Return to zhpgv.f CVS log

Up to [local] / rpl / lapack / lapack

Patches pour OS/2

    1:       SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
    2:      $                  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, LDZ, N
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   RWORK( * ), W( * )
   15:       COMPLEX*16         AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
   16: *     ..
   17: *
   18: *  Purpose
   19: *  =======
   20: *
   21: *  ZHPGV 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, stored in packed format,
   25: *  and B is also 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: *  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
   48: *          On entry, the upper or lower triangle of the Hermitian matrix
   49: *          A, packed columnwise in a linear array.  The j-th column of A
   50: *          is stored in the array AP as follows:
   51: *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   52: *          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
   53: *
   54: *          On exit, the contents of AP are destroyed.
   55: *
   56: *  BP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
   57: *          On entry, the upper or lower triangle of the Hermitian matrix
   58: *          B, packed columnwise in a linear array.  The j-th column of B
   59: *          is stored in the array BP as follows:
   60: *          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
   61: *          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
   62: *
   63: *          On exit, the triangular factor U or L from the Cholesky
   64: *          factorization B = U**H*U or B = L*L**H, in the same storage
   65: *          format as B.
   66: *
   67: *  W       (output) DOUBLE PRECISION array, dimension (N)
   68: *          If INFO = 0, the eigenvalues in ascending order.
   69: *
   70: *  Z       (output) COMPLEX*16 array, dimension (LDZ, N)
   71: *          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
   72: *          eigenvectors.  The eigenvectors are normalized as follows:
   73: *          if ITYPE = 1 or 2, Z**H*B*Z = I;
   74: *          if ITYPE = 3, Z**H*inv(B)*Z = I.
   75: *          If JOBZ = 'N', then Z is not referenced.
   76: *
   77: *  LDZ     (input) INTEGER
   78: *          The leading dimension of the array Z.  LDZ >= 1, and if
   79: *          JOBZ = 'V', LDZ >= max(1,N).
   80: *
   81: *  WORK    (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1))
   82: *
   83: *  RWORK   (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
   84: *
   85: *  INFO    (output) INTEGER
   86: *          = 0:  successful exit
   87: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   88: *          > 0:  ZPPTRF or ZHPEV returned an error code:
   89: *             <= N:  if INFO = i, ZHPEV failed to converge;
   90: *                    i off-diagonal elements of an intermediate
   91: *                    tridiagonal form did not convergeto zero;
   92: *             > N:   if INFO = N + i, for 1 <= i <= n, then the leading
   93: *                    minor of order i of B is not positive definite.
   94: *                    The factorization of B could not be completed and
   95: *                    no eigenvalues or eigenvectors were computed.
   96: *
   97: *  =====================================================================
   98: *
   99: *     .. Local Scalars ..
  100:       LOGICAL            UPPER, WANTZ
  101:       CHARACTER          TRANS
  102:       INTEGER            J, NEIG
  103: *     ..
  104: *     .. External Functions ..
  105:       LOGICAL            LSAME
  106:       EXTERNAL           LSAME
  107: *     ..
  108: *     .. External Subroutines ..
  109:       EXTERNAL           XERBLA, ZHPEV, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
  110: *     ..
  111: *     .. Executable Statements ..
  112: *
  113: *     Test the input parameters.
  114: *
  115:       WANTZ = LSAME( JOBZ, 'V' )
  116:       UPPER = LSAME( UPLO, 'U' )
  117: *
  118:       INFO = 0
  119:       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
  120:          INFO = -1
  121:       ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  122:          INFO = -2
  123:       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
  124:          INFO = -3
  125:       ELSE IF( N.LT.0 ) THEN
  126:          INFO = -4
  127:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
  128:          INFO = -9
  129:       END IF
  130:       IF( INFO.NE.0 ) THEN
  131:          CALL XERBLA( 'ZHPGV ', -INFO )
  132:          RETURN
  133:       END IF
  134: *
  135: *     Quick return if possible
  136: *
  137:       IF( N.EQ.0 )
  138:      $   RETURN
  139: *
  140: *     Form a Cholesky factorization of B.
  141: *
  142:       CALL ZPPTRF( UPLO, N, BP, INFO )
  143:       IF( INFO.NE.0 ) THEN
  144:          INFO = N + INFO
  145:          RETURN
  146:       END IF
  147: *
  148: *     Transform problem to standard eigenvalue problem and solve.
  149: *
  150:       CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
  151:       CALL ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO )
  152: *
  153:       IF( WANTZ ) THEN
  154: *
  155: *        Backtransform eigenvectors to the original problem.
  156: *
  157:          NEIG = N
  158:          IF( INFO.GT.0 )
  159:      $      NEIG = INFO - 1
  160:          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
  161: *
  162: *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
  163: *           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
  164: *
  165:             IF( UPPER ) THEN
  166:                TRANS = 'N'
  167:             ELSE
  168:                TRANS = 'C'
  169:             END IF
  170: *
  171:             DO 10 J = 1, NEIG
  172:                CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
  173:      $                     1 )
  174:    10       CONTINUE
  175: *
  176:          ELSE IF( ITYPE.EQ.3 ) THEN
  177: *
  178: *           For B*A*x=(lambda)*x;
  179: *           backtransform eigenvectors: x = L*y or U'*y
  180: *
  181:             IF( UPPER ) THEN
  182:                TRANS = 'C'
  183:             ELSE
  184:                TRANS = 'N'
  185:             END IF
  186: *
  187:             DO 20 J = 1, NEIG
  188:                CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
  189:      $                     1 )
  190:    20       CONTINUE
  191:          END IF
  192:       END IF
  193:       RETURN
  194: *
  195: *     End of ZHPGV
  196: *
  197:       END