sspgv.f

*> \brief \b SSPGV
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
*                         INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          JOBZ, UPLO
*       INTEGER            INFO, ITYPE, LDZ, N
*       ..
*       .. Array Arguments ..
*       REAL               AP( * ), BP( * ), W( * ), WORK( * ),
*      $                   Z( LDZ, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SSPGV computes all the eigenvalues and, optionally, the eigenvectors
*> of a real generalized symmetric-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 symmetric, stored in packed format,
*> and B is also positive definite.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] ITYPE
*> \verbatim
*>          ITYPE is 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
*> \endverbatim
*>
*> \param[in] JOBZ
*> \verbatim
*>          JOBZ is CHARACTER*1
*>          = 'N':  Compute eigenvalues only;
*>          = 'V':  Compute eigenvalues and eigenvectors.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  Upper triangles of A and B are stored;
*>          = 'L':  Lower triangles of A and B are stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrices A and B.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*>          AP is REAL array, dimension (N*(N+1)/2)
*>          On entry, the upper or lower triangle of the symmetric 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.
*> \endverbatim
*>
*> \param[in,out] BP
*> \verbatim
*>          BP is REAL array, dimension (N*(N+1)/2)
*>          On entry, the upper or lower triangle of the symmetric 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**T*U or B = L*L**T, in the same storage
*>          format as B.
*> \endverbatim
*>
*> \param[out] W
*> \verbatim
*>          W is REAL array, dimension (N)
*>          If INFO = 0, the eigenvalues in ascending order.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*>          Z is REAL 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**T*B*Z = I;
*>          if ITYPE = 3, Z**T*inv(B)*Z = I.
*>          If JOBZ = 'N', then Z is not referenced.
*> \endverbatim
*>
*> \param[in] LDZ
*> \verbatim
*>          LDZ is INTEGER
*>          The leading dimension of the array Z.  LDZ >= 1, and if
*>          JOBZ = 'V', LDZ >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (3*N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*>          > 0:  SPPTRF or SSPEV returned an error code:
*>             <= N:  if INFO = i, SSPEV 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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hpgv
*
*  =====================================================================
      SUBROUTINE sspgv( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
     $                  INFO )
*
*  -- LAPACK driver routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, UPLO
      INTEGER            INFO, ITYPE, LDZ, N
*     ..
*     .. Array Arguments ..
      REAL               AP( * ), BP( * ), W( * ), WORK( * ),
     $                   z( ldz, * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            UPPER, WANTZ
      CHARACTER          TRANS
      INTEGER            J, NEIG
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           spptrf, sspev, sspgst, stpmv, stpsv, xerbla
*     ..
*     .. 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( 'SSPGV ', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Form a Cholesky factorization of B.
*
      CALL spptrf( uplo, n, bp, info )
      IF( info.NE.0 ) THEN
         info = n + info
         RETURN
      END IF
*
*     Transform problem to standard eigenvalue problem and solve.
*
      CALL sspgst( itype, uplo, n, ap, bp, info )
      CALL sspev( jobz, uplo, n, ap, w, z, ldz, work, 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)**T*y or inv(U)*y
*
            IF( upper ) THEN
               trans = 'N'
            ELSE
               trans = 'T'
            END IF
*
            DO 10 j = 1, neig
               CALL stpsv( 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**T*y
*
            IF( upper ) THEN
               trans = 'T'
            ELSE
               trans = 'N'
            END IF
*
            DO 20 j = 1, neig
               CALL stpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
     $                     1 )
   20       CONTINUE
         END IF
      END IF
      RETURN
*
*     End of SSPGV
*
      END