*> \brief \b SSPGV
*
* =========== DOCUMENTATION ===========
*
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* http://www.netlib.org/lapack/explore-html/
*
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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.
*
*> \date November 2015
*
*> \ingroup realOTHEReigen
*
* =====================================================================
SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
$ INFO )
*
* -- LAPACK driver routine (version 3.6.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2015
*
* .. 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