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