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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZHEGST 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZHEGV + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegv.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhegv.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhegv.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, 00022 * LWORK, RWORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER JOBZ, UPLO 00026 * INTEGER INFO, ITYPE, LDA, LDB, LWORK, N 00027 * .. 00028 * .. Array Arguments .. 00029 * DOUBLE PRECISION RWORK( * ), W( * ) 00030 * COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) 00031 * .. 00032 * 00033 * 00034 *> \par Purpose: 00035 * ============= 00036 *> 00037 *> \verbatim 00038 *> 00039 *> ZHEGV computes all the eigenvalues, and optionally, the eigenvectors 00040 *> of a complex generalized Hermitian-definite eigenproblem, of the form 00041 *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. 00042 *> Here A and B are assumed to be Hermitian and B is also 00043 *> positive definite. 00044 *> \endverbatim 00045 * 00046 * Arguments: 00047 * ========== 00048 * 00049 *> \param[in] ITYPE 00050 *> \verbatim 00051 *> ITYPE is INTEGER 00052 *> Specifies the problem type to be solved: 00053 *> = 1: A*x = (lambda)*B*x 00054 *> = 2: A*B*x = (lambda)*x 00055 *> = 3: B*A*x = (lambda)*x 00056 *> \endverbatim 00057 *> 00058 *> \param[in] JOBZ 00059 *> \verbatim 00060 *> JOBZ is CHARACTER*1 00061 *> = 'N': Compute eigenvalues only; 00062 *> = 'V': Compute eigenvalues and eigenvectors. 00063 *> \endverbatim 00064 *> 00065 *> \param[in] UPLO 00066 *> \verbatim 00067 *> UPLO is CHARACTER*1 00068 *> = 'U': Upper triangles of A and B are stored; 00069 *> = 'L': Lower triangles of A and B are stored. 00070 *> \endverbatim 00071 *> 00072 *> \param[in] N 00073 *> \verbatim 00074 *> N is INTEGER 00075 *> The order of the matrices A and B. N >= 0. 00076 *> \endverbatim 00077 *> 00078 *> \param[in,out] A 00079 *> \verbatim 00080 *> A is COMPLEX*16 array, dimension (LDA, N) 00081 *> On entry, the Hermitian matrix A. If UPLO = 'U', the 00082 *> leading N-by-N upper triangular part of A contains the 00083 *> upper triangular part of the matrix A. If UPLO = 'L', 00084 *> the leading N-by-N lower triangular part of A contains 00085 *> the lower triangular part of the matrix A. 00086 *> 00087 *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the 00088 *> matrix Z of eigenvectors. The eigenvectors are normalized 00089 *> as follows: 00090 *> if ITYPE = 1 or 2, Z**H*B*Z = I; 00091 *> if ITYPE = 3, Z**H*inv(B)*Z = I. 00092 *> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') 00093 *> or the lower triangle (if UPLO='L') of A, including the 00094 *> diagonal, is destroyed. 00095 *> \endverbatim 00096 *> 00097 *> \param[in] LDA 00098 *> \verbatim 00099 *> LDA is INTEGER 00100 *> The leading dimension of the array A. LDA >= max(1,N). 00101 *> \endverbatim 00102 *> 00103 *> \param[in,out] B 00104 *> \verbatim 00105 *> B is COMPLEX*16 array, dimension (LDB, N) 00106 *> On entry, the Hermitian positive definite matrix B. 00107 *> If UPLO = 'U', the leading N-by-N upper triangular part of B 00108 *> contains the upper triangular part of the matrix B. 00109 *> If UPLO = 'L', the leading N-by-N lower triangular part of B 00110 *> contains the lower triangular part of the matrix B. 00111 *> 00112 *> On exit, if INFO <= N, the part of B containing the matrix is 00113 *> overwritten by the triangular factor U or L from the Cholesky 00114 *> factorization B = U**H*U or B = L*L**H. 00115 *> \endverbatim 00116 *> 00117 *> \param[in] LDB 00118 *> \verbatim 00119 *> LDB is INTEGER 00120 *> The leading dimension of the array B. LDB >= max(1,N). 00121 *> \endverbatim 00122 *> 00123 *> \param[out] W 00124 *> \verbatim 00125 *> W is DOUBLE PRECISION array, dimension (N) 00126 *> If INFO = 0, the eigenvalues in ascending order. 00127 *> \endverbatim 00128 *> 00129 *> \param[out] WORK 00130 *> \verbatim 00131 *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) 00132 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00133 *> \endverbatim 00134 *> 00135 *> \param[in] LWORK 00136 *> \verbatim 00137 *> LWORK is INTEGER 00138 *> The length of the array WORK. LWORK >= max(1,2*N-1). 00139 *> For optimal efficiency, LWORK >= (NB+1)*N, 00140 *> where NB is the blocksize for ZHETRD returned by ILAENV. 00141 *> 00142 *> If LWORK = -1, then a workspace query is assumed; the routine 00143 *> only calculates the optimal size of the WORK array, returns 00144 *> this value as the first entry of the WORK array, and no error 00145 *> message related to LWORK is issued by XERBLA. 00146 *> \endverbatim 00147 *> 00148 *> \param[out] RWORK 00149 *> \verbatim 00150 *> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) 00151 *> \endverbatim 00152 *> 00153 *> \param[out] INFO 00154 *> \verbatim 00155 *> INFO is INTEGER 00156 *> = 0: successful exit 00157 *> < 0: if INFO = -i, the i-th argument had an illegal value 00158 *> > 0: ZPOTRF or ZHEEV returned an error code: 00159 *> <= N: if INFO = i, ZHEEV failed to converge; 00160 *> i off-diagonal elements of an intermediate 00161 *> tridiagonal form did not converge to zero; 00162 *> > N: if INFO = N + i, for 1 <= i <= N, then the leading 00163 *> minor of order i of B is not positive definite. 00164 *> The factorization of B could not be completed and 00165 *> no eigenvalues or eigenvectors were computed. 00166 *> \endverbatim 00167 * 00168 * Authors: 00169 * ======== 00170 * 00171 *> \author Univ. of Tennessee 00172 *> \author Univ. of California Berkeley 00173 *> \author Univ. of Colorado Denver 00174 *> \author NAG Ltd. 00175 * 00176 *> \date November 2011 00177 * 00178 *> \ingroup complex16HEeigen 00179 * 00180 * ===================================================================== 00181 SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, 00182 $ LWORK, RWORK, INFO ) 00183 * 00184 * -- LAPACK driver routine (version 3.4.0) -- 00185 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00186 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00187 * November 2011 00188 * 00189 * .. Scalar Arguments .. 00190 CHARACTER JOBZ, UPLO 00191 INTEGER INFO, ITYPE, LDA, LDB, LWORK, N 00192 * .. 00193 * .. Array Arguments .. 00194 DOUBLE PRECISION RWORK( * ), W( * ) 00195 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) 00196 * .. 00197 * 00198 * ===================================================================== 00199 * 00200 * .. Parameters .. 00201 COMPLEX*16 ONE 00202 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) 00203 * .. 00204 * .. Local Scalars .. 00205 LOGICAL LQUERY, UPPER, WANTZ 00206 CHARACTER TRANS 00207 INTEGER LWKOPT, NB, NEIG 00208 * .. 00209 * .. External Functions .. 00210 LOGICAL LSAME 00211 INTEGER ILAENV 00212 EXTERNAL LSAME, ILAENV 00213 * .. 00214 * .. External Subroutines .. 00215 EXTERNAL XERBLA, ZHEEV, ZHEGST, ZPOTRF, ZTRMM, ZTRSM 00216 * .. 00217 * .. Intrinsic Functions .. 00218 INTRINSIC MAX 00219 * .. 00220 * .. Executable Statements .. 00221 * 00222 * Test the input parameters. 00223 * 00224 WANTZ = LSAME( JOBZ, 'V' ) 00225 UPPER = LSAME( UPLO, 'U' ) 00226 LQUERY = ( LWORK.EQ.-1 ) 00227 * 00228 INFO = 0 00229 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 00230 INFO = -1 00231 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00232 INFO = -2 00233 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 00234 INFO = -3 00235 ELSE IF( N.LT.0 ) THEN 00236 INFO = -4 00237 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00238 INFO = -6 00239 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00240 INFO = -8 00241 END IF 00242 * 00243 IF( INFO.EQ.0 ) THEN 00244 NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) 00245 LWKOPT = MAX( 1, ( NB + 1 )*N ) 00246 WORK( 1 ) = LWKOPT 00247 * 00248 IF( LWORK.LT.MAX( 1, 2*N - 1 ) .AND. .NOT.LQUERY ) THEN 00249 INFO = -11 00250 END IF 00251 END IF 00252 * 00253 IF( INFO.NE.0 ) THEN 00254 CALL XERBLA( 'ZHEGV ', -INFO ) 00255 RETURN 00256 ELSE IF( LQUERY ) THEN 00257 RETURN 00258 END IF 00259 * 00260 * Quick return if possible 00261 * 00262 IF( N.EQ.0 ) 00263 $ RETURN 00264 * 00265 * Form a Cholesky factorization of B. 00266 * 00267 CALL ZPOTRF( UPLO, N, B, LDB, INFO ) 00268 IF( INFO.NE.0 ) THEN 00269 INFO = N + INFO 00270 RETURN 00271 END IF 00272 * 00273 * Transform problem to standard eigenvalue problem and solve. 00274 * 00275 CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 00276 CALL ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO ) 00277 * 00278 IF( WANTZ ) THEN 00279 * 00280 * Backtransform eigenvectors to the original problem. 00281 * 00282 NEIG = N 00283 IF( INFO.GT.0 ) 00284 $ NEIG = INFO - 1 00285 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 00286 * 00287 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 00288 * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y 00289 * 00290 IF( UPPER ) THEN 00291 TRANS = 'N' 00292 ELSE 00293 TRANS = 'C' 00294 END IF 00295 * 00296 CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, 00297 $ B, LDB, A, LDA ) 00298 * 00299 ELSE IF( ITYPE.EQ.3 ) THEN 00300 * 00301 * For B*A*x=(lambda)*x; 00302 * backtransform eigenvectors: x = L*y or U**H *y 00303 * 00304 IF( UPPER ) THEN 00305 TRANS = 'C' 00306 ELSE 00307 TRANS = 'N' 00308 END IF 00309 * 00310 CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, 00311 $ B, LDB, A, LDA ) 00312 END IF 00313 END IF 00314 * 00315 WORK( 1 ) = LWKOPT 00316 * 00317 RETURN 00318 * 00319 * End of ZHEGV 00320 * 00321 END