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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLA_GBRCOND_X 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZLA_GBRCOND_X + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_gbrcond_x.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_gbrcond_x.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_gbrcond_x.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB, 00022 * LDAB, AFB, LDAFB, IPIV, 00023 * X, INFO, WORK, RWORK ) 00024 * 00025 * .. Scalar Arguments .. 00026 * CHARACTER TRANS 00027 * INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO 00028 * .. 00029 * .. Array Arguments .. 00030 * INTEGER IPIV( * ) 00031 * COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), 00032 * $ X( * ) 00033 * DOUBLE PRECISION RWORK( * ) 00034 * 00035 * 00036 * 00037 *> \par Purpose: 00038 * ============= 00039 *> 00040 *> \verbatim 00041 *> 00042 *> ZLA_GBRCOND_X Computes the infinity norm condition number of 00043 *> op(A) * diag(X) where X is a COMPLEX*16 vector. 00044 *> \endverbatim 00045 * 00046 * Arguments: 00047 * ========== 00048 * 00049 *> \param[in] TRANS 00050 *> \verbatim 00051 *> TRANS is CHARACTER*1 00052 *> Specifies the form of the system of equations: 00053 *> = 'N': A * X = B (No transpose) 00054 *> = 'T': A**T * X = B (Transpose) 00055 *> = 'C': A**H * X = B (Conjugate Transpose = Transpose) 00056 *> \endverbatim 00057 *> 00058 *> \param[in] N 00059 *> \verbatim 00060 *> N is INTEGER 00061 *> The number of linear equations, i.e., the order of the 00062 *> matrix A. N >= 0. 00063 *> \endverbatim 00064 *> 00065 *> \param[in] KL 00066 *> \verbatim 00067 *> KL is INTEGER 00068 *> The number of subdiagonals within the band of A. KL >= 0. 00069 *> \endverbatim 00070 *> 00071 *> \param[in] KU 00072 *> \verbatim 00073 *> KU is INTEGER 00074 *> The number of superdiagonals within the band of A. KU >= 0. 00075 *> \endverbatim 00076 *> 00077 *> \param[in] AB 00078 *> \verbatim 00079 *> AB is COMPLEX*16 array, dimension (LDAB,N) 00080 *> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. 00081 *> The j-th column of A is stored in the j-th column of the 00082 *> array AB as follows: 00083 *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) 00084 *> \endverbatim 00085 *> 00086 *> \param[in] LDAB 00087 *> \verbatim 00088 *> LDAB is INTEGER 00089 *> The leading dimension of the array AB. LDAB >= KL+KU+1. 00090 *> \endverbatim 00091 *> 00092 *> \param[in] AFB 00093 *> \verbatim 00094 *> AFB is COMPLEX*16 array, dimension (LDAFB,N) 00095 *> Details of the LU factorization of the band matrix A, as 00096 *> computed by ZGBTRF. U is stored as an upper triangular 00097 *> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, 00098 *> and the multipliers used during the factorization are stored 00099 *> in rows KL+KU+2 to 2*KL+KU+1. 00100 *> \endverbatim 00101 *> 00102 *> \param[in] LDAFB 00103 *> \verbatim 00104 *> LDAFB is INTEGER 00105 *> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. 00106 *> \endverbatim 00107 *> 00108 *> \param[in] IPIV 00109 *> \verbatim 00110 *> IPIV is INTEGER array, dimension (N) 00111 *> The pivot indices from the factorization A = P*L*U 00112 *> as computed by ZGBTRF; row i of the matrix was interchanged 00113 *> with row IPIV(i). 00114 *> \endverbatim 00115 *> 00116 *> \param[in] X 00117 *> \verbatim 00118 *> X is COMPLEX*16 array, dimension (N) 00119 *> The vector X in the formula op(A) * diag(X). 00120 *> \endverbatim 00121 *> 00122 *> \param[out] INFO 00123 *> \verbatim 00124 *> INFO is INTEGER 00125 *> = 0: Successful exit. 00126 *> i > 0: The ith argument is invalid. 00127 *> \endverbatim 00128 *> 00129 *> \param[in] WORK 00130 *> \verbatim 00131 *> WORK is COMPLEX*16 array, dimension (2*N). 00132 *> Workspace. 00133 *> \endverbatim 00134 *> 00135 *> \param[in] RWORK 00136 *> \verbatim 00137 *> RWORK is DOUBLE PRECISION array, dimension (N). 00138 *> Workspace. 00139 *> \endverbatim 00140 * 00141 * Authors: 00142 * ======== 00143 * 00144 *> \author Univ. of Tennessee 00145 *> \author Univ. of California Berkeley 00146 *> \author Univ. of Colorado Denver 00147 *> \author NAG Ltd. 00148 * 00149 *> \date November 2011 00150 * 00151 *> \ingroup complex16GBcomputational 00152 * 00153 * ===================================================================== 00154 DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB, 00155 $ LDAB, AFB, LDAFB, IPIV, 00156 $ X, INFO, WORK, RWORK ) 00157 * 00158 * -- LAPACK computational routine (version 3.4.0) -- 00159 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00160 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00161 * November 2011 00162 * 00163 * .. Scalar Arguments .. 00164 CHARACTER TRANS 00165 INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO 00166 * .. 00167 * .. Array Arguments .. 00168 INTEGER IPIV( * ) 00169 COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), 00170 $ X( * ) 00171 DOUBLE PRECISION RWORK( * ) 00172 * 00173 * 00174 * ===================================================================== 00175 * 00176 * .. Local Scalars .. 00177 LOGICAL NOTRANS 00178 INTEGER KASE, I, J 00179 DOUBLE PRECISION AINVNM, ANORM, TMP 00180 COMPLEX*16 ZDUM 00181 * .. 00182 * .. Local Arrays .. 00183 INTEGER ISAVE( 3 ) 00184 * .. 00185 * .. External Functions .. 00186 LOGICAL LSAME 00187 EXTERNAL LSAME 00188 * .. 00189 * .. External Subroutines .. 00190 EXTERNAL ZLACN2, ZGBTRS, XERBLA 00191 * .. 00192 * .. Intrinsic Functions .. 00193 INTRINSIC ABS, MAX 00194 * .. 00195 * .. Statement Functions .. 00196 DOUBLE PRECISION CABS1 00197 * .. 00198 * .. Statement Function Definitions .. 00199 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 00200 * .. 00201 * .. Executable Statements .. 00202 * 00203 ZLA_GBRCOND_X = 0.0D+0 00204 * 00205 INFO = 0 00206 NOTRANS = LSAME( TRANS, 'N' ) 00207 IF ( .NOT. NOTRANS .AND. .NOT. LSAME(TRANS, 'T') .AND. .NOT. 00208 $ LSAME( TRANS, 'C' ) ) THEN 00209 INFO = -1 00210 ELSE IF( N.LT.0 ) THEN 00211 INFO = -2 00212 ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN 00213 INFO = -3 00214 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN 00215 INFO = -4 00216 ELSE IF( LDAB.LT.KL+KU+1 ) THEN 00217 INFO = -6 00218 ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN 00219 INFO = -8 00220 END IF 00221 IF( INFO.NE.0 ) THEN 00222 CALL XERBLA( 'ZLA_GBRCOND_X', -INFO ) 00223 RETURN 00224 END IF 00225 * 00226 * Compute norm of op(A)*op2(C). 00227 * 00228 KD = KU + 1 00229 KE = KL + 1 00230 ANORM = 0.0D+0 00231 IF ( NOTRANS ) THEN 00232 DO I = 1, N 00233 TMP = 0.0D+0 00234 DO J = MAX( I-KL, 1 ), MIN( I+KU, N ) 00235 TMP = TMP + CABS1( AB( KD+I-J, J) * X( J ) ) 00236 END DO 00237 RWORK( I ) = TMP 00238 ANORM = MAX( ANORM, TMP ) 00239 END DO 00240 ELSE 00241 DO I = 1, N 00242 TMP = 0.0D+0 00243 DO J = MAX( I-KL, 1 ), MIN( I+KU, N ) 00244 TMP = TMP + CABS1( AB( KE-I+J, I ) * X( J ) ) 00245 END DO 00246 RWORK( I ) = TMP 00247 ANORM = MAX( ANORM, TMP ) 00248 END DO 00249 END IF 00250 * 00251 * Quick return if possible. 00252 * 00253 IF( N.EQ.0 ) THEN 00254 ZLA_GBRCOND_X = 1.0D+0 00255 RETURN 00256 ELSE IF( ANORM .EQ. 0.0D+0 ) THEN 00257 RETURN 00258 END IF 00259 * 00260 * Estimate the norm of inv(op(A)). 00261 * 00262 AINVNM = 0.0D+0 00263 * 00264 KASE = 0 00265 10 CONTINUE 00266 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 00267 IF( KASE.NE.0 ) THEN 00268 IF( KASE.EQ.2 ) THEN 00269 * 00270 * Multiply by R. 00271 * 00272 DO I = 1, N 00273 WORK( I ) = WORK( I ) * RWORK( I ) 00274 END DO 00275 * 00276 IF ( NOTRANS ) THEN 00277 CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB, 00278 $ IPIV, WORK, N, INFO ) 00279 ELSE 00280 CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB, 00281 $ LDAFB, IPIV, WORK, N, INFO ) 00282 ENDIF 00283 * 00284 * Multiply by inv(X). 00285 * 00286 DO I = 1, N 00287 WORK( I ) = WORK( I ) / X( I ) 00288 END DO 00289 ELSE 00290 * 00291 * Multiply by inv(X**H). 00292 * 00293 DO I = 1, N 00294 WORK( I ) = WORK( I ) / X( I ) 00295 END DO 00296 * 00297 IF ( NOTRANS ) THEN 00298 CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB, 00299 $ LDAFB, IPIV, WORK, N, INFO ) 00300 ELSE 00301 CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB, 00302 $ IPIV, WORK, N, INFO ) 00303 END IF 00304 * 00305 * Multiply by R. 00306 * 00307 DO I = 1, N 00308 WORK( I ) = WORK( I ) * RWORK( I ) 00309 END DO 00310 END IF 00311 GO TO 10 00312 END IF 00313 * 00314 * Compute the estimate of the reciprocal condition number. 00315 * 00316 IF( AINVNM .NE. 0.0D+0 ) 00317 $ ZLA_GBRCOND_X = 1.0D+0 / AINVNM 00318 * 00319 RETURN 00320 * 00321 END