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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZHBGST 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZHBGVD + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbgvd.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbgvd.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbgvd.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, 00022 * Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, 00023 * LIWORK, INFO ) 00024 * 00025 * .. Scalar Arguments .. 00026 * CHARACTER JOBZ, UPLO 00027 * INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK, 00028 * $ LWORK, N 00029 * .. 00030 * .. Array Arguments .. 00031 * INTEGER IWORK( * ) 00032 * DOUBLE PRECISION RWORK( * ), W( * ) 00033 * COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), 00034 * $ Z( LDZ, * ) 00035 * .. 00036 * 00037 * 00038 *> \par Purpose: 00039 * ============= 00040 *> 00041 *> \verbatim 00042 *> 00043 *> ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors 00044 *> of a complex generalized Hermitian-definite banded eigenproblem, of 00045 *> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian 00046 *> and banded, and B is also positive definite. If eigenvectors are 00047 *> desired, it uses a divide and conquer algorithm. 00048 *> 00049 *> The divide and conquer algorithm makes very mild assumptions about 00050 *> floating point arithmetic. It will work on machines with a guard 00051 *> digit in add/subtract, or on those binary machines without guard 00052 *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or 00053 *> Cray-2. It could conceivably fail on hexadecimal or decimal machines 00054 *> without guard digits, but we know of none. 00055 *> \endverbatim 00056 * 00057 * Arguments: 00058 * ========== 00059 * 00060 *> \param[in] JOBZ 00061 *> \verbatim 00062 *> JOBZ is CHARACTER*1 00063 *> = 'N': Compute eigenvalues only; 00064 *> = 'V': Compute eigenvalues and eigenvectors. 00065 *> \endverbatim 00066 *> 00067 *> \param[in] UPLO 00068 *> \verbatim 00069 *> UPLO is CHARACTER*1 00070 *> = 'U': Upper triangles of A and B are stored; 00071 *> = 'L': Lower triangles of A and B are stored. 00072 *> \endverbatim 00073 *> 00074 *> \param[in] N 00075 *> \verbatim 00076 *> N is INTEGER 00077 *> The order of the matrices A and B. N >= 0. 00078 *> \endverbatim 00079 *> 00080 *> \param[in] KA 00081 *> \verbatim 00082 *> KA is INTEGER 00083 *> The number of superdiagonals of the matrix A if UPLO = 'U', 00084 *> or the number of subdiagonals if UPLO = 'L'. KA >= 0. 00085 *> \endverbatim 00086 *> 00087 *> \param[in] KB 00088 *> \verbatim 00089 *> KB is INTEGER 00090 *> The number of superdiagonals of the matrix B if UPLO = 'U', 00091 *> or the number of subdiagonals if UPLO = 'L'. KB >= 0. 00092 *> \endverbatim 00093 *> 00094 *> \param[in,out] AB 00095 *> \verbatim 00096 *> AB is COMPLEX*16 array, dimension (LDAB, N) 00097 *> On entry, the upper or lower triangle of the Hermitian band 00098 *> matrix A, stored in the first ka+1 rows of the array. The 00099 *> j-th column of A is stored in the j-th column of the array AB 00100 *> as follows: 00101 *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; 00102 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). 00103 *> 00104 *> On exit, the contents of AB are destroyed. 00105 *> \endverbatim 00106 *> 00107 *> \param[in] LDAB 00108 *> \verbatim 00109 *> LDAB is INTEGER 00110 *> The leading dimension of the array AB. LDAB >= KA+1. 00111 *> \endverbatim 00112 *> 00113 *> \param[in,out] BB 00114 *> \verbatim 00115 *> BB is COMPLEX*16 array, dimension (LDBB, N) 00116 *> On entry, the upper or lower triangle of the Hermitian band 00117 *> matrix B, stored in the first kb+1 rows of the array. The 00118 *> j-th column of B is stored in the j-th column of the array BB 00119 *> as follows: 00120 *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; 00121 *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). 00122 *> 00123 *> On exit, the factor S from the split Cholesky factorization 00124 *> B = S**H*S, as returned by ZPBSTF. 00125 *> \endverbatim 00126 *> 00127 *> \param[in] LDBB 00128 *> \verbatim 00129 *> LDBB is INTEGER 00130 *> The leading dimension of the array BB. LDBB >= KB+1. 00131 *> \endverbatim 00132 *> 00133 *> \param[out] W 00134 *> \verbatim 00135 *> W is DOUBLE PRECISION array, dimension (N) 00136 *> If INFO = 0, the eigenvalues in ascending order. 00137 *> \endverbatim 00138 *> 00139 *> \param[out] Z 00140 *> \verbatim 00141 *> Z is COMPLEX*16 array, dimension (LDZ, N) 00142 *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 00143 *> eigenvectors, with the i-th column of Z holding the 00144 *> eigenvector associated with W(i). The eigenvectors are 00145 *> normalized so that Z**H*B*Z = I. 00146 *> If JOBZ = 'N', then Z is not referenced. 00147 *> \endverbatim 00148 *> 00149 *> \param[in] LDZ 00150 *> \verbatim 00151 *> LDZ is INTEGER 00152 *> The leading dimension of the array Z. LDZ >= 1, and if 00153 *> JOBZ = 'V', LDZ >= N. 00154 *> \endverbatim 00155 *> 00156 *> \param[out] WORK 00157 *> \verbatim 00158 *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) 00159 *> On exit, if INFO=0, WORK(1) returns the optimal LWORK. 00160 *> \endverbatim 00161 *> 00162 *> \param[in] LWORK 00163 *> \verbatim 00164 *> LWORK is INTEGER 00165 *> The dimension of the array WORK. 00166 *> If N <= 1, LWORK >= 1. 00167 *> If JOBZ = 'N' and N > 1, LWORK >= N. 00168 *> If JOBZ = 'V' and N > 1, LWORK >= 2*N**2. 00169 *> 00170 *> If LWORK = -1, then a workspace query is assumed; the routine 00171 *> only calculates the optimal sizes of the WORK, RWORK and 00172 *> IWORK arrays, returns these values as the first entries of 00173 *> the WORK, RWORK and IWORK arrays, and no error message 00174 *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00175 *> \endverbatim 00176 *> 00177 *> \param[out] RWORK 00178 *> \verbatim 00179 *> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) 00180 *> On exit, if INFO=0, RWORK(1) returns the optimal LRWORK. 00181 *> \endverbatim 00182 *> 00183 *> \param[in] LRWORK 00184 *> \verbatim 00185 *> LRWORK is INTEGER 00186 *> The dimension of array RWORK. 00187 *> If N <= 1, LRWORK >= 1. 00188 *> If JOBZ = 'N' and N > 1, LRWORK >= N. 00189 *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. 00190 *> 00191 *> If LRWORK = -1, then a workspace query is assumed; the 00192 *> routine only calculates the optimal sizes of the WORK, RWORK 00193 *> and IWORK arrays, returns these values as the first entries 00194 *> of the WORK, RWORK and IWORK arrays, and no error message 00195 *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00196 *> \endverbatim 00197 *> 00198 *> \param[out] IWORK 00199 *> \verbatim 00200 *> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) 00201 *> On exit, if INFO=0, IWORK(1) returns the optimal LIWORK. 00202 *> \endverbatim 00203 *> 00204 *> \param[in] LIWORK 00205 *> \verbatim 00206 *> LIWORK is INTEGER 00207 *> The dimension of array IWORK. 00208 *> If JOBZ = 'N' or N <= 1, LIWORK >= 1. 00209 *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. 00210 *> 00211 *> If LIWORK = -1, then a workspace query is assumed; the 00212 *> routine only calculates the optimal sizes of the WORK, RWORK 00213 *> and IWORK arrays, returns these values as the first entries 00214 *> of the WORK, RWORK and IWORK arrays, and no error message 00215 *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00216 *> \endverbatim 00217 *> 00218 *> \param[out] INFO 00219 *> \verbatim 00220 *> INFO is INTEGER 00221 *> = 0: successful exit 00222 *> < 0: if INFO = -i, the i-th argument had an illegal value 00223 *> > 0: if INFO = i, and i is: 00224 *> <= N: the algorithm failed to converge: 00225 *> i off-diagonal elements of an intermediate 00226 *> tridiagonal form did not converge to zero; 00227 *> > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF 00228 *> returned INFO = i: B is not positive definite. 00229 *> The factorization of B could not be completed and 00230 *> no eigenvalues or eigenvectors were computed. 00231 *> \endverbatim 00232 * 00233 * Authors: 00234 * ======== 00235 * 00236 *> \author Univ. of Tennessee 00237 *> \author Univ. of California Berkeley 00238 *> \author Univ. of Colorado Denver 00239 *> \author NAG Ltd. 00240 * 00241 *> \date November 2011 00242 * 00243 *> \ingroup complex16OTHEReigen 00244 * 00245 *> \par Contributors: 00246 * ================== 00247 *> 00248 *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 00249 * 00250 * ===================================================================== 00251 SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, 00252 $ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, 00253 $ LIWORK, INFO ) 00254 * 00255 * -- LAPACK driver routine (version 3.4.0) -- 00256 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00257 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00258 * November 2011 00259 * 00260 * .. Scalar Arguments .. 00261 CHARACTER JOBZ, UPLO 00262 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK, 00263 $ LWORK, N 00264 * .. 00265 * .. Array Arguments .. 00266 INTEGER IWORK( * ) 00267 DOUBLE PRECISION RWORK( * ), W( * ) 00268 COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), 00269 $ Z( LDZ, * ) 00270 * .. 00271 * 00272 * ===================================================================== 00273 * 00274 * .. Parameters .. 00275 COMPLEX*16 CONE, CZERO 00276 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ), 00277 $ CZERO = ( 0.0D+0, 0.0D+0 ) ) 00278 * .. 00279 * .. Local Scalars .. 00280 LOGICAL LQUERY, UPPER, WANTZ 00281 CHARACTER VECT 00282 INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLRWK, 00283 $ LLWK2, LRWMIN, LWMIN 00284 * .. 00285 * .. External Functions .. 00286 LOGICAL LSAME 00287 EXTERNAL LSAME 00288 * .. 00289 * .. External Subroutines .. 00290 EXTERNAL DSTERF, XERBLA, ZGEMM, ZHBGST, ZHBTRD, ZLACPY, 00291 $ ZPBSTF, ZSTEDC 00292 * .. 00293 * .. Executable Statements .. 00294 * 00295 * Test the input parameters. 00296 * 00297 WANTZ = LSAME( JOBZ, 'V' ) 00298 UPPER = LSAME( UPLO, 'U' ) 00299 LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) 00300 * 00301 INFO = 0 00302 IF( N.LE.1 ) THEN 00303 LWMIN = 1+N 00304 LRWMIN = 1+N 00305 LIWMIN = 1 00306 ELSE IF( WANTZ ) THEN 00307 LWMIN = 2*N**2 00308 LRWMIN = 1 + 5*N + 2*N**2 00309 LIWMIN = 3 + 5*N 00310 ELSE 00311 LWMIN = N 00312 LRWMIN = N 00313 LIWMIN = 1 00314 END IF 00315 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00316 INFO = -1 00317 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 00318 INFO = -2 00319 ELSE IF( N.LT.0 ) THEN 00320 INFO = -3 00321 ELSE IF( KA.LT.0 ) THEN 00322 INFO = -4 00323 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN 00324 INFO = -5 00325 ELSE IF( LDAB.LT.KA+1 ) THEN 00326 INFO = -7 00327 ELSE IF( LDBB.LT.KB+1 ) THEN 00328 INFO = -9 00329 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 00330 INFO = -12 00331 END IF 00332 * 00333 IF( INFO.EQ.0 ) THEN 00334 WORK( 1 ) = LWMIN 00335 RWORK( 1 ) = LRWMIN 00336 IWORK( 1 ) = LIWMIN 00337 * 00338 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 00339 INFO = -14 00340 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN 00341 INFO = -16 00342 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 00343 INFO = -18 00344 END IF 00345 END IF 00346 * 00347 IF( INFO.NE.0 ) THEN 00348 CALL XERBLA( 'ZHBGVD', -INFO ) 00349 RETURN 00350 ELSE IF( LQUERY ) THEN 00351 RETURN 00352 END IF 00353 * 00354 * Quick return if possible 00355 * 00356 IF( N.EQ.0 ) 00357 $ RETURN 00358 * 00359 * Form a split Cholesky factorization of B. 00360 * 00361 CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO ) 00362 IF( INFO.NE.0 ) THEN 00363 INFO = N + INFO 00364 RETURN 00365 END IF 00366 * 00367 * Transform problem to standard eigenvalue problem. 00368 * 00369 INDE = 1 00370 INDWRK = INDE + N 00371 INDWK2 = 1 + N*N 00372 LLWK2 = LWORK - INDWK2 + 2 00373 LLRWK = LRWORK - INDWRK + 2 00374 CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ, 00375 $ WORK, RWORK( INDWRK ), IINFO ) 00376 * 00377 * Reduce Hermitian band matrix to tridiagonal form. 00378 * 00379 IF( WANTZ ) THEN 00380 VECT = 'U' 00381 ELSE 00382 VECT = 'N' 00383 END IF 00384 CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z, 00385 $ LDZ, WORK, IINFO ) 00386 * 00387 * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEDC. 00388 * 00389 IF( .NOT.WANTZ ) THEN 00390 CALL DSTERF( N, W, RWORK( INDE ), INFO ) 00391 ELSE 00392 CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ), 00393 $ LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK, 00394 $ INFO ) 00395 CALL ZGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO, 00396 $ WORK( INDWK2 ), N ) 00397 CALL ZLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ ) 00398 END IF 00399 * 00400 WORK( 1 ) = LWMIN 00401 RWORK( 1 ) = LRWMIN 00402 IWORK( 1 ) = LIWMIN 00403 RETURN 00404 * 00405 * End of ZHBGVD 00406 * 00407 END