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SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
$ LDZ, WORK, INFO )
*
* -- LAPACK driver routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER JOBZ, UPLO
INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
$ WORK( * ), Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* DSBGV 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.
*
* Arguments
* =========
*
* 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.
*
* KA (input) INTEGER
* The number of superdiagonals of the matrix A if UPLO = 'U',
* or the number of subdiagonals if UPLO = 'L'. KA >= 0.
*
* KB (input) INTEGER
* The number of superdiagonals of the matrix B if UPLO = 'U',
* or the number of subdiagonals if UPLO = 'L'. KB >= 0.
*
* AB (input/output) DOUBLE PRECISION 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.
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= KA+1.
*
* BB (input/output) DOUBLE PRECISION 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 DPBSTF.
*
* LDBB (input) INTEGER
* The leading dimension of the array BB. LDBB >= KB+1.
*
* W (output) DOUBLE PRECISION array, dimension (N)
* If INFO = 0, the eigenvalues in ascending order.
*
* Z (output) DOUBLE PRECISION 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.
*
* LDZ (input) INTEGER
* The leading dimension of the array Z. LDZ >= 1, and if
* JOBZ = 'V', LDZ >= N.
*
* WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
*
* INFO (output) 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 DPBSTF
* returned INFO = i: 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 VECT
INTEGER IINFO, INDE, INDWRK
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DPBSTF, DSBGST, DSBTRD, DSTEQR, DSTERF, 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( 'DSBGV ', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Form a split Cholesky factorization of B.
*
CALL DPBSTF( 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 DSBGST( 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 DSBTRD( VECT, UPLO, N, KA, AB, LDAB, W, WORK( INDE ), Z, LDZ,
$ WORK( INDWRK ), IINFO )
*
* For eigenvalues only, call DSTERF. For eigenvectors, call SSTEQR.
*
IF( .NOT.WANTZ ) THEN
CALL DSTERF( N, W, WORK( INDE ), INFO )
ELSE
CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
$ INFO )
END IF
RETURN
*
* End of DSBGV
*
END
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