dspgv()

subroutine dspgv	(	integer	itype,
		character	jobz,
		character	uplo,
		integer	n,
		double precision, dimension( * )	ap,
		double precision, dimension( * )	bp,
		double precision, dimension( * )	w,
		double precision, dimension( ldz, * )	z,
		integer	ldz,
		double precision, dimension( * )	work,
		integer	info
	)

DSPGV

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Purpose:

 DSPGV 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.

Parameters

[in]	ITYPE	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
[in]	JOBZ	JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.
[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored.
[in]	N	N is INTEGER The order of the matrices A and B. N >= 0.
[in,out]	AP	AP is DOUBLE PRECISION 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.
[in,out]	BP	BP is DOUBLE PRECISION 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.
[out]	W	W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order.
[out]	Z	Z is DOUBLE PRECISION 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.
[in]	LDZ	LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (3*N)
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: DPPTRF or DSPEV returned an error code: <= N: if INFO = i, DSPEV 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 principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 158 of file dspgv.f.

*
*  -- 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 ..
      DOUBLE PRECISION   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           dpptrf, dspev, dspgst, dtpmv, dtpsv, 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( 'DSPGV ', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Form a Cholesky factorization of B.
*
      CALL dpptrf( uplo, n, bp, info )
      IF( info.NE.0 ) THEN
         info = n + info
         RETURN
      END IF
*
*     Transform problem to standard eigenvalue problem and solve.
*
      CALL dspgst( itype, uplo, n, ap, bp, info )
      CALL dspev( 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 dtpsv( 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 dtpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
     $                     1 )
   20       CONTINUE
         END IF
      END IF
      RETURN
*
*     End of DSPGV
*

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