1
       2
       3
       4
       5
       6
       7
       8
       9
      10
      11
      12
      13
      14
      15
      16
      17
      18
      19
      20
      21
      22
      23
      24
      25
      26
      27
      28
      29
      30
      31
      32
      33
      34
      35
      36
      37
      38
      39
      40
      41
      42
      43
      44
      45
      46
      47
      48
      49
      50
      51
      52
      53
      54
      55
      56
      57
      58
      59
      60
      61
      62
      63
      64
      65
      66
      67
      68
      69
      70
      71
      72
      73
      74
      75
      76
      77
      78
      79
      80
      81
      82
      83
      84
      85
      86
      87
      88
      89
      90
      91
      92
      93
      94
      95
      96
      97
      98
      99
     100
     101
     102
     103
     104
     105
     106
     107
     108
     109
     110
     111
     112
     113
     114
     115
     116
     117
     118
     119
     120
     121
     122
     123
     124
     125
     126
     127
     128
     129
     130
     131
     132
     133
     134
     135
     136
     137
     138
     139
     140
     141
     142
     143
     144
     145
     146
     147
     148
     149
     150
     151
     152
     153
     154
     155
     156
     157
     158
     159
     160
     161
     162
     163
     164
     165
     166
     167
     168
     169
     170
     171
     172
     173
     174
     175
     176
     177
     178
     179
     180
     181
     182
     183
     184
     185
     186
     187
     188
     189
     190
     191
     192
     193
     194
     195
     196
     197
     198
     199
     200
     201
     202
     203
     204
     205
     206
     207
     208
     209
     210
     211
     212
     213
     214
     215
     216
     217
     218
     219
     220
     221
     222
     223
     224
     225
     226
     227
     228
     229
     230
     231
     232
     233
      SUBROUTINE CHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
     $                  LWORK, RWORK, INFO )
*
*  -- LAPACK driver routine (version 3.3.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*  -- April 2011                                                      --
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, UPLO
      INTEGER            INFO, ITYPE, LDA, LDB, LWORK, N
*     ..
*     .. Array Arguments ..
      REAL               RWORK( * ), W( * )
      COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  CHEGV computes all the eigenvalues, and optionally, the eigenvectors
*  of a complex generalized Hermitian-definite eigenproblem, of the form
*  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
*  Here A and B are assumed to be Hermitian and B is also
*  positive definite.
*
*  Arguments
*  =========
*
*  ITYPE   (input) INTEGER
*          Specifies the problem type to be solved:
*          = 1:  A*x = (lambda)*B*x
*          = 2:  A*B*x = (lambda)*x
*          = 3:  B*A*x = (lambda)*x
*
*  JOBZ    (input) CHARACTER*1
*          = 'N':  Compute eigenvalues only;
*          = 'V':  Compute eigenvalues and eigenvectors.
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangles of A and B are stored;
*          = 'L':  Lower triangles of A and B are stored.
*
*  N       (input) INTEGER
*          The order of the matrices A and B.  N >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA, N)
*          On entry, the Hermitian matrix A.  If UPLO = 'U', the
*          leading N-by-N upper triangular part of A contains the
*          upper triangular part of the matrix A.  If UPLO = 'L',
*          the leading N-by-N lower triangular part of A contains
*          the lower triangular part of the matrix A.
*
*          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
*          matrix Z of eigenvectors.  The eigenvectors are normalized
*          as follows:
*          if ITYPE = 1 or 2, Z**H*B*Z = I;
*          if ITYPE = 3, Z**H*inv(B)*Z = I.
*          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
*          or the lower triangle (if UPLO='L') of A, including the
*          diagonal, is destroyed.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  B       (input/output) COMPLEX array, dimension (LDB, N)
*          On entry, the Hermitian positive definite matrix B.
*          If UPLO = 'U', the leading N-by-N upper triangular part of B
*          contains the upper triangular part of the matrix B.
*          If UPLO = 'L', the leading N-by-N lower triangular part of B
*          contains the lower triangular part of the matrix B.
*
*          On exit, if INFO <= N, the part of B containing the matrix is
*          overwritten by the triangular factor U or L from the Cholesky
*          factorization B = U**H*U or B = L*L**H.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B.  LDB >= max(1,N).
*
*  W       (output) REAL array, dimension (N)
*          If INFO = 0, the eigenvalues in ascending order.
*
*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
*  LWORK   (input) INTEGER
*          The length of the array WORK.  LWORK >= max(1,2*N-1).
*          For optimal efficiency, LWORK >= (NB+1)*N,
*          where NB is the blocksize for CHETRD returned by ILAENV.
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued by XERBLA.
*
*  RWORK   (workspace) REAL array, dimension (max(1, 3*N-2))
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*          > 0:  CPOTRF or CHEEV returned an error code:
*             <= N:  if INFO = i, CHEEV failed to converge;
*                    i off-diagonal elements of an intermediate
*                    tridiagonal form did not converge to zero;
*             > N:   if INFO = N + i, for 1 <= i <= N, then the leading
*                    minor of order i of B is not positive definite.
*                    The factorization of B could not be completed and
*                    no eigenvalues or eigenvectors were computed.
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX            ONE
      PARAMETER          ( ONE = ( 1.0E+00.0E+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, UPPER, WANTZ
      CHARACTER          TRANS
      INTEGER            LWKOPT, NB, NEIG
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           ILAENV, LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           CHEEV, CHEGST, CPOTRF, CTRMM, CTRSM, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      WANTZ = LSAME( JOBZ, 'V' )
      UPPER = LSAME( UPLO, 'U' )
      LQUERY = ( LWORK.EQ. -1 )
*
      INFO = 0
      IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
         INFO = -1
      ELSE IF.NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
         INFO = -2
      ELSE IF.NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDA.LT.MAX1, N ) ) THEN
         INFO = -6
      ELSE IF( LDB.LT.MAX1, N ) ) THEN
         INFO = -8
      END IF
*
      IF( INFO.EQ.0 ) THEN
         NB = ILAENV( 1'CHETRD', UPLO, N, -1-1-1 )
         LWKOPT = MAX1, ( NB + 1 )*N )
         WORK( 1 ) = LWKOPT
*
         IF( LWORK.LT.MAX12*N-1 ) .AND. .NOT.LQUERY ) THEN
            INFO = -11
         END IF
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CHEGV '-INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 )
     $   RETURN
*
*     Form a Cholesky factorization of B.
*
      CALL CPOTRF( UPLO, N, B, LDB, INFO )
      IF( INFO.NE.0 ) THEN
         INFO = N + INFO
         RETURN
      END IF
*
*     Transform problem to standard eigenvalue problem and solve.
*
      CALL CHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
      CALL CHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )
*
      IF( WANTZ ) THEN
*
*        Backtransform eigenvectors to the original problem.
*
         NEIG = N
         IF( INFO.GT.0 )
     $      NEIG = INFO - 1
         IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
*
*           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
*           backtransform eigenvectors: x = inv(L)**H*y or inv(U)*y
*
            IF( UPPER ) THEN
               TRANS = 'N'
            ELSE
               TRANS = 'C'
            END IF
*
            CALL CTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
     $                  B, LDB, A, LDA )
*
         ELSE IF( ITYPE.EQ.3 ) THEN
*
*           For B*A*x=(lambda)*x;
*           backtransform eigenvectors: x = L*y or U**H*y
*
            IF( UPPER ) THEN
               TRANS = 'C'
            ELSE
               TRANS = 'N'
            END IF
*
            CALL CTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
     $                  B, LDB, A, LDA )
         END IF
      END IF
*
      WORK( 1 ) = LWKOPT
*
      RETURN
*
*     End of CHEGV
*
      END