> \verbatim 00102 *> LDAB is INTEGER 00103 *> The leading dimension of the array AB. LDAB >= KD+1. 00104 *> \endverbatim 00105 *> 00106 *> \param[out] RCOND 00107 *> \verbatim 00108 *> RCOND is DOUBLE PRECISION 00109 *> The reciprocal of the condition number of the matrix A, 00110 *> computed as RCOND = 1/(norm(A) * norm(inv(A))). 00111 *> \endverbatim 00112 *> 00113 *> \param[out] WORK 00114 *> \verbatim 00115 *> WORK is COMPLEX*16 array, dimension (2*N) 00116 *> \endverbatim 00117 *> 00118 *> \param[out] RWORK 00119 *> \verbatim 00120 *> RWORK is DOUBLE PRECISION array, dimension (N) 00121 *> \endverbatim 00122 *> 00123 *> \param[out] INFO 00124 *> \verbatim 00125 *> INFO is INTEGER 00126 *> = 0: successful exit 00127 *> < 0: if INFO = -i, the i-th argument had an illegal value 00128 *> \endverbatim 00129 * 00130 * Authors: 00131 * ======== 00132 * 00133 *> \author Univ. of Tennessee 00134 *> \author Univ. of California Berkeley 00135 *> \author Univ. of Colorado Denver 00136 *> \author NAG Ltd. 00137 * 00138 *> \date November 2011 00139 * 00140 *> \ingroup complex16OTHERcomputational 00141 * 00142 * ===================================================================== 00143 SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, 00144 $ RWORK, INFO ) 00145 * 00146 * -- LAPACK computational routine (version 3.4.0) -- 00147 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00149 * November 2011 00150 * 00151 * .. Scalar Arguments .. 00152 CHARACTER DIAG, NORM, UPLO 00153 INTEGER INFO, KD, LDAB, N 00154 DOUBLE PRECISION RCOND 00155 * .. 00156 * .. Array Arguments .. 00157 DOUBLE PRECISION RWORK( * ) 00158 COMPLEX*16 AB( LDAB, * ), WORK( * ) 00159 * .. 00160 * 00161 * ===================================================================== 00162 * 00163 * .. Parameters .. 00164 DOUBLE PRECISION ONE, ZERO 00165 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00166 * .. 00167 * .. Local Scalars .. 00168 LOGICAL NOUNIT, ONENRM, UPPER 00169 CHARACTER NORMIN 00170 INTEGER IX, KASE, KASE1 00171 DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM 00172 COMPLEX*16 ZDUM 00173 * .. 00174 * .. Local Arrays .. 00175 INTEGER ISAVE( 3 ) 00176 * .. 00177 * .. External Functions .. 00178 LOGICAL LSAME 00179 INTEGER IZAMAX 00180 DOUBLE PRECISION DLAMCH, ZLANTB 00181 EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANTB 00182 * .. 00183 * .. External Subroutines .. 00184 EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATBS 00185 * .. 00186 * .. Intrinsic Functions .. 00187 INTRINSIC ABS, DBLE, DIMAG, MAX 00188 * .. 00189 * .. Statement Functions .. 00190 DOUBLE PRECISION CABS1 00191 * .. 00192 * .. Statement Function definitions .. 00193 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00194 * .. 00195 * .. Executable Statements .. 00196 * 00197 * Test the input parameters. 00198 * 00199 INFO = 0 00200 UPPER = LSAME( UPLO, 'U' ) 00201 ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) 00202 NOUNIT = LSAME( DIAG, 'N' ) 00203 * 00204 IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN 00205 INFO = -1 00206 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00207 INFO = -2 00208 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN 00209 INFO = -3 00210 ELSE IF( N.LT.0 ) THEN 00211 INFO = -4 00212 ELSE IF( KD.LT.0 ) THEN 00213 INFO = -5 00214 ELSE IF( LDAB.LT.KD+1 ) THEN 00215 INFO = -7 00216 END IF 00217 IF( INFO.NE.0 ) THEN 00218 CALL XERBLA( 'ZTBCON', -INFO ) 00219 RETURN 00220 END IF 00221 * 00222 * Quick return if possible 00223 * 00224 IF( N.EQ.0 ) THEN 00225 RCOND = ONE 00226 RETURN 00227 END IF 00228 * 00229 RCOND = ZERO 00230 SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( N, 1 ) ) 00231 * 00232 * Compute the 1-norm of the triangular matrix A or A**H. 00233 * 00234 ANORM = ZLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, RWORK ) 00235 * 00236 * Continue only if ANORM > 0. 00237 * 00238 IF( ANORM.GT.ZERO ) THEN 00239 * 00240 * Estimate the 1-norm of the inverse of A. 00241 * 00242 AINVNM = ZERO 00243 NORMIN = 'N' 00244 IF( ONENRM ) THEN 00245 KASE1 = 1 00246 ELSE 00247 KASE1 = 2 00248 END IF 00249 KASE = 0 00250 10 CONTINUE 00251 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00252 IF( KASE.NE.0 ) THEN 00253 IF( KASE.EQ.KASE1 ) THEN 00254 * 00255 * Multiply by inv(A). 00256 * 00257 CALL ZLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD, 00258 $ AB, LDAB, WORK, SCALE, RWORK, INFO ) 00259 ELSE 00260 * 00261 * Multiply by inv(A**H). 00262 * 00263 CALL ZLATBS( UPLO, 'Conjugate transpose', DIAG, NORMIN, 00264 $ N, KD, AB, LDAB, WORK, SCALE, RWORK, INFO ) 00265 END IF 00266 NORMIN = 'Y' 00267 * 00268 * Multiply by 1/SCALE if doing so will not cause overflow. 00269 * 00270 IF( SCALE.NE.ONE ) THEN 00271 IX = IZAMAX( N, WORK, 1 ) 00272 XNORM = CABS1( WORK( IX ) ) 00273 IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO ) 00274 $ GO TO 20 00275 CALL ZDRSCL( N, SCALE, WORK, 1 ) 00276 END IF 00277 GO TO 10 00278 END IF 00279 * 00280 * Compute the estimate of the reciprocal condition number. 00281 * 00282 IF( AINVNM.NE.ZERO ) 00283 $ RCOND = ( ONE / ANORM ) / AINVNM 00284 END IF 00285 * 00286 20 CONTINUE 00287 RETURN 00288 * 00289 * End of ZTBCON 00290 * 00291 END