ssbgv()

subroutine ssbgv	(	character	jobz,
		character	uplo,
		integer	n,
		integer	ka,
		integer	kb,
		real, dimension( ldab, * )	ab,
		integer	ldab,
		real, dimension( ldbb, * )	bb,
		integer	ldbb,
		real, dimension( * )	w,
		real, dimension( ldz, * )	z,
		integer	ldz,
		real, dimension( * )	work,
		integer	info
	)

SSBGV

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Purpose:

 SSBGV computes all the eigenvalues, and optionally, the eigenvectors
 of a real generalized symmetric-definite banded eigenproblem, of
 the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
 and banded, and B is also positive definite.

Parameters

[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]	KA	KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.
[in]	KB	KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 0.
[in,out]	AB	AB is REAL array, dimension (LDAB, N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the contents of AB are destroyed.
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1.
[in,out]	BB	BB is REAL array, dimension (LDBB, N) On entry, the upper or lower triangle of the symmetric band matrix B, stored in the first kb+1 rows of the array. The j-th column of B is stored in the j-th column of the array BB as follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). On exit, the factor S from the split Cholesky factorization B = S**T*S, as returned by SPBSTF.
[in]	LDBB	LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1.
[out]	W	W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order.
[out]	Z	Z is REAL array, dimension (LDZ, N) If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors, with the i-th column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized so that Z**T*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 >= N.
[out]	WORK	WORK is REAL 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: if INFO = i, and i is: <= N: the algorithm 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 SPBSTF returned INFO = i: B is not positive definite. 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 175 of file ssbgv.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, KA, KB, LDAB, LDBB, LDZ, N
*     ..
*     .. Array Arguments ..
      REAL               AB( LDAB, * ), BB( LDBB, * ), W( * ),
     $                   WORK( * ), Z( LDZ, * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            UPPER, WANTZ
      CHARACTER          VECT
      INTEGER            IINFO, INDE, INDWRK
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           spbstf, ssbgst, ssbtrd, ssteqr, ssterf, xerbla
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      wantz = lsame( jobz, 'V' )
      upper = lsame( uplo, 'U' )
*
      info = 0
      IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
         info = -1
      ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
         info = -2
      ELSE IF( n.LT.0 ) THEN
         info = -3
      ELSE IF( ka.LT.0 ) THEN
         info = -4
      ELSE IF( kb.LT.0 .OR. kb.GT.ka ) THEN
         info = -5
      ELSE IF( ldab.LT.ka+1 ) THEN
         info = -7
      ELSE IF( ldbb.LT.kb+1 ) THEN
         info = -9
      ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
         info = -12
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SSBGV', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Form a split Cholesky factorization of B.
*
      CALL spbstf( uplo, n, kb, bb, ldbb, info )
      IF( info.NE.0 ) THEN
         info = n + info
         RETURN
      END IF
*
*     Transform problem to standard eigenvalue problem.
*
      inde = 1
      indwrk = inde + n
      CALL ssbgst( jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, z, ldz,
     $             work( indwrk ), iinfo )
*
*     Reduce to tridiagonal form.
*
      IF( wantz ) THEN
         vect = 'U'
      ELSE
         vect = 'N'
      END IF
      CALL ssbtrd( vect, uplo, n, ka, ab, ldab, w, work( inde ), z, ldz,
     $             work( indwrk ), iinfo )
*
*     For eigenvalues only, call SSTERF.  For eigenvectors, call SSTEQR.
*
      IF( .NOT.wantz ) THEN
         CALL ssterf( n, w, work( inde ), info )
      ELSE
         CALL ssteqr( jobz, n, w, work( inde ), z, ldz, work( indwrk ),
     $                info )
      END IF
      RETURN
*
*     End of SSBGV
*

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