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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CHEGST 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CHEGVD + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chegvd.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chegvd.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chegvd.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, 00022 * LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER JOBZ, UPLO 00026 * INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N 00027 * .. 00028 * .. Array Arguments .. 00029 * INTEGER IWORK( * ) 00030 * REAL RWORK( * ), W( * ) 00031 * COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) 00032 * .. 00033 * 00034 * 00035 *> \par Purpose: 00036 * ============= 00037 *> 00038 *> \verbatim 00039 *> 00040 *> CHEGVD computes all the eigenvalues, and optionally, the eigenvectors 00041 *> of a complex generalized Hermitian-definite eigenproblem, of the form 00042 *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and 00043 *> B are assumed to be Hermitian and B is also positive definite. 00044 *> If eigenvectors are desired, it uses a divide and conquer algorithm. 00045 *> 00046 *> The divide and conquer algorithm makes very mild assumptions about 00047 *> floating point arithmetic. It will work on machines with a guard 00048 *> digit in add/subtract, or on those binary machines without guard 00049 *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or 00050 *> Cray-2. It could conceivably fail on hexadecimal or decimal machines 00051 *> without guard digits, but we know of none. 00052 *> \endverbatim 00053 * 00054 * Arguments: 00055 * ========== 00056 * 00057 *> \param[in] ITYPE 00058 *> \verbatim 00059 *> ITYPE is INTEGER 00060 *> Specifies the problem type to be solved: 00061 *> = 1: A*x = (lambda)*B*x 00062 *> = 2: A*B*x = (lambda)*x 00063 *> = 3: B*A*x = (lambda)*x 00064 *> \endverbatim 00065 *> 00066 *> \param[in] JOBZ 00067 *> \verbatim 00068 *> JOBZ is CHARACTER*1 00069 *> = 'N': Compute eigenvalues only; 00070 *> = 'V': Compute eigenvalues and eigenvectors. 00071 *> \endverbatim 00072 *> 00073 *> \param[in] UPLO 00074 *> \verbatim 00075 *> UPLO is CHARACTER*1 00076 *> = 'U': Upper triangles of A and B are stored; 00077 *> = 'L': Lower triangles of A and B are stored. 00078 *> \endverbatim 00079 *> 00080 *> \param[in] N 00081 *> \verbatim 00082 *> N is INTEGER 00083 *> The order of the matrices A and B. N >= 0. 00084 *> \endverbatim 00085 *> 00086 *> \param[in,out] A 00087 *> \verbatim 00088 *> A is COMPLEX array, dimension (LDA, N) 00089 *> On entry, the Hermitian matrix A. If UPLO = 'U', the 00090 *> leading N-by-N upper triangular part of A contains the 00091 *> upper triangular part of the matrix A. If UPLO = 'L', 00092 *> the leading N-by-N lower triangular part of A contains 00093 *> the lower triangular part of the matrix A. 00094 *> 00095 *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the 00096 *> matrix Z of eigenvectors. The eigenvectors are normalized 00097 *> as follows: 00098 *> if ITYPE = 1 or 2, Z**H*B*Z = I; 00099 *> if ITYPE = 3, Z**H*inv(B)*Z = I. 00100 *> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') 00101 *> or the lower triangle (if UPLO='L') of A, including the 00102 *> diagonal, is destroyed. 00103 *> \endverbatim 00104 *> 00105 *> \param[in] LDA 00106 *> \verbatim 00107 *> LDA is INTEGER 00108 *> The leading dimension of the array A. LDA >= max(1,N). 00109 *> \endverbatim 00110 *> 00111 *> \param[in,out] B 00112 *> \verbatim 00113 *> B is COMPLEX array, dimension (LDB, N) 00114 *> On entry, the Hermitian matrix B. If UPLO = 'U', the 00115 *> leading N-by-N upper triangular part of B contains the 00116 *> upper triangular part of the matrix B. If UPLO = 'L', 00117 *> the leading N-by-N lower triangular part of B contains 00118 *> the lower triangular part of the matrix B. 00119 *> 00120 *> On exit, if INFO <= N, the part of B containing the matrix is 00121 *> overwritten by the triangular factor U or L from the Cholesky 00122 *> factorization B = U**H*U or B = L*L**H. 00123 *> \endverbatim 00124 *> 00125 *> \param[in] LDB 00126 *> \verbatim 00127 *> LDB is INTEGER 00128 *> The leading dimension of the array B. LDB >= max(1,N). 00129 *> \endverbatim 00130 *> 00131 *> \param[out] W 00132 *> \verbatim 00133 *> W is REAL array, dimension (N) 00134 *> If INFO = 0, the eigenvalues in ascending order. 00135 *> \endverbatim 00136 *> 00137 *> \param[out] WORK 00138 *> \verbatim 00139 *> WORK is COMPLEX array, dimension (MAX(1,LWORK)) 00140 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00141 *> \endverbatim 00142 *> 00143 *> \param[in] LWORK 00144 *> \verbatim 00145 *> LWORK is INTEGER 00146 *> The length of the array WORK. 00147 *> If N <= 1, LWORK >= 1. 00148 *> If JOBZ = 'N' and N > 1, LWORK >= N + 1. 00149 *> If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2. 00150 *> 00151 *> If LWORK = -1, then a workspace query is assumed; the routine 00152 *> only calculates the optimal sizes of the WORK, RWORK and 00153 *> IWORK arrays, returns these values as the first entries of 00154 *> the WORK, RWORK and IWORK arrays, and no error message 00155 *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00156 *> \endverbatim 00157 *> 00158 *> \param[out] RWORK 00159 *> \verbatim 00160 *> RWORK is REAL array, dimension (MAX(1,LRWORK)) 00161 *> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. 00162 *> \endverbatim 00163 *> 00164 *> \param[in] LRWORK 00165 *> \verbatim 00166 *> LRWORK is INTEGER 00167 *> The dimension of the array RWORK. 00168 *> If N <= 1, LRWORK >= 1. 00169 *> If JOBZ = 'N' and N > 1, LRWORK >= N. 00170 *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. 00171 *> 00172 *> If LRWORK = -1, then a workspace query is assumed; the 00173 *> routine only calculates the optimal sizes of the WORK, RWORK 00174 *> and IWORK arrays, returns these values as the first entries 00175 *> of the WORK, RWORK and IWORK arrays, and no error message 00176 *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00177 *> \endverbatim 00178 *> 00179 *> \param[out] IWORK 00180 *> \verbatim 00181 *> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) 00182 *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. 00183 *> \endverbatim 00184 *> 00185 *> \param[in] LIWORK 00186 *> \verbatim 00187 *> LIWORK is INTEGER 00188 *> The dimension of the array IWORK. 00189 *> If N <= 1, LIWORK >= 1. 00190 *> If JOBZ = 'N' and N > 1, LIWORK >= 1. 00191 *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. 00192 *> 00193 *> If LIWORK = -1, then a workspace query is assumed; the 00194 *> routine only calculates the optimal sizes of the WORK, RWORK 00195 *> and IWORK arrays, returns these values as the first entries 00196 *> of the WORK, RWORK and IWORK arrays, and no error message 00197 *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00198 *> \endverbatim 00199 *> 00200 *> \param[out] INFO 00201 *> \verbatim 00202 *> INFO is INTEGER 00203 *> = 0: successful exit 00204 *> < 0: if INFO = -i, the i-th argument had an illegal value 00205 *> > 0: CPOTRF or CHEEVD returned an error code: 00206 *> <= N: if INFO = i and JOBZ = 'N', then the algorithm 00207 *> failed to converge; i off-diagonal elements of an 00208 *> intermediate tridiagonal form did not converge to 00209 *> zero; 00210 *> if INFO = i and JOBZ = 'V', then the algorithm 00211 *> failed to compute an eigenvalue while working on 00212 *> the submatrix lying in rows and columns INFO/(N+1) 00213 *> through mod(INFO,N+1); 00214 *> > N: if INFO = N + i, for 1 <= i <= N, then the leading 00215 *> minor of order i of B is not positive definite. 00216 *> The factorization of B could not be completed and 00217 *> no eigenvalues or eigenvectors were computed. 00218 *> \endverbatim 00219 * 00220 * Authors: 00221 * ======== 00222 * 00223 *> \author Univ. of Tennessee 00224 *> \author Univ. of California Berkeley 00225 *> \author Univ. of Colorado Denver 00226 *> \author NAG Ltd. 00227 * 00228 *> \date November 2011 00229 * 00230 *> \ingroup complexHEeigen 00231 * 00232 *> \par Further Details: 00233 * ===================== 00234 *> 00235 *> \verbatim 00236 *> 00237 *> Modified so that no backsubstitution is performed if CHEEVD fails to 00238 *> converge (NEIG in old code could be greater than N causing out of 00239 *> bounds reference to A - reported by Ralf Meyer). Also corrected the 00240 *> description of INFO and the test on ITYPE. Sven, 16 Feb 05. 00241 *> \endverbatim 00242 * 00243 *> \par Contributors: 00244 * ================== 00245 *> 00246 *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 00247 *> 00248 * ===================================================================== 00249 SUBROUTINE CHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, 00250 $ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO ) 00251 * 00252 * -- LAPACK driver routine (version 3.4.0) -- 00253 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00254 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00255 * November 2011 00256 * 00257 * .. Scalar Arguments .. 00258 CHARACTER JOBZ, UPLO 00259 INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N 00260 * .. 00261 * .. Array Arguments .. 00262 INTEGER IWORK( * ) 00263 REAL RWORK( * ), W( * ) 00264 COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) 00265 * .. 00266 * 00267 * ===================================================================== 00268 * 00269 * .. Parameters .. 00270 COMPLEX CONE 00271 PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) 00272 * .. 00273 * .. Local Scalars .. 00274 LOGICAL LQUERY, UPPER, WANTZ 00275 CHARACTER TRANS 00276 INTEGER LIOPT, LIWMIN, LOPT, LROPT, LRWMIN, LWMIN 00277 * .. 00278 * .. External Functions .. 00279 LOGICAL LSAME 00280 EXTERNAL LSAME 00281 * .. 00282 * .. External Subroutines .. 00283 EXTERNAL CHEEVD, CHEGST, CPOTRF, CTRMM, CTRSM, XERBLA 00284 * .. 00285 * .. Intrinsic Functions .. 00286 INTRINSIC MAX, REAL 00287 * .. 00288 * .. Executable Statements .. 00289 * 00290 * Test the input parameters. 00291 * 00292 WANTZ = LSAME( JOBZ, 'V' ) 00293 UPPER = LSAME( UPLO, 'U' ) 00294 LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) 00295 * 00296 INFO = 0 00297 IF( N.LE.1 ) THEN 00298 LWMIN = 1 00299 LRWMIN = 1 00300 LIWMIN = 1 00301 ELSE IF( WANTZ ) THEN 00302 LWMIN = 2*N + N*N 00303 LRWMIN = 1 + 5*N + 2*N*N 00304 LIWMIN = 3 + 5*N 00305 ELSE 00306 LWMIN = N + 1 00307 LRWMIN = N 00308 LIWMIN = 1 00309 END IF 00310 LOPT = LWMIN 00311 LROPT = LRWMIN 00312 LIOPT = LIWMIN 00313 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 00314 INFO = -1 00315 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00316 INFO = -2 00317 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 00318 INFO = -3 00319 ELSE IF( N.LT.0 ) THEN 00320 INFO = -4 00321 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00322 INFO = -6 00323 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00324 INFO = -8 00325 END IF 00326 * 00327 IF( INFO.EQ.0 ) THEN 00328 WORK( 1 ) = LOPT 00329 RWORK( 1 ) = LROPT 00330 IWORK( 1 ) = LIOPT 00331 * 00332 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 00333 INFO = -11 00334 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN 00335 INFO = -13 00336 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 00337 INFO = -15 00338 END IF 00339 END IF 00340 * 00341 IF( INFO.NE.0 ) THEN 00342 CALL XERBLA( 'CHEGVD', -INFO ) 00343 RETURN 00344 ELSE IF( LQUERY ) THEN 00345 RETURN 00346 END IF 00347 * 00348 * Quick return if possible 00349 * 00350 IF( N.EQ.0 ) 00351 $ RETURN 00352 * 00353 * Form a Cholesky factorization of B. 00354 * 00355 CALL CPOTRF( UPLO, N, B, LDB, INFO ) 00356 IF( INFO.NE.0 ) THEN 00357 INFO = N + INFO 00358 RETURN 00359 END IF 00360 * 00361 * Transform problem to standard eigenvalue problem and solve. 00362 * 00363 CALL CHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 00364 CALL CHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK, 00365 $ IWORK, LIWORK, INFO ) 00366 LOPT = MAX( REAL( LOPT ), REAL( WORK( 1 ) ) ) 00367 LROPT = MAX( REAL( LROPT ), REAL( RWORK( 1 ) ) ) 00368 LIOPT = MAX( REAL( LIOPT ), REAL( IWORK( 1 ) ) ) 00369 * 00370 IF( WANTZ .AND. INFO.EQ.0 ) THEN 00371 * 00372 * Backtransform eigenvectors to the original problem. 00373 * 00374 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 00375 * 00376 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 00377 * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y 00378 * 00379 IF( UPPER ) THEN 00380 TRANS = 'N' 00381 ELSE 00382 TRANS = 'C' 00383 END IF 00384 * 00385 CALL CTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE, 00386 $ B, LDB, A, LDA ) 00387 * 00388 ELSE IF( ITYPE.EQ.3 ) THEN 00389 * 00390 * For B*A*x=(lambda)*x; 00391 * backtransform eigenvectors: x = L*y or U**H *y 00392 * 00393 IF( UPPER ) THEN 00394 TRANS = 'C' 00395 ELSE 00396 TRANS = 'N' 00397 END IF 00398 * 00399 CALL CTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE, 00400 $ B, LDB, A, LDA ) 00401 END IF 00402 END IF 00403 * 00404 WORK( 1 ) = LOPT 00405 RWORK( 1 ) = LROPT 00406 IWORK( 1 ) = LIOPT 00407 * 00408 RETURN 00409 * 00410 * End of CHEGVD 00411 * 00412 END