zhpgv.f

          SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
         $                  RWORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBZ, UPLO
          INTEGER            INFO, ITYPE, LDZ, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   RWORK( * ), W( * )
          COMPLEX*16         AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZHPGV 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, stored in packed format,
    *  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.
    *
    *  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
    *          On entry, the upper or lower triangle of the Hermitian matrix
    *          A, packed columnwise in a linear array.  The j-th column of A
    *          is stored in the array AP as follows:
    *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    *          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
    *
    *          On exit, the contents of AP are destroyed.
    *
    *  BP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
    *          On entry, the upper or lower triangle of the Hermitian matrix
    *          B, packed columnwise in a linear array.  The j-th column of B
    *          is stored in the array BP as follows:
    *          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
    *          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
    *
    *          On exit, the triangular factor U or L from the Cholesky
    *          factorization B = U**H*U or B = L*L**H, in the same storage
    *          format as B.
    *
    *  W       (output) DOUBLE PRECISION array, dimension (N)
    *          If INFO = 0, the eigenvalues in ascending order.
    *
    *  Z       (output) COMPLEX*16 array, dimension (LDZ, N)
    *          If JOBZ = 'V', then if INFO = 0, Z 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 Z is not referenced.
    *
    *  LDZ     (input) INTEGER
    *          The leading dimension of the array Z.  LDZ >= 1, and if
    *          JOBZ = 'V', LDZ >= max(1,N).
    *
    *  WORK    (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1))
    *
    *  RWORK   (workspace) DOUBLE PRECISION 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:  ZPPTRF or ZHPEV returned an error code:
    *             <= N:  if INFO = i, ZHPEV failed to converge;
    *                    i off-diagonal elements of an intermediate
    *                    tridiagonal form did not convergeto 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.
    *
    *  =====================================================================
    *
    *     .. Local Scalars ..
          LOGICAL            UPPER, WANTZ
          CHARACTER          TRANS
          INTEGER            J, NEIG
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA, ZHPEV, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          WANTZ = LSAME( JOBZ, 'V' )
          UPPER = LSAME( UPLO, 'U' )
    *
          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( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
             INFO = -9
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'ZHPGV ', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     Form a Cholesky factorization of B.
    *
          CALL ZPPTRF( UPLO, N, BP, INFO )
          IF( INFO.NE.0 ) THEN
             INFO = N + INFO
             RETURN
          END IF
    *
    *     Transform problem to standard eigenvalue problem and solve.
    *
          CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
          CALL ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, 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)'*y or inv(U)*y
    *
                IF( UPPER ) THEN
                   TRANS = 'N'
                ELSE
                   TRANS = 'C'
                END IF
    *
                DO 10 J = 1, NEIG
                   CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
         $                     1 )
       10       CONTINUE
    *
             ELSE IF( ITYPE.EQ.3 ) THEN
    *
    *           For B*A*x=(lambda)*x;
    *           backtransform eigenvectors: x = L*y or U'*y
    *
                IF( UPPER ) THEN
                   TRANS = 'C'
                ELSE
                   TRANS = 'N'
                END IF
    *
                DO 20 J = 1, NEIG
                   CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
         $                     1 )
       20       CONTINUE
             END IF
          END IF
          RETURN
    *
    *     End of ZHPGV
    *
          END