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Patches pour OS/2

    1:       SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
    2:      $                  LWORK, RWORK, INFO )
    3: *
    4: *  -- LAPACK driver routine (version 3.2) --
    5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    7: *     November 2006
    8: *
    9: *     .. Scalar Arguments ..
   10:       CHARACTER          JOBZ, UPLO
   11:       INTEGER            INFO, ITYPE, LDA, LDB, LWORK, N
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   RWORK( * ), W( * )
   15:       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
   16: *     ..
   17: *
   18: *  Purpose
   19: *  =======
   20: *
   21: *  ZHEGV computes all the eigenvalues, and optionally, the eigenvectors
   22: *  of a complex generalized Hermitian-definite eigenproblem, of the form
   23: *  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
   24: *  Here A and B are assumed to be Hermitian and B is also
   25: *  positive definite.
   26: *
   27: *  Arguments
   28: *  =========
   29: *
   30: *  ITYPE   (input) INTEGER
   31: *          Specifies the problem type to be solved:
   32: *          = 1:  A*x = (lambda)*B*x
   33: *          = 2:  A*B*x = (lambda)*x
   34: *          = 3:  B*A*x = (lambda)*x
   35: *
   36: *  JOBZ    (input) CHARACTER*1
   37: *          = 'N':  Compute eigenvalues only;
   38: *          = 'V':  Compute eigenvalues and eigenvectors.
   39: *
   40: *  UPLO    (input) CHARACTER*1
   41: *          = 'U':  Upper triangles of A and B are stored;
   42: *          = 'L':  Lower triangles of A and B are stored.
   43: *
   44: *  N       (input) INTEGER
   45: *          The order of the matrices A and B.  N >= 0.
   46: *
   47: *  A       (input/output) COMPLEX*16 array, dimension (LDA, N)
   48: *          On entry, the Hermitian matrix A.  If UPLO = 'U', the
   49: *          leading N-by-N upper triangular part of A contains the
   50: *          upper triangular part of the matrix A.  If UPLO = 'L',
   51: *          the leading N-by-N lower triangular part of A contains
   52: *          the lower triangular part of the matrix A.
   53: *
   54: *          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
   55: *          matrix Z of eigenvectors.  The eigenvectors are normalized
   56: *          as follows:
   57: *          if ITYPE = 1 or 2, Z**H*B*Z = I;
   58: *          if ITYPE = 3, Z**H*inv(B)*Z = I.
   59: *          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
   60: *          or the lower triangle (if UPLO='L') of A, including the
   61: *          diagonal, is destroyed.
   62: *
   63: *  LDA     (input) INTEGER
   64: *          The leading dimension of the array A.  LDA >= max(1,N).
   65: *
   66: *  B       (input/output) COMPLEX*16 array, dimension (LDB, N)
   67: *          On entry, the Hermitian positive definite matrix B.
   68: *          If UPLO = 'U', the leading N-by-N upper triangular part of B
   69: *          contains the upper triangular part of the matrix B.
   70: *          If UPLO = 'L', the leading N-by-N lower triangular part of B
   71: *          contains the lower triangular part of the matrix B.
   72: *
   73: *          On exit, if INFO <= N, the part of B containing the matrix is
   74: *          overwritten by the triangular factor U or L from the Cholesky
   75: *          factorization B = U**H*U or B = L*L**H.
   76: *
   77: *  LDB     (input) INTEGER
   78: *          The leading dimension of the array B.  LDB >= max(1,N).
   79: *
   80: *  W       (output) DOUBLE PRECISION array, dimension (N)
   81: *          If INFO = 0, the eigenvalues in ascending order.
   82: *
   83: *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
   84: *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   85: *
   86: *  LWORK   (input) INTEGER
   87: *          The length of the array WORK.  LWORK >= max(1,2*N-1).
   88: *          For optimal efficiency, LWORK >= (NB+1)*N,
   89: *          where NB is the blocksize for ZHETRD returned by ILAENV.
   90: *
   91: *          If LWORK = -1, then a workspace query is assumed; the routine
   92: *          only calculates the optimal size of the WORK array, returns
   93: *          this value as the first entry of the WORK array, and no error
   94: *          message related to LWORK is issued by XERBLA.
   95: *
   96: *  RWORK   (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
   97: *
   98: *  INFO    (output) INTEGER
   99: *          = 0:  successful exit
  100: *          < 0:  if INFO = -i, the i-th argument had an illegal value
  101: *          > 0:  ZPOTRF or ZHEEV returned an error code:
  102: *             <= N:  if INFO = i, ZHEEV failed to converge;
  103: *                    i off-diagonal elements of an intermediate
  104: *                    tridiagonal form did not converge to zero;
  105: *             > N:   if INFO = N + i, for 1 <= i <= N, then the leading
  106: *                    minor of order i of B is not positive definite.
  107: *                    The factorization of B could not be completed and
  108: *                    no eigenvalues or eigenvectors were computed.
  109: *
  110: *  =====================================================================
  111: *
  112: *     .. Parameters ..
  113:       COMPLEX*16         ONE
  114:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
  115: *     ..
  116: *     .. Local Scalars ..
  117:       LOGICAL            LQUERY, UPPER, WANTZ
  118:       CHARACTER          TRANS
  119:       INTEGER            LWKOPT, NB, NEIG
  120: *     ..
  121: *     .. External Functions ..
  122:       LOGICAL            LSAME
  123:       INTEGER            ILAENV
  124:       EXTERNAL           LSAME, ILAENV
  125: *     ..
  126: *     .. External Subroutines ..
  127:       EXTERNAL           XERBLA, ZHEEV, ZHEGST, ZPOTRF, ZTRMM, ZTRSM
  128: *     ..
  129: *     .. Intrinsic Functions ..
  130:       INTRINSIC          MAX
  131: *     ..
  132: *     .. Executable Statements ..
  133: *
  134: *     Test the input parameters.
  135: *
  136:       WANTZ = LSAME( JOBZ, 'V' )
  137:       UPPER = LSAME( UPLO, 'U' )
  138:       LQUERY = ( LWORK.EQ.-1 )
  139: *
  140:       INFO = 0
  141:       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
  142:          INFO = -1
  143:       ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  144:          INFO = -2
  145:       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
  146:          INFO = -3
  147:       ELSE IF( N.LT.0 ) THEN
  148:          INFO = -4
  149:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  150:          INFO = -6
  151:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  152:          INFO = -8
  153:       END IF
  154: *
  155:       IF( INFO.EQ.0 ) THEN
  156:          NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 )
  157:          LWKOPT = MAX( 1, ( NB + 1 )*N )
  158:          WORK( 1 ) = LWKOPT
  159: *
  160:          IF( LWORK.LT.MAX( 1, 2*N - 1 ) .AND. .NOT.LQUERY ) THEN
  161:             INFO = -11
  162:          END IF
  163:       END IF
  164: *
  165:       IF( INFO.NE.0 ) THEN
  166:          CALL XERBLA( 'ZHEGV ', -INFO )
  167:          RETURN
  168:       ELSE IF( LQUERY ) THEN
  169:          RETURN
  170:       END IF
  171: *
  172: *     Quick return if possible
  173: *
  174:       IF( N.EQ.0 )
  175:      $   RETURN
  176: *
  177: *     Form a Cholesky factorization of B.
  178: *
  179:       CALL ZPOTRF( UPLO, N, B, LDB, INFO )
  180:       IF( INFO.NE.0 ) THEN
  181:          INFO = N + INFO
  182:          RETURN
  183:       END IF
  184: *
  185: *     Transform problem to standard eigenvalue problem and solve.
  186: *
  187:       CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
  188:       CALL ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )
  189: *
  190:       IF( WANTZ ) THEN
  191: *
  192: *        Backtransform eigenvectors to the original problem.
  193: *
  194:          NEIG = N
  195:          IF( INFO.GT.0 )
  196:      $      NEIG = INFO - 1
  197:          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
  198: *
  199: *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
  200: *           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
  201: *
  202:             IF( UPPER ) THEN
  203:                TRANS = 'N'
  204:             ELSE
  205:                TRANS = 'C'
  206:             END IF
  207: *
  208:             CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
  209:      $                  B, LDB, A, LDA )
  210: *
  211:          ELSE IF( ITYPE.EQ.3 ) THEN
  212: *
  213: *           For B*A*x=(lambda)*x;
  214: *           backtransform eigenvectors: x = L*y or U'*y
  215: *
  216:             IF( UPPER ) THEN
  217:                TRANS = 'C'
  218:             ELSE
  219:                TRANS = 'N'
  220:             END IF
  221: *
  222:             CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
  223:      $                  B, LDB, A, LDA )
  224:          END IF
  225:       END IF
  226: *
  227:       WORK( 1 ) = LWKOPT
  228: *
  229:       RETURN
  230: *
  231: *     End of ZHEGV
  232: *
  233:       END